TEST BANK for Algebra and Trigonometry 12e (Global Edition) Michael Sullivan. Answers at the end of by StudyGuide

TEST BANK for Algebra and Trigonometry 12e (Global Edition) Michael Sullivan. Answers at the end of each Chapter. 1 Exam Name

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Tell whether the expression is a monomial. If it is, name the variable(s) and coefficient, and give the degree of the monomial. 1) 5x2y5 1) A) Monomial; variables x, y; coefficient 5; degree 2 B) Monomial; variables x, y; coefficient 5; degree 7 C) Monomial; variables x, y; coefficient 5; degree 5 D) Not a monomial Evaluate the expression. 5 4 2) 7 6 1 A) 21

2) 1 B) 7

1 C) 42

Factor the polynomial by removing the common monomial factor. 3) 3x2 - 9x A) 3x(x + 3)

B) 3(x2 - 3x)

Reduce the rational expression to lowest terms. 3x2 - 27x + 54 4) x-6 1 A) B) 3x - 9 x-6

2 D) 7

C) 3x(x - 3)

D) 3x2(x - 3)

4) C) 3x2 - 36

3x2 - 27x + 54 x-6

List all the elements of B that belong to the given set. 5 8 5) B = {17, 8, -19, 0, , - , 3.3, 25L, 0.258258258...} 8 5 Integers A) {17, -19} Factor the polynomial by grouping. 6) 10x2 + 15x - 8x - 12 A) (10x - 4)(x + 3)

B) {17, 0}

C) {17, -19, 0}

D) {17, 0,

B) (5x - 4)(2x + 3)

C) (5x + 4)(2x - 3)

D) (10x + 4)(x - 3)

Perform the indicated operations and simplify the result. Leave the answer in factored form. 7) 1 1x 8+

1 x

8x + 1 x-1

x-1 8x + 1

x+1 8x - 1

x-1 8x

2 4+ x x 1 + 3 6

x 12

B) 12

C) 1

12 x

Multiply the polynomials using the special product formulas. Express the answer as a single polynomial in standard form. 9) (3x + 4y)(3x - 4y) 9) A) 9x2 + 24xy - 16y2 B) 9x2 - 24xy - 16y2

C) 9x2 - 16y2

D) 6x2 - 8y2

Perform the indicated operations and simplify the result. Leave the answer in factored form. 1 11 + 10) 3x 12x A)

5 4x

B) 1

15 24x

4 5x

Perform the indicated operations. Express the answer as a single polynomial in standard form. 11) -2x(-5x - 4) A) -5x2 + 8x B) 10x2 + 8x C) 10x2 - 4x D) 18x2 Tell whether the expression is a polynomial. If it is, give its degree. 4 12) 6x2 x A) Polynomial; degree 2 C) Polynomial; degree -1

11)

12)

B) Polynomial; degree 1 D) Not a polynomial

Simplify the expression. Assume that all variables are positive when they appear. 13) (5 11 + 4)2 A) 259 + 40 11

10)

B) 291 + 40 11

C) 279 + 40 11

13) D) 291 - 40 11

Simplify the expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, we assume that the base is not 0. x-2y2 14) 14) xy7

y5 x3

1 x3 y5

xy5

Factor completely. If the polynomial cannot be factored, say it is prime. 15) 4x2 - 24x - 16x + 96 A) 4(x + 6)(x + 4)

B) (x - 6)(4x - 16)

C) 4(x - 6)(x - 4)

x y5

D) (x - 6)(x - 4)

15)

Use U = universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 5, 8}, B = {2, 3, 5, 7}, and C = {1, 4, 9} to find the set. 16) B

A) {0, 1, 4, 6, 7, 8, 9} C) {0, 1, 4, 6, 9}

16)

B) {1, 4, 6, 8, 9} D) {0, 1, 4, 6, 8, 9}

Use synthetic division to determine whether x - c is a factor of the given polynomial. 17) 4x3 - 27x2 + 8x + 60; x + 4 A) Yes

17)

B) No

Add or subtract as indicated. Express the answer as a single polynomial in standard form. 18) (x2 + 1) - (4x2 + 7) + (x2 + x - 8)

18)

Graph the numbers on the real number line. 19) x > -3

19)

A) -2x2 + 8x - 7

B) -4x2 + x - 14

C) -3x2 + x - 14

D) -2x2 + x - 14

Use U = universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 5, 8}, B = {2, 3, 5, 7}, and C = {1, 4, 9} to find the set. 20) A B A) {0, 4, 6, 9} Solve. 21) What is the value of A) 16

B) {1, 2, 3, 5, 7, 8}

C) {1, 4, 6, 8, 9}

D) {4, 6, 9}

(6,666)4 ? (3,333)4

20)

21) C) (2,222)4

B) 48

D) (3,333)4

Perform the indicated operations and simplify the result. Leave the answer in factored form. 22) 10 11 + 11 - x x - 11

22)

7 4 + x x - 11

A) -

23)

21x 11x - 77

B) -

x 11x - 77

21x 11x - 77

x 11x - 77

23)

x2 - 81 x x-9 x-7

A) (x + 9)(x - 7)

(x - 9)(x2 - 9) x(x - 7)

x (x + 9)(x - 7)

(x + 9)(x - 7) x

Evaluate the expression using the given values. 6x - 7y x = 10, y = 6 24) x+3 A)

34 13

24)

B) 2

18 13

34 9

Perform the indicated operations. Express the answer as a single polynomial in standard form. 25) 6x6 (3x5 + 2x4 - 6) A) 18x11 + 2x4 - 6

B) 18x5 + 12x4 - 36

C) 18x11 + 12x10

D) 18x11 + 12x10 - 36x6

List all the elements of B that belong to the given set. 0 26) B = 19, 5, -8, 0, , 0.2 3 Irrational numbers 0 5, A) 3

26)

B) { 5}

0 , 0.2 3

D) { 5, 0.2}

Add or subtract as indicated. Express the answer as a single polynomial in standard form. 27) (2x2 + 13x - 10) - (7x2 + 16x + 4) A) -5x2 + 20x - 6

B) -5x2 - 3x - 14

C) -5x2 - 3x + 14

D) -5x2 - 3x - 6

Reduce the rational expression to lowest terms. 10x2 + 30x3 28) 9x + 27x2 A)

10 9

25)

27)

28)

10 + 30x3 9x + 27

10x2 + 30x3 9x + 27x2

10x 9

Solve the problem. 29) Find the surface area S of a right circular cylinder with radius 10 cm, and height 4 cm. Use 3.14 for . Round your answer to one decimal place. A) 753.6 cm2 B) 879.2 cm2 C) 439.6 cm2 D) 1,256.0 cm2 Simplify the expression. 30) 165/4 A) 35

29)

30) B)

C) 32

Find the quotient and the remainder. 31) 7x2 + 33x - 54 divided by x + 6 A) 7x - 9; remainder 9 C) 7x + 9; remainder 0

D) 1,024

31)

B) 7x - 9; remainder 0 D) x - 9; remainder 0

Simplify the expression. Assume that all variables are positive when they appear. 32) ( 12 + 2)( 12 - 2) A) 8 B) 10 C) 16

32) D) 12 - 2 2

Use U = universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 5, 8}, B = {2, 3, 5, 7}, and C = {1, 4, 9} to find the set. 33) (A B) C 33) A) {1, 2, 3} B) {2, 3, 5} C) {1, 2, 3, 4, 5, 9} D) {1, 2, 3, 5} Determine which value(s), if any, must be excluded from the domain of the variable in the expression. x3 + 7x4 34) x2 + 36 A) x = -36

Simplify the expression. 35) 125-4/3 A) 625

B) x = -6

C) x = 0, x = -

1 B) 625

1 C) 625

1 7

D) none

35) D) -625

Determine which value(s), if any, must be excluded from the domain of the variable in the expression. x2 + 6x + 9 36) x3 - 9x A) x = 3, x = -3, x = 0 C) x = 3, x = -3

34)

36)

B) x = 3, x = 0 D) x = 0

Write the number in scientific notation. 37) 0.000486 A) 4.86 × 104 B) 4.86 10-4

37) C) 4.86 × 10-5

Factor completely. If the polynomial cannot be factored, say it is prime. 38) x4 - 64 A) (x2 + 8)2 B) prime C) (x2 + 8)(x2 - 8) 5

D) 4.86 × 10-3

D) (x2 - 8)2

38)

Evaluate the expression. 39) -9 - (-2 + 6 · 7 + 8) A) -57

B) 39

C) -61

D) -41

Simplify the expression. Assume that all variables are positive when they appear. 6 40) 7 B) 6 7

A) 55

36 7 7

Use a calculator to evaluate the expression. Round the answer to three decimal places. 41) (4.49)2 A) 20.160

B) 0.050

C) -0.050

39)

40) D)

6 7 7

D) -20.160

Solve the problem. 42) Find the area of the window. Approximate the result to the nearest tenth using 3.14 for .

41)

42)

8 ft

4 ft

A) 35.1 ft2

B) 57.1 ft2

C) 38.3 ft2

D) 82.2 ft2

Use U = universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 5, 8}, B = {2, 3, 5, 7}, and C = {1, 4, 9} to find the set. 43) A C A) {1, 2, 3, 4, 5, 7, 8, 9} C) {0, 2, 3, 4, 5, 6, 7, 8, 9}

43)

B) {1, 2, 3, 4, 5, 6, 7, 8, 9} D) {1}

Perform the indicated operations and simplify the result. Leave the answer in factored form. 44) x xx+2 x+1

x x+1

x x+2

x2 x+2

x x-2

44)

Solve the problem. 45) Find the area of the shaded region. Express the answer in terms of .

45)

A) 81 -

81 4

square units

D) 81 -

C) 324 - 81 square units

Factor the perfect square. 46) x2 + 12x + 36 A) (x + 6)2

81 4

+ 81 square units 81 2

square units

C) (x - 6)2

B) (x + 12)(x - 12)

46) D) (x + 6)(x - 6)

Use U = universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 5, 8}, B = {2, 3, 5, 7}, and C = {1, 4, 9} to find the set. 47) A C 47) A) {1, 2, 3, 4, 5, 8, 9} B) {1} C) {1, 2, 3, 5, 7, 9} D) {4, 6, 7, 9} Perform the indicated operations. Express the answer as a single polynomial in standard form. 48) -4x5 (3x7 - 10)

48)

Factor the polynomial. 49) 9y2 + 18y + 8

49)

A) -12x7 + 40

A) (9y + 4)(y + 2)

B) -12x12 - 10

C) 28x5

B) (3y + 4)(3y + 2)

C) (3y - 4)(3y - 2)

D) -12x12 + 40x5

D) prime

Simplify the expression. Express the answer so that only positive exponents occur. Assume that all variables are positive. 50) (9x1/5 · y1/5 )2 50) A) 81x1/10y1/10

B) 81x2/5 y2/5

C) 81x2 y2

D) 81x1/25y1/25

On the real number line, label the points with the given coordinates. 51) -1.75, 1, 3, 5.25

51)

Add or subtract as indicated. Express the answer as a single polynomial in standard form. 52) (13x2 + 4x - 2) + (8x + 2) A) 13x2 + 12x

B) 25x3

C) 13x2 + 4x + 4

D) 13x2 + 12x - 4

Solve the problem. 53) The weekly production cost C of manufacturing x calendars is given by C(x) = 29 + 3x, where the variable C is in dollars. What is the cost of producing 213 calendars? A) $242.00 B) $668.00 C) $639.00 D) $6,180.00 The triangles are similar. Find the missing length x and the missing angles A, B, C. 54)

52)

53)

54)

94° 16

36°

50°

A) x = 8 units; A = 50°; B = 36°; C = 94° C) x = 16 units; A = 94°; B = 36°; C = 50°

B) x = 16 units; A = 36°; B = 94°; C = 50° D) x = 8 units; A = 94°; B = 36°; C = 50°

Factor completely. If the polynomial cannot be factored, say it is prime. 55) 18x2 - 63x - 36 A) (18x - 9)(x + 4)

B) 9(2x - 1)(x + 4)

C) 9(2x + 1)(x - 4)

D) prime

55)

Use synthetic division to find the quotient and the remainder. 56) x4 + 16 is divided by x - 2 A) x3 + 2x2 + 4x + 8; remainder 32 C) x3 + 2x2 + 4x + 8; remainder 0

B) x3 - 2x2 + 4x - 8; remainder 32 D) x3 + 2x2 + 4x + 8; remainder 16

56)

Use U = universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 5, 8}, B = {2, 3, 5, 7}, and C = {1, 4, 9} to find the set. 57) (B C) A 57) A) { } B) {1, 2, 3, 5} C) {1, 2, 3, 4, 5, 7, 9} D) {1, 2, 3} Insert <, >, or = to make the statement true. -3.9 58) 6.7 A) =

58) B) >

C) <

Write the number in scientific notation. 59) 0.00006693 A) 6.693 × 10-5 B) 6.693 × 105

C) 6.693 × 104

59) D) 6.693 ± 10-4

Factor completely. If the polynomial cannot be factored, say it is prime. 60) 98x2 - 112x + 32

60)

B) 2(7x - 4)2

A) 2(7x - 4)(7x + 4) C) 2(7x + 4)2

D) prime

Add or subtract as indicated. Express the answer as a single polynomial in standard form. 61) (8x4 - 17x3 ) - (12x4 + 11x3 ) A) 20x4 - 6x3

B) -32x7

C) -4x4 - 6x3

D) -4x4 - 28x3

61)

Tell whether the expression is a monomial. If it is, name the variable(s) and coefficient, and give the degree of the monomial. 6x 62) 62) y

A) Monomial; variables x, y; coefficient 6; degree -2 B) Monomial; variables x, y; coefficient 6; degree 2 C) Monomial; variables x, y; coefficient 6; degree 1 D) Not a monomial Find the LCM of the given polynomials. 63) x2 - 4x, (x - 4)2 A) x(x - 4)2

B) x(x + 4)2

C) x(x - 4)

Factor completely. If the polynomial cannot be factored, say it is prime. 64) 3x2 - 18x + 24 A) 3(x - 4)(x - 2)

B) (x - 4)(3x - 6)

C) 3(x - 8)(x + 1)

D) (x + 4)(x - 4)2

D) prime

63)

64)

Tell whether the expression is a polynomial. If it is, give its degree. 65) -2z 4 + z A) Polynomial; degree 1 C) Polynomial; degree 5

65)

B) Polynomial; degree 4 D) Not a polynomial

Reduce the rational expression to lowest terms. 4x + 2 66) 12x2 + 26x + 10 A)

1 3x + 5

66)

4x + 2 2 12x + 26x + 10

4x 3x + 5

4x + 3 3x + 26

Use synthetic division to determine whether x - c is a factor of the given polynomial. 1 67) 6x5 - 5x4 + x - 4; x + 2 A) Yes Factor the polynomial. 68) 4x2 + 12x + 9

A) (2x - 3)(2x - 3)

67)

B) No

B) (2x + 3)(2x + 3)

Write the statement as an inequality. 69) y is greater than or equal to 65 A) y < 65 B) y 65

C) (4x + 3)(x + 3)

D) prime

C) y > 65

D) y 65

Factor the polynomial by removing the common monomial factor. 70) 9x - 9 A) 9(x + 1) B) x(x + 9) C) x(x - 9)

D) 9(x - 1)

Perform the indicated operations and simplify the result. Leave the answer in factored form. 71) 2 +1 x

68)

69)

70)

71)

2 -1 x

x2 x2 + 2

2+x 2-x

C) x2 + 2

The lengths of the legs of a right triangle are given. Find the hypotenuse. 72) a = 24, b = 7 A) 625 B) 5 C) 20 Simplify the expression. Assume that all variables are positive when they appear. 73) ( 12 + z)( 12 - z) A) 12 - 2 12z B) 12z C) 12 - z

D) 2

D) 25

72)

73) D) 12 - 2 z

Factor completely. If the polynomial cannot be factored, say it is prime. 74) 15x4 + 16x2 + 4 A) (5x2 - 2)(3x2 - 2) C) (15x2 + 2)(x2 + 2)

74)

B) (3x2 + 1)(5x2 + 4) D) (3x2 + 2)(5x2 + 2)

Perform the indicated operations and simplify the result. Leave the answer in factored form. 75) x 1 81 x 1+

9 x

81 x+9

x+9 81

x-9 81

81 x-9

Solve the problem. 76) Police use the formula s = 30fd to estimate the speed s of a car in miles per hour, where d is the distance in feet that the car skidded and f is the coefficient of friction. If the coefficient of friction on a certain gravel road is 0.28 and a car skidded 330 feet, find the speed of the car, to the nearest mile per hour. A) 99 mph B) 2,772 mph C) 53 mph D) 288 mph Approximate the number rounded to three decimal places, and truncated to three decimal places. 77) 7.1134 A) 7.112 B) 7.114 C) 7.113 D) 7.113 7.114 7.113 7.113 7.114 Factor the polynomial by grouping. 78) 15x2 - 6x + 10x - 4 A) (15x - 2)(x + 2)

B) (3x - 2)(5x + 2)

C) (15x + 2)(x - 2)

D) (3x + 2)(5x - 2)

C) (x + 2)(x - 2)

D) (x2 + 2)(x2 - 2)

Factor the difference of two squares. 79) x2 - 4 A) (x - 2)(x - 2)

B) (x + 4)(x - 4)

75)

Solve the problem. 80) A circular swimming pool, 20 feet in diameter, is enclosed by a circular deck that is 4 feet wide. What is the area of the deck? Use = 3.1416. A) 314.2 ft2 B) 301.6 ft2 C) 703.7 ft2 D) 584.3 ft2

76)

77)

78)

79)

80)

Multiply the polynomials using the special product formulas. Express the answer as a single polynomial in standard form. 81) (x + 5y)(x - 5y) 81) 2 2 2 2 x 10xy 25y x 10xy 25y + A) B)

C) x2 - 25y2

Simplify the expression. 82) 2434/5 A) 19,683

D) x2 - 10y2

B) 2,187

C) 6,561 11

D) 81

82)

Factor the expression. Express your answer so that only positive exponents occur. 83) (3m + 9)-2/5 + (3m + 9) 1/5 + (3m + 9) 7/5

83)

A) (3m + 9)-2/5 [1 + (3m + 9) 4/5 + (3m + 9) 7/5] B) (3m + 9)-2/5 [1 + (3m + 9) 3/5 + (3m + 9) 9/5]

C) (3m + 9)-2/5 [1 + (3m + 9) 3/5 - (3m + 9) 9/5] D) (3m + 9)-2/5 [1 + (3m + 9)-3/5 + (3m + 9) -9/5] An expression that occurs in calculus is given. Factor completely. 84) 3(x + 5)2 (2x - 1)2 + 4(x + 5)3 (2x - 1)

84)

B) (x + 5)2 (2x - 1)(x + 17) D) (x + 5)2 (2x - 1)(10x + 17)

A) (x + 5)(2x - 1)(10x + 17) C) (x + 5)2 (10x + 17)

Perform the indicated operations and simplify the result. Leave the answer in factored form. 3x x-1 1 + 85) x2 - 5x - 36 x2 - 16 x2 - 13x + 36 A)

2x2 - x - 5 (x - 9)(x + 4)(x - 4)

2x - 1 (x - 9)(x + 4)

2x - 1 (x - 9)(x - 4)

2x2 - 21x + 13 (x - 9)(x + 4)(x - 4)

Solve the problem. 86) An electrical circuit contains two resistors connected in parallel. If the resistance of each is R1 and

85)

86)

R2 ohms, respectively, then their combined resistance R is given the formula R=

1 1 + R 1 R2

If their combined resistance R is 2 ohms and R2 is 9 ohms, find R 1 .

18 ohms 7

B) 7 ohms

2 ohms 7

Factor completely. If the polynomial cannot be factored, say it is prime. 87) 8x4 - x A) x(2x - 1)(4x2 + 1) C) x(2x - 1)(4x2 + 2x + 1)

B) x(8x - 1)(x2 + 2x + 1) D) x(2x + 1)(4x2 - 2x + 1)

7 ohm 18

87)

Multiply the polynomials using the FOIL method. Express the answer as a single polynomial in standard form. 88) (3x - 8)(x + 5) 88) A) 3x2 - 40x + 7 B) 3x2 + 7x - 40 C) 3x2 + 5x - 40 D) 3x2 + 7x + 7 Use synthetic division to determine whether x - c is a factor of the given polynomial. 89) x3 - 7x2 - 9x + 63; x + 3 A) Yes

B) No

90) x3 - 13x2 + 46x - 48; x - 2 A) Yes

B) No

89)

90)

Tell whether the expression is a monomial. If it is, name the variable(s) and coefficient, and give the degree of the monomial. 91) -4xy3 91)

A) Monomial; variables x, y; coefficient -4; degree 1 B) Monomial; variables x, y; coefficient -4; degree 3 C) Monomial; variables x, y; coefficient -4; degree 4 D) Not a monomial

Multiply the polynomials using the special product formulas. Express the answer as a single polynomial in standard form. 92) (6x - 5y)2 92)

A) 6x2 - 60xy + 25y2 C) 6x2 + 25y2

B) 36x2 + 25y2 D) 36x2 - 60xy + 25y2

Evaluate the expression using the given values. 93) x + y x = -8, y = 3 A) -11 B) 5

C) 11

Simplify the expression. Assume that all variables are positive when they appear. 3 3 94) 21 · 49 3 6 3 A) 7 3 B) 1,029 C) 7 21

D) -5

93)

94) D)

1,029

Simplify the expression. Express the answer so that only positive exponents occur. Assume that all variables are positive. x5/3 · x3/4 95) 95) x-4/7 A)

1 251/84 x

B) x251/84

C) x155/84

Simplify the expression. 96) -243-4/5

1 81

96)

D) not a real number

Find the LCM of the given polynomials. 97) 3x - 9, x2 - 3x A) 3x2 - 9

1 155/84 x

1 B) 81

A) 81 C)

B) 3x - 3

C) 3x(x - 3)

D) 3x2 - 3

97)

Tell whether the expression is a monomial. If it is, name the variable(s) and coefficient, and give the degree of the monomial. 98) -5x-9 98)

A) Monomial; variable x; coefficient 9; degree -5 B) Monomial; variable x; coefficient -5; degree 9 C) Monomial; variable x; coefficient -5; degree -9 D) Not a monomial

List all the elements of B that belong to the given set. 4 9 99) B = 17, 7, -11, 0, , - , 1.8 9 4 Natural numbers 9 A) 17, 0, 4

99)

B) {-11, 0, 17}

C) {17}

D) {17, 0}

Perform the indicated operations and simplify the result. Leave the answer in factored form. 8x2 8x 100) x-1 x-1 A)

8x(x + 1) x-1

B) 8x

C) 0

Simplify the expression. Assume that all variables are positive when they appear. 3 3 101) 8y - 128y 3 3 3 3 3 A) 4 2y - 2 y B) 2 y - 4 2y C) 6 y 102)

147x2

A) 7x 3

100)

8x x-1

101) D) 2 - 4

102) C) 3x2 7

B) 7 3x

D) 147x

Perform the indicated operations and simplify the result. Leave the answer in factored form. 3 7 + 103) 2 2 x - 3x + 2 x - 1 A)

10x - 11 (x - 1)(x + 1)(x - 2)

10x - 11 (x - 1)(x - 2)

42x - 11 (x - 1)(x + 1)(x - 2)

11x - 10 (x - 1)(x + 1)(x - 2)

Write the number as a decimal. 104) 5.378 × 105 A) 537,800

B) 5,378,000

C) 268.9

D) 53,780

103)

104)

Use U = universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 5, 8}, B = {2, 3, 5, 7}, and C = {1, 4, 9} to find the set. 105) A B 105) A) {1, 2, 3, 5, 7, 8} B) {2, 3, 5, 7} C) {2, 3, 5} D) {1, 2, 3, 5, 8} An expression that occurs in calculus is given. Write the expression as a single quotient in which only positive exponents and/or radicals appear. 3 1 (x2 + 2)1/2 · (2x + 1)1/2 · 2 - (2x + 1)3/2 · (x2 + 2)-1/2 · 2x 2 2 106) 106) x2 + 2

(2x + 1)1/2(x2 - x + 6) (x2 + 2)3/2

B) (x2 + 2)3/2(2x + 1)-1/2(x2 - x + 6)

C) (x2 + 2)3/2(2x + 1)1/2(x2 - x + 6)

(2x + 1)1/2(x2 - x + 6) (x2 + 2)-3/2

Factor completely. If the polynomial cannot be factored, say it is prime. 107) 7y6 - 39y3 + 20 A) y2 (7y2 - 4)(y2 - 5) C) (7y3 - 5y2 + y - 4)(y3 - 4y2 + y - 5)

107)

B) (7y3 - 4)(y3 - 5) D) y4 (7y - 4)(y - 5)

Simplify the expression. 1 1/2 108) 16 A) 4

108) B)

1 4

-1 4

D) -4

Graph the numbers on the real number line. 109) x < -7

109)

Add or subtract as indicated. Express the answer as a single polynomial in standard form. 110) (8x2 + 8x + 2) + (9x2 + 5x - 6)

110)

Simplify the expression. 111) -4 -2

111)

A) 17x2 + 13x + 4

1 A) 8

B) 17x2 + 13x - 4

B) -16

C) 11x2 + 13x + 2

D) 17x2 - 13x - 4

C) 16

1 D) 16

Multiply the polynomials using the FOIL method. Express the answer as a single polynomial in standard form. 112) (-5x - 11)(-3x + 3) 112) 2 2 2 2 A) -8x + 18x - 33 B) -8x + 18x + 18 C) 15x + 18x + 18 D) 15x + 18x - 33 Express the statement as an equation involving the indicated variables. 113) The area A of a triangle is one-half the product of its base b and its height h. 1 1 A) A = (b + h) B) A = bh C) A = bh 2 2

113) D) A = 2bh

Simplify the expression. Assume that all variables are positive when they appear. 114) 7 2 + 5 8 A) 17 2 B) 3 2 C) -17 2 Write the number in scientific notation. 115) A computer compiles a program in 0.0000266 seconds. A) 2.66 × 10-7 B) 2.66 × 104 C) 2.66 × 10-5

114) D) 12 2

115) D) 2.66 × 10-6

An expression that occurs in calculus is given. Reduce the expression to lowest terms. (2x + 5)4x - 2x2 (2) 116) (2x + 5)2 A)

(x + 5)2

4(x + 5) (2x + 5)2

(2x + 5)2

116) D)

4x(x + 5) (2x + 5)2

Reduce the rational expression to lowest terms. x2 + 5x + 6 117) x2 + 9x + 18 A)

5x + 6 9x + 18

B) -

117)

x2 + 5x + 6 x2 + 9x + 18

x+2 x+6

5x + 1 9x + 3

Perform the indicated operations and simplify the result. Leave the answer in factored form. 4 6 118) x+5 x-5 A)

-2 (x + 5)(x - 5)

-2x - 50 (x + 5)(x - 5)

-2x + 50 (x + 5)(x - 5)

-2x + 10 (x + 5)(x - 5)

Find the quotient and the remainder. 119) 45x2 + 35x - 11 divided by 5x A) 9x2 + 7x -

119)

11 ; remainder 0 5

B) 9x + 7; remainder -11

C) 9x - 4; remainder 0

D) 45x + 35; remainder -11

Add or subtract as indicated. Express the answer as a single polynomial in standard form. 120) (2x5 - 5x3) + (3x5 + 3x3 ) A) 3x8

118)

B) 5x5 - 2x3

C) 5x10 - 2x6

121) 6(1 - y3 ) - 4(1 + y + y2 + y3 ) A) -10y3 - 4 - ay2 - 4y + 2

D) 3x16

121)

B) -10y3 + 4y2 - 4y - 2 D) -10y3 - 4y2 - 4y + 2

C) 10y3 - 4y2 - 4y + 2

Write the statement as an inequality. 122) z is less than or equal to 1 A) z > 1 B) z < 1

C) z = 1

120)

D) z 1

122)

An expression that occurs in calculus is given. Factor completely. 123) 2(x + 6)(x - 5)3 + (x + 6)2 · 6(x - 5)2 A) (x + 6)(x - 5)2 (4x + 13) C) 2(x + 5)(x - 6)2 (4x + 13)

123)

B) 2(x + 6)(x - 5)2 (4x + 13) D) (x + 6)(x - 5)2 (8x + 26)

Reduce the rational expression to lowest terms. y2 + 11y + 28 124) y2 + 13y + 42 A)

11y + 28 13y + 42

B) -

124)

y2 + 11y + 28 y2 + 13y + 42

11y + 2 13y + 3

Simplify the expression. 125) (4-1 )-2 1 A) 16

B) 4

C) 16

y+ 4 y+ 6

1 D) 4

Determine which value(s), if any, must be excluded from the domain of the variable in the expression. x2 - 64 126) x A) x = -8

B) x = 8, x = 0

C) x = 8, x = -8

5 2

5x 2

5x 8

Simplify the expression. Assume that all variables are positive when they appear. 5 3+ 6 129) 6+ 3

130)

11 + 2 10 -9

B) 5 2 - 3

C) 5 2 - 7

127)

x 2

Solve the problem. 128) The maximum distance d in kilometers that you can see from a height h in meters is given by the formula d = 3.5 h. How far can you see from the top of a 383-meter building? (Round to the nearest tenth of a kilometer.) A) 19.6 km B) 68.5 km C) 36.6 km D) 716.5 km

A) 4 2 - 3

126)

D) x = 0

Perform the indicated operations and simplify the result. Leave the answer in factored form. 4x 10x + 5 · 127) 8x + 4 2 A)

125)

128)

129) D) 6 2 + 7 130)

-9 - 2 10 11

11 - 2 10 -9

D) 1

Find the quotient and the remainder. 131) 27x8 - 45x4 divided by 9x

A) 3x8 - 5x4 ; remainder 0 C) 3x7 - 5x3 ; remainder 0

Find the value of the expression using the given values. x = 15, y = 20 132) x2 + y2 A) 24

Factor the polynomial. 133) x2 + 49

A) (x - 7)2

131)

B) 27x7 - 45x3 ; remainder 0 D) 3x9 - 5x5 ; remainder 0

132)

B) 18

C) 25

D) 13

B) (x + 7)2

C) (x + 7)(x - 7)

D) prime

133)

Insert <, >, or = to make the statement true. -4 134) 4

134)

A) >

B) =

C) <

Simplify the expression. Assume that all variables are positive when they appear. 5 135) 3 3 A) 5

3 3

C) 5

135)

3 3

Multiply the polynomials using the FOIL method. Express the answer as a single polynomial in standard form. 136) (-5x + 11y)(-3x + 11y) 136) 2 2 2 2 A) 15x - 88xy + 121y B) 15x - 55xy + 121y C) 15x2 - 88xy - 88y2

D) 15x2 - 33xy + 121y2

Find the LCM of the given polynomials. 137) x2 + 6x + 8, -3x - 12 A) -3(x - 2)(x + 4)

B) -3(x + 2)(x - 4)

C) -3(x - 2)(x - 4)

D) -3(x + 2)(x + 4)

Evaluate the expression. 1 1 1 138) + · 5 8 9 A)

13 360

138) B)

1 180

49 40

77 360

Determine which value(s), if any, must be excluded from the domain of the variable in the expression. 7x - 2 139) x2 - 16 A) x = 4, x = -4

137)

C) x =

B) x = 16

2 7

D) x = 4

139)

Simplify the expression. Express the answer so that only positive exponents occur. Assume that all variables are positive. 140) (9x10y-16)1/2 140) A)

9x5 y8

3 x5 y8

C) 3x5 y8

3x5 y8

Solve the problem. 141) Find the volume V and surface area S of a sphere of radius 2 centimeters. Express the answer in terms of . 8 32 cm3 ; S = cm2 A) V = 32 cm3 ; S = 1 cm2 B) V = 3 3 C) V = 8 cm3 ; S = 4

cm2

D) V =

32 3

cm3 ; S = 16 cm2

142) A bicycle wheel makes 4 revolutions. Determine how far the bicycle travels in inches if the diameter of the wheel is 22 in. Use 3.14. Round to the nearest tenth. A) 552.6 in. B) 88 in. C) 69.1 in. D) 276.3 in. Find the value of the expression using the given values. x = -9, y = -4 143) x2 + y2 A) 13

B) 97

C) -5

Find the LCM of the given polynomials. 144) x2 - 7x + 12, x2 - 4x + 3 A) (x - 4)(x - 3) C) (x - 3)(x - 1)

A) 16 C)

146)

D) 5

B) -

1 16

143)

145)

1 16

D) not a real number

146)

A) 16 C)

142)

144)

B) (x + 4)(x + 3)(x - 1) D) (x - 4)(x - 3)(x - 1)

Simplify the expression. 145) 32-4/5

141)

B) 2

1 4

Evaluate the expression. 147) 2 · [3(7 - 2) - 4] A) 22 148) 2 · [4 + 6 · (3 + 4)] A) 92

D) not a real number

B) 7

C) -10

D) -14

B) 50

C) 136

D) 140

147)

148)

The lengths of the legs of a right triangle are given. Find the hypotenuse. 149) a = 6, b = 8 A) 5 B) 10 C) 7 Simplify the expression. Assume that all variables are positive when they appear. 150) 9y10 A) 3y8

B) 3y10

C) 3y5

Use synthetic division to find the quotient and the remainder. 151) x4 - 4 is divided by x - 2 A) x3 + 2x2 + 4x + 8; remainder 12 C) x3 + 4x2 + 16x + 64; remainder 254

D) 9

D) 9y5

B) x3 + 6x2 + 4x + 2; remainder 12 D) x3 + 2x2 + 4x + 8; remainder 254

Perform the indicated operations and simplify the result. Leave the answer in factored form. 6x + 5 6x - 5 152) 2 2 A) 5

B) 25

C) 0

Use synthetic division to find the quotient and the remainder. 153) 3x3 + 16x2 - 14x - 12 is divided by x + 6

149)

150)

151)

152)

D) 6x

A) -3x2 - 6x - 2; remainder 0

8 B) 3x2 x + - 2; remainder0 3

C) 3x2 - 2x - 2; remainder 0

153)

1 2 8 7 x + x - ; remainder 0 2 3 3

Solve. b, 154) If the three lengths of the sides of a triangle are known, Heron's formula can be used to find its area. If a, 154) and c are the three lengths of the sides, Heron's formula for area is: A = s(s - a)(s - b)(s - c) 1 where s is half the perimeter of the triangle, or s = (a + b + c). 2 Use this formula to find the area of the triangle if a = 7 cm, b = 9 cm and c = 14 cm.

A) 19 3.98891967 sq. cm C) 19 1.99445983 sq. cm

B) 139 11.9993789 sq. cm D) 5 1.92 sq. cm

Use the Distributive Property to remove the parentheses. 155) 7(4x + 8) A) 11x + 15 B) 84x

C) 28x + 56

Factor the expression. Express your answer so that only positive exponents occur. 156) x5/4 - x3/4 A) x3/4 (x1/2 - 1)

B) x3/4 (x1/2 + 1)

C) x3/4 (x1/2 )

D) 28x + 8

D) x3/4 (x1/2 - x)

155)

156)

Perform the indicated operations and simplify the result. Leave the answer in factored form. 157) 1 x+6

157)

x2 - 36

x-6 5

5 x-6

C) x - 6

x+6 5

Use U = universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 5, 8}, B = {2, 3, 5, 7}, and C = {1, 4, 9} to find the set. 158) B C 158) A) { } B) {0} C) {1, 2, 3, 5, 7, 9} D) {1, 2, 3, 4, 5, 7, 9} Factor the expression. Express your answer so that only positive exponents occur. 159) x8/5 + x2/5 A) x2/5 (x6/5 )

B) x2/5 (x6/5 + x)

C) x2/5 (x6/5 + 1)

D) x2/5 (x6/5 - 1)

Simplify the expression. 8 2/3 160) 64 A) -

1 4

160) B)

1 6

Find the LCM of the given polynomials. 161) 12x - 7, 12x + 7 A) (12x - 7) or (12x + 7) C) (12x - 7)(12x + 7) Write the number as a decimal. 162) 4.13 × 107 A) 4,130,000

1 2

1 4

161)

B) (12x - 7) D) (12x + 7)

B) 289.1

C) 41,300,000

D) 413,000,000

Tell whether the expression is a polynomial. If it is, give its degree. 163) 6x5 - 4 A) Polynomial; degree 6 C) Polynomial; degree 4

2x - 2 45

1 27

9(6x - 6) 2x - 2

12(x - 1)2 225

162)

163)

B) Polynomial; degree 5 D) Not a polynomial

Perform the indicated operations and simplify the result. Leave the answer in factored form. 164) 6x - 6 5

159)

D) 27

164)

Write the statement using symbols. 165) The sum of four times x and 5 decreased by 7 is 8. A) 4(x + 5 - 7) = 8 B) 4(x + 5) - 7 = 8

C) 7 - (4x + 5) = 8

D) 4x + 5 - 7 = 8

Perform the indicated operations and simplify the result. Leave the answer in factored form. 2x2 2x 166) x-1 x-1 A)

167)

2x(x + 1) x-1

x2 + 2x

B) 0

C) 2x

166)

2x x-1

2 5 + x x+2

7 x

Factor the polynomial. 168) x2 + 7x - 44

A) (x - 11)(x + 4)

167) B)

10 x

B) (x - 11)(x + 1)

2 x

C) (x + 11)(x - 4)

5 x

168)

D) prime

Evaluate the expression. 4 1 169) + 5 14 A)

61 19

169) B)

5 19

1 14

61 70

Perform the indicated operations. Express the answer as a single polynomial in standard form. 170) -8x3 (-10x - 3) A) 80x + 24

B) 80x4 - 3

C) 104x3

D) 80x4 + 24x3

Solve. If necessary, round to the nearest tenth. 171) If a flagpole 9 feet tall casts a shadow that is 12 feet long, find the length of the shadow cast by an antenna which is 18 feet tall. A) 6 ft B) 13.5 ft C) 21 ft D) 24 ft Simplify the expression. Assume that all variables are positive when they appear. 3 3 172) 27 + 12 - 18 3 3 3 3 A) 15 18 B) 27 + 12 - 18 C) 15 - 2 9

2 9

1 9

1 6

170)

171)

172) D) 15 -

What number should be added to complete the square of the expression? 2 173) x2 + x 3 A)

165)

173) D)

4 9

Simplify the expression. 174) 2164/3 A) 279,936

B) 1,296

C) 7,776

D) 46,656

174)

Multiply the polynomials using the FOIL method. Express the answer as a single polynomial in standard form. 175) (x - 8y)(-5x + 6y) 175) 2 2 2 2 A) x + 46xy + 46y B) x + 46xy - 48y C) -5x2 + 46xy - 48y2

D) -5x2 + 46xy + 46y2

Evaluate the expression using the given values. 176) -10x + y x = -3, y = -3 A) -6 B) 27

C) -13

D) -33

Write the number in scientific notation. 177) 0.000000666012 A) 6.66012 × 107 B) 6.66012 × 10-6

C) 6.66012 × 106

D) 6.66012 × 10-7

177)

Determine which value(s), if any, must be excluded from the domain of the variable in the expression. 2 178) x+2 A) x = 2

B) x = 0

C) x = -2

179)

Use synthetic division to determine whether x - c is a factor of the given polynomial. 180) x3 - 11x2 + 12x + 80; x + 5 A) Yes

180)

B) No

Write the statement as an inequality. 181) x is less than 5 A) x 5 B) x > 5

C) x < 5

178)

D) none

On the real number line, label the points with the given coordinates. 4 4 179) , 3 3

176)

D) x 5

181)

Simplify the expression. Express the answer so that only positive exponents occur. Assume that all variables are positive. 182) x-2/5 · x3/5 182) A) x6/5

B) x5/6

C) x1/5

D) x-1/5

Simplify the expression. Assume that all variables are positive when they appear. 3 183) -27x21 A) -3x18 B) -3x7 C) 3x7

D) -3x21

183)

Simplify the expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, we assume that the base is not 0. 184) (-5x3 )-1 184)

A) -

125x3

C) -

125x3

5x3

Perform the indicated operations and simplify the result. Leave the answer in factored form. 185) 7 -7 3x - 1

185)

7 +7 3x - 1

3x 2 - 3x

Write the number as a decimal. 186) 7.306 × 10-6 A) 0.000007306

2-x x

B) 0.00007306

2 - 3x 3x

C) -7,306,000

2 + 3x 3x

D) 0.0000007306

Solve. If necessary, round to the nearest tenth. 187) A flagpole casts a shadow of 20 feet. Nearby, a 5-foot tree casts a shadow of 3 feet. What is the height of the flagpole? A) 0.8 ft B) 33.3 ft C) 300 ft D) 12 ft Write the statement as an inequality. 188) y is greater than -92 A) y > -92 B) y -92

C) y -92

D) y < -92

Factor completely. If the polynomial cannot be factored, say it is prime. 189) x4 + 2x2 - 35 A) (x2 + 5)(x2 + 7)

B) (x2 + 5)(x2 + 1)

C) (x2 - 5)(x2 + 7)

Write the number in scientific notation. 190) 10,913 A) 1.0913 × 104 B) 1.0913 × 101

C) 1.0913 × 105

186)

187)

188)

189) D) Prime

190) D) 1.0913 × 10-4

Perform the indicated operations and simplify the result. Leave the answer in factored form. x2 - 5x + 4 x2 - 11x + 30 · 191) x2 - 8x + 15 x2 - 14x + 40 A)

(x - 1) (x - 10)

(x2 - 5x + 4)(x2 - 11x + 30) (x2 - 8x + 15)(x2 - 14x + 40)

(x + 1)(x + 6) (x + 3)(x + 10)

(x - 1)(x - 6) (x - 3)(x - 10)

Factor the sum or difference of two cubes. 192) 125x3 + 1 A) (5x + 1)(25x2 - 5x - 1) C) (5x + 1)(25x2 - 5x + 1)

192)

B) (5x + 1)(25x2 + 1) D) (5x + 1)(25x2 + 5x + 1)

Factor completely. If the polynomial cannot be factored, say it is prime. 193) 15x4 + 10x2 - 6x2 - 4 A) (15x2 + 2)(x2 - 2)

D) (5x4 - 2)(3x + 2)

Find the value of the expression using the given values. x=9 194) ( x)2 A) 81

193)

B) (5x2 - 2)(3x2 + 2)

C) (5x2 + 2)(3x2 - 2)

191)

1 B) 9

1 C) 81

194) D) 9

Multiply the polynomials using the FOIL method. Express the answer as a single polynomial in standard form. 195) (x + 7y)(x + 11y) 195) 2 2 A) x + 18xy + 77y B) x + 18xy + 77y C) x2 + 15xy + 77y2

D) x2 + 18xy + 18y2

Factor completely. If the polynomial cannot be factored, say it is prime. 196) (7 - x)3 - x3 A) (7 + 2x)(x2 - 7x + 49) C) (7 - 2x)(x2 - 7x + 49)

196)

B) (7 - 2x)(3x2 - 7x + 49) D) (7 - x)(x2 - 7x + 49)

Perform the indicated operations and simplify the result. Leave the answer in factored form. 197) x2 - 14x + 49

197)

2x - 14 6x - 42 12

x2 - 14x + 49 (x - 7)2

(x - 7)2 4

C) 1

Find the LCM of the given polynomials. 198) x2 + 12x + 36, x2 + 6x A) x(x + 6)

B) x(x + 6)2

C) (x + 6)2 25

D) 12

198) D) x(x + 1)(x + 6)

Simplify the expression. Assume that all variables are positive when they appear. 199) (9 7)(9 70) A) 81 490 B) 3,969 10 C) 567 10

199) D) 567 70

Solve. If necessary, round to the nearest tenth. 200) If a tree 42.5 feet tall casts a shadow that is 17 feet long, find the height of a tree casting a shadow that is 7 feet long. A) 103.2 ft B) 17.5 ft C) 2.8 ft D) 32.5 ft Evaluate the expression. 9 13 201) 6 7 A)

21 26

201)

54 91

26 21

91 54

Multiply the polynomials. Express the answer as a single polynomial in standard form. 202) (3x - 4y)2 A) 3x2 - 24xy + 16y2

202)

B) 9x2 - 24xy + 16y2

C) 3x2 + 16y2

D) 9x2 + 16y2

Insert <, >, or = to make the statement true. -92 203) -38 A) =

203) B) >

C) <

Evaluate the expression using the given values. 4xy + 15 x = 5, y = 7 204) x A) 7

204)

B) 31

C) 3

D) 43

Add or subtract as indicated. Express the answer as a single polynomial in standard form. 205) 2(4x3 + x2 - 1) - 7(4x3 - 4x + 2) A) -20x3 + 2x2 + 28x - 16

205)

B) -20x3 + x2 + 28x - 16

C) -20x3 + 2x2 - 28x - 16

D) -20x3 + 2x2 + 28x + 16

List all the elements of B that belong to the given set. 8 9 206) B = 13, 8, -2, 0, , - , 2.1 9 8 Integers A) {13, -2}

200)

206)

B) {13, 0}

C) {13, -2, 0}

Find the quotient and the remainder. 207) 7x3 + 24x2 - 12x + 16 divided by x + 4 A) 7x2 - 4x + 4; remainder 0 C) 7x2 + 4x + 4; remainder 0

D) {13, 0,

B) x2 + 5x + 6; remainder 0 D) x2 + 4x + 7; remainder 0

207)

Simplify the expression. Assume that all variables are positive when they appear. 24 208) 3 x30 2

3 A) 27 x

Simplify the expression. 209) 271/3 A) 243

24 B) 10 x

3 10 x

B) 9

C) 81

Factor completely. If the polynomial cannot be factored, say it is prime. 210) 10y2 + 45y - 25 A) (10y - 5)(y + 5)

B) 5(2y - 1)(y + 5)

C) 5(2y + 1)(y - 5)

208) D) 3

24 x30

D) 3

D) prime

Simplify the expression. Assume that all variables are positive when they appear. 4 211) 625 A) 625 B) 5 C) -5 D) not a real number Use the Distributive Property to remove the parentheses. 212) (x + 4)(x - 4) A) x2 + 8x - 16 B) x2 - 8

C) x2 - 16

209)

210)

211)

D) x2 - 8x - 16

212)

Simplify the expression. Express the answer so that only positive exponents occur. Assume that all variables are positive. 213) (3x2/3 )(6x3/2 ) 213) A) 18x5/6

B) 18x13/6

C) 18x13/5

D) 18x2/3

Simplify the expression. Assume that all variables are positive when they appear. 3 214) 511 A) 63

B) 8

C) 23

214) D) ±8

Factor completely. If the polynomial cannot be factored, say it is prime. 215) (x + 4)2 - 5(x + 4) + 6

B) (x2 + 4x - 3)(x2 + 4x - 2)

A) (x + 1)(x + 2)

D) (x2 - 4x + 3)(x2 - 4x + 2)

C) (x + 7)(x + 6) 216) 15x6 + 8x3 - 16 A) (5x3 + 4)(3x3 - 4)

216)

B) 15(x3 - 4)(x3 + 4)

C) (3x3 + 1)(5x3 - 16)

D) (3x3 + 4)(5x3 - 4)

Simplify the expression. Assume that all variables are positive when they appear. 217) 5x2 - 2 45x2 - 3 45x2 A) -14x 5

215)

B) -5x 36

C) -14x 36

217) D) -5x 5

Tell whether the expression is a polynomial. If it is, give its degree. 218) 1 - 3x A) Polynomial; degree 3 B) Polynomial; degree -3 C) Polynomial; degree 1 D) Not a polynomial Simplify the expression. Assume that all variables are positive when they appear. 3 3 219) 20 2 - 4 128 3 3 3 3 A) 16 2 B) -4 2 C) 20 2 - 4 128 Use the formula C =

218)

219) D) 4

5 (F - 32) for converting degrees Fahrenheit into degrees Celsius to find the Celsius measure of the 9

Fahrenheit temperature. 220) F = -13° A) -30° C

B) -20° C

C) -15° C

Find the quotient and the remainder. 221) x4 + 81 divided by x - 3

A) x3 + 3x2 + 9x + 27; remainder 162 C) x3 - 3x2 + 9x - 27; remainder 162

B) x3 + 3x2 + 9x + 27; remainder 0 D) x3 + 3x2 + 9x + 27; remainder 81

Use a calculator to evaluate the expression. Round the answer to three decimal places. 222) -(-1.57)-2 A) -2.465

D) -25° C

B) 2.465

C) -0.406

D) 0.406

Add or subtract as indicated. Express the answer as a single polynomial in standard form. 223) (5x5 + 5x3) + (3x5 + 2x3 + 5) A) -5x5 + 7x3 + 5x

B) 8x5 + 7x3 + 5

C) 12x9

D) 5x + 7x5 - 3x3

Solve the problem. 224) Find the volume V of a sphere of radius 2.5 yd. Use 3.14 for . If necessary, round the result to the nearest tenth. A) V = 36.8 yd3 B) V = 65.4 yd3 C) V = 26.2 yd3 D) V = 523.3 yd3 Perform the indicated operations and simplify the result. Leave the answer in factored form. 225) 5 +4 x

220)

221)

222)

223)

224)

225)

25 - 16 x2

x 5x - 4

1 5 - 4x

Evaluate the expression using the given value of the variables. 226) (x + 4y)2 for x = 2, y = 2 A) 20

B) 35

1 5x - 4

C) 100

x 5 - 4x

D) 10

226)

Perform the indicated operations and simplify the result. Leave the answer in factored form. 3x + 5 5x - 8 + 227) x 9x A)

22x + 37 9x

Evaluate the expression. 228) 3 + 1 - 9 A) -7

32x + 37 9x

B) 13

32x + 37 9x2

C) -5

32x - 53 9x

D) 11

Perform the indicated operations and simplify the result. Leave the answer in factored form. x-1 5x + 2 + 229) x2 - 7x + 12 x2 - 5x + 4 A)

6x + 1

2x2 - 12x + 16

C) 6x + 1

6x2 - 15x - 5 (x - 4)(x - 3)(x - 1)

6x2 - 15x - 5 (x + 4)(x + 3)(x + 1)

Find the value of the expression using the given values. x = -1, y = 4 230) yx A) 4

1 B) 4

1 D) 4

C) -4

Factor the sum or difference of two cubes. 231) 8 - x3 A) (2 - x)(4 + 2x + x2 )

A) <

A) 16,384

229)

230)

D) (2 + x)(4 - 2x + x2 )

Insert <, >, or = to make the statement true. 1 0.11 232) 9

Simplify the expression. 233) 2565/4

228)

231)

B) (2 - x)(4 + x2 )

C) (2 + x)(4 - x2 )

227)

232) B) =

C) >

B) 1,024

C) 65,536

D) 262,144

233)

Simplify the expression. Express the answer so that only positive exponents occur. Assume that all variables are positive. (4x3/4 )3 234) 234) x-6/5 A) 4x69/20 Factor the difference of two squares. 235) 4x2 - 49 A) (2x + 7)(2x - 7)

B) 4x21/20

B) (2x - 7)2

C) 64x21/20

D) 64x69/20

C) (4x + 1)(x - 49)

D) (2x + 7)2

235)

Factor completely. If the polynomial cannot be factored, say it is prime. 236) (2x - 2)3 + 125 A) (2x + 3)(4x2 + 2x + 19) C) (2x + 3)(4x2 + 2x + 39)

Write the statement using symbols. 237) The quotient 18 divided by 9 is 2. A) 18 - 9 = 9

Factor the polynomial. 238) x2 - 3x - 54

A) (x + 6)(x - 9)

236)

B) (2x + 3)(4x2 - 18x + 39) D) (2x - 7)(4x2 + 2x + 19)

B) 18 · 9 = 162

C) 18 + 9 = 27

18 =2 D) 9

B) (x - 6)(x + 1)

C) (x - 6)(x - 9)

D) prime

237)

238)

Tell whether the expression is a monomial. If it is, name the variable(s) and coefficient, and give the degree of the monomial. 4 239) 239) x

A) Monomial; variable x; coefficient 4; degree 0 B) Monomial; variable x; coefficient 4; degree -1 C) Monomial; variable x; coefficient 4; degree 1 D) Not a monomial Simplify the expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, we assume that the base is not 0. 9x-3 -1 240) 240) 8y-3

8x3 9y3

8y3 9x3

9x31 8y31

Simplify the expression. Assume that all variables are positive when they appear. 241) 7 12 - 2 192 A) 30 3 B) 2 3 C) -2 3

9x3 8y3

241) D) -30 3

Solve the problem. 242) Find the volume V of a right circular cylinder with radius 10 cm and height 20 cm. Express the answer in terms of . A) V = 100 cm3 B) V = 200 cm3 C) V = 2,000 cm3 D) V = 500 cm3

242)

Multiply the polynomials using the special product formulas. Express the answer as a single polynomial in standard form. 243) (7x + y)(7x - y) 243) 2 2 2 2 A) 49x - 14xy - y B) 49x - y

C) 14x2 - y2

D) 49x2 + 14xy - y2

Tell whether the expression is a monomial. If it is, name the variable(s) and coefficient, and give the degree of the monomial. 244) 3x2 - 5 244)

A) Monomial; variable x; coefficient 3; degree 1 B) Monomial; variable x; coefficient 3; degree 2 C) Monomial; variable x; coefficient 5 ; degree 2 D) Not a monomial

Solve the problem. 245) Find the surface area S of a rectangular box with length 5 ft, width 3 ft, and height 2 ft. A) 62 ft2 B) 56 ft2 C) 31 ft2 D) 72 ft2 Factor completely. If the polynomial cannot be factored, say it is prime. 246) (x - 2)2 - 9 A) (x - 1)(x + 5)

B) (x - 5)2

246)

C) (x + 7)(x - 11)

D) (x + 1)(x - 5)

List all the elements of B that belong to the given set. 0 247) B = {3, 5, -6, 0, , 9, 0.12, -5 , 0.999...} 8

247)

Rational numbers 0 A) 3, -6, 0, , 9, 0.12, -5 , 0.999... 8

C) 3, -6, 0,

245)

0 , 0.12 8

B) 3, -6, 0,

0 , 0.12, 0.999... 8

D) 3, -6, 0,

0 , 8

9, 0.12, 0.999...

Perform the indicated operations and simplify the result. Leave the answer in factored form. 248) 4x2 - 49

248)

x2 - 16 2x - 7 x-4

2x - 7 x-4

(2x - 7)(4x2 - 49) (x2 - 4)(x -4)

x+4 2x + 7

2x + 7 x+4

Find the quotient and the remainder. 249) x4 + 8x2 + 9 divided by x2 + 1

249)

A) x2 + 7; remainder 2 C) x2 + 7x +

B) x2 + 7x + 1; remainder 2

1 ; remainder 0 2

D) x2 + 7; remainder 0

Simplify the expression. 25 3/2 250) 9 A)

27 125

250) B) -

125 27

D) -

27 125

Multiply the polynomials using the FOIL method. Express the answer as a single polynomial in standard form. 251) (3x + 10y)(-3x + 7y) 251) A) -9x2 - 9xy - 9y2 B) -9x2 + 21xy + 70y2 C) -9x2 - 9xy + 70y2

D) -9x2 - 30xy + 70y2

Multiply the polynomials. Express the answer as a single polynomial in standard form. 252) (x + 12)(x - 12) A) x2 - 24 B) x2 + 24x - 144 C) x2 - 144 D) x2 - 24x - 144 Perform the indicated operations and simplify the result. Leave the answer in factored form. x 10 253) 2 11 A)

x - 10 22

11x - 20 22

Use the Distributive Property to remove the parentheses. 254) 5x(x + 9) A) 45x2 B) 5x2 + 9

x - 10 13

C) 5x2 + 45x

253) 11x + 20 20

D) x2 + 45x

Factor the expression. Express your answer so that only positive exponents occur. 255) 10x1/7 - 13x-4/7 A) x1/3(10 - 13x5/13) C) x-4/7 (10x5/7 - 13x)

B) x = -8

C) x = 8

257)

B) 10x2 - 220x + 121 D) 100x2 - 220x + 121

Simplify the expression. Assume that all variables are positive when they appear. 3 3 258) 4 64x + 4 8x 3 3 3 A) 6 x B) 4 72x C) 24 x

256)

D) none

Multiply the polynomials. Express the answer as a single polynomial in standard form. 257) (10x - 11)2 A) 100x2 + 121 C) 10x2 + 121

254)

255)

B) x-4/7 (10x5/7 - 13) D) x1/7 (10x5/7 - 13x5/13)

Determine which value(s), if any, must be excluded from the domain of the variable in the expression. x 256) x-8 A) x = 0

252)

258) D) 24x

Perform the indicated operations and simplify the result. Leave the answer in factored form. 259) 3 5 + x x2

259)

9 25 2 x x

3x2 + 5 9 - 25x

1 3x - 5

1 3 - 5x

3x + 5 9 - 25x

Evaluate the expression. 4 2 1 + 260) · 5 5 10 A)

261)

8 25

260) B) 2

1 10

2 5

5+2 9+2

261)

A) 1

Factor the polynomial by grouping. 262) x2 + 4x + 7x + 28 A) (x - 4)(x + 7)

3 11

B) (x + 4)(x + 7)

7 11

C) (x - 4)(x - 7)

Find the quotient and the remainder. 263) x4 + 625 divided by x - 5

A) x3 + 5x2 + 25x + 125; remainder 625

D) prime

B) x3 - 5x2 + 25x - 125; remainder 1,250

C) x3 + 5x2 + 25x + 125; remainder 1,250

262)

263)

D) x3 + 5x2 + 25x + 125; remainder 0

Simplify the expression. 27 -4/3 264) 64 A) -

3 7

264)

2.849934139e+15 9.007199255e+15

9.007199255e+15 2.849934139e+15

2.849934139e+15 9.007199255e+15

D) not a real number

Find the quotient and the remainder. 265) 5x3 - 7x2 + 7x - 8 divided by 5x - 2 A) x2 + x -1; remainder -6

B) x2 - x + 1; remainder -6

C) x2 - x + 1; remainder 10

265)

D) x2 - x + 1; remainder 6

Use synthetic division to determine whether x - c is a factor of the given polynomial. 266) 4x3 - 17x2 + 23x - 10; x - 5 A) Yes

B) No

266)

Write the number as a decimal. 267) 4.464 × 10-5 A) 0.0004464

B) 0.000004464

C) -446,400

D) 0.00004464

Solve the problem. 268) Find the area of the shaded region. Express the answer in terms of .

267)

268)

5 5

25 - 25 square units 4

C) 5 - 5 square units

25 2

- 25 square units

D) 25 square units

What number should be added to complete the square of the expression? 269) x2 - x A) 4

B) 1

1 2

1 4

Insert <, >, or = to make the statement true. 270) 3.14 A) <

270) B) =

C) >

Multiply the polynomials. Express the answer as a single polynomial in standard form. 271) (13y + x)(13y - x) A) 169y2 - 26xy - x2 B) 26y2 - x2 C) 169y2 - x2

Simplify the expression. 272) 2 -5 · 2 2 A) 4

269)

271)

D) 169y2 + 26xy - x2

1 B) 16

1 C) 8

Multiply the polynomials. Express the answer as a single polynomial in standard form. 273) (x + 3)3 A) x3 + 3x2 + 3x + 27 C) x3 + 9x2 + 9x + 27

B) x3 + 9x2 + 27x + 27 D) x3 + 9x2 + 3x + 27

272) D) 8

273)

Use U = universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 5, 8}, B = {2, 3, 5, 7}, and C = {1, 4, 9} to find the set. 274) A C 274) A) {4, 6, 7, 9} B) {1, 2, 3, 5, 7, 9} C) {1} D) {1, 2, 3, 4, 5, 7, 8, 9} Simplify the expression. 275) -4 2 A) 16

B) -16

C) -8

Factor the sum or difference of two cubes. 276) 512x3 - 343 A) (8x + 7)(64x2 - 56x + 49) C) (8x - 7)(64x2 + 56x + 49)

275)

D) 8

276)

B) (512x - 7)(x2 + 56x + 49) D) (8x - 7)(64x2 + 49)

Simplify the expression. 277) 16-5/4

277)

1 A) 32

B) 32

1 32

278) -321/5 A) -2

D) not a real number

B) -8

C) 32

278)

D) 16

An expression that occurs in calculus is given. Write the expression as a single quotient in which only positive exponents and/or radicals appear. (49 - x2)1/2 + 3x2 (49 - x2 )-1/2 279) 279) 49 - x2

3x2 (49 - x2)3/2

49 - 4x2 (49 - x2)3/2

49 + 2x2 (49 - x2)3/2

3x2 49 - x2

Simplify the expression. Assume that all variables are positive when they appear. 3 280) 343x4y5 3 3 A) 7xy xy B) 2xy xy2 C) 7xy xy2

D) 7xy xy2

Write the number in scientific notation. 281) 754.294 A) 7.54294 × 10-1 B) 7.54294 × 10-2

C) 7.54294 × 101

D) 7.54294 × 102

Evaluate the expression using the given values. 282) |6x + 10y| x = -3, y = -2 A) 18 B) 42

C) 38

D) 2

280) 3

281)

282)

List all the elements of B that belong to the given set. 0 283) B = 11, 8, -16, 0, , 0.42 4

283)

Rational numbers 0 8, , 0.42 A) 4

B) {11, 0} D) 11, -16, 0,

C) { 8}

0 , 0.42 4

The lengths of the sides of a triangle are given. Determine if the triangle is a right triangle. If it is, identify the hypotenuse. 284) 28, 96, 100 284) A) right triangle; 96 B) right triangle; 100 C) right triangle; 28 D) not a right triangle

Solve the problem. 285) The formula v = 2.5r can be used to estimate the maximum safe velocity v, in miles per hour, at which a car can travel along a curved road with a radius of curvature r, in feet. To the nearest whole number, find the maximum safe speed for a curve in a road with a radius of curvature of 200 feet. A) 14 mph B) 35 mph C) 9 mph D) 22 mph 286) Find the area A of a rectangle with length 7.2 in and width 11.1 in. A) A = 28.8 in2 B) A = 159.84 in2 C) A = 79.92 in2 Express the statement as an equation involving the indicated variables. 287) The area A of a rectangle is the product of its length l and its width w. l A) A = 2(l + w) B) A = lw C) A = w Write the number in scientific notation. 288) 0.0000027813 A) 2.7813 × 10-6 B) 2.7813 × 10-7 Factor the perfect square. 289) 25x2 + 90x + 81 A) (5x - 9)2

C) 2.7813 × 10-5

B) (5x + 9)2

C) (5x - 10)2

D) A = 18.3 in2

C) (3x2 + 6x)(x - 4)

B) 3x(x - 2)(x + 4)

D) A = l + w

D) 2.7813 × 106

288)

289) D) (5x + 9)(5x - 9)

290) D) 3x(x + 2)(x - 4)

Solve the problem. 291) A rectangular patio has dimensions 10 feet by 15 feet. The patio is surrounded by a border with a uniform width of 3 feet. Find the area of the border. A) 114 ft2 B) 186 ft2 C) 84 ft2 D) 162 ft2

286)

287)

Factor completely. If the polynomial cannot be factored, say it is prime. 290) 3x3 + 6x2 - 24x A) (x - 2)(3x2 + 12)

285)

291)

Factor the polynomial by grouping. 292) 2x2 + 9x + 18x + 81 A) (2x + 9)(2x + 9)

B) (x + 9)(2x + 9)

C) (2x + 9)(9x + 2)

D) prime

Perform the indicated operations and simplify the result. Leave the answer in factored form. x2 - 7x 12 + 293) x-3 x-3 A) x + 3

B) x - 4

C) x - 3

Use synthetic division to find the quotient and the remainder. 294) x3 - x2 + 4 is divided by x + 2 A) x2 - 3x + 6; remainder 2

C) x2 - 3x + 6; remainder -8

Simplify the expression. 295) (-4)3 A) 64

293)

D) x + 4

B) 3x2 - 4x + 2; remainder 0

294)

D) x2 + x + 2; remainder -8

B) -64

C) -12

296) -64-4/3 1 A) 256 C) -

292)

D) 12

295)

296) B) 256

1 256

D) not a real number

Write the number in scientific notation. 297) 0.0000000968011 A) 9.68011 × 108 B) 9.68011 × 10-9

297) C) 9.68011 × 10-8

D) 9.68011 × 10-7

Add or subtract as indicated. Express the answer as a single polynomial in standard form. 298) (6x6 + 8x4 + 7) - (8x6 + 6x4 - 9)

298)

Find the quotient and the remainder. 299) -20x3 - 41x2 - 35x + 5 divided by 5x + 4

299)

A) 16x10

B) -2x6 + 16x4 - 2

C) -2x6 + 2x4 - 2

A) -4x2 - 5x - 3; remainder 20

D) -2x6 + 2x4 + 16

B) x2 - 3; remainder -5

C) -4x2 - 5x - 3; remainder 0

D) -4x2 - 5x - 3; remainder 17

Solve. If necessary, round to the nearest tenth. 300) The zoo has hired a landscape architect to design the triangular lobby of the children's petting zoo. In his scale drawing, the longest side of the lobby is 15 cm. The shortest side of the lobby is 6 cm. The longest side of the actual lobby will be 49 m. How long will the shortest side of the actual lobby be? A) 1.2 m B) 122.5 m C) 19.6 m D) 0.2 m Use the Distributive Property to remove the parentheses. 301) (x - 7)(x - 3) A) x2 - 10x + 21 B) x2 - 10x - 10

C) x2 - 11x + 21 37

D) x2 + 21x - 10

300)

301)

Factor the sum or difference of two cubes. 302) 729y3 - 1 A) (729y - 1)(y2 + 9y + 1) C) (9y + 1)(81y2 - 9y + 1)

302)

B) (9y - 1)(81y2 + 9y + 1) D) (9y - 1)(81y2 + 1)

Perform the indicated operations and simplify the result. Leave the answer in factored form. 303) 8 1x x-

64 x

A) x + 8

304)

303)

1 x+8

C) x - 8

1 x-8

304)

x2 + 9x + 18

x2 + 11x+ 24 x2 + 6x

x2 + 16x + 64

x+8 x

x (x + 8)(x + 3)

x+8 x(x + 8)

D) x + 8

List all the elements of B that belong to the given set. 7 9 305) B = {12, 8, -15, 0, , - , 8.8, 8 , 0.848484...} 9 7 Natural numbers 9 A) 12, 0, 7

305)

B) {12}

C) {12, 0}

Find the quotient and the remainder. 306) x2 + 12x + 27 divided by x + 4 A) x + 8; remainder 0 C) x + 8; remainder -5

D) {-15, 0, 12}

306)

B) x + 9; remainder 0 D) x + 8; remainder 5

Perform the indicated operations and simplify the result. Leave the answer in factored form. 10x2 - 3x - 4 15x2 + 12x · 307) 5x2 - x - 4 1 - 4x2 A)

3x (1 - 2x)(x - 1)

3x(5x + 4) (1 - 2x)(x - 1)

(5x + 4)(5x - 4) (1 - 2x)(x - 1)

3x(5x - 4) (1 - 2x)(x - 1)

Solve the problem. 308) At the beginning of the month, Christopher had a balance of $196 in his checking account. During the next month, he wrote a check for $19, deposited $90, and wrote another check for $180. What was his balance at the end of the month? A) -$87 B) $87 C) $93 D) -$93

307)

308)

Evaluate the expression. 5 309) 7 + 6 A)

309)

42 6

47 6

47 5

42 5

Solve the problem. 310) Find the area of the shaded region. Express the answer in terms of .

310)

1 1

square units

1 square units 2

C) 1 square units

1 4

1 2

square units

Find the value of the expression using the given values. x = -3, y = 1 311) x2 + y2 A) 4

311)

C) 3

D) -2

Perform the indicated operations and simplify the result. Leave the answer in factored form. 8 - x 2x + 4 312) x-2 2-x A) -

x+4 x-2

x + 12 x-2

D) -

Insert <, >, or = to make the statement true. -6 313) -5 A) <

312) x + 12 x-2

313) B) =

C) >

Find the quotient and the remainder. 314) x2 + 10x + 16 divided by x + 8 A) x3 - 8; remainder 0

B) x2 + 2; remainder 0

C) x - 8; remainder 0

D) x + 2; remainder 0

314)

Simplify the expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, we assume that the base is not 0. 4x-1 -3 315) 315) 5y-1

64x3 125y3

125y3 64x3

64y3 125x3

Express the statement as an equation involving the indicated variables. 316) The perimeter P of a rectangle is twice the sum of its length l and its width w. A) P = l + w B) P = 2(l + w) C) P = lw An expression that occurs in calculus is given. Factor completely. 317) (2x + 1)2 + 3(2x + 1) - 4 A) 2x - 6

B) 2x(2x + 5)

C) 2x - 1

125x3 64y3

D) P = 2lw

D) 2x(2x + 1)

Simplify the expression. Assume that all variables are positive when they appear. 3 318) x23 A) x

x20

x23

C) x7

1 x-8

x(x + 7) x-8

D) x9

x2 + 15x + 56

319)

x x-8

Insert <, >, or = to make the statement true. 7 320) 2.64 A) =

320) B) <

C) >

Simplify the expression. Assume that all variables are positive when they appear. 11 321) 3 y21 A)

11 y7

Simplify the expression. 322) 1,4441/2 A) 38

317)

318)

Perform the indicated operations and simplify the result. Leave the answer in factored form. x2 + 14x + 48 x2 + 7x · 319) x2 + 15x + 56 x2 - 2x - 48 A)

316)

11 y7

C) 3

B) 19

11 y21

C) 152

321)

11 18 y

D) 76

322)

Multiply the polynomials using the special product formulas. Express the answer as a single polynomial in standard form. 323) (x - 9y)2 323)

A) x2 - 9xy + 81y2 C) x2 - 18xy + 81y2

B) x2 - y2 D) x2 + 18xy + 81y2

The lengths of the sides of a triangle are given. Determine if the triangle is a right triangle. If it is, identify the hypotenuse. 324) 6, 8, 12 324) A) right triangle; 6 B) right triangle; 8 C) right triangle; 12 D) not a right triangle

Simplify the expression. Assume that all variables are positive when they appear. 325) y7 A)

B) y3 y

C) y6 y

Use synthetic division to find the quotient and the remainder. 326) x2 + 12x + 30 is divided by x + 4 A) x + 8; remainder -2 C) x + 8; remainder 2

325) D) y y5

326)

B) x + 8; remainder 0 D) x + 9; remainder 0

Reduce the rational expression to lowest terms. 2x2 - 3x - 2 327) 3x2 - 11x + 10 A)

2x+ 1 3x - 5

327)

x- 1 x+5

Use the Distributive Property to remove the parentheses. 328) 8(x + 7) A) 8x + 7 B) 56x

x+2 x-4

C) x + 56

Write the statement using symbols. 329) The product of 30 and 6 equals 180. 30 =5 A) B) 30 + 6 = 36 6

2x - 2 3x + 2

D) 8x + 56

329) C) 30 · 6 = 180

D) 30 - 6 = 24

Solve the problem. 330) Find the area A and circumference C of a circle of radius 11 yd. Express the answer in terms of . A) A = 22 yd2 ; C = 22 yd B) A = 44 yd2; C = 11 yd C) A = 121 yd2 ; C = 22 yd

330)

D) A = 484 yd2 ; C = 11 yd

Add or subtract as indicated. Express the answer as a single polynomial in standard form. 331) -1(x2 + 6x + 1) + (3x2 - x - 4) A) 2x2 - 7x - 3

328)

B) -4x2 - 7x - 5

C) 2x2 - 6x - 5

Solve the problem. 332) Find the area A of a triangle with height 2 cm and base 5 cm. A) A = 5 cm2 B) A = 10 cm C) A = 5 cm Factor completely. If the polynomial cannot be factored, say it is prime. 333) x9 + 1 A) (x3 + 1)(x6 - x3 + 1) C) (x - 1)(x + 1)(x6 - x3 + 1)

D) 2x2 - 7x - 5

D) A = 10 cm2

B) (x - 1)(x2 + x + 1)(x6 + x3 + 1) D) (x + 1)(x2 - x + 1)(x6 - x3 + 1)

331)

332)

333)

Simplify the expression. Assume that all variables are positive when they appear. 3 334) -729 A) 27

B) 81

C) ±9

Write the statement using symbols. 335) Three times the difference of x and 8 is -10. A) 3x - 8 = -10 B) 3(x - 8) = -10

A) (2 - x)2

D) -9

C) 3 - x - 8 = -10

Factor the difference of two squares. 336) 4 - x2

D) (2 - x)(2 + x)

Multiply the polynomials. Express the answer as a single polynomial in standard form. 337) (a - b)2 A) a 2 - 2ab - b2

B) a 2 - ab + b2

D) 3 + x - 8 = -10

C) a 2 + 2ab + b2

D) a 2 - 2ab + b2

List all the elements of B that belong to the given set. 0 338) B = 12, 6, -5, 0, 8 Real numbers

A) 12,

6, -5, 0,

0 8

B) 12, -5, 0,

0 8

D) 12, -5

Perform the indicated operations and simplify the result. Leave the answer in factored form. 339) 5 +5 x 5 -5 x x2

5 - x2

337)

338)

C) {12, -5, 0}

335)

336)

C) (2 + x)2

B) prime

334)

1+x 1-x

5(1 + x) 1-x

D) 5 - x2

339)

Solve the problem. 340) Find the perimeter. Approximate the result to the nearest tenth using 3.14 for .

340)

6 cm

3 cm A) 19.7 cm

B) 27.4 cm

C) 22.7 cm

D) 24.4 cm

An expression that occurs in calculus is given. Reduce the expression to lowest terms. (x2 + 2) · 3 - (3x + 4) · 3x 341) (x2 + 2)3 A)

-9x2 - 12x + 3 (x2 + 2)2

-6x2 - 12x + 6 (x2 + 2)3

6x2 + 12x - 6 (x2 + 2)3

-12x2 - 12x + 6 (x2 + 2)3

341)

Graph the numbers on the real number line. 342) x 4

342)

Use synthetic division to determine whether x - c is a factor of the given polynomial. 343) 3x3 - 20x2 - 9x + 126; x - 6 A) Yes

343)

B) No

Express the statement as an equation involving the indicated variables. 344) The volume V of a cube is the cube of the length x of a side. 3 A) V = 3x B) V = x C) V = x2 43

344) D) V = x3

Tell whether the expression is a monomial. If it is, name the variable(s) and coefficient, and give the degree of the monomial. 345) 10x4 345)

A) Monomial; variable x; coefficient 4; degree 10 B) Monomial; variable x; coefficient 10; degree 4 C) Monomial; variable x; coefficient 4; degree 0 D) Not a monomial

Simplify the expression. Assume that all variables are positive when they appear. -9 346) 28 A) -

9 7 7

B) -

9 7 14

C) -9 7

346) D) -28

Perform the indicated operations and simplify the result. Leave the answer in factored form. x2 + 14x + 45 x2 + 8x · 347) x2 + 17x + 72 x2 + 12x + 35 A)

1 x+7

x x+7

x 2 x + 17x + 72

Write the number in scientific notation. 348) In a certain city, the bus system carried a total of 11,800,000,000 passengers. A) 1.18 × 1011 B) 11.8 × 1010 C) 1.18 × 1010

x2 + 8x x+7

D) 1.18 × 109

Multiply the polynomials. Express the answer as a single polynomial in standard form. 349) (9x + 10)2 A) 9x2 + 180x + 100 C) 9x2 + 100

347)

348)

349)

B) 81x2 + 100 D) 81x2 + 180x + 100

Simplify the expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, we assume that the base is not 0. x-3y8 350) 350) x5 y11

y3 x8

1 x8 y3

C) x8 y3

x8 y3

Solve the problem. 351) Find the area A and circumference C of a circle of diameter 22 in.. Use 3.14 for . Round the result to the nearest tenth. A) A = 69.1 in.2 ; C = 69.1 in. B) A = 138.2 in.2 ; C = 34.5 in. C) A = 379.9 in.2 ; C = 69.1 in.

351)

D) A = 1,519.8 in.2 ; C = 34.5 in.

Factor the sum or difference of two cubes. 352) 8 - 125x3 A) (8 - 5x)(1 + 10x + 25x2 )

B) (2 - 5x)(4 + 25x2 )

C) (2 + 5x2 )(4 - 10x + 25x2 )

D) (2 - 5x)(4 + 10x + 25x2 ) 44

352)

Use the Distributive Property to remove the parentheses. 1 1 353) 4 x + 2 8 A) 2x +

1 4

B) 2x +

353)

1 8

1 1 x+ 2 2

D) 2x +

1 2

Factor completely. If the polynomial cannot be factored, say it is prime. 354) 15x2 - 9xy - 20xy + 12y2

354)

Simplify the expression. 355) 16-7/4

355)

A) (15x - 4y)(x - 3y) C) (3x + 4y)(5x - 3y)

A) -128

B) (3x - 4)(5x - 3) D) (3x - 4y)(5x - 3y)

1 128

C) -

1 128

D) -16,384

Evaluate the expression. 9-6 356) 6-9 A) 3

356) B) -

3 2

C) -1

3 2

What number should be added to complete the square of the expression? 4 357) x2 - x 5 A)

4 25

16 25

C) -

1 5

357) D) -

8 25

Perform the indicated operations and simplify the result. Leave the answer in factored form. x2 + 11x + 18 x2 + 14x + 48 · 358) x2 + 8x + 12 x2 + 17x + 72 A)

x+6 x+8

x+9 x+6

1 x+8

358)

D) 1

Use synthetic division to determine whether x - c is a factor of the given polynomial. 359) x3 + 12x2 + 29x - 42; x - 4 A) Yes

359)

B) No

Multiply the polynomials. Express the answer as a single polynomial in standard form. 360) (13x + 6)(13x - 6) A) 169x2 + 156x - 36 B) 169x2 - 36

360)

Simplify the expression. Assume that all variables are positive when they appear. 3 361) 2x2 - 375 + 242x2 3 3 A) 12x 2 - 5 15 B) 12x 2 - 5 3 C) 12 2x2 - 375

361)

C) 169x2 - 156x - 36

D) x2 - 36

D) 11x 2 - 5

362)

16 11

A) 125

362) B) 4 11

16 11 11

4 11 11

Simplify the expression. Express the answer so that only positive exponents occur. Assume that all variables are positive. 363) x3/8 · x5/8 363) A) x

B) x15/64

Write the number in scientific notation. 364) 308.57 A) 3.0857 × 10-2 B) 3.0857 × 102

1 x

C) x15/8

C) 3.0857 × 10-1

D) 3.0857 × 101

Approximate the number rounded to three decimal places, and truncated to three decimal places. 24 365) 7 A) 3.429 3.428

B) 3.43 3.429

C) 3.429 3.429

365)

D) 3.43 3.428

Tell whether the expression is a polynomial. If it is, give its degree. 366) -2y5 - 3 A) Polynomial; degree 3 C) Polynomial; degree 5

364)

366)

B) Polynomial; degree -2 D) Not a polynomial

Tell whether the expression is a monomial. If it is, name the variable(s) and coefficient, and give the degree of the monomial. 3x6 367) 367) y2

A) Monomial; variables x, y; coefficient 3; degree 2 B) Monomial; variables x, y; coefficient 3; degree 6 C) Monomial; variables x, y; coefficient 3; degree 4 D) Not a monomial Evaluate the expression using the given value of the variables. 368) 4x2 + 5y2 for x = -3, y = 3 A) -9

B) 51

C) 81

D) 33

Perform the indicated operations and simplify the result. Leave the answer in factored form. 369) x+6 x-6 + x-6 x+6 x+6 x-6 x-6 x+6

A) 1

x2 + 36 12x

(x + 6)2 12x

(x + 6)3 24x(x + 7)

368)

369)

370)

1 3 (x + 5)(x + 4) (x + 4)(x + 7)

370)

-2(x + 6) (x + 5)(x + 4)(x + 7)

2(2x + 11) (x + 5)(x + 4)(x + 7)

2(x + 4) (x + 5)(x + 4)(x + 7)

-2(x + 4) (x + 5)(x + 4)(x + 7)

Use the given real number line to compute the distance. 371) Find d(A, B)

A) 3 Factor the polynomial. 372) x2 - x - 35

A) (x - 35)(x + 1)

371)

B) 1

C) -2

B) (x - 5)(x + 7)

C) (x + 5)(x - 7)

D) 2

D) prime

The triangles are similar. Find the missing length x and the missing angles A, B, C. 373) 13° 27° 48 7 21 140°

A) x = 16; A = 140; B = 13; C = 27 C) x = 48; A = 13; B = 27; C = 140

373)

B) x = 16; A = 27; B = 13; C = 140 D) x = 48; A = 27; B = 13; C = 140

Factor completely. If the polynomial cannot be factored, say it is prime. 374) 3x2 - 75 A) 3(x + 5)(x - 5) 375) x3 + 12x2 + 36x A) x(x - 6)2

B) 3(x + 5)2

C) 3(x - 5)2

374) D) prime 375)

B) x(x + 6)2

C) x(x + 6)(x - 6)

D) prime

Perform the indicated operations and simplify the result. Leave the answer in factored form. 7x 5 + 376) x-8 8-x A)

2x x-8

Factor the perfect square. 377) x2 + 40x + 400 A) (x + 20)(x - 20)

372)

7x - 5 x-8

B) (x + 20)2

7x + 5 x-8

C) (x - 20)2 47

376)

7x - 5 8-x

D) x2 + 40x + 400

377)

Factor the polynomial. 378) 20z 2 - 3z - 9

A) (20z - 3)(z + 3)

B) (4z + 3)(5z - 3)

C) (4z - 3)(5z + 3)

Factor completely. If the polynomial cannot be factored, say it is prime. 379) 10x2 - 34x + 28 A) (5x - 7)(2x - 2)

B) 2(5x + 7)(x + 2)

C) 2(5x - 7)(x - 2)

Write the number in scientific notation. 380) A business projects next year's profits to be $741,000,000. A) 7.41 × 107 B) 7.41 × 109 C) 7.41 × 108

D) prime

11 11

D) 7.41 × 10-9

381) D) 11 11

Find the LCM of the given polynomials. 382) x2 - 5x - 36, x2 - 16, x2 - 13x + 36

382)

A) (x - 9)(x + 4) C) (x + 9)(x - 4)2

B) (x - 9)(x + 4)(x - 4) D) (x + 9)(x + 4)(x - 4)

Simplify the expression. Assume that all variables are positive when they appear. 3 383) - -8x12y24 A) -2x12y8

Factor the polynomial. 384) 15z 2 - 4z - 4

A) (3z - 2)(5z + 2)

B) 4x4 y8

C) 2x4 y12

D) 2x4 y8

B) (15z - 2)(z + 2)

C) (3z + 2)(5z - 2)

D) prime

Simplify the expression. Assume that all variables are positive when they appear. 56x5 y6 385) 2y4 A) 28xy x

379)

380)

Simplify the expression. Assume that all variables are positive when they appear. 1 381) 11 A) 11

378)

B) 2x2 y 7x

C) 4x2 y 7x

383)

384)

385) D) 2x4 y2 7xy

Multiply the polynomials using the special product formulas. Express the answer as a single polynomial in standard form. 386) (x - y)2 386)

A) x2 - 2x2 y2 + y2

B) x2 - xy + y2

C) x2 - y2

D) x2 - 2xy + y2

The lengths of the sides of a triangle are given. Determine if the triangle is a right triangle. If it is, identify the hypotenuse. 387) 15, 36, 39 387) A) right triangle; 36 B) right triangle; 39 C) right triangle; 15 D) not a right triangle

Factor the difference of two squares. 388) 36x2 - 1 A) (6x - 1)(6x + 1)

B) (6x - 1)2

C) prime

Find the LCM of the given polynomials. 389) x, x + 4 A) x2 (x + 4) B) x

D) (6x + 1)2

389) C) x(x + 4)

D) x + 4

Solve. Use the fact that the radius of the Earth is 3960 miles and 1 mile = 5280 feet. 390) A person who is 5 feet tall is standing on the beach and looks out onto the ocean. Suddenly, a ship appears on the horizon. How far is the ship from the shore? Round to the nearest tenth of a mile. A) 5,600.3 mi B) 3.9 mi C) 2.7 mi D) 199.1 mi Write the statement using symbols. 391) The difference 21 less 7 equals 14. 21 =3 A) 21 + 7 = 28 B) 7 Factor the polynomial. 392) 20z 2 + 7z - 6

A) (4z - 3)(5z + 2)

390)

391)

B) (20z + 3)(z - 2)

C) 21 - 7 = 14

D) 21 · 7 = 147

C) (4z + 3)(5z - 2)

D) prime

Add or subtract as indicated. Express the answer as a single polynomial in standard form. 393) (6x5 - 12x3 - 8) - (8x3 + 3x5 - 2) A) 3x5 - 20x3 - 10

388)

B) 3x5 - 9x3 - 10

Write the number in scientific notation. 394) 33,000,000 A) 3.3 × 10-7 B) 3.3 × 107

C) -23x8

D) 3x5 - 20x3 - 6

C) 3.3 × 10-8

D) 3.3 × 108

Solve. Use the fact that the radius of the Earth is 3960 miles and 1 mile = 5280 feet. 395) A guard tower at a state prison stands 117 feet tall. How far can a guard see from the top of the tower? Round to the nearest tenth of a mile. A) 969.7 mi B) 18.7 mi C) 13.2 mi D) 5,600.3 mi Evaluate the expression using the given values. 396) 4 x + 5 y x = 9, y = -6 A) -66 B) 6

C) 66

D) -6

392)

393)

394)

395)

396)

The lengths of the sides of a triangle are given. Determine if the triangle is a right triangle. If it is, identify the hypotenuse. 397) 7, 24, 25 397) A) right triangle; 25 B) right triangle; 7 C) right triangle; 24 D) not right triangle

Express the statement as an equation involving the indicated variables. 4 398) The volume V of a sphere is times times the cube of the radius r. 3 A) V =

4 3

B) V =

4 3 r 3

C) V =

4 2 r 3

398) D) V =

4 r 3

Factor completely. If the polynomial cannot be factored, say it is prime. 399) 12x3 + 7x2 - 12x

399)

B) (3x2 + 4)(4x - 3)

A) x(3x + 4)(4x - 3) C) x2 (3x + 4)(4x - 3)

D) x(4x + 4)(3x - 3)

Find the value of the expression using the given values. x = -6 400) x2 A) -2 3

400) C) 2 3

B) 6

What number should be added to complete the square of the expression? 401) x2 - 6x A) -3

B) 18

C) 5

D) -6

D) 9

401)

The lengths of the sides of a triangle are given. Determine if the triangle is a right triangle. If it is, identify the hypotenuse. 402) 2, 3, 4 402) A) right triangle; 3 B) right triangle; 4 C) right triangle; 2 D) not right triangle

Evaluate the expression using the given value of the variables. 403) -3x-1y2 for x = -2, y = -2 3 A) 8

Simplify the expression. 404) 165/4 A) 256

403)

B) 24

2 C) 3

D) 6

B) 512

C) 128

D) 32

404)

Simplify the expression. Express the answer so that only positive exponents occur. Assume that all variables are positive. 405) (27x6 y6 )1/3 405) A) 3x2 y2

B) x2 y2

C) 3x2 y

D) 3x6 y2

On the real number line, label the points with the given coordinates. 406) -11, -9, -7, -5

406)

Perform the indicated operations and simplify the result. Leave the answer in factored form. 407) 4 1x 1+

407)

4 x

x+4 x-4

B) x + 4

C) x - 4

Express the statement as an equation involving the indicated variables. 408) The surface area S of a cube is 6 times the square of the length x of a side. A) S = 6x2 B) S = x2 C) S = 6 + x2

x-4 x+4

408) D) S = 6x

List all the elements of B that belong to the given set. 0 409) B = {2, 5, -4, 0, , , 0.29, -5 , 0.161616...} 5

409)

Irrational numbers

0 -5 5,

A) { 5}

C) { 5 , -5 }

D) { 5, -5 , 0.161616...}

Find the quotient and the remainder. 410) 6x3 - 13x2 - 4x + 35 divided by -2x + 3 A) -3x2 + 2x + 5; remainder 20

B) -3x2 + 2x + 5; remainder 0

C) x2 + 5; remainder 2

410)

D) -3x2 + 2x + 5; remainder 23

Tell whether the expression is a polynomial. If it is, give its degree. -10x10 - 45x6 411) -5x2 A) Polynomial; degree 10 C) Polynomial; degree 6

B) Polynomial; degree 0 D) Not a polynomial

411)

Simplify the expression. 412) (-5)2 A) 5

1 B) 25

C) 625

D) not a real number

Write the number in scientific notation. 413) 820,000 A) 8.2 × 104 B) 8.2 × 10-4 Write the statement using symbols. 414) The sum of 18 and 6 is 24. A) 18 · 6 = 108

C) 8.2 × 105

412)

413) D) 8.2 × 10-5

414)

18 =3 B) 6

C) 18 + 6 = 24

Factor the polynomial. 415) 9x2 - 18xt + 8t2

A) (9x - 2t)(x - 4t) C) (3x + 2t)(3x + 4t)

D) 18 - 6 = 12

415)

B) (3x - 2t)(3x - 4t) D) prime

Factor completely. If the polynomial cannot be factored, say it is prime. 416) 12(x - 7)2 - 19(x - 7) - 21 A) (3x + 7)(4x + 3) C) (3x + 24)(4x + 35)

417) 6x4 - 5x2 - 6 A) (2x2 + 1)(3x2 - 6)

417) B) (3x - 2)(2x + 3) D) (6x2 - 3)(x2 + 2)

C) (2x2 - 3)(3x2 + 2)

Factor the polynomial. 418) x2 - x - 30

A) (x + 1)(x - 30)

416)

B) (3x + 14)(4x + 10) D) (3x - 28)(4x - 25)

B) (x + 5)(x - 6)

C) (x + 6)(x - 5)

D) prime

418)

Multiply the polynomials using the FOIL method. Express the answer as a single polynomial in standard form. 419) (x - 7)(x - 6) 419) A) x2 - 14x + 42 B) x2 + 42x - 13 C) x2 - 13x + 42 D) x2 - 13x - 13 Factor completely. If the polynomial cannot be factored, say it is prime. 420) 24x2 + 68x + 48 A) (2x + 1)(3x + 12) C) 4(12x + 3)(x + 4)

B) 4(2x + 3)(3x + 4) D) 4(2x + 1)(3x + 12)

420)

Perform the indicated operations and simplify the result. Leave the answer in factored form. 8x - 8 2x2 · 421) x 9x - 9 A)

72x2 + 144x + 72 2x3

9 16x

16x 9

16x3 - 16x2 9x2 - 9x

Simplify the expression. 422) (-64)4/3 A) -256 C) 256

422)

B) 4,096 D) not a real number

Find the LCM of the given polynomials. 423) x - 7, 7 - x A) (x - 7)(7 - x) B) x + 7

C) -1

421)

D) (x - 7) or (7 - x)

423)

Simplify the expression. Express the answer so that only positive exponents occur. Assume that all variables are positive. 424) (x5 y2 )3/4 424) A) x15/4 y3/2

B) x20/3 y8/3

C) x23/4 y11/4

Simplify the expression. Assume that all variables are positive when they appear. 3 3 425) 10 7 · 11 6 3 3 3 3 A) 110 13 B) 110 7 · 6 C) 21 42 Factor completely. If the polynomial cannot be factored, say it is prime. 426) 27x2 - 117x - 90 A) 9(3x - 2)(x + 5)

B) 9(3x + 2)(x - 5)

C) (27x + 18)(x - 5)

427) 12x3 + 8x2 y - 15xy2 - 10y3 A) (4x2 - 5y2)(3x + 2y)

D) x3/2 y15/4

425) 3 D) 110 42

D) prime

427)

B) (12x2 - 5y2 )(x + 2y)

C) (4x2 + 5y2)(3x - 2y)

D) (4x2 - 5y)(3x + 2y)

Simplify the expression. Assume that all variables are positive when they appear. -5 428) 3 9 A) -5

426)

B) -5

3 -5 3 3

428)

3 -5 9 3

Simplify the expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, we assume that the base is not 0. 429) (x-2 y)6 429)

y6 x12

1 12 x y6

C) x12y6

y6 x2

Perform the indicated operations and simplify the result. Leave the answer in factored form. 430) 3 1 x2 - 3x - 18 x - 6

430)

1 +1 x+3

x 2 x - 4x - 24

B) -1

C) -

Solve the problem. 431) The focal length f of a lens with index of refraction n is

x 2 x - 3x - 18

D) -

x 2 x - 2x - 24

1 1 + 1 = (n - 1) R1 R2 where R1 and R2 are f

431)

the radii of curvature of the front and back surfaces of the lens. Express f as a rational expression. R1 R 2 R1 R 2 A) f = B) f = (n - 1)(R1 + R2 ) (n + 1)(R1 - R2 )

C) f =

(n - 1)(R1 + R2 )

D) f =

R1 R 2

n(R1 - R2 ) R1 R2

Multiply the polynomials using the special product formulas. Express the answer as a single polynomial in standard form. 432) (12x - y)2 432)

A) 144x2 + y2 C) 144x2 - 24xy - 2y2

B) 144x2 - 24xy + y2 D) 144x2 - 12xy + y2

Perform the indicated operations. Express the answer as a single polynomial in standard form. 433) (x - 11)(x2 + 2x - 7) A) x3 + 13x2 + 29x + 77

B) x3 - 9x2 - 15x - 77

C) x3 - 9x2 - 29x + 77

Simplify the expression. 434) 5 4 A) 625

433)

D) x3 + 13x2 + 15x - 77

B) 20

C) -20

D) -625

434)

Use U = universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 5, 8}, B = {2, 3, 5, 7}, and C = {1, 4, 9} to find the set. 435) B C A) {1, 2, 3, 4, 5, 7, 9} C) {0, 6, 8}

435)

B) {6, 8} D) { }

Solve the problem. 436) Find the area A of a rectangle with length 20 yd and width 24 yd. A) A = 44 yd2 B) A = 480 yd2 C) A = 80 yd2

D) A = 960 yd2

436)

Perform the indicated operations. Express the answer as a single polynomial in standard form. 437) (5y + 11)(8y2 - 2y - 10)

437)

Multiply the polynomials. Express the answer as a single polynomial in standard form. 438) (5x + 4)3

438)

A) 40y3 + 78y2 - 72y - 110 C) 40y3 + 98y2 + 72y + 110

B) 40y3 - 10y2 - 50y + 11 D) 128y2 - 32y - 160

A) 25x6 + 20x3 + 4,096

B) 125x3 + 299x2 + 240x + 64

C) 125x3 + 299x2 + 299x + 64

D) 25x2 + 40x + 16

Tell whether the expression is a polynomial. If it is, give its degree. 439) 2 A) polynomial, degree 2 B) polynomial, degree 1 C) polynomial, degree 0 D) not a polynomial

439)

Evaluate the expression using the given values. 15x - 5y x = 9, y = 7 440) 5 A) 20

440)

B) 34

C) 26

D) 12

Perform the indicated operations and simplify the result. Leave the answer in factored form. 441) 7 14 + x+5 x+7

441)

3x + 17

x2 + 12x + 35

A) 21

442)

1 7

C) 7

D) 3x + 17

x3 + 1 7x · 3 2 -42x - 42 x -x +x

A) -

x3 + 1 6(x + 1)

442) B) -

1 6

C) -

x2 + 1 6

x+1 6(-x - 1)

Solve the problem. 443) Find the volume V of a sphere of diameter 10 m. Use 3.14 for . If necessary, round the result to the nearest tenth. A) V = 523.3 m 3 B) V = 104.7 m 3 C) V = 4,186.7 m 3 D) V = 294.4 m 3 Multiply the polynomials. Express the answer as a single polynomial in standard form. 444) (x - 5)2 A) x2 - 10x + 25

B) x2 + 25

C) x + 25

D) 25x2 - 10x + 25

443)

444)

Express the statement as an equation involving the indicated variables. 445) The circumference C of a circle is the product of and its diameter d. A) C = d

Write the number as a decimal. 446) 5.0458 × 10-7 A) 0.00000050458

B) C = 2 d

C) C =

B) 0.000000050458

C) -504,580,000

445) D) C =

D) 0.0000050458

Perform the indicated operations and simplify the result. Leave the answer in factored form. 447) 2x - 2 x

446)

447)

7x - 7 9x2

18x2 (x - 1) 7x(x - 1)

7 18x

14(x + 1)2 9x3

What number should be added to complete the square of the expression? 448) x2 + 16x A) 64

B) 128

C) 8

18x 7

D) 32

Factor completely. If the polynomial cannot be factored, say it is prime. 449) x4 - 256

449)

B) (x2 - 16)2

A) (x2 + 16)(x + 4)(x - 4) C) (x2 + 16)2

448)

D) prime

450) x3 - 4x + 5x2 - 20 A) (x2 - 4)(x + 5)

450) B) (x + 2)(x - 2)(x + 5)

C) (x - 2)2 (x + 5)

D) prime

Evaluate the expression using the given values. 451) x + 8y x = -2, y = -3 A) 6 B) -5

C) -19

Simplify the expression. Assume that all variables are positive when they appear. 452) -10 48 + 7 27 - 10 147 A) -89 3 B) -10 3 C) 17 3

D) -26

452) D) -17 3

Approximate the number rounded to three decimal places, and truncated to three decimal places. 453) 0.28571429 A) 0.287 B) 0.286 C) 0.286 D) 0.285 0.285 0.285 0.286 0.286

451)

453)

Simplify the expression. 454) 8 4/3 A) 64

B) 16

C) 128

Express the statement as an equation involving the indicated variables. 455) The surface area S of a sphere is 4 times times the square of the radius r. r A) S = 4 r2 B) S = 4 C) S = r2

454)

D) 32

455) D) S = 4 r

Simplify the expression. Assume that all variables are positive when they appear. 2 456) 5+9 A)

3 10 + 5 2 45

10 - 9 2 -76

10 + 9 2 -76

456) 10 - 9 2 14

The lengths of the sides of a triangle are given. Determine if the triangle is a right triangle. If it is, identify the hypotenuse. 457) 10, 20, 25 457) A) right triangle; 10 B) right triangle; 20 C) right triangle; 25 D) not a right triangle

Factor the sum or difference of two cubes. 458) 343x3 + 729 A) (343x - 9)(x2 + 63x + 81) C) (7x + 9)(49x2 - 63x + 81)

458)

B) (7x - 9)(49x2 + 63x + 81) D) (7x + 9)(49x2 + 63x + 81)

Factor completely. If the polynomial cannot be factored, say it is prime. 459) 2y3 + 6y2 - 14y2 - 42y A) 2y(y - 3)(y + 7) C) (y + 3)(2y2 - 14y)

459)

B) (y + 3)(y - 7) D) 2y(y + 3)(y - 7)

Simplify the expression. Assume that all variables are positive when they appear. 125x2y 460) 49 A)

5 5x2 y 7

Simplify the expression. 461) 5 -2 A) 25

5x 5y 7

C) 25x 5y

1 B) 25

1 C) 10

460) D) x

125y 7

461) D) -25

Simplify the expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, we assume that the base is not 0. 462) (x9 y-1 )8 462)

x72 y8

y8 x72

C) x72y8

1 72 x y8

Factor the expression. Express your answer so that only positive exponents occur. 463) x7/8 + 3x6/8 A) x1/8 (x1/8 + 3)

B) x3/4 (x1/8 + 3)

C) x3/4 (x-1/8 + 3)

D) x1/8 (x7/8 + 3)

Tell whether the expression is a polynomial. If it is, give its degree. 464) 9 A) Polynomial, degree 9 B) Polynomial, degree 0 C) Polynomial, degree 1 D) Not a polynomial

464)

Multiply the polynomials. Express the answer as a single polynomial in standard form. 465) (7x + 8y)2 A) 49x2 + 64y2

465)

B) 7x2 + 112xy + 64y2

C) 49x2 + 112xy + 64y2

D) 7x2 + 64y2

Use synthetic division to find the quotient and the remainder. 466) x5 - 2x4 - 12x3 - 13x2 - 12x + 11 is divided by x - 5 A) x4 + 3x3 + 3x2 + 2x + 2; remainder 3 C) x3 + 3x2 + 3x + 2; remainder 1

B) x4 + 3x3 + 3x2 + 2x - 2; remainder 1 D) x4 + 3x3 + 3x2 + 2x + 1; remainder 0

Simplify the expression. Assume that all variables are positive when they appear. 4 467) x+h- x A)

4 x+h+ h

4( x + h + h

463)

4( x + h h

4 h h

466)

467)

Simplify the expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, we assume that the base is not 0. -4x4 y-4 -1 468) 468) 5z 7

5z 7 -4x4 y4

5y4z 7 -4x4

5y4 -4x4 z 7

-4x4 5y4z 7

Simplify the expression. Assume that all variables are positive when they appear. 3 469) 6- 7 A)

18 + 3 7 29

18 + 3 7 1

3 3 6 7

469) D)

18 - 3 7 29

Solve the problem. 470) Find the volume V of a rectangular box with length 4 in., width 6 in., and height 7 in.. A) V = 168 in.3 B) V = 294 in.3 C) V = 112 in.3 D) V = 144 in.3

470)

Write the statement using symbols. 471) The quotient of x and the sum of 5 and x. x+5 A) B) x + 5 + x x

x C) 5+x

471) D) x(5 + x)

Simplify the expression. Assume that all variables are positive when they appear. 2 472) 2 7- 2 A)

7+1 13

14 + 1 13

14 - 1 13

Factor the sum or difference of two cubes. 473) x3 + 512 A) (x + 8)(x2 + 64)

472) 14 + 1 15

473)

B) (x + 8)(x2 - 8x + 64)

C) (x - 512)(x2 - 1)

D) (x - 8)(x2 + 8x + 64)

Solve. 474) When an object is dropped to the ground from a height of h meters, the time it takes for the object h to reach the ground is given by the equation t = , where t is measured in seconds. If an object 4.9

474)

falls 176.4 meters before it hits the ground, find the time it took for the object to fall. A) 9 seconds B) 6 seconds C) 36 seconds D) 7 seconds

Evaluate the expression using the given value of the variables. 475) 7x3 + 4x2 - 2x - 3 for x = 1 A) -2

Factor the perfect square. 476) x4 - 14x2 + 49 A) (x - 7)2

B) 12

C) 6

D) 10

B) (x2 - 7)2

C) (x2 + 7)2

D) (x - 7)(x + 7)

476)

Perform the indicated operations and simplify the result. Leave the answer in factored form. 1 8 477) - 2 5x A)

5x - 16 10x

-5x + 16 10x

Find the quotient and the remainder. 478) x2 + 3x - 49 divided by x + 9 A) x - 5; remainder 6 C) x - 6; remainder 5

-13 10 - 5x

35x - 13 x(7 - x)

478)

B) x - 6; remainder 0 D) x + 6; remainder 5

35x - 13 x(x - 7)

13x - 35 x(x - 7)

477)

-5x - 16 10x

Perform the indicated operations and simplify the result. Leave the answer in factored form. 5 8 479) + x x-7 A)

475)

13x - 35 x(7 - x)

479)

Simplify the expression. 64 -1/2 480) 25

480)

32 25

8 5

5 8

D) not a real number

Perform the indicated operations and simplify the result. Leave the answer in factored form. 8 6 481) x2 x A)

2(4x + 3) x2

2(3x - 4) x

2(4 - 3x) x2

2(4 + 3x) x2

Simplify the expression. Assume that all variables are positive when they appear. 3 482) 10 A)

9 10 10

3 10 10

C) 103

481)

482) D) 3 10

An expression that occurs in calculus is given. Write the expression as a single quotient in which only positive exponents and/or radicals appear. 3 1 483) (x2 - 1)1/2 · (2x + 5)1/2 · 2 + (2x + 5)3/2 · (x2 - 1)-1/2 · 2x 483) 2 2

A) (x2 - 1)1/2 (2x + 5)1/2(5x2 + 5x - 3) C)

(2x + 5)1/2(5x2 + 5x - 3) (x2 - 1)-1/2

(2x + 5)1/2(5x2 + 5x - 3) (x2 - 1)1/2

D) (x2 - 1)1/2 (2x + 5)-1/2(5x2 + 5x - 3)

The lengths of the sides of a triangle are given. Determine if the triangle is a right triangle. If it is, identify the hypotenuse. 484) 15, 20, 25 484) A) right triangle; 20 B) right triangle; 25 C) right triangle; 15 D) not a right triangle

Simplify the expression. 485) 729-1/3 1 A) 9

1 C) 27

B) -9

485) D) 9

Reduce the rational expression to lowest terms. x2 - 36 486) x-6 A)

1 x-6

486)

1 x+6

C) x - 6

D) x + 6

Factor the sum or difference of two cubes. 487) x3 - 125 A) (x + 5)(x2 - 5x + 25) C) (x + 125)(x2 - 1)

487)

B) (x - 5)(x2 + 25) D) (x - 5)(x2 + 5x + 25)

Use synthetic division to find the quotient and the remainder. 1 488) 6x5 - 5x4 + x - 4 is divided by x + 2 B) 6x4 - 2x3 - x2 +

A) 6x4 - 8x3 + 4x2 - 2x + 2; remainder -5 C) 6x4 - 2x3 + x2 -

488)

1 5 37 x + ; remainder 2 4 8

1 5 27 x + ; remainder 2 4 8 13 2

D) 6x4 - 8x3 + 5; remainder -

489) x5 + x3 + 2 is divided by x + 3 A) x4 - 2x2 ; remainder 8

489)

B) x4 - 3x3 + 10x2 - 30x + 90; remainder -268 C) x4 - 3x3 + 9x2 - 26x + 78; remainder -232

D) x4 - 2; remainder 8

Perform the indicated operations and simplify the result. Leave the answer in factored form. 4x 5 8 + 490) x + 1 x - 1 x2 - 1 A)

x+1 x-1

Write the number as a decimal. 491) 3.66 × 10-4 A) 0.00366

Simplify the expression. 492) 4,0961/4 A) 32

4x - 3 x-1

4x - 3 x+1

4x x-1

B) 0.0000366

C) -366,000

D) 0.000366

B) 8

C) 32,768

D) 256

Perform the indicated operations and simplify the result. Leave the answer in factored form. 2 8 493) + x x-6 A)

10x - 12 x(x - 6)

Factor the perfect square. 494) 25x2 - 20x + 4 A) (5x + 2)(5x - 2) Write the number as a decimal. 495) 2.9135 × 107 A) 2,913,500

12x - 10 x(6 - x)

10x - 12 x(6 - x)

491)

492)

493)

12x - 10 x(x - 6)

B) (5x - 2)2

C) (5x - 3)2

D) (5x + 2)2

B) 203.945

C) 29,135,000

D) 291,350,000

490)

494)

495)

Use the Distributive Property to remove the parentheses. 496) (x + 4)(x + 7) A) x2 + 11x + 28 B) x2 + 10x + 28

C) x2 + 11x + 11

D) x2 + 28x + 11

Write the statement as an inequality. 497) y is positive A) y 0 B) y 0

C) y < 0

D) y > 0

Evaluate the expression using the given values. 498) x + y x = -8, y = 2 A) 6 B) -10

C) -6

D) 10

Graph the numbers on the real number line. 499) x 1

496)

497)

498)

499)

Simplify the expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, we assume that the base is not 0. 500) (x-9 y2 )-4 z 3 500)

x36z 3 y8

x36 y8 z3

y8 x36z 3

y8 z3 x36

Tell whether the expression is a polynomial. If it is, give its degree. 25 +1 501) x A) Polynomial, degree 25 C) Polynomial, degree 0

501)

B) Polynomial, degree -1 D) Not a Polynomial

An expression that occurs in calculus is given. Write the expression as a single quotient in which only positive exponents and/or radicals appear. 502) 10x3/2(x3 + x2 ) - 12x5/2 - 12x3/2 502)

A) x3/2(x - 1)[10(x2 - 1) - 2] + 10x3 C) 10x3/2(x + 1)(5x2 - 6)

B) 10x3/2(x3 - 1) + 10x3 - 2x3/2(x - 1) D) 2x3/2(x + 1)(5x2 - 6)

Evaluate the expression using the given values. |x| |y| x = 6 and y = -3 + 503) x y A) -1

503)

B) 2

C) 0

Simplify the expression. 504) 64-4/3

1 256

D) not a real number

505) 25-1/2

1 A) 5

504)

1 B) 256

A) 256 C) -

D) 1

1 C) 5

B) 5

505) D) -5

Solve the problem. 506) A formula used to determine the velocity v in feet per second of an object (neglecting air resistance) after it has fallen a certain height is v = 2gh, where g is the acceleration due to gravity and h is the height the object has fallen. If the acceleration g due to gravity on Earth is approximately 32 feet per second, find the velocity of a bowling ball after it has fallen 20 feet. (Round to the nearest tenth.) A) 1,280 ft per sec B) 35.8 ft per sec C) 25.3 ft per sec D) 6.3 ft per sec Evaluate the expression. 30 2 · 507) 14 5 A)

7 5

507) B)

6 7

15 7

Write the number as a decimal. 508) There are 2.711 × 102 miles of highways, roads, and streets in a certain city. A) 271.1

506)

B) 27.11

C) 27,110

7 6

D) 2,711

Multiply the polynomials. Express the answer as a single polynomial in standard form. 509) (x + 12y)(x - 12y) A) x2 - 24y2 B) x2 + 24xy - 144y2 C) x2 - 24xy - 144y2

508)

509)

D) x2 - 144y2

Simplify the expression. Express the answer so that only positive exponents occur. Assume that all variables are positive. 510) (x14y7 )1/7 510) A) x2 |y|

B) x2 y

C) x2

D) x14y

Simplify the expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, we assume that the base is not 0. 511) (6xy)3 511)

216x3 y3

B) 216x3 y3

C) 6x3 y3

D) 216xy

Perform the indicated operations and simplify the result. Leave the answer in factored form. 17 6 + 512) x-5 x-5 A)

23 x-5

11 x

11 x-5

512)

17(x - 5) 6(x - 5)

Factor the expression. Express your answer so that only positive exponents occur. 513) (x + 8)-3/5 + (x + 8)-1/5 + (x + 8) 1/5

513)

Multiply the polynomials. Express the answer as a single polynomial in standard form. 514) (x + 10)2

514)

A) (x + 8)-3/5 [1 + (x + 8)1/5 + (x + 8)3/5 ] C) (x + 8)-3/5 [1 + (x + 8) 2/5 + (x + 8)4/5 ]

B) (x + 8)-3/5 [1 + (x + 8)4/5 + (x + 8)6/5 ] D) (x + 8)-3/5 [1 + (x + 8) -2/5 + (x + 8) -4/5 ]

A) x2 + 20x + 100 C) x2 + 100

B) 100x2 + 20x + 100

D) x + 100

Multiply the polynomials using the FOIL method. Express the answer as a single polynomial in standard form. 515) (x + 8y)(x - 3y) 515) A) x2 + 5xy - 24y2 B) x + 5xy - 24y C) x2 + 2xy - 24y2 D) x2 + 5xy + 5y2 Use synthetic division to determine whether x - c is a factor of the given polynomial. 516) 3x3 - 22x2 - 3x + 70; x - 7 A) Yes

516)

B) No

Tell whether the expression is a monomial. If it is, name the variable(s) and coefficient, and give the degree of the monomial. 517) -15x 517) A) Monomial,; variable x; coefficient -15; degree 0 B) Monomial, variable x; coefficient 1; degree -15 C) Monomial; variable x; coefficient -15; degree 1 D) Not a monomial

Perform the indicated operations and simplify the result. Leave the answer in factored form. 6 4 518) 7x 7x A)

519)

1 7x

2 7x

7 2x

x 4 2 2 x - 16 x + 5x + 4

518)

D) 1

519)

x2 - 3 (x - 4)(x + 4)(x +1)

x2 - 3x + 16 (x - 4)(x + 4)(x + 1)

x2 + 3x + 16 (x - 4)(x + 4)(x + 1)

x2 - 3x + 16 (x - 4)(x + 4)

Evaluate the expression. 1 1 +8 520) · 10 4 5 A)

57 20

520) B)

89 5

209 20

103 10

Perform the indicated operations and simplify the result. Leave the answer in factored form. 9x4 - 72x x2 + x - 2 · 521) 2 3 3x - 12 4x + 8x2 +16x A)

3(x - 1) 4

3x(x - 1)(x - 2)2 4(x + 2)2

3x(x + 1) 4

3x(x - 1) 4

Factor completely. If the polynomial cannot be factored, say it is prime. 522) (x + 8)2 - 49 A) (x - 1)(x - 15) Simplify the expression. 523) 36-3/2 A) -216

B) (x + 57)(x - 41)

C) x2 + 16x + 15

1 B) 216

1 C) 216

522) D) (x + 15)(x + 1)

523) D) 216

Find the quotient and the remainder. 524) x2 - 121a 2 divided by x - 11a A) x2 - 22xa

524)

B) x2 + 22xa

C) x - 11a

D) x + 11a

Simplify the expression. Assume that all variables are positive when they appear. 3 525) -64x24y36 A) 16x8 y12

526)

x7x +

A) C)

B) -4x8 y12

C) -4x12y18

D) 4x8 y12

y 3y

525)

526)

x 7-

3xy - 7xy + y 3 7x - 3y

x 7-

3xy - 7xy + y 3 7x + 3y

7x -

10xy + 7x + 3y

7x -

10xy + 7x - 3y

Perform the indicated operations and simplify the result. Leave the answer in factored form. x+4 x+4 527) x+2 x-6 A)

521)

8(x + 4) (x + 2)(x - 6)

-8(x + 4) (x + 2)(x - 6)

C) 0

-4(x + 4) (x + 2)(x - 6)

527)

Reduce the rational expression to lowest terms. y3 - 64 528) y- 4 A) y2 + 4y + 16

528)

B) y2 - 16

1 y-4

y3 - 64 y- 4

Simplify the expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, we assume that the base is not 0. 529) (12x3 )-2 529)

144x6

B) 144x6

144 x6

x6 144

Perform the indicated operations and simplify the result. Leave the answer in factored form. 530) x +1 x-4 12

x2 - 16

530)

x+4 x+2

2x + 8 x-2

2x - 8 x-2

2x + 8 x+2

Determine which value(s), if any, must be excluded from the domain of the variable in the expression. x-8 531) x-3 A) x = 3

B) x = 0

C) x = -3

D) none

Add or subtract as indicated. Express the answer as a single polynomial in standard form. 532) (8x2 + 5) - (-x3 - 10x2 + 4) A) 9x3 - 5x2 - 4

B) x3 - 2x2 + 9

Evaluate the expression using the given values. 533) -6xy + 6y - 4 x = -2, y = -1 A) -14 B) -22 Find the quotient and the remainder. 534) 20x3 - 29x2 + 15x + 12 divided by 5x - 1 A) 4x2 - 5x + 2; remainder 17 C) x2 + 2; remainder -5

Simplify the expression. 535) (-5)-4 A) 625

C) 9x3 - 10x2 + 1

D) x3 + 18x2 + 1

C) -18

D) 2

B) 4x2 - 5x + 2; remainder 14 D) 4x2 - 5x + 2; remainder 0

1 B) 625

C) -625

531)

1 D) 625

532)

533)

534)

535)

Use a calculator to evaluate the expression. Round the answer to three decimal places. 536) (-1.57)-5 A) -9.539

B) -0.105

C) 9.539

536)

D) 0.105

Add or subtract as indicated. Express the answer as a single polynomial in standard form. 537) (9x6 + 6x5 - 2x) + (6x6 + 7x5 - 8x) A) 4x6 + 16x5 - 2x

537)

B) 15x + 13x6 - 10x5

C) 15x6 + 13x5 - 10x

D) 18x12

Simplify the expression. Assume that all variables are positive when they appear. 3 3 538) 4 81x - 3 192x 3 3 3 A) 24 x B) 12 x - 3 192x C) 0

538)

D) cannot simplify

Evaluate the expression using the given values. 539) 6x - 7y x = 9, y = 9 A) -9 B) -117

C) 117

539)

D) 9

Multiply the polynomials using the special product formulas. Express the answer as a single polynomial in standard form. 540) (2x + 9y)2 540)

A) 2x2 + 36xy + 81y2 C) 2x2 + 81y2

B) 4x2 + 81y2 D) 4x2 + 36xy + 81y2

Perform the indicated operations and simplify the result. Leave the answer in factored form. 541) 1 1 + x+8 x-8

541)

x2 - 64

A) x2

B) 16

C) -16

D) 2x

Simplify the expression. Assume that all variables are positive when they appear. 542) 27x7 y8 A) 3y4

3x7

B) 3x3 y4

C) 3x3 y4

Factor completely. If the polynomial cannot be factored, say it is prime. 543) 2x2 - 2x - 12 A) 2(x + 2)(x - 3)

B) 2(x - 2)(x + 3)

C) (2x + 4)(x - 3)

542) D) 3x7 y8

D) prime

543)

Answer Key Testname: CHAPTER 0 1) B 2) A 3) C 4) B 5) C 6) B 7) B 8) D 9) C 10) A 11) B 12) D 13) B 14) B 15) C 16) D 17) B 18) D 19) D 20) A 21) A 22) D 23) D 24) C 25) D 26) B 27) B 28) D 29) B 30) C 31) B 32) A 33) C 34) D 35) B 36) A 37) B 38) C 39) A 40) D 41) A 42) C 43) C 44) B 45) A 46) A 47) A 48) D 49) B 50) B 68

Answer Key Testname: CHAPTER 0 51) D 52) A 53) B 54) D 55) C 56) A 57) B 58) B 59) A 60) B 61) D 62) D 63) A 64) A 65) B 66) A 67) B 68) B 69) B 70) D 71) B 72) D 73) C 74) D 75) C 76) C 77) C 78) D 79) C 80) B 81) C 82) D 83) B 84) D 85) A 86) A 87) C 88) B 89) A 90) A 91) C 92) D 93) B 94) A 95) B 96) B 97) C 98) D 99) C 100) B 69

Answer Key Testname: CHAPTER 0 101) B 102) A 103) A 104) A 105) C 106) A 107) B 108) B 109) D 110) B 111) D 112) D 113) B 114) A 115) C 116) D 117) C 118) B 119) B 120) B 121) D 122) D 123) B 124) D 125) C 126) D 127) B 128) B 129) A 130) C 131) C 132) C 133) D 134) A 135) D 136) A 137) D 138) D 139) A 140) D 141) D 142) D 143) A 144) D 145) C 146) B 147) A 148) A 149) B 150) C 70

Answer Key Testname: CHAPTER 0 151) A 152) A 153) C 154) C 155) C 156) A 157) A 158) D 159) C 160) D 161) C 162) C 163) B 164) D 165) D 166) C 167) A 168) C 169) D 170) D 171) D 172) D 173) B 174) B 175) C 176) B 177) D 178) C 179) B 180) B 181) C 182) C 183) B 184) C 185) C 186) A 187) B 188) A 189) C 190) A 191) D 192) C 193) B 194) D 195) B 196) C 197) C 198) B 199) C 200) B 71

Answer Key Testname: CHAPTER 0 201) A 202) B 203) B 204) B 205) A 206) C 207) A 208) C 209) D 210) B 211) B 212) C 213) B 214) B 215) A 216) D 217) A 218) C 219) D 220) D 221) A 222) C 223) B 224) B 225) D 226) C 227) B 228) C 229) B 230) D 231) A 232) C 233) B 234) D 235) A 236) B 237) D 238) A 239) D 240) A 241) C 242) C 243) B 244) D 245) A 246) D 247) D 248) D 249) A 250) C 72

Answer Key Testname: CHAPTER 0 251) C 252) C 253) B 254) C 255) B 256) C 257) D 258) C 259) D 260) D 261) C 262) B 263) C 264) C 265) B 266) B 267) D 268) B 269) D 270) A 271) C 272) C 273) B 274) C 275) B 276) C 277) C 278) A 279) C 280) D 281) D 282) C 283) D 284) B 285) D 286) C 287) B 288) A 289) B 290) B 291) B 292) B 293) B 294) C 295) B 296) C 297) C 298) D 299) D 300) C 73

Answer Key Testname: CHAPTER 0 301) A 302) B 303) B 304) A 305) B 306) C 307) D 308) B 309) B 310) A 311) B 312) C 313) C 314) D 315) D 316) B 317) B 318) C 319) D 320) B 321) A 322) A 323) C 324) D 325) B 326) A 327) A 328) D 329) C 330) C 331) D 332) A 333) D 334) D 335) B 336) D 337) D 338) A 339) B 340) A 341) B 342) B 343) A 344) D 345) B 346) B 347) B 348) C 349) D 350) B 74

Answer Key Testname: CHAPTER 0 351) C 352) D 353) D 354) D 355) B 356) C 357) A 358) D 359) B 360) B 361) B 362) D 363) A 364) B 365) A 366) C 367) D 368) C 369) B 370) D 371) D 372) D 373) B 374) A 375) B 376) B 377) B 378) C 379) C 380) C 381) C 382) B 383) D 384) A 385) B 386) D 387) B 388) A 389) C 390) C 391) C 392) C 393) D 394) B 395) C 396) C 397) A 398) B 399) A 400) B 75

Answer Key Testname: CHAPTER 0 401) D 402) D 403) D 404) D 405) A 406) D 407) D 408) A 409) C 410) A 411) D 412) A 413) C 414) C 415) B 416) D 417) C 418) B 419) C 420) B 421) C 422) C 423) D 424) A 425) D 426) B 427) A 428) C 429) A 430) D 431) A 432) B 433) C 434) A 435) C 436) B 437) A 438) B 439) C 440) A 441) C 442) B 443) A 444) A 445) A 446) A 447) D 448) A 449) A 450) B 76

Answer Key Testname: CHAPTER 0 451) D 452) A 453) B 454) B 455) A 456) B 457) D 458) C 459) D 460) B 461) B 462) A 463) B 464) B 465) C 466) B 467) C 468) B 469) A 470) A 471) C 472) B 473) B 474) B 475) C 476) B 477) D 478) C 479) C 480) C 481) C 482) B 483) B 484) B 485) A 486) D 487) D 488) A 489) B 490) B 491) D 492) B 493) A 494) B 495) C 496) A 497) D 498) D 499) D 500) A 77

Answer Key Testname: CHAPTER 0 501) D 502) D 503) C 504) B 505) C 506) B 507) B 508) A 509) D 510) B 511) B 512) A 513) C 514) A 515) A 516) A 517) C 518) B 519) B 520) C 521) A 522) D 523) B 524) D 525) B 526) A 527) B 528) A 529) A 530) D 531) A 532) D 533) B 534) B 535) B 536) B 537) C 538) C 539) D 540) D 541) D 542) C 543) A

Chapter 1 Exam Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the real solutions of the equation. 1) (x - 4)2 + 3(x - 4) - 18 = 0 A) {-6, 1}

B) {-1, 6}

C) {-7, 2}

D) {-2, 7}

Solve the problem. 2) Brandon can paint a fence in 12 hours and Elaine can paint the same fence in 11 hours. How long will they take to paint the fence if they work together? 13 1 17 3 hr hr A) 5 B) 11 hr C) 5 D) 5 hr 24 2 23 4 3) Susan purchased some municipal bonds yielding 7% annually and some certificates of deposit yielding 9% annually. If Susan's investment amounts to $19,000 and the annual income is $1590, how much money is invested in bonds and how much is invested in certificates of deposit? A) $5500 in bonds; $13,500 in certificates of deposit B) $13,000 in bonds; $6000 in certificates of deposit C) $6000 in bonds; $13,000 in certificates of deposit D) $13,500 in bonds; $5500 in certificates of deposit SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the equation by factoring. 4) x2 - x = 72

Solve the problem. 5) Two pumps can fill a water tank in 45 minutes when working together. Alone, the second pump takes 3 times longer than the first to fill the tank. How long does it take the first pump alone to fill the tank? 6) At Bargain Car Rental, the cost of renting an economy car for one day is $19.95 plus 20 cents per mile. At Best Deal Car Rental, the cost of renting a similar car for one day is $24.95 plus 15 cents per mile. Solve the inequality 24.95 + 0.15x < 19.95 + 0.20x to find the range of miles driven such that Best Deal is a better deal than Bargain. Find the real solutions of the equation. 3 7) 4x - 5 + 7 = 8

Solve the problem. 8) What is the domain of the variable in the expression

4x - 12 ?

9) Marianne is planning a shopping trip to buy birthday gifts for her son. She estimates that the total price of the items she plans to purchase will be between $350 and $400 inclusive. If sales are taxed at a rate of 8.375% in her area, what is the range of the amount of sales tax she should expect to pay on her purchases? If Marianne's budget for the shopping trip is $425, will she necessarily be able to buy all the gifts that she has planned? Find the real solutions of the equation. 3 10) 4x - 5 + 7 = 8

10)

Solve the problem.

11) The surface area A of a right circular cylinder is A = 2 r2 + 2 rh, where r is the radius and h is the height. Find the radius of a right circular cylinder whose surface area is 95.36 square inches and whose height is 11.7 inches.

11)

12) Chi is assigned to construct a triangle with the measure b of the base and the measure h of the height differing by no more than 0.2 centimeters. Express the relationship between b and h as an inequality involving absolute value.

12)

13) Martin purchased some municipal bonds yielding 8% annually and some certificates of deposit yielding 11% annually. If Martin's investment amounts to $23,000 and the annual income is $2230, how much money is invested in bonds and how much is invested in certificates of deposit?

13)

Write the expression in the standard form a + bi. 14) If z = 3 - 6i and w = 1 + 5i, evaluate z + w.

14)

Solve the problem. 15) Express that x differs from -7 by more than 3 as an inequality involving absolute value. Solve for x.

15)

16) In his algebra class, Rob has scores of 79, 85, 81, and 65 on his first four tests. To get a grade of C, the average of the first five tests must be greater than or equal to 70 and less than 80. Solve an inequality to find the range of scores that Rob can earn on the fifth test to get a C.

16)

17) A landscaping company sells 40-pound bags of top soil. The actual weight x of a bag, however, may differ from the advertised weight by as much as 0.75 pound. Write an inequality involving absolute value that expresses the relationship between the actual weight x of a bag and 40 pounds. Over what range may the weight of a 40-pound bag of to soil vary?

17)

Solve the equation by completing the square. 18) x2 - 4x + 1 = 0

18)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the inequality. Express your answer using interval notation. 19) -2x + 5 > -3x + 3

19)

A) [-2, )

B) (- , -2]

C) (8, )

D) (-2, )

Write the inequality using interval notation, and illustrate the inequality using the real number line. 20) -1 < x < 3

A) [-1, 3]

B) (-1, 3)

C) [-1, 3)

D) (-1, 3)

Find the real solutions of the equation. 21) (2x - 4)2 - 6(2x - 4) + 5 = 0 A) {-

3 1 , } 4 2

3 1 B) { , - } 2 2

5 9 C) { , } 2 2

D) {-

5 9 ,- } 2 2

20)

21)

Solve the inequality. Express your answer using interval notation. 22) x - 4 < -5

22)

A) (-1, )

B) (- , -9)

C) (- , -9]

D) (- , -1)

Solve the equation.

23) (x + 9)(x - 1) = (x + 1)2 5 A) 3 24) 13x - 8 = 5x - 72 A) {8}

B) {10}

3 C) 2

10 D) 9

B) {-9}

C) {-8}

D) {9}

C) {5, -9}

D) { 7, -1}

Solve the equation by completing the square. 25) x2 + 4x - 45 = 0 A) {-5, 9}

Find the real solutions of the equation. 26) (x2 - 1)1/2 = 12 B) { 145, -

26) 145}

C) { 13}

D) {145, -145}

Solve the inequality. Express your answer using interval notation. 27) |5x - 1| 5 4 6 4 6 A) [- , ] B) (- , ) 5 5 5 5 C) (- , -

4 6 ) or ( , ) 5 5

D) (- , -

1 9 B) {- , - } 2 2

1 9 C) { , } 2 2

27)

4 6 ] or [ , ) 5 5

Find the real solutions, if any, of the equation. Use the quadratic formula. 28) 4x2 + 9 = -20x 1 9 A) {- , - } 4 4

24)

25)

B) {-36, -9}

A) {13}

23)

9 9 D) {- , } 4 2

28)

Solve the problem. 29) Two cars start from the same point and travel in the same direction. If one car is traveling 60 miles per hour and the other car is traveling at 53 miles per hour, how far apart will they be after 9.4 hours? A) 65.8 mi B) 564 mi C) 498.2 mi D) 1,062.2 mi Translate the sentence into a mathematical equation. Be sure to identify the meaning of all symbols. 30) The profit derived from the sale of x video cameras is $350 per unit less the sum of $2,000 costs plus $150 per unit. A) If P is profit and x the units sold, then P = 350x - (2,000 + 150x) or P = 200x - 2,000. B) If P is profit and x the units sold, then P = 350x + 2,000 - 150x or P = 200x + 2,000. 350 150 200 ) or P = - (2,000 + - 2,000. C) If P is profit and x the units sold, then P = x x x

29)

30)

D) If P is profit and x the units sold, then P = 350x - (2,000 - 150x) or P = 500x - 2,000. Find the real solutions of the equation. 31) x4 - 5x2 + 4 = 0

32)

A) {-4, 4}

B) {-2, 2}

2x + 1 = -5 125 } A) {2

127 } B) {2

C) {-5, 5}

D) {-1, 1, -2, 2}

32) C) {- 63}

D) {12}

D) >

Fill in the blank with the correct inequality symbol. 0. 33) If x < -8, then x + 8 A)

31)

33)

B) <

Find the real solutions, if any, of the equation. Use the quadratic formula. 34) 2x2 = -10x - 6 A) {

-5 - 37 -5 + 37 , } 2 2

B) {

-5 - 13 -5 + 13 , } 4 4

C) {

-10 - 13 -10 + 13 , } 2 2

D) {

-5 - 13 -5 + 13 , } 2 2

Find the real solutions of the equation. 5 35) 1 - x = -2 A) {-33} B) {32}

C) {33}

Write the expression in the standard form a + bi. 36) (9 + 7i)(3 - 4i) A) 55 + 15i B) -28i2 - 15i + 27

34)

D) {-32}

35)

36) C) 55 - 15i

D) -1 + 57i

Solve the problem. 37) During an intramural basketball game, Team A scored 17 fewer points than Team B. Together, both teams scored a total of 151 points. How many points did Team A score during the game? A) 67 points B) 84 points C) 75 points D) 68 points

37)

Without solving, determine the character of the solutions of the equation in the complex number system. 38) x2 + 2x - 5 = 0

38)

Find the real solutions of the equation. 39) x + 3x1/2 + 2 = 0

39)

A) two complex solutions that are conjugates of each other B) a repeated real solution C) two unequal real solutions

1 A) { } 4

B) {1, 4}

C) {- 1, - 2}

D) no real solution

B) {0}

11 , 0} C) {2

11 D) { , 0} 2

Solve the equation by factoring. 40) 2x2 - 11x = 0 11 11 } A) { , 2 2

40)

Write the expression in the standard form a + bi. 41) If z = 9 - 3i, evaluate z + z. A) 18 + 6i B) 18 - 6i Find the real solutions of the equation. 3 42) 1 + x = -1 A) {-2} B) {1} Solve the equation. 43) 6x - 17 = 0 17 A) 6 44) 7x - 6 = x - 4 1 ,- 1 A) 3

6 17

D) 18

C) {2}

D) {-1}

C) -

1 5 B) - , 3 4

Write the expression in the standard form a + bi. 45) i15 A) 1

C) -6i

B) -1

6 17

17 6

C) i

D) -i

equation for h. Use the result to determine the height from which an object was dropped if it hits the ground after falling for 6 seconds. A) h = 24.01t2 ; 864.4 meters B) h = 24.01t; 144.1 meters

D) h = 4.9t2 ; 176.4 meters

42)

43)

44)

1 5 , C) 3 4

Solve the problem. 46) When an object is dropped to the ground from a height of h meters, the time it takes for the object h to reach the ground is given by the equation t = , where t is measured in seconds. Solve the 4.9

C) h = 4.9t; 29.4 meters

41)

45)

46)

Find the real solutions of the equation. 47) x2 - 3x + 83 = x + 7 A) {-2}

B) {2}

C) {-5}

D) {9}

Solve the problem. 48) Sue can sew a precut dress in 3 hours. Helen can sew the same dress in 2 hours. If they work together, how long will it take them to complete sewing that dress? Give your answer rounded to one decimal place, if necessary. A) 1.2 hr B) 2.5 hr C) 5 hr D) 1.8 hr Solve the equation by the Square Root Method. 49) x2 = 25 A) {5}

B) {6, -6}

C) {12.5}

D) {5, -5}

Solve the problem. 50) A bank loaned out $56,000, part of it at the rate of 13% per year and the rest at a rate of 8% per year. If the interest received was $5,730, how much was loaned at 13%? A) $30,000 B) $31,000 C) $26,000 D) $25,000 Write the interval as an inequality involving x, and illustrate the inequality using the real number line. 51) [-2, )

A) x > -2

B) x -2

C) x -2

D) x > -2

Solve the equation. 52) -7.4x + 1.8 = -15.9 - 1.5x A) {3}

B) {2.6}

C) {-24}

Solve the inequality. Express your answer using interval notation. 53) |x - 1| < 0 A) (-1, ) B) (- , 1) C) (-1, 1)

D) {2.4}

D) no solution

Write the expression in the standard form a + bi. 2 2 2 i + 54) 2 2 A) i

47)

48)

49)

50)

51)

52)

53)

54)

i 2

C) -i

55) If w = 8 + 6i, evaluate w - w. A) 0 B) 16

C) 12i

D) -

i 2

D) -16 + 12i

55)

Solve the equation. 56) |x| - 12 = -13 A) {-1}

B) {1, -1}

C) {1}

D) no solution

56)

Find the real solutions, if any, of the equation. Use the quadratic formula and a calculator. Express any solutions rounded to two decimal places. 57) x2 + 3x - 3 = 0 57)

A) {-2.8, 2.8}

B) {-1.07, 2.8}

Solve the equation. The letters a, b, and c are constants. 58) ax - b = c, a 0 c-b b-c A) x = B) x = a a

C) {-2.8, 1.07}

D) {-2.8, -1.07}

b+c C) x = a

b+ c D) x = a

Find the real solutions, if any, of the equation. Use the quadratic formula. 59) 4x2 + 12x + 2 = 0

59)

A) {

-3 - 11 -3 + 11 , } 2 2

B) {

-12 2

C) {

-3 - 7 -3 + 7 , } 2 2

D) {

-3 - 7 -3 + 7 , } 8 8

7 -12 + , 2

}

Write the expression in the standard form a + bi. 9 60) 6 - 8i A) -

27 18 i 14 7

B) -

60)

27 18 i + 14 7

27 18 i + 50 25

27 18 i 50 25

Solve the problem. 61) During the first five months of the year, Len earned commissions of $3,850, $2,790, $2,450, $2,360, and $3,580. If Len must have average monthly earnings of at least $3,140 in order to qualify for retirement benefits, what must he earn in the sixth month in order to qualify for benefits? A) at least $3,140 B) at least $3,810 C) at least $3,028 D) at least $3,006 Write the inequality obtained by performing the indicated operation on the given inequality. 62) Add 4 to each side of the inequality 5 + 5x < -4. A) 9 + 5x > 0 B) 9 + 5x < 0 C) 9 + 9x < 0 D) 9 + 9x > 0 Find the real solutions of the equation. 63) x2 + 5x - x2 + 5x = 12

61)

62)

63)

A) {25, -25} C) {

58)

B) {3}

-5 + 89 -5 - 89 , } 2 2

D) {5}

Find the real solutions, if any, of the equation. Use the quadratic formula. 64) x2 + 4x - 3 = 0 A) {-1 - 7, -1 + C) {2 + 7}

64)

B) {-2 - 7, -2 + 7} D) {-2 - 2 7, -2 + 2 7}

Solve the problem. 65) For a cone, the formula r =

3V describes the relationship between the radius r of the base, the h

65)

volume V, and the height h. Find the volume if the radius is 7 inches and the cone is 9 inches high. (Use 3.14 as an approximation for , and round to the nearest tenth.) A) 461.6 cubic in. B) 4,154.2 cubic in. C) 51.3 cubic in. D) 65.9 cubic in.

Solve the equation by factoring. x-4 15 = 66) x x+4 A) {16, 1}

66) B) {4, -1}

C) {4, 1}

D) {16, -1}

Solve the equation. The letters a, b, and c are constants. a b 67) + = c, c 0 x x A) x =

a+b c

B) x =

67)

ab c

C) x =

Find the real solutions of the equation. 68) x + 7 + x = 3 1 A) { } B) {1} 9 69) x3/2 - 9x1/2 = 0 A) { 2}

c ab

D) x =

c a+b

68) C) {4}

D) no real solution

C) {3}

D) {0, 81}

69) B) {0, 9}

Solve the equation. 5 8 = 70) 1 8x 7 A) -

35 8

70) B) - 7

Solve the equation by the Square Root Method. 71) (2x - 5)2 = 25 A) {0, -10}

35 8

D) - 5

C) {10, 0}

D) {5, 0}

B) {0, -5}

71)

Translate the sentence into a mathematical equation. Be sure to identify the meaning of all symbols. 72) The total cost of producing refrigerators in one production line is $5,000 plus $500 per unit produced. 5,000 . A) If C is the total cost and x is the number of units produced, then C = 500x

72)

B) If C is the total cost and x is the number of units produced, then C = 5,000 + 500x. C) If C is the total cost and x is the number of units produced, then C = (5,000 + 500)x. D) If C is the total cost and x is the number of units produced, then C = 5,000x + 500. Write the expression in the standard form a + bi. 73) (9 + 5i)(9 - 5i) A) 56

B) 81 - 25i

C) 106

D) 81 - 25i2

C) {-3}

3 D) {- } 2

Find the real solutions of the equation. 74) x2 - 3x + 64 = x + 5 A) {8}

B) {3}

Solve the inequality. Express your answer using interval notation. 75) 4x + 5 < 37

73)

74)

75)

A) (- , 8] B) [8, )

C) (8, )

D) (- , 8)

Find the real solutions of the equation. 76) 2x + 3 - x + 1 = 1 A) {-3, -1} B) {3}

C) {3, -1}

D) no real solution

77) x5/4 - 4x1/4 = 0 A) {-4, 0, 4}

B) {0}

C) {0, 2}

D) {0, 4}

78) 4x-2 - 11x-1 - 3 = 0 1 A) {- 4, } 3

1 B) {- , -3} 4

1 C) {4, } 3

1 D) {- , 3} 4

76)

77)

78)

Fill in the blank with the correct inequality symbol. -28. 79) If x > -7, then 4x A) <

79)

C) >

Find the real solutions, if any, of the equation. Use the quadratic formula. 80) 5x2 + x - 5 = 0 A) { C) {

-1 1-

101 -1 + ,

101

80)

-1 - 101 -1 + 101 , } B) { 10 10

}

101 1 + 101 , } 10 10

D) no real solution

Solve the inequality. Express your answer using interval notation. 3 5 81) 0 < < x 2

81)

6 A) ( , ) 5

B) (- ,

6 ) 5

5 D) ( , ) 6

C) (- ,

Write the expression in the standard form a + bi. 82) 8(8 - 8i) A) 64 + 64i B) 8 - 64i

5 ) 6

C) 64 - 64i

D) 64i - 8i

82)

Use the discriminant to determine whether the quadratic equation has two unequal real solutions, a repeated real solution, or no real solution without solving the equation. 83) x2 + 3x + 3 = 0 83)

A) repeated real solution B) two unequal real solutions C) no real solution

Solve the equation by the Square Root Method. 84) (x - 3)2 = 9 A) {3, -3}

B) {0, -6}

C) {12}

D) {6, 0}

84)

Write the inequality using interval notation, and illustrate the inequality using the real number line. 85) 1 x 7

A) (1, 7)

B) [1, 7]

C) (1, 7]

D) [1, 7]

Find the real solutions of the equation by factoring. 86) 2x4 = 128x A) {0, 4}

B) {0, 2, 4}

C) {0}

D) {-4, 0, 4}

Solve the problem. 87) The formula v = 2.5r can be used to estimate the maximum safe velocity v, in miles per hour, at which a car can travel along a curved road with a radius of curvature r, in feet. To the nearest whole number, find the radius of curvature if the maximum safe velocity is 15 miles per hour. A) 563 ft B) 90 ft C) 36 ft D) 225 ft Express the graph shown using interval notation. Also express it as an inequality involving x. 88)

A) (1, 9] 1<x 9

B) [1, 9] 1 x 9

Write the expression in the standard form a + bi. 89) i10 A) 1

B) i

C) [1, 9) 1 x<9

D) (1, 9) 1<x<9

C) -1

D) -i

Solve the equation. 90) |2x2 - x - 1|= 3 A) {C) {

85)

86)

87)

88)

89)

90) ,-

33 1 + ,

}

B) {

}

D) no solution

Solve the problem. 91) x represents the number of cassette tapes sold at $8.75 per tape, and y represents the total cost of the cassette tapes. After writing an equation for this situation, what is the total cost of 14 cassettes? A) $122.5 B) $0.62 C) $245 D) $61.25

91)

Solve the equation. 3 7 4 = 92) x + 2 x - 2 x2 - 4 A) { 21} 93)

92) B) {6}

C) {-6}

D) {24}

2x x =3+ 5 3

93)

A) {-45}

B) {-90}

C) {45}

D) {90}

Solve the inequality. Express your answer using interval notation. 94) (3x + 5)-1 < 0

A) (-

5 , ) 3

C) (- , -

94)

B) [-

5 ) 3

5 , ) 3

D) (- , -

5 ] 3

Find a and b.

95) If 0 < 2x < 6, then a < x2 < b. A) a = 0, b = 9 B) a = 0, b = 16

C) a = 0, b = 3

D) a = 0, b = 36

95)

Find the real solutions of the equation. Use a calculator to express the solutions rounded to two decimal places. 96) (1 + x)2 - 5 = 2(1 + x) 96) A) {0.62, -1.98}

B) {-1.62, -0.62}

C) {-0.62, -0.18}

D) {-0.62, 0.82}

Translate the sentence into a mathematical equation. Be sure to identify the meaning of all symbols. 97) Speed is measured by distance divided by time. d A) If S represents speed, d distance, and t time, then S = . t B) If S represents speed, d distance, and t time, then t =

S . d

C) If S represents speed, d distance, and t time, then S =

t . d

D) If S represents speed, d distance, and t time, then d =

S . t

97)

Write the inequality using interval notation, and illustrate the inequality using the real number line. 98) y < -4

A) (- , -4]

B) (- , -4)

C) [- , -4)

D) [- , -4]

98)

Find the real solutions, if any, of the equation. Use the quadratic formula and a calculator. Express any solutions rounded to two decimal places. Use 3.14 to approximate . 99) x2 + x - 4 = 0 99)

A) {0.73, 1.73}

B) {-0.73, 1.73}

C) {-1.73, 0.73}

D) {-1.73, -0.73}

Find the real solutions, if any, of the equation. Use the quadratic formula. 100) 2x2 - x + 4 = 0 -1 - 33 -1 + 33 , } A) { 4 4

C) {

100)

-1 - 33 1 + 33 , } B) { 4 4

-1 + 33 1 + 33 , } 4 4

D) no real solution

Translate the sentence into a mathematical equation. Be sure to identify the meaning of all symbols. 101) The surface area of a sphere is 4 times the square of the radius. A) If S represents the surface area and r the radius, then 4 S =r2 .

101)

B) If S represents the surface area and r the radius, then S = 4 r. C) If S represents the surface area and r the radius, then S = 4 r2 .

D) If S represents the surface area and r the radius, then S = r2 . Find the real solutions of the equation. 102) x + x = 20 A) {25} B) {4}

C) {5}

D) {16}

Solve the problem. 103) The radiator in a certain make of car needs to contain 60 liters of 40% antifreeze. The radiator now contains 60 liters of 20% antifreeze. How many liters of this solution must be drained and replaced with 100% antifreeze to get the desired strength? A) 20.0 L B) 15.0 L C) 30 L D) 24 L

102)

103)

Solve the inequality. Express your answer using interval notation. 104) x(4x - 6) (2x + 6)2

104)

A) (- , -

6 ] 5

6 B) [ , ) 5

C) (- , -

6 ] 5

D) [-

Write the expression in the standard form a + bi. 105) (-7 + i)(-7 - i) A) 49 B) -7

6 , ) 5

C) -48

D) 50

Express the graph shown using interval notation. Also express it as an inequality involving x. 106)

A) (-4, 1] -4 < x 1

B) [-4, 1) -4 x < 1

C) [-4, 1] -4 x 1

D) (- , 1) x<1

C) { 7i, i}

D) { 7, 7}

Solve the equation in the complex number system. 107) x4 - 6x2 - 7 = 0 A) {- 7i, -i}

B) {-

105)

106)

107)

7, i, -i}

Solve the inequality. Express your answer using interval notation. 108) 8 < 2x 12

A) (4, 6]

B) [-6, -4)

C) (-6, -4]

D) [4, 6)

108)

Solve the problem. 109) BJ can overhaul a boat's diesel inboard engine in 20 hours. His apprentice takes 60 hours to do the same job. How long would it take them working together assuming no gain or loss in efficiency? A) 6 hr B) 15 hr C) 80 hr D) 12 hr Solve the equation. 5-x 3 7 + = 110) x 4 x A) -

8 7

109)

110) B) {-8}

C) {8}

D) {-4}

Solve the problem. 111) A loan officer at a bank has $100,000 to lend and is required to obtain an average return of 13% per year. If he can lend at the rate of 14% or the rate of 11%, how much can he lend at the 11% rate and still meet his required return? A) $33,333.33 B) $7,142.86 C) $900,000.00 D) $4,000.00 Translate the sentence into a mathematical equation. Be sure to identify the meaning of all symbols. 112) The volume of a right prism is the area of the base times the height of the prism. 1 A) If V represents the volume, B the area of the base, and h the height, then V = Bh. 2

111)

112)

B) If V represents the volume, B the area of the base, and h the height, then V = Bh. C) If V represents the volume, B the area of the base, and h the height, then V = B + h. B D) If V represents the volume, B the area of the base, and h the height, then V = . h Solve the inequality. Express your answer using interval notation. 113) |x + 8| 0 A) {8} B) (- , -8) C) {-8} Find the real solutions of the equation by factoring. 114) x3 + 3x2 + 4x + 12 = 0 A) {3}

B) {-2, 2, -3}

C) {-3}

D) no solution

D) no real solution

Write the inequality using interval notation, and illustrate the inequality using the real number line. 115) -2 x < 8

A) (-2, 8]

B) [-2, 8)

C) (- , 8)

D) [-2, 8)

113)

114)

115)

Solve the equation by factoring. 116) 12x2 - 5x - 25 = 0 5 5 A) {- , - } 4 3

5 5 B) {- , } 4 3

5 5 C) { , } 4 3

5 5 D) { , - } 4 3

Solve the inequality. Express your answer using interval notation. 117) 7x - 6 > 6x + 1

116)

117)

A) [7, )

B) (-5, )

C) (7, )

D) (- , 7]

Solve the equation. 118) 4x + 14 = 0 2 A) 7

2 B) 7

Find the real solutions of the equation. 119) x2 + 2 - 2x + 5 = 0

120)

7 C) 2

7 D) 2

118)

A) {-3, 1}

B) {3, -1}

C) {3}

D) no real solution

26x + 13 = x + 7 A) {-5}

B) {7}

C) {6}

D) {-6}

C) 25 - 36i

D) 25 - 36i2

Write the expression in the standard form a + bi. 121) (5 + 6i)(5 - 6i) A) 61

B) -11

120)

Solve the formula for the indicated variable. 122) S = 2 rh + 2 r2 for h A) h = S - r

121)

122)

S - 2 r2 B) h = 2 r

C) h = 2 (S - r)

D) h =

Fill in the blank with the correct inequality symbol. 0. 123) If x < 2, then x - 2 A) >

119)

S -1 2 r

123)

C) 17

D) <

Write the expression in the standard form a + bi. 9 124) 7-i A)

21 3 i 16 16

124)

63 9 i 50 50

63 9 i + 50 50

21 3 i + 16 16

Solve the equation by completing the square. 3 5 =0 125) x2 + x + 2 16 A) {-

1 5 ,- } 4 4

125)

1 5 B) { , } 4 4

1 5 C) { , - } 4 4

D) {-

1 5 , } 4 4

Solve the equation. The letters a, b, and c are constants. x x 126) + = c, a 0, b 0, a -b a b A) x = abc

B) x =

126)

abc a+b

C) x =

a+b abc

D) x =

c ab

Solve the equation. 11x + 33 = 11 127) 3

127)

A) {6, 0}

B) {-6, 0}

C) {-6, 6}

D) no solution

Solve the equation by factoring. 128) x(x - 11) + 30 = 0 A) {-6, -5}

B) {-6, 5}

C) {6, -5}

D) {6, 5}

Write the expression in the standard form a + bi. 129) (9 - 6i) + (8 + 8i) A) 17 + 2i B) -17 - 2i

C) 1 + 14i

D) 17 - 2i

Solve the problem. 130) A circular pool measures 8 feet across. One cubic yard of concrete is to be used to create a circular border of uniform width around the pool. If the border is to have a depth of 3 inches, how wide will the border be? Use 3.14 to approximate . Express your solution rounded to two decimal places. (1 cubic yard = 27 cubic feet)

A) 3.1 ft

B) 5.43 ft

C) 2.88 ft

D) 8.37 ft

128)

129)

130)

Without solving, determine the character of the solutions of the equation in the complex number system. 131) x2 + 2x - 3 = 0 A) two unequal real solutions B) two complex solutions that are conjugates of each other C) a repeated real solution

Solve the equation. 132) 11x = -15 + 10x A) {15}

B) {-5}

C) {-14}

D) {-15}

Solve the equation in the complex number system. 133) x2 + x + 2 = 0 1 7 1 7 i, - + i} B) {- 2 2 2 2

-1 - 7 -1 + 7 , } 2 2

Solve the equation. 134) 3x + 12 = 0 A) {4} 135) 5(2x - 2) = 9(x + 4) A) {-26}

D) {

1 7 1 7 i, + i} 2 2 2 2

B) {-3}

C) {-4}

D) {3}

B) {-46}

C) {46}

D) {31}

Solve the inequality. Express your answer using interval notation. 136) |x| < 9 A) (-9, 9) B) (- , -9) and (9, ) C) (- , -9) or (9, ) D) [0, 9]

A) {2 + 15, 2 - 15} C) {-2 + 19, -2 - 19}

B) {4 + D) {2 +

Solve the equation. 138) 5(x + 3) = (5x + 15) A) {0} C) all real numbers

19, 4 19, 2 -

19} 19}

138)

D) -10i

Find the real solutions, if any, of the equation. Use the quadratic formula. 140) 16x2 - 56x + 49 = 0 7 B) {- } 4

7 C) { } 4

135)

137)

B) {30} D) no solution

Perform the indicated operations and express your answer in the form a + bi. 139) (8 + 6i)(6i - 8) A) 10i B) -10 C) 10

134)

136)

Find the real solutions, if any, of the equation. Use the quadratic formula. 137) x2 - 4x - 15 = 0

7 A) { , -28} 4

132)

133)

1- 7 1+ 7 , } A) { 2 2

C) {

131)

139)

140) D) no real solution

Write the expression in the standard form a + bi. 141) 2i(3 - 4i) A) 6i - 8i2 B) 6i- 8

C) 8+ 6i

D) 6i + 8i2

Write the interval as an inequality involving x, and illustrate the inequality using the real number line. 142) (- , -2)

A) x < -2

B) x -2

C) x < -2

D) x -2

Solve the equation in the complex number system. 143) x4 = 16 A) {-2, 2, -2i, 2i}

B) {-2, 2, 2i}

C) {-2, 2}

D) {2}

Solve the problem. 144) x represents the number of textbooks purchased at $25 per book, and y represents the total amount of money spent on textbooks. What is an equation of the form y = ax for this situation? A) y = 75x B) y = 50x C) y = 13x D) y = 25x

141)

142)

143)

144)

145) Using a phone card to make a long distance call costs a flat fee of $0.67 plus $0.25 per minute starting with the first minute. What is an equation of the form y = ax + b for this situation? A) y = 0.67x B) y = 0.25x C) y = 0.25x + 0.67 D) y = 0.67x + 0.25

145)

146) A college student earned $7,700 during summer vacation working as a waiter in a popular restaurant. The student invested part of the money at 9% and the rest at 8%. If the student received a total of $644 in interest at the end of the year, how much was invested at 9%? A) $4,900 B) $3,850 C) $2,800 D) $962

146)

Write the expression in the standard form a + bi. 4 - 7i 147) 7 + 4i A) -i

147)

B) i

C) 1

D) -1

Solve the problem. 148) The number of centimeters, d, that a spring is compressed from its natural, uncompressed position 2W is given by the formula d = , where W is the number of joules of work done to move the k

148)

spring and k is the spring constant. Solve this equation for W. Use the result to determine the work needed to move a spring 9 centimeters if it has a spring constant of 0.2. 2d2 ; 810 joules A) W = 2d2 k; 32.4 joules B) W = k

C) W =

d2 k ; 8.1 joules 2

D) W =

d2 k2 ; 0.8 joules 4

Solve the equation by completing the square. 149) x2 - 8x - 13 = 0 A) {4 C) {8 -

13, 4 + 77, 8 +

149)

13} 77 }

B) {4 - 29, 4 + 29} D) {-4 - 29, -4 + 29}

Write the expression in the standard form a + bi. 150) 5i5 (1 + i3 ) A) -5 - 5i

B) -5 + 5i

C) 5 + 5i

D) 5 - 5i

Solve the equation. 151) x(1 + 3x) = (3x - 1)(x - 3) 3 A) 121

3 B) 121

3 C) 11

3 D) 11

150)

151)

Translate the sentence into a mathematical equation. Be sure to identify the meaning of all symbols. 152) Momentum is the product of the mass of an object and its velocity. A) If M represents momentum, m mass, and v velocity, then M = m + v. m B) If M represents momentum, m mass, and v velocity, then M = . v C) If M represents momentum, m mass, and v velocity, then M =

152)

1 mv. 2

D) If M represents momentum, m mass, and v velocity, then M = mv. Find a and b. 153) If -4 < x < -1, then a < A) a =

2 x < b. 3

8 2 ,b= 3 3

B) a = -

153) 8 2 ,b= 3 3

C) a =

8 2 ,b=3 3

D) a = -

8 2 ,b=3 3

Write the expression in the standard form a + bi. 154) If z = 4 - 6i, evaluate zz. A) 52

154)

B) 16 - 36i2

C) 16 - 36i

D) -20

Solve the inequality. Express your answer in set notation. 155) x2 < 4 A) {x| x < 2} C) {x| x < -2 or x > 2}

155)

B) {x| -2 < x < 2} D) {x| -2 x 2}

Solve the problem. 156) The maximum number of volts, E, that can be placed across a resistor is given by the formula E = PR, where P is the number of watts of power that the resistor can absorb and R is the resistance of the resistor in ohms. Solve this equation for R. Use the result to determine the 1 resistance of a resistor if P is watts and E is 40 volts. 8 A) R =

E2 ; 12,800 ohms P

B) R = E2 P2 ; 102,400 ohms

C) R = E2 P; 12,800 ohms

D) R =

E2 ; 102,400 ohms P2

157) Inclusive of a 6.8% sales tax, a diamond ring sold for $2,029.20. Find the price of the ring before the tax was added. (Round to the nearest cent, if necessary.) A) $2,167.19 B) $1,891.21 C) $137.99 D) $1,900 Solve the inequality. Express your answer in set notation. 158) x2 64 A) {x| x -8 or x C) {x| x < -8 or x

8} 8}

B) {x| x < -8 or x > 8} D) {x| -8 x 8}

B) {-0.21, 14.67}

C) {0.82, -14.67}

159) D) {0.21, -14.67}

Solve the formula for the indicated variable. 9 160) F = C + 32 for C 5 A) C =

9 (F - 32) 5

Solve the equation. 161) |3x + 8| = 9 1 17 } A) {- , 3 3 162) |x + 1| = 7 A) {8, 6}

B) C =

157)

158)

Solve using the quadratic formula. Round any answers to two decimal places. 1 159) x2 - 2 3x = 3 4 A) {-0.82, 14.67}

156)

160) 5 F - 32

C) C =

F - 32 9

D) C =

5 (F - 32) 9

161)

1 17 } B) { , 3 3

1 17 } C) { , 8 8

D) no solution

B) {-6}

C) {-8, 6}

D) no solution

162)

Solve the problem. 163) An airplane flies 440 miles with the wind and 330 against the wind in the same length of time. If the speed of the wind is 40, what is the speed of the airplane in still air? A) 120 mph B) 270 mph C) 285 mph D) 280 mph 164) It costs $27 per hour plus a flat fee of $19 for a plumber to make a house call. After writing an equation for this situation, what is the total cost to have a plumber come to a house for 4 hours? A) $517 B) $127 C) $103 D) $108 Find the real solutions, if any, of the equation. Use the quadratic formula. 165) 3x2 + 7x - 20 = 0 5 A) {- , -4} 3

5 B) {- , 4} 3

5 C) { , 4} 3

5 D) { , -4} 3

Solve the problem. 166) The function f(x) = 6.75 x + 12 models the amount, f(x), in billions of dollars of new student loans x years after 1993. According to the model, in what year is the amount loaned expected to reach $25.5 billion? A) 2,002 B) 1,997 C) 2,001 D) 2,000 Solve the equation. 3 2 4 + = 167) x + 5 2x + 1 x - 2 A) -

47 46

46 47

5+3 5 } B) { 2

C) {-5 - 3 5, -5 + 3 5}

D) {

D) -

166)

46 47

-5 - 3 5 } 2

Solve the equation. 6x - 4 9x - 3 = 169) 2x - 9 3x + 1

169) B)

23 81

31 81

D) -

C) {121}

D) {79}

14 C) { } 5

59 D) { } 2

Find the real solutions of the equation. 170) x + 2 = 9 A) {83} B) {81} 171) (5x + 2)1/3 = 4 62 A) { } 5

165)

168)

-5 - 3 5 -5 + 3 5 , } A) { 2 2

1 3

164)

167)

Solve the equation by completing the square. 168) x2 + 5x - 5 = 0

A) -

163)

64 B) { } 5

23 93

170)

171)

172)

5x + 36 = x A) {- 9}

Solve the equation. 173) -8x + 14 = -6x - 4 A) {-7}

B) {-4, 9}

C) {9}

D) no real solution

B) {-9}

C) {9}

D) {7}

172)

173)

Solve the inequality. Express your answer using interval notation. 174) -3(3x + 11) < -12x - 21

174)

A) (- , 18]

B) (- , 4)

C) (- , 4]

D) (4, )

Solve the equation by factoring. 8 175) 9x - 71 = x A) {-

1 , 8} 9

175) B) {

1 1 ,- } 71 9

D) {-

B) {-1, 1, -3}

C) {9}

D) {-3, 3}

51 B) 8

15 C) 4

15 D) 4

Find the real solutions of the equation by factoring. 176) x3 + 3x2 - x - 3 = 0 A) {1, -3, 3}

Solve the equation. 177) 6(x + 5) = 7 x - (3 - x) 51 A) 8 178)

1 , 9} 9

C) {-9, 8}

8x - 6 20x + 6 = 2x - 7 5x - 1

18 83

176)

177)

178) B) -

2 5

24 83

D) -

8 15

179)

x -5=1 6

179)

A) {24}

B) {-24}

C) {36}

D) {-36}

Solve the inequality. Express your answer using interval notation. 5 x + 2 < 27 180) 7 2

180)

A) [2, 10)

B) [2, 3)

C) (2, 3]

D) (2, 10]

Solve the problem. 181) Mary and her brother John collect foreign coins. Mary has twice the number of coins that John has. Together they have 120 foreign coins. Find how many coins Mary has. A) 40 coins B) 80 coins C) 72 coins D) 16 coins Solve the equation by completing the square. 1 1 1 x- =0 182) x2 + 4 16 8

182)

1 1 A) { , - } 8 8

C) {

33 - 1 , 8

33 + 1 } 8

B) {

33 ,8

33 } 8

D) {

33 - 1 ,8

33 + 1 } 8

Solve the problem. 183) During a hurricane evacuation from the east coast of Georgia, a family traveled 270 miles west. For part of the trip, they averaged 70 mph, but as the congestion got bad, they had to slow to 10 mph. If the total time of travel was 6 hours, how many miles did they drive at the reduced speed? A) 30 mi B) 20 mi C) 35 mi D) 25 mi Find the real solutions of the equation by factoring. 184) x3 + 6x2 - 16x - 96 = 0 A) {4, -6}

181)

B) {-4, 4, -6}

C) {16, -6}

D) {-4, 4, 6}

183)

184)

Solve the inequality. Express your answer using interval notation. 185) 1 3x - 5 10

185)

A) (-5, -2)

B) (2, 5)

C) [-5, -2]

D) [2, 5]

Solve the problem. 186) A ball is thrown vertically upward from the top of a building 112 feet tall with an initial velocity of 96 feet per second. The distance s (in feet) of the ball from the ground after t seconds is s = 112 + 96t - 16t2 . After how many seconds will the ball pass the top of the building on its way down? A) 113 sec

B) 7 sec

C) 6 sec

186)

D) 9 sec

187) Center City East Parking Garage has a capacity of 253 cars more than Center City West Parking Garage. If the combined capacity for the two garages is 1,215 cars, find the capacity for each garage. A) Center City East: 481 cars B) Center City East: 734 cars Center City West: 734 cars Center City West: 481 cars C) Center City East: 471 cars D) Center City East: 744 cars Center City West: 744 cars Center City West: 471 cars

187)

188) Tracy can wallpaper 5 rooms in a new house in 35 hours. Together with her trainee they can wallpaper the 5 rooms in 19 hours. How long would it take the trainee working by herself to do the job? A) 75 hr B) 80 hr C) 40 hr D) 35 hr

188)

189) A rectangular carpet has a perimeter of 240 inches. The length of the carpet is 72 inches more than the width. What are the dimensions of the carpet? A) 72 in. by 96 in. B) 108 in. by 120 in. C) 96 in. by 24 in. D) 96 in. by 120 in.

189)

Solve the equation. 190) |x2 - 4x - 4| = 8 A) {-2, 2}

191) 5(x + 4) = 6(x - 7) A) {-22}

B) {-2, 2, 6}

C) {-2, 2, -6}

D) {2, 6}

B) {6}

C) {-62}

D) {62}

190)

191)

192) |7x + 5| + 3 = 5 3 A) { , 1} 7

3 7 B) {- , - } 5 5

Solve the equation in the complex number system. 193) x2 - 12x + 61 = 0 A) {1, 11}

B) {6 - 25i, 6 + 25i}

192)

3 C) {- , - 1} 7

D) no solution

C) {6 + 5i}

D) {6 - 5i, 6 + 5i}

Solve the equation. 194) |x2 - 4x + 4|= 2 A) {2 +

195) -7x + 5 + 6(x + 1) = 2x - 3 A) {2}

194) B) {2 -

2, 2 +

C) {2 -

1 B) 8

2 C) 5

D) no solution

14 D) 3

Write the expression in the standard form a + bi. 2i 196) 1-i A) -1 - i Solve the equation. 197) 3(2x - 1) = 12 5 A) 2 198)

195)

196)

B) -1 + i

C) -1 + 2i

D) 1 + i

13 B) 6

3 C) 2

11 D) 6

x 1 - = -5 2 2

197)

198)

A) {-11}

B) {-9}

C) {11}

D) {9}

Solve the problem. 199) How many gallons of a 30% alcohol solution must be mixed with 60 gallons of a 14% solution to obtain a solution that is 20% alcohol? A) 12 gal B) 7 gal C) 36 gal D) 27 gal Solve the inequality. Express your answer using interval notation. 200) 5 - 7x > 9 4 4 A) (- , 2) B) (- , ) or (2, ) 7 7 C) (- , -

193)

4 4 ) or ( , ) 7 7

D) (- , -

200)

4 ) or (2, ) 7

Solve the problem. 201) The manager of a candy shop sells chocolate covered peanuts for $10 per pound and chocolate covered cashews for $13 per pound. The manager wishes to mix 30 pounds of the cashews to get a cashew-peanut mixture that will sell for $12 per pound. How many pounds of peanuts should be used? A) 22.5 lb B) 45 lb C) 15 lb D) 7.5 lb 27

199)

201)

Solve the equation by factoring. 202) 49x2 - 84x + 36 = 0 7 A) { } 6

6 B) {- } 7

7 C) {- } 6

6 D) { } 7

Perform the indicated operations and express your answer in the form a + bi. 203) -81 A) -9i

C) 9i

B) ±9

202)

203) D) i 9

Solve the inequality. Express your answer using interval notation. 204) -3x - 7 -4x - 6

204)

A) [1, )

B) [-13, )

C) (- , 1)

D) (- , 1]

Solve the problem. x+3 and k2 - 3k = 18, find x. 205) If k = x-3 7 3 A) { , } 2 2

B) {

205)

21 3 , } 5 2

C) {6,

3 } 2

D) {

21 1 , } 5 4

Write the inequality obtained by performing the indicated operation on the given inequality. 206) Multiply each side of the inequality 5 - 5x > 3 by 3. A) 15 - 15x < 9 B) 15 - 5x < 9 C) 15 - 5x > 9 D) 15 - 15x > 9 Fill in the blank with the correct inequality symbol. 1 1 207) If x < - , then x _____ -1. 4 4 A) >

207)

B) <

Solve the equation by completing the square. 208) 25x2 + 30x + 8 = 0 A) {-

4 12 , } 25 25

206)

2 4 B) { , } 5 5

C) {-

2 4 ,- } 5 5

D) {-

2 4 ,} 25 25

208)

Find the real solutions of the equation. Use a calculator to express the solutions rounded to two decimal places. 209) x2/5 - 3x1/5 - 4 = 0 209) A) {-1, 1.32}

B) {-1, 1024}

C) {-1, 4}

D) {-1}

Write the expression in the standard form a + bi. 210) If z = 7 - 9i and w = 6 + 7i, evaluate z + w. A) 13 + 2i B) -13 + 2i Solve the equation. 211) 6x - (5x - 1) = 2 1 A) 11

C) 1 + 16i

D) 13 - 2i

211)

1 C) 11

B) 1

D) - 1

Solve the problem. 212) x represents the number of textbooks purchased at $58 per book, and y represents the total amount of money spent on textbooks. After writing an equation for this situation, what is the cost of 4 textbooks? A) $232 B) $116.00 C) $464 D) $14.50 Solve the equation. 6 4 = 213) 2x - 3 2x + 5 A) -

2 21

212)

213) B)

2 21

C) -

Solve the inequality. Express your answer in set notation. 214) x2 49 A) {x| x 7} C) {x| -7 x 7}

21 2

B) {x| x -7 or x D) {x| -7 < x < 7}

A) (18, )

B) [18, )

C) (- , 18]

D) [-18, )

Write the expression in the standard form a + bi. 216) i17 B) i

C) -i

21 2

214)

Solve the inequality. Express your answer using interval notation. x x 5+ 215) 3 18

A) -1

210)

215)

D) 1

216)

Solve the equation. 217) 3x = -18 A) {3}

B) {6}

C) {-3}

D) {-6}

Without solving, determine the character of the solutions of the equation in the complex number system. 218) x2 - 12x + 36 = 0 A) two complex solutions that are conjugates of each other B) two unequal real solutions C) a repeated real solution

Write the expression in the standard form a + bi. 219) (7 + 8i) - (-8 + i) A) 15 - 7i B) -15 - 7i

C) -1 + 9i

D) 15 + 7i

Solve the equation. 220) x(4x - 1) = (4x + 1)(x - 5) 5 A) 19

5 C) 18

5 D) 3

B) {2}

Solve the inequality. Express your answer using interval notation. 221) |3x + 3| + 9 > 4 8 2 8 2 A) (- , - ) or ( , ) B) (- , ) 3 3 3 3 C) (- , )

218)

219)

220)

221)

D) no solution

Fill in the blank with the correct inequality symbol. -12. 222) If x < 3, then -4x A)

217)

222)

C) <

D) >

Solve the inequality. Express your answer using interval notation. 223) |x - 8| - 5 0 A) (- , 3) or (13, ) B) [3, 13] C) [-3, 0] D) no solution Write the interval as an inequality involving x, and illustrate the inequality using the real number line. 224) [-5, 1)

A) -5 x < 1

B) -5 x < 1

C) -5 < x 1

D) x < 1

223)

224)

Solve the equation. 225) |x2 + 2x| = 0 A) {2, 0}

B) {0, -2}

C) {2, 0, -2}

D) no solution

Solve the problem. 226) A real estate agent agrees to sell an office building according to the following commission schedule: $30,000 plus 30% of the selling price in excess of $700,000. Assuming that the office building will sell at some price between $700,000 and $1,000,000, inclusive, over what range does the agent's commission vary? A) The commission will vary between $30,000 and $120,000, inclusive. B) The commission will vary between $240,000 and $330,000, inclusive. C) The commission will vary between $31,000 and$120,000, inclusive. D) The commission will vary between $30,000 and $320,000, inclusive. Solve the equation. 2 3 227) x = 7 4 A) -

B) -

228) 12 - 5x = 2 - 3x A) {6}

8 21

B) {5}

21 4

C) {-5}

21 8

D) {-6}

Solve the problem. 229) The manager of a coffee shop has one type of coffee that sells for $8 per pound and another type that sells for $15 per pound. The manager wishes to mix 60 pounds of the $15 coffee to get a mixture that will sell for $11 per pound. How many pounds of the $8 coffee should be used? A) 70 lb B) 80 lb C) 140 lb D) 40 lb Solve the equation by completing the square. 230) x2 + 8x - 5 = 0

228)

229)

230)

A) {-4 - 2 21, -4 + 2 21} C) {-4 - 21, -4 + 21}

B) {4 + 21} D) {-1 - 21, -1 +

21}

231) 11} 11}

B) {-2 - 2 11, -2 + 2 11} D) { 2 + 11}

Find a and b. 232) If x - 3 < 4, then a < x + 2 < b. A) a = -6, b = 2 B) a = -1, b = 7

C) a = 1, b = 9

Find the real solutions, if any, of the equation. Use the quadratic formula. 233) 4x2 + 6x = - 1 -3 - 5 -3 + 5 , } A) { 4 4

C) {

226)

227)

21 8

231) x2 + 4x = 7 A) {-1 - 11, -1 + C) {-2 - 11, -2 +

225)

-3 - 5 -3 + 5 , } B) { 8 8

-3 - 13 -3 + 13 , } 4 4

D) {

-6 - 5 -6 + 5 , } 4 4

D) a = -2, b = 6

232)

233)

Find the real solutions of the equation. 1 2 =3 234) 2 x -2 (x - 2) A) {1,

7 } 3

B) {1,

234) 1 } 3

C) {-1,

7 } 3

D) {-1,

1 } 3

Solve the problem. 235) Two friends decide to meet in Chicago to attend a Cub's baseball game. Rob travels 305 miles in the same time that Carl travels 290 miles. Rob's trip uses more interstate highways and he can average 3 mph more than Carl. What is Rob's average speed? A) 58 mph B) 61 mph C) 65 mph D) 57 mph Solve the inequality. Express your answer using interval notation. 236) x + 7 < 9

235)

236)

A) (- , 2)

B) (- , 16)

C) (- , 2]

D) (2, )

Find the real solutions, if any, of the equation. Use the quadratic formula. 237) 12x = 2x2 A) {0, 6}

B) {0, - 6}

C) {6, - 6}

D) {0}

Write the expression in the standard form a + bi. 238) (5 + 7i)2 A) 74 + 70i

237)

238)

B) 25 + 70i + 49i2

C) -24

D) -24 + 70i

Translate the sentence into a mathematical equation. Be sure to identify the meaning of all symbols. 239) The force of gravity between two objects is the gravitational constant times the product of their masses divided by the square of the distance between them. A) If F is the force of gravity, G the gravitational constant, m 1 the mass of one object, m 2 the mass of the second, and d the distance between them, then F = G

m1 + m2 d2

239)

B) If F is the force of gravity, G the gravitational constant, m 1 the mass of one object, m 2 the mass of the second, and d the distance between them, then FG =

m1m2 d2

C) If F is the force of gravity, G the gravitational constant, m 1 the mass of one object, m 2 the mass of the second, and d the distance between them, then F = G

m1m2 d

D) If F is the force of gravity, G the gravitational constant, m 1 the mass of one object, m 2 the mass of the second, and d the distance between them, then F = G

m1m2 d2

Solve the equation. 1 x 11 240) + = 3 4 12 A)

7 4

240) B)

7 3

C) -

7 3

D) -

Solve the equation in the complex number system. 241) 16x2 + 1 = 5x A) {

241)

5 39 5 39 i, i} + 32 32 32 32

C) {-

7 4

B) {

5 39 5 39 i, i} + 32 32 32 32

D) {-

5 39 5 39 i, i} + 32 32 32 32

Solve the inequality. Express your answer using interval notation. 242) -2x - 2 -3x + 4

242)

A) (- , 6]

B) (- , 6)

C) [6, )

D) (2, )

Solve the equation. x-2 x+6 = 243) x-5 x-7 A)

244)

243)

8 5

22 5

C) -

15 7

D) {-4}

3 6 + = -3 x x

244)

A) - 3

B) 3

C) -

1 3

Without solving, determine the character of the solutions of the equation in the complex number system. 245) x2 + 4x + 7 = 0

245)

Write the expression in the standard form a + bi. 246) i14 + i12 + i10 + 1

246)

A) a repeated real solution B) two complex solutions that are conjugates of each other C) two unequal real solutions

A) 0

B) 1

C) -1

D) i

Solve the inequality. Express your answer using interval notation. 247) |7x + 4| + |-5| 8 1 1 A) [ , 1] B) (- , ] or [1, ) 7 7 C) (- , - 1] or [-

1 , ) 7

D) [- 1, -

1 ] 7

247)

Solve the problem.

248) The area of a circle is found by the equation A = r2 . If the area A of a certain circle is 81 square centimeters, find its radius r. cm A) 9 cm B) 9 C) {9 cm, -9 cm} D) 9 cm

Write the expression in the standard form a + bi. 249) (-4 - 7i)(3 + i) A) -5 - 25i B) -19 - 25i

C) -19 + 17i

D) -5 + 17i

248)

249)

Solve the problem. 250) The net income y (in millions of dollars) of Pet Products Unlimited from 1997 to 1999 is given by the equation y = 9x2 + 15x + 52, where x represents the number of years after 1997. Assume this

250)

Solve the equation. 251) 3|x - 3| = 18 A) {3, -9}

251)

trend continues and predict the year in which Pet Products Unlimited's net income will be $352 million. A) 2,001 B) 2,003 C) 2,004 D) 2,002

B) {3}

C) {9, -3}

B) {2}

1 C) 3

252) x(x2 + 2) = 6 + x3 A) 3

253) 12(3x - 2) = 2x - 9 15 A) 34 254)

33 34

D) no solution

252) D) {6}

15 38

253)

15 34

3x + 12 =3 4

A) {-8, 0}

254) B) {8, 0}

C) {-8, 8}

Solve the formula for the indicated variable. 7Q P + 5 = + 1 for P 255) P 3 2 A) P =

9 - 14Q 3

B) P =

255) 21 - 14Q 3

C) P =

9 + 14Q 3

D) P =

21 + 14Q 3

Solve the equation by the Square Root Method. 256) x2 = 7 A) { 7, - 7}

256)

B) { 7}

C) {7, -7}

D) no real solution

Solve the problem. 257) It costs $27 per hour plus a flat fee of $20 for a plumber to make a house call. After writing an equation for this situation, suppose the total cost to have a plumber come to a house is $290. How many hours did the plumber work? A) 17 hr B) 21 hr C) 6 hr D) 10 hr

257)

Write the interval as an inequality involving x, and illustrate the inequality using the real number line. 258) [-6, 1]

A) -6 < x < 1

B) -6 < x 1

C) -6 x < 1

D) -6 x 1

Solve the equation. 259) |x| = -1 A) {-1}

B) {1}

C) {1, -1}

D) no solution

Solve the problem. 260) Ken and Kara are 30 miles apart on a calm lake paddling toward each other. Ken paddles at 4 miles per hour, while Kara paddles at 7 miles per hour. How long will it take them to meet? 1 8 hr A) 2 hr B) 10 hr C) 19 hr D) 2 4 11 Solve the equation. 261) 2(x + 1) + 4 = 10 A) {-8, 0}

B) {-6, 0}

C) {-8, 2}

D) {-6, 4}

Solve the problem. 262) Going into the final exam, which will count as three tests, Jerome has test scores of 61, 72, 59, 75, and 77. What score does Jerome need on the final in order to earn a C, which requires an average of 70? A) 70 B) 79 C) 72 D) 75 Write the interval as an inequality involving x, and illustrate the inequality using the real number line. 263) (4, )

A) x > 4

B) x 4

C) x > 4

D) x 4

Solve the equation by completing the square. 264) x2 + 16x + 43 = 0 A) {8 C) {8 +

43, 8 + 21}

258)

259)

260)

261)

262)

263)

264)

43}

B) {-8 - 21, -8 + D) {-16 + 43} 36

21}

Find the real solutions of the equation. 265) 2(x + 1)2 + 13(x + 1) + 20 = 0

7 B) {- , -5} 2

A) {2, 3}

5 C) {- , -5} 2

7 D) {- , -4} 2

Solve the problem. 266) Gary can hike on level ground 3 miles an hour faster than he can on uphill terrain. Yesterday, he hiked 37 miles, spending 2 hours on level ground and 5 hours on uphill terrain. Find his average speed on level ground. 6 3 3 2 A) 7 mph B) 7 mph C) 4 mph D) 5 mph 7 7 7 7

265)

266)

Find the real solutions of the equation. 267)

2-3 x=6 34 } A) { 3

Solve the equation by factoring. 268) x2 - 4x - 12 = 0 A) {2, -6}

269) 3x2 - 9 = 0 A) {- 3,

267) 2 } B) { 3

34 } C) { 3

B) {-2, 6}

D) no real solution

C) {-2, -6}

268)

D) {2, 6}

269) 3}

B) {4.5}

Find the real solutions of the equation. 270) x1/2 - 6x1/4 + 8 = 0 A) {-2, -4}

B) {2, 4}

Solve the inequality. Express your answer in set notation. 271) x2 > 1 A) {x| x < -1 or x 1} C) {x| x < -1 or x > 1}

C) {4}

D) {-3, 3}

C) {4, 16}

D) {16, 256}

B) {x| -1 x 1} D) {x| x -1 or x

271) 1}

Solve the equation by factoring. 18 = - 39 272) 15x + x A) {-

1 3 , } 2 5

270)

272) B) {15,

5 } 3

C) {2,

3 } 5

D) {- 2, -

3 } 5

Solve the inequality. Express your answer using interval notation. 273) -19 -2x - 5 < -11

273)

A) [3, 7)

B) (-7, -3]

C) (3, 7]

D) [-7, -3)

Solve the problem. 274) If a polygon, of n sides has have? A) 24 sides

1 n(n - 3) diagonals, how many sides will a polygon with 230 diagonals 2

B) 22 sides

C) 25 sides

D) 23 sides

275) The owners of a candy store want to sell, for $6 per pound, a mixture of chocolate-covered raisins, which usually sells for $3 per pound, and chocolate-covered macadamia nuts, which usually sells for $8 per pound. They have a 70-pound barrel of the raisins. How many pounds of the nuts should they mix with the barrel of raisins so that they hit their target value of $6 per pound for the mixture? A) 91 lb B) 105 lb C) 98 lb D) 112 lb Solve the equation in the complex number system. 276) x3 - 125 = 0 A) {5, -

B) {5} D) {5, -

C) {5, -5i, 5i}

Find the real solutions of the equation. 277) 3x - 2 = 2

4 B) { } 3

5 5 3 5 5 3 ,- + } 2 2 2 2

2 C) { } 3

Write the expression in the standard form a + bi. 278) -2i(-7 + 8i) A) -16 + 14i

275)

276)

5 5 3 5 5 3 i, - + i} 2 2 2 2

A) {4}

274)

B) 14i + 16i2

C) 14i - 16i2

277) D) {2}

278) D) 16 + 14i

Solve the inequality. Express your answer using interval notation. 279) -15 -2x - 3 -11

279)

A) [-6, -4]

B) (-6, -4)

C) [4, 6]

D) (4, 6)

Find the real solutions, if any, of the equation. Use the quadratic formula. -7 280) 4x = 1 + x A) {C) {

113 1 ,

113

Solve the equation. 281) 10x = 16 8 A) 5

113

}

B) {

}

113 1 + ,

280) 8

113

}

D) no real solution

8 B) 5

5 C) 8

5 D) 8

Find the real solutions of the equation by factoring. 282) 8x3 + 64x2 + 120x = 0 A) {-3, -5}

281)

282)

1 B) {- , -5} 3

C) {0, 3, 5}

D) {0, -3, -5}

Solve the problem. 283) An experienced bank auditor can check a bank's deposits twice as fast as a new auditor. Working together it takes the auditors 18 hours to do the job. How long would it take the experienced auditor working alone? A) 36 hr B) 18 hr C) 27 hr D) 54 hr 284) A 33-inch-square TV is on sale at the local electronics store. If 33 inches is the measure of the diagonal of the screen, use the Pythagorean theorem to find the length of the side of the screen. 33 2 33 1,089 in. in. in. A) 33 in. B) C) D) 2 2 2

283)

284)

Solve the inequality. Express your answer using interval notation. 285) |5x + 2| > 3 1 1 A) (- , -1] or [ , ) B) (-1, ) 5 5 C) [-1,

1 ] 5

285)

1 D) (- , -1) or ( , ) 5

Solve the problem. 286) An open box is to be constructed from a square sheet of plastic by removing a square of side 4 inches from each corner, and then turning up the sides. If the box must have a volume of 1,600 cubic inches, find the length of one side of the open box. A) 19 in. B) 28 in. C) 20 in. D) 24 in. Find the real solutions of the equation. 287) x6 + 63x3 - 64 = 0 A) {-4, 1}

B) {4, -1}

C) {64}

Solve the equation in the complex number system. 288) x2 + 49 = 0 A) {7}

B) {-7i, 7i}

C) {-7, 7}

D) {4}

D) {7i}

Solve the equation. 5 2 7 289) + = x 5 x A) {5}

286)

287)

288)

289) B) {-2}

C) {2}

D) {-5}

Use the discriminant to determine whether the quadratic equation has two unequal real solutions, a repeated real solution, or no real solution without solving the equation. 290) x2 - 6x + 9 = 0 290)

A) repeated real solution B) two unequal real solutions C) no real solution

Solve the problem. 291) An auto repair shop charged a customer $384 to repair a car. The bill listed $54 for parts and the remainder for labor. If the cost of labor is $55 per hour, how many hours of labor did it take to repair the car? A) 6 hr B) 7 hr C) 6.5 hr D) 5 hr 292) The perimeter of a triangle is 65 centimeters. Find the lengths of its sides, if the longest side is 7 centimeters longer than the shorter side, and the remaining side is 4 centimeters longer than the shorter side. A) 20 cm, 22 cm, 23 cm B) 18 cm, 22 cm, 25 cm C) 16 cm, 20 cm, 29 cm D) 17 cm, 20 cm, 28 cm Solve the equation by the Square Root Method. 293) (x + 4)2 = 11

291)

292)

293)

A) { 11, - 11} C) {7}

B) {-4 + 11, -4 - 11} D) {4 + 11, 4 - 11} 40

Solve the problem. 294) The length of a vegetable garden is 7 feet longer than its width. If the area of the garden is 98 square feet, find its dimensions. A) 8 ft by 15 ft B) 6 ft by 13 ft C) 6 ft by 15 ft D) 7 ft by 14 ft Solve the inequality. Express your answer using interval notation. 295) |x| < -2 A) {-2} B) (-2, 2) C) (- , )

D) no solution

Solve the equation. 4x -2x + 9 +2=296) 2 3 A)

39 14

3 7 - i 4 8

15 2

C) -

39 2

D) -

15 2

297)

36 8 i + 17 17

9 7 - i 4 8

12 14 i + 17 17

Express the graph shown using interval notation. Also express it as an inequality involving x. 298)

A) (- , 5] x 5

B) (- , 5) x<5

C) (5, ) x>5

B) 21.9 sec

Find the real solutions of the equation. 300) 3x + 10 - x + 2 = 2 A) {-3} B) {-2, 2}

298)

D) [5, ) x 5

Solve the problem. 299) As part of a physics experiment, Ming drops a baseball from the top of a 350-foot building. To the nearest tenth of a second, for how many seconds will the baseball fall? (Hint: Use the formula h = 16t2 , which gives the distance h, in feet, that a free-falling object travels in t seconds.) A) 87.5 sec

295)

296)

Write the expression in the standard form a + bi. 6 + 2i 297) 5 - 3i A)

294)

C) 4.7 sec

D) 1.2 sec

C) {-2}

D) {2}

299)

300)

Solve the inequality. Express your answer using interval notation. 301) -9x - 6 -3(2x - 3)

301)

A) [-5, )

B) (- , -5)

C) (- , -5]

D) [-5, )

Solve the equation. 1 1 x+5 = 302) + x x+4 x+4 A) {-1}

302) B) {-4}

C) {4}

D) {1}

Solve the inequality. Express your answer using interval notation. 303) |7x - 7| - 6 < 0 1 13 1 ) A) ( , B) (- , ) 7 7 7 C) (- ,

1 13 ) or ( , ) 7 7

303)

D) no solution

Solve the problem. 304) It costs $42 per hour plus a flat fee of $33 for a plumber to make a house call. What is an equation of the form y = ax + b for this situation? A) y = 33x B) y = 42x C) y = 42x + 33 D) y = 33x + 42 Solve the equation. 2x 3 1 = 305) x2 - 16 x2 - 16 x + 4 A)

7 3

305) B) - 1

C) -

1 3

D) 1

Express the graph shown using interval notation. Also express it as an inequality involving x. 306)

A) (4, 7) 4<x<7

304)

B) [4, 7) 4 x<7

C) (4, 7] 4<x 7 42

D) [4, 7] 4 x 7

306)

Find the real solutions of the equation. 307) 2x + 5 - x - 2 = 3 A) {3, 8} B) {-2}

C) {2}

D) {2, 38}

Solve the problem. 308) In one city, the local cable TV company charges $1.05 for each pay-per-view movie watched. In addition, each monthly bill contains a basic customer charge of $16.50. If last month's bills ranged from a low of $22.80 to a high of $38.55, over what range did customers watch pay-per-view movies? A) movies watched varied from 5 to 22 inclusive B) movies watched varied from 7 to 22 inclusive C) movies watched varied from 6 to 21 inclusive D) movies watched varied from 5 to 20 inclusive Find the real solutions of the equation by factoring. 309) 2x5 = 162x3 A) {-9 2, 0, 9 2}

49 7 i + 50 50

B) {-9, 9}

C) {-9, 0, 9}

D) {0}

310)

49 7 i + 48 48

49 7 i 48 48

49 7 i 50 50

Express the graph shown using interval notation. Also express it as an inequality involving x. 311)

A) [-6, -5) -6 x < -5

308)

309)

Write the expression in the standard form a + bi. 7 310) 7+i A)

307)

B) [-6, -5] -6 x -5

C) (-6, -5] -6 < x -5

D) (-6, -5) -6 < x < -5

Find the real solutions of the equation. 312) x = 6 x A) {0, 36} B) {-6, 6}

C) {0, 6}

D) {-36, 36}

Solve the equation. 313) |x| = 8 A) {-8}

C) {8}

D) {64}

B) {-8, 8}

311)

312)

313)

Use the discriminant to determine whether the quadratic equation has two unequal real solutions, a repeated real solution, or no real solution without solving the equation. 314) x2 - 6x + 5 = 0 314)

A) repeated real solution B) two unequal real solutions C) no real solution

Solve the problem. 315) A chemist needs 140 milliliters of a 62% solution but has only 56% and 84% solutions available. Find how many milliliters of each that should be mixed to get the desired solution. A) 30 mL of 56%; 110 mL of 84% B) 20 mL of 56%; 120 mL of 84% C) 110 mL of 56%; 30 mL of 84% D) 120 mL of 56%; 20 mL of 84% Find the real solutions, if any, of the equation. Use the quadratic formula. 316) x2 + 7x + 2 = 0 -7 - 41 -7 + 41 , } A) { 2 2

B) {

-7 - 57 -7 + 57 , } 2 2

D) {

C) {

41 7 + ,

316) 2

}

-7 - 41 -7 + 41 , } 14 14

Find the real solutions of the equation by factoring. 317) 3x4 - 27x2 = 0

317)

B) {-3 3, 0, 3 3}

A) {-3, 3}

C) {-3, 0, 3}

D) {0}

Find the real solutions of the equation. 5 -2 = 318) 2 + 2x - 1 (2x - 1)2 A) {-2, -

1 } 2

B) {-

318) 1 1 ,- } 2 4

C) {-

1 1 , } 2 4

D) {-

1 , 0} 2

Write the inequality using interval notation, and illustrate the inequality using the real number line. 319) t -10

A) (-10, ]

B) [-10, )

C) [-10, ]

D) (-10, )

Solve the formula for the indicated variable. 320) A = P(1 + rt) for r A+P P-A A) r = B) r = tP tP Write the expression in the standard form a + bi. 321) (1 + i)5 A) 4 - 4i

315)

B) -4 + 4i

A-P C) r = tP

A+P D) r = tP

C) -4 - 4i

D) -4 + i

319)

320)

321)

Solve the problem. 322) Five friends drove at an average rate of 60 miles per hour to a weekend retreat. On the way home, they took the same route but averaged 65 miles per hour. What was the distance between home and the retreat if the round trip took 10 hours? 1 A) 312 mi B) 7800 mi C) 624 mi D) 5 mi 5 Find the real solutions of the equation. 323) 5x + 6 = 6 42 A) { } B) {6} 5

C) {

36 } 5

323) D) {36}

Solve the problem. 324) After a 16% price reduction, a boat sold for $26,880. What was the boat's price before the reduction? (Round to the nearest cent, if necessary.) A) $168,000.00 B) $31,180.80 C) $32,000 D) $4,300.80 Find the real solutions of the equation. 325) (2x + 3)1/2 = 5 3 A) {- } 2

B) -10 - 62i

Find the real solutions of the equation. 327) x2/3 - 9x1/3 + 20 = 0 A) {4, 5}

C) {6}

D) {11}

C) -10 + 62i

D) 24i2 + 62i + 14

B) {-125, -64}

C) {64, 125}

D) {-5, -4}

Fill in the blank with the correct inequality symbol. 12. 328) If x > -6, then -2x A) >

Find the real solutions of the equation by factoring. 329) x3 - 36x = 0 B) {0, 6, -6}

D) <

C) {0, 6}

D) {0, -6}

Solve the problem. 330) How many liters of 80% hydrochloric acid must be mixed with 40% hydrochloric acid to get 15 liters of 65% hydrochloric acid? Write your answer rounded to three decimals. A) 8 L B) 3.125 L C) 4.688 L D) 9.375 L Solve the equation. 4 1 1 = 331) 3x x+1 x(2x + 2) A) -

5 2

326)

327)

328)

A) {0, 36}

324)

325)

25 B) { } 2

Write the expression in the standard form a + bi. 326) (7 + 3i)(2 + 8i) A) 38 - 50i

322)

329)

330)

331) B) -

5 6

C) no solution

D) {-5}

Solve the problem. 332) Kevin invested part of his $10,000 bonus in a certificate of deposit that paid 6% annual simple interest, and the remainder in a mutual fund that paid 11% annual simple interest. If his total interest for that year was $800, how much did Kevin invest in the mutual fund? A) $5,000 B) $4,000 C) $6,000 D) $3,000 Solve the equation. x x 333) - 4 = - 2 3 2

332)

333)

A) - 12

B) 12

1 3

D) -

1 3

Solve the problem. 334) How much pure acid should be mixed with 3 gallons of a 50% acid solution in order to get an 80% acid solution? A) 7.5 gal B) 12 gal C) 4.5 gal D) 1.5 gal Solve the inequality. Express your answer using interval notation. 1 335) 0 < (2x - 4)-1 < 2

334)

335)

A) (- , 3)

B) [3, )

C) (- , 3]

D) (3, )

Write the expression in the standard form a + bi. 336) If z = 6 + 6i and w = -3 + i, evaluate z - w. A) 3 + 7i B) 9 - 5i

C) -9 - 5i

D) 9 + 5i

Solve the equation by completing the square. 337) 3x2 - 2x - 6 = 0 A) { C) {

337)

-1 - 19 -1 + 19 , } 3 3 3-

19 3 + ,

336)

B) {-6,

}

D) {

20 } 3 3

19 1 + ,

}

Write the expression in the standard form a + bi. 338) i12 A) -1

B) i

C) -i

Solve the inequality. Express your answer using interval notation. 339) |x| > -2 A) (-2, 2) B) {2} C) (- , )

D) 1

D) no solution

Solve the problem. 340) A boat heads upstream a distance of 30 miles on the Mississippi river, whose current is running at 5 miles per hour. If the trip back takes an hour less, what was the speed of the boat in still water? Give the answer rounded to two decimal places, if necessary. A) 6 mph B) 18.03 mph C) 15 mph D) 16.58 mph Solve the equation by factoring. 341) 3x2 + 12x - 15 = 0 A) {- 1, - 5}

342) x2 - 100 = 0 A) {100}

B) {1, 5}

C) {1, - 5}

D) {- 1, 5}

B) {-10}

C) {10, -10}

D) {10}

Find the real solutions of the equation by factoring. 343) x3 + 7x2 + 12x = 0 A) {-3, -4}

B) {0, -3, -4}

C) {3, 4}

Solve the equation. 344) -7x + 2 + 5x = -2x + 7 A) no solution C) all real numbers

D) {0, 3, 4}

B) {5} D) {-2}

Solve the problem. 345) A freight train leaves a station traveling at 32 km/h. Two hours later, a passenger train leaves the same station traveling in the same direction at 52 km/h. How long does it takes the passenger train to catch up to the freight train? A) 4.2 hr B) 5.2 hr C) 2.2 hr D) 3.2 hr Solve the inequality. Express your answer using interval notation. 346) 5 - 3(1 - x) -7

A) [-3, )

B) (- , -3]

C) (- , -2]

D) (- , -3)

338)

339)

340)

341)

342)

343)

344)

345)

346)

Solve the problem. 347) Jim has gotten scores of 82 and 65 on his first two tests. What score must he get on his third test to keep an average of 80 or better? A) at least 75 B) at least 93 C) at least 73.5 D) at least 91 Solve the equation by factoring. 348) 54x2 + 30x = 0 5 5 A) { , - } 9 9

Solve the equation. 349) |x + 4| = 0 A) {-4} Find a and b. 350) If |x + 1| 2, then a A) a =

1 1 ,b= 6 2

1 x+5

5 B) { , 0} 9

C) {-

5 , 0} 9

B) {4}

C) {4, -4}

348) D) {0}

D) no solution

B) a =

1 1 ,b= 2 6

C) a =

1 1 ,b= 8 6

D) a =

1 1 ,b= 6 8

352) Don James wants to invest $50,000 to earn $5,820 per year. He can invest in B-rated bonds paying 15% per year or in a Certificate of Deposit (CD) paying 8% per year. How much money should be invested in each to realize exactly $5,820 in interest per year? A) $24,000 in B-rated bonds and $26,000 in a CD B) $23,000 in B-rated bonds and $27,000 in a CD C) $26,000 in B-rated bonds and $24,000 in a CD D) $27,000 in B-rated bonds and $23,000 in a CD Solve the formula for the indicated variable. 353) PV = nRT for T nPV PVR A) T = B) T = R n

PV C) T = R

PV D) T = nR

Solve the problem. 354) 1 - i is a solution of a quadratic equation with real coefficients. Find the other solution. A) -1 + i B) 1 + i C) 1 - i D) -1 - i Write the expression in the standard form a + bi. 355) 2i15 - i7

356)

B) -i

C) i

D) 1

-12 - 48i 3 - 5i

A) -6 + 6i

349)

350)

Solve the problem. 351) Two trains leave a train station at the same time. One travels east at 10 miles per hour. The other train travels west at 8 miles per hour. In how many hours will the two trains be 153 miles apart? A) 9 hr B) 4.3 hr C) 8.5 hr D) 17 hr

A) -1

347)

351)

352)

353)

354)

355)

356) B) -6 - 6i

C) 6 + 6i 48

D) 6 - 6i

Solve the equation by factoring. 357) x2 - 7x + 12 = 0 A) {-4, -3}

B) {4, 3}

C) {4, -3}

357)

D) {-4, 3}

Find the real solutions of the equation. 358) 5x4 + 13x2 - 6 = 0 A) {-

3 , 5

3 } 5

358)

2 2 B) {- , } 5 5

C) {-

D) {-

2 , 5

2 } 5

Solve the inequality. Express your answer using interval notation. 1 -1/2 >0 359) 4 - x 2

A) (8, )

B) (- , 8]

C) [8, )

D) (- , 8)

359)

Solve the problem.

360) The formula A = P(1 + r)2 is used to find the amount of money, A, in an account after P dollars have been invested in the account paying an annual interest rate, r, for 2 years. Find the interest rate r if $500 grows to $1,125 in 2 years. A) 50% B) 250% C) 125% D) 5%

Find the real solutions of the equation. 361) (x + 3)1/3 = -2 A) {-9}

B) {-11}

C) {1}

D) no real solution

360)

361)

Solve the inequality. Express your answer using interval notation. 3x + 1 <3 362) 0 2

362)

A) [-

1 5 , ] 3 3

B) [-

1 5 , ) 3 3

C) (-

1 5 , ) 3 3

D) (-

1 5 , ] 3 3

Perform the indicated operations and express your answer in the form a + bi. 363) -16 A) -4i

B) 4i

C) -i 4

363) D) ±4

Express the graph shown using interval notation. Also express it as an inequality involving x. 364)

A) (-6, ) x > -6

B) (- , -6] x -6

C) (- , -6) x < -6

D) [-6, ) x -6

B) {-5, 2}

C) {-2, 5}

D) {-8, 125}

23 B) { } 3

11 C) { } 3

Find the real solutions of the equation. 365) x2/3 - 3x1/3 - 10 = 0 A) {-125, 8}

366) (3x - 7)1/2 = 4 22 A) { } 3

364)

365)

366) D) no real solution

Answer Key Testname: CHAPTER 1 1) D 2) C 3) C 4) {-8, 9} 5) 60 min 6) x > 100 mi 3 7) { } 2 8) x 3 9) $29.31 x $33.50, where x represents the amount of sales tax; no 3 10) { } 2 11) 3.2 in. 12) |b - h| 0.2 13) $10,000 in bonds; $13,000 in certificates of deposit 14) 4 - i 15) |x + 7| > 3; x < -10 or x > -4 16) 40 x < 90, where x represents Bob's score on the fifth test 17) |x - 40| 0.75; 39.25 x 40.75 18) {2 + 3, 2 - 3} 19) D 20) D 21) C 22) D 23) A 24) C 25) C 26) B 27) D 28) B 29) A 30) A 31) D 32) C 33) B 34) D 35) C 36) C 37) A 38) C 39) D 40) D 41) D 42) A 43) D 44) C 45) D 46) D 47) B 51

Answer Key Testname: CHAPTER 1 48) A 49) D 50) D 51) C 52) A 53) D 54) A 55) C 56) D 57) C 58) C 59) C 60) C 61) B 62) B 63) C 64) B 65) A 66) D 67) A 68) A 69) B 70) A 71) D 72) B 73) C 74) B 75) D 76) C 77) D 78) A 79) C 80) B 81) A 82) C 83) C 84) D 85) B 86) A 87) B 88) C 89) C 90) C 91) A 92) C 93) C 94) C 95) A 96) A 97) A 52

Answer Key Testname: CHAPTER 1 98) B 99) C 100) D 101) C 102) D 103) B 104) D 105) D 106) B 107) B 108) A 109) B 110) B 111) A 112) B 113) C 114) C 115) D 116) B 117) C 118) C 119) B 120) C 121) A 122) B 123) D 124) C 125) A 126) B 127) B 128) D 129) A 130) A 131) A 132) D 133) B 134) C 135) C 136) A 137) D 138) C 139) A 140) C 141) C 142) C 143) A 144) D 145) C 146) C 147) A 53

Answer Key Testname: CHAPTER 1 148) C 149) B 150) C 151) C 152) D 153) D 154) A 155) B 156) A 157) D 158) A 159) A 160) D 161) B 162) C 163) D 164) B 165) D 166) B 167) D 168) A 169) C 170) D 171) A 172) C 173) C 174) B 175) A 176) B 177) A 178) D 179) C 180) A 181) B 182) D 183) D 184) B 185) D 186) B 187) B 188) C 189) C 190) B 191) D 192) C 193) D 194) B 195) D 196) B 197) A 54

Answer Key Testname: CHAPTER 1 198) B 199) C 200) D 201) C 202) D 203) C 204) D 205) B 206) D 207) B 208) C 209) B 210) D 211) B 212) A 213) C 214) C 215) B 216) B 217) D 218) C 219) D 220) C 221) C 222) D 223) B 224) A 225) B 226) A 227) A 228) B 229) B 230) C 231) C 232) C 233) A 234) A 235) B 236) A 237) A 238) D 239) D 240) B 241) A 242) C 243) B 244) A 245) B 246) A 247) D 55

Answer Key Testname: CHAPTER 1 248) D 249) A 250) D 251) C 252) A 253) D 254) A 255) D 256) A 257) D 258) D 259) D 260) D 261) C 262) C 263) C 264) B 265) B 266) B 267) D 268) B 269) A 270) D 271) C 272) D 273) C 274) D 275) B 276) A 277) D 278) D 279) C 280) D 281) A 282) D 283) C 284) C 285) D 286) C 287) A 288) B 289) A 290) A 291) A 292) B 293) B 294) D 295) D 296) C 297) D 56

Answer Key Testname: CHAPTER 1 298) C 299) C 300) B 301) D 302) D 303) A 304) C 305) A 306) D 307) D 308) C 309) C 310) D 311) D 312) A 313) B 314) B 315) C 316) A 317) C 318) C 319) B 320) C 321) C 322) A 323) B 324) C 325) D 326) C 327) C 328) D 329) B 330) D 331) A 332) B 333) A 334) C 335) D 336) B 337) D 338) D 339) C 340) B 341) C 342) C 343) B 344) A 345) D 346) B 347) B 57

Answer Key Testname: CHAPTER 1 348) C 349) A 350) A 351) C 352) C 353) D 354) B 355) B 356) D 357) B 358) D 359) D 360) A 361) B 362) B 363) B 364) B 365) D 366) B

Chapter 2 Exam Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem.

1) The height of a baseball (in feet) at time t (in seconds) is given by y = -16x2 + 80x + 5. Which one of the following points is not on the graph of the equation? A) (4, 69) B) (2, 117) C) (3, 101) D) (1, 69)

Find the slope of the line and sketch its graph. 2) 4x - 5y = -3

A) slope = -

4 5

B) slope = -

5 4

C) slope =

5 4

D) slope =

4 5

Find the distance d(P1 , P2 ) between the points P1 and P2 .

3) P1 = (-0.5, -0.1); P2 = (1.4, -1.2) Round to three decimal places, if necessary. A) 15

B) 2.295

C) 2.195

3) D) 6.943

Write a general formula to describe the variation. 4) The centrifugal force F of an object speeding around a circular course varies directly as the product of the object's mass m and the square of it's velocity v and inversely as the radius of the turn r. kmv2 km 2 v kmr kmv A) F = B) F = C) F = D) F = r r r v2 Solve.

5) A truck rental company rents a moving truck one day by charging $29 plus $0.11 per mile. Write a linear equation that relates the cost C, in dollars, of renting the truck to the number x of miles driven. What is the cost of renting the truck if the truck is driven 180 miles? A) C = 29x + 0.11; $5,220.11 B) C = 0.11x - 29; $9.20 C) C = 0.11x + 29; $48.80 D) C = 0.11x + 29; $30.98

Write a general formula to describe the variation. 6) The volume V of a right circular cone varies directly with the square of its base radius r and its 1 height h. The constant of proportionality is . 3 A) V =

1 2 r h 3

B) V =

1 2 r h 3

C) V =

1 rh 3

Write the standard form of the equation of the circle with radius r and center (h, k). 7) r = 19; (h, k) = (0, -1) A) (x + 1)2 + y2 = 361 B) (x - 1)2 + y2 = 361 C) x2 + (y - 1)2 = 19

D) x2 + (y + 1)2 = 19

D) V =

1 2 2 r h 3

Write a general formula to describe the variation. 8) R varies directly with g and inversely with the square of h; R = 3 when g = 3 and h = 5. h2 g g A) R = 25gh 2 B) R = 25 C) R = 5 D) R = 5 2 g h h2 Graph the line containing the point P and having slope m. 9) P = (8, 4); slope undefined

Find the center (h, k) and radius r of the circle. Graph the circle.

10) x2 + y2 + 6x + 2y + 6 = 0

10)

A) (h, k) = (3, -1); r = 2

B) (h, k) = (3, 1); r = 2

C) (h, k) = (-3, -1); r = 2

D) (h, k) = (-3, 1); r = 2

Solve the problem. 11) A middle school's baseball playing field is a square, 50 feet on a side. How far is it directly from home plate to second base (the diagonal of the square)? If necessary, round to the nearest foot. A) 72 feet B) 70 feet C) 78 feet D) 71 feet Find an equation for the line with the given properties. 12) Perpendicular to the line -7x - 6y = -25; containing the point (7, -6) A) -6x - 7y = -84 B) -6x + 7y = -84 C) -6x - 7y = -25

D) -7x + 6y = -84

11)

12)

Find the midpoint of the line segment joining the points P1 and P2 .

13) P1 = (7, 1); P2 = (-16, -16) A) -9, -15

23 17 , B) 2 2

9 15 C) - , 2 2

13) D) 9, 15

Solve the problem. 14) Find all the points having an x-coordinate of 9 whose distance from the point (3, -2) is 10. A) (9, -12), (9, 8) B) (9, 2), (9, -4) C) (9, 13), (9, -7) D) (9, 6), (9, -10)

14)

Find the slope-intercept form of the equation of the line with the given properties. 15) Horizontal; containing the point (-8.1, -3.0) A) y = 0 B) y = -8.1 C) y = -3.0

15)

D) y = 11.1

Solve the problem. 16) The amount of simple interest earned on an investment over a fixed amount of time is jointly proportional to the principle invested and the interest rate. A principle investment of $4,200.00 with an interest rate of 2% earned $84.00 in simple interest. Find the amount of simple interest earned if the principle is $2,800.00 and the interest rate is 6%. A) $56.00 B) $168.00 C) $16,800.00 D) $252.00 Find the distance d(P1 , P2 ) between the points P1 and P2 .

17) P1 = (7, -2); P2 = (3, -4) A) 2

16)

17) C) 12 3

B) 12

D) 2 5

Solve the problem. 18) If a circle of radius 4 is made to roll along the x-axis, what is the equation for the path of the center of the circle? A) x = 4 B) y = 8 C) y = 0 D) y = 4 Graph the equation. 19) x2 + (y - 3)2 = 9

18)

19)

List the intercepts for the graph of the equation. 20) y2 = x + 25 A) (5, 0), (0, 25), (0, -25) C) (0, -5), (25, 0), (0, 5)

20)

B) (0, -5), (-25, 0), (0, 5) D) (-5, 0), (0, -25), (5, 0)

Solve the problem. 21) If the force acting on an object stays the same, then the acceleration of the object is inversely proportional to its mass. If an object with a mass of 25 kilograms accelerates at a rate of 9 meters per second per second (m/sec2 ) by a force, find the rate of acceleration of an object with a mass of 5 kilograms that is pulled by the same force. 9 A) 45 m/sec2 B) m/sec2 5

C) 40 m/sec2

D) 36 m/sec2

21)

Write the standard form of the equation of the circle. 22)

22)

A) (x - 6)2 + (y - 5)2 = 2 C) (x + 6)2 + (y + 5)2 = 2

B) (x - 6)2 + (y - 5)2 = 4 D) (x + 6)2 + (y + 5)2 = 4

Find the center (h, k) and radius r of the circle with the given equation. 23) x2 + y2 + 2x - 14y = 14

23)

List the intercepts of the graph. 24)

24)

A) (h, k) = (-7, 1); r = 64 C) (h, k) = (7, -1); r = 8

A) C) -

2 2

, 0 , (-3, 0), , 0 , (0, -3),

2 2

B) (h, k) = (1, -7); r = 64 D) (h, k) = (-1, 7); r = 8

B) 0, -

D) 0, -

2 2

, (0, -3), 0, , (-3, 0), 0,

2 2

List the intercepts of the graph.Tell whether the graph is symmetric with respect to the x-axis, y-axis, origin, or none of these. 25) 25)

A) intercepts: (2, 0) and (-2, 0 symmetric with respect to y-axis B) intercepts: (2, 0) and (-2, 0) symmetric with respect to x-axis, y-axis, and origin C) intercepts: (0, 2) and (0, -2) symmetric with respect to x-axis, y-axis, and origin D) intercepts: (0, 2) and (0, -2) symmetric with respect to origin Find the general form of the equation of the the circle. 26) Center at the point (-5, -3); tangent to y-axis A) x2 + y2 - 10x - 6y + 9 = 0

B) x2 + y2 + 10x + 6y + 25 = 0

C) x2 + y2 + 10x + 6y + 59 = 0

D) x2 + y2 + 10x + 6y + 9 = 0

26)

Graph the equation by plotting points. 27) y = 3x - 9

27)

List the intercepts and type(s) of symmetry, if any. 28) y2 = -x + 4 A) intercepts: (-4, 0), (0, 2), (0, -2) symmetric with respect to x-axis C) intercepts: (4, 0), (0, 2), (0, -2) symmetric with respect to x-axis

B) intercepts: (0, -4), (2, 0), (-2, 0) symmetric with respect to y-axis D) intercepts: (0, 4), (2, 0), (-2, 0) symmetric with respect to y-axis

28)

Find an equation for the line, in the indicated form, with the given properties. 29) Containing the points (4, 6) and (-7, -1); slope-intercept form 7 38 7 x+ (x - 4) A) y = B) y - 6 = 11 11 11 C) y = mx +

38 11

D) y = -

29)

7 38 x+ 11 11

Identify the points in the graph for the ordered pairs.

30) (0, 2), (4, 3) A) C and E

B) C and K

C) F and E

D) B and C

If y varies inversely as x, write a general formula to describe the variation. 31) y = 35 when x = 7 1 245 A) y = B) y = C) y = 5x 245x x

x D) y = 245

Give the coordinates of the points shown on the graph. 32)

30)

31)

32)

A) C = (-5, 4), D = (6, -3) C) C = (4, -5), D = (-3, 6)

B) C = (-5, -3), D = (4, -3) D) C = (-5, 4), D = (-3, 6)

Find an equation for the line with the given properties. 1 33) Perpendicular to the line y = x + 3; containing the point (2, -2) 6 A) y = - 6x - 10

B) y = 6x - 10

C) y = - 6x + 10

Find the slope and y-intercept of the line. 34) 3x + y = 4

D) y = -

1 4 B) slope = - ; y-intercept = 3 3

A) slope = -3; y-intercept = 4 C) slope =

33)

3 1 ; y-intercept = 4 4

1 6

34)

D) slope = 3; y-intercept = 4

Find the slope of the line. 35)

A) -

1 5 x6 3

35)

B) 6

Graph the line containing the point P and having slope m. 13 36) P = (-7, -5); m = 10

1 6

D) -6

36)

Write a general formula to describe the variation. 37) The illumination I produced on a surface by a source of light varies directly as the candlepower c of the source and inversely as the square of the distance d between the source and the surface. kc2 kd2 kc A) I = kcd2 B) I = C) I = D) I = 2 c d d2 38) The square of G varies directly with the cube of x and inversely with the square of y; G = 3 when x = 3 and y = 5 3.419920967e+16 y3 7.91648372e+13 3 (x + y2 ) A) G2 = B) G2 = 3.518437209e+15 x2 5.93736279e+15 C) G2 =

25 x3 3 y2

D) G2 = 5

38)

x3 y2

39) The safety load of a beam with a rectangular cross section that is supported at each end varies directly as the product of the width W and the square of the depth D and inversely as the length L of the beam between the supports. k(W + D2 ) kWD2 kL kWD A) = B) = C) = D) = L L L WD2

37)

39)

Give the coordinates of the points shown on the graph. 40)

40)

A) A = (6, 24), B = (1, -3) C) A = (4, 6), B = (-3, 1)

B) A = (4, 1), B = (6, 1) D) A = (4, 6), B = (1, -3)

Graph the circle with radius r and center (h, k). 41) r = 6; (h, k) = (3, 0)

41)

Solve the problem. 42) If (5, 2) is the endpoint of a line segment, and (10, 5) is its midpoint, find the other endpoint. A) (15, -1) B) (11, 12) C) (-5, -4) D) (15, 8) Solve.

43) Each month a gas station sells x gallons of gas at $1.92/gallon. The cost to the owner of the gas station for each gallon of gas is $1.32. The monthly fixed cost for running the gas station is $37,000. Write an equation that relates the monthly profit, in dollars, to the number of gallons of gasoline sold. Then use the equation to find the monthly profit when 75,000 gallons of gas are sold in a month. A) P = 1.32x - 37,000; $62,000 B) P = 0.60x - 37,000; $8000 C) P = 0.60x + 37,000; $82,000 D) P = 1.92x - 37,000; $107,000

Solve the problem. 44) The amount of water used to take a shower is directly proportional to the amount of time that the shower is in use. A shower lasting 24 minutes requires 4.8 gallons of water. Find the amount of water used in a shower lasting 4 minutes. A) 28.8 gal B) 20 gal C) 1.2 gal D) 0.8 gal Find the center (h, k) and radius r of the circle with the given equation. 45) x2 + y2 = 9 A) (h, k) = (3, 3); r = 3 C) (h, k) = (0, 0); r = 3

B) (h, k) = (3, 3); r = 9 D) (h, k) = (0, 0); r = 9

42)

43)

44)

45)

Find an equation for the line with the given properties. 46) The solid line L contains the point (3, 1) and is parallel to the dotted line whose equation is y = 2x. Give the equation for the line L in slope-intercept form.

A) y = 2x - 5

B) y - 1 = 2(x - 3)

C) y = 2x - 2

Decide whether the pair of lines is parallel, perpendicular, or neither. 47) 6x + 2y = 8 15x + 5y = 23 A) parallel B) perpendicular

46)

D) y = 2x + b

47) C) neither

Identify the points in the graph for the ordered pairs.

48) (3, 5), (-3, 0) A) I and G

B) D and J

C) D and G

D) L and J

48)

Solve.

49) A school has just purchased new computer equipment for $18,000.00. The graph shows the depreciation of the equipment over 5 years. The point (0, 18,000) represents the purchase price and the point (5, 0) represents when the equipment will be replaced. Write a linear equation in slope-intercept form that relates the value of the equipment, y, to years after purchase x . Use the equation to predict the value of the equipment after 4 years.

A) y = - 3600x + 18,000; value after 4 years is $3,600.00; C) y = - 18,000x + 18,000; value after 4 years is $-54,000.00

B) y = 18,000x + 5; value after 4 years is $3,600.00 D) y = 3600x - 18,000; value after 4 years is $3,600.00

Find an equation for the line with the given properties. 50) Perpendicular to the line y = 3; containing the point (2, 1) A) x = 2 B) y = 2 C) x = 1 51) Parallel to the line x - 3y = 3; containing the point (0, 0) 2 1 1 A) y = B) y = x + 3 C) y = x 3 3 3 Solve the problem. 52) Find all values of k so that the given points are (-5, 5), (k, 0) A) -7 B) 7

D) y = 1

1 D) y = - x 3

29 units apart.

C) -3, -7

50)

51)

52) D) 3, 7

Find the distance d(P1 , P2 ) between the points P1 and P2 .

53) P1 = (-3, -1); P2 = (6, -7) A) 45

49)

53)

B) 45 5

C) 3 13

Find an equation for the line with the given properties. 54) Parallel to the line -3x - y = 8; containing the point (0, 0) 1 1 A) y = -3x B) y = x C) y = x + 8 3 3

D) 15

1 D) y = - x 3

Write a general formula to describe the variation. 55) The surface area S of a right circular cone varies directly as the radius r times the square root of the sum of the squares of the base radius r and the height h. The constant of proportionality is . r2 + h 2 A) S = r r2 h B) S = r r2 + h 2 C) S = D) S = r r2 h 2

54)

55)

Plot the point A. Plot the point B that has the given symmetry with point A. 56) A = (-2, 3); B is symmetric to A with respect to the y-axis

56)

Find the slope of the line. 57)

A) -

1 8

57)

B) 8

Find an equation for the line with the given properties. 58) Vertical line; containing the point (8.9, 6.0) A) x = 6.0 B) x = 8.9 Solve.

1 8

C) x = 0

D) - 8

D) x = 14.9

59) An investment is worth $2,384 in 1,992. By 1,995 it has grown to $3,755. Let y be the value of the investment in the year x, where x = 0 represents 1,992. Write a linear equation that relates the value of the investment, y, to the year x. 1 x + 2,384 A) y = B) y = -457x + 2,384 457 C) y = 457x + 2,384

58)

59)

D) y = -457x + 5,126

Solve the problem. 60) Body-mass index, or BMI, takes both weight and height into account when assessing whether an individual is underweight or overweight. BMI varies directly as one's weight, in pounds, and inversely as the square of one's height, in inches. In adults, normal values for the BMI are between 20 and 25. A person who weighs 173 pounds and is 72 inches tall has a BMI of 23.46. What is the BMI, to the nearest tenth, for a person who weighs 120 pounds and who is 66 inches tall? A) 19.4 B) 18.7 C) 19 D) 19.7 If y varies inversely as x, write a general formula to describe the variation. 61) y = 0.2 when x = 0.5 10 A) y = 0.4x B) y = C) y = 10x x

0.1 D) y = x

Find an equation for the line, in the indicated form, with the given properties. 62) Containing the points (9, -6) and (0, 5); general form A) -15x + 5y = -25 B) 15x - 5y = -25 C) -11x + 9y = 45

D) 11x + 9y = 45

Find the slope-intercept form of the equation of the line with the given properties. 63) Slope = -7; y-intercept = 10 A) y = 10x + 7 B) y = -7x + 10 C) y = -7x - 10

D) y = 10x - 7

60)

61)

62)

63)

Graph the equation. 64) (x - 3)2 + y2 = 36

64)

Find the slope of the line through the points and interpret the slope. 65)

65)

A) 3; for every 1-unit increase in x, y will increase by 3 units 1 B) ; for every 3-unit increase in x, y will increase by 1 unit 3 C) -3; for every 1-unit increase in x, y will decrease by 3 units 1 D) - ; for every 3-unit increase in x, y will decrease by 1 unit 3 List the intercepts of the graph. 66)

66)

A) (-5, 0), (0, -5), (0, 5), (5, 0) C) (-5, 0), (0, 5)

B) (0, 5), (5, 0) D) (-5, 0), (0, -5), (0, 0), (0, 5), (5, 0)

Find the midpoint of the line segment joining the points P1 and P2 .

67) P1 = (4, 6); P2 = (-9, -3) A) -5, 3

13 9 , 2 2

C) 13, 9

Write the standard form of the equation of the circle with radius r and center (h, k). 68) r = 8; (h, k) = (0, 4) A) x2 + (y - 4)2 = 64 B) x2 + (y + 4)2 = 8 C) (x + 4)2 + y2 = 64

D) (x - 4)2 + y2 = 64

67) D) -

5 3 , 2 2

68)

List the intercepts of the graph.Tell whether the graph is symmetric with respect to the x-axis, y-axis, origin, or none of these. 69) 69)

A) intercepts: (-2, 0) and (2, 0) symmetric with respect to x-axis, y-axis, and origin B) intercepts: (0, -2) and (0, 2) symmetric with respect to x-axis, y-axis, and origin C) intercepts: (0, -2) and (0, 2) symmetric with respect to y-axis D) intercepts: (-2, 0) and (2, 0) symmetric with respect to origin Find the distance d(P1 , P2 ) between the points P1 and P2 .

70)

A) 5

70)

B) 6 2.91666667

233

D) 104

71)

A) 2

B) 1

C) 0

Give the coordinates of the points shown on the graph. 72)

72)

A) G = (7, -3), H = (2, -3) C) G = (7, 2), H = (-3, 2) Solve.

B) G = (7, 2), H = (2, -3) D) G = (2, 7), H = (-3, 2)

73) The relationship between Celsius (°C) and Fahrenheit (°F) degrees of measuring temperature is linear. Find an equation relating °C and °F if 10°C corresponds to 50°F and 30°C corresponds to 86°F. Use the equation to find the Celsius measure of 35° F. 9 5 160 5 ; °C A) C = F - 80; - 17 °C B) C = F 5 9 9 3 C) C =

5 160 335 F+ ; °C 9 9 9

D) C =

Write the equation in slope-intercept form. 74) x = 4y + 7 A) y = 4x - 7

1 7 B) y = x 4 4

5 85 F - 10; °C 9 9

1 C) y = x - 7 4

73)

7 D) y = x 4

74)

Solve the problem. 75) A power outage affected all homes and businesses within a 6 mi radius of the power station. If the power station is located 4 mi west and 2 mi north of the center of town, find an equation of the circle consisting of the furthest points from the station affected by the power outage. A) (x - 4)2 + (y + 2)2 = 36 B) (x + 4)2 + (y + 2)2 = 36 C) (x - 4)2 + (y - 2)2 = 36

Solve.

D) (x + 4)2 + (y - 2)2 = 36

76) When making a telephone call using a calling card, a call lasting 6 minutes cost $1.70. A call lasting 14 minutes cost $3.30. Let y be the cost of making a call lasting x minutes using a calling card. Write a linear equation that relates the cost of a making a call, y, to the time x. 283 A) y = 0.2x + 0.5 B) y = -0.2x + 2.9 C) y = 5x D) y = 0.2x - 10.7 10

Decide whether or not the points are the vertices of a right triangle. 77) (-5, -6), (1, -4), (0, -9) A) Yes B) No Solve the problem. 78) If (3, b) is a point on the graph of 3x - 2y = 17, what is b? 23 11 A) -4 B) C) 3 3 Solve.

75)

77)

78) D) 4

79) The average value of a certain type of automobile was $14,700 in 1,994 and depreciated to $9,360 in 1,999. Let y be the average value of the automobile in the year x, where x = 0 represents 1,994. Write a linear equation that relates the average value of the automobile, y, to the year x. 1 x - 9360 A) y = B) y = -1,068x + 9,360 1068 C) y = -1,068x + 14,700

76)

79)

D) y = -1,068x + 4,020

Determine whether the graph of the equation is symmetric with respect to the x-axis, the y-axis, and/or the origin. 4x 80) y = 80) x2 + 16 A) x-axis B) origin C) y-axis D) x-axis, y-axis, origin E) none Find the center (h, k) and radius r of the circle with the given equation. 81) x2 + y2 - 6x - 8y + 25 = 9 A) (h, k) = (-4, -3); r = 9 C) (h, k) = (4, 3); r = 3

B) (h, k) = (-3, -4); r = 9 D) (h, k) = (3, 4); r = 3

81)

Find an equation for the line with the given properties. 82) Perpendicular to the line x - 3y = 3; containing the point (3, 5) A) y = 3x - 14

B) y = - 3x - 14

C) y = - 3x + 14

Find the slope-intercept form of the equation of the line with the given properties. 83) Slope = 0; containing the point (8, -1) A) x = -1 B) y = 8 C) y = -1 Graph the equation by plotting points. 84) y = -x2 - 1

1 14 D) y = - x 3 3

D) x = 8

82)

83)

84)

Find the slope-intercept form of the equation of the line with the given properties. 85) Horizontal; containing the point (7, 9) A) x = 9 B) y = 7 C) x = 7

D) y = 9

Solve the problem. 86) x varies inversely as v, and x = 18 when v = 5. Find x when v = 45. A) x = 9 B) x = 2 C) x = 10

D) x = 25

Write a general formula to describe the variation. 87) z varies directly with the sum of the squares of x and y; z = 20 when x = 12 and y = 16 1 2 1 2 (x + y2) (x + y2) A) z = B) z = 40 20 C) z 2 = x2 + y2

D) z =

89) The amount of time it takes a swimmer to swim a race is inversely proportional to the average speed of the swimmer. A swimmer finishes a race in 30 seconds with an average speed of 5 feet per second. Find the average speed of the swimmer if it takes 37.5 seconds to finish the race. A) 6 ft/sec B) 3 ft/sec C) 4 ft/sec D) 5 ft/sec If y varies directly as x, write a general formula to describe the variation. 90) y = 6.4 when x = 0.8 A) y = 0.8x B) y = 0.125x C) y = 8x

D) y = x + 5.6

Solve the problem. 91) The power that a resistor must dissipate is jointly proportional to the square of the current flowing through the resistor and the resistance of the resistor. If a resistor needs to dissipate 24 watts of power when 2 amperes of current is flowing through the resistor whose resistance is 6 ohms, find the power that a resistor needs to dissipate when 6 amperes of current are flowing through a resistor whose resistance is 4 ohms. A) 48 watts B) 24 watts C) 144 watts D) 96 watts 92) A power outage affected all homes and businesses within a 16 mi radius of the power station. If the power station is located 9 mi north of the center of town, find an equation of the circle consisting of the furthest points from the station affected by the power outage. A) x2 + (y + 9)2 = 256 B) x2 + (y - 9)2 = 256 D) x2 + y2 = 256

86)

87)

1 (x2 + y2 ) 400

Solve the problem. 88) A motorcycle and a car leave an intersection at the same time. The motorcycle heads north at an average speed of 20 miles per hour, while the car heads east at an average speed of 48 miles per hour. Find an expression for their distance apart in miles at the end of t hours. A) 2t 13 miles B) 52t miles C) 52 t miles D) t 68 miles

C) x2 + (y - 9)2 = 16

85)

88)

89)

90)

91)

92)

Find the slope and y-intercept of the line. 3 93) y = x - 2 2 A) slope =

2 ; y-intercept = 2 3

C) slope = -

Solve.

93) B) slope =

3 ; y-intercept = 2 2

3 ; y-intercept = - 2 2

D) slope = - 2; y-intercept =

3 2

94) Each month a beauty salon gives x manicures for $12.00/manicure. The cost to the owner of the beauty salon for each manicure is $7.35. The monthly fixed cost to maintain a manicure station is $120.00. Write an equation that relates the monthly profit, in dollars, to the number of manicures given each month. Then use the equation to find the monthly profit when 200 manicures are given in a month. A) P = 4.65x; $930 B) P = 7.35x - 120; $1350 C) P = 4.65x - 120; $810 D) P =12x - 120; $2280

Solve the problem. 95) A rectangular city park has a jogging loop that goes along a length, width, and diagonal of the park. To the nearest yard, find the length of the jogging loop, if the length of the park is 125 yards and its width is 75 yards. A) 346 yards B) 145 yards C) 146 yards D) 345 yards

94)

95)

Determine whether the graph of the equation is symmetric with respect to the x-axis, the y-axis, and/or the origin. 96) y = -4x 96) A) y-axis B) origin C) x-axis D) x-axis, y-axis, origin E) none

Graph the equation by plotting points. 97) y = x - 2

97)

Find the general form of the equation for the line with the given properties. 2 98) Slope = ; y-intercept = 2 3 A) y =

2 x+2 3

B) y =

2 x-2 3

C) 2x - 3y = -6

Graph the line containing the point P and having slope m.

98) D) 2x + 3y = -6

99) P = (3, 0); m = - 2

99)

Find the center (h, k) and radius r of the circle with the given equation. 100) (x - 3)2 + (y + 9)2 = 36 A) (h, k) = (-9, 3); r = 6 C) (h, k) = (-9, 3); r = 36

100)

B) (h, k) = (3, -9); r = 6 D) (h, k) = (3, -9); r = 36

Find an equation for the line with the given properties. 101) Parallel to the line x = 7; containing the point (8, 4) A) y = 4 B) x = 8

C) y = 7

D) x = 4

101)

Determine whether the graph of the equation is symmetric with respect to the x-axis, the y-axis, and/or the origin. 102) 9x2 + y2 = 9 102) A) x-axis B) y-axis C) origin D) x-axis, y-axis, origin E) none

Find the center (h, k) and radius r of the circle with the given equation. 103) x2 + (y - 8)2 = 81 A) (h, k) = (8, 0); r = 81 C) (h, k) = (0, 8); r = 9

103)

B) (h, k) = (8, 0); r = 9 D) (h, k) = (0, 8); r = 81

Find the slope and y-intercept of the line. 104) x = 4 A) slope = 0; y-intercept = 4 C) slope undefined; no y-intercept

B) slope = 4; y-intercept = 0 D) slope undefined; y-intercept = 4

Find an equation for the line with the given properties. 105) Perpendicular to the line 7x + 4y = 24; containing the point (4, 1) A) -4x - 7y = -9 B) 7x - 4 = 7 C) -4x + 7y = -9

D) 4x - 4y = 24

Determine whether the given point is on the graph of the equation. 106) Equation: y = x2 - x Point: (-9, 78) A) No

104)

105)

106)

B) Yes

List the intercepts of the graph.Tell whether the graph is symmetric with respect to the x-axis, y-axis, origin, or none of these. 107) 107)

A) intercept: (0, 4) symmetric with respect to y-axis C) intercept: (0, 4) symmetric with respect to origin

B) intercept: (4, 0) symmetric with respect to x-axis D) intercept: (4, 0) symmetric with respect to y-axis

Determine whether the graph of the equation is symmetric with respect to the x-axis, the y-axis, and/or the origin. 108) y = 4x2 + 4 108) A) x-axis B) y-axis C) origin D) x-axis, y-axis, origin E) none

Graph the equation by plotting points. 109) x2 + 4y = 4

109)

Find the center (h, k) and radius r of the circle with the given equation. 110) x2 - 10x + 25 + (y - 9)2 = 4

110)

Find the slope and y-intercept of the line. 111) 15x + 8y = 3

111)

A) (h, k) = (5, 9); r = 2 C) (h, k) = (-5, -9); r = 4

B) (h, k) = (-9, -5); r = 4 D) (h, k) = (9, 5); r = 2

B) slope =

A) slope = 15; y-intercept = 3 C) slope =

15 3 ; y-intercept = 8 8

D) slope = -

15 3 ; y-intercept = 8 8

Write the standard form of the equation of the circle with radius r and center (h, k). 112) r = 19; (h, k) = (10, -1) A) (x - 1)2 + (y + 10)2 = 361 B) (x + 1)2 + (y - 10)2 = 361

112)

Find an equation for the line with the given properties. 113) Perpendicular to the line -5x - 2y = 5; y-intercept = 5 A) -2x + 5y = 25 B) -2x + 5y = -10 C) -5x - 2y = -10

113)

C) (x + 10)2 + (y - 1)2 = 19

D) (x - 10)2 + (y + 1)2 = 19

List the intercepts for the graph of the equation. 114) 9x2 + y2 = 9 A) (-1, 0), (0, -3), (0, 3), (1, 0) C) (-1, 0), (0, -9), (0, 9), (1, 0)

D) -5x - 2y = -25

B) (-9, 0), (0, -1), (0, 1), (9, 0) D) (-3, 0), (0, -1), (0, 1), (3, 0)

114)

Solve the problem. 115) A Ferris wheel has a diameter of 320 feet and the bottom of the Ferris wheel is 15 feet above the 115) ground. Find the equation of the wheel if the origin is placed on the ground directly below the center of the wheel, as illustrated.

320 ft.

15 ft.

A) x2 + (y - 175)2 = 25,600 C) x2 + (y - 160)2 = 102,400

B) x2 + y2 = 25,600 D) x2 + (y - 160)2 = 25,600

Write a general formula to describe the variation. 116) z varies jointly as the square root of x and the cube of y; z = 6 when x = 4 and y = 3. A) z = 3 xy2

B) z =

2.814749767e+14 x 7.599824371e+15 y2

1 3

D) z =

7.599824371e+15 x 2.814749767e+14 y2

C) z =

xy2

116)

Solve the problem. 117) If the voltage, V, in an electric circuit is held constant, the current, I, is inversely proportional to the resistance, R. If the current is 200 milliamperes (mA) when the resistance is 3 ohms, find the current when the resistance is 15 ohms. A) 40 mA B) 120 mA C) 995 mA D) 1,000 mA If y varies inversely as x, write a general formula to describe the variation. 1 118) y = when x = 32 8 A) y =

4 x

B) y =

1 4x

C) y =

Name the quadrant in which the point is located. 119) (11, -18) A) I B) II

C) III

Draw a complete graph so that it has the given type of symmetry. 120) origin

x 4

117)

118) D) y =

D) IV

1 x 256

119)

120)

Find an equation for the line with the given properties. 121) Vertical line; containing the point (7, -4) A) y = -4 B) x = -4

C) y = 7

D) x = 7

Write the standard form of the equation of the circle with radius r and center (h, k). 122) r = 4; (h, k) = (7, 4) A) (x + 7)2 + (y + 4)2 = 4 B) (x - 7)2 + (y - 4)2 = 16 C) (x + 7)2 + (y + 4)2 = 16

121)

122)

D) (x - 7)2 + (y - 4)2 = 4

Find the center (h, k) and radius r of the circle with the given equation. 123) 2(x + 5)2 + 2(y - 4)2 = 16 A) (h, k) = (5, -4); r = 4 2 C) (h, k) = (5, -4); r = 2 2

123)

B) (h, k) = (-5, 4); r = 4 2 D) (h, k) = (-5, 4); r = 2 2

Decide whether the pair of lines is parallel, perpendicular, or neither. 124) 3x - 6y = -20 18x + 9y = -18 A) parallel B) perpendicular

124) C) neither

List the intercepts for the graph of the equation. 125) x2 + y - 25 = 0 A) (5, 0), (0, 25), (0, -25) C) (-5, 0), (0, -25), (5, 0)

Find the slope and y-intercept of the line. 126) 6x - 3y = 18 1 A) slope = ; y-intercept = 3 2

126) B) slope = - 2; y-intercept = 6

C) slope = 2; y-intercept = -6

D) slope = 6; y-intercept = 18

Find an equation for the line with the given properties. 127) Perpendicular to the line -3x - y = 2; containing the point (0, A) y =

1 x+2 3

B) y = -

125)

B) (0, -5), (25, 0), (0, 5) D) (-5, 0), (0, 25), (5, 0)

1 2 x3 3

C) y =

Graph the circle with radius r and center (h, k). 128) r = 3; (h, k) = (3, 2)

2 ) 3

1 2 x3 3

127) D) y = -

1 3

128)

Name the quadrant in which the point is located. 129) (13, 17) A) I B) II

C) III

D) IV

Write the standard form of the equation of the circle with radius r and center (h, k). 130) r = 5; (h, k) = (3, 0) A) x2 + (y + 3)2 = 5 B) (x + 3)2 + y2 = 25 C) x2 + (y - 3)2 = 5

130)

D) (x - 3)2 + y2 = 25

Find the general form of the equation for the line with the given properties. 2 131) Slope = - ; containing the point (0, 3) 7 A) 2x + 7y = 21

129)

B) 7x + 2y = -21

C) 2x - 7y = 21

131) D) 2x + 7y = -21

List the intercepts of the graph. 132)

132)

A) (3, 0), (0, -3), (0, 1), (0, 5) C) (3, 0), (1, 0) (-5, 0), (0, 3)

B) (3, 0), (0, 3), (0, 1), (0, -5) D) (-3, 0), (1, 0), (5, 0), (0, 3)

Plot the point in the xy-plane. Tell in which quadrant or on what axis the point lies.

133) (3, 1)

133)

Quadrant IV

Quadrant II

Quadrant I

Find an equation for the line with the given properties. 134) The solid line L contains the point (4, 2) and is perpendicular to the dotted line whose equation is y = 2x. Give the equation of line L in slope-intercept form.

A) y =

1 x+4 2

C) y - 2 = -

134)

B) y - 2 = 2(x - 4)

1 (x - 4) 2

D) y = -

1 x+4 2

Plot the point in the xy-plane. Tell in which quadrant or on what axis the point lies. 135) (-5, 6)

Quadrant I

Quadrant III

135)

Quadrant II

Quadrant IV

Decide whether or not the points are the vertices of a right triangle. 136) (5, 1), (11, 1), (11, 4) A) Yes B) No

136)

Find the midpoint of the line segment joining the points P1 and P2 .

137) P1 = (y, 6); P2 = (0, 9) A)

y 15 , 2 2

B) y,

15 2

C) y, 15

137) D) -

y ,3 2

Solve the problem. 138) Find an equation in general form for the line graphed on a graphing utility.

A) x + 2y = -2

B) 2x + y = -1

7 2 x B) A = 16

1 x-1 2

C) y = -2x - 1

D) y = -

C) A = 28x2

28 D) A = x2

Write a general formula to describe the variation. 139) A varies inversely with x2 ; A = 7 when x = 4 112 A) A = x2

138)

139)

Solve. 140) A vendor has learned that, by pricing carmel apples at $1.75, sales will reach 81 carmel apples per day. Raising the price to $2.75 will cause the sales to fall to 41 carmel apples per day. Let y be the number of carmel apples the vendor sells at x dollars each. Write a linear equation that relates the number of carmel apples sold per day, y, to the price x. A) y = -40x + 151 C) y = -

B) y = -40x - 151

1 12953 x+ 40 160

D) y = 40x + 11

List the intercepts for the graph of the equation. 141) y = x2 + 9 A) (9, 0), (0, -3), (0, 3) C) (0, 9)

141)

B) (9, 0) D) (0, 9), (-3, 0), (3, 0)

Write an equation that expresses the relationship. Use k as the constant of variation. 142) a varies inversely as the square of t. k A) a = t2

140)

t C) a = k

k B) a = t

Graph the line containing the point P and having slope m. 143) P = (-6, 3); m = 0

t2 D) a = k

142)

143)

Write the equation in slope-intercept form. 144) 9x - 7y = 1 9 1 7 1 A) y = x + B) y = x + 7 7 9 9

C) y = 9x - 1

Find an equation for the line, in the indicated form, with the given properties. 145) Containing the points (-5, 2) and (3, -3); general form A) 7x - 6y = 3 B) -7x + 6y = 3 C) 5x - 8y = 9 146) Containing the points (4, 7) and (-8, -6); general form A) 13x + 12y = 32 B) -3x - 2y = -12 C) 3x + 2y = -12

9 1 D) y = x 7 7

D) -5x - 8y = 9

D) -13x + 12y = 32

Find the general form of the equation of the the circle. 147) Center at the point (2, -3); containing the point (5, -3) A) x2 + y2 - 4x + 6y + 22 = 0 B) x2 + y2 + 4x - 6y + 22 = 0 C) x2 + y2 + 4x - 6y + 4 = 0

A) b, 3

145)

146)

147)

D) x2 + y2 - 4x + 6y + 4 = 0

Find the midpoint of the line segment joining the points P1 and P2 .

148) P1 = (6b, 4); P2 = (7b, 1)

144)

13b 5 , B) 2 2

C) 13b, 5

148) 5b 13 , D) 2 2

Find the center (h, k) and radius r of the circle with the given equation. 149) 4x2 + 4y2 - 12x + 16y - 5 = 0

149)

A) (h, k) = (-

3 3 5 , 2); r= 2 2

3 3 5 B) (h, k) = ( , -2); r = 2 2

C) (h, k) = (-

3 , 2); r = 2

3 D) (h, k) = ( , -2); r = 2

30 2

Determine whether the graph of the equation is symmetric with respect to the x-axis, the y-axis, and/or the origin. 150) y = 6x4 - 8x + 4 150) A) y-axis B) origin C) x-axis D) x-axis, y-axis, origin E) none

Solve the problem. 151) If the resistance in an electrical circuit is held constant, the amount of current flowing through the circuit is directly proportional to the amount of voltage applied to the circuit. When 4 volts are applied to a circuit, 100 milliamperes (mA) of current flow through the circuit. Find the new current if the voltage is increased to 5 volts. A) 125 mA B) 150 mA C) 20 mA D) 120 mA 152) Find the equation of a circle in standard form with center at the point (-3, 2) and tangent to the line y = 4. A) (x - 3)2 + (y + 2)2 = 16 B) (x + 3)2 + (y - 2)2 = 4 C) (x + 3)2 + (y - 2)2 = 16

151)

152)

D) (x - 3)2 + (y + 2)2 = 4

Find the center (h, k) and radius r of the circle. Graph the circle. 153) x2 + y2 - 8x - 8y + 28 = 0

A) (h, k) = (4, -4); r = 2

153)

B) (h, k) = (4, 4); r = 2

C) (h, k) = (-4, -4); r = 2

D) (h, k) = (-4, 4); r = 2

Write an equation that expresses the relationship. Use k as the constant of variation. 154) c varies inversely as z. z A) c = B) kc = z C) c = kz k

k D) c = z

Solve the problem. 155) If a graph is symmetric with respect to the y-axis and it contains the point (5, -6), which of the following points is also on the graph? A) (-5, -6) B) (-6, 5) C) (-5, 6) D) (5, -6) If y varies directly as x, write a general formula to describe the variation. 156) y = 27 when x = 12 9 4 A) y = 3x B) y = x C) y = x 4 9 List the intercepts for the graph of the equation. 157) y = x4 - 1 A) (0, 1), (-1, 0), (1, 0) C) (0, -1)

B) (0, -1), (-1, 0), (1, 0) D) (0, 1)

Graph the line containing the point P and having slope m. 3 158) P = (-2, -5); m = 5

154)

155)

156) D) y = x + 15

157)

158)

Solve the problem. 159) In simplified form, the period of vibration P for a pendulum varies directly as the square root of its length L. If P is 1 sec. when L is 16 in., what is the period when the length is 81 in.? A) 324 sec B) 20.25 sec C) 2.25 sec D) 36 sec List the intercepts for the graph of the equation. x2 - 25 160) y = 5x4

159)

160)

A) (0, 0) C) (0, -5), (0, 5)

B) (-5, 0), (5, 0) D) (-25, 0), (0, 0), (25, 0)

Determine whether the graph of the equation is symmetric with respect to the x-axis, the y-axis, and/or the origin. 161) 9x2 + 16y2 = 144 161) A) y-axis B) x-axis C) origin D) x-axis, y-axis, origin E) none

Solve the problem. 162) Find the length of each side of the triangle determined by the three points P1 , P2 , and P3 . State

162)

whether the triangle is an isosceles triangle, a right triangle, neither of these, or both. P1 = (-5, -4), P2 = (-3, 4), P3 = (0, -1)

A) d(P1 , P2 ) = 2 17; d(P2 , P3 ) = isosceles triangle B) d(P1 , P2 ) = 2 17; d(P2 , P3 ) =

both C) d(P1 , P2 ) = 2 17; d(P2 , P3 ) =

34; d(P1 , P3 ) =

34; d(P1 , P3 ) = 5 2

right triangle D) d(P1 , P2 ) = 2 17; d(P2 , P3 ) =

34; d(P1 , P3 ) = 5 2

neither

List the intercepts of the graph. 163)

A) (6, 0)

163)

B) (0, -6)

Find the slope of the line containing the two points. 164) (6, -5); (-7, 1) 13 6 A) B) 6 13

C) (0, 6)

D) (-6, 0)

13 C) 6

6 D) 13

Find an equation for the line with the given properties. 1 165) Slope undefined; containing the point - , 3 2 A) y = -

1 2

B) x = -

164)

165)

1 2

C) x = 3

D) y = 3

List the intercepts of the graph.Tell whether the graph is symmetric with respect to the x-axis, y-axis, origin, or none of these. 166) 166)

A) intercept: (0, 7) no symmetry C) intercept: (7, 0) symmetric with respect to y-axis

B) intercept: (0, 7) symmetric with respect to x-axis D) intercept: (7, 0) no symmetry

Find the distance d(P1 , P2 ) between the points P1 and P2 .

167) P1 = (3, 6); P2 = (-6, -5) A) 2

167)

202

C) 2 10

D) 99

C) B, C, and L

D) F, K, and L

C) y = 6x + 12

6 7 D) y = x + 5 5

Identify the points in the graph for the ordered pairs.

168) (-3, 4), (2, 0), (4, -5) A) A, B, and F

B) B, F, and L

Write the equation in slope-intercept form. 169) 6x + 5y = 7 5 7 12 7 x+ A) y = x B) y = 6 6 5 5

168)

169)

If y varies directly as x, write a general formula to describe the variation. 1 170) y = 6 when x = 7 A) y = 42x

B) y = x +

41 7

C) y =

1 x 42

170) D) y =

1 x 6

Find the general form of the equation for the line with the given properties. 2 171) Slope = - ; containing the point (2, 4) 7 A) 2x + 7y = 32

B) 7x + 2y = -32

C) 2x - 7y = 32

171) D) 2x + 7y = -32

Solve the problem. 172) Find an equation of the line containing the centers of the two circles x2 + y2 + 8x + 12y + 51 = 0 and x2 + y2 - 2x - 2y - 2 = 0 A) -7x - 5y + 2 = 0 B) -5x + 3y + 2 = 0

C) 7x + 5y + 2 = 0

172)

D) -7x + 5y + 2 = 0

Find the general form of the equation of the the circle. 173) Center at the point (-4, -3); containing the point (-3, 3) A) x2 + y2 - 6x + 6y - 12 = 0 B) x2 + y2 + 6x - 6y - 17 = 0 C) x2 + y2 + 6x + 8y - 17 = 0

173)

D) x2 + y2 + 8x + 6y - 12 = 0

Determine whether the graph of the equation is symmetric with respect to the x-axis, the y-axis, and/or the origin. 174) x2 + y - 81 = 0 174) A) origin B) x-axis C) y-axis D) x-axis, y-axis, origin E) none

Plot the point in the xy-plane. Tell in which quadrant or on what axis the point lies. 175) (1, -6)

175)

Quadrant III

Quadrant II

Quadrant I

Quadrant IV

List the intercepts of the graph. 176)

176)

A) (0, -3), (0, 3), (1, 0) C) (-3, 0), (0, 3), (0, 1)

B) (-3, 0), (0, 3), (1, 0) D) (0, -3), (3, 0), (0, 1)

177)

A) (1, 1)

B) (1, 0)

C) (0, 1)

D) (0, 0)

Find the distance d(P1 , P2 ) between the points P1 and P2 .

178) P1 = (0, 0); P2 = (-1, 7) A) 50

178) C) i 7

B) 6

Find the slope and y-intercept of the line. 179) 4x - 3y = 2 4 2 A) slope = ; y-intercept = 3 3 C) slope = 4; y-intercept = 2

B) slope =

4 2 ; y-intercept = 3 3

D) slope =

3 2 ; y-intercept = 4 4

Plot the point A. Plot the point B that has the given symmetry with point A. 180) A = (0, -2); B is symmetric to A with respect to the origin

179)

180)

Solve the problem. 181) While traveling at a constant speed in a car, the centrifugal acceleration passengers feel while the car is turning is inversely proportional to the radius of the turn. If the passengers feel an acceleration of 9 feet per second per second (ft/sec2 ) when the radius of the turn is 60 feet, find the acceleration the passengers feel when the radius of the turn is 180 feet. A) 4 ft/sec2 B) 3 ft/sec2 C) 5 ft/sec2

D) 6 ft/sec2

Find the center (h, k) and radius r of the circle with the given equation. 182) x2 - 16x + 64 + y2 - 8y + 16 = 9 A) (h, k) = (-4, -8); r = 9 C) (h, k) = (4, 8); r = 3

B) (h, k) = (8, 4); r = 3 D) (h, k) = (-8, -4); r = 9

Solve the problem. 183) The voltage across a resistor is jointly proportional to the resistance of the resistor and the current flowing through the resistor. If the voltage across a resistor is 16 volts (V) for a resistor whose resistance is 2 ohms and when the current flowing through the resistor is 8 amperes, find the voltage across a resistor whose resistance is 6 ohms and when the current flowing through the resistor is 3 amperes. A) 6 V B) 48 V C) 24 V D) 18 V

181)

182)

183)

Name the quadrant in which the point is located. 184) (-3, -5) A) I B) II

C) III

Draw a complete graph so that it has the given type of symmetry. 185) Symmetric with respect to the x-axis

D) IV

184)

185)

Determine whether the graph of the equation is symmetric with respect to the x-axis, the y-axis, and/or the origin. 186) y2 - x - 4 = 0 186) A) x-axis B) origin C) y-axis D) x-axis, y-axis, origin E) none

Find an equation for the line, in the indicated form, with the given properties. 187) Containing the points (6, 0) and (4, 7); general form A) -7x + 2y = 42 B) 7x + 2y = 42 C) 6x - 3y = -45

D) -6x + 3y = -45

Solve the problem. 188) If a satellite is placed in a circular orbit of 360 kilometers above the Earth, what is the equation of the path of the satellite if the origin is placed at the center of the Earth (the diameter of the Earth is approximately 12,740 kilometers)? A) x2 + y2 = 129,600 B) x2 + y2 = 171,610,000 C) x2 + y2 = 40,576,900

187)

188)

D) x2 + y2 = 45,292,900

Graph the equation by plotting points. 1 189) y = x

189)

Solve the problem. 190) Find the area of the right triangle ABC with A = (-2, 7), B = (7, -1), C = (3, 9). 29 square units A) 29 square units B) 2 C) 58 square units

190)

58 square units 2

191) The medians of a triangle intersect at a point. The distance from the vertex to the point is exactly two-thirds of the distance from the vertex to the midpoint of the opposite side. Find the exact distance of that point from the vertex A(3, 4) of a triangle, given that the other two vertices are at (0, 0) and (8, 0). 17 2 17 8 A) B) C) 2 D) 3 3 3

191)

192) If (-2, 2) is the endpoint of a line segment, and (-6, 5) is its midpoint, find the other endpoint. A) (-10, -1) B) (4, -6) C) (-10, 8) D) (6, -4)

192)

Solve. 193) A vendor has learned that, by pricing pretzels at $1.00, sales will reach 159 pretzels per day. Raising the price to $1.75 will cause the sales to fall to 129 pretzels per day. Let y be the number of pretzels the vendor sells at x dollars each. Write a linear equation that relates the number of pretzels sold per day to the price x. 1 6359 x+ A) y = -40x - 199 B) y = 40 40 C) y = 40x + 119

D) y = -40x + 199

Find the slope of the line and sketch its graph.

193)

194) y - 2 = 0

194)

A) slope = 2

B) slope = 0

C) slope is undefined

D) slope =

1 2

Plot the point in the xy-plane. Tell in which quadrant or on what axis the point lies.

195) (0, 2)

195)

Quadrant II

y-axis

x-axis

y-axis

Solve the problem. 196) If a graph is symmetric with respect to the origin and it contains the point (-4, 7), which of the following points is also on the graph? A) (-4, -7) B) (7, -4) C) (4, 7) D) (4, -7) Find the distance d(P1 , P2 ) between the points P1 and P2 .

197) P1 = (2, 2); P2 = (2, 5) A) 2

196)

197)

C) 4

D) 3

Find an equation for the line with the given properties. 198) Parallel to the line 5x + 6y = 6; x-intercept = 2 A) 5x + 6y = 12 B) 5x + 6y = 10

C) 6x - 5y = -10

D) 6x - 5y = 12

Solve the problem. 199) When the temperature stays the same, the volume of a gas is inversely proportional to the pressure of the gas. If a balloon is filled with 100 cubic inches of a gas at a pressure of 14 pounds per square inch, find the new pressure of the gas if the volume is decreased to 25 cubic inches. 25 psi A) B) 42 psi C) 52 psi D) 56 psi 14

198)

199)

Determine whether the graph of the equation is symmetric with respect to the x-axis, the y-axis, and/or the origin. 200) y = (x + 9)(x - 1) 200) A) origin B) y-axis C) x-axis D) x-axis, y-axis, origin E) none Write the equation in slope-intercept form. 201) 3x + 5y = 4 3 4 A) y = x B) y = 3x - 4 5 5

3 4 C) y = - x + 5 5

Find the slope and y-intercept of the line. 202) -x + 7y = 77 1 A) slope = ; y-intercept = 11 7 C) slope = -

201)

202) B) slope = -1; y-intercept = 77

1 ; y-intercept = 11 7

D) slope = 7; y-intercept = -77

Find an equation for the line with the given properties. 203) Slope undefined; containing the point (2, 10) A) y = 2 B) y = 10

C) x = 2

Write a general formula to describe the variation. 204) A varies directly with t2 ; A = 75 when t = 5 15 A) A = t2

3 4 D) y = x + 5 5

3 C) A = t2

B) A = 15t2

Find an equation for the line with the given properties. 205) Perpendicular to the line x = 7; containing the point (4, 9) A) y = 9 B) x = 4 C) x = 9 Graph the line containing the point P and having slope m.

D) x = 10

203)

204) D) A = 3t2

D) y = 4

205)

206) P = (0, 4); m =

4 3

206)

Find the slope and y-intercept of the line. 207) -3x + 7y = 1 3 1 A) slope = ; y-intercept = 7 7 C) slope =

207) B) slope = 3; y-intercept = 13

7 1 ; y-intercept = 3 3

D) slope =

13 1 ; y-intercept = 7 7

List the intercepts for the graph of the equation. 208) y = x + 6 A) (6, 0), (0, 6) B) (-6, 0), (0, 6)

C) (6, 0), (0, -6)

D) (-6, 0), (0, -6)

Name the quadrant in which the point is located. 209) (-15, 18) A) I B) II

C) III

D) IV

208)

209)

Solve the problem. 210) The volume V of a given mass of gas varies directly as the temperature T and inversely as the pressure P. A measuring device is calibrated to give V = 198 in3 when T = 360° and P = 20 lb/in2 .

210)

List the intercepts for the graph of the equation. 211) y = -4x A) (-4, -4) B) (0, 0)

211)

What is the volume on this device when the temperature is 140° and the pressure is 25 lb/in2 ? A) V = 71.6 in3 B) V = 51.6 in3 C) V = 5.6 in3 D) V = 61.6 in3

C) (0, -4)

D) (-4, 0)

Find the equation of the line in slope-intercept form. 212)

A) y = - 7x + 25

B) y = -

212)

1 1 x7 25

C) y = - 7x - 31

Graph the equation by plotting points. 213) y = x3

D) y = - 7x - 25

213)

Solve the problem. 214) If (a, 3) is a point on the graph of y = 2x - 5, what is a? A) 4 B) -1 C) 1

D) -4

Solve. 215) Each day the commuter train transports x passengers to or from the city at $1.75/passenger. The daily fixed cost for running the train is $1200. Write an equation that relates the daily profit, P, in dollars to the number of passengers each day. Then use the equation to find the daily profit when the train has 920 passengers in a day. A) P = 1.75x; $1610 B) P = 1.75x + 1200; $2810 C) P = 1.75x - 1200; $410 D) P = 1200 - 1.75x; $410

214)

215)

List the intercepts of the graph. 216)

216)

A) (-4, 0), (0, 4), (4, 0) C) (-2, 0), (0, 2), (2, 0)

B) (-2, 0), (0, 4), (2, 0) D) (-2, 0), (2, 0)

List the intercepts and type(s) of symmetry, if any. -x5 217) y = x2 - 3

217)

A) intercept: (0, 0) symmetric with respect to origin C) intercept: (0, 0) symmetric with respect to y-axis

B) intercept: (0, 0) symmetric with respect to x-axis D) intercepts: ( 3, 0), (- 3, 0), (0, 0) symmetric with respect to origin

Find an equation for the line, in the indicated form, with the given properties. 218) Containing the points (3, 0) and (0, -6); general form A) y = - 2x + 3 B) y = - 2x - 6 C) 6x - 3y = 18

D) 6x + 3y = 18

Solve the problem. 219) A wildlife researcher is monitoring a black bear that has a radio telemetry collar with a transmitting range of 28 miles. The researcher is in a research station with her receiver and tracking the bear's movements. If we put the origin of a coordinate system at the research station, what is the equation of all possible locations of the bear where the transmitter would be at its maximum range? A) x2 + y2 = 56 B) x2 + y2 = 28 C) x2 - y2 = 28 D) x2 + y2 = 784 220) While traveling in a car, the centrifugal force a passenger experiences as the car drives in a circle varies jointly as the mass of the passenger and the square of the speed of the car. If a passenger experiences a force of 100.8 newtons (N) when the car is moving at a speed of 40 kilometers per hour and the passenger has a mass of 70 kilograms, find the force a passenger experiences when the car is moving at 50 kilometers per hour and the passenger has a mass of 60 kilograms. A) 120 N B) 175 N C) 150 N D) 135 N Find the slope-intercept form of the equation of the line with the given properties. 221) Slope = 0; containing the point (-8, 8) A) x = 8 B) x = -8 C) y = 8

D) y = -8

218)

219)

220)

221)

Solve the problem. 222) The amount of paint needed to cover the walls of a room varies jointly as the perimeter of the room and the height of the wall. If a room with a perimeter of 65 feet and 10-foot walls requires 6.5 quarts of paint, find the amount of paint needed to cover the walls of a room with a perimeter of 55 feet and 6-foot walls. A) 33 qt B) 3.3 qt C) 6.6 qt D) 330 qt Find the slope and y-intercept of the line. 223) y = 2 A) slope = 0; no y-intercept C) slope = 2; y-intercept = 0

B) slope = 0; y-intercept = 2 D) slope = 1; y-intercept = 2

222)

223)

List the intercepts and type(s) of symmetry, if any. 224) 16x2 + y2 = 16

224)

Find the slope of the line and sketch its graph. 225) 3x + 4y = 22

225)

A) intercepts: (4, 0), (-4, 0), (0, 1), (0, -1) symmetric with respect to the origin B) intercepts: (4, 0), (-4, 0), (0, 1), (0, -1) symmetric with respect to x-axis and y-axis C) intercepts: (1, 0), (-1, 0), (0, 4), (0, -4) symmetric with respect to x-axis, y-axis, and origin D) intercepts: (1, 0), (-1, 0), (0, 4), (0, -4) symmetric with respect to x-axis and y-axis

A) slope =

4 3

B) slope = -

3 4

C) slope =

3 4

D) slope = -

4 3

Find the distance d(P1 , P2 ) between the points P1 and P2 .

226) P1 = (-1, -1); P2 = (-5, -4) A) 6

226)

B) 5

C) 25

Graph the circle with radius r and center (h, k). 227) r = 4; (h, k) = (0, 0)

D) 10

227)

Draw a complete graph so that it has the given type of symmetry. 228) Symmetric with respect to the y-axis

228)

List the intercepts for the graph of the equation. 229) y = x2 + 11x + 24 A) (0, -8), (0, -3), (24, 0) C) (0, 8), (0, 3), (24, 0)

B) (8, 0), (3, 0), (0, 24) D) (-8, 0), (-3, 0), (0, 24)

Give the coordinates of the points shown on the graph. 230)

229)

230)

A) E = (7, -3), F = (-3, -2) C) E = (-3, 7), F = (-2, -3)

B) E = (-2, -3) , F = (-3, 7) D) E = (-3, -3), F = (7, -3)

Graph the line containing the point P and having slope m. 231) P = (-3, -7); m = -1

231)

List the intercepts for the graph of the equation. 232) y = x3 - 8 A) (0, -8), (2, 0)

B) (0, -2), (-2, 0)

C) (-8, 0), (0, 2)

D) (0, -2), (0, 2)

Find the general form of the equation for the line with the given properties. 7 233) Slope = ; containing (0, 4) 9 A) -7x - 9y = 36

B) -7x + 9y = -36

C) 9x - 7y = -36

If y varies inversely as x, write a general formula to describe the variation. 234) y = 8 when x = 2 16 1 A) y = B) y = 4x C) y = x 16x List the intercepts for the graph of the equation. 235) 4x2 + 9y2 = 36 A) (-2, 0), (-3, 0), (3, 0), (2, 0) C) (-4, 0), (-9, 0), (9, 0), (4, 0)

233) D) -7x + 9y = 36

x D) y = 16

B) (-3, 0), (0, -2), (0, 2), (3, 0) D) (-9, 0), (0, -4), (0, 4), (9, 0)

232)

234)

235)

Find the slope of the line containing the two points. 236) (7, 0); (0, 4) 7 7 A) B) 4 4

4 C) 7

237) (7, -8); (5, -2) A) - 3

B) 3

1 3

If y varies directly as x, write a general formula to describe the variation. 238) y = 8 when x = 72 1 1 A) y = x B) y = 9x C) y = x 9 8

4 D) 7

D) -

1 3

236)

237)

238) D) y = x + 64

Determine whether the graph of the equation is symmetric with respect to the x-axis, the y-axis, and/or the origin. x2 - 36 239) y = 239) 6x4 A) origin B) x-axis C) y-axis D) x-axis, y-axis, origin E) none Plot the point in the xy-plane. Tell in which quadrant or on what axis the point lies. 240) (-5, -6)

Quadrant IV

Quadrant III

240)

Quadrant II

Quadrant III

Graph the equation. 241) (x - 1)2 + (y + 4)2 = 16

241)

Write the standard form of the equation of the circle. 242)

242)

A) (x + 4)2 + (y + 3)2 = 36 C) (x - 3)2 + (y - 4)2 = 36

B) (x + 3)2 + (y + 4)2 = 36 D) (x - 4)2 + (y - 3)2 = 36

Solve the problem.

243) x varies inversely as y2 , and x = 3 when y = 15. Find x when y = 3. A) x = 75 B) x = 27 C) x = 45

D) x = 5

244) If (1, 9) is the endpoint of a line segment, and (6, 8) is its midpoint, find the other endpoint. A) (-1, 19) B) (11, 10) C) (-9, 11) D) (11, 7) Find the midpoint of the line segment joining the points P1 and P2 .

245) P1 = (0.5, 0.1); P2 = (1.9, -1.5) A) (1.2, -0.7)

B) (-0.8, 0.7)

C) (-0.7, 1.2)

B) y = -

4 7

C) y = 6

Graph the equation by plotting points. 67

244)

245) D) (0.7, -0.8)

Find the slope-intercept form of the equation of the line with the given properties. 4 246) Horizontal; containing the point - , 6 7 A) y = 0

243)

246) D) y = -6

247) y =

247)

Identify the points in the graph for the ordered pairs.

248) (-5, -4), (0, -3) A) I and J

B) A and J

C) G and I

D) A and G

Find the distance d(P1 , P2 ) between the points P1 and P2 .

249)

A) 60

248)

249)

B) 2 17

C) 6

If y varies directly as x, write a general formula to describe the variation. 250) y = 0.2 when x = 1.6 A) y = 0.125x B) y = 0.2x C) y = 8x Plot the point in the xy-plane. Tell in which quadrant or on what axis the point lies. 251) (6, 0)

D) 60 15

D) y = x - 1.4

250)

251)

Quadrant II

x-axis

y-axis

Solve the problem. 252) Find the equation of a circle in standard form that is tangent to the line x = -3 at (-3, 5) and also tangent to the line x = 9. A) (x - 3)2 + (y + 5)2 = 36 B) (x - 3)2 + (y - 5)2 = 36 C) (x + 3)2 + (y - 5)2 = 36

252)

D) (x + 3)2 + (y + 5)2 = 36

Graph the line containing the point P and having slope m. 4 253) P = (-2, 0); m = 5

253)

Find the distance d(P1 , P2 ) between the points P1 and P2 .

254) P1 = (0, -1); P2 = (-9, -1) A) 1

254)

C) 81

D) 9

Solve the problem. 255) The pressure of a gas varies jointly as the amount of the gas (measured in moles) and the temperature and inversely as the volume of the gas. If the pressure is 900 kiloPascals (kPa) when the number of moles is 7, the temperature is 250° Kelvin, and the volume is 560 cc, find the pressure when the number of moles is 10, the temperature is 260° K, and the volume is 1,200 cc. A) 1,248 kPa B) 1,344 kPa C) 576 kPa D) 624 kPa

255)

Graph the equation by plotting points. 256) 2x + 3y = 6

256)

Find an equation for the line with the given properties. 257) Parallel to the line 5x + 3y = 21; containing the point (3, 3) A) 5x - 3y = 24 B) 3x + 3y = 21 C) 5x + 3y = 24 Find the slope and y-intercept of the line. 258) x + 5y = 1

D) 3x + 5y = 3

A) slope = 1; y-intercept = 1

1 1 B) slope = ; y-intercept = 5 5

C) slope = -5; y-intercept = 5

D) slope = -

1 1 ; y-intercept = 5 5

257)

258)

Find an equation for the line with the given properties. 259) Perpendicular to the line y = 2x - 3; containing the point (-3, -2) 1 7 7 7 A) y = x B) y = 2x C) y = -2x 2 2 2 2 Graph the line containing the point P and having slope m. 3 260) P = (0, 6); m = 2

1 7 D) y = - x 2 2

259)

260)

Find the slope of the line containing the two points. 261) (-9, -2); (-9, -6) A) -4

261)

1 C) 4

B) 0

D) undefined

If y varies inversely as x, write a general formula to describe the variation. 1 262) y = 20 when x = 5 A) y =

x 4

B) y =

1 4x

C) y =

4 x

262) D) y = 100x

Decide whether or not the points are the vertices of a right triangle. 263) (10, -1), (16, 1), (22, -6) A) Yes B) No Write a general formula to describe the variation. 264) v varies directly with t; v = 8 when t = 2 1 A) v = 4t B) v = t 4

2 C) v = 8t

263)

8 D) v = 2t

Find the center (h, k) and radius r of the circle with the given equation. 265) (x - 3)2 + y2 = 16 A) (h, k) = (0, 3); r = 4 C) (h, k) = (3, 0); r = 16

265)

B) (h, k) = (3, 0); r = 4 D) (h, k) = (0, 3); r = 16

Solve. 266) A faucet is used to add water to a large bottle that already contained some water. After it has been filling for 3 seconds, the gauge on the bottle indicates that it contains 17 ounces of water. After it has been filling for 11 seconds, the gauge indicates the bottle contains 49 ounces of water. Let y be the amount of water in the bottle x seconds after the faucet was turned on. Write a linear equation that relates the amount of water in the bottle,y, to the time x. 1 65 A) y = 4x + 38 B) y = x + C) y = -4x + 29 D) y = 4x + 5 4 4 Find an equation for the line with the given properties. 267) Parallel to the line y = 4x; containing the point (7, 3) A) y = 4x B) y - 3 = 4x - 7 C) y = 4x - 25 Determine whether the given point is on the graph of the equation. 268) Equation: x2 - y2 = 36 Point: (3 4, 0) A) No

B) Yes

264)

D) y = 4x + 25

266)

267)

268)

List the intercepts of the graph.Tell whether the graph is symmetric with respect to the x-axis, y-axis, origin, or none of these. 269) 269)

A) intercepts: (-3, 0), (0, 0), (3, 0) symmetric with respect to origin B) intercepts: (-3, 0), (0, 0), (3, 0) symmetric with respect to x-axis C) intercepts: (-3, 0), (0, 0), (3, 0) symmetric with respect to x-axis, y-axis, and origin D) intercepts: (-3, 0), (0, 0), (3, 0) symmetric with respect to y-axis Graph the circle with radius r and center (h, k). 270) r = 4; (h, k) = (0, 1)

270)

Find the slope of the line. 271)

A) -1

271)

B) 4

C) -4

D) 1

Solve the problem. 272) The time in hours it takes a satellite to complete an orbit around the earth varies directly as the radius of the orbit (from the center of the earth) and inversely as the orbital velocity. If a satellite completes an orbit 840 miles above the earth in 8 hours at a velocity of 28,000 mph, how long would it take a satellite to complete an orbit if it is at 1,900 miles above the earth at a velocity of 23,000 mph? (Use 3960 miles as the radius of the earth.) A) 118.9 hr B) 22.03 hr C) 11.89 hr D) 3.86 hr Find the slope-intercept form of the equation of the line with the given properties. 273) x-intercept = 4; y-intercept = 5 4 5 5 A) y = - x + 4 B) y = - x + 4 C) y = - x + 5 5 4 4

5 D) y = x + 5 4

Solve. 274) Each week a soft drink machine sells x cans of soda for $0.75/soda. The cost to the owner of the soda machine for each soda is $0.10. The weekly fixed cost for maintaining the soda machine is $25/week. Write an equation that relates the weekly profit, P, in dollars to the number of cans sold each week. Then use the equation to find the weekly profit when 92 cans of soda are sold in a week. A) P = 0.75x - 25; $44.00 B) P = 0.65x + 25; $84.80 C) P = 0.75x + 25; $94.00 D) P = 0.65x - 25; $34.80 Graph the equation by plotting points. 76

272)

273)

274)

275) x = y2

275)

Graph the equation.

276) x2 + y2 = 16

276)

Find the midpoint of the line segment joining the points P1 and P2 .

277) P1 = (4, 1); P2 = (7, 7) A) (4,

11 ) 2

B) (

11 , 4) 2

C) (11, 8)

277) D) (-3, -6)

Solve the problem. 278) Find the equation of a circle in standard form where C(6, -2) and D(-4, 4) are endpoints of a diameter. A) (x + 1)2 + (y + 1)2 = 136 B) (x - 1)2 + (y - 1)2 = 34 C) (x + 1)2 + (y + 1)2 = 34

D) (x - 1)2 + (y - 1)2 = 136

278)

Find the slope of the line containing the two points. 279) (8, -4); (-4, -4) 1 A) B) 0 12

279)

List the intercepts for the graph of the equation. 6 280) y = x A) (0, 1) B) (1, 1)

C) -12

D) undefined

C) (0, 0)

D) (1, 0)

Find the slope-intercept form of the equation of the line with the given properties. 281) Slope = 2; containing the point (-6, -6) A) y = -2x - 6 B) y = -2x + 6 C) y = 2x - 6

D) y = 2x + 6

Write the standard form of the equation of the circle with radius r and center (h, k). 282) r = 4; (h, k) = (0, 0) A) x2 + y2 = 4 B) x2 + y2 = 16 C) (x - 4)2 + (y - 4)2 = 4

281)

282)

D) (x - 4)2 + (y - 4)2 = 16

List the intercepts for the graph of the equation. 3x 283) y = x2 + 9

283)

A) (-3, 0), (0, 0), (3, 0) C) (0, -3), (0, 0), (0, 3)

B) (0, 0) D) (-9, 0), (0, 0), (9, 0)

List the intercepts of the graph. 284)

A) (0, -3), (0, 3)

280)

284)

B) (-3, 0), (0, 3)

C) (0, -3), (3, 0)

Find the slope and y-intercept of the line. 285) x + y = -12 A) slope = 1; y-intercept = -12 C) slope = -1; y-intercept = -12

D) (-3, 0), (3, 0)

B) slope = 0; y-intercept = -12 D) slope = -1; y-intercept = 12

285)

Solve the problem. 286) Earth is represented on a map of the solar system so that its surface is a circle with the equation x2 + y2 + 2x + 10y - 3,943 = 0. A weather satellite circles 0.4 units above the Earth with the center of

286)

its circular orbit at the center of the Earth. Find the general form of the equation for the orbit of the satellite on this map. A) x2 + y2 - 2x - 10y - 3,993.56 = 0 B) x2 + y2 + 2x + 10y + 25.84 = 0

C) x2 + y2 + 2x + 10y - 3,993.56 = 0

D) x2 + y2 + 2x + 10y - 36.84 = 0

Find an equation for the line, in the indicated form, with the given properties. 287) Containing the points (9, -5) and (-4, 3); general form A) 14x - 7y = 35 B) -14x + 7y = 35 C) -8x + 13y = 7

D) 8x + 13y = 7

Find the slope of the line. 288)

A) -1

287)

288)

B) 3

C) 1

D) -3

Solve the problem. 289) The amount of gas that a helicopter uses is directly proportional to the number of hours spent flying. The helicopter flies for 2 hours and uses 28 gallons of fuel. Find the number of gallons of fuel that the helicopter uses to fly for 3 hours. A) 42 gal B) 56 gal C) 45 gal D) 6 gal Decide whether the pair of lines is parallel, perpendicular, or neither. 290) 3x - 6y = -12 18x + 9y = 6 A) parallel B) perpendicular

289)

290) C) neither

Solve the problem. 291) Find the standard form of the equation of the circle. Assume that the center has integer coordinates and the radius is an integer.

A) x2 + y2 + 2x - 4y - 4 = 0 C) (x + 1)2 + (y - 2)2 = 9

291)

B) x2 + y2 - 2x + 4y - 4 = 0 D) (x - 1)2 + (y + 2)2 = 9

Determine whether the graph of the equation is symmetric with respect to the x-axis, the y-axis, and/or the origin. 292) y = x2 + 16x + 63 292) A) origin B) y-axis C) x-axis D) x-axis, y-axis, origin E) none

Solve the problem. 293) The distance that an object falls when it is dropped is directly proportional to the square of the amount of time since it was dropped. An object falls 39.2 meters in 2 seconds. Find the distance the object falls in 5 seconds. A) 10 m B) 49 m C) 98 m D) 245 m 294) If (-4, 2) is the endpoint of a line segment, and (-9, -1) is its midpoint, find the other endpoint. A) (-10, -8) B) (-14, -4) C) (6, 8) D) (-14, 5)

293)

294)

Determine whether the graph of the equation is symmetric with respect to the x-axis, the y-axis, and/or the origin. 295) y = x - 2 295) A) y-axis B) x-axis C) origin D) x-axis, y-axis, origin E) none Decide whether or not the points are the vertices of a right triangle. 296) (-9, 3), (-7, 7), (-5, 6) A) Yes B) No

296)

Find the distance d(P1 , P2 ) between the points P1 and P2 .

297)

A) 12

297)

C) 2 5

B) 6

Find an equation for the line with the given properties. 298) Parallel to the line y = -8; containing the point (9, 4) A) y = 4 B) y = 9 C) y = -4

D) 12 3

D) y = -8

298)

Determine whether the graph of the equation is symmetric with respect to the x-axis, the y-axis, and/or the origin. 299) y = -7x3 + 2x 299) A) x-axis B) y-axis C) origin D) x-axis, y-axis, origin E) none

Find the slope and y-intercept of the line. 300) y = -3x

300)

A) slope = 3; y-intercept = 0 C) slope = -

B) slope = 0; y-intercept = -3

1 ; y-intercept = 0 3

D) slope = -3; y-intercept = 0

Answer Key Testname: CHAPTER 2 1) B 2) D 3) C 4) B 5) C 6) A 7) D 8) B 9) B 10) C 11) D 12) B 13) C 14) D 15) C 16) B 17) D 18) D 19) A 20) B 21) A 22) B 23) D 24) C 25) C 26) D 27) C 28) C 29) A 30) A 31) B 32) A 33) C 34) A 35) C 36) A 37) D 38) C 39) D 40) C 41) B 42) D 43) B 44) D 45) C 46) A 47) A 48) C 49) A 50) A 83

Answer Key Testname: CHAPTER 2 51) C 52) C 53) C 54) A 55) B 56) C 57) B 58) B 59) C 60) A 61) D 62) D 63) B 64) D 65) B 66) A 67) D 68) A 69) A 70) C 71) D 72) B 73) B 74) B 75) D 76) A 77) B 78) A 79) C 80) B 81) D 82) C 83) C 84) D 85) D 86) B 87) B 88) B 89) C 90) C 91) C 92) B 93) B 94) C 95) A 96) B 97) B 98) C 99) B 100) B 84

Answer Key Testname: CHAPTER 2 101) B 102) D 103) C 104) C 105) C 106) A 107) A 108) B 109) D 110) A 111) D 112) D 113) A 114) A 115) A 116) C 117) A 118) A 119) D 120) D 121) D 122) B 123) D 124) B 125) D 126) C 127) C 128) A 129) A 130) D 131) A 132) C 133) B 134) D 135) C 136) A 137) A 138) A 139) A 140) A 141) C 142) A 143) D 144) D 145) D 146) D 147) D 148) B 149) D 150) E 85

Answer Key Testname: CHAPTER 2 151) A 152) B 153) B 154) D 155) C 156) B 157) B 158) C 159) C 160) B 161) D 162) B 163) D 164) D 165) B 166) A 167) B 168) B 169) D 170) A 171) A 172) D 173) D 174) C 175) D 176) B 177) C 178) D 179) B 180) D 181) B 182) B 183) D 184) C 185) C 186) A 187) B 188) D 189) B 190) A 191) B 192) C 193) D 194) B 195) C 196) D 197) D 198) B 199) D 200) E 86

Answer Key Testname: CHAPTER 2 201) C 202) A 203) C 204) D 205) A 206) B 207) A 208) B 209) B 210) D 211) B 212) A 213) D 214) A 215) C 216) A 217) A 218) C 219) D 220) D 221) C 222) B 223) B 224) C 225) B 226) B 227) A 228) A 229) D 230) C 231) C 232) A 233) D 234) A 235) B 236) D 237) A 238) A 239) C 240) D 241) D 242) C 243) A 244) D 245) A 246) C 247) D 248) A 249) B 250) A 87

Answer Key Testname: CHAPTER 2 251) C 252) B 253) B 254) D 255) D 256) D 257) C 258) D 259) D 260) B 261) D 262) C 263) B 264) A 265) B 266) D 267) C 268) B 269) A 270) C 271) A 272) C 273) C 274) D 275) A 276) A 277) B 278) B 279) B 280) C 281) D 282) B 283) B 284) D 285) C 286) C 287) D 288) C 289) A 290) B 291) C 292) E 293) D 294) B 295) E 296) A 297) C 298) A 299) C 300) D 88

Chapter 3 Exam Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. The graph of a function f is given. Use the graph to answer the question. 1) For which of the following values of x does f(x) = -20?

-25

A) 0

B) 15

C) 10

D) -20

Match the correct function to the graph. 2)

A) y =

B) y =

x-1

C) y = x - 1

D) y =

x+1

A) y = |x + 2|

B) y = x - 2

C) y = |2 - x|

D) y = |1 - x|

Match the graph to the function listed whose graph most resembles the one given. 4)

A) linear function C) absolute value function

B) reciprocal function D) constant function

A) cube root function C) square root function Solve the problem. 6) Let P = (x, y) be a point on the graph of y = function of x. A) d(x) = x2 - x + 1

B) square function D) cube function

x. Express the distance d from P to the point (1, 0) as a

B) d(x) = x2 + 2x + 2 D) d(x) = x2 + 2x + 2

C) d(x) = x2 - x + 1

Match the graph to the function listed whose graph most resembles the one given. 7)

A) cube function C) square root function

B) square function D) cube root function

Match the function with the graph that best describes the situation. 8) The amount of rainfall as a function of time, if the rain fell more and more softly. A) B)

Match the graph to the function listed whose graph most resembles the one given. 9)

A) absolute value function C) square function

B) linear function D) reciprocal function

10)

A) reciprocal function C) absolute value function

B) square function D) square root function

Match the function with the graph that best describes the situation. 11) The height of an animal as a function of time. A) B)

11)

Match the correct function to the graph. 12)

A) y = 1 - x2

12)

B) y = -2x2 + 1

C) y = -2x2

D) y = -2x2 - 1

Match the graph to the function listed whose graph most resembles the one given. 13)

A) cube root function C) square function

13)

B) cube function D) square root function

14)

A) constant function C) reciprocal function

B) linear function D) absolute value function

15)

A) absolute value function C) square function

B) cube function D) reciprocal function

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 16) The wind chill factor represents the equivalent air temperature at a standard wind speed that 16) would produce the same heat loss as the given temperature and wind speed. One formula for computing the equivalent temperature is if 0 v < 1.79

t W(t) = 33 -

(10.45 + 10 v - v)(33 - t ) 22.04

33 - 1.5958(33 - t)

if 1.79 v < 20 if v 20

where v represents the wind speed (in meters per second) and t represents the air temperature (°C). Compute the wind chill for an air temperature of 15°C and a wind speed of 12 meters per second. (Round the answer to one decimal place.)

17) The price p and x, the quantity of a certain product sold, obey the demand equation 1 p=x + 100, {x|0 x 1000} 10 a) b) c) d) e)

17)

Express the revenue R as a function of x. What is the revenue if 450 units are sold? Graph the revenue function using a graphing utility. What quantity x maximizes revenue? What is the maximum revenue? What price should the company charge to maximize revenue?

Use a graphing utility to graph the function over the indicated interval and approximate any local maxima and local minima. Determine where the function is increasing and where it is decreasing. If necessary, round answers to two decimal places. 18) f(x) = x5 - x2 ; (-2, 2) 18)

19) f(x) = -0.3x3 + 0.2x2 + 4x - 5; (-4, 5)

19)

Solve the problem. 20) A gas company has the following rate schedule for natural gas usage in single-family residences: Monthly service charge

$8.80

Per therm service charge 1st 25 therms Over 25 therms

$0.6686/therm $0.85870/therm

20)

What is the charge for using 25 therms in one month? What is the charge for using 45 therms in one month? Construct a function that gives the monthly charge C for x therms of gas.

21) One Internet service provider has the following rate schedule for high-speed Internet service: Monthly service charge 1st 50 hours of use Next 50 hours of use Over 100 hours of use

$18.00 free $0.25/hour $1.00/hour

What is the charge for 50 hours of high-speed Internet use in one month? What is the charge for 75 hours of high-speed Internet use in one month? What is the charge for 135 hours of high-speed Internet use in one month?

21)

22) An electric company has the following rate schedule for electricity usage in single-family residences: Monthly service charge

$4.93

Per kilowatt service charge 1st 300 kilowatts Over 300 kilowatts

$0.11589/kW $0.13321/kW

22)

What is the charge for using 300 kilowatts in one month? What is the charge for using 375 kilowatts in one month? Construct a function that gives the monthly charge C for x kilowatts of electricity.

23) Michael decides to walk to the mall to do some errands. He leaves home, walks 2 blocks in 23) 8 minutes at a constant speed, and realizes that he forgot his wallet at home. So Michael runs back in 7 minutes. At home, it takes him 4 minutes to find his wallet and close the door. Michael walks 4 blocks in 12 minutes and then decides to jog to the mall. It takes him 7 minutes to get to the mall which is 2 blocks away. Draw a graph of Michael's distance from home (in blocks) as a function of time.

Solve the problem. 25) The volume V of a square-based pyramid with base sides s and height h is V =

1 2 s h. If the 3

25)

height is half of the length of a base side, express the volume V as a function of s.

Solve the problem. 27) A cellular phone plan had the following schedule of charges: Basic service, including 100 minutes of calls 2nd 100 minutes of calls Additional minutes of calls

27)

$20.00 per month $0.075 per minute $0.10 per minute

What is the charge for 200 minutes of calls in one month? What is the charge for 250 minutes of calls in one month? Construct a function that relates the monthly charge C for x minutes of calls.

28) A right triangle has one vertex on the graph of y = x2 at (x, y), another at the origin, and the third on the (positive) y-axis at (0, y). Express the area A of the triangle as a function of x.

28)

29) Two boats leave a dock at the same time. One boat is headed directly east at a constant speed of 35 knots (nautical miles per hour), and the other is headed directly south at a constant speed of 22 knots. Express the distance d between the boats as a function of the time t.

29)

30) A wire 20 feet long is to be cut into two pieces. One piece will be shaped as a square and the other piece will be shaped as an equilateral triangle. Express the total area A enclosed by the pieces of wire as a function of the length x of a side of the equilateral triangle. What is the domain of A?

30)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 31) f(x) = (-x)3 31)

32) f(x) = 4x3

32)

Solve the problem. 33) If f(x) = int(2x), find f(1.8). A) 4

B) 2

C) 3

D) 1

Find the average rate of change for the function between the given values. 34) f(x) = x3 + x2 - 8x - 7; from 0 to 2 A) -28

B) -

1 6

C) -2

1 2

Answer the question about the given function. x2 - 2 , if x = 2, what is f(x)? What point is on the graph of f? 35) Given the function f(x) = x+3 A)

2 2 ; (2, ) 5 5

2 2 ; ( , 2) 5 5

6 6 ; ( , 2) 5 5

34)

35)

6 6 ; (2, ) 5 5

Solve the problem. 36) Jacey, a commissioned salesperson, earns $290 base pay plus $48 per item sold. Express Jacey's gross salary G as a function of the number x of items sold. A) G(x) = 290(x + 48) B) G(x) = 290x +48 C) G(x) = 48(x + 290) D) G(x) = 48x + 290

33)

36)

Determine algebraically whether the function is even, odd, or neither. 37) f(x) = -7x2 - 9 A) even

B) odd

C) neither

37)

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 38) f(x) = -(x - 4)2 - 5 38)

Find the average rate of change for the function between the given values. 39) f(x) = -3x2 - x; from 5 to 6 A) -2

1 B) 6

1 C) 2

39) D) -34

Solve the problem. 40) The function P(d) = 1 +

d gives the pressure, in atmospheres (atm), at a depth d feet in the sea. 33

Find the pressure at 40 feet. 41 7 atm atm A) B) 33 33

73 atm 33

40)

40 atm 33

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. 41) (0, 2) 41)

A) increasing

B) decreasing

C) constant

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 42) f(x) = 5x2 42)

The graph of a function f is given. Use the graph to answer the question. 43) Is f(-20) positive or negative?

43)

-20

A) positive

B) negative

Find the domain of the function. 44) f(x) = -4x + 5 A) {x|x -5} C) {x|x > 0}

B) all real numbers D) {x|x 0} 14

44)

Solve the problem. 45) Elissa wants to set up a rectangular dog run in her backyard. She has 30 feet of fencing to work with and wants to use it all. If the dog run is to be x feet long, express the area of the dog run as a function of x. A) A(x) = 16x - x2 B) A(x) = 17x2 - x C) A(x) = 15x - x2 D) A(x) = 14x - x2 46) The concentration C (arbitrary units) of a certain drug in a patient's bloodstream can be modeled t using C(t) = , where t is the number of hours since a 500 milligram oral dose was 0.542t + 1.844 2

45)

46)

administered. Using the TABLE feature of a graphing utility, find the time at which the concentration of the drug is greatest. Round to the nearest tenth of an hour. A) 4.9 hours B) 4.2 hours C) 3.4 hours D) 5.7 hours

The graph of a function f is given. Use the graph to answer the question. 47) Find the numbers, if any, at which f has a local minimum. What are the local minima?

47)

A) f has a local minimum at x = - and ; the local minimum is 1 B) f has a local minimum at x = 0; the local minimum is -1 C) f has a local minimum at x = - ; the local minimum is -1 D) f has no local minimum For the function, find the average rate of change of f from 1 to x: f(x) - f(1) ,x 1 x-1

48) f(x) =

6 x+5

A) -

1 x+5

48) B)

6 (x - 1)(x + 5)

6 x(x + 5)

Complete the square and then use the shifting technique to graph the function.

1 x+5

49) f(x) = x2 - 4x

49)

Use the accompanying graph of y = f(x) to sketch the graph of the indicated equation.

50) y = - 4f(x + 5) + 4

50)

Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts, if any, and any symmetry with respect to the x-axis, the y-axis, or the origin. 51) 51)

A) function domain: all real numbers range: {y|-1 y 1} intercepts: (- , 0), (-

, 0), (-

, 0), (0, 0), (

, 0), ( , 0), ( , 0), ( , 0), ( , 0) 2 4 4

symmetry: origin B) function domain: {x|x } range: {y|-1 y 1} intercepts: (- , 0), (-

, 0), (-

, 0), (0, 0), (

symmetry: origin C) function domain: {x|-1 x 1} range: {y|y } intercepts: (- , 0), (-

, 0), (-

, 0), (0, 0), (

symmetry: none D) not a function

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 52) f(x) = x - 6 - 2 52)

53) f(x) = |x + 5| - 3

53)

54) f(x) =

54)

x-3+7

The graph of a function f is given. Use the graph to answer the question. 55) Use the graph of f given below to find f(16).

55)

-20

A) 16

B) 8

C) 28

D) 20

56) Find the numbers, if any, at which f has a local maximum. What are the local maxima?

56)

A) f has a local maximum at x = -1 and 1; the local maximum is 0 B) f has a local maximum at x = 0; the local maximum is 1 C) f has a local maximum at x = 1; the local maximum is 1 D) f has no local maximum Use a graphing utility to graph the function over the indicated interval and approximate any local maxima and local minima. If necessary, round answers to two decimal places. 57) f(x) = x2 + 2x - 3; (-5, 5) 57)

A) local minimum at (1, 4) C) local maximum at (1, -4)

Find the value for the function. 58) Find f(-x) when f(x) = A)

B) local maximum at (-1, 4) D) local minimum at (-1, -4)

x . 2 x +6

-x

x2 - 6

58) x

-x2 + 6

-x

x2 + 6

-x

-x2 + 6

Solve the problem. 59) A farmer's silo is the shape of a cylinder with a hemisphere as the roof. If the height of the silo is 99 feet and the radius of the hemisphere is r feet, express the volume of the silo as a function of r. 8 2 3 r3 r A) V(r) = 99 r2 + B) V(r) = (99 - r)r2 + 3 3 C) V(r) = (99 - r) +

4 3

4 D) V(r) = (99 - r)r3 + 3

Graph the function.

59)

60) f(x) =

60)

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting.

61) f(x) = x3 + 2

61)

The graph of a function f is given. Use the graph to answer the question. 62) What are the x-intercepts?

62)

100

-100

A) -60, 70, 100 C) -60

B) -100, -60, 70, 100 D) -60, 70

Find the value for the function. 63) Find f(x + 1) when f(x) =

x2 - 6 . x-2

x2 + 2x - 5 x+3

Graph the function. 64) -x + 2 f(x) = x+3

63)

x2 + 2x + 7 x-1

x2 + 2x - 5 x-1

x2 - 5 x-1

64)

x<0 x 0

65) f(x) =

x+4 -8 -x + 3

65)

if -8 x < 2 if x = 2 if x > 2

For the graph of the function y = f(x), find the absolute maximum and the absolute minimum, if it exists. 66)

A) Absolute maximum: f(6) = 5; Absolute minimum: f(1) = 2 B) Absolute maximum: f(5) = 6; Absolute minimum: f(2) = 1 C) Absolute maximum: f(2) = 7; Absolute minimum: f(3) = 0 D) Absolute maximum: f(7) = 2; Absolute minimum: f(0) = 3

66)

Solve the problem. 67) If an object weighs m pounds at sea level, then its weight W (in pounds) at a height of h miles 4000 2 above sea level is given approximately by W(h) = m . How much will a man who 4000 + h

67)

weighs 165 pounds at sea level weigh on the top of a mountain which is 14,494 feet above sea level? Round to the nearest hundredth of a pound, if necessary. A) 165.23 pounds B) 164.77 pounds C) 165 pounds D) 7.72 pounds

Find the value for the function.

68) Find f(2x) when f(x) = 2x2 + 4x - 1. A) 8x2 + 8x - 2 B) 8x2 + 8x - 1

C) 4x2 + 8x - 2

D) 4x2 + 8x - 1

68)

Solve the problem.

69) Find (fg)(-5) when f(x) = x + 2 and g(x) = 4x2 + 20x - 3. A) 21 B) 9 C) 234

D) -679

Answer the question about the given function. x2 + 4 , list the y-intercept, if there is one, of the graph of f. 70) Given the function f(x) = x-7 A) (0, -4)

B) (-

4 , 0) 7

C) (0, -

4 ) 7

69)

70)

D) (0, 7)

Solve the problem. 71) Along with incomes, people's charitable contributions have steadily increased over the past few years. The 71) table below shows the average deduction for charitable contributions reported on individual income tax returns for the period 1993 to 1998. Find the average rate of change between 1995 and 1997. Year Charitable Contributions 1993 $1900 1994 $2410 1995 $2450 1996 $2830 1997 $3000 1998 $3180 A) $275 per year B) $295 per year C) $550 per year D) $365 per year

72) The height s of a ball (in feet) thrown with an initial velocity of 70 feet per second from an initial height of 5 feet is given as a function of time t (in seconds) by s(t) = -16t2 + 70t + 5. What is the

72)

maximum height? Round to the nearest hundredth, if necessary.

A) 92.5 ft Find the value for the function. 73) Find f(2) when f(x) = A) -

1 5

B) -54.37 ft

C) 76.88 ft

D) 81.56 ft

x2 - 5 . x+3

73)

B) 3

4 5

9 5

A) function domain: {x|x 0} range: {y|y -2} intercepts: (-2, 0), (0, -2), (2, 0) symmetry: y-axis C) function domain: {x|x -2} range: {y|y 0} intercepts: (-2, 0), (0, -2), (2, 0) symmetry: none

B) function domain: all real numbers range: all real numbers intercepts: (-2, 0), (0, -2), (2, 0) symmetry: none D) not a function

Solve the problem. 75) From a 24-inch by 24-inch piece of metal, squares are cut out of the four corners so that the sides can then be folded up to make a box. Let x represent the length of the sides of the squares, in inches, that are cut out. Express the volume of the box as a function of x. A) V(x) = 2x3 - 72x2 + 24x B) V(x) = 4x3 - 96x2 + 576x C) V(x) = 2x3 - 72x2

75)

D) V(x) = 4x3 - 96x2

76) Express the gross salary G of a person who earns $15 per hour as a function of the number x of hours worked. 15 A) G(x) = 15x2 B) G(x) = 15 + x C) G(x) = 15x D) G(x) = x

76)

Use a graphing utility to graph the function over the indicated interval and approximate any local maxima and local minima. If necessary, round answers to two decimal places. 77) f(x) = x3 - 12x + 2; (-5, 5) 77)

A) local maximum at (-2, 18) local minimum at (0, 0) local minimum at (2, -14) C) local minimum at (0, 0)

B) local maximum at (-2, 18) local minimum at (2, -14)

D) none

Determine whether the equation defines y as a function of x. 78) y = ± 1 - 2x A) function

78)

B) not a function

Find an equation of the secant line containing (1, f(1)) and (2, f(2)). 2 79) f(x) = x+1 A) y = -

1 4 x+ 3 3

B) y =

2 1 x+ 3 3

C) y =

79) 1 x+2 3

D) y =

1 2 x+ 3 3

Solve the problem. 80) A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 80) 13 inches by 20 inches by cutting out equal squares of side x at each corner and then folding up the sides as in the figure. Express the volume V of the box as a function of x. 20

A) V(x) = x(13 - 2x)(20 - 2x) C) V(x) = (13 - x)(20 - x)

B) V(x) = (13 - 2x)(20 - 2x) D) V(x) = x(13 - x)(20 - x)

The graph of a function is given. Decide whether it is even, odd, or neither. 81)

A) even

B) odd

81)

C) neither

A) function domain: {x|-1 x 1} range: all real numbers intercepts: (-1, 0), (1, 0) symmetry: x-axis, y-axis C) function domain: all real numbers range: {y|y -1 or y 1} intercepts: (-1, 0), (1, 0) symmetry: y-axis

B) function domain: {x|x -1 or x 1} range: all real numbers intercepts: (-1, 0), (1, 0) symmetry: x-axis, y-axis, origin D) not a function

Suppose the point (2, 4) is on the graph of y = f(x). Find a point on the graph of the given function. 83) y = f(x + 3) A) (2, 7) B) (-1, 4) C) (2, 1) D) (5, 4)

83)

For the given functions f and g, find the requested function and state its domain. 84) f(x) = 16 - x2 ; g(x) = 4 - x Find f + g. A) (f + g)(x) = 4 + x; {x|x -4} B) (f + g)(x) = x3 - 4x2 - 16x + 64; all real numbers

84)

C) (f + g)(x) = -x2 - x + 20; all real numbers D) (f + g)(x) = -x2 + x + 12; all real numbers

Determine whether the relation represents a function. If it is a function, state the domain and range. 3 85) {(4.11, 12.41), (4.111, -12.4), ( , 0), (0.43, -4)} 7

85)

A) function domain: {12.41, -12.4, 0, -4} 3 range: {4.11, 4.111, , 0.43} 7 B) function domain: {4.11, 4.111,

3 , 0.43} 7

range: {12.41, -12.4, 0, -4} C) not a function

The graph of a function is given. Decide whether it is even, odd, or neither. 86)

A) even

B) odd

86)

C) neither

The graph of a function f is given. Use the graph to answer the question. 87) How often does the line y = -10 intersect the graph?

87)

-10

A) once C) three times

B) twice D) does not intersect

Solve the problem. 88) Find (f + g)(-3) when f(x) = x + 5 and g(x) = x + 7. A) 6 B) -18

C) -8

D) -4

88)

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 1 89) f(x) = 89) 7x

A) function domain: {x|x > 0} range: all real numbers intercept: (1, 0) symmetry: none C) function domain: {x|x > 0} range: all real numbers intercept: (0, 1) symmetry: origin Solve.

B) function domain: all real numbers range: {y|y > 0} intercept: (1, 0) symmetry: none D) not a function

91) A rock falls from a tower that is 58.8 m high. As it is falling, its height is given by the formula h(t) = 58.8 - 4.9t2 . How many seconds will it take for the rock to hit the ground (h=0)? Round to the nearest tenth. A) 7.7 sec

B) 700 sec

C) 3.5 sec

91)

D) 12.3 sec

Solve the problem. 92) The following numerical representation for f computes the average number of hours of television watched 92) per day based on year of birth x. x 1975 1980 1983 1988 1990 1992 1995 f(x) 2 2.5 3 3.5 4 3.5 4 Give a numerical representation for a function g that computes the average number of hours of television watched per day for the year x, where x = 0 corresponds to the birth year 1975. Write an equation that shows the relationship between f(x) and g(x). 75 80 83 88 90 92 95 0 5 8 13 15 17 20 A) x B) x g(x) 2 2.5 3 3.5 4 3.5 4 g(x) 2 2.5 3 3.5 4 3.5 4 f(x) = g(x - 1900) f(x) = g(x - 1975) 0 5 8 13 15 17 20 0 5 8 13 15 17 20 C) x D) x g(x) 2 2.5 3 3.5 4 3.5 4 g(x) 2 2.5 3 3.5 4 3.5 4 f(x) = g(x) - 1975 f(x) = g(x + 1975)

Determine algebraically whether the function is even, odd, or neither. x 93) f(x) = 2 x -4 A) even

B) odd

93) C) neither

Write the equation of a sine function that has the given characteristics. 94) The graph of y = x, shifted 9 units to the right A) y = x + 9 B) y = x + 9 C) y = x - 9

94) D) y =

x-9

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 95) f(x) = (x - 4)3 - 2 95)

Solve the problem.

96) The function f(t) = -0.14t2 + 0.49t + 30.7 models the U.S. population in millions, ages 65 and older, where t represents years after 1990. The function g(t) = 0.52t2 + 11.32t + 107.8 models the total

96)

yearly cost of Medicare in billions of dollars, where t represents years after 1990. What does the g g function represent? Find (15). f f

A) Cost per person in thousands of dollars. $7.38 thousand B) Cost per person in thousands of dollars. $0.02 thousand C) Cost per person in thousands of dollars. $60.24 thousand D) Cost per person in thousands of dollars. $0.18 thousand Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 97) f(x) = x2 - 2 97)

Solve the problem. 98) Suppose a cold front is passing through the United States at noon with a shape described by the 1 2 function y = x , where each unit represents 100 miles. St. Louis, Missouri is located at (0, 0), and 29

98)

the positive y-axis points north. N

S Suppose the front moves south 340 miles and west 120 miles and maintains its shape. Give the equation for the new front and plot the new position of the front. 1 1 (x - 1.2)2 + 3.4 (x + 1.2)2 - 3.4 A) y = B) y = 29 29

C) y =

1 (x - 1.2)2 - 3.4 29

D) y =

1 (x + 1.2)2 - 3.4 29 N

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 99) f(x) = (x - 2)2 99)

Find the domain of the function. 100) f(x) = x2 + 9 A) {x|x -9} C) {x|x -9}

101) f(x) = 16 - x A) {x|x 4}

100)

B) all real numbers D) {x|x > -9}

B) {x|x 16}

C) {x|x 16}

D) {x|x 4}

101)

Determine algebraically whether the function is even, odd, or neither. 102) f(x) = x A) even B) odd

102)

C) neither

Determine whether the relation represents a function. If it is a function, state the domain and range. 103) 3 6 9 12

103)

9 18 27 36

A) function domain: {3, 6, 9, 12} range: {9, 18, 27, 36}

B) function domain:{9, 18, 27, 36} range: {3, 6, 9, 12}

C) not a function

Solve the problem. 104) A deep sea diving bell is being lowered at a constant rate. After 12 minutes, the bell is at a depth of 500 ft. After 50 minutes the bell is at a depth of 1,900 ft. What is the average rate of lowering per minute? Round to the nearest hundredth is needed. A) 0.03 ft per minute B) 36.8 ft per minute C) 28.0 ft per minute D) 38.0 ft per minute Determine whether the relation represents a function. If it is a function, state the domain and range. 105) {(-3, -6), (0, 4), (4, 0), (8, -1)} A) function B) function C) not a function domain: {-6, 4, 0, -1} domain: {-3, 0, 4, 8} range: {-3, 0, 4, 8} range: {-6, 4, 0, -1} Determine algebraically whether the function is even, odd, or neither. 2x 106) f(x) = |x| A) even

B) odd

104)

105)

106) C) neither

Find the value for the function. 107) Find f(2x) when f(x) = A) 2 2x2 + 9x

2x2 + 9x.

107) 4x2 + 36x

4x2 + 18x

8x2 + 18x

Locate any intercepts of the function. 108) 1 if -3 x < -8 if -8 x < 3 f(x) = |x| x A) (0, 0)

if 3 x 32

108)

B) (0, 0), (0, 1)

C) (0, 0), (1, 0)

D) none

Find and simplify the difference quotient of f,

f(x + h) - f(x) , h 0, for the function. h

109) f(x) = x2 + 7x + 1 A) 2x+ h + 1

2x2 + 2x + 2xh + h 2 + h + 2 B) h

C) 1

D) 2x+ h + 7

109)

Solve the problem. 110) A steel can in the shape of a right circular cylinder must be designed to hold 350 cubic centimeters 110) of juice (see figure). It can be shown that the total surface area of the can (including the ends) is 700 given by S(r) = 2 r2 + , where r is the radius of the can in centimeters. Using the TABLE feature of a r graphing utility, find the radius that minimizes the surface area (and thus the cost) of the can. Round to the nearest tenth of a centimeter.

A) 3.8 cm

B) 5 cm

C) 0 cm

D) 3 cm

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. 111) (- 4, - 2) 111)

A) decreasing

B) constant

C) increasing

The graph of a function f is given. Use the graph to answer the question. 112) What is the domain of f?

112)

-25

A) {x|-20 x 27.5} C) {x|-25 x 25}

B) {x|x 0} D) all real numbers

Find the function. 113) Find the function that is finally graphed after the following transformations are applied to the graph of y = |x|. The graph is shifted right 3 units, stretched by a factor of 3, shifted vertically down 2 units, and finally reflected across the x-axis. A) y = -(3|x + 3| - 2) B) y = -(3|x - 3| - 2) C) y = 3|-x - 3| - 2 D) y = -3|x - 3| - 2 For the given functions f and g, find the requested function and state its domain. 114) f(x) = x; g(x) = 3x - 7 f Find . g

114)

f x (x) = ; g 3x - 7

7 3

f x (x) = ; {x|x 0} g 3x - 7

f 3x - 7 (x) = ; {x|x 0} g x

f x (x) = ; g 3x - 7

x|x

113)

x|x 0, x

7 3

Find the value for the function.

115) Find f(-x) when f(x) = -3x2 + 3x - 5. A) -3x2 - 3x - 5 B) 3x2 - 3x - 5

C) 3x2 - 3x + 5

D) -3x2 - 3x + 5

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting.

115)

116) f(x) = |-x|

116)

Graph the function.

117) f(x) = x2

117)

Use a graphing utility to graph the function over the indicated interval and approximate any local maxima and local minima. If necessary, round answers to two decimal places. 118) f(x) = x3 - 3x2 + 1; (-5, 5) 118)

A) local minimum at (0, 1) local maximum at (2, -3) C) local minimum at (2, -3)

B) local maximum at (0, 1) local minimum at (2, -3) D) none

Based on the graph, find the range of y = f(x). 119) 4 if -5 x < -2 if -2 x < 5 f(x) = |x| 3 x if 5 x 13

A) [0, )

119)

C) [0,

B) [0, 5)

13]

Write the equation of a sine function that has the given characteristics. 120) The graph of y = x, shifted 5 units to the left A) y = x - 5 B) y = x + 5 C) y = x - 5

D) [0, 5]

120) D) y =

x+5

Solve the problem. 121) A farmer has 1,200 yards of fencing to enclose a rectangular garden. Express the area A of the rectangle as a function of the width x of the rectangle. What is the domain of A? A) A(x) = -x2 + 1,200x; {x|0 < x < 1,200} B) A(x) = x2 + 600x; {x|0 < x < 600} C) A(x) = -x2 + 600x; {x|0 < x < 1,200}

121)

D) A(x) = -x2 + 600x; {x|0 < x < 600}

Graph the function. 122) f(x) = x

122)

The graph of a piecewise-defined function is given. Write a definition for the function. 123)

A) f(x) =

-2x x

C) f(x) =

1 x 2

if -4 x 0 if 0 < x 3

f(x) =

D) if -4 x 0

f(x) =

if 0 < x 3

1 x 2

if -4 < x < 0

if 0 < x < 3

1 x 2

if -4 < x < 0

if 0 < x < 3

123)

Find the domain of the function. 124) if x 0 f(x) = -2x -3 if x = 0 A) {x|x 0} C) all real numbers

124)

B) {0} D) {x|x 0}

Determine whether the relation represents a function. If it is a function, state the domain and range. 125) Bob Ann Dave

125)

carrots peas squash

A) function domain: {Bob, Ann, Dave} range: {carrots, peas, squash} B) function domain: {carrots, peas, squash} range: {Bob, Ann, Dave} C) not a function Determine whether the equation defines y as a function of x. 126) y = |x| A) function

126)

B) not a function

The graph of a piecewise-defined function is given. Write a definition for the function. 127)

A) f(x) =

C) f(x) =

4 x+4 3

if -3 x 0

2 x 3

if 0 < x 3

f(x) =

3 x+4 4

if -3 x 0

3 x 2

if x 0

f(x) =

3 x+4 4

if -3 x 0

3 x 2

if x > 0

4 x+4 3

if -3 x 0

2 x 3

if x > 0

127)

Find the domain of the function. 128) 1 if -4 x < -3 if -3 x < 4 f(x) = |x| 3 x if 4 x 30 A) {x|4 x 30} C) {x|x -4}

128)

B) {x|-4 x 30} D) {x|-4 x < 4 or 4 < x 30}

Answer the question about the given function. x2 + 8 , what is the domain of f? 129) Given the function f(x) = x+3 A) {x|x 8}

C) {x|x -

B) {x|x -3}

129) 8 } 3

D) {x|x 3}

Find the value for the function.

130) Find f(x - 1) when f(x) = 3x2 - 3x + 2. A) -9x2 + 3x + 8 B) 3x2 + 3x + 2

C) 3x2 - 9x + 2

D) 3x2 - 9x + 8

Answer the question about the given function. 131) Given the function f(x) = -6x2 + 12x - 4, if x = 1, what is f(x)? What point is on the graph of f? A) 2; (1, 2)

B) 2; (2, 1)

C) -22; (-22, 1)

D) -22; (1, -22)

Determine algebraically whether the function is even, odd, or neither. -x3 132) f(x) = 8x2 - 4 A) even

B) odd

131)

132) C) neither

The graph of a function is given. Decide whether it is even, odd, or neither. 133)

A) even

130)

B) odd

133)

C) neither

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting.

134) f(x) =

1 3

134)

Solve the problem.

135) Find (f - g)(-3) when f(x) = -4x2 - 6 and g(x) = x - 4. A) -43 B) -41 C) 45

D) -35

135)

Find the value for the function. 136) Find f(5) when f(x) = A) 34

x2 + 3x. B) 2 10

136) C) 2 7

D) 2 3

Determine algebraically whether the function is even, odd, or neither. 137) f(x) = 4x3 - 9 A) even

B) odd

C) neither

Find the domain of the function. x 138) g(x) = 2 x - 25

137)

138)

A) {x|x > 25} C) {x|x 0}

B) all real numbers D) {x|x -5, 5}

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 1 139) f(x) = x2 139) 6

Solve the problem.

140) If f(x) = 7x3 + 5x2 - x + C and f(2) = 1, what is the value of C? A) C = -73 B) C = 39 C) C = -9 141) If f(x) =

D) C = 79

x-B , f(-9) = 0, and f(4) is undefined, what are the values of A and B? x-A

A) A = -4, B = 9

B) A = 4, B = -9

C) A = 9, B = -4

140)

141) D) A = -9, B = 4

142) The following graph shows the private, public and total national school enrollment for students for select 142) years from 1970 through 2000.

i) How is the graph for total school enrollment, T, determined from the graph of the private enrollment, r, and the public enrollment, u? ii) During which 10-year period did the total number of students enrolled increase the least? iii) During which 10-year period did the total number of students enrolled increase the most? A) i) T is the sum of r and u. B) i) T is the sum of r and u. ii) 1990-2000 ii) 1970 - 1980 iii) 1970-1980 iii) 1980-1990 C) i) T is the difference of r and u. D) i) T is the sum of r and u. ii) 1970 - 1980 ii) 1970 - 1980 iii) 1990-2000 iii) 1990-2000

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. 143) (1, ) 143)

A) decreasing

B) constant

C) increasing

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 144) f(x) = -x3 144)

Suppose the point (2, 4) is on the graph of y = f(x). Find a point on the graph of the given function. 145) y = 4f(x) A) (2, 16) B) (5, 3) C) (8, 4) D) (3, 8)

145)

Solve the problem. 146) From April through December 2000, the stock price of QRS Company had a roller coaster ride. The chart 146) below indicates the price of the stock at the beginning of each month during that period. Find the monthly average rate of change in price between June and September. Month Price April (x = 1) 115 May 108 June 87 July 99 August 95 September 112 October 92 November 84 December 64 A) -$12.50 per month B) $8.33 per month C) -$8.33 per month D) $12.50 per month 147) Suppose that the function y = f(x) is decreasing on the interval (4, 2). What can be said about the graph of y = -f(x)? A) decreasing on (4, 2) B) increasing on (-4, -2) C) decreasing on (-4, -2) D) increasing on (4, 2)

147)

Find the value for the function.

148) Find f(3) when f(x) = x2 + 5x + 4. A) 20 B) -2

C) 28

D) -10

148)

A) function domain: {x|-2 x 2} range: {y|-2 y 2} intercepts: (-2, 0), (0, -2), (0, 2), (2, 0) symmetry: x-axis, y-axis, origin C) function domain: {x|-2 x 2} range: {y|-2 y 2} intercepts: (-2, 0), (0, -2), (0, 2), (2, 0) symmetry: x-axis, y-axis

B) function domain: {x|-2 x 2} range: {y|-2 y 2} intercepts: (-2, 0), (0, -2), (0, 0), (0, 2), (2, 0) symmetry: origin D) not a function

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 150) f(x) = -x2 150)

Graph the function. 1 151) f(x) = x

151)

Solve the problem. 152) Suppose that the x-intercepts of the graph of y = f(x) are 3 and 4. What are the x-intercepts of y = 2f(x)? A) 1 and 2 B) 12 and 8 C) 3 and 4 D) 5 and 6 Determine algebraically whether the function is even, odd, or neither. 3 153) 7x2 + 4 A) even B) odd

C) neither

152)

153)

The graph of a function f is given. Use the graph to answer the question. 154) Find the numbers, if any, at which f has a local maximum. What are the local maxima?

154)

A) f has a local maximum at - ; the local maximum is 2 B) f has no local maximum C) f has a local maximum at x = - and ; the local maximum is -2 D) f has a local maximum at x = 0; the local maximum is 2 Solve the problem. 155) A wire of length 9x is bent into the shape of a square. Express the area A of the square as a function of x. 81 2 9 81 2 1 2 x x x A) A(x) = B) A(x) = x2 C) A(x) = D) A(x) = 16 4 8 16 156) The function F described by F(C) =

9 C + 32 gives the Fahrenheit temperature corresponding to the 5

Celsius temperature C. Find the Fahrenheit temperature equivalent to 20°C. A) 68°F B) 140°F C) 176°F

Find the average rate of change for the function between the given values. 157) f(x) = 2x; from 2 to 8 1 3 A) B) C) 2 3 10 Find and simplify the difference quotient of f,

155)

156)

D) 104°F

157) D) 7

f(x + h) - f(x) , h 0, for the function. h

158) f(x) = 5x2

158)

A) 5

10 + x + 5h h

C) 5(2x+h)

5(2x2 + 2xh + h 2 ) h

Suppose the point (2, 4) is on the graph of y = f(x). Find a point on the graph of the given function. 159) f(x) + 4 A) (2, 8) B) (6, 4) C) (-2, 4) D) (2, -4)

159)

For the given functions f and g, find the requested function and state its domain. 2 160) f(x) = x + 11; g(x) = x

160)

Find f · g.

A) (f · g)(x) =

2x + 22 ; {x|x -11, x 0} x

B) (f · g)(x) =

2x + 22 ; {x|x -11, x 0} x

C) (f · g)(x) =

13 ; {x|x 0} x

D) (f · g)(x) =

2 x + 11 ; {x|x -11, x 0} x

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. 3 161) (- , 0) 161) 2

A) constant

B) increasing

C) decreasing

Solve. 162) A rock falls from a tower that is 432 ft high. As it is falling, its height is given by the formula h(t) = 432 - 16t2 . How many seconds will it take for the rock to hit the ground (h=0)? Round to the nearest tenth. A) 27 sec

B) 20.8 sec

Find the value for the function. 163) Find f(-9) when f(x) = |x|- 6. A) -15 B) -3

C) 11,664 sec

D) 5.2 sec

C) 3

D) 15

162)

163)

The graph of a function is given. Decide whether it is even, odd, or neither. 164)

A) even

B) odd

164)

C) neither

The graph of a function f is given. Use the graph to answer the question. 165) What is the y-intercept?

165)

-25

A) -20

B) 25

C) -15

D) 17.5

Solve the problem. 166) A firm is considering a new product. The accounting department estimates that the total cost, C(x), of 166) producing x units will be C(x) = 50x + 5,040. The sales department estimates that the revenue, R(x), from selling x units will be R(x) = 60x, but that no more than 662 units can be sold at that price. Find and interpret (R - C)(662). A) -$1,580 loss, cost exceeds income B) $77,860 profit, income exceeds cost It is not worth it to develop product. It is worth it to develop product. C) $1,580 profit, income exceeds cost D) $1,166 profit, income exceeds cost It is worth it to develop product. It is worth it to develop product.

For the given functions f and g, find the requested function and state its domain. 167) f(x) = 7x + 7; g(x) = 8x - 2 Find f · g. A) (f · g)(x) = 15x2 + 42x + 5; all real numbers

167)

B) (f · g)(x) = 56x2 - 14; {x|x -14} C) (f · g)(x) = 56x2 + 54x - 14; {x|x -14}

D) (f · g)(x) = 56x2 + 42x - 14; all real numbers Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 1 168) f(x) = 168) x-2

Find the average rate of change for the function between the given values. 3 ; from 1 to 4 169) f(x) = x+2 A)

1 2

B) -

1 6

C) -28

169) D) -2

Determine whether the relation represents a function. If it is a function, state the domain and range. 170) {(-1, -4), (-2, -3), (-2, 0), (7, 3), (23, 5)} A) function B) function C) not a function domain: {-4, -3, 0, 3, 5} domain: {-1, 7, -2, 23} range: {-1, 7, -2, 23} range: {-4, -3, 0, 3, 5}

170)

A) function domain: {x|x = 5 or x = -9} range: all real numbers intercept: (-9, 0) symmetry: x-axis C) function domain: all real numbers range: all real numbers intercept: (0, -9) symmetry: none

B) function domain: all real numbers range: {y|y = 5 or y = -9} intercept: (0, -9) symmetry: none D) not a function

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting.

172) f(x) =

1 3 x 6

172)

Solve the problem. 173) A rectangular sign is being designed so that the length of its base, in feet, is 12 feet less than 4 times the height, h. Express the area of the sign as a function of h. A) A(h) = -12h + 4h 2 B) A(h) = -12h + h 2 C) A(h) = -12h 2 + 2h

D) A(h) = 12h - 2h 2

173)

For the given functions f and g, find the requested function and state its domain. 174) f(x) = x - 6; g(x) = 5x2 Find f - g.

A) (f - g)(x) = 5x2 + x - 6; all real numbers C) (f - g)(x) = 5x2 - x + 6; all real numbers

174)

B) (f - g)(x) = 5x2 + x - 6; {x|x 6} D) (f - g)(x) = -5x2 + x - 6; all real numbers

175) f(x) = 5x + 2; g(x) = 4x - 1 f Find . g

175)

f 5x + 2 (x) = ; g 4x - 1

x|x

1 4

f 4x - 1 (x) = ; g 5x + 2

x|x -

2 5

f 5x + 2 (x) = ; g 4x - 1

x|x -

f 4x - 1 (x) = ; g 5x + 2

x|x

2 5

1 4

Solve the problem. 176) Suppose that P(x) represents the percentage of income spent on food in year x and I(x) represents income in year x. Determine a function F that represents total food expenditures in year x. I (x) A) F(x) = B) F(x) = (P + I)(x) C) F(x) = (I - P)(x) D) F(x) = (P · I)(x) P Graph the function. 177) 1 f(x) = |x| 3 x

176)

177)

if -2 x < 4 if 4 x < 9 if 9 x 14

The graph of a piecewise-defined function is given. Write a definition for the function. 178)

A) f(x) =

C) f(x) =

4 x+4 3

if -3 x 0

2 x+2 3

if 0 < x 3

f(x) =

4 x+4 3

if -3 x 0

2 x 3

if 0 < x 3

f(x) =

3 x+4 4

if -3 x 0

3 x 2

if 0 < x 3

178)

4 x - 4 if -3 x 0 3 2 x 3

if 0 x 3

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 179) f(x) = x + 5 179)

Find the domain of the function. x2 180) f(x) = x2 + 20

180)

A) {x|x 0} C) {x|x -20}

B) {x|x > -20} D) all real numbers

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. 181) (1, 3) 181)

A) decreasing

B) constant

C) increasing

Suppose the point (2, 4) is on the graph of y = f(x). Find a point on the graph of the given function. 182) The reflection of the graph of y = f(x) across the y-axis A) (2, 4) B) (-2, -4) C) (-2, 4) D) (2, -4) Solve the problem. 183) Suppose that the x-intercepts of the graph of y = f(x) are 9 and 7. What are the x-intercepts of y = f(x - 2)? A) 18 and 14 B) 9 and 5 C) 11 and 9 D) 7 and 5 For the given functions f and g, find the requested function and state its domain. 184) f(x) = 5x3 + 3; g(x) = 6x2 + 1 Find f · g.

182)

183)

184)

A) (f · g)(x) = 5x3 + 6x2 + 3; all real numbers B) (f · g)(x) = 30x5 + 5x3 + 18x2 + 3; all real numbers C) (f · g)(x) = 30x6 + 5x3 + 18x2 + 3; all real numbers D) (f · g)(x) = 30x5 + 5x3 + 18x2 + 3; {x|x 0}

The graph of a function f is given. Use the graph to answer the question. 185) For what numbers x is f(x) = 0? 25

-25

A) (-15, 17.5) C) -15

B) -15, 17.5, 25 D) (-25, -15), (17.5, 25)

185)

For the graph of the function y = f(x), find the absolute maximum and the absolute minimum, if it exists. 186)

186)

A) Absolute maximum: f(3) = 5; Absolute minimum: f(1) = 2 B) Absolute maximum: none; Absolute minimum: f(1) = 2 C) Absolute maximum: f(-1) = 6; Absolute minimum: f(1) = 2 D) Absolute maximum: none; Absolute minimum: none Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 1 187) f(x) = 187) x

A) local maximum at (0, 3) local minimum at (2, -1) increasing on (0, 2) decreasing on (-1, 0) and (2, 3) C) local maximum at (2, -1) local minimum at (0, 3) increasing on (-1, 0) decreasing on (0, 2)

B) local maximum at (0, 3) local minimum at (2, -1) increasing on (-1, 0) and (2, 3) decreasing on (0, 2) D) local maximum at (2, -1) local minimum at (0, 3) increasing on (-1, 0) and (2, 3) decreasing on (0, 2)

Solve the problem. 189) Suppose that the x-intercepts of the graph of y = f(x) are 4 and 5. What are the x-intercepts of y = f(-x)? A) -4 and -5 B) 4 and 5 C) -4 and 5 D) 4 and -5 The graph of a function is given. Decide whether it is even, odd, or neither. 190)

A) even

B) odd

190)

C) neither

189)

Use the accompanying graph of y = f(x) to sketch the graph of the indicated equation. 191) y = 2f(x)

191)

The graph of a function is given. Decide whether it is even, odd, or neither. 192)

A) even

B) odd

192)

C) neither

Use a graphing utility to graph the function over the indicated interval and approximate any local maxima and local minima. If necessary, round answers to two decimal places. 193) f(x) = 2 + 8x - x2; (-5, 5) 193)

A) local maximum at (-4, 50) C) local minimum at (4, 50)

B) local minimum at (-4, 18) D) local maximum at (4, 18)

Find the value for the function.

194) Find -f(x) when f(x) = -3x2 - 5x - 1. A) -3x2 + 5x + 1 B) 3x2 + 5x - 1

C) 3x2 + 5x + 1

D) -3x2 + 5x - 1

Solve the problem. 195) A rocket is shot straight up in the air from the ground at a rate of 77 feet per second. The rocket is tracked by a range finder that is 496 feet from the launch pad. Let d represent the distance from the rocket to the range finder and t represent the time, in seconds, since "blastoff". Express d as a function of t. A) d(t) = 4962 + (77t)2 B) d(t) = 4962 + (77t)2 C) d(t) = 496 + 77t2

D) d(t) =

C) 27 watches

3,504 x

D) C(x) = 3x2 +

196)

D) 55 watches

Solve the problem. 197) A rectangular box with volume 438 cubic feet is built with a square base and top. The cost is $1.50 per square foot for the top and the bottom and $2.00 per square foot for the sides. Let x represent the length of a side of the base. Express the cost the box as a function of x. 3,504 1,752 A) C(x) = 3x2 + B) C(x) = 4x + x x2 C) C(x) = 2x2 +

195)

772 + (496t)2

Solve. 196) Bob owns a watch repair shop. He has found that the cost of operating his shop is given by c(x) = 3x2 - 204x + 55, where c is cost and x is the number of watches repaired. How many watches must he repair to have the lowest cost? A) 30 watches B) 34 watches

194)

3,504 x

197)

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 198) f(x) = |x + 5| 198)

Find the domain of the function. x 199) x-4

199)

A) all real numbers C) {x|x 4}

B) {x|x > 4} D) {x|x 4}

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting.

200) f(x) = (x + 3)3

200)

Solve the problem. 201) If a rock falls from a height of 60 meters on Earth, the height H (in meters) after x seconds is approximately H(x) = 60 - 4.9x2 .

When does the rock strike the ground? Round to the nearest hundredth, if necessary. A) 2.5 sec B) 12.24 sec C) 3.5 sec D) 1.58 sec

201)

Find the value for the function.

202) Find f(x + h) when f(x) = 3x2 + 2x + 1. A) 3x2 + 3h 2 + 2x + 2h + 1

B) 3x2 + 3h 2 + 8x + 8h + 1 D) 3x2 + 6xh + 3h 2 + 2x + 2h + 1

C) 3x2 + 3xh + 3h 2 + 2x + 2h + 1

Answer the question about the given function. x2 - 8 4 , is the point (-2, ) on the graph of f? 203) Given the function f(x) = x-3 5 A) Yes

202)

203)

B) No

Graph the function. 204) f(x) = -3

204)

Find an equation of the secant line containing (1, f(1)) and (2, f(2)). 205) f(x) = x3 - x A) y = -6x - 6

B) y = 6x + 6

C) y = 6x - 6

Determine whether the equation defines y as a function of x. 206) y2 + x = 7 A) function

D) y = -6x + 6

206)

B) not a function

Solve the problem. f (-3) when f(x) = 3x - 7 and g(x) = 4x2 + 14x + 5. 207) Find g A) 16

B) 0

C) - 4

207) D) 2

Determine whether the equation defines y as a function of x. 5x + 2 208) y = x+1 A) function

205)

208) B) not a function

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. 209) (0, 3) 209)

A) decreasing

B) constant

C) increasing

Determine whether the equation defines y as a function of x. 210) 7x + x2 + 76 = y A) function

B) not a function

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting.

210)

211) f(x) = -|x|

211)

Find the value for the function. 212) Find f(x + h) when f(x) = A)

4x + 4h + 3 7x + 7h + 5

4x + 3 . 7x + 5

212)

4x + 4h + 3 7x + 5

4x + 3h 7x + 5h

4x + 7h 7x + 12h

Locate any intercepts of the function. 213) if x < 1 f(x) = -2x + 6 6x - 2 if x 1 1 A) (0, -2), (3, 0), ( , 0) 3

213)

B) (0, 6) 1 D) (0, 6), (3, 0), ( , 0) 3

C) (0, -2)

Determine whether the relation represents a function. If it is a function, state the domain and range. 214) {(-3, 5), (-2, 0), (0, -4), (2, 0), (4, 12)} A) function B) function C) not a function domain: {-3, -2, 0, 2, 4} domain: {5, 0, -4, 12} range: {5, 0, -4, 12} range: {-3, -2, 0, 2, 4}

214)

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 215) f(x) = -3(x + 1)2 + 3 215)

Complete the square and then use the shifting technique to graph the function. 216) f(x) = x2 + 2x - 1

216)

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. 217) (0, ) 217)

A) constant

B) increasing

C) decreasing

For the given functions f and g, find the requested function and state its domain. 218) f(x) = 6x - 8; g(x) = 8x - 7 Find f - g.

218) 15 } 2

A) (f - g)(x) = 14x - 15; {x|x 1}

B) (f - g)(x) = -2x - 15; {x|x -

C) (f - g)(x) = 2x + 1; all real numbers

D) (f - g)(x) = -2x - 1; all real numbers

Find the function. 219) Find the function that is finally graphed after the following transformations are applied to the graph of y = x . The graph is shifted down 8 units, reflected about the y-axis, and finally shifted right 6 units. A) y = -x + 6 - 8 B) y = -x + 6 + 8 C) y = - x - 6 + 8 D) y = -x - 6 - 8

219)

For the graph of the function y = f(x), find the absolute maximum and the absolute minimum, if it exists. 220)

220)

A) Absolute maximum: f(4) = 7; Absolute minimum: f(1) = 2 B) Absolute maximum: f(4) = 7; Absolute minimum: none C) Absolute maximum: none; Absolute minimum: f(1) = 2 D) Absolute maximum: none; Absolute minimum: none Answer the question about the given function. 221) Given the function f(x) = -6x2 - 12x - 3, is the point (-1, 3) on the graph of f?

221)

Determine algebraically whether the function is even, odd, or neither. 222) f(x) = 4x3

222)

A) Yes

A) even

B) No

B) odd

C) neither

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. 223) (-2, 0) 223)

A) constant

B) increasing

C) decreasing

The graph of a function f is given. Use the graph to answer the question. 224) Is f(40) positive or negative?

224)

100

-100

A) positive

B) negative

Answer the question about the given function. 225) Given the function f(x) = x2 + 2x - 63, list the x-intercepts, if any, of the graph of f. A) (9, 0), (-7, 0)

B) (-9, 0), (1, 0)

C) (9, 0), (7, 0)

D) (-9, 0), (7, 0)

Solve the problem. 226) The price p and the quantity x sold of a certain product obey the demand equation: 1 p = - x + 400, {x|0 x 800} 8 What is the revenue to the nearest dollar when 300 units are sold? A) $131,250 B) $50,000 C) $200,000

Write the equation of a sine function that has the given characteristics. 227) The graph of y = x, shifted 8 units downward A) y = x + 8 B) y = x - 8 C) y = x + 8 Answer the question about the given function. x2 - 4 , is the point (2, 8) on the graph of f? 228) Given the function f(x) = x-1 A) Yes

B) No

225)

226)

D) $108,750

227) D) y =

x-8

228)

The graph of a function is given. Decide whether it is even, odd, or neither. 229)

A) even

B) odd

229)

C) neither

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 6 230) f(x) = 230) x

Determine whether the equation defines y as a function of x. 231) y = x2 A) function

B) not a function

Using transformations, sketch the graph of the requested function. 232) The graph of a function f is illustrated. Use the graph of f as the first step toward graphing the function F(x), where F(x) = f(x + 2) - 1.

231)

232)

Determine whether the equation defines y as a function of x. 233) y = 3x2 - 8x + 8 A) function

B) not a function

Solve the problem. 234) Suppose that the function y = f(x) is increasing on the interval (2, 9). Over what interval is the graph of y = f(x - 4) increasing? A) (6, 13) B) (-2, 5) C) (2, 9) D) (8 , 36)

233)

234)

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 235) f(x) = x - 5 235)

Solve the problem. 236) It has been determined that the number of fish f(t) that can be caught in t minutes in a certain pond using a certain bait is f(t) = 0.23t + 1, for t > 10. Find the approximate number of fish that can be caught if you fish for 25 minutes. A) About 15 fish B) About 27 fish C) About 6 fish D) About 29 fish 237) Given f(x) = A) g(x) =

1 f x-8 and ( )(x) = , find the function g. x g x2 - 2x

x-8 x-2

B) g(x) =

x+2 x+8

C) g(x) =

237) x-2 x-8

D) g(x) =

x+8 x+2

238) A farmer's silo is the shape of a cylinder with a hemisphere as the roof. If the radius of the hemisphere is 10 feet and the height of the silo is h feet, express the volume of the silo as a function of h. 4000 2000 h2 A) V(h) = 100 h + B) V(h) = 100 (h - 10) + 3 3 C) V(h) = 100 (h 2 - 10) +

5000 3

D) V(h) = 4100 (h - 10) +

Write the equation of a sine function that has the given characteristics. 239) The graph of y = x , shifted 9 units to the right A) y = x + 9 B) y = x - 9 C) y = x + 9

238)

500 7

D) y = x - 9

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting.

236)

239)

240) f(x) =

1 +1 x

240)

The graph of a function f is given. Use the graph to answer the question. 241) For what numbers x is f(x) < 0?

241)

-10

A) [-10, -6), (7, 10)

B) (-6, )

C) (- , -6)

D) (-6, 7)

Use a graphing utility to graph the function over the indicated interval and approximate any local maxima and local minima. If necessary, round answers to two decimal places. 242) f(x) = x4 - 5x3 + 3x2 + 9x - 3; (-5, 5) 242)

A) local minimum at (-3, -3) local maximum at (-1.32, 5.64) local minimum at (0.57, -6.12) C) local minimum at (-0.57, -6.12) local maximum at (1.32, 5.64) local minimum at (3, -3)

B) local minimum at (-1, -6) local maximum at (1, 6) local minimum at (3, -3) D) local minimum at (-0.61, -5.64) local maximum at (1.41, 6.12) local minimum at (3, -3)

Determine whether the equation defines y as a function of x. 243) y2 = 9 - x2 A) function

B) not a function

Solve the problem. 244) A retail store buys 30 VCRs from a distributor at a cost of $150 each plus an overhead charge of $40 per order. The retail markup is 35% on the total price paid. Find the profit on the sale of one VCR. A) $5,296.67 B) $52.03 C) $52.50 D) $52.97 Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting.

243)

244)

245) f(x) = (x + 1)2 + 5

245)

246) f(x) =

1 +6 x+4

246)

Find and simplify the difference quotient of f,

f(x + h) - f(x) , h 0, for the function. h

247) f(x) = 6x - 6 A) 0

C) 6 +

B) 6

-12 h

D) 6 +

12(x - 6) h

247)

Determine algebraically whether the function is even, odd, or neither. 1 248) f(x) = x2 A) even

B) odd

248) C) neither

For the given functions f and g, find the requested function and state its domain. 249) f(x) = 7 - x; g(x) = x - 4 Find f · g. A) (f · g)(x) = (7 - x)(x - 4); {x|x 0} B) (f · g)(x) = -x2 - 28; {x|x 28} C) (f · g)(x) =

(7 - x)(x - 4); {x|x 4, x 7}

D) (f · g)(x) =

(7 - x)(x - 4); {x|4 x 7}

Solve. 250) A projectile is thrown upward so that its distance above the ground after t seconds is h(t) = -16t2 + 440t. After how many seconds does it reach its maximum height? Round to the nearest second. A) 44 sec

B) 14 sec

C) 11 sec

B) A = 227

C) A = 693

251) D) A = -227

252) The figure shown here shows a rectangle inscribed in an isosceles right triangle whose hypotenuse is 2 units long. Express the area A of the rectangle in terms of x.

-1

A) A(x) = x(1 - x)

250)

D) 33 sec

Solve the problem. x - 5A and f(15) = -15, what is the value of A? 251) If f(x) = 15x + 5 A) A = -693

249)

252)

B) A(x) = 2x(x - 1)

C) A(x) = 2x(1 - x)

D) A(x) = 2x2

Suppose the point (2, 4) is on the graph of y = f(x). Find a point on the graph of the given function. 253) The reflection of the graph of y = f(x) across the x-axis A) (2, 4) B) (2, -4) C) (-2, 4) D) (-2, -4)

253)

Determine whether the relation represents a function. If it is a function, state the domain and range. 254) Bob Ann Dave

254)

Ms. Lee Mr. Bar

A) function domain: {Ms. Lee, Mr. Bar} range: {Bob, Ann, Dave} B) function domain: {Bob, Ann, Dave} range: {Ms. Lee, Mr. Bar} C) not a function Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 255) f(x) = (-x)2 255)

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. 256) ({ , -8) 256)

A) decreasing

B) constant

C) increasing

The graph of a function f is given. Use the graph to answer the question. 257)

257)

Find the numbers, if any, at which f has a local maximum. What are the local maxima? A) f has a local minimum at x = -8 and 2.20000005; the local minimum at -8 is 5; the local minimum at 2.20000005 is 3.9000001 B) f has a local maximum at x = 5 and 3.9000001; the local maximum at 5 is -8; the local maximum at 3.9000001 is 2.20000005 C) f has a local minimum at x = 5 and 3.9000001; the local minimum at 5 is -8; the local minimum at 3.9000001 is 2.20000005 D) f has a local maximum at x = -8 and 2.20000005; the local maximum at -8 is 5; the local maximum at 2.20000005 is 3.9000001

Find the average rate of change for the function between the given values. 3 ; from 4 to 7 258) f(x) = x-2 A)

1 3

B) -

3 10

C) 2

258) D) 7

Solve the problem. 259) If a rock falls from a height of 70 meters on Earth, the height H (in meters) after x seconds is approximately H(x) = 70 - 4.9x2 .

What is the height of the rock when x = 1.1 seconds? Round to the nearest hundredth, if necessary. A) 64.19 m B) 75.93 m C) 64.07 m D) 64.61 m

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting.

259)

260) f(x) =

1 |x| 3

260)

Use the graph to find the intervals on which it is increasing, decreasing, or constant. 261)

261)

A) Decreasing on (-3, -1) and (1, 4); increasing on (-2, 1) B) Decreasing on (-3, -2) and (2, 4); increasing on (-1, 1) C) Increasing on (-3, -2) and (2, 4); decreasing on (-1, 1); constant on (-2, -1) and (1, 2) D) Decreasing on (-3, -2) and (2, 4); increasing on (-1, 1); constant on (-2, -1) and (1, 2) Graph the function. 262) f(x) = x

262)

Find the average rate of change for the function between the given values. 263) f(x) = x2 + 8x; from 2 to 7 85 A) 7

B) 17

263)

C) 15

D) 21

Based on the graph, find the range of y = f(x). 264) 1 if x 0 - x f(x) = 2 -6

264)

if x = 0

A) (- , 0) or {0} or (0, ) C) (- , )

B) (-10, 10) D) (- , 0) or (0, )

Determine algebraically whether the function is even, odd, or neither. 265) f(x) = -2x4 - x2 A) even

B) odd

C) neither

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting.

265)

266) f(x) = 4|x|

266)

Find the average rate of change for the function between the given values. 267) f(x) = -2x + 4; from 1 to 2 A) 4 B) 2 C) -2 Find the domain of the function. x-2 268) h(x) = 3 x - 25x

D) -4

267)

268)

A) {x|x -5, 0, 5} C) {x|x 0}

B) all real numbers D) {x|x 2}

Graph the function. 98

269) f(x) = x3

269)

Find and simplify the difference quotient of f,

f(x + h) - f(x) , h 0, for the function. h

270) f(x) = 5 A) 1

10 C) 1 + h

B) 5

Graph the function.

270) D) 0

271)

f(x) = -x + 3 2x - 3

271)

if x < 2 if x 2

Solve the problem. 272) Suppose that the function y = f(x) is increasing on the interval (5, 7). Over what interval is the graph of y = f(x + 2) increasing? A) (5, 7) B) (10, 14) C) (3, 5) D) (7, 9) Answer the question about the given function. 273) Given the function f(x) = 4x2 - 8x + 1, is the point (2, 9) on the graph of f? A) Yes

B) No

100

272)

273)

Write the equation of a sine function that has the given characteristics. 274) The graph of y = x, shifted 5 units upward A) y = x + 5 B) y = x + 5 C) y = x - 5 Find and simplify the difference quotient of f,

275) f(x) =

274) D) y =

x-5

f(x + h) - f(x) , h 0, for the function. h

1 4x

A) 0

275) B)

1 4x

-1 4x (x + h)

-1 x(x + h)

Solve the problem. 276) Bob wants to fence in a rectangular garden in his yard. He has 88 feet of fencing to work with and wants to use it all. If the garden is to be x feet wide, express the area of the garden as a function of x. A) A(x) = 46x2 - x B) A(x) = 43x - x2 C) A(x) = 44x - x2 D) A(x) = 45x - x2 For the graph of the function y = f(x), find the absolute maximum and the absolute minimum, if it exists. 277)

A) Absolute maximum: f(3) = 6; Absolute minimum: f(5) = 1 B) Absolute maximum: f(3) = 6; Absolute minimum: none C) Absolute maximum: f(7) = 4; Absolute minimum: f(0) = 2 D) Absolute maximum: f(3) = 6; Absolute minimum: f(0) = 2

101

276)

277)

Use the graph to find the intervals on which it is increasing, decreasing, or constant. 278)

A) Decreasing on (- , 0); increasing on (0, ) C) Decreasing on (- , )

278)

B) Increasing on (- , 0); decreasing on (0, ) D) Increasing on (- , )

Write the equation of a sine function that has the given characteristics. 279) The graph of y = x , shifted 9 units upward A) y = x - 9 B) y = x + 9 C) y = x - 9

D) y = x + 9

Answer the question about the given function. x2 + 4 , list the x-intercepts, if any, of the graph of f. 280) Given the function f(x) = x+5 A) (4, 0), (-4, 0)

B) (-2, 0)

C) (-5, 0)

279)

280) D) none

For the given functions f and g, find the requested function and state its domain. 281) f(x) = 2 - 7x; g(x) = -5x + 7 Find f + g.

281)

A) (f + g)(x) = -12x + 9; all real numbers

B) (f + g)(x) = -2x + 9; {x|x -

C) (f + g)(x) = -3x; all real numbers

D) (f + g)(x) = -5x + 2; {x| x

9 } 2

2 } 5

For the function, find the average rate of change of f from 1 to x: f(x) - f(1) ,x 1 x-1

282) f(x) = 4x A) 4

B) 3

C) 0

Answer the question about the given function. 283) Given the function f(x) = 4x2 + 8x + 5, what is the domain of f? A) all real numbers C) {x|x 1}

B) {x|x -1} D) {x|x -1}

102

4 x-1

282)

283)

Find the value for the function. 284) Find -f(x) when f(x) = |x| + 1. A) |-x| + 1 B) -|x| - 1

C) -|x| + 1

D) |-x| - 1

284)

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 285) f(x) = 3 x 285)

Write the equation that results in the desired transformation. 286) The graph of y = x2 , vertically stretched by a factor of 3 A) y = -3x2

B) y = 3x2

C) y = 3(x - 3)x2

103

D) y = (x - 3)2

286)

Find the function. 287) Find the function that is finally graphed after the following transformations are applied to the graph of y = x. The graph is shifted down 3 units, reflected about the y-axis, and finally shifted left 9 units. A) y = - x + 9 + 3 B) y = -x - 9 - 3 C) y = -x - 9 + 3 D) y = -x + 9 - 3 Use the graph to find the intervals on which it is increasing, decreasing, or constant. 288)

A) Decreasing on (- , 0); increasing on (0, ) C) Increasing on (- , )

288)

B) Increasing on (- , 0); decreasing on (0, ) D) Decreasing on (- , )

Write the equation that results in the desired transformation. 289) The graph of y = x3 , vertically compressed by a factor of 0.7 A) y = (x + 0.7)3

287)

B) y = (x - 0.7)3

C) y = 0.7x3

Find an equation of the secant line containing (1, f(1)) and (2, f(2)). 290) f(x) = x + 24 A) y = ( 26 - 5)x + 26 - 10 B) y = (- 26 - 5)x C) y = ( 26 - 5)x - 26 + 10 D) y = (- 26 + 5)x +

104

289) D) y = 0.7

290) 26 + 10 26 - 10

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 291) f(x) = 2(x + 1)2 - 4 291)

For the function, find the average rate of change of f from 1 to x: f(x) - f(1) ,x 1 x-1

292) f(x) = A)

x+3 x+3+2 x-1

292) B)

x+3+2 x+1

105

x+3-2 x+1

x+3-2 x-1

A) function domain: all real numbers range: {y|y 4} intercepts: (0, -3), (3, 0), (0, 1) symmetry: none C) function domain: all real numbers range: {y|y 4} intercepts: (-3, 0), (0, 3), (1, 0) symmetry: none

B) function domain: {x|x 4} range: all real numbers intercepts: (-3, 0), (0, 3), (1, 0) symmetry: y-axis D) not a function

Solve the problem. 294) A rectangle that is x feet wide is inscribed in a circle of radius 32 feet. Express the area of the rectangle as a function of x. A) A(x) = x 4,096 - x2 B) A(x) = x(4,096 -x2 )

294)

D) A(x) = x2 2,048 - x2

C) A(x) = x 3,072 - x

For the function, find the average rate of change of f from 1 to x: f(x) - f(1) ,x 1 x-1

295) f(x) = x2 - 2x A) 1

x2 - 2x - 1 C) x-1

B) x - 1

Use the accompanying graph of y = f(x) to sketch the graph of the indicated equation.

106

295) D) x + 1

296) y = -

1 f(x) 2

296)

107

The graph of a function is given. Decide whether it is even, odd, or neither. 297)

A) even

B) odd

297)

C) neither

The graph of a function f is given. Use the graph to answer the question. 298) Find the numbers, if any, at which f has a local minimum. What are the local minima?

A) f has a local minimum at x = -1; the local minimum is 0 B) f has a local minimum at x = 0; the local minimum is 1 C) f has a local minimum at x = -1 and 1; the local minimum is 0 D) f has no local minimum

108

298)

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. 299) (0, 1) 299)

A) decreasing

B) constant

C) increasing

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 300) f(x) = |x| + 2 300)

109

For the given functions f and g, find the requested function and state its domain. 7x + 8 2x ; g(x) = 301) f(x) = 2x - 7 2x - 7 Find f - g.

301)

A) (f - g)(x) =

9x + 8 ; 2x - 7

x|x

7 2

B) (f - g)(x) =

9x + 8 ; {x|x 0} 2x - 7

C) (f - g)(x) =

9x + 8 ; 2x - 7

x|x

7 8 ,x 2 9

D) (f - g)(x) =

5x - 8 ; 2x - 7

x|x

7 2

Solve the problem. 302) Suppose that the x-intercepts of the graph of y = f(x) are 4 and 9. What are the x-intercepts of y = f(x + 2)? A) 4 and 11 B) 8 and 18 C) 2 and 7 D) 6 and 11

302)

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. 303) (-1, 1) 303)

A) decreasing

B) constant

C) increasing

110

Find the average rate of change for the function between the given values. 304) f(x) = 2x - 1; from 1 to 5 1 1 A) -2 B) C) 6 2 Determine whether the equation defines y as a function of x. 305) x + 3y = 4 A) function

304) D) -28

305)

B) not a function

Solve.

306) John owns a hotdog stand. His profit is represented by the equation P(x) = -x2 + 10x + 33, with P being profits and x the number of hotdogs sold. What is the most he can earn? A) $43 B) $25 C) $88 D) $58

Determine whether the equation defines y as a function of x. 1 307) y = x

306)

307)

A) function

B) not a function

308) x = y2 A) function

B) not a function

308)

Answer the question about the given function. 309) Given the function f(x) = -6x2 + 12x + 7, list the y-intercept, if there is one, of the graph of f.

309)

The graph of a function f is given. Use the graph to answer the question. 310) For what numbers x is f(x) > 0?

310)

A) 7

B) -5

C) -11

D) 13

-10

A) (-6, )

B) [-10, -6), (7, 10)

C) (- -6)

111

D) (-6, 7)

311) How often does the line y = 4 intersect the graph?

311)

-20

A) once C) three times

B) twice D) does not intersect

Solve the problem. 312) Sue wants to put a rectangular garden on her property using 84 meters of fencing. There is a river that runs through her property so she decides to increase the size of the garden by using the river as one side of the rectangle. (Fencing is then needed only on the other three sides.) Let x represent the length of the side of the rectangle along the river. Express the garden's area as a function of x. 1 A) A(x) = 43x - 2x2 B) A(x) = 41x - x2 4 C) A(x) = 42x -

1 2 x 2

D) A(x) = 42x2 - x

Find the average rate of change for the function between the given values. 313) f(x) = 7x3 + 5x2 + 1; from 2 to 8 4.208930511e+15 A) 6.597069767e+12

A) 7

313)

4.208930511e+15 B) 8.796093022e+12

4.293592906e+15 8.796093022e+12

314) f(x) = 4x2 ; from 0 to

312)

1.431197635e+15 2.199023256e+12

7 4

314) B) 2

C) -

Graph the function.

112

3 10

1 3

315) f(x) = x

315)

113

Use the graph to find the intervals on which it is increasing, decreasing, or constant. 316)

316)

A) Decreasing on - , 0 ; increasing on 0, B) Increasing on - , -

and

; decreasing on -

, 2 2

; increasing on -

, 2 2

C) Increasing on (- , ) D) Decreasing on - , -

and

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 317) f(x) = - x 317)

114

Determine algebraically whether the function is even, odd, or neither. 3 318) f(x) = x A) even B) odd

318)

C) neither

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. 319) (-4, 1) 319)

A) increasing

B) constant

C) decreasing

Write the equation of a sine function that has the given characteristics. 320) The graph of y = x2 , shifted 2 units upward A) y = 2x2

B) y = x2 + 2

C) y = x2 - 2

D) y =

x2 2

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting.

115

320)

321) f(x) =

321)

-x

Determine whether the equation defines y as a function of x. 322) x2 + 5y2 = 1 A) function

116

B) not a function

322)

The graph of a piecewise-defined function is given. Write a definition for the function. 323)

A) f(x) =

x+1 1 1 x2 2

x+1 f(x) = 1 x 2

if 0 x 3 if 3 < x 5

if 0 x 3

f(x) =

x+1 1 1 x+ 2 2

if 0 x 3

f(x) =

x+1 1 x+2 2

if 0 x 3 if 3 < x 5

323)

if 3 < x 5

Solve. 324) John owns a hotdog stand. He has found that his profit is represented by the equation P(x) = -x2 + 76x + 86, with P being profits and x the number of hotdogs sold. How many hotdogs must he sell to earn the most profit? A) 24 hotdogs B) 39 hotdogs

Graph the function. 325) f(x) = x + 1 5

C) 38 hotdogs

324)

D) 48 hotdogs

325)

if x < 1 if x 1

117

118

Answer Key Testname: CHAPTER 3 1) C 2) B 3) C 4) A 5) A 6) A 7) A 8) D 9) A 10) A 11) D 12) B 13) D 14) A 15) C 16) 6.0°C 17) a. b. c.

R(x) = -

1 2 x + 100x 10

R(450) = $24,750.00

d. 500; $25,000.00 e. $50.00 18) local maximum at (0, 0) local minimum at (0.74, -0.33) increasing on (-2, 0) and (0.74, 2) decreasing on (0, 0.74) 19) local maximum at (2.34, 1.61) local minimum at (-1.9, -9.82) increasing on (-1.9, 2.34) decreasing on (-4, -1.9) and (2.34, 5) 20) $25.52 $42.69 if 0 x 25 C(x) = 8.8 + 0.6686x 4.0475 + 0.8587x if x > 25 21) $18.00 $24.25 $65.50 22) $39.70 $49.69 if 0 x 300 C(x) = 4.93 + 0.11589x -0.266 + 0.13321x if x > 300

119

Answer Key Testname: CHAPTER 3

23) 24) local maximum at (0, 5) local minima at (-2.55, 1.17) and (1.05, 4.65) increasing on (-2.55, 0) and (1.05, 2) decreasing on (-4, -2.55) and (0, 1.05) 1 25) V(s) = s3 6 26) local maximum at (0, 6) local minimum at (2.67, -3.48) increasing on (-1, 0) and (2.67, 4) decreasing on (0, 2.67) 27) $27.50 $32.50; 20 if 0 x 100 C(x) = 12.5 + 0.075x if 100 < x 200 7.5 + 0.1x if x > 200 1 28) A(x) = x3 2 29) d(t) =

1709t 4 3 + 9 2 15 x x + 25; {x|0 x 30) A(x) = 16 2

20 } 3

31) A 32) C 33) C 34) C 35) A 36) D 37) A 38) C 39) D 40) C 41) A 42) D 43) A 44) B 45) C 120

Answer Key Testname: CHAPTER 3 46) C 47) B 48) A 49) C 50) A 51) B 52) B 53) B 54) B 55) B 56) B 57) D 58) C 59) B 60) A 61) D 62) A 63) C 64) C 65) B 66) B 67) B 68) B 69) B 70) C 71) A 72) D 73) A 74) C 75) B 76) C 77) B 78) B 79) A 80) A 81) C 82) D 83) B 84) C 85) B 86) A 87) D 88) A 89) B 90) A 91) C 92) B 93) B 94) D 95) C 121

Answer Key Testname: CHAPTER 3 96) C 97) D 98) D 99) C 100) B 101) B 102) C 103) A 104) B 105) B 106) B 107) D 108) A 109) D 110) A 111) A 112) C 113) B 114) D 115) A 116) B 117) A 118) B 119) B 120) D 121) D 122) A 123) C 124) C 125) C 126) A 127) D 128) B 129) B 130) D 131) A 132) B 133) A 134) D 135) D 136) B 137) C 138) D 139) B 140) A 141) B 142) D 143) A 144) A 145) A 122

Answer Key Testname: CHAPTER 3 146) B 147) D 148) C 149) D 150) B 151) B 152) C 153) A 154) D 155) A 156) A 157) A 158) C 159) A 160) D 161) B 162) D 163) C 164) B 165) C 166) C 167) D 168) B 169) B 170) C 171) D 172) C 173) A 174) A 175) A 176) D 177) A 178) C 179) D 180) D 181) C 182) C 183) C 184) B 185) B 186) B 187) C 188) B 189) A 190) B 191) D 192) A 193) D 194) C 195) A 123

Answer Key Testname: CHAPTER 3 196) B 197) D 198) D 199) B 200) B 201) C 202) D 203) A 204) A 205) C 206) B 207) A 208) A 209) B 210) A 211) D 212) A 213) B 214) A 215) C 216) D 217) B 218) D 219) B 220) D 221) A 222) B 223) B 224) B 225) D 226) D 227) B 228) B 229) B 230) B 231) A 232) B 233) A 234) A 235) A 236) C 237) C 238) B 239) D 240) D 241) D 242) C 243) B 244) D 245) C 124

Answer Key Testname: CHAPTER 3 246) A 247) B 248) A 249) D 250) B 251) C 252) C 253) B 254) B 255) B 256) A 257) D 258) B 259) C 260) A 261) D 262) B 263) B 264) D 265) A 266) D 267) C 268) A 269) D 270) D 271) C 272) C 273) B 274) A 275) C 276) C 277) B 278) B 279) D 280) D 281) A 282) A 283) A 284) B 285) A 286) B 287) C 288) C 289) C 290) C 291) C 292) D 293) C 294) A 295) B 125

Answer Key Testname: CHAPTER 3 296) C 297) C 298) C 299) A 300) B 301) A 302) C 303) A 304) C 305) A 306) D 307) A 308) B 309) B 310) B 311) C 312) C 313) A 314) A 315) C 316) D 317) A 318) B 319) A 320) B 321) C 322) B 323) B 324) C 325) B

126

Chapter 4 Exam Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) Identify the scatter diagram of the relation that appears linear. A) B)

Match the graph to one of the listed functions. 2)

A) f(x) = -x2 + 8

B) f(x) = -x2 + 8x

C) f(x) = x2 + 8

D) f(x) = x2 + 8x

A) f(x) = x2 - 12x

B) f(x) = -x2 - 12x

C) f(x) = -x2 - 12

D) f(x) = x2 - 12 4)

A) f(x) = x2 + 2x + 1 C) f(x) = x2 - 2x

B) f(x) = x2 - 2x + 1 D) f(x) = x2 + 2x

A) f(x) = x2 - 2x

B) f(x) = -x2 - 2

C) f(x) = -x2 - 2x

D) f(x) = x2 - 2

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 6) The following data represents the Olympic winning time in Women's 100 m Freestyle.

year 1972 1976 1980 1984 1988 1992 1996 time 58.59 55.65 54.79 55.92 54.93 54.65 54.50 Using the line of best fit (with slope correct to 5 decimal places) for the data set, predict the Olympic winning time in 2000.

7) The following data represents the amount of money Tom is saving each month since he graduated from college.

month 1 2 3 4 5 6 7 savings $52 $70 $81 $91 $102 $118 $132 Find the slope of the line of best fit for the data set and interpret it.

8) The following data represents the Olympic winning time in Women's 100 m Freestyle. year 1972 1976 1980 1984 1988 1992 1996 time 58.59 55.65 54.79 55.92 54.93 54.65 54.50 Find the slope of the line of best fit for the data set and interpret it.

9) Ultraviolet radiation from the sun is thought to be one factor causing skin cancer. The amount of 9) UV radiation a person receives is a function of the thickness of the earth's ozone layer which depends on the latitude of the area where the person lives. The following data represent the latitudes and melanoma rates for nine randomly selected areas in the United States. The melanoma rates refer to a three-year period. Degrees North Melanoma Rate Latitude, x (per 100,000), y 32.4 7.3 33.7 6.8 34.4 6.3 36.5 5.5 38.1 4.7 39.9 4.2 41.6 4.1 43.2 3.3 44.0 3.0 Graph the data on a scatter diagram treating latitude as the independent variable. Find an equation of the line containing the points (32.4, 7.3) and (43.2, 3.3). Express the relationship using function notation. Graph the line on the scatter diagram. Interpret the slope of the line. Use the line to predict the melanoma rate of an area with a latitude of 33.1 degrees north.

10) The following data represents the height (in inches) and weight (in pounds) of 9 randomly selected adults.

10)

Height, x (in.) Weight, y (lb) 65 143 72 189 61 112 68 155 74 196 66 170 62 124 70 178 67 185 Graph the data on a scatter diagram treating height as the independent variable. Find an equation of the line containing the points (62, 124) and (70, 178). Express the relationship using function notation. Graph the line on the scatter diagram. Interpret the slope of the line. Use the line to predict the weight of a person who is 71.5 inches tall. Round to the nearest pound.

Height (inches)

11) The following data represents the number of employees at a company at the start of each year 11) since the company began. month 1 2 3 4 5 6 7 number 3 172 403 571 823 1061 1194 Using the line of best fit for the data set, predict the number of employees at the start of the 10th year.

Use a graphing calculator to plot the data and find the quadratic function of best fit. at 12) The following data represents the total revenue, R (in dollars), received from selling x bicycles 12) Tunney's Bicycle Shop. Using a graphing utility, find the quadratic function of best fit using coefficients rounded to the nearest hundredth. Number of Bicycles, x Total Revenue, R (in dollars) 0 0 22 27,000 70 46,000 96 55,200 149 61,300 200 64,000 230 64,500 250 67,000

Solve the problem. 13) The following data represents the number of employees at a company at the start of each year 13) since the company began. month 1 2 3 4 5 6 7 number 3 172 403 571 823 1061 1194 Find the slope of the line of best fit for the data set and interpret it.

Use a graphing calculator to plot the data and find the quadratic function of best fit. 14) The following table shows the median number of hours of leisure time that Americans had each 14) week in various years. Year 1973 1980 1987 1993 1997 Median # of Leisure hrs per Week 26.2 19.2 16.6 18.8 19.5 Use x = 0 to represent the year 1973. Using a graphing utility, determine the quadratic regression equation for the data given. What year corresponds to the time when Americans had the least time to spend on leisure?

Solve the problem. 15) The following data represents the amount of money Tom is saving each month since he graduated from college.

15)

month 1 2 3 4 5 6 7 savings $52 $70 $81 $91 $102 $118 $132 Using the line of best fit for the data set, predict the amount he will save in the 24th month after graduating from college.

16) The one-day temperatures for 12 world cities along with their latitudes are shown in the table 16) below. Make a scatter diagram for the data. Then find the line of best fit and graph it on the scatter diagram. City Temperature (F) Latitude Oslo, Norway 30° 59° Seattle, WA 57° 47° Anchorage, AK 40° 61° Paris, France 61° 48° Vancouver, Canada 54° 49° London, England 48° 51° Tokyo, Japan 55° 35° Cairo, Egypt 82° 30° Mexico City, Mexico 84° 19° Miami, FL 81° 25° New Delhi, India 95° 28° Manila, Philippines 93° 14° Latitude (degrees)

Temperature (F)°

17) A suspension bridge has twin towers that are 1300 feet apart. Each tower extends 180 feet above the road surface. The cables are parabolic in shape and are suspended from the tops of the towers. The cables touch the road surface at the center of the bridge. Find the height of the cable at a point 200 feet from the center of the bridge.

17)

Plot and interpret the appropriate scatter diagram. 18) The one-day temperatures for 12 world cities along with their latitudes are shown in the table below. Make a scatter diagram for the data. Describe what happens to the one-day temperatures as the latitude increases.

18)

City Temperature (F) Latitude Oslo, Norway 30° 59° Seattle, WA 57° 47° Anchorage, AK 40° 61° Paris, France 61° 48° Vancouver, Canada 54° 49° London, England 48° 51° Tokyo, Japan 55° 35° Cairo, Egypt 82° 30° Mexico City, Mexico 84° 19° Miami, FL 81° 25° New Delhi, India 95° 28° Manila, Philippines 93° 14° Latitude (degrees)

Temperature (F)°

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine where the function is increasing and where it is decreasing. 19) g(x) = 7x2 + 70x + 126 A) decreasing on (- , -5] increasing on [-5, ) C) increasing on (- , -5] decreasing on [-5, )

B) increasing on (- , -35] decreasing on [-35, ) D) decreasing on (- , 5] increasing on [5, )

19)

Graph the function. State whether it is increasing, decreasing, or constant.. 20) F(x) = 1

A) constant

B) constant

C) decreasing

D) constant

20)

Solve the problem.

21) The quadratic function f(x) = 0.0036x2 - 0.41x + 36.93 models the median, or average, age, y, at which U.S. men were first married x years after 1900. In which year was this average age at a minimum? (Round to the nearest year.) What was the average age at first marriage for that year? (Round to the nearest tenth.) A) 1952, 36 years old B) 1957, 48.6 years old C) 1957, 25.3 years old D) 1936, 48.6 years old

21)

22) In a certain city, the cost of a taxi ride is computed as follows: There is a fixed charge of $2.10 as soon as you get in the taxi, to which a charge of $1.75 per mile is added. Find an equation that can be used to determine the cost, C(x), of an x-mile taxi ride, and use this equation to find the cost of a 4-mile taxi ride. A) $10.00 B) $9.10 C) $9.28 D) $8.98

22)

23) The owner of a video store has determined that the profits P of the store are approximately given by P(x) = -x2 + 80x + 58, where x is the number of videos rented daily. Find the maximum profit to

23)

the nearest dollar. A) $3,200

B) $3,258

C) $1,600

Determine the slope and y-intercept of the function. 24) p(x) = -x - 9 A) m = 0; b = -9 B) m = -1; b = 9

C) m = -1; b =-9

D) $1,658

D) m =1; b = 9

Determine where the function is increasing and where it is decreasing. 25) f(x) = -x2 + 6x A) increasing on [-3, ) decreasing on (- , -3] C) increasing on (- , -3] decreasing on [-3, )

25)

B) increasing on (- , 3] decreasing on [3, ) D) increasing on [3, ) decreasing on [- , 3]

Solve the problem. 26) A projectile is fired from a cliff 600 feet above the water at an inclination of 45° to the horizontal, with a muzzle velocity of 250 feet per second. The height h of the projectile above the water is -32x2 given by h(x) = + x + 600, where x is the horizontal distance of the projectile from the base of (250)2 the cliff. Find the maximum height of the projectile. A) 1,088.28 ft B) 2,064.84 ft

Use the slope and y-intercept to graph the linear function. 27) p(x) = -x - 4

C) 976.56 ft

24)

26)

D) 488.28 ft

27)

Solve the problem. 28) A lumber yard has fixed costs of $1,705.00 per day and variable costs of $0.4 per board-foot produced. Lumber sells for $1.40 per board-foot. How many board-feet must be produced and sold daily to break even? A) 947 board-feet B) 4,262 board-feet C) 1,705 board-feet D) 1,136 board-feet 29) The price p (in dollars) and the quantity x sold of a certain product obey the demand equation x = -5p + 120, 0 p 24. What quantity x maximizes revenue? What is the maximum revenue? A) 90; $540 B) 60; $720 C) 120; $720 D) 30; $540

28)

29)

Use a graphing calculator to plot the data and find the quadratic function of best fit. 30) A small manufacturing firm collected the following data on advertising expenditures (in thousands of 30) dollars) and total revenue (in thousands of dollars). Advertising, x Total Revenue, R 25 6430 28 6432 31 6434 32 6434 34 6434 39 6431 40 6432 45 6420 Find the quadratic function of best fit. A) R(x) = -0.015x2 + 4.53x + 6123

B) R(x) = -0.091x2 + 5.95x + 6337 D) R(x) = -0.31x2 + 2.63x + 6128

C) R(x) = -0.024x2 + 7.13x + 6209

Solve the inequality. 31) x2 - 6x 0

A) [-6, 0]

B) (- , 0] or [6, )

C) (- , -6] or [0, )

Solve the problem. 32) Suppose that f(x) = -x - 7 and g(x) = x - 18. (a) Solve f(x) = 0. (b) Solve g(x) = 0. (c) Solve f(x) = g(x). A) (a) x = -7; (b) x = 18; (c) x = -12.5 C) (a) x = 7; (b) x = 18; (c) x = 5.5

D) [0, 6]

32)

B) (a) x = -7; (b) x = 18; (c) x = 5.5 D) (a) x = -7; (b) x = -18; (c) x = 5.5

33) The profit that the vendor makes per day by selling x pretzels is given by the function P(x) = -0.004x2 + 2.4x - 300. Find the number of pretzels that must be sold to maximize profit. A) 60 pretzels

B) 1.2 pretzels

C) 600 pretzels

Find the vertex and axis of symmetry of the graph of the function. 34) f(x) = x2 + 6x + 8 A) (3, -1); x = 3

31)

B) (3, 1); x = 3

C) (-3, 1); x = -3

33)

D) 300 pretzels

D) (-3, -1); x = -3

34)

Use a graphing calculator to plot the data and find the quadratic function of best fit. 35) The number of housing starts in one beachside community remained fairly level until 1992 and then began to increase. The following data shows the number of housing starts since 1992 (x = 1). Use a graphing calculator to plot a scatter diagram. What is the quadratic function of best fit?

35)

Year, x Housing Starts, H 1 200 2 205 3 210 4 240 5 245 6 230 7 220 8 210

A) H(x) = 2.679x2 + 26.607x + 168.571 C) H(x) = -2.679x2 + 26.607x + 168.571 Solve the inequality. 36) x2 + 7x 0 A) [0, 7]

B) H(x) = -2.679x2 - 26.607x + 168.571 D) H(x) = -2.679x2 + 26.607x - 168.571

B) (- , -7] or [0, )

C) (- , 0] or [7, )

Plot and interpret the appropriate scatter diagram. 37) The table gives the times spent watching TV and the grades of several students. Weekly TV (h) 6 12 18 24 30 36 Grade (%) 92.5 87.5 72.5 77.5 62.5 57.5 Effect of Watching TV on Grades

D) [-7, 0]

36)

37)

Effect of Watching TV on Grades

More hours spent watching TV may increase grades. C) Effect of Watching TV on Grades

More hours spent watching TV may reduce grades. D) Effect of Watching TV on Grades

More hours spent watching TV may increase grades.

More hours spent watching TV may reduce grades.

Graph the function using its vertex, axis of symmetry, and intercepts. 38) f(x) = -4x2 - 2x - 11

38)

A) vertex -

1 43 , 4 4

B) vertex

intercept (0, 11)

C) vertex

1 43 , 4 4

intercept (0, 11)

1 43 ,4 4

D) vertex -

1 43 ,4 4

intercept (0, -11)

Solve the inequality. 39) 9x2 + 64 < 48x 8 A) - , 3

8 B) - , 3

C) No real solution

D) -

39)

8 , 3

Solve the problem. 40) A projectile is thrown upward so that its distance above the ground after t seconds is h = -13t2 + 494t. After how many seconds does it reach its maximum height? A) 9 s

B) 28.5 s

C) 19 s

D) 38 s

40)

Use a graphing utility to find the equation of the line of best fit. Round to two decimal places, if necessary. 41) Managers rate employees according to job performance and attitude. The results for several randomly 41) selected employees are given below. Performance 59 63 65 69 58 77 76 69 70 64 Attitude 72 67 78 82 75 87 92 83 87 78 A) y = 92.3 - 0.669x B) y = -47.3 + 2.02x C) y = 11.7 + 1.02x D) y = 2.81 + 1.35x 42) x 10 20 30 40 50 y 3.9 4.6 5.4 6.9 8.3 A) y = 0.11x + 2.49

42) B) y = x - 8

C) y = 0.17x + 2.11

D) y = 0.5x - 2

Use the figure to solve the inequality. 43) f(x) < 0

43)

A) {x|x < -3 or x > 2}; ( , -3) or (2, ) C) {x|x -3 or x 2}; ( , -3] or [2, )

B) {x|-3 x 2}; [-3, 2] D) {x|-3 < x < 2}; (-3, 2)

Solve the problem. 44) Let f(x) be the function represented by the dashed line and g(x) be the function represented by the solid line. Solve the equation f(x) < g(x).

A) x > 3

B) x > -3

C) x < 3

D) x < -3

44)

45) The manufacturer of a CD player has found that the revenue R (in dollars) is R(p) = -4p2 + 1,060p, when the unit price is p dollars. If the manufacturer sets the price p to

45)

maximize revenue, what is the maximum revenue to the nearest whole dollar? A) $561,800 B) $70,225 C) $280,900 D) $140,450

Graph the function f by starting with the graph of y = x 2 and using transformations (shifting, compressing, stretching, and/or reflection). 46) f(x) = x2 + 6x + 8 46)

Use a graphing utility to find the equation of the line of best fit. Round to two decimal places, if necessary. 47) x 0 3 4 5 12 y 8 2 6 9 12 A) y = 0.73x + 4.98 B) y = 0.43x + 4.98 C) y = 0.63x + 4.88 D) y = 0.53x + 4.88 Find the vertex and axis of symmetry of the graph of the function. 48) f(x) = -9x2 - 2x - 6 A) -

1 53 1 ,;x=9 9 9

C) -9, -

53 ; x = -9 9

47)

48)

1 53 1 , ;x= 9 9 9

D) (9, -6); x = 9

Solve the problem. 49) Super Sally, a truly amazing individual, picks up a rock and throws it as hard as she can. The table below 49) displays the relationship between the rock's horizontal distance, d (in feet) from Sally and the initial speed with which she throws. Initial speed( in ft/sec), v 10 Horizontal distance of the rock (in feet), d 9.9

15 14.8

20 19.1

25 24.5

30 28.2

Assume that the horizontal distance travelled varies linearly with the speed with which the rock is thrown. Using a graphing utility, find the line of best fit, and estimate, rounded to two decimal places, the horizontal distance of the rock if the initial speed is 33 ft/sec. A) 34.76 feet B) 31.34 feet C) 26.67 feet D) 31.33 feet

Find the vertex and axis of symmetry of the graph of the function. 50) f(x) = 4x2 - 40x A) (5, -100); x = 5 C) (-5, 0); x = -5

50)

B) (-5, -100); x = -5 D) (5, 0); x = 5

Determine the slope and y-intercept of the function. 1 51) F(x) = - x 2 A) m = -

1 ; b=0 2

B) m =

51)

1 ; b=0 2

C) m = 0; b = -

1 2

D) m = -2; b = 0

Solve the problem.

52) If f(x) = 6x2 - 5x and g(x) = 2x + 3 , solve f(x) g(x). 1 3 1 3 1 3 A) - , B) - , C) - , 3 2 3 2 3 2

3 1 D) - , 2 3

53) Marty's Tee Shirt & Jacket Company is to produce a new line of jackets with a embroidery of a Great Pyrenees dog on the front. There are fixed costs of $590 to set up for production, and variable costs of $41 per jacket. Write an equation that can be used to determine the total cost, C(x), encountered by Marty's Company in producing x jackets, and use the equation to find the total cost of producing 70 jackets. A) $3,440 B) $3,452 C) $3,460 D) $3,472

52)

53)

Determine if the type of relation is linear, nonlinear, or none. 54)

A) linear

54)

B) none

C) nonlinear

Determine the slope and y-intercept of the function. 55) G(x) = -2x A) m = 2; b = 0

B) m = 0; b = -2

C) m = -2; b = 0

1 D) m = - ; b = 0 2

Find the vertex and axis of symmetry of the graph of the function. 56) f(x) = -4x2 + 8x - 8 A) (1, -4) ; x = 1 C) (-2, -40) ; x = -2

B) (2, -16) ; x = 2 D) (-1, -20) ; x = -1

55)

56)

Use a graphing calculator to plot the data and find the quadratic function of best fit. Use 57) An engineer collects data showing the speed s of a given car model and its average miles per gallon M.57) a graphing calculator to plot the scatter diagram. What is the quadratic function of best fit? Speed, s mph, M 20 18 30 20 40 23 50 25 60 28 70 24 80 22

A) M(s) = -0.0063x2 + 0.720x + 5.142 C) M(s) = -6.309x2 + 0.720x + 5.142

B) M(s) = -0.631x2 + 0.720x + 5.142 D) M(s) = 0.063x2 + 0.720x + 5.142

Use a graphing utility to find the equation of the line of best fit. Round to two decimal places, if necessary. 58) x 3 5 7 15 16 y 8 11 7 14 20 A) y = 0.95x + 3.07 B) y = 0.75x + 4.07 C) y = 0.75x + 5.07 D) y = 0.85x + 3.07

58)

Solve the problem. 59) An object is propelled vertically upward from the top of a 160-foot building. The quadratic function s(t) = -16t2 + 208t + 160 models the ball's height above the ground, s(t), in feet, t seconds

59)

Use a graphing utility to find the equation of the line of best fit. Round to two decimal places, if necessary. 60) x 1 2 3 4 5 6 y 17 20 19 22 21 24 A) y = 1.03x + 18.9 B) y = 1.17x + 18.9 C) y = 1.17x + 16.4 D) y = 1.03x + 16.4

60)

after it was thrown. How many seconds does it take until the object finally hits the ground? Round to the nearest tenth of a second if necessary. A) 2 seconds B) 6.5 seconds C) 0.7 seconds D) 13.7 seconds

Graph the function using its vertex, axis of symmetry, and intercepts. 61) f(x) = -x2 + 12x

A) vertex (-6, 36) intercepts (0, 0), (- 12, 0)

B) vertex (6, -36) intercept (0, -72)

61)

C) vertex (-6, -36) intercept (0, -72)

D) vertex (6, 36) intercepts (0, 0), (12, 0)

Graph the function f by starting with the graph of y = x 2 and using transformations (shifting, compressing, stretching, and/or reflection). 62) f(x) = -4x2 - 8x + 3 62)

Solve the problem. 63) A coin is tossed upward from a balcony 178 ft high with an initial velocity of 32 ft/sec. During what interval of time will the coin be at a height of at least 50 ft? (h = -16t2 + vot + ho.)

A) 0 t 4

B) 4 t 8

C) 3 t 4

63)

D) 0 t 1

Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value. 64) f(x) = x2 + 2x - 7 64)

A) minimum; - 8

B) maximum; - 1

C) maximum; - 8

D) minimum; - 1

Use a graphing utility to find the equation of the line of best fit. Round to two decimal places, if necessary. 65) Two different tests are designed to measure employee productivity and dexterity. Several employees are 65) randomly selected and tested with these results. Productivity 23 25 28 21 21 25 26 30 34 36 Dexterity 49 53 59 42 47 53 55 63 67 75 A) y = 75.3 - 0.329x B) y = 5.05 + 1.91x C) y = 2.36 + 2.03x D) y = 10.7 + 1.53x Solve the problem. 66) A coin is tossed upward from a balcony 280 ft high with an initial velocity of 32 ft/sec. During what interval of time will the coin be at a height of at least 40 ft? (h = -16t2 + vot + ho.)

66)

67)

A) 4 t 5

B) 0 t 5

C) 0 t 1

D) 5 t 10

Determine the slope and y-intercept of the function. 67) h(x) = -9x + 1 A) m = 9; b = 1 B) m = -9; b = -1

C) m = 9; b = -1

D) m = -9; b = 1

Determine the average rate of change for the function. 68) p(x) = -x + 10 A) - 10 B) 1

C) 10

D) -1

68)

Solve the problem. 69) If an object is dropped from a tower, then the velocity, V (in feet per second), of the object after t seconds can be obtained by multiplying t by 32 and adding 10 to the result. Find V as a linear function of t, and use this function to evaluate V(3.4), the velocity of the object at time t = 3.4 seconds. A) V(3.4) = 116.8 feet per second B) V(3.4) = 118.1 feet per second C) V(3.4) = 118.8 feet per second D) V(3.4) = 120.1 feet per second 70) If a rocket is propelled upward from ground level, its height in meters after t seconds is given by h = -9.8t2 + 117.6t. During what interval of time will the rocket be higher than 343 m? A) 5 < t < 7

B) 7 < t < 10

C) 0 < t < 5

69)

70)

D) 10 < t < 12

Graph the function f by starting with the graph of y = x 2 and using transformations (shifting, compressing, stretching, and/or reflection). 71) f(x) = -x2 + 8x - 14 71)

Determine if the type of relation is linear, nonlinear, or none. 72)

A) none

72)

B) linear

C) nonlinear

Solve the problem. 73) Northwest Molded molds plastic handles which cost $0.30 per handle to mold. The fixed cost to run the molding machine is $4,084 per week. If the company sells the handles for $4.30 each, how many handles must be molded and sold weekly to break even? A) 887 handles B) 680 handles C) 13,613 handles D) 1,021 handles Determine where the function is increasing and where it is decreasing. 74) f(x) = x2 - 2x - 8 A) increasing on (- , -9] decreasing on [-9, ) C) increasing on (- , 1] decreasing on [1, )

B) increasing on [1, ) decreasing on (- , 1] D) increasing on [-9, ) decreasing on (- , -9]

Use the slope and y-intercept to graph the linear function.

73)

74)

75) h(x) = -

3 x+2 4

75)

Solve the problem. 76) A developer wants to enclose a rectangular grassy lot that borders a city street for parking. If the developer has 236 feet of fencing and does not fence the side along the street, what is the largest area that can be enclosed? A) 6,962 ft2 B) 10,443 ft2 C) 13,924 ft2 D) 3,481 ft2

76)

Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value. 77) f(x) = x2 + 6 77)

A) maximum; 6

B) minimum; 6

C) minimum; 0

D) maximum; 0

Find the vertex and axis of symmetry of the graph of the function. 78) f(x) = x2 + 6x A) (-3, -9); x = -3

B) (-9, 3); x = -9

C) (9, -3); x = 9

D) (3, -9); x = 3

Solve the problem. 79) You have 356 feet of fencing to enclose a rectangular region. Find the dimensions of the rectangle that maximize the enclosed area. A) 89 ft by 89 ft B) 91 ft by 87 ft C) 178 ft by 178 ft D) 178 ft by 44.5 ft Determine the average rate of change for the function. 80) h(x) = -5x - 12 A) 12 B) 5

C) - 12

Graph the function. State whether it is increasing, decreasing, or constant.. 81) h(x) = -4x - 6 A) decreasing B) increasing

C) increasing

D) -5

78)

79)

80)

81)

D) decreasing

Graph the function f by starting with the graph of y = x 2 and using transformations (shifting, compressing, stretching, and/or reflection).

82) f(x) = -x2 - 2

82)

Use the slope and y-intercept to graph the linear function. 83) g(x) = -3x + 1

83)

Solve the problem.

84) If f(x) = 6x2 - 5x and g(x) = 2x + 3, solve for f(x) = g(x) 1 3 1 3 1 ,,1 ,A) B) C) 3 2 6 2 3

1 D) - , 1 2

85) Regrind, Inc. regrinds used typewriter platens. The variable cost per platen is $1.00. The total cost to regrind 120 platens is $400. Find the linear cost function to regrind platens. If reground platens sell for $8.30 each, how many must be reground and sold to break even? A) C(x) = 1.00x + 400; 43 platens B) C(x) = 1.00x + 400; 55 platens C) C(x) = 1.00x + 280; 31 platens D) C(x) = 1.00x + 280; 39 platens

84)

85)

86) Consider the quadratic model h(t) = -16t2 + 40t + 50 for the height (in feet), h, of an object t seconds after the object has been projected straight up into the air. Find the maximum height attained by the object. How much time does it take to fall back to the ground? Assume that it takes the same time for going up and coming down. A) maximum height = 75 ft; time to reach ground = 1.25 seconds B) maximum height = 75 ft; time to reach ground = 2.5 seconds C) maximum height = 50 ft; time to reach ground = 2.5 seconds D) maximum height = 50 ft; time to reach ground = 1.25 seconds Determine where the function is increasing and where it is decreasing. 87) f(x) = x2 + 4x - 5 A) increasing on (- , -9] decreasing on [-9, ) C) increasing on (- , -2] decreasing on [-2, )

B) increasing on [-2, ) decreasing on (- , -2] D) increasing on [-9, ) decreasing on (- , -9]

Plot a scatter diagram. 88) Draw a scatter diagram of the given data. Find the equation of the line containing the points (2.2, 8.3) and (4.6, 2.9). Graph the line on the scatter diagram. x 1.4 2.2 2.9 3.6 4.6 y 9.3 8.3 5.9 4.7 2.9

A) y = -2.25x + 13.25

B) y = -1.76x + 11.02

86)

87)

88)

C) y = -2.47x + 13.75

D) y = 2.25x + 13.25

Determine the slope and y-intercept of the function. 89) F(x) = 1 A) m = 1; b = 0 B) m = 0; b = 0

C) m = 1; b = 1

89)

D) m = 0; b = 1

Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value. 90) f(x) = 3x2 - 2x + 2 90)

A) maximum;

5 3

B) minimum;

5 3

C) minimum;

1 3

D) maximum;

1 3

Solve the problem. 91) The cost for labor associated with fixing a washing machine is computed as follows: There is a fixed charge of $25 for the repairman to come to the house, to which a charge of $24 per hour is added. Find an equation that can be used to determine the labor cost, C(x), of a repair that takes x hours. A) C(x) = 24 + 25x B) C(x) = 25 - 24x C) C(x) = ( 25 + 24) x D) C(x) = 25 + 24x Graph the function using its vertex, axis of symmetry, and intercepts. 92) f(x) = -x2 + 4x - 3

91)

92)

A) vertex (-2, 1) intercepts (-3, 0), (- 1, 0), (0, -3)

B) vertex (-2, -1) intercepts (-3, 0), (- 1, 0), (0, 3)

C) vertex (2, -1) intercepts (3, 0), (1, 0), (0, 3)

D) vertex (2, 1) intercepts (3, 0), (1, 0), (0, -3)

Solve the problem. 93) Suppose that the quantity supplied S and quantity demanded D of baseball caps at a major league game are given by the functions S(p) = 4,800 - 90p and D(p) = 110p, where p is the price. Find the equilibrium price for caps at the game. Then find the equilibrium quantity. A) $43, $930 B) $20, $3,000 C) $20, $2,640 D) $24, $2,640

93)

Graph the function f by starting with the graph of y = x 2 and using transformations (shifting, compressing, stretching, and/or reflection). 94) f(x) = 5x2 94)

95) f(x) = -3x2 - 5

95)

Solve the problem. 96) A rock falls from a tower that is 127.4 m high. As it is falling, its height is given by the formula h = 127.4 - 4.9t2 . How many seconds will it take for the rock to hit the ground (h=0)?

96)

Determine the average rate of change for the function. 97) f(x) = 8x - 12 A) 12 B) -8

97)

A) 3,300 s

B) 11.3 s

C) 5.1 s

D) 11.1 s

C) 8

D) - 12

Solve the problem. 98) A flare fired from the bottom of a gorge is visible only when the flare is above the rim. If it is fired 98) with an initial velocity of 112 ft/sec, and the gorge is 192 ft deep, during what interval can the flare be seen? (h = -16t2 + vot + ho.) A) 0 < t < 3

B) 3 < t < 4

C) 6 < t < 7

D) 9 < t < 10

Determine the average rate of change for the function. 1 99) h(x) = - x + 2 2 A)

1 2

99)

B) 2

C) - 2

Determine where the function is increasing and where it is decreasing. 100) f(x) = x2 + 4x A) increasing on (- , -2] decreasing on [-2, ) C) increasing on [-2, ) decreasing on (- , -2]

B) increasing on [2, ) decreasing on (- , 2] D) increasing on (- , 2] decreasing on [2, )

Graph the function. State whether it is increasing, decreasing, or constant.. 3 101) f(x) = x - 3 4

A) increasing

B) decreasing

D) -

1 2

100)

101)

C) increasing

D) increasing

Determine if the type of relation is linear, nonlinear, or none. 102)

A) none

B) nonlinear

102)

C) linear

Use the figure to solve the inequality. 103)

103)

f(x) < g(x) A) {x|x < -1 or x > 3}; ( , -1) or (3, ) C) {x|x -1 or x 3}; ( , -1] or [3, )

B) {x|-1 x 3}; [-1, 3] D) {x|-1 < x < 3}; (-1, 3)

Solve the problem. 104) The owner of a video store has determined that the cost C, in dollars, of operating the store is approximately given by C(x) = 2x2 - 32x + 610, where x is the number of videos rented daily. Find the lowest cost to the nearest dollar. A) $98 B) $354

Solve the inequality. 105) x2 - 9x + 14 > 0 A) (2, 7)

B) (- , 2)

C) $482

D) $738

C) (- , 2) or (7, )

D) (7, )

104)

105)

Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value. 106) f(x) = -8x2 - 2x - 10 106)

A) minimum; -

79 8

B) maximum;

79 8

C) maximum; -

79 8

D) minimum;

79 8

Solve the problem. 107) Alan is building a garden shaped like a rectangle with a semicircle attached to one short side. If he has 50 feet of fencing to go around it, what dimensions will give him the maximum area in the garden? 100 100 14, length = 18 9, length = 13.5 A) width = B) width = +4 +8 C) width =

50 +4

7, length = 14

D) width =

Graph the function using its vertex, axis of symmetry, and intercepts. 108) f(x) = -x2 - 6x - 8

100 +4

107)

14, length = 7

108)

A) vertex (-3, -1) intercepts (-2, 0), (- 4, 0), (0, 8)

B) vertex (-3, 1) intercepts (-2, 0), (- 4, 0), (0, -8)

C) vertex (3, -1) intercepts (2, 0), (4, 0), (0, 8)

D) vertex (3, 1) intercepts (2, 0), (4, 0), (0, -8)

Determine where the function is increasing and where it is decreasing. 109) f(x) = -x2 - 6x - 8 A) increasing on [1, ) decreasing on (- , 1] C) increasing on [-3, ) decreasing on (- , -3]

109)

B) increasing on (- , 1] decreasing on [1, ) D) increasing on (- , -3] decreasing on [-3, )

Solve the problem. 110) The number of mosquitoes M(x), in millions, in a certain area depends on the June rainfall x, in inches: M(x) = 12x - x2 . What rainfall produces the maximum number of mosquitoes? A) 144 in.

B) 6 in.

C) 0 in.

D) 12 in.

111) The owner of a video store has determined that the cost C, in dollars, of operating the store is approximately given by C(x) = 2x2 - 20x + 690, where x is the number of videos rented daily. Find the lowest cost to the nearest dollar. A) $740 B) $490

C) $640

111)

D) $590

Use a graphing utility to find the equation of the line of best fit. Round to two decimal places, if necessary. 3 5 7 9 112) x 1 y 143 116 100 98 90 A) y = 6.8x - 150.7 B) y = 6.2x - 140.4 C) y = -6.8x + 150.7 D) y = -6.2x + 140.4 37

110)

112)

Determine if the type of relation is linear, nonlinear, or none. 113)

A) none

113)

B) nonlinear

C) linear

Solve the problem. 114) A marina owner wishes to estimate a linear function that relates boat length in feet and its draft (depth of boat below water line) in feet. He collects the following data. Let boat length represent the independent variable and draft represent the dependent variable. Use a graphing utility to draw a scatter diagram and to find the line of best fit. What is the draft for a boat 60 ft in length (to the nearest tenth)?

114)

Boat Length (ft) Draft (ft) 25 2.5 25 2 30 3 30 3.5 45 6 45 7 50 7 50 8

A) 10.5

B) 9.7

C) 15.7

D) 10.3

115) A survey of the interest rates earned by Certificates of Deposit (CDs) showed the following percents for the length of time (in years) for holding the CD. Let length of time represent the independent variable and interest rate represent the dependent variable. Use a graphing utility to draw a scatter diagram and to find the line of best fit. What is the estimate of the interest rate for a CD held for 30 years (to the nearest thousandth)? CD Maturity (yrs) Interest rate (%) 5 8.458 10 8.470 15 8.496 20 8.580 25 8.625 A) 8.675

B) 8.669

C) 8.874

D) 9.064

115)

116) The quadratic function f(x) = 0.0040x2 - 0.45x + 36.78 models the median, or average, age, y, at which U.S. men were first married x years after 1900. In which year was this average age at a minimum? (Round to the nearest year.) What was the average age at first marriage for that year? (Round to the nearest tenth.) A) 1956, 24.1 years old B) 1936, 49.4 years old C) 1956, 49.4 years old D) 1953, 36 years old

116)

Use a graphing calculator to plot the data and find the quadratic function of best fit. 117) A rock is dropped from a tall building and its distance (in feet) below the point of release is recorded as117) accurately as possible at various times after the moment of release. The results are shown in the table. Find the regression equation of the best model. x (seconds after release) 1 2 3 4 5 6 y (distance in feet) 16 63 146 255 403 572 A) y = 13.0 e0.686x

C) y = -74.9 + 290 lnx

B) y = 15.95x2 D) y = - 148.4 + 112x

Solve the problem. 118) To convert a temperature from degrees Celsius to degrees Fahrenheit, you multiply the temperature in degrees Celsius by 1.8 and then add 32 to the result. Express F as a linear function of c. c - 32 A) F(c) = 33.8c B) F(c) = 1.8 + 32c C) F(c) = 1.8c + 32 D) F(c) = 1.8

118)

119) In a certain city, the cost of a taxi ride is computed as follows: There is a fixed charge of $2.95 as soon as you get in the taxi, to which a charge of $1.85 per mile is added. Find an equation that can be used to determine the cost, C(x), of an x-mile taxi ride. A) C(x) = 4.80x B) C(x) = 1.85 + 2.95x C) C(x) = 2.95 + 1.85x D) C(x) = 3.30x

119)

120) Linda needs to have her car towed. Little Town Auto charges a flat fee of $60 plus $3 per mile towed. Write a function expressing Linda's towing cost, c, in terms of miles towed, x. Find the cost of having a car towed 11 miles. A) c(x) = 3x; $63 B) c(x) = 3x + 60; $93 C) c(x) = 3x; $33 D) c(x) = 3x + 60; $83

120)

Use the slope and y-intercept to graph the linear function. 121) f(x) = 3x + 3

121)

Determine the domain and the range of the function. 122) f(x) = -x2 - 6x A) domain: all real numbers range: {y|y -9} C) domain: {x|x 3} range: {y|y 9}

B) domain: {x|x -3} range: {y|y 9} D) domain: all real numbers range: {y|y 9}

Graph the function using its vertex, axis of symmetry, and intercepts.

122)

123) f(x) = -3x2 + 12x - 15

123)

A) vertex (-2, -3) intercept (0, -15)

B) vertex (-2, -3)

C) vertex (2, -3) intercept (0, -15)

D) vertex (2, -3)

intercept 0, -

13 3

124) f(x) = x2 + 4x + 3

124)

A) vertex (-2, -1) intercepts (-1, 0), (- 3, 0), (0, 3)

B) vertex (2, 1) intercepts (1, 0), (3, 0), (0, -3)

C) vertex (2, -1) intercepts (1, 0), (3, 0), (0, 3)

D) vertex (-2, 1) intercepts (-1, 0), (- 3, 0), (0, -3)

Determine the domain and the range of the function. 125) f(x) = -x2 + 4x + 5 A) domain: all real numbers range: all real numbers C) domain: all real numbers range: {y|y 9}

B) domain: {x|x -2} range: {y|y 9} D) domain: all real numbers range: {y|y -9}

125)

Use a graphing utility to find the equation of the line of best fit. Round to two decimal places, if necessary. 126) x 2 4 6 8 10 y 15 37 60 75 94 A) y = 9x - 3 B) y = 10x - 3 C) y = 9.8x - 2.6 D) y = 9.2x - 2.1 Use a graphing calculator to plot the data and find the quadratic function of best fit. 127) The number of housing starts in one beachside community remained fairly level until 1992 and then began to increase. The following data shows the number of housing starts since 1992 (x = 1). Use a graphing calculator to plot a scatter diagram. What is the quadratic function of best fit?

126)

127)

Year, x Housing Starts, H 1 200 2 210 3 230 4 240 5 250 6 230 7 215 8 208

A) H(x) = -3.268x2 + 30.494x - 168.982 C) H(x) = -3.268x2 + 30.494x + 168.982

B) H(x) = 3.268x2 + 30.494x + 168.982 D) H(x) = -3.268x2 - 30.494x + 168.982

Use the figure to solve the inequality. 128)

128)

f(x) > g(x) A) {x|x -1 or x 2}; ( , -1] or [2, ) C) {x|-1 x 2}; [-1, 2]

B) {x|x < -1 or x > 2}; ( , -1) or (2, ) D) {x|-1 < x < 2}; (-1, 2)

Graph the function using its vertex, axis of symmetry, and intercepts.

129) f(x) = x2 - 4x - 5

129)

A) vertex (2, 9) intercepts (5, 0), (- 1, 0), (0, 5)

B) vertex (-2, -9) intercepts (-5, 0), (1, 0), (0, -5)

C) vertex (-2, 9) intercepts (-5, 0), (1, 0), (0, 5)

D) vertex (2, -9) intercepts (5, 0), (- 1, 0), (0, -5)

Graph the function. State whether it is increasing, decreasing, or constant..

130) h(x) = -

1 x-1 2

130)

A) decreasing

B) increasing

C) decreasing

D) decreasing

Solve the problem. 131) A projectile is fired from a cliff 600 feet above the water at an inclination of 45° to the horizontal, with a muzzle velocity of 190 feet per second. The height h of the projectile above the water is -32x2 given by h(x) = + x + 600, where x is the horizontal distance of the projectile from the base of (190)2 the cliff. How far from the base of the cliff is the height of the projectile a maximum? A) 1,446.09 ft B) 564.06 ft C) 282.03 ft D) 882.03 ft

131)

Determine if the type of relation is linear, nonlinear, or none. 132)

A) nonlinear

B) none

132)

C) linear

Solve the problem. 133) The price p and the quantity x sold of a certain product obey the demand equation 1 p = - x + 180, 0 x 720. 4 What price should the company charge to maximize revenue? A) $108 B) $135 C) $90

D) $45

Use a graphing utility to find the equation of the line of best fit. Round to two decimal places, if necessary. 134) x 2 4 5 6 y 7 11 13 20 A) y = 2.8x + 0.15 B) y = 2.8x C) y = 3x D) y = 3x + 0.15 Solve the problem. 135) You have 68 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river, find the length and width of the plot that will maximize the area. A) length: 17 feet, width: 17 feet B) length: 34 feet, width: 17 feet C) length: 34 feet, width: 34 feet D) length: 51 feet, width: 17 feet Plot a scatter diagram. 136) x 23 -13 9 -7 -2 19 y 60 22 41 -16 -2 30

5 8

25 67

4 -6 1 3

133)

134)

135)

136)

Graph the function. State whether it is increasing, decreasing, or constant.. 137) p(x) = -x - 2

137)

A) increasing

B) increasing

C) decreasing

D) decreasing

Solve the problem. 138) A truck rental company rents a moving truck one day by charging $35 plus $0.11 per mile. Write a linear equation that relates the cost C, in dollars, of renting the truck to the number x of miles driven. What is the cost of renting the truck if the truck is driven 130 miles? A) C(x) = 0.11x + 35; $36.43 B) C(x) = 0.11x + 35; $49.30 C) C(x) = 0.11x - 35; -$20.70 D) C(x) = 35x + 0.11; $4,550.11 139) If an object is dropped off of a tower, the velocity, V, of the object after t seconds can be obtained by multiplying t by 32 and adding 10 to the result. Express V as a linear function of t. t - 10 A) V(t) = B) V(t) = 42t C) V(t) = 32t + 10 D) V(t) = 32 + 10t 32

138)

139)

Determine the quadratic function whose graph is given. 140)

140)

Vertex: (- 1, 4) y-intercept: (0, 3)

A) f(x) = -x2 - 4x + 3 C) f(x) = -x2 - 2x - 3

B) f(x) = x2 - 4x + 3 D) f(x) = -x2 - 2x + 3

Determine the average rate of change for the function. 141) F(x) = -5 1 A) B) 5 5 Plot a scatter diagram. 142) x 16 18 36 y 11 20 42

50 49

56 66

62 47

72 64

78 90

141) C) -5

D) 0

142)

90 80

Graph the function. State whether it is increasing, decreasing, or constant.. 143) g(x) = 3x - 5

A) decreasing

B) decreasing

C) increasing

D) increasing

143)

Solve the problem. 144) A projectile is thrown upward so that its distance above the ground after t seconds is h = -10t2 + 400t. After how many seconds does it reach its maximum height? A) 20 s

B) 30 s

C) 10 s

Find the vertex and axis of symmetry of the graph of the function. 145) f(x) = -x2 + 12x - 7 A) (-6, -115) ; x = -6 C) (6, 29) ; x = 6

B) (-6, -43) ; x = -6 D) (12, -7) ; x = 12

144)

D) 40 s

145)

Determine if the type of relation is linear, nonlinear, or none. 146)

A) linear

146)

B) nonlinear

C) none

Determine the domain and the range of the function. 147) f(x) = x2 + 2x - 3 A) domain: all real numbers range: {y|y -4} C) domain: range: {x|x 1} range: {y|y -4}

B) domain: all real numbers range: {y|y 4} D) domain: range: {x|x 1} range: {y|y 4}

Solve the problem. 148) Suppose that f(x) = -x - 6 and g(x) = x - 15. (a) Solve f(x) > 0. (b) Solve g(x) > 0. (c) Solve f(x) g(x). A) (a) x > 6; (b) x > 15; (c) x > 4.5 C) (a) x < -6; (b) x < 15; (c) x -10.5

148)

B) (a) x < -6; (b) x > 15; (c) x 4.5 D) (a) x < -6; (b) x < -15; (c) x 4.5

149) Alan is building a garden shaped like a rectangle with a semicircle attached to one short side along its diameter. The diameter of the semicircle is equal to the width of the short side of the rectangle. If he has 20 feet of fencing to go around the garden, what dimensions will give him the maximum area in the garden? 20 40 2.8, length = 5.6 5.6, length = 2.8 A) width = B) width = +4 +4 C) width =

Solve the inequality. 150) x2 - 2x 0

A) [-2, 0]

40 +8

147)

3.6, length = 5.4

D) width =

B) (- , 0] or [2, )

40 +4

C) (- , -2] or [0, )

Graph the function using its vertex, axis of symmetry, and intercepts.

149)

5.6, length = 7.2

D) [0, 2]

150)

151) f(x) = x2 + 10x

151)

A) vertex (5, 25) intercept (0, 50)

B) vertex (5, -25) intercepts (0, 0), (10, 0)

C) vertex (-5, 25) intercept (0, 50)

D) vertex (-5, -25) intercepts (0, 0), (- 10, 0)

Solve the inequality. 152) 30(x2 - 1) > 11x

6 5 or , A) - , 5 6

5 6 B) - , 6 5

6 5 , 5 6

D) - , -

C) -

153) x2 + 4x 0 A) (- , -4] or [0, )

B) [0, 4]

C) [-4, 0] 53

152)

5 6 or , 6 5

D) (- , 0] or [4, )

153)

Solve the problem. 154) The following scatter diagram shows heights (in inches) of children and their ages.

154)

Height (inches)

Age (years) What happens to height as age increases? A) Height and age do not appear to be related. B) Height stays the same as age increases. C) Height increases as age increases. D) Height decreases as age increases.

Determine where the function is increasing and where it is decreasing. 155) f(x) = -3x2 - 2x - 12 1 A) increasing on - , 3 decreasing on

1 , 3

C) increasing on - , decreasing on -

155)

1 B) increasing on - , 3 decreasing on -

35 3

1 , 3

D) decreasing on - , -

35 , 3

increasing on -

1 3

1 , 3

Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value. 156) f(x) = -x2 + 2x - 1 156)

A) minimum; 1

B) minimum; 0

C) maximum; 0

D) maximum; 1

Use a graphing utility to find the equation of the line of best fit. Round to two decimal places, if necessary. 157) x 1.2 1.4 1.6 1.8 2.0 y 54 53 55 54 56 A) y = 54 B) y = 3x + 50 C) y = 2.5x + 50.4 D) y = 55.3

157)

Solve the problem. 158) Let f(x) be the function represented by the dashed line and g(x) be the function represented by the solid line. Solve the equation f(x) = g(x).

A) x = -3

B) x = -1

C) x = 1

D) x = 3

158)

Graph the function. State whether it is increasing, decreasing, or constant.. 159) f(x) = 2x + 6

A) increasing

B) decreasing

C) increasing

D) increasing

159)

Graph the function f by starting with the graph of y = x 2 and using transformations (shifting, compressing, stretching, and/or reflection).

160) f(x) = -

1 2 x 2

160)

Use a graphing utility to find the equation of the line of best fit. Round to two decimal places, if necessary. 161) Ten students in a graduate program were randomly selected. Their grade point averages (GPAs) when161) they entered the program were between 3.5 and 4.0. The following data were obtained regarding their GPAs on entering the program versus their current GPAs. Entering GPA 3.5 3.8 3.6 3.6 3.5 3.9 4.0 3.9 3.5 3.7 A) y = 0.33x + 2.51

Current GPA 3.6 3.7 3.9 3.6 3.9 3.8 3.7 3.9 3.8 4.0 B) y= 0.02x + 4.91

C) y = 0.03x + 3.67

D) y = 0.50x + 5.81

Solve the problem.

162) If g(x) = x2 - 5x - 14 , solve g(x) 0. A) (- , -2] or [7, ) C) (- , -2]

B) [7, ) D) [-2, 7]

162)

Graph the function f by starting with the graph of y = x 2 and using transformations (shifting, compressing, stretching, and/or reflection). 1 2 163) f(x) = x2 + x - 1 163) 3 3

164) f(x) =

1 2 x +4 5

164)

Solve the problem. 165) The price p (in dollars) and the quantity x sold of a certain product obey the demand equation p = -10x + 320, 0 x 32. What price should the company charge to maximize revenue? A) $8 B) $19.2 C) $24 D) $16 Use a graphing utility to find the equation of the line of best fit. Round to two decimal places, if necessary. 166) x 2 3 7 8 10 y 3 4 4 5 6 A) y = 0.30x + 4.29 B) y = 0.32x + 2.57 C) y = 0.32x + 4.29 D) y = 0.30x + 2.57 Find the vertex and axis of symmetry of the graph of the function. 167) f(x) = -x2 - 6x A) (-9, 3); x = -9

B) (-3, 9); x = -3

C) (3, -9); x = 3

D) (9, -3); x = 9

165)

166)

167)

Solve the problem.

168) If h(x) = x2 + 2x - 35 , solve h(x) > 0. A) (- , -7) or (5, ) C) (5, )

B) (- , -7) D) (-7, 5)

168)

Use a graphing calculator to plot the data and find the quadratic function of best fit. 169) Southern Granite and Marble sells granite and marble by the square yard. One of its granite patterns is price sensitive. If the price is too low, customers perceive that it has less quality. If the price is too high, customers perceive that it is overpriced. The company conducted a pricing test with potential customers. The following data was collected. Use a graphing calculator to plot the data. What is the quadratic function of best fit? Price, x $20 $30 $40 $60 $80 $100 $110

169)

Buyers, B 30 50 65 75 72 50 25

A) B(x) = -0.0243x2 + 3.115x + 22.13 C) B(x) = 0.0243x2 - 3.115x - 22.13

B) B(x) = -0.0243x2 + 3.115x - 22.13 D) B(x) = -0.243x2 + 3.115x - 22.13

Solve the problem. 170) The revenue achieved by selling x graphing calculators is figured to be x(43 - 0.2x) dollars. The cost of each calculator is $35. How many graphing calculators must be sold to make a profit (revenue cost) of at least $46.20? A) {x 8 < x < 6} B) {x 7 < x < 33} C) {x 9 < x < 31} D) {x -3 < x < 23}

170)

171) A flare fired from the bottom of a gorge is visible only when the flare is above the rim. If it is fired with an initial velocity of 176 ft/sec, and the gorge is 448 ft deep, during what interval can the flare be seen? (h = -16t2 + vot + ho.)

171)

172) The price p and the quantity x sold of a certain product obey the demand equation 1 p = - x + 160, 0 x 800. 5

172)

A) 8 < t < 11

B) 0 < t < 4

C) 12 < t < 15

What quantity x maximizes revenue? What is the maximum revenue? A) 200; $24,000 B) 800; $32,000 C) 400; $32,000

D) 4 < t < 7

D) 600; $24,000

Use the figure to solve the inequality. 173)

173)

g(x) f(x) A) {x|-1 x 2}; [-1, 2] C) {x|x -1 or x 2}; ( , -1] or [2, )

B) {x|x < -1 or x > 2}; ( , -1) or (2, ) D) {x|-1 < x < 2}; (-1, 2)

Solve the problem. 174) A drug company establishes that the most effective dose of a new drug relates to body weight as shown below. Let body weight be the independent variable and drug dosage be the dependent variable. Use a graphing utility to draw a scatter diagram and to find the line of best fit. What is the most effective dosage for a person weighing 130 lbs? Body Drug Weight (lbs)Dosage (mg) 50 10 100 12 150 15 200 19 250 22

A) 13.5 mg

B) 22.84 mg

C) 12.07 mg

D) 14.36 mg

174)

175) The following scatter diagram shows heights (in inches) of children and their ages.

175)

Height (inches)

Age (years) Based on this data, how old do you think a child is who is about 39 inches tall? A) 3 months B) 3 years C) 1 year D) 7 years

176) The manufacturer of a CD player has found that the revenue R (in dollars) is R(p) = -5p2 + 1,230p, when the unit price is p dollars. If the manufacturer sets the price p to

176)

maximize revenue, what is the maximum revenue to the nearest whole dollar? A) $75,645 B) $151,290 C) $605,160 D) $302,580

Find the vertex and axis of symmetry of the graph of the function. 177) f(x) = x2 - 13x - 8 13 201 13 ,;x= A) 2 4 2

C) -

B) (15, -8) ; x = 15

13 475 13 , ;x=2 4 2

D) (-13, 330) ; x = -13

177)

Use the figure to solve the inequality. 178) g(x) 0

178)

A) {x|-4 x 4}; [-4, 4] C) {x|x < -4 or x > 4}; ( , -4) or (4, )

B) {x|-4 < x < 4}; (-4, 4) D) {x|x -4 or x 4}; ( , -4] or [4, )

Determine whether the given function is linear or nonlinear. 179) x y = f(x) 5 15 9 27 13 39 17 51 A) linear Determine the domain and the range of the function. 180) f(x) = x2 - 12x A) domain: {x|x 6} range: {y|y -36} C) domain: all real numbers range: {y|y -36}

179)

B) nonlinear

B) domain: {x|x -6} range: {y|y 36} D) domain: all real numbers range: {y|y 36}

Find the vertex and axis of symmetry of the graph of the function. 181) f(x) = x2 - 4x A) (-2, 4); x = -2

B) (4, -2); x = 4

C) (2, -4); x = 2

D) (-4, 2); x = -4

180)

181)

Solve the problem. 182) Let f(x) be the function represented by the dashed line and g(x) be the function represented by the solid line. Solve the equation f(x) g(x).

A) x < -3

B) x 3

C) x 3

D) x -3

Plot a scatter diagram. 183) Draw a scatter diagram of the given data. Find the equation of the line containing the points (2, 1.2) and (9, 4.3). Graph the line on the scatter diagram. x 2 4 5 8 9 y 1.2 1.9 2.8 3.4 4.3

A) y = 0.37x + 0.47

B) y = 0.49x + 0.31

182)

183)

C) y = 0.44x + 0.31

D) y = 0.44x + 0.37

Use the figure to solve the inequality. 184)

184)

f(x) g(x) A) {x|x < -1 or x > 3}; ( , -1) or (3, ) C) {x|x -1 or x 3}; ( , -1] or [3, )

B) {x|-1 < x < 3}; (-1, 3) D) {x|-1 x 3}; [-1, 3]

Use the slope and y-intercept to graph the linear function. 185) F(x) = -6

185)

Determine the domain and the range of the function. 186) f(x) = x2 + 10x + 25 A) domain: {x|x -5} range: {y|y 0} C) domain: all real numbers range: {y|y 25}

B) domain: all real numbers range: {y|y 0} D) domain: {x|x 5} range: {y|y 0}

Use the slope and y-intercept to graph the linear function.

186)

187) f(x) =

2 x-2 5

187)

Solve the problem. 188) A developer wants to enclose a rectangular grassy lot that borders a city street for parking. If the developer has 292 feet of fencing and does not fence the side along the street, what is the largest area that can be enclosed? A) 10,658 ft2 B) 21,316 ft2 C) 15,987 ft2 D) 5,329 ft2

188)

Determine the domain and the range of the function. 189) f(x) = -x2 - 8x - 7 A) domain: {x|x -4} range: {y|y -9} C) domain: {x|x -4} range: {y|y 9}

B) domain: all real numbers range: {y|y -9} D) domain: all real numbers range: {y|y 9}

189)

Graph the function f by starting with the graph of y = x 2 and using transformations (shifting, compressing, stretching, and/or reflection). 190) f(x) = 4x2 - 1 190)

Solve the problem. 191) Marty's Tee Shirt & Jacket Company is to produce a new line of jackets with an embroidery of a Great Pyrenees dog on the front. There are fixed costs of $580 to set up for production, and variable costs of $41 per jacket. Write an equation that can be used to determine the total cost, C(x), encountered by Marty's Company in producing x jackets. A) C(x) = 580 - 41x B) C(x) = 580x + 41 C) C(x) = 580 + 41x D) C(x) = (580 + 41) x Graph the function. State whether it is increasing, decreasing, or constant.. 192) h(x) = -3x + 5

A) increasing

B) decreasing

C) increasing

D) decreasing

191)

192)

Determine where the function is increasing and where it is decreasing. 193) f(x) = -x2 + 2x + 3 A) increasing on (- , 4] decreasing on [4, ) C) increasing on [4, ) decreasing on (- , 4]

193)

B) increasing on (- , 1] decreasing on [1, ) D) increasing on [1, ) decreasing on (- , 1]

Solve the problem. 194) A rock falls from a tower that is 176 ft high. As it is falling, its height is given by the formula h = 176 - 16t2 . How many seconds will it take for the rock to hit the ground (h=0)? A) 1,936 s

B) 12.6 s

C) 3.3 s

Graph the function using its vertex, axis of symmetry, and intercepts. 195) f(x) = x2 - 6x + 9

A) vertex (3, 9) intercept (0, 18)

B) vertex (-3, 9) intercept (0, 18)

194)

D) 13.3 s

195)

C) vertex (-3, 0) intercepts (0, 9), (-3, 0)

D) vertex (3, 0) intercepts (0, 9), (3, 0)

Determine the quadratic function whose graph is given. 196)

196)

A) f(x) = x2 + 8x + 3 C) f(x) = -x2 + 4x - 3

B) f(x) = x2 - 4x + 3 D) f(x) = -x2 - 4x + 3

Determine the slope and y-intercept of the function. 5 197) f(x) = x + 2 8 A) m = 2; b = C) m =

197)

5 8

B) m = -

5 ; b=2 8

D) m =

5 ; b=-2 8

8 ; b=-2 5

Solve the problem. 198) If a rocket is propelled upward from ground level, its height in meters after t seconds is given by h = -9.8t2 + 88.2t. During what interval of time will the rocket be higher than 176.4 m? A) 6 < t < 9

B) 6 < t < 6

C) 0 < t < 3

D) 3 < t < 6

Use a graphing utility to find the equation of the line of best fit. Round to two decimal places, if necessary. 199) x 2 3 7 8 10 y 2 4 4 6 6 A) y = -1.86x + 1.79 B) y = 1.79x + 0.43 C) y = 1.79x - 1.86 D) y = 0.43x + 1.79 72

198)

199)

Use the slope and y-intercept to graph the linear function. 1 200) F(x) = - x 3

200)

Determine where the function is increasing and where it is decreasing. 201) f(x) = x2 + 12x + 36 A) increasing on [-6, ) decreasing on (- , -6] C) increasing on (- , -6] decreasing on [-6, )

B) increasing on (- , 6] decreasing on [6, ) D) increasing on [6, ) decreasing on (- , 6]

201)

Solve the problem.

202) If g(x) = 28x2 - 28 and h(x) = 33x, then solve g(x) > h(x). 4 7 7 4 or , A) - , B) - , 7 4 4 7 C) - , -

7 4 or , 4 7

D) -

4 7 , 7 4

Find the vertex and axis of symmetry of the graph of the function. 203) f(x) = -x2 + 4x A) (2, 4); x = 2

B) (4, -2); x = 4

202)

C) (-2, -4); x = -2

D) (-4, 2); x = -4

Solve the problem. 204) The following scatter diagram shows heights (in inches) of children and their ages.

203)

204)

Height (inches)

Age (years) What is the expected height range for a 2-year old child? A) 20-30 inches B) 40-50 inches C) 35-45 inches

Determine the domain and the range of the function. 205) f(x) = -3x2 - 2x - 7

D) 25-38 inches

A) domain: all real numbers 20 range: y y 3

B) domain: all real numbers 20 range: y y 3

C) domain: all real numbers 20 range: y y 3

D) domain: all real numbers 20 range: y y 3

205)

Determine the average rate of change for the function. 2 206) f(x) = x + 1 5 A) - 1

206)

B) 1

2 5

D) -

2 5

Determine the domain and the range of the function. 207) f(x) = x2 - 4x + 3 A) domain: all real numbers range: {y|y -1} C) domain: {x|x -2} range: {y|y -1}

B) domain: all real numbers range: all real numbers D) domain: all real numbers range: {y|y 1}

Solve the inequality. 208) x2 - 16 > 0

A) (-16, 16) C) (-4, 4)

B) (- , -4) or (4, ) D) (- , -16) or (16, )

207)

208)

Graph the function f by starting with the graph of y = x 2 and using transformations (shifting, compressing, stretching, and/or reflection). 209) f(x) = -x2 + 4x 209)

Solve the inequality. 210) x2 - 81 0

A) [-9, 9] C) (- , -9] or [9, )

B) (- , -81] or [81, ) D) [-81, 81]

210)

Use the slope and y-intercept to graph the linear function. 211) G(x) = 3x

211)

Use a graphing utility to find the equation of the line of best fit. Round to two decimal places, if necessary. 212) x 6 8 20 28 36 y 2 4 13 20 30 A) y = 0.85x - 2.79 B) y = 0.95x - 2.79 C) y = 0.90x - 3.79 D) y = 0.80x - 3.79

212)

Determine the slope and y-intercept of the function. 213) f(x) = 6x - 7 A) m = 6; b = 7 B) m = 6; b = -7

213)

C) m = -6; b = -7

D) m = -6; b = 7

Use a graphing utility to find the equation of the line of best fit. Round to two decimal places, if necessary. 214) x 24 26 28 30 32 y 15 13 20 16 24 A) y = 0.95x + 11.8 B) y = 0.95x - 11.8 C) y = 1.05x + 11.8 D) y = 1.05x - 11.8

214)

Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value. 215) f(x) = -4x2 + 12x 215)

A) maximum; 9

B) minimum; 9

C) maximum; - 9

Solve the inequality. 216) x2 - 3x - 28 0 A) (- , -4] C) (- , -4] or [7, ) 217) 2x2 - 12 < -2x A) -3, 2

D) minimum; - 9

216)

B) [7, ) D) [-4, 7]

B) -3, - 2

C) - 2, 3

D) 2, 3

217)

Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value. 218) f(x) = 2x2 - 4x 218)

A) maximum; - 2

B) maximum; 1

C) minimum; - 2

D) minimum; 1

219) f(x) = x2 - 5 A) maximum; -5

B) maximum; 0

C) minimum; -5

D) minimum; 0

219)

Plot and interpret the appropriate scatter diagram. 220) The table shows the study times and test scores for a number of students. Draw a scatter plot of score 220) versus time treating time as the independent variable. Study Time (min) 9 16 21 26 33 36 40 47 Test Score 59 61 64 65 73 74 78 78 Effect of Study on Test Score

Time (min)

Effect of Study on Test Score

Time (min) More time spent studying may increase test scores. Effect of Study on Test Score C)

Time (min) More time spent studying may decrease test scores. Effect of Study on Test Score D)

Time (min) More time spent studying may decrease test scores.

Time (min) More time spent studying may increase test scores.

Solve the inequality. 221) x2 + 3x 4

A) [1, ) C) (- , -4] or [1, )

B) (- , -4] D) [-4, 1]

Solve the problem. 222) You have 332 feet of fencing to enclose a rectangular region. What is the maximum area? A) 6,889 square feet B) 110,224 square feet C) 27,556 square feet D) 6,885 square feet

221)

222)

Answer Key Testname: CHAPTER 4 1) C 2) B 3) C 4) A 5) D 6) 53.56 7) The slope is 12.75 which means that the amount Tom saves increases $12.75 each month. 8) The slope is about -0.12616 which means that the winning time is decreasing by 0.12616 of a second each year. 9)

10)

y = -0.370x + 19.3 M(L) = -0.370L + 19.3 If latitude is increased by one degree north, then melanoma rate will decrease by 0.37 per 100,000 7.04 per 100,000

Height (inches) y = 6.75x - 294.5; W(h) = 6.75h - 294.5; If height is increased by one inch, then weight will increase by 6.75 pounds; 188 lb 11) 1840 12) R(x) = -1.65x2 + 634.42x + 7089.93

Answer Key Testname: CHAPTER 4 13) The slope is about 206.1 which means that the number of employees is increasing by about 206 employees each year. 14) M(x) = 0.04x2 - 1.21x + 26.03; 1988 15) $347.29 16) Latitude (degrees)

Temperature (F)° Line of best fit = -0.68x + 82.91 17) The height is approximately 17 ft. 18) Latitude (degrees)

Temperature (F)° As the latitude increases, the one-day temperatures decrease. 19) A 20) D 21) C 22) B 23) D 24) C 25) B 26) A

Answer Key Testname: CHAPTER 4 27) A 28) C 29) B 30) B 31) D 32) B 33) D 34) D 35) C 36) D 37) D 38) D 39) C 40) C 41) C 42) A 43) D 44) A 45) B 46) A 47) D 48) A 49) B 50) A 51) A 52) C 53) C 54) B 55) C 56) A 57) A 58) C 59) D 60) C 61) D 62) B 63) A 64) A 65) B 66) B 67) D 68) D 69) C 70) A 71) A 72) B 73) D 74) B 75) B 76) A 82

Answer Key Testname: CHAPTER 4 77) B 78) A 79) A 80) D 81) A 82) B 83) C 84) C 85) D 86) B 87) B 88) A 89) D 90) B 91) D 92) D 93) D 94) B 95) D 96) C 97) C 98) B 99) D 100) C 101) D 102) B 103) A 104) C 105) C 106) C 107) D 108) B 109) D 110) B 111) C 112) D 113) C 114) B 115) B 116) A 117) B 118) C 119) C 120) B 121) C 122) D 123) C 124) A 125) C 126) C 83

Answer Key Testname: CHAPTER 4 127) C 128) B 129) D 130) C 131) B 132) A 133) C 134) C 135) B 136) D 137) C 138) B 139) C 140) D 141) D 142) C 143) C 144) A 145) C 146) B 147) A 148) B 149) B 150) B 151) D 152) D 153) A 154) C 155) B 156) C 157) C 158) D 159) D 160) A 161) C 162) D 163) C 164) C 165) D 166) D 167) B 168) A 169) B 170) B 171) D 172) C 173) A 174) D 175) B 176) A 84

Answer Key Testname: CHAPTER 4 177) A 178) D 179) A 180) C 181) C 182) C 183) C 184) D 185) C 186) B 187) C 188) A 189) D 190) A 191) C 192) D 193) B 194) C 195) D 196) B 197) C 198) D 199) D 200) C 201) A 202) A 203) A 204) D 205) B 206) C 207) A 208) B 209) C 210) A 211) C 212) C 213) B 214) D 215) A 216) D 217) A 218) C 219) C 220) D 221) C 222) A

Chapter 5 Exam Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) Decide which of the rational functions might have the given graph.

A) f(x) = 1 - x

B) f(x) = 1 -

1 x

C) f(x) =

1 -1 x

D) f(x) = 1 +

1 x

2) Decide which of the rational functions might have the given graph.

A) R(x) =

x-2 (x + 2)(x - 3)

B) R(x) =

x-2 (x + 2)2 (x - 3)2

C) R(x) =

x+2 (x - 2)(x + 3)

D) R(x) =

2-x (x + 2)(x - 3)

3) Determine which rational function R(x) has a graph that crosses the x-axis at -1, touches the x-axis at -4, has vertical asymptotes at x = -2 and x = 3, and has one horizontal asymptote at y = -2. -2(x -3)(x + 2)2 -(x + 1)(x + 4)2 , x -4, -1 , x 2, -3 A) R(x) = B) R(x) = (x + 4)2 (x +1) 2(x - 2)2 (x + 3) C) R(x) =

-2(x + 1)(x + 4)2 , x -2, 3 (x + 2)2 (x - 3)

D) R(x) =

-2(x + 1)(x + 4) , x -2, 3 (x + 2)(x - 3)

4) Which of the following functions could have this graph?

A) y =

(x + 1)(x - 4)2 (x - 2)2(x - 6)

B) y =

(x - 2)(x - 6)2 (x + 1)2(x - 4)

C) y =

2(x - 2)2 (x - 6) (x + 1)(x - 4)2

D) y =

(x - 2)2 (x - 6) (x + 1)(x - 4)2

5) Decide which of the rational functions might have the given graph.

A) f(x) = 2x +

1 x

B) f(x) = x +

2 x

C) f(x) = x + 2

D) f(x) = x +

1 x

6) A can in the shape of a right circular cylinder is required to have a volume of 700 cubic centimeters. The top and bottom are made up of a material that costs 8¢ per square centimeter, while the sides are made of material that costs 5¢ per square centimeter. Which function below describes the total cost of the material as a function of the radius r of the cylinder? 140 70 A) C(r) = 0.16 r2 + B) C(r) = 0.08 r2 + r r 70 C) C(r) = 0.16 r2 + r

140 D) C(r) = 0.08 r2 + r

7) Decide which of the rational functions might have the given graph.

A) f(x) =

1 x

B) f(x) =

1 2x

C) f(x) = x2

D) f(x) =

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. The equation has a solution r in the interval indicated. Approximate this solution correct to two decimal places. 8) x3 - 8x - 3 = 0; -1 r 0 8) Analyze the graph of the given function f as follows: (a) Determine the end behavior: find the power function that the graph of f resembles for large values of |x|. (b) Find the x- and y-intercepts of the graph. (c) Determine whether the graph crosses or touches the x-axis at each x-intercept. (d) Graph f using a graphing utility. (e) Use the graph to determine the local maxima and local minima, if any exist. Round turning points to two decimal places. (f) Use the information obtained in (a) - (e) to draw a complete graph of f by hand. Label all intercepts and turning points. (g) Find the domain of f. Use the graph to find the range of f. (h) Use the graph to determine where f is increasing and where f is decreasing. 9) f(x) = 8x5 + 36x4 + 36x3 9)

Solve the problem. 10) The formula y =

fx models the relationships needed to focus an image where y is the distance 10) x-f

between the film and projector lens, x is the distance between the move screen and the projector lens, and f is the focal length. a) Sketch the graph of this rational function for f = 5 centimeters.

b) Bob and Carol are showing home movies. Use the graph to describe the desired distance between the film and the projector lens as Carol moves the projector further from the screen.

Analyze the graph of the given function f as follows: (a) Determine the end behavior: find the power function that the graph of f resembles for large values of |x|. (b) Graph f using a graphing utility. (c) Find the x- and y-intercepts of the graph. (d) Use the graph to determine the local maxima and local minima, if any exist. Round turning points to two decimal places. (e) Use the information obtained in (a) - (d) to draw a complete graph of f by hand. Label all intercepts and turning points. (f) Find the domain of f. Use the graph to find the range of f. (g) Use the graph to determine where f is increasing and where f is decreasing. 11) f(x) = x3 - 0.6x2 - 3.3856x + 2.03136 11)

Solve the problem. 12) The acceleration due to gravity g (in meters per second per second) at a height h meters 3.99 × 1014 above sea level is given by g(h) = where 6.374 × 106 is the radius of Earth (6.374 × 106 + h)2

12)

in meters. Death Valley in California is 86 m below sea level. a) Find the value of g(h) at Death Valley to four decimal places. b) Compare the value in (a) to the value of g(h) at sea level.

13) A lens can be used to create an image of an object on the opposite side of the lens, such as the image created on a movie screen. Every lens has a measurement called its focal length, f. The distance s1 of the object to the lens is related to the distance s2 of the lens to the image by the function fs2 s1 = . s2 - f

For a lens with f = 0.3 m, what are the asymptotes of this function?

13)

Solve the problem. 15) The price of electric guitars has varied considerably in recent years. The data in the table relates15) the price P, in dollars, to time t, in years. a) Use a graphing utility to find the cubic function of best fit that models the relation between year and the price of an electric guitar. Round all values to three decimal places. b) Use the model found in part (a) to predict the price of an electric guitar in year 10. Average price, p, Year, t of an electric guitar 1 $618.20 2 783.20 3 674.30 4 721.60 5 825.00 6 891.00 7 852.50 8 819.50 9 783.20

Analyze the graph of the given function f as follows: (a) Determine the end behavior: find the power function that the graph of f resembles for large values of |x|. (b) Find the x- and y-intercepts of the graph. (c) Determine whether the graph crosses or touches the x-axis at each x-intercept. (d) Graph f using a graphing utility. (e) Use the graph to determine the local maxima and local minima, if any exist. Round turning points to two decimal places. (f) Use the information obtained in (a) - (e) to draw a complete graph of f by hand. Label all intercepts and turning points. (g) Find the domain of f. Use the graph to find the range of f. (h) Use the graph to determine where f is increasing and where f is decreasing. 16) f(x) = x2 (x2 - 4)(x + 4) 16)

17) f(x) = (x + 2)(x - 3)2

17)

Solve the problem. 18) The profits (in millions) for a company for 8 years was as follows:

18)

Year, x Profits 1993, 1 1.1 1994, 2 1.7 1995, 3 2.0 1996, 4 1.4 1997, 5 1.3 1998, 6 1.5 1999, 7 1.8 2000, 8 2.1 Find the cubic function of best fit to the data. Analyze the graph of the given function f as follows: (a) Determine the end behavior: find the power function that the graph of f resembles for large values of |x|. (b) Graph f using a graphing utility. (c) Find the x- and y-intercepts of the graph. (d) Use the graph to determine the local maxima and local minima, if any exist. Round turning points to two decimal places. (e) Use the information obtained in (a) - (d) to draw a complete graph of f by hand. Label all intercepts and turning points. (f) Find the domain of f. Use the graph to find the range of f. (g) Use the graph to determine where f is increasing and where f is decreasing. 19) f(x) = -3x4 + x3 - 7x + 4 19)

Solve the problem. 20) The following data represents the temperature T (°Fahrenheit) in a certain city x hours after midnight over the course of one day. Hours after Midnight, x 3 6 9 Temperature (in °F), T 60.4 59.3 62.2

12 65.7

15 65.6

18 70.4

21 69.4

20)

24 61.9

a) Find the average rate of change in temperature from 6 AM to 12 noon. Round to two decimal places. b) Find the average rate of change in temperature from 6 PM to 9 PM. Round to two decimal places. c) Decide on a function of best fit to these data (linear, quadratic, or cubic) and use this function to predict the temperature at 4 PM. Round to one decimal place.

21) The distance formula states that d = rt. If a car drives 50 miles, the function r = rational function. Find the asymptotes of this function.

50 is a t

21)

23) f(x) = -x2 (x - 1)(x + 3)

23)

The equation has a solution r in the interval indicated. Approximate this solution correct to two decimal places. 25) x3 - 8x - 3 = 0; -3 r -2 25) Solve the problem. 26) The concentration C of a certain drug in a patient's bloodstream is given by 30t . 2 t + 49

26)

a) Find the horizontal asymptote of C(t). b) Using a graphing utility, determine the time at which the concentration is highest.

27) A box has a base whose length is twice its width. The volume of the box is 7000 cubic inches. 27) a) Find a function for the surface area of the box. b) What are the dimensions of the box that minimizes surface area? 28) A rare species of insect was discovered in the rain forest of Costa Rica. Environmentalists transplant the insect into a protected area. The population of the insect t months after being transplanted is 45(1 + 0.6t) P(t) = . (3 + 0.02t) a) What was the population when t = 0? b) What will the population be after 10 years? c) What is the largest value the population could reach?

28)

30) f(x) = -2(x - 3)(x + 1)3

30)

Solve the problem. 31) When two lenses are placed next to each other, their combined focal length (a measurement that 31) can be negative or positive) is described by the equation f1 f2 f= . f1 + f2 If f1 = 0.001, what are the asymptotes of this function?

The equation has a solution r in the interval indicated. Approximate this solution correct to two decimal places. 32) x4 - x3 - 7x2 + 5x + 10 = 0; -3 r -2 32) Analyze the graph of the given function f as follows: (a) Determine the end behavior: find the power function that the graph of f resembles for large values of |x|. (b) Find the x- and y-intercepts of the graph. (c) Determine whether the graph crosses or touches the x-axis at each x-intercept. (d) Graph f using a graphing utility. (e) Use the graph to determine the local maxima and local minima, if any exist. Round turning points to two decimal places. (f) Use the information obtained in (a) - (e) to draw a complete graph of f by hand. Label all intercepts and turning points. (g) Find the domain of f. Use the graph to find the range of f. (h) Use the graph to determine where f is increasing and where f is decreasing. 33) f(x) = x2 (x + 3) 33)

Solve the problem.

34) For the polynomial function f(x) = 2x4 - 7x3 + 11x - 4 34) a) Find the x- and y-intercepts of the graph of f. Round to two decimal places, if necessary. b) Determine whether the graph crosses or touches the x-axis at each x-intercept. c) End behavior: find the power function that the graph of f resembles for large values of |x|. d) Use a graphing utility to graph the function.Approximate the local maxima rounded to two decimal places, if necessary. Approximate the local minima rounded to two decimal places, if necessary. e) Determine the number of turning points on the graph. f) Put all the information together, and connect the points with a smooth, continuous curve to obtain the graph of f.

The equation has a solution r in the interval indicated. Approximate this solution correct to two decimal places. 35) x4 - x3 - 7x2 + 5x + 10 = 0; 2 < r 3 35) Analyze the graph of the given function f as follows: (a) Determine the end behavior: find the power function that the graph of f resembles for large values of |x|. (b) Find the x- and y-intercepts of the graph. (c) Determine whether the graph crosses or touches the x-axis at each x-intercept. (d) Graph f using a graphing utility. (e) Use the graph to determine the local maxima and local minima, if any exist. Round turning points to two decimal places. (f) Use the information obtained in (a) - (e) to draw a complete graph of f by hand. Label all intercepts and turning points. (g) Find the domain of f. Use the graph to find the range of f. (h) Use the graph to determine where f is increasing and where f is decreasing. 36) f(x) = -x5 + 6x4 + 4x3 - 24x2 36) Analyze the graph of the given function f as follows: (a) Determine the end behavior: find the power function that the graph of f resembles for large values of |x|. (b) Graph f using a graphing utility. (c) Find the x- and y-intercepts of the graph. (d) Use the graph to determine the local maxima and local minima, if any exist. Round turning points to two decimal places. (e) Use the information obtained in (a) - (d) to draw a complete graph of f by hand. Label all intercepts and turning points. (f) Find the domain of f. Use the graph to find the range of f. (g) Use the graph to determine where f is increasing and where f is decreasing. 37) f(x) = x4 - 1.8x2 + 0.5184 37)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use the graph to find the vertical asymptotes, if any, of the function. 39)

A) x = 3

B) x = 2, y = 4

39)

C) x = 3, x = 0

Find the intercepts of the function f(x). 40) f(x) = (x + 4)(x - 2)(x + 2) A) x-intercepts: -4, -2, 2; y-intercept: 16 C) x-intercepts: -2, 2, 4; y-intercept: 16

D) y = 4

B) x-intercepts: -4, -2, 2; y-intercept: -16 D) x-intercepts: -2, 2, 4; y-intercept: -16

Form a polynomial f(x) with real coefficients having the given degree and zeros. 41) Degree: 4; zeros: -1, 2, and 1 - 2i. A) f(x) = x4 - x3 + x2 + 9x - 10 B) f(x) = x4 - 3x3 - 3x2 + 7x + 6 C) f(x) = x4 - x3 + 3x2 - 5x - 10

40)

41)

D) f(x) = x4 - 3x3 + 5x2 - x - 10

Give the equation of the oblique asymptote, if any, of the function. 7x2 - 9x - 7 42) h(x) = 2x2 - 8x + 2

42)

A) y =

7 2

B) y = x +

C) y =

7 x 2

D) no oblique asymptote

7 2

Find the power function that the graph of f resembles for large values of |x|. 43) f(x) = 2x - x3 A) y = x3

B) y = x2

C) y = x4

D) y = -x3

Find the indicated intercept(s) of the graph of the function. 5x 44) y-intercept of f(x) = 2 x - 19 A) (0, 5)

44) C) 0, -

B) (0, 0)

45) x-intercepts of f(x) = A) (5, 0)

43)

5 19

D) none

2x + 3 x-5

45) B)

3 ,0 2

C) -

3 ,0 2

D) (-5, 0)

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x -intercept. 1 4 2 (x + 8)4 46) f(x) = x + 46) 3

A) B)

1 , multiplicity 4, touches x-axis 3

1 , multiplicity 4, touches x-axis; 8, multiplicity 4, crosses x-axis 3

C) -

1 , multiplicity 4, touches x-axis; -8, multiplicity 4, crosses x-axis 3

D) -

1 , multiplicity 4, crosses x-axis 3

Solve the inequality. (x - 6)(x + 6) 47) x

A) [-6, 0) or [6, )

47) B) (- , -6] or [6, )

C) [-6, 0) or (0, 6]

Solve the equation in the real number system. 48) 3x4 - 16x3 + 56x2 - 56x + 13 = 0 1 A) 1, 3

1 B) 1, 3

1 C) -1, 3

Find the intercepts of the function f(x). 49) f(x) = (x - 2)2 (x2 - 25)

A) x-intercepts: -2, -25; y-intercept: 50 C) x-intercepts: -5, 2, 5; y-intercept: 100

D) (- , -6] or (0, 6]

1 -1, 3

B) x-intercepts: 2, 25; y-intercept: 50 D) x-intercepts: -5, 2, 5; y-intercept: -100

48)

49)

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval. 50) f(x) = 8x3 - 4x + 6; [-2, -1] 50) A) f(-2) = 50 and f(-1) = -2; yes C) f(-2) = -50 and f(-1) = 2; yes

B) f(-2) = -50 and f(-1) = -2; no D) f(-2) = 50 and f(-1) = 2; no

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x -intercept. 51) f(x) = 3(x2 + 4)(x2 + 7)2 51)

A) No real zeros B) 2, multiplicity 1, crosses x-axis; -2, multiplicity 1, crosses x-axis; 7, multiplicity 2, touches x-axis; - 7, multiplicity 2, touches x-axis C) -4, multiplicity 1, touches x-axis; -7, multiplicity 2, crosses x-axis D) -4, multiplicity 1, crosses x-axis; -7, multiplicity 2, touches x-axis

Graph the function. 52) f(x) =

3x (x + 1)(x + 3)

52)

Find the domain of the rational function. -2x(x + 2) 53) f(x) = 4x2 - 3x - 7 A) x x

7 , -1 4

53) 4 , -1 7

B) x x

C) x x -

4 ,1 7

D) x x -

7 ,1 4

Find the indicated intercept(s) of the graph of the function. x2 - 2x 54) y-intercept of f(x) = x2 + 7x - 11 A) (0, 2)

B) 0, -

54)

11 2

C) (0, 0)

D) 0,

2 11

Give the equation of the oblique asymptote, if any, of the function. x2 + 5x + 6 55) f(x) = x+2 A) y = x + 3 C) y = x - 7

55)

B) x = y + 3 D) no oblique asymptotes

Find the domain of the rational function. x+5 56) f(x) = 2 x - 64x

56)

A) {x|x -8, 8, -5} C) {x|x -8, 8}

B) {x|x 0, 64} D) all real numbers

Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f. 57) Degree 5; zeros: -2, i, 2i 57) A) 2, -i B) 2, -2i C) -i, -2i D) 2, -i, -2i Find the x- and y-intercepts of f. 58) f(x) = -x2 (x + 5)(x2 + 1)

A) x-intercepts: -5, -1, 0; y-intercept: 5 C) x-intercepts: -5, -1, 0; y-intercept: -5

B) x-intercepts: -5, -1, 0, 1; y-intercept: 0 D) x-intercepts: -5, 0; y-intercept: 0

Solve the equation in the real number system. 59) x3 + 3x2 - 8x + 10 = 0 A) {5}

B) {-5}

C) {1}

D) {-5, 5}

List the potential rational zeros of the polynomial function. Do not find the zeros. 60) f(x) = -4x4 + 2x2 - 3x + 6 1 1 2 3 3 A) ± , ± , ± , ± , ± , ± 1, ± 2, ± 3, ± 6 4 2 3 4 2

C) ±

1 1 3 3 B) ± , ± , ± , ± , ± 1, ± 2, ± 3, ± 6 4 2 4 2

1 1 3 3 , ± , ± , ± , ± 1, ± 2, ± 3, ± 4, ± 6 4 2 4 2

D) ±

1 1 1 2 4 , ± , ± , ± , ± , ± 1, ± 2, ± 4 6 2 3 3 3

58)

59)

60)

Find all zeros of the function and write the polynomial as a product of linear factors. 61) f(x) = x3 + 7x2 + 17x + 11 A) f(x) = (x - 1)(x + 2 + 3i)(x + 2 - 3i) C) f(x) = (x + 1)(x + 3 + i 2)(x - 3 - i 2)

Find the power function that the graph of f resembles for large values of |x|. 62) f(x) = -x2 (x + 8)3 (x2 - 1) A) y = x7

61)

B) f(x) = (x - 1)(x + 2 + 3i)(x - 2 - 3i) D) f(x) = (x + 1)(x + 3 + i 2)(x + 3 - i 2)

B) y = x2

C) y = -x7

D) y = x3

Use the Factor Theorem to determine whether x - c is a factor of f(x). 11 63) f(x) = 63x3 + 85x2 - 43x - 33; x + 7 A) Yes

62)

63)

B) No

Find all zeros of the function and write the polynomial as a product of linear factors. 64) f(x) = x3 - x2 + 4x - 4

64)

List the potential rational zeros of the polynomial function. Do not find the zeros. 65) f(x) = x5 - 6x2 + 4x + 15

65)

A) f(x) = (x - 1)(x + 2)(x - 2) C) f(x) = (x - 25)(x + i)(x - i)

B) f(x) = (x - 1)(x + 1)(x + 4) D) f(x) = (x - 1)(x + 2i)(x - 2i)

1 1 1 , ± 5, ± 3, ± 15 A) ± 1, ± , ± , ± 5 3 15

B) ± 1, ± 5, ± 3

C) ± 1, ± 5, ± 3, ± 15

D) ± 1, ±

1 1 1 ,± ,± 5 3 15

Use transformations of the graph of y = x 4 or y = x 5 to graph the function. 66) f(x) = -2(x + 4)4 + 4

66)

Determine the real zeros of the polynomial and their multiplicities. Then decide whether the graph touches or crosses the x-axis at each zero. 67) f(x) = 3(x2 + 2)(x + 4)2 67)

A) -4, multiplicity 2, crosses x-axis B) -2, multiplicity 1, crosses x-axis; -4, multiplicity 2, touches x-axis C) -4, multiplicity 2, touches x-axis D) -2, multiplicity 1, touches x-axis; -4, multiplicity 2, crosses x-axis

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. 68) f(x) = x( x -9) A) Yes; degree 1 B) No; it is a product C) No; x is raised to non-integer power D) Yes; degree 2

68)

Use the graph to find the oblique asymptote, if any, of the function. 69)

A) no oblique asymptote C) y = 2x

69)

B) y = x D) y = -x

Solve the problem. 70) Economists use what is called a Leffer curve to predict the government revenue for tax rates from 0% to70) 100%. Economists agree that the end points of the curve generate 0 revenue, but disagree on the tax rate that produces the maximum revenue. Suppose an economist produces this rational function 10x(100 - x) R(x) = , where R is revenue in millions at a tax rate of x percent. Use a graphing 50 + x calculator to graph the function. What tax rate produces the maximum revenue? What is the maximum revenue? A) 36.6%; $268 million B) 34.0%; $271 million C) 41.2%; $264 million D) 35.8%; $276 million

Find the intercepts of the function f(x). 71) f(x) = x3 + 3x2 - 4x - 12

A) x-intercepts: -3, -2, 2; y-intercept: -12 C) x-intercept: -3; y-intercept: -12

B) x-intercept: -2; y-intercept: -12 D) x-intercepts: -2, 2, 3; y-intercept: -12

Determine the maximum number of turning points of f. 72) f(x) = (x - 4)2 (x + 5)2 A) 2

B) 3

Solve the equation in the real number system. 73) 3x3 - x2 + 3x - 1 = 0 1 A) -3, , -1 3

1 B) -3, - , -1 3

C) 1

D) 4

1 C) 3

1 , -1 D) 3

71)

72)

73)

Identify which of the graphs could be the graph of a polynomial function. 74) f(x) = 6x3 - 5x - x5 A)

74)

Find the vertical asymptotes of the rational function. -2x(x + 2) 75) f(x) = 4x2 - 5x - 9 A) x = -

4 ,x=1 9

B) x =

75)

4 , x = -1 9

C) x = -

Solve the inequality. 76) (b + 6)(b + 4)(b - 5) < 0 A) (- , -6) or (-4, 5) C) (-6, -4) or (5, )

9 ,x=1 4

D) x =

B) (5, ) D) (- , -4)

Give the equation of the horizontal asymptote, if any, of the function. 2x3 - 5x - 9 77) h(x) = 4x + 5 A) y =

1 2

B) y = 2

C) y = 0

D) no horizontal asymptotes

9 , x = -1 4

76)

77)

Use the x-intercepts to find the intervals on which the graph of f is above and below the x-axis. 1 2 (x - 2)5 78) f(x) = x 3 A) above the x-axis: - ,

1 1 , ,2 3 3

B) above the x-axis: (2, ) 1 1 below the x-axis: - , , , 2 3 3

below the x-axis: (2, )

C) above the x-axis: - , below the x-axis:

1 , (2, ) 3

D) above the x-axis:

1 ,2 3

below the x-axis: - ,

Use the Remainder Theorem to find the remainder when f(x) is divided by x - c. 79) f(x) = x4 + 8x3 + 12x2 ; x + 1 A) R = 21

78)

B) R = -5

C) R = -21

Use transformations of the graph of y = x 4 or y = x 5 to graph the function. 80) f(x) = (x - 4)5 + 2

1 , (2, ) 3

D) R = 5

79)

80)

Identify which of the graphs could be the graph of a polynomial function. 81) f(x) = x3 + 4x2 - 5x - 6 A)

81)

Use the graph to find the oblique asymptote, if any, of the function. 82)

A) no oblique asymptote C) y = -x

82)

B) y = x + 1 D) y = x

Find the domain of the rational function. 3x 83) g(x) = x+7

83)

A) {x|x 0} C) {x|x 7}

B) {x|x -7} D) all real numbers

Solve the inequality. 84) x2 + 2x 8

A) [-4, 2] C) (- , -4]

B) [2, ) D) (- , -4] or [2, )

Give the equation of the oblique asymptote, if any, of the function. 6x2 - 3x - 7 85) h(x) = 5x2 - 4x + 7 A) y =

6 x 5

85)

B) y = x + D) y =

C) no oblique asymptote

6 5

Use the x-intercepts to find the intervals on which the graph of f is above and below the x-axis. 86) f(x) = (x + 11)2 A) above the x-axis: (- , -11), (-11, ) below the x-axis: no intervals C) above the x-axis: (- , -11) below the x-axis: (-11, )

84)

B) above the x-axis: (-11, ) below the x-axis: (- , -11) D) above the x-axis: no intervals below the x-axis: (- , -11), (-11, )

86)

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval. 87) f(x) = 9x5 - 8x3 - 3x2 + 1; [-1, 0] 87) A) f(-1) = -3 and f(0) = 1; yes C) f(-1) = -3 and f(0) = -1; no

B) f(-1) = 3 and f(0) = -1; yes D) f(-1) = 3 and f(0) = 1; no

Form a polynomial f(x) with real coefficients having the given degree and zeros. 88) Degree: 4; zeros: 2i and -5i A) f(x) = x4 - 2x3 + 29x2 + 100 B) f(x) = x4 - 5x2 + 100 C) f(x) = x4 + 29x2 -5x + 100

88)

D) f(x) = x4 + 29x2 + 100

Use the Factor Theorem to determine whether x - c is a factor of f(x). 89) f(x) = 8x3 + 36x2 - 19x - 5; x + 5

89)

Use the graph to find the vertical asymptotes, if any, of the function. 90)

90)

A) Yes

B) No

A) x = -4, x = 4, x = 0 C) x = -4, x = 4, y = 0 Solve the inequality. 4x2 - 3x - 7 91) x+4

B) none D) x = -4, x = 4

A) (-4, -1] or

91) 7 , 4

C) (- , -4) or -1,

B) (- , -1] or 7 4

7 , 4

D) (- , -4] or -1,

7 4

Find the indicated intercept(s) of the graph of the function. x2 - 6x + 1 92) y-intercept of f(x) = 13x A) 0,

1 13

92)

B) 0, - 13

C) (0, 1)

D) none

Use the graph to determine the domain and range of the function. 93)

A) domain: {x|x 4} range: {y|y 5} C) domain: {x|x 5} range: {y|y -4}

93)

B) domain: {x|x -4} range: {y|y 5} D) domain: {x|x 5} range: {y|y 4}

Use the Factor Theorem to determine whether x - c is a factor of f(x). 94) f(x) = x3 + 8x2 - 18x + 20; x + 10 A) Yes

94)

B) No

Find the indicated intercept(s) of the graph of the function. 23 95) y-intercept of f(x) = (x + 10)(x2 - 5) A) 0,

23 50

B) 0, -

95)

23 50

C) 0, 23

D) none

Find the intercepts of the function f(x). 96) f(x) = 5x4 - 9x3 + 24x2 - 36x + 16

96)

4 A) x-intercepts: 1, ; y-intercept: 16 5

B) x-intercepts: -4, -1, 1, C) x-intercepts: 4,

4 ; y-intercept: 16 5

D) x-intercepts: -4, -1, 1, -

4 ; y-intercept: 16 5

Find the domain of the rational function. -2x(x + 2) 97) f(x) = 3x2 - 4x - 7 A) x x -

3 ,1 7

B) x x -

97) 7 ,1 3

C) x x

3 , -1 7

D) x x

7 , -1 3

Solve the inequality. 98) x2 - 3x - 4 0 A) [4, ) C) (- , -1] or [4, )

98)

B) [-1, 4] D) (- , -1]

Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f. 99) Degree 4; zeros: 4 - 5i, 7i 99) A) 4 + 5i, -7i B) -4 - 5i, -7i C) -4 + 5i, -7i D) 4 + 5i, 7 - i 100) Degree 4; zeros: i, 3 + i A) -3 + i, 3 - i

B) 3 - i

C) -i, 3 - i

D) -i, -3 + i

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. 2 101) f(x) = 6 x2 A) Yes; degree

1 2

100)

101)

B) Yes; degree -2

C) Yes; degree 2

D) No; x is raised to the negative 2 power

Graph the function using transformations. 1 102) f(x) = + 4 x

102)

Use transformations of the graph of y = x 4 or y = x 5 to graph the function. 1 103) f(x) = (x - 3)4 + 2 2

103)

Give the equation of the horizontal asymptote, if any, of the function. -3x2 104) R(x) = x2 + 9x - 22 A) y = 0 C) y = -11, y = 2

104)

B) no horizontal asymptotes D) y = -3

Use the graph to find the horizontal asymptote, if any, of the function. 105)

A) y = 0, y = 5

B) x = 3

C) y = 5

105)

D) y = 0

Find the domain of the rational function. x+3 106) h(x) = 2 x + 49x

106)

A) {x|x -7, x 7} C) all real numbers

B) {x|x -7, x 7, x -3} D) {x|x 0, x -49}

Find the x- and y-intercepts of f. 107) f(x) = -x2 (x + 9)(x2 - 1)

A) x-intercepts: -9, -1, 0, 1; y-intercept: -9 C) x-intercepts: -9, -1, 0, 1; y-intercept: 0

B) x-intercepts: -9, 0, 1; y-intercept: -9 D) x-intercepts: -1, 0, 1, 9; y-intercept: 0

107)

Give the equation of the horizontal asymptote, if any, of the function. x2 + 5x - 2 108) g(x) = x-2 A) y = 2 C) y = 1

108)

B) y = 0 D) no horizontal asymptotes

Find the x- and y-intercepts of f. 109) f(x) = (x - 2)2 (x2 - 16)

A) x-intercepts: -2, -16; y-intercept: 32 C) x-intercepts: 2, 16; y-intercept: 32

B) x-intercepts: -4, 2, 4; y-intercept: -64 D) x-intercepts: -4, 2, 4; y-intercept: 64

Use the Factor Theorem to determine whether x - c is a factor of f(x). 110) f(x) = 7x3 + 17x2 - 11x + 3; x + 3 A) Yes

110)

B) No

Solve the inequality. x-2 >0 111) x+6

111)

A) (- , -6) or (2, ) C) (-6, 2)

B) (- , -6) D) (2, )

Solve the equation in the real number system. 112) 3x3 - x2 - 30x + 10 = 0 1 A) - , 3

10, -

C) { 3,

112)

1 , B) 3

10, -

10, - 10 }

D) { -3,

10, -

10 }

Find a bound on the real zeros of the polynomial function. 113) f(x) = x4 - 15x2 - 16 A) -16 and 16

B) -31 and 31

C) -32 and 32

Solve the inequality. 114) (x + 6)(x + 3) > 0 A) (- , -6) or (-3, ) C) (-6, -3) 115)

109)

B) (- , -6) D) (-3, )

12 9 > x-3 x+1

D) -17 and 17

113)

114)

115)

A) (- , -13) or (-1, 3) C) (-13, -1) or (-1, 3)

B) (- , -13) or (3, ) D) (-13, -1) or (3, )

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x -intercept. 1 116) f(x) = x2(x2 - 5)(x + 5) 116) 5

A) 0, multiplicity 2, touches x-axis; -5, multiplicity 1, crosses x-axis

B) 0, multiplicity 2, crosses x-axis; -5, multiplicity 1, touches x-axis

C) 0, multiplicity 2, touches x-axis; -5, multiplicity 1, crosses x-axis; 5, multiplicity 1, crosses x-axis; - 5, multiplicity 1, crosses x-axis

D) 0, multiplicity 2, crosses x-axis; -5, multiplicity 1, touches x-axis; 5, multiplicity 1, touches x-axis; - 5, multiplicity 1, touches x-axis

Find the indicated intercept(s) of the graph of the function. (5x - 20)(x - 4) 117) y-intercept of f(x) = x2 + 16x- 19 A) 0,

80 19

117)

B) (0, 4)

C) (0, 4)

D) 0, -

80 19

Give the equation of the horizontal asymptote, if any, of the function. -x2 + 16 118) f(x) = x2 + 5x + 4 A) y = -1 C) y = 0

118)

B) no horizontal asymptotes D) y = -16

Find the vertical asymptotes of the rational function. x-2 119) f(x) = 4x - x3

119)

A) x = 0, x = -2, x = 2 C) x = 0, x = 2

B) x = -2, x = 2 D) x = 0, x = -2

Find all zeros of the function and write the polynomial as a product of linear factors. 120) f(x) = 2x4 - 3x3 + 16x2 - 27x - 18 A) f(x) = (2x - 1)(x + 2)(x + 3i)(x - 3i) C) f(x) = (2x + 1)(x - 2)(x + 3i)(x - 3i)

B) f(x) = (2x + 1)(x - 2)(x + 3)(x - 3) D) f(x) = (2x - 1)(x + 2)(x + 3)(x - 3)

120)

Use the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. 121) f(x) = x3 + 3x2 - 4x - 12 121)

A) -3; f(x) = (x + 3)(x2 - x - 4) C) -2; f(x) = (x + 2)(x2 + x - 6)

B) -2, 2, 3; f(x) = (x + 2)(x - 2)(x - 3) D) -3, -2, 2; f(x) = (x + 3)(x + 2)(x - 2)

Use the graph to find the horizontal asymptote, if any, of the function. 122)

A) none

B) y = 0

C) y = -2

122)

D) y = 2

Solve the equation in the real number system. 123) 2x4 - 2x3 + x2 - 5x - 10 = 0 A) {1, -2}

123)

5 5 B) - , 2 2

C) {-1, 2}

Solve the inequality. 124) x4 - 45x2 - 196 > 0

A) (- , -7) or (7, ) C) (-7, 7)

125) x4 < 64x2 A) (-8, 0) or (8, )

B) (- , -7) or (-2, 2) or (7, ) D) (-7, -2) or (2, 7)

B) (-8, 0) or (0, 8)

C) (- , -8) or (8, )

Find the intercepts of the function f(x). 126) f(x) = -x2 (x + 3)(x2 + 1)

A) x-intercepts: -3, -1, 0; y-intercept: -3 C) x-intercepts: -3, -1, 0, 1; y-intercept: 0

D) (- , -8) or (0, 8)

B) x-intercepts: -3, 0; y-intercept: 0 D) x-intercepts: -3, -1, 0; y-intercept: 3

Find a bound on the real zeros of the polynomial function. 127) f(x) = 13x3 - x2 + 0.3x - 0.06 A) -1.36 and 1.36

D) -

10 10 , 2 2

B) -1 and 1

C) -13 and 13

D) -2 and 2

Find the vertical asymptotes of the rational function. 5x 128) g(x) = x-2 A) x = -2

125)

126)

127)

128)

B) x = 5

Solve the equation in the real number system. 129) x3 + 2x2 - 5x - 6 = 0 A) {-3, -1}

124)

B) {-3, -1, 2}

C) x = 2

D) none

C) {1, 3}

D) {-2, 1, 3}

129)

Solve the inequality. 130) 30(x2 - 1) > 91x 3 10 , A) 10 3

C) - , -

10 3 or , B) - , 3 10

3 10 or , 10 3

D) -

130)

10 3 , 3 10

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval. 131) f(x) = 10x3 - 7x2 - 10x - 2; [1, 2] 131) A) f(1) = 9 and f(2) = 30; no C) f(1) = -9 and f(2) = -30; no

B) f(1) = 9 and f(2) = -30; yes D) f(1) = -9 and f(2) = 30; yes

Identify which of the graphs could be the graph of a polynomial function. 132) f(x) = x3 + 5x2 - x - 5 A)

Find the intercepts of the function f(x). 133) f(x) = (x + 1)(x - 4)(x - 1)2

A) x-intercepts: -1, 1, 4; y-intercept: 4 C) x-intercepts: -1, 1, 4; y-intercept: -4

B) x-intercepts: -1, 1, -4; y-intercept: -4 D) x-intercepts: -1, 1, -4; y-intercept: 4

132)

133)

Form a polynomial f(x) with real coefficients having the given degree and zeros. 134) Degree: 3; zeros: -3 and 3 - 2i A) f(x) = x3 - 3x2 + 5x - 52 B) f(x) = x3 - x2 - 5x + 39 C) f(x) = x3 - x2 + 11x + 39

134)

D) f(x) = x3 - 3x2 - 5x + 39

Use transformations of the graph of y = x 4 or y = x 5 to graph the function. 135) f(x) = x5 - 3

135)

Form a polynomial f(x) with real coefficients having the given degree and zeros. 136) Degree: 4; zeros: 1, -1, and 4 - 2i A) f(x) = x4 - 8x3 + 16x2 + 8x + 17 B) f(x) = x4 - 8x3 + 16x2 + 8x - 17 C) f(x) = x4 + 8x3 + 16x2 - 8x - 17

D) f(x) = x4 + 8x3 + 16x2 - 8x + 17

Find the vertical asymptotes of the rational function. 8x 137) h(x) = (x - 9)(x - 4)

137)

A) x = 9, x = 4 C) x = -8 Solve the inequality. (x - 1)(3 - x) 138) (x - 2)2

B) x = 9, x = 4, x = -8 D) x = -9, x = -4

138)

A) (- , -3] or (-2, -1) or [1, ) C) (- , -3) or (-1, ) 139) x2 + 9x 0 A) [0, 9]

B) (- , 1) or (3, ) D) (- , 1] or [3, )

B) (- , 0] or [9, )

C) [-9, 0]

Solve the equation in the real number system. 140) x4 - 3x3 + 5x2 - x - 10 = 0 A) {1, 2}

B) {-2, 1}

C) {-1, 2}

D) (- , -9] or [0, )

D) {-1, -2}

Give the equation of the horizontal asymptote, if any, of the function. 8x2 - 7x - 3 141) h(x) = 7x2 - 3x + 8 B) y =

A) y = 0 C) y =

8 7

139)

140)

141) 7 3

D) no horizontal asymptotes

Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1. 142) Zeros: -4, -5, 5; degree 3 A) f(x) = x3 - 25x + 4x2 - 100 B) f(x) = x3 + 25x - 4x2 - 100 C) f(x) = x3 + 25x + 4x2 + 100

Find the indicated intercept(s) of the graph of the function. x-5 144) y-intercept of f(x) = x2 + 10x - 8 B) 0, -

142)

D) f(x) = x3 - 25x - 4x2 + 100

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. 143) f(x) = x(x - 6) A) Yes; degree 1 B) No; it is a product C) Yes; degree 0 D) Yes; degree 2

A) (0, 5)

136)

143)

144)

8 5

C) 0,

5 8

D) none

Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f. 145) Degree 3; zeros: 1, 3 - i 145) A) -1 B) 3 + i C) -3 + i D) no other zeros Use the Factor Theorem to determine whether x - c is a factor of f(x). 146) f(x) = x4 - 12x2 - 64; x - 8

146)

Find the x- and y-intercepts of f. 147) f(x) = (x + 3)2

147)

A) Yes

B) No

A) x-intercept: -3; y-intercept: 9 C) x-intercept: 3; y-intercept: 0

B) x-intercept: -3; y-intercept: 0 D) x-intercept: 3; y-intercept: 9

Use transformations of the graph of y = x 4 or y = x 5 to graph the function. 1 148) f(x) = (x + 3)5 + 3 2

148)

Solve the inequality. 149) x(x - 7) -12 A) [3, 4]

B) (- , 3]

C) (- , 3] or [4, )

Graph the function. 16 150) f(x) = x x

D) [4, )

149)

150)

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x -intercept. 151) f(x) = 4(x - 3)(x + 4)4 151)

A) -3, multiplicity 1, crosses x-axis; 4, multiplicity 4, touches x-axis B) 3, multiplicity 1, crosses x-axis; -4, multiplicity 4, touches x-axis C) -3, multiplicity 1, touches x-axis; 4, multiplicity 4, crosses x-axis D) 3, multiplicity 1, touches x-axis; -4, multiplicity 4, crosses x-axis

Find the intercepts of the function f(x). 152) f(x) = -x2 (x + 7)(x2 - 1)

A) x-intercepts: -7, -1, 0, 1; y-intercept: -7 C) x-intercepts: -1, 0, 1, 7; y-intercept: 0

B) x-intercepts: -7, -1, 0, 1; y-intercept: 0 D) x-intercepts: -7, 0, 1; y-intercept: -7

152)

Use the Factor Theorem to determine whether x - c is a factor of f(x). 153) f(x) = x4 + 9x3 + 8x2 + 65x - 63; x + 9

153)

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. 154) f(x) = -17x4 - 3x3 - 8

154)

A) Yes

B) No

A) Yes; degree 7 C) No; the last term has no variable

B) Yes; degree 4 D) Yes; degree 8

Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1. 155) Zeros: 0, - 4, 3; degree 3 A) f(x) = x3 + x2 + x + 12 B) f(x) = x3 + x2 - 12x C) f(x) = x3 + x2 + 12x

Solve the inequality. 156) x3 > 9x2 A) (0, 9)

155)

D) f(x) = x3 + x2 + x - 12

B) (- , 9)

C) (- , 0) or (9, )

D) (9, )

156)

Find the intercepts of the function f(x). 157) f(x) = 2x3 - 13x2 + 22x - 8 A) x-intercepts: - 2, 1, -2; y-intercept: -8

1 B) x-intercepts: , 2, 4; y-intercept: -8 2

C) x-intercepts: 2, 1, 2; y-intercept: -8

D) x-intercepts: -

1 , 2, -4; y-intercept: -8 2

Use the graph to determine the domain and range of the function. 158)

A) domain: {x|x 0} range: {y|y 5} C) domain: {x|x 5} range: {y|y 0}

158)

B) domain: {x|x > 0} range: {y|y 5} D) domain: {x|x 5} range: {y|y > 0}

Find the indicated intercept(s) of the graph of the function. x 159) y-intercept of f(x) = (x + 10)(x - 3) B) 0, -

A) (0, 3)

160) y-intercept of f(x) = A) (0, 13)

157)

159)

1 30

C) (0, 0)

D) none

x - 13 3x - 14

160) B) 0, -

14 13

C) 0,

13 14

Use transformations of the graph of y = x 4 or y = x 5 to graph the function.

D) none

161) f(x) = x4 - 5

161)

Find the indicated intercept(s) of the graph of the function. x2 - x - 30 . 162) x-intercepts of f(x) = x2 + 5 A) (-6, 0), (0, 0)

162)

B) (- 30, 0)

C) (-5, 0), (6, 0)

Use the Factor Theorem to determine whether x - c is a factor of f(x). 163) f(x) = x4 - 5x2 - 36; x - 3 A) Yes

B) No

D) (-6, 0), (5, 0)

163)

Solve the inequality. 164) x2 - 9x + 20 > 0 A) (5, )

B) (- , 4) or (5, )

C) (- , 4)

D) (4, 5)

Find the indicated intercept(s) of the graph of the function. 16 165) y-intercept of f(x) = x + x A) (0, 0)

165)

B) (0, 16)

C) (0, 4)

D) none

Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1. 166) Zeros: -3, 1, 3, 5; degree 4 A) x4 + 6x3 - 4x2 - 54x - 45 B) x4 - 6x3 - 4x2 + 54x - 45 C) x4 + 12x2 - 45

166)

D) x4 - 6x3 - 4x2 - 45x - 45

Find the vertical asymptotes of the rational function. x + 11 167) g(x) = x2 - 4x

167)

A) x = 0, x = 4 C) x = 0, x = -2, x = 2

B) x = -2, x = 2 D) x = 4, x = -11

Solve the inequality. 168) x2 - 49 0

A) [-49, 49] C) [-7, 7]

168)

B) (- , -49] or [49, ) D) (- , -7] or [7, )

Use the graph to find the vertical asymptotes, if any, of the function. 169)

A) y = 0

164)

B) none

C) x = 0

169)

D) x = 0, y = 0

Determine the real zeros of the polynomial and their multiplicities. Then decide whether the graph touches or crosses the x-axis at each zero. 170) f(x) = 3(x - 2)(x - 5)3 170)

A) -2, multiplicity 1, crosses x-axis; -5, multiplicity 3, crosses x-axis B) -2, multiplicity 1, touches x-axis; -5, multiplicity 3 C) 2, multiplicity 1, crosses x-axis; 5, multiplicity 3, crosses x-axis D) 2, multiplicity 1, touches x-axis; 5, multiplicity 3

Graph the function. 37

171) f(x) =

x4 - 1 x2 - 64

171)

Give the equation of the oblique asymptote, if any, of the function. x2 + 4x - 8 172) f(x) = x-7 A) no oblique asymptotes C) x = y + 11

B) y = x + 11 D) y = x - 3

Solve the equation in the real number system. 173) x4 - 32x2 - 144 = 0 A) {-2, 2}

172)

B) {-12, 12}

C) {-6, -2, 2, 6}

D) {-6, 6}

173)

Use the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. 174) f(x) = 2x3 - 3x2 + 8x - 12 174)

A) 4, C)

3 , 1; f(x) = (2x - 3)(x - 1)(x - 4) 2

B) 12; f(x) = (x - 12)(2x2 + 1)

3 ; f(x) = (2x - 3)(x2 + 4) 2

D) -4, -1,

3 ; f(x) = (2x - 3)(x + 1)(x + 4) 2

Solve the problem. 175) The revenue achieved by selling x graphing calculators is figured to be x(47 - 0.2x) dollars. The cost of each calculator is $39. How many graphing calculators must be sold to make a profit (revenue cost) of at least $60.00? A) {x 0 < x < 20} B) {x 12 < x < 28} C) {x 11 < x < 9} D) {x 10 < x < 30} State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. 11 176) f(x) = 1 + x A) Yes; degree 0 C) Yes; degree 1

175)

176)

B) No; x is raised to a negative power D) Yes; degree 11

Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1. 177) Zeros: 3, multiplicity 2; -3, multiplicity 2; degree 4 A) f(x) = x4 - 18x2 + 81 B) f(x) = x4 + 18x2 + 81 C) f(x) = x4 + 6x3 - 18x2 + 27x - 81

177)

D) f(x) = x4 - 6x3 + 18x2 - 27x + 81

Find the x- and y-intercepts of f. 178) f(x) = (x + 5)(x - 6)(x + 6) A) x-intercepts: -6, 6, 5; y-intercept: 180 C) x-intercepts: -5, -6, 6; y-intercept: -180

B) x-intercepts: -6, 6, 5; y-intercept: -180 D) x-intercepts: -5, -6, 6; y-intercept: 180

Graph the function.

178)

179) f(x) =

x2 + 3x (x - 3)2

179)

Use the graph to determine the domain and range of the function. 180)

A) domain: {x|x 0 or x > 1} range: {y|y -4, y 4} C) domain: {x|x -4, x 4} range: {y|y 0 or y > 1}

180)

B) domain: {x|x -4, x 4} range: {y|y 0 or y 1} D) domain: all real numbers range: all real numbers

Find the vertical asymptotes of the rational function. x+3 181) g(x) = x2 - 36

181)

A) x = 0, x = 36 C) x = -6, x = 6

B) x = -6, x = 6, x = -3 D) x = 36, x = -3

Find the domain of the rational function. x+4 182) g(x) = x2 + 49

182)

A) {x|x 0, x -49} C) {x|x -7, x 7, x -4}

B) all real numbers D) {x|x -7, x 7}

Find the x- and y-intercepts of f. 183) f(x) = 7x - x3

183) B) x-intercepts: 0, D) x-intercepts: 0,

A) x-intercepts: 0, -7; y-intercept: 0 C) x-intercepts: 0, -7; y-intercept: 7

7, - 7; y-intercept: 0 7, - 7; y-intercept: 7

List the potential rational zeros of the polynomial function. Do not find the zeros. 184) f(x) = -2x3 + 4x2 - 3x + 8 1 A) ± , ± 1, ± 2, ± 4 2

C) ±

1 B) ± , ± 1, ± 2, ± 4, ± 8 2

1 1 , ± , ± 1, ± 2, ± 4, ± 8 4 2

D) ±

1 1 1 , ± , ± , ± 1, ± 2, ± 4, ± 8 8 4 2

184)

Identify which of the graphs could be the graph of a polynomial function. 185) f(x) = x4 - 4x2 A)

185)

Use the Factor Theorem to determine whether x - c is a factor of f(x). 186) f(x) = x4 + 10x3 + 2x2 + 13x - 70; x - 10 A) Yes

186)

B) No

Solve the inequality. 3x <x 187) 7-x A) (- , 4) or (7, )

187) B) (4, 7)

C) (7, )

Use the given zero to find the remaining zeros of the function. 188) f(x) = x3 - 3x2 - 5x + 39; zero: -3 A) 1 + 2i, 1 - 2i C) 1 + 2 13i, 1 - 2 13i

D) (0, 4) or (7, )

188) B) 3 + 2i, 3 - 2i D) 6 + 4i, 6 - 4i

Find the domain of the rational function. 2x2 - 4 189) f(x) = 3x2 + 6x - 24

189)

A) {x|x -4, -2, 2} C) {x|x -4, 2}

B) {x|x -2, 4} D) all real numbers

Use the graph to find the horizontal asymptote, if any, of the function. 190)

A) y = 0, y = 1 C) y = 1

190)

B) x = -3, x = 3, y = 1 D) y = -3, y = 3

Solve the problem. 191) For what positive numbers will the cube of a number exceed 8 times its square? A) x|0 < x < 8} B) x|x > 64} C) x|0 < x < 64} D) {x|x > 8} Solve the inequality. 192) x2 - 64 > 0

A) (-8, 8) C) (- , -8) or (8, )

192)

B) (- , -64) or (64, ) D) (-64, 64)

Find the indicated intercept(s) of the graph of the function. 5 193) x-intercepts of f(x) = x2 - x - 6 A) (3, 0), (-2, 0) Solve the inequality. 194) x2 - 6x 0

A) [-6, 0]

191)

193)

B) (5, 0)

C) (2, 0), (-3, 0)

D) none

B) (- , 0] or [6, )

C) (- , -6] or [0, )

D) [0, 6]

Find the domain of the rational function. 3x2 195) g(x) = (x - 1)(x - 8)

194)

195)

A) {x|x -1, x -8} C) all real numbers

B) {x|x 1, x 8, x -3} D) {x|x 1, x 8}

Solve the problem. 196) A ball is thrown vertically upward with an initial velocity of 128 feet per second. The distance in feet of the ball from the ground after t seconds is s = 128t - 16t2 . For what interval of time is the ball more than 192 above the ground? A) {x 3.5 sec < x < 4.5 sec} C) {x 2 sec < x < 6 sec}

B) {x 1.5 sec < x < 6.5 sec} D) {x 6 sec < x < 10 sec}

Graph the function. 43

196)

197) f(x) =

(x - 5)(x - 5) x2 - 36

197)

Find the intercepts of the function f(x). 198) f(x) = 3x4 - 30x3 + 76x2 - 10x + 25

A) x-intercepts: none; y-intercept: 25 C) x-intercept: -5; y-intercept: 25

B) x-intercepts: -5, 5; y-intercept: 25 D) x-intercept: 5; y-intercept: 25

198)

Give the equation of the oblique asymptote, if any, of the function. x2 - 5 199) f(x) = 25x - x4 A) no oblique asymptote C) y = 25x

199)

B) y = 0 D) y = x - 5

Solve the inequality. 18 < 11 200) x + x

200)

A) (- , 0) or (9, )

B) (0, 2) or (2, 9)

C) (- , 0) or (2, 9)

D) (0, 2) or (9, )

Find the indicated intercept(s) of the graph of the function. x3 - 216 201) x-intercepts of f(x) = x2 - 25 A) (-6, 0), (6, 0)

201)

B) (- 216, 0)

C) (6, 0)

D) (5, 0)

Find a polynomial function f(x) of least possible degree having the graph shown. 202)

A) f(x) =

1 (x - 2)(x + 3)2 2

B) f(x) =

1 (x - 2)(x + 3) 2

C) f(x) =

1 (x + 2)(x - 3) 2

D) f(x) =

1 (x + 2)(x - 3)2 2

Find a bound on the real zeros of the polynomial function. 203) f(x) = x5 + 3x4 + 9x3 - 6x2 - 3x - 12 A) -10 and 10

B) -13 and 13

C) - 12 and 12

Find the x- and y-intercepts of f. 204) f(x) = 2x5 (x + 8)5

A) x-intercepts: 0, -8; y-intercept: 0 C) x-intercepts: 0, -8; y-intercept: 2

202)

D) -33 and 33

B) x-intercepts: 0, 8; y-intercept: 2 D) x-intercepts: 0, 8; y-intercept: 0

203)

204)

Solve the problem. fit 205) The amount of water (in gallons) in a leaky bathtub is given in the table below. Using a graphing utility, 205) the data to a third degree polynomial (or a cubic). Then approximate the time at which there is maximum amount of water in the tub, and estimate the time when the water runs out of the tub. Express all your answers rounded to two decimal places. t (in minutes) 0 V ( in gallons) 20

1 26

2 45

3 63

4 86

5 94

6 90

7 67

A) maximum amount of water after 5.31 minutes; water never runs out B) maximum amount of water after 8.23 minutes; water runs out after 19.73 minutes C) maximum amount of water after 5.37 minutes; water runs out after 11.06 minutes D) maximum amount of water after 5.31 minutes; water runs out after 8.23 minutes Solve the inequality. 206) (x - 3)(x2 + x + 1) > A) (3, )

B) (- , 3)

C) (- , -1) or (1, )

206)

D) (-1, 1)

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x -intercept. 1 207) f(x) = x(x2 - 3) 207) 5

A) 0, multiplicity 1, touches x-axis; 3, multiplicity 1, touches x-axis; - 3, multiplicity 1, touches x-axis C) 0, multiplicity 1, crosses x-axis; 3, multiplicity 1, crosses x-axis; - 3, multiplicity 1, crosses x-axis

3, multiplicity 1, touches x-axis; - 3, multiplicity 1, touches x-axis

D) 0, multiplicity 1

Use the given zero to find the remaining zeros of the function. 208) f(x) = 2x4 - 13x3 + 48x2 - 73x + 26; zero: 2 + 3i A) 2 - 3i, 2,

1 2

B) 2 - 3i, -2,

1 2

C) 3 - 2i, -2, -

1 2

D) 3 - 2i, 2, -

List the potential rational zeros of the polynomial function. Do not find the zeros. 209) f(x) = x5 - 3x2 + 5x + 5 A) ± 1, ±

1 5

B) ± 5, ±

1 5

C) ± 1, ± 5

D) ±

1 5 ,± ,±5 3 3

Find all zeros of the function and write the polynomial as a product of linear factors. 210) f(x) = x3 + 12x2 + 46x + 52 A) f(x) = (x + 1)(x + 5 + i 3)(x - 2 - i 3) C) f(x) = (x + 2)(x + 5 + i)(x - 5 - i)

B) f(x) = (x - 1)(x + 5 + i 3)(x + 5 - i 3) D) f(x) = (x + 2)(x + 5 + i)(x + 5 - i)

1 2

208)

209)

210)

Solve the problem. 211) A ball is thrown vertically upward with an initial velocity of 96 feet per second. The distance in feet of the ball from the ground after t seconds is s = 96t - 16t2 . For what intervals of time is the ball less

211)

than 80 above the ground (after it is tossed until it returns to the ground)? A) {x 0 sec < x < 1 sec and 5 sec > x > 6 sec} B) {x 0 sec < x < 0.5 sec and 5.5 sec > x > 6 sec} C) {x 0 sec < x < 2.5 sec and 3.5 sec > x > 6 sec} D) {x 1 sec < x < 5 sec}

Find the indicated intercept(s) of the graph of the function. x-1 212) x-intercepts of f(x) = 2 x + 5x - 1 A) (5, 0)

212)

B) (-1, 0)

C) (1, 0)

D) none

Give the equation of the oblique asymptote, if any, of the function. 10x3 - 9x2 + 12x + 13 213) f(x) = -2x + 1

213)

A) y = -5x2 + 2x - 5

B) y = 0

C) no oblique asymptote

D) y = -5x - 5

Determine the maximum number of turning points of f. 214) f(x) = x3 ( x3 - 4)(2x - 7) A) 12

B) 6

C) 7

D) 3

214)

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval. 215) f(x) = -2x4 - 7x3 + 2x - 4; [-2, -1] 215) A) f(-2) = 16 and f(-1) = 1; no C) f(-2) = -16 and f(-1) = -1; no

B) f(-2) = 16 and f(-1) = -1; yes D) f(-2) = -16 and f(-1) = 1; yes

Find the indicated intercept(s) of the graph of the function. (x - 9)(2x + 3) 216) x-intercepts of f(x) = x2 + 9x - 9 A) (9, 0), (-3, 0)

B) (9, 0), -

216)

3 ,0 2

C) (-9, 0),

3 ,0 2

D) none

Find a polynomial function f(x) of least possible degree having the graph shown. 217)

A) f(x) = 2(x - 2)2(x + 1) C) f(x) = -2(x - 2)2 (x + 1)

217)

B) f(x) = -2(x + 2)2 (x - 1) D) f(x) = 2(x + 2)2(x - 1)

Identify which of the graphs could be the graph of a polynomial function. 218) f(x) = -4x4 + 4x3 A)

218)

Find the vertical asymptotes of the rational function. x+5 219) h(x) = x2 + 4

219)

A) x = -2, x = 2 C) x = -2, x = 2, x = -5

B) none D) x = -2, x = -5

Determine the maximum number of turning points of f. 220) f(x) = -x2 (x + 7)3 (x2 - 1) A) 5

B) 6

C) 7

D) 2

Give the equation of the horizontal asymptote, if any, of the function. x(x - 1) 221) f(x) = x3 + 49x A) y = 0 C) y = 1

221)

B) no horizontal asymptotes D) x = 0, x = -49

Find the intercepts of the function f(x). 222) f(x) = x3 - 4x2 - x + 4

A) x-intercepts: 1, -1, 4; y-intercept: 4 C) x-intercepts: 1, -1, -4; y-intercept: 4

B) x-intercepts: 1, -1, -4; y-intercept: 4 D) x-intercepts: -1, -1, 4; y-intercept: 4

List the potential rational zeros of the polynomial function. Do not find the zeros. 223) f(x) = 7x5 - 5x2 + 5x - 1 1 A) ± 7, ± 7

220)

1 B) ± 1, ± 7

C) ± 1, ± 7

1 D) ± 1, ± 7, ± 7

222)

223)

Identify which of the graphs could be the graph of a polynomial function. 224) f(x) = x4 - 2x3 - x2 + 2 A)

224)

Use the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. 225) f(x) = 5x4 - 9x3 + 24x2 - 36x + 16 225)

A) -4, -1, 1, B) -4, -1, 1,

4 ; f(x) = (x - 1)(5x + 4)(x + 1)(x + 4) 5

4 ; f(x) = (x - 1)(5x - 4)(x + 1)(x + 4) 5

C) 4,

4 ; f(x) = (x - 4)(5x - 4)(x2 + 1) 5

D) 1,

4 ; f(x) = (x - 1)(5x - 4)(x2 + 4) 5

Use the given zero to find the remaining zeros of the function. 226) f(x) = x5 - 10x4 + 42x3 -124 x2 + 297x - 306 ; zero: 3i A) -2, -3i, -4 - i, -4 + i C) 2, -3i, -4 - i, -4 + i

B) 2, -3i, 4 - i, 4 + i D) -2, -3i, 4 - i, 4 + i

226)

Find the indicated intercept(s) of the graph of the function. x2 - 12 227) y-intercept of f(x) = x2 + 14x - 12 A) 0, 1

227)

B) 0, - 1

C) (0, 12)

Solve the inequality. 228) (a + 5)(a + 4)(a - 7) > 0 A) (-5, -4) or (7, ) C) (- , -4)

D) none

B) (7, ) D) (- , -5) or (-4, 7)

Find a polynomial function f(x) of least possible degree having the graph shown. 229)

B) f(x) =

A) f(x) = (x + 3)(x - 1) C) f(x) =

1 (x + 3)(x - 1)(x - 4) 2

1 (x - 3)(x + 1)(x + 4) 2

D) f(x) = (x + 3)(x - 1)(x - 4)

228)

229)

Identify which of the graphs could be the graph of a polynomial function. 230) f(x) = -x2 (x - 1)(x + 1) A)

Graph the function. x2 + 3x + 2 231) f(x) = (x - 3)2

230)

231)

Use transformations of the graph of y = x 4 or y = x 5 to graph the function. 232) f(x) = -2(x - 3)5 + 3

232)

Use the Remainder Theorem to find the remainder when f(x) is divided by x - c. 233) f(x) = 5x6 - 3x3 + 8; x + 1 A) R = 16

B) R = 8

C) R = 6

D) R = 10

Use the graph to find the vertical asymptotes, if any, of the function. 234)

A) x = -3, x = 3, x = 0 C) x = -3, x = 3, y = 1

B) x = -3, x = 3 D) x = -3, x = 3, x = 0, y = 1

233)

234)

Find the indicated intercept(s) of the graph of the function. x2 - 5x + 3 235) y-intercept of f(x) = x2 + 15x - 3 A) (0, 15)

235)

B) (0, 3)

C) (0, -1)

D) none

Use the graph to determine the domain and range of the function. 236)

A) domain: {x|x -4, x 4} range: {y|y 0} C) domain: all real numbers range: all real numbers

236)

B) domain: {x|x -4, x 4} range: all real numbers D) domain: all real numbers range: {y|y -4, y 4}

Find the vertical asymptotes of the rational function. 9x 237) h(x) = x+8 A) none

237)

B) x = 9

C) x = 8

Use the graph to find the horizontal asymptote, if any, of the function. 238)

A) no horizontal asymptotes C) y = -3, y = 3

B) x = -3, x = 3, y = 0 D) y = 0

D) x = -8

238)

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval. 239) f(x) = -8x4 + 7x2 + 6; [-2, -1] 239) A) f(-2) = 94 and f(-1) = -5; yes C) f(-2) = -94 and f(-1) = -5; no

B) f(-2) = 94 and f(-1) = 6; no D) f(-2) = -94 and f(-1) = 5; yes

Solve the inequality. x + 26 <9 240) x+8 A) - , -

240) 23 or 8, 4

B) -8, -

23 4

D) - , -8 or -

C) - , -8 or 8,

Use transformations of the graph of y = x 4 or y = x 5 to graph the function. 1 241) f(x) = x5 4

23 , 4

241)

List the potential rational zeros of the polynomial function. Do not find the zeros. 242) f(x) = 6x4 + 3x3 - 4x2 + 2 1 1 1 2 A) ± , ± , ± , ± , ± 1, ± 2, ± 3 6 3 2 3

C) ±

242)

1 1 1 B) ± , ± , ± , ± 1, ± 2 6 3 2

1 1 1 2 , ± , ± , ± , ± 1, ± 2 6 3 2 3

D) ±

1 3 , ± , ± 1, ± 2, ± 3, ± 6 2 2

Solve the problem. 243) Economists use what is called a Leffer curve to predict the government revenue for tax rates from 0% to243) 100%. Economists agree that the end points of the curve generate 0 revenue, but disagree on the tax rate that produces the maximum revenue. Suppose an economist produces this rational function 10x(100 - x) R(x) = , where R is revenue in millions at a tax rate of x percent. Use a graphing 75 + x calculator to graph the function. What tax rate produces the maximum revenue? What is the maximum revenue? A) 37.5%; $210 million B) 39.6%; $209 million C) 34.9%; $207 million D) 35.8%; $209 million

Determine the maximum number of turning points of f. 244) f(x) = 2x - x3 A) 2

B) 4

C) 3

D) 1

Find the indicated intercept(s) of the graph of the function. x2 + 8 245) x-intercepts of f(x) = x2 + 7x + 5

245)

A) ( 8, 0), (- 8, 0) C) (5, 0) 246) x-intercepts of f(x) = A) (0, 0), (6, 0)

244)

B) (-8, 0) D) none

x2 + 6x 2 x + 3x - 6

246)

B) (6, 0)

C) (0, 0), (-6, 0)

D) (-6, 0)

Find the vertical asymptotes of the rational function. x+2 247) g(x) = x2 - 9

247)

A) x = -3, x = 3, x = -2 C) x = 9, x = -2

B) x = 0, x = 9 D) x = -3, x = 3

Determine the maximum number of turning points of f. 248) f(x) = x7 + 5x8 A) 1

B) 7

C) 5

D) 8

Find all zeros of the function and write the polynomial as a product of linear factors. 249) f(x) = x4 + 29x2 + 100

B) f(x) = (x + 2 + 5i)2 (x + 2 - 5i)2

A) f(x) = (x + 2i)(x - 2i)(x + 5i)(x - 5i) C) f(x) = (x + 2i)2 (x + 5i)2

249)

D) f(x) = (x + i)(x - i)(x + 10i)(x - 10i)

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. 250) f(x) = 5x + 2x3 A) Yes; degree 5

248)

B) Yes; degree 2

C) Yes; degree 3

Graph the function. x2 + 3x - 4 251) f(x) = x2 + 5

D) Yes; degree 1

250)

251)

Find the vertical asymptotes of the rational function. -2x(x + 2) 252) f(x) = 5x2 - 4x - 9 A) x =

9 , x = -1 5

B) x = -

252)

9 ,x=1 5

C) x = -

Find the x- and y-intercepts of f. 253) f(x) = (x - 1)(x - 2) A) x-intercepts: 1, 2; y-intercept: 2 C) x-intercepts: -1, -2; y-intercept: 2

5 ,x=1 9

D) x =

5 , x = -1 9

B) x-intercepts: -1, -2; y-intercept: -3 D) x-intercepts: 1, 2; y-intercept: -3

Graph the function using transformations. 1 +1 254) f(x) = x2

253)

254)

Solve the equation in the real number system. 255) x4 - 8x3 + 16x2 + 8x - 17 = 0 A) {-1, 4}

B) {-1, 1}

C) {-4, 4}

D) {-4, 1}

255)

Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f. 256) Degree 6; zeros: -5, 4, 5 - 5i, -4 + i 256) A) -5 + 5i, 4 - i B) 5, 5 + 5i, -4 - i C) 5, 5 + 5i D) 5 + 5i, -4 - i Solve the problem. 257) The revenue achieved by selling x graphing calculators is figured to be x(21 - 0.5x) dollars. The cost of each calculator is $13. How many graphing calculators must be sold to make a profit (revenue cost) of at least $24.00? A) {x 6 < x < 10} B) {x 6 < x < 14} C) {x 5 < x < 11} D) {x 4 < x < 12} Find the domain of the rational function. 2x2 - 4 . 258) f(x) = 3x2 + 6x - 45

257)

258)

A) {x|x -3, x 5} C) {x|x 3, x -5}

B) {x|x 3, x -3, x -5} D) all real numbers

Find the indicated intercept(s) of the graph of the function. (x - 5)2 259) y-intercept of f(x) = (x + 11)3 A) 0,

25 1331

Solve the inequality. (x + 12)(x - 2) 260) x-1

259) C) 0, -

B) (0, 5)

25 1331

D) 0, -

5 11

260)

A) [-12, 1) or [2, ) C) (- , -12] or (1, 2]

B) [-12, 1) or (1, 2] D) (- , -12] or [2, )

Determine the maximum number of turning points of f. 261) f(x) = (x - 6)(x - 7)(x - 4)(x + 4) A) 4 B) 3

C) 1

Use transformations of the graph of y = x 4 or y = x 5 to graph the function. 262) f(x) = (x - 5)5

D) 0

261)

262)

Use the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. 263) f(x) = x4 - 5x2 - 36 263)

A) -2, 2; f(x) = (x - 2)(x + 2)(x2 + 9) B) -3, 3; f(x) = (x - 3)(x + 3)(x2 + 4)

C) 3; f(x) = (x - 3)2 (x2 + 4) D) -3, -2, 3, 2; f(x) = (x - 3)(x + 3)(x - 2)(x + 2) Solve the inequality. x-2 <1 264) x+7

264)

A) (- , -7) C) (-7, 2)

B) (- , -7) or (2, ) D) (-7, )

Use the x-intercepts to find the intervals on which the graph of f is above and below the x-axis. 265) f(x) = (x - 3)2 (x + 5)2 A) above the x-axis: (- , -5), (-5, 3), (3, ) below the x-axis: no intervals C) above the x-axis: (- , -5), (3, ) below the x-axis: (-5, 3)

Solve the inequality. 266) x(x + 3)(5 - x) 0 A) [0, 5]

B) above the x-axis: (-5, 3) below the x-axis: (- , -5), (3, ) D) above the x-axis: no intervals below the x-axis: (- , -5), (-5, 3), (3, )

B) [-3, 0] or [5, )

C) [-3, 5]

Find the vertical asymptotes of the rational function. x(x - 1) 267) f(x) = 49x2 + 28x + 3

D) (- , -3] or [0, 5]

265)

266)

267)

A) x = -

1 3 ,x=49 49

B) x =

C) x = -

3 6 ,x= 49 49

D) x = -

1 3 ,x= 7 7 1 3 ,x=7 7

Find a polynomial function f(x) of least possible degree having the graph shown. 268)

268)

B) f(x) = 6(x + 1)2(x - 1)2

A) f(x) = -6(x + 1)(x - 1) C) f(x) = -6(x + 1)2 (x - 1)2

D) f(x) = 6(x + 1)(x - 1)

Find the vertical asymptotes of the rational function. x(x - 1) 269) f(x) = x3 + 4x

269)

A) none C) x = 0, x = -2, x = 2

B) x = -2, x = 2 D) x = 0, x = -4

Determine the real zeros of the polynomial and their multiplicities. Then decide whether the graph touches or crosses the x-axis at each zero. 270) f(x) = 5(x + 2)(x - 7)4 270)

A) 2, multiplicity 1, touches x-axis; -7, multiplicity 4, crosses x-axis B) -2, multiplicity 1, crosses x-axis; 7, multiplicity 4, touches x-axis C) -2, multiplicity 1, touches x-axis; 7, multiplicity 4, crosses x-axis D) 2, multiplicity 1, crosses x-axis; -7, multiplicity 4, touches x-axis

Solve the inequality. 271) (x + 2)(x - 5) A) [5, ) C) [-2, 5]

271)

B) (- , -2] D) (- , -2] or [5, )

Determine the maximum number of turning points of f. 1 272) g(x) = x + 4 5 A) 3

272)

B) 2

C) 0

D) 1

Give the equation of the horizontal asymptote, if any, of the function. 36x5 - 6 273) f(x) = x - x3 A) y = 0 C) y = -36

B) no horizontal asymptotes D) y = -1, y = 1

273)

Solve the inequality. 274) x2 + 9x 0

A) [-9, 0]

B) [0, 9]

C) (- , -9] or [0, )

D) (- , 0] or [9, )

Use the Factor Theorem to determine whether x - c is a factor of f(x). 275) f(x) = 5x4 + 9x3 - 2x2 + x - 2; x + 2 A) Yes

274)

275)

B) No

Use the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. 276) f(x) = 3x3 - 14x2 + 3x + 20 276) 5 , 4; f(x) = (3x - 5)(x - 4)(x + 1) 3

B) -1,

3 , -4; f(x) = (3x - 5)(x - 4)(x + 1) 5

3 , -4; f(x) = (3x - 5)(x - 1)(x + 4) 5

D) -4,

5 , 1; f(x) = (3x - 5)(x - 1)(x + 4) 3

A) -1, C) 1,

Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1. 277) Zeros: -3, -1, 2; degree 3 A) f(x) = x3 + 2x2 + 5x + 6 B) f(x) = x3 - 2x2 - 5x + 6 C) f(x) = x3 + 2x2 - 5x - 6

277)

D) f(x) = x3 - 2x2 + 5x - 6

Solve the inequality. (x - 5)2 >0 278) x2 - 36 A) (-6, 5) or (5, 6)

278) B) (- , -6) or (5, 6)

C) (- , -6) or (6, )

D) (-6, 5) or (6, )

Identify which of the graphs could be the graph of a polynomial function. 279) f(x) = 3x2 - x3 A)

279)

Give the equation of the horizontal asymptote, if any, of the function. x2 - 7 280) f(x) = 49x - x4 A) y = -1 C) y = 0

280)

B) y = -7, y = 7 D) no horizontal asymptotes

Find the domain of the rational function. x+4 281) f(x) = x2 - 25

281)

A) {x|x -5, x 5} C) {x|x 0, x 25}

B) all real numbers D) {x|x -5, x 5, x -4}

Find the indicated intercept(s) of the graph of the function. 2x 282) x-intercepts of f(x) = 2 x - 49 A) (49, 0)

282)

B) (0, 0)

C) (2, 0)

D) (-7, 0), (7, 0)

Solve the equation in the real number system. 283) 2x3 - 9x2 + 7x + 6 = 0 3 , -1, 2 A) 2

1 B) - , 2, 3 2

3 C) - , -1, -2 2

Find the intercepts of the function f(x). 284) f(x) = 3x3 - x2 - 21x + 7

1 , 2, -3 D) 2

283)

284)

A) x-intercepts: -3, 7, - 7; y-intercept: 7 1 B) x-intercepts: , 7, - 7; y-intercept: 7 3 C) x-intercepts: 3,

7, - 7; y-intercept: 7 1 D) x-intercepts: - , 7, - 7; y-intercept: 7 3

Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f. 285) Degree 5; zeros: 7, 4 + 5i, -7i 285) A) -4 + 5i, 7i B) 4 - 5i, 7i C) -7, 4 - 5i, 7i D) -4 - 5i, 7i Graph the function using transformations. -2 286) f(x) = x-3

286)

Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f. 287) Degree 6; zeros: 1, 1 + i, -4 - i, 0 287) A) -1, 1 - i, -4 + i B) -1 - i, 4 + i C) 1 - i, -4 + i D) -1 + i, 4 - i Determine the maximum number of turning points of f. 288) f(x) = (2x + 1)2( x2 - 5)(x - 3) A) 4

B) 2

C) 5

D) 10

288)

Find the x- and y-intercepts of f.

289) f(x) = (x + 1)(x - 7)(x - 1)2 A) x-intercepts: -1, 1, -7; y-intercept: 7 C) x-intercepts: -1, 1, 7; y-intercept: 7

Graph the function. 290) f(x) = x2 +

B) x-intercepts: -1, 1, -7; y-intercept: -7 D) x-intercepts: -1, 1, 7; y-intercept: -7

9 x

289)

290)

Solve the problem. 291) Economists use what is called a Leffer curve to predict the government revenue for tax rates from 0% to291) 100%. Economists agree that the end points of the curve generate 0 revenue, but disagree on the tax rate that produces the maximum revenue. Suppose an economist produces this rational function 10x(100 - x) R(x) = , where R is revenue in millions at a tax rate of x percent. Use a graphing 25 + x calculator to graph the function. What tax rate produces the maximum revenue? What is the maximum revenue? A) 30.9%; $382 million B) 38.4%; $383 million C) 28.8%; $272 million D) 27.0%; $379 million

Find the domain of the rational function. x(x - 1) 292) f(x) = 9x2 + 36x + 20 A) x x C) x x

292)

2 10 ,9 9

2 10 , 3 3

Find the intercepts of the function f(x). 293) f(x) = 2x5 (x + 7)5

A) x-intercepts: 0, 7; y-intercept: 0 C) x-intercepts: 0, 7; y-intercept: 2

B) x x -

10 10 , 3 3

D) x x -

2 10 ,3 3

B) x-intercepts: 0, -7; y-intercept: 2 D) x-intercepts: 0, -7; y-intercept: 0 68

293)

Find the indicated intercept(s) of the graph of the function. 1 294) x-intercepts of f(x) = x + x A) (-1, 0), (1, 0)

294)

B) (-1, 0)

C) (1, 0)

D) none

Find the domain of the rational function. 4x2 295) f(x) = (x + 7)(x - 7)

295)

A) {x|x 7, -7} C) {x|x -7, 7, -4}

B) {x|x -7, 7} D) all real numbers

Use the graph to determine the domain and range of the function. 296)

A) domain: {x|x -4 or x 4} range: {y|y 0} C) domain: {x|x 0} range: {y|y -4 or y 4}

296)

B) domain: all real numbers range: {y|y -4 or y 4} D) domain: {x|x 0} range: all real numbers

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x -intercept. 1 2 (x - 9)3 297) f(x) = x + 297) 4

1 , multiplicity 2, crosses x-axis; -9, multiplicity 3, touches x-axis 4

1 , multiplicity 2, touches x-axis; -9, multiplicity 3, crosses x-axis 4

C) -

1 , multiplicity 2, touches x-axis; 9, multiplicity 3, crosses x-axis 4

D) -

1 , multiplicity 2, crosses x-axis; 9, multiplicity 3, touches x-axis 4

Use transformations of the graph of y = x 4 or y = x 5 to graph the function.

298) f(x) = -4x4

298)

Use the graph to find the oblique asymptote, if any, of the function. 299)

A) y = 1 C) no oblique asymptote

299)

B) y = x + 1 D) y = x

Use transformations of the graph of y = x 4 or y = x 5 to graph the function. 300) f(x) = 3 - (x + 3)4

300)

Solve the inequality. x-5 <0 301) x+9

301)

A) (- , -9) or (5, ) C) (-9, 5)

B) (5, ) D) (- , -9)

Use the graph to determine the domain and range of the function. 302)

A) domain: all real numbers range: all real numbers C) domain: all real numbers range: {y|y 0}

B) domain: {x|x 0} range: {y|y 0} D) domain: {x|x 0} range: all real numbers

Use the given zero to find the remaining zeros of the function. 303) f(x) = x3 + 4x2 - 10x + 12; zero: 1 + i A) 1 - i, 6i

302)

B) -6, 6

C) 1 - i, -6

303)

D) 1 - i, 6

Find the domain of the rational function. x 304) g(x) = 3 x - 27 A) x x

-3

B) x x

304) 9

C) x x

-3, 3

D) x x

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. 305) f(x) = x4/3 - x3 + 5 A) No; x is raised to non-integer 4/3 power C) Yes; degree 4

B) Yes; degree 3 D) Yes; degree 4/3

Graph the function using transformations. 1 306) f(x) = 3 (x + 5)2

305)

306)

Graph the function.

307) f(x) =

x2 + x - 2 x2 - x - 6

307)

Use the Factor Theorem to determine whether x - c is a factor of f(x). 308) f(x) = x3 + 4x2 - 10x + 12; x - 6 A) Yes

B) No

308)

Find the intercepts of the function f(x). 309) f(x) = 5x - x3 A) x-intercepts: 0, C) x-intercepts: 0,

309)

5, - 5; y-intercept: 5 5, - 5; y-intercept: 0

B) x-intercepts: 0, -5; y-intercept: 0 D) x-intercepts: 0, -5; y-intercept: 5

Use the Factor Theorem to determine whether x - c is a factor of f(x). 310) f(x) = 7x4 + 20x3 - 3x2 + x + 3; x + 3

310)

Use transformations of the graph of y = x 4 or y = x 5 to graph the function. 311) f(x) = (x - 2)4

311)

A) Yes

B) No

Find the indicated intercept(s) of the graph of the function. 6 312) y-intercept of f(x) = 2 x - 3x - 23 A) 0,

6 23

312) C) 0, -

B) (0, 6)

6 23

D) none

Give the equation of the horizontal asymptote, if any, of the function. 9x - 4 313) h(x) = x-6 A) y = 0 C) y = 6

B) y = 9 D) no horizontal asymptotes

Use the given zero to find the remaining zeros of the function. 314) f(x) = x3 + 6x2 + 21x + 26; zero: -2 + 3i A) -2 - 3i, -2

Solve the inequality. x2 (x - 12)(x + 1) 315) (x - 5)(x + 8)

313)

B) -2 - 3i, 2

C) 3 - 2i, -2

D) 3 - 2i, 2

315)

A) (- , -8) or [12, ) C) (- , -8) or [-1, 0) or (0, 5) or [12, )

B) (-8, -1] or (5, 12] D) (- , -8) or [-1, 5) or [12, )

Find the intercepts of the function f(x). 316) f(x) = x2 (x - 1)(x - 3)

A) x-intercepts: 0, -1, -3; y-intercept: 3 C) x-intercepts: 0, 1, 3; y-intercept: 0

B) x-intercepts: 0, 1, 3; y-intercept: 3 D) x-intercepts: 0, -1, -3; y-intercept: 0

Find the domain of the rational function. -3x2 317) R(x) = 2 x + 3x - 10 A) {x|x 5, 2}

316)

317)

B) {x|x -5, 2}

C) {x|x - 10, 1}

Find the power function that the graph of f resembles for large values of |x|. 318) f(x) = (x + 9)2 A) y = x2

314)

B) y = x9

C) y = x18

D) {x|x 5, -2}

D) y = x81

318)

Use the graph to find the oblique asymptote, if any, of the function. 319)

A) y = x + 3 C) no oblique asymptote

319)

B) y = 4 D) y = 4x + 3

Graph the function using transformations. 4 320) f(x) = (2 + x)2

320)

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. 321) f(x) = 12 A) Yes; degree 0 B) No; it contains no variables C) No; it is a constant D) Yes; degree 1 Determine the maximum number of turning points of f. 322) f(x) = (x - 6)(x - 1)(6x - 4) A) 6 B) 2

C) 0

Use transformations of the graph of y = x 4 or y = x 5 to graph the function. 323) f(x) = 2 - (x + 4)5

D) 3

321)

322)

323)

Solve the problem.

324) The polyniomial function f(x) = 6x3 + 19x2 + 8x - 5 has exactly one positive zero. Use the Intermediate Value Theorem to approximate the zero correct to 2 decimal places. A) 0.10 B) 0.50 C) 0.66 D) 0.33

Determine the maximum number of turning points of f. 325) f(x) = - x2 - 4x + 3 A) 1

B) 2

C) 3

Graph the function. x 326) f(x) = 2 x - 25

D) 0

324)

325)

326)

Give the equation of the oblique asymptote, if any, of the function. x2 - 9x + 9 327) f(x) = x+8 A) y = x - 17 C) y = x + 18 328) f(x) =

327)

B) x = y + 9 D) no oblique asymptote

2x3 + 11x2 + 5x - 1 . x2 + 6x + 5

A) y = 2x - 1

328) B) y = 2x + 1

C) y = 2x

Use transformations of the graph of y = x 4 or y = x 5 to graph the function. 329) f(x) = -5x5

D) y = 0

329)

Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1. 330) Zeros: -1, 1, - 4; degree 3 A) f(x) = x3 - 4x2 + x - 4 B) f(x) = x3 - 4x2 - x + 4 C) f(x) = x3 + 4x2 + x + 4

330)

D) f(x) = x3 + 4x2 - x - 4

Solve the problem. 331) The concentration of a drug in the bloodstream, measured in milligrams per liter, can be modeled 12t + 4 by the function, C(t) = , where t is the number of minutes after injection of the drug. When 3t2 + 2

331)

will the drug be at its highest concentration? Approximate your answer rounded to two decimal places. A) t = 3.65 minutes after the injection is given B) t = 4 minutes after the injection is given C) at the time of injection D) t = 0.55 minutes after the injection is given

Find the domain of the rational function. 8x 332) f(x) = x+1

332)

A) {x|x 0} C) {x|x -1}

B) all real numbers D) {x|x 1}

Give the equation of the horizontal asymptote, if any, of the function. x2 + 9x - 7 333) g(x) = x-7 A) y = 1 C) y = 0

333)

B) no horizontal asymptote D) y = 7

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x -intercept. 334) f(x) = 3(x + 5)(x + 6)3 334)

A) -5, multiplicity 1, crosses x-axis; -6, multiplicity 3, crosses x-axis B) 5, multiplicity 1, crosses x-axis; 6, multiplicity 3, crosses x-axis C) 5, multiplicity 1, touches x-axis; 6, multiplicity 3 D) -5, multiplicity 1, touches x-axis; -6, multiplicity 3

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. 8 - x3 335) f(x) = 3 A) No; x is a negative term C) Yes; degree 3

B) Yes; degree 1 D) No; it is a ratio

Find the indicated intercept(s) of the graph of the function. x3 - 2 336) y-intercept of f(x) = x2 - 2 A) (0, 11)

336)

B) (0, 1)

C) (0, -2)

D) none

Find a polynomial function f(x) of least possible degree having the graph shown. 337)

A) f(x) = (x + 2)(x - 1)3

337)

B) f(x) = -4(x + 2)(x - 1) D) f(x) = 4(x + 2)(x - 1)3

C) f(x) = -4(x + 2)(x - 1)3

Find the indicated intercept(s) of the graph of the function. x2 - 64 338) x-intercepts of f(x) = 5 + x4 A) (5, 0)

335)

338)

B) (64, 0)

C) (-8, 0), (8, 0) 82

D) none

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. x5 - 1 339) f(x) = x6 A) Yes; degree 6 C) Yes; degree -6 Solve the inequality. 340) x3 - 2x2 - 3x > 0

A) (-1, 0) or (3, )

B) No; it is a ratio of polynomials D) Yes; degree 5

B) (-3, 0) or (1, )

C) (- ,-1) or (0, 3)

Identify which of the graphs could be the graph of a polynomial function. 1 1 341) f(x) = - x4 3 3 A)

List the potential rational zeros of the polynomial function. Do not find the zeros. 342) f(x) = 5x4 - x2 + 2 1 1 A) ± , ± , ± 1, ± 2, ± 5 5 2

C) ±

339)

1 5 B) ± , ± , ± 1, ± 5 2 2

1 2 , ± , ± 1, ± 2, ± 5 5 5

D) ±

1 2 , ± , ± 1, ± 2 5 5

D) (-1, )

340)

341)

342)

Form a polynomial f(x) with real coefficients having the given degree and zeros. 343) Degree: 3; zeros: -2 and 3 + i. A) f(x) = x3 - 8x2 + 2x + 20 B) f(x) = x3 - 4x2 - 10x + 20 C) f(x) = x3 - 6x2 - 10x + 20

343)

D) f(x) = x3 - 4x2 - 2x + 20

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x -intercept. 344) f(x) = 4(x2 + 1)(x + 4)2 344)

A) -1, multiplicity 1, touches x-axis; -4, multiplicity 2, crosses x-axis B) -4, multiplicity 2, touches x-axis C) -1, multiplicity 1, crosses x-axis; -4, multiplicity 2, touches x-axis D) -4, multiplicity 2, crosses x-axis

Give the equation of the horizontal asymptote, if any, of the function. x+2 345) h(x) = x2 - 1 A) y = 1 C) no horizontal asymptotes

345)

B) y = -1, y = 1 D) y = 0

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. 2 346) f(x) = 7x4 + x3 5 A) Yes; degree 7

346)

B) Yes; degree 4 D) No; x3 has a non-integer coefficient

C) Yes; degree 8 Find the vertical asymptotes of the rational function. -3x2 347) R(x) = x2 + 9x - 22

347)

A) x = 11, x = -2 C) x = -11, x = 2, x = -3

B) x = -11, x = 2 D) x = - 22

Give the equation of the horizontal asymptote, if any, of the function. 4x2 + 3 348) f(x) = 4x2 - 3 A) y = 4 C) y = 1

348)

B) y = 3 D) no horizontal asymptotes

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. 2 1 349) f(x) = - x 3 4 A) No; x has a fractional coefficient C) Yes; degree 1

B) Yes; degree 0 D) Yes; degree 4

349)

Form a polynomial f(x) with real coefficients having the given degree and zeros. 350) Degree: 5; zeros: 2, -3i, and 4 - i A) f(x) = x5 - 10x4 - 42x3 -124 x2 + 297x + 306

350)

B) f(x) = x5 - 10x4 + 42x3 -124 x2 + 297x - 306 C) f(x) = x5 - 10x4 + 26x3 -124 x2 - 72x - 306

D) f(x) = x5 - 10x4 + 26x3 -124 x2 + 72x + 306

Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f. 351) Degree 3; zeros: -7, 7 - 5i 351) A) 7, 7 + 5i B) 7, -7 + 5i C) -7 + 5i D) 7 + 5i Find all zeros of the function and write the polynomial as a product of linear factors. 352) f(x) = x4 + 5x3 + 8x2 + 20x + 16

352)

B) f(x) = (x - i 4)(x + i 4)(x - 2)(x +2) D) f(x) = (x - 1)(x - 4)(x - 2i)(x + 2i)

A) f(x) = (x - 1)(x + 4)(x - 2)(x + 2) C) f(x) = (x + 1)(x + 4)(x - 2i)(x + 2i) Find the vertical asymptotes of the rational function. x 353) g(x) = 3 x - 125 A) x = -5, x = 5

353)

B) x = 25

C) x = 5

D) x = -5

Give the equation of the horizontal asymptote, if any, of the function. 3x3 - 8x - 3 354) h(x) = 6x + 6 A) no horizontal asymptote C) y =

354)

B) y = 0

1 2

D) y = 3

Solve the problem. 355) A closed box with a square base has to have a volume of 17,000 cubic inches. Find a function for the surface area of the box. 68,000 68,000 A) S(x) = 2x2 + B) S(x) = x2 + x x C) S(x) = 2x2 +

17,000 x

D) S(x) = 2x2 +

355)

102,000 x

Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1. 356) Zeros: -4, multiplicity 2; 3, multiplicity 1; degree 3 A) x3 + 8x2 - 8x - 48 B) x3 - 5x2 - 24x + 48

356)

Form a polynomial f(x) with real coefficients having the given degree and zeros. 357) Degree 3: zeros: 1 + i and -10 A) f(x) = x3 + x2 - 18x + 20 B) f(x) = x3 -10x2 - 18x - 12

357)

C) x3 + 5x2 - 8x - 48

D) x3 - 5x2 - 8x + 48

C) f(x) = x3 + 8x2 + 20x - 18

D) f(x) = x3 + 8x2 - 18x + 20

Find the x- and y-intercepts of f. 358) f(x) = x2 (x - 6)(x - 3)

A) x-intercepts: 0, -6, -3; y-intercept: 0 C) x-intercepts: 0, -6, -3; y-intercept: 18

Solve the inequality. 359) x2 - 2x 0

A) (- , -2] or [0, )

B) x-intercepts: 0, 6, 3; y-intercept: 0 D) x-intercepts: 0, 6, 3; y-intercept: 18

B) (- , 0] or [2, )

Determine the maximum number of turning points of f. 360) f(x) = 6x8 - 4x7 - 9x - 21 A) 6

B) 7

Use the given zero to find the remaining zeros of the function. 361) f(x) = x4 - 12x2 - 64; zero: -2i A) 2i, 8, -8

B) 2i, 4, -4

C) [-2, 0]

D) [0, 2]

C) 0

D) 8

C) 2i, 4i, -4i

D) 2i, 8i, -8i

Find the domain of the rational function. x 362) g(x) = 3 x - 125 A) {x|x -5, 5}

358)

359)

360)

361)

362)

B) {x|x -5}

C) {x|x 25}

D) {x|x 5}

Identify which of the graphs could be the graph of a polynomial function. 363) f(x) = 5x - x3 - x5 A)

Use transformations of the graph of y = x 4 or y = x 5 to graph the function. 364) f(x) = (x - 3)4 + 3

363)

364)

Solve the inequality. 4x 2x 365) 7-x A) [0, 5] or [7, )

365) B) [7, )

C) (- , 5] or [7, )

D) (- , 0] or [5, 7)

Use the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. 366) f(x) = 3x4 - 30x3 + 76x2 - 10x + 25 366)

A) no real roots; f(x) = (x2 + 25)(3x2 + 1) C) -5, 5; f(x) = (x - 5)(x + 5)(3x2 + 1)

B) -5, multiplicity 2; f(x) = (x + 5)2 (3x2 + 1) D) 5, multiplicity 2; f(x) = (x - 5)2 (3x2 + 1)

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x -intercept. 1 367) f(x) = x2(x2 - 5) 367) 3

A) 0, multiplicity 2, touches x-axis; 5, multiplicity 1, crosses x-axis; - 5, multiplicity 1, crosses x-axis C) 0, multiplicity 2, touches x-axis

B) 0, multiplicity 2, crosses x-axis

D) 0, multiplicity 2, crosses x-axis; 5, multiplicity 1, touches x-axis; - 5, multiplicity 1, touches x-axis

Use the graph to find the vertical asymptotes, if any, of the function. 368)

A) x = 0, y = 0

B) x = 0

368)

C) y = -8, y = 8

D) none

Find the vertical asymptotes of the rational function. -x2 + 16 369) f(x) = x2 + 5x + 4 A) x = -1

369)

B) x = 1, x = -4

C) x = -1, x = 4

Find the power function that the graph of f resembles for large values of |x|. 370) f(x) = (x + 11)3 (x + 7)4 A) y = x4

B) y = x3

C) y = x12

D) y = x7

Find the domain of the rational function. x+6 371) h(x) = x2 - 4

370)

371)

A) {x|x 0, 4} C) {x|x -2, 2}

B) {x|x -2, 2, -6} D) all real numbers

Solve the inequality. 372) 3x2 + 17x < 6

372)

1 B) -6 , 3

A) (-6, ) C) - ,

D) x = -1, x = -4

1 3

D) (- , -6) or

Use the Factor Theorem to determine whether x - c is a factor of f(x). 11 373) f(x) = 27x3 + 15x2 - 76x - 66; x 9 A) Yes

1 , 3

373)

B) No

Give the equation of the oblique asymptote, if any, of the function. x+7 374) f(x) = x2 - 36 A) no oblique asymptote C) y = 0

B) y = x + 7 D) y = 7x 89

374)

Solve the inequality. 375) x3 64

A) (- , -4] or [4, )

B) [-4, 4]

C) (- , 4]

Find the power function that the graph of f resembles for large values of |x|. 376) f(x) = (x + 4)3 A) y = x64

B) y = x4

C) y = x12

Use transformations of the graph of y = x 4 or y = x 5 to graph the function. 1 377) f(x) = x4 4

D) [4, )

D) y = x3

375)

376)

377)

Find the domain of the rational function. -3x2 378) R(x) = x2 + 2x - 15 A) x x 5, 3

378)

B) x x - 15, 1

C) x x -5, 3

D) x x 5, -3

Use the x-intercepts to find the intervals on which the graph of f is above and below the x-axis. 379) f(x) = (x - 5)3 A) above the x-axis: no intervals below the x-axis: (- , 5), (5, ) C) above the x-axis: (5, ) below the x-axis: (- , 5)

B) above the x-axis: (- , 5), (5, ) below the x-axis: no intervals D) above the x-axis: (- , 5) below the x-axis: (5, )

Graph the function using transformations. 1 +1 380) f(x) = x-2

379)

380)

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. 381) 7(x - 1)12(x + 1)8 A) Yes; degree 12

B) Yes; degree 7

C) Yes; degree 20

D) Yes; degree 84

Give the equation of the oblique asymptote, if any, of the function. 2x3 + 11x2 + 5x - 1 382) f(x) = x2 + 6x + 5 A) y = 2x - 1

B) y = 2x

C) y = 0

381)

382) D) y = 2x + 1

Solve the problem. 383) Economists use what is called a Leffer curve to predict the government revenue for tax rates from 0% to383) 100%. Economists agree that the end points of the curve generate 0 revenue, but disagree on the tax rate that produces the maximum revenue. Suppose an economist produces this rational function 10x(100 - x) R(x) = , where R is revenue in millions at a tax rate of x percent. Use a graphing 15 + x calculator to graph the function. What tax rate produces the maximum revenue? What is the maximum revenue? A) 31.4%; $464 million B) 26.5%; $469 million C) 28.1%; $470 million D) 29.7%; $467 million

Use the graph to find the vertical asymptotes, if any, of the function. 384)

A) x = 2

B) none

C) x = 2, x = 0 92

384)

D) y = 2

Answer Key Testname: CHAPTER 5 1) B 2) A 3) C 4) D 5) B 6) C 7) D 8) -0.38

9) (a) For large values of |x|, the graph of f(x) will resemble the graph of y = 8x5 . 3 (b) y-intercept: (0, 0), x-intercepts: (-3, 0), (- , 0), and (0, 0) 2 3 (c) The graph of f crosses the x-axis at each of the intercepts (-3, 0), (- , 0), and (0, 0). 2 (e) Local maximum at (-2.53, 62.72); Local minimum at (-1.07, -8.13) (f)

(g) Domain of f: all real numbers; range of f: all real numbers (h) f is increasing on ( , -2.53), (-1.07, 0), and (0, ); f is decreasing on (-2.53, -1.07) 10) a)

b) To remain focused, the desired distance between the film and the projector lens decreases and approaches 5 centimeters as the distance between the movie screen and the projector lens increases.

Answer Key Testname: CHAPTER 5 11) (a) For large values of |x|, the graph of f(x) will resemble the graph of y = x3 . (c) y-intercept: (0, 2.03136), x-intercepts: (-1.84, 0), (0.6, 0), and (1.84, 0) (d) Local maximum at (-0.88, 3.86); Local minimum at (1.28, -1.19) (e)

(f) domain of f: all real numbers; range of f: all real numbers (g) f is increasing on ( , -0.88) and (1.28, ); f is decreasing on (-0.88, 1.28) 12) a) g(-86) 9.8211 m/sec2

b) g(0) 9.8208 m/sec2 13) vertical asymptote: s2 = 0.3; horizontal asymptote: s1 = 0.3

Answer Key Testname: CHAPTER 5 14) (a) For large values of |x|, the graph of f(x) will resemble the graph of y = x3 . (c) y-intercept: (0, 3.0912), x-intercept: (-1.87, 0) (d) Local maximum at (-0.80, 4.39); Local minimum at (1.07, 1.09) (e)

(f) domain of f: all real numbers; range of f: all real numbers (g) f is increasing on (- , -0.80) and (1.07, ); f is decreasing on (-0.80, 1.07) 15) a) y = -1.503x3 + 16.405x2 - 12.028x + 653.060

b) $670.28

16) (a) For large values of |x|, the graph of f(x) will resemble the graph of y = x5 . (b) y-intercept: (0, 0), x-intercepts: (-4, 0), (-2, 0), (0, 0), and (2, 0) (c) The graph of f crosses the x-axis at (-4, 0), (-2, 0), and (2, 0) and touches the x-axis at (0, 0). (e) Local maxima at (-3.35, 52.69) and (0,0); Local minima at (-1.31, -10.54) and (1.46, -21.75) (f)

(g) Domain of f: all real numbers; range of f: all real numbers (h) f is increasing on (- , -3.35), (-1.31, 0), and (1.46, ); f is decreasing on (-3.35, -1.31) and (0, 1.46)

Answer Key Testname: CHAPTER 5 17) (a) For large values of |x|, the graph of f(x) will resemble the graph of y = x3 . (b) y-intercept: (0, 18), x-intercepts: (3, 0) and (-2, 0) (c) The graph of f crosses the x-axis at (-2, 0) and touches the x-axis at (3, 0). (e) Local minimum at (3, 0); Local maximum at (-0.33, 18.52) (f)

(g) Domain of f: all real numbers; range of f: all real numbers (h) f is increasing on (- , -0.33) and (3, ); f is decreasing on (18.52, 3) 18) y = 0.03x 3 - 0.34x 2 + 1.31x + 0.17

19) (a) For large values of |x|, the graph of f(x) will resemble the graph of y = -3x4 . (c) y-intercept: (0, 4), x-intercepts: (-1.03, 0) and (1.20, 0) (d) Local maximum at (-0.43, 4.79); no local minima (e)

(f) domain of f: all real numbers; range of f: , 4.79 (g) f is increasing on ( , -0.43); f is decreasing on (-0.43, ) 20) a) 1.07°/hr; b) -0.33°/hr; c) 68.8°F 21) horizontal asymptote: r = 0; vertical asymptote: t = 0

Answer Key Testname: CHAPTER 5 22) (a) For large values of |x|, the graph of f(x) will resemble the graph of y = -x3 . (b) y-intercept: (0, 0), x-intercepts: (-4, 0), (0, 0), and (4, 0) (c) The graph of f crosses the x-axis at each of the intercepts (-4, 0), (0 ,0), and (4, 0). (e) Local maximum at (2.31, 24.63); Local minimum at (-2.31, -24.63) (f)

(g) Domain of f: all real numbers; range of f: all real numbers (h) f is increasing on (-2.31, 2.31); f is decreasing on ( , -2.31) and (2.31, )

23) (a) For large values of |x|, the graph of f(x) will resemble the graph of y = -x4 . (b) y-intercept: (0, 0), x-intercepts: (-3, 0), (0, 0), and (1, 0) (c) The graph of f crosses the x-axis at (1, 0) and (-3, 0) and touches the x-axis at (0, 0). (e) Local maxima at (-2.19, 12.39) and (0.69, 0.55); Local minimum at (0, 0) (f)

(g) Domain of f: all real numbers; range of f: (- , 12.39] (h) f is increasing on (- , -2.19) and (0, 0.69); f is decreasing on (-2.19, 0) and (0.69, )

Answer Key Testname: CHAPTER 5 24) (a) For large values of |x|, the graph of f(x) will resemble the graph of y = x3 . (c) y-intercept: (0, 2.08), x-intercepts: (-3.25, 0) and (0.8, 0) (d) Local maximum at (-1.90, 9.84); Local minimum at (0.8,0) (e)

(f) domain of f: all real numbers; range of f: all real numbers (g) f is increasing on ( , -1.90) and (0.8, ); f is decreasing on (-1.90, 0.8) 25) -2.62 26) a) y = 0 b) t = 7 21,000 , x > 0, where x equals the width of the box. 27) a) Surface area equals A(x) = 4x2 + x

b) 28) a) b) c)

width 13.8 in, length 27.6 in, height 18.4 in P(0) = 15 insects P(120) 608 insects 1,350

Answer Key Testname: CHAPTER 5 29) (a) For large values of |x|, the graph of f(x) will resemble the graph of y = x3 . (b) y-intercept: (0, 6), x-intercepts: (-2, 0), (1, 0), and (3, 0) (c) The graph of f crosses the x-axis at each of the intercepts (-2, 0), (1, 0), and (3, 0) (e) Local maximum at (-0.79, 8.21); Local minimum at (2.12, -4.06) (f)

(g) Domain of f: all real numbers; range of f: all real numbers (h) f is increasing on (- , -0.79) and (2.12, ); f is decreasing on (-0.79, 2.12)

30) (a) For large values of |x|, the graph of f(x) will resemble the graph of y = -2x4 . (b) y-intercept: (0, 6), x-intercepts: (-1, 0) and (3, 0) (c) The graph of f crosses the x-axis at (3, 0) and crosses the x-axis at (-1, 0). (e) Local maximum at (2.00, 54.00) (f)

(g) Domain of f: all real numbers; range of f: (- , 54.00] (h) f is increasing on (- , -1) and (-1, 2.00); f is decreasing on (2.00, ) 31) vertical asymptote: f2 = -0.001; horizontal asymptote: f = 0.001

32) -2.24

Answer Key Testname: CHAPTER 5 33) (a) For large values of |x|, the graph of f(x) will resemble the graph of y = x3 . (b) y-intercept: (0, 0), x-intercepts: (0, 0) and (-3, 0) (c) The graph of f crosses the x-axis at (-3, 0) and touches the x-axis at (0, 0). (e) Local minimum at (0, 0), Local maximum at (-2.00, 4.00) (f)

(g) Domain of f: all real numbers; range of f: all real numbers (h) f is increasing on (- , -2.00) and (0, ); f is decreasing on (-2.00, 0) 34) a) The x-intercepts are -1.23, 0.40, 1.38, and 2.94. The y-intercept is -4. b) The graph crosses the x-axis at each x-intercept. c) The graph resembles f(x) = 2x4 for large values of |x|. d) Maximum at (0.89, 2.11); minima at (-0.65, -8.87) and (2.38, -8.02) e) The graph has 3 turning points. f)

35) 2.24

100

Answer Key Testname: CHAPTER 5 36) (a) For large values of |x|, the graph of f(x) will resemble the graph of y = -x5 . (b) y-intercept: (0, 0), x-intercepts: (-2, 0), (0, 0), (2, 0), and (6, 0) (c) The graph of f crosses the x-axis at (-2, 0), (2, 0), and (6, 0) and touches the x-axis at (0, 0). (e) Local maxima at (0, 0) and (4.89, 528.52); Local minima at (-1.45, -29.72) and (1.36, -18.46) (f)

(g) Domain of f: all real numbers; range of f: all real numbers (h) f is increasing on (-1.45, 0) and (1.36, 4.89); f is decreasing on (- , -1.45) (0, 1.36) and (4.89, ) 37) (a) For large values of |x|, the graph of f(x) will resemble the graph of y = x4 . (c) y-intercept: (0, 0.5184), x-intercepts: (-1.2, 0), (-0.6, 0), (0.6, 0), and (1.2, 0) (d) Local maximum at (0, 0.5184); Local minima at (-0.95, -0.29) and (0.95, -0.29) (e)

(f) domain of f: all real numbers; range of f: -0.29, (g) f is increasing on (-0.95, 0) and (0.95, ); f is decreasing on ( , -0.95) and (0, 0.95)

101

Answer Key Testname: CHAPTER 5

38) (a) For large values of |x|, the graph of f(x) will resemble the graph of y =

1 3 x . 3

(b) y-intercept: (0, 15), x-intercepts: (-3, 0), (3, 0), and (5, 0) (c) The graph of f crosses the x-axis at each of the intercepts (-3, 0), (3, 0), and (5, 0). (e) Local maximum at (-0.74, 16.17); Local minimum at (4.07, -2.35) (f)

(g) Domain of f: all real numbers; range of f: all real numbers (h) f is increasing on ( , -0.74) and (4.07, ); f is decreasing on (-0.74, 4.07) 39) A 40) B 41) D 42) D 43) D 44) B 45) C 46) A 47) D 48) A 49) D 50) C 51) A 52) A 53) A 54) C 55) A 56) B 57) C 58) D 59) B 60) B 61) D 62) C 63) A 64) D 65) C

102

Answer Key Testname: CHAPTER 5 66) C 67) C 68) C 69) B 70) A 71) A 72) B 73) C 74) A 75) D 76) A 77) D 78) B 79) D 80) C 81) D 82) D 83) B 84) D 85) C 86) A 87) A 88) D 89) B 90) D 91) C 92) D 93) A 94) A 95) B 96) A 97) D 98) B 99) A 100) C 101) D 102) B 103) B 104) D 105) C 106) D 107) C 108) D 109) B 110) A 111) A 112) B 113) D 114) A 115) D 103

Answer Key Testname: CHAPTER 5 116) C 117) D 118) A 119) D 120) C 121) D 122) A 123) C 124) A 125) B 126) B 127) B 128) C 129) B 130) C 131) D 132) C 133) C 134) D 135) D 136) D 137) A 138) D 139) C 140) C 141) C 142) A 143) D 144) C 145) B 146) B 147) A 148) B 149) C 150) B 151) B 152) B 153) A 154) B 155) B 156) D 157) B 158) D 159) C 160) C 161) C 162) C 163) A 164) B 165) D 104

Answer Key Testname: CHAPTER 5 166) B 167) A 168) C 169) C 170) C 171) D 172) B 173) D 174) C 175) D 176) B 177) A 178) C 179) D 180) C 181) C 182) B 183) B 184) B 185) A 186) B 187) D 188) B 189) C 190) C 191) D 192) C 193) D 194) D 195) D 196) C 197) A 198) D 199) A 200) C 201) C 202) D 203) B 204) A 205) D 206) A 207) C 208) A 209) C 210) D 211) A 212) C 213) C 214) B 215) B 105

Answer Key Testname: CHAPTER 5 216) B 217) B 218) D 219) B 220) B 221) A 222) A 223) B 224) D 225) D 226) A 227) A 228) A 229) C 230) C 231) D 232) A 233) A 234) B 235) C 236) B 237) D 238) D 239) D 240) D 241) A 242) C 243) B 244) A 245) D 246) C 247) D 248) B 249) A 250) C 251) D 252) A 253) A 254) B 255) B 256) D 257) D 258) C 259) A 260) A 261) B 262) D 263) B 264) D 265) A 106

Answer Key Testname: CHAPTER 5 266) D 267) D 268) C 269) A 270) B 271) C 272) C 273) B 274) C 275) B 276) A 277) C 278) C 279) B 280) C 281) A 282) B 283) B 284) B 285) B 286) B 287) C 288) A 289) D 290) B 291) A 292) D 293) D 294) D 295) B 296) C 297) C 298) C 299) C 300) A 301) C 302) D 303) C 304) D 305) A 306) B 307) D 308) B 309) C 310) A 311) D 312) C 313) B 314) A 315) D 107

Answer Key Testname: CHAPTER 5 316) C 317) B 318) A 319) C 320) C 321) A 322) B 323) D 324) D 325) A 326) A 327) A 328) A 329) C 330) D 331) D 332) C 333) B 334) A 335) C 336) B 337) C 338) C 339) B 340) A 341) C 342) D 343) D 344) B 345) D 346) B 347) B 348) C 349) C 350) D 351) D 352) C 353) C 354) A 355) A 356) C 357) D 358) B 359) B 360) B 361) B 362) D 363) D 364) C 365) D 108

Answer Key Testname: CHAPTER 5 366) D 367) A 368) B 369) A 370) D 371) C 372) B 373) B 374) A 375) D 376) D 377) C 378) C 379) C 380) B 381) C 382) A 383) B 384) A

109

Chapter 6 Exam Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. The graph of a logarithmic function is shown. Select the function which matches the graph. 1)

A) y = 2 - log x

B) y = log(2 - x)

C) y = log x - 2

D) y = log(x - 2)

A) y = log(1 - x)

B) y = log(x - 1)

C) y = log x - 1

D) y = 1 - log x

A) y = log

(x - 2)

B) y = log

C) y = log

(x + 2)

D) y = log

x+2

A) y = log(-x)

B) y = -log(-x)

C) y = log x

D) y = -log x

The graph of an exponential function is given. Match the graph to one of the following functions. 5)

A) f(x) = -2 x

C) f(x) = 2 x

B) f(x) = -2 -x

D) f(x) = 2 -x

A) f(x) = - 3 x

B) f(x) = 3 x

C) f(x) = - 3 -x

D) f(x) = 3 -x

The graph of a logarithmic function is shown. Select the function which matches the graph. 7)

A) y = 1 - log

B) y = log

C) y = log

(-x)

D) y = - log

The graph of an exponential function is given. Match the graph to one of the following functions. 8)

A) f(x) = 3 x + 2

B) f(x) = 3 x

C) f(x) = 3 x - 2

D) f(x) = 3 x - 2

A) f(x) = 5 x + 1

B) f(x) = 5 x - 1

C) f(x) = 5 x - 1

D) f(x) = 5 x

The graph of a logarithmic function is shown. Select the function which matches the graph. 10)

A) y = log x - 2

B) y = 2 - log x

C) y = log(x - 2)

10)

D) y = log(2 - x)

11)

A) y = log(-x)

B) y = -log x

C) y = -log(-x)

D) y = log x

12)

A) y = log

B) y = log

C) y = log

(x - 1)

x-1

D) y = log

(x + 1)

13)

A) y = 1 - log

B) y = log

C) y = log

(-x)

D) y = - log

14)

A) y = log

(-x)

B) y = - log

C) y = log

D) y = 1 - log

15)

A) y = log(x - 3)

B) y = 3 - log x

C) y = log(3 - x)

D) y = log x - 3

The graph of an exponential function is given. Match the graph to one of the following functions. 16)

A) f(x) = 4 x + 2

B) f(x) = 4 x - 2

C) f(x) = 4 x - 2

16)

D) f(x) = 4 x

The graph of a logarithmic function is shown. Select the function which matches the graph. 17)

A) y = log

(x - 1)

B) y = log

C) y = log

x+1

D) y = log

17)

(x + 1)

18)

A) y = log x

B) y = log(-x)

C) y = -log x

D) y = -log(-x)

The graph of an exponential function is given. Match the graph to one of the following functions. 19)

A) f(x) = 2 -x

C) f(x) = 2 x

B) f(x) = - 2 -x

19)

D) f(x) = - 2 x

20)

A) y = 3.5x

B) y = 0.65x

C) y = 2.4x

D) y = 0.32x

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 21) The rates of death (in number of deaths per 100,000 population) for 20-24 year olds in the United States between 1985-1993 are given below. (Source: NCHS Data Warehouse) Year Rate of Death 1985 134.9 1987 154.7 1989 162.9 1991 174.5 1993 182.2 A logarithmic equation that models this data is y = 57.76 + 48.56 ln x where x represents the number of years since 1980 and y represents the rate of death in that year. Use this equation to predict the year in which the rate of death for 20-24 year olds first exceeds 200.

21)

22) Meike earned $1565 in tips while working a summer job at a coffee shop. She wants to use this money to take a trip to Europe next summer. If she places the money in an account which pays 6.5% compounded continuously, how much money will she have in nine months?

22)

23) Carla has just inherited a building that is worth $250,000. The building is in a high demand area, and the value of the building is projected to increase at a rate of 25% per year for the next 4 years. How much more money will she make if she waits four years to sell the building instead of selling now?

23)

24) A music store manager collected data regarding price and quantity demanded of cassette tapes every week for 10 weeks, and found that the exponential function of best fit to the data was p = 25 · 0.89q. Express the function of best fit in the form p = p0 ekq, and use this

24)

25) A rumor is spread at an elementary school with 1200 students according to the model N = 1200(1 - e-0.16d) where N is the number of students who have heard the rumor and d

25)

26) A rumor is spread at an elementary school with 1200 students according to the model N = 1200(1 - e-0.16d) where N is the number of students who have heard the rumor and d

26)

27) The surface area S (in square inches) of a cylindrical pipe with length 12 inches is given by S(r) = 2 r2 + 24 r, where r is the radius of the piston (in inches). If the radius is increasing

27)

expression to predict the quantity demanded if the price is $8.50.

is the number of days that have elapsed since the rumor began. How many students will have heard the rumor after 5 days?

is the number of days that have elapsed since the rumor began. How many days must elapse for 500 to have heard the rumor?

with time t (in minutes) according to the formula r(t) =

1 2 t ,t 6

0, find the surface area S of

the pipe as a function of the time t.

28) Gillian has $10,000 to invest in a mutual fund. The average annual rate of return for the past five years was 12.25%. Assuming this rate, determine how long it will take for her investment to double.

28)

29) What principal invested at 6%, compounded continuously for 3 years, will yield $1500? Round the answer to two decimal places.

29)

30) Assume that the half-life of Carbon-14 is 5700 years. Find the age (to the nearest year) of a wooden axe in which the amount of Carbon-14 is 30% of what it originally had.

30)

31) The concentration of alcohol in a person's blood is measurable. Suppose that the risk R (given as 31)a percent) of having an accident while driving a car can be modeled by the equation R = 5ekx where x is the variable concentration of alcohol in the blood and k is a constant.

Suppose that a concentration of alcohol in the blood of 0.07 results in a 10% risk (R = 10) of an accident. Find the constant k in the equation. Using this value of k, what is the risk if the concentration is 0.11?

32) Bob, the incredible shrinking man, loses half of his height each day after he was exposed to a mysterious form of cosmic radiation. How many days before he is literally "knee-high to a grasshopper"? Assume that a grasshopper's knee is 4 millimeters high and that Bob is 2 meters tall. Round your answer to the nearest whole day. (1000 millimeters = 1 meter) Find the effective rate of interest. 3 33) 4 % compounded quarterly 4

32)

33)

Solve the problem. 34) If $5,000 is invested for 6 years at 5%, compounded continuously, find the future value.

34)

35) The size P of a certain insect population at time t (in days) obeys the function P = 700e0.03t. After how many days will the population reach 1500?

35)

36) Julio figures that he can save $5000 per year. If, at the end of each year, he invests the money in a certificate of deposit (CD) which pays 7% interest annually, how much money will he have saved in six years?

36)

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to two decimal places. 37) log(2/3)19 37) Solve the problem. 38) The price p of a certain product and the quantity sold x obey the demand equation p = 2 x + 800. x + 200, 0 x 300. Suppose that the cost C of producing x units is C = 3 20

38)

Assuming that all items produced are sold, find the cost C as a function of the price p.

39) The half-life of carbon-14 is 5700 years. Find the age of a sample in which 8% of the radioactive nuclei originally present have decayed.

39)

40) If a single pane of glass obliterates 15% of the light passing through it, then the percent P of light 40) that passes through n successive panes can be approximated by the equation P = 100e-0.15n How many panes are necessary to block at least 50% of the light?

41) The half-life of radium is 1690 years. If 150 grams is present now, how long (to the nearest year) till only 100 grams are present?

41)

42) A fully cooked turkey is taken out of an oven set at 200°C (Celsius) and placed in a sink of chilled water of temperature 4°C. After 3 minutes, the temperature of the turkey is measured to be 50°C. How long (to the nearest minute) will it take for the temperature of the turkey to reach 15°C? Assume the cooling follows Newton's Law of Cooling: U = T + (Uo - T)ekt.

42)

43) The bacteria in a container quadruples every day. If there are initially 100 bacteria, write an equation that models the number of bacteria A after d days. How many bacteria will there be after 1 week?

43)

(Round your answer to the nearest minute.)

44) If f(x) =

1 2 x + 4 and g(x) = 2x - a, find a so that the graph of f g crosses the y-axis at 36. 2

44)

45) A venture capital firm invested $2,000,000 in a new company in 1995. In 1999, they sold their stake in the company for $10,500,000. What was the average annual rate of return on their investment?

45)

46) The revenue for a dot.com company is projected to double each year for the first 5 years. If the revenue for the first year is $2 million, write a function showing the revenue R after x years. What is the revenue for the fourth year?

46)

47) The formula

47)

D = 8e-0.6h can be used to find the number of milligrams D of a certain drug that is in a patient's bloodstream h hours after the drug has been administered. The drug is to be administered again when the amount in the bloodstream reaches 4 milligrams. What is the time between injections?

48) The rates of death (in number of deaths per 100,000 population) for 1-4 year olds in the United States between 1980-1995 are given below. (Source: NCHS Data Warehouse)

48)

Year Rate of Death 1980 91.4 1985 74.5 1990 69.3 1995 61.3 A logarithmic equation that models this data is y = 822.99 - 167.55 ln x where x represents the number of years since 1900. Use this equation to predict the rate of death for 1-4 year olds in 2005.

Write as the sum and/or difference of logarithms. Express powers as factors. 3 x5 y8 logb 49) z2 10

49)

Solve the problem.

50) If f(x) = x2 and g(x) = -1 + 5x, find (f g)(x) and find the domain of (f g)(x).

50)

51) The population (in hundred thousands) for the Colonial United States in ten-year increments for the years 1700-1780 is given in the table. (Source: 1998 Information Please Almanac)

51)

Decade 0 1 2 3 4

Population 251 332 466 629 906

Decade 5 6 7 8

Population 1171 1594 2148 2780

State whether the data can be more accurately modeled using an exponential function or a logarithmic function. Using a graphing utility, find a model for population (in hundred thousands) as a function of decades since 1700.

52) A culture of bacteria obeys the law of uninhibited growth. If 140,000 bacteria are present initially and there are 609,000 after 6 hours, how long will it take for the population to reach one million?

52)

53) In 1992, the population of a country was estimated at 5 million. For any subsequent year, the population, P(t) (in millions), can be modeled using the equation 250 P(t) = , where t is the number of years since 1992. Determine the year 5 + 44.99e-0.0208t

53)

when the population will be 39 million.

54) A cancer patient undergoing chemotherapy is injected with a particular drug. The function D(h) = 4e-0.35h gives the number of milligrams D of this drug that is in the patient's

54)

55) The profit P for selling x items is given by the equation P(x) = 2x - 500. Express the sales amount x as a function of the profit P.

55)

56) The temperature (in degrees Fahrenheit) of a dead body that has been cooling in a room set at 70° is measured as 88°. One hour later, the body temperature is 87.5°. How long (to the nearest hour) before the first measurement was the time of death, assuming that the body temperature of the deceased at the time of death was 98.6°. Assume the cooling follows Newton's Law of Cooling: U = T + (Uo - T)ekt.

56)

57) Instruments on a satellite measure the amount of power generated by the satellite's power supply. The time t and the power P can be modeled by the function P = 50e-t/300, where t

57)

bloodstream h hours after the drug has been administered. How many milligrams of the drug were injected? To the nearest milligram, how much of the drug will be present after 2 hours?

is in days and P is in watts. How much power will be available after 378 days? Round to the nearest hundredth.

58) A thermometer is taken from a room at 71°F to the outdoors where the temperature is 14°F. Determine what the reading on the thermometer will be after 5 minutes, if the reading drops to 45°F after 1 minute. Assume the cooling follows Newton's Law of Cooling: U = T + (Uo - T)ekt.

58)

59) John Forgetsalot deposited $100 at a 3% annual interest rate in a savings account fifty years ago, and then he promptly forgot he had done it. Recently, he was cleaning out his home office and discovered the forgotten bank book. How much money is in the account?

59)

(Round your answer to two decimal places.)

60) Between 8:30 a.m. and 9:30 a.m., cars drive through the Cappuccino Express at a rate of 12 cars60) per hour (0.2 per minute). The following formula from probability can be used to determine the probability that a car will arrive within t minutes of 8:30a.m. F(t) = 1 - e-0.2t Determine how many minutes are needed for the probability to reach 0.6.

61) Find the value of log3 4 · log4 5 · log5 6 · log6 7 · log7 8 · log8 9

61)

62) Data representing the price and quantity demanded for hand-held electronic organizers were analyzed every day for 15 days. The logarithmic function of best fit to the data was found to be p = 398 - 73 ln(q). Use this to predict the number of hand-held electronic organizers that would be demanded if the price were $275.

62)

63) The function f(x) = |x|- 5 is not one-to-one. (a) Find a suitable restriction on the domain of f so that the new function that results is one-to-one. (b) Find the inverse of f.

63)

64) How long does it take $1700 to double if it is invested at 5% interest, compounded monthly? Round your answer to the nearest tenth.

64)

65) The weight W of a bird's brain (in ounces) is related to the volume V of the bird's skull (in 3 cubic ounces) through the function W(V) = 3.34 V + 1.27. (a) Express the skull volume V as a function of brain weight W. (b) Predict the skull volume of a bird whose brain weighs 2 oz.

65)

66) The volume V (in cubic inches) of a cylindrical pipe with length 12 inches is given by V(r) = 12 r2 , where r is the radius of the piston (in inches). If the radius is increasing with time t

66)

(in minutes) according to the formula r(t) =

1 2 t , t 0, find the volume V of the pipe as a 6

function of the time t.

67) A biologist has a bacteria sample. She records the amount of bacteria every week for 8 weeks and finds that the exponential function of best fit to the data is A = 150 · 1.79t. Express the function of best fit in the form A = A0 ekt.

67)

68) In a networking marketing plan for a company, each distributor is expected to recruit 3 new distributors. Jack was the first distributor hired by the company, so he is considered a level 1 distributor. The 3 people he recruits are considered level 2 distributors. The people recruited by the level 2 distributors are considered level 3 distributors, and so on. Write a function that models the number of distributors D at each level L. How many distributors would there be at the fifth level?

68)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the amount that results from the investment. 69) $14,000 invested at 12% compounded semiannually after a period of 7 years A) $30,949.54 B) $29,861.00 C) $17,652.66

D) $31,652.66

Write as the sum and/or difference of logarithms. Express powers as factors. x 70) log 4 16 A)

1 log x - 2 4 2

B) log

C) - 2 log

x-2

70) D) 8 -

1 log x 4 2

Use the horizontal line test to determine whether the function is one-to-one. 71)

A) Yes

69)

71)

B) No

Solve the problem. 72) The logistic growth function f(t) =

360 describes the population of a species of butterflies 1 + 8.0e-0.17t

72)

t months after they are introduced to a non-threatening habitat. How many butterflies were initially introduced to the habitat? A) 2 butterflies B) 8 butterflies C) 360 butterflies D) 40 butterflies

Solve the equation. 73) 3 6 - 3x = A) {3}

1 27

73) B) {-3}

1 9

D) {9}

Solve the problem.

74) The amount of a certain drug in the bloodstream is modeled by the function y = y0 e- 0.40t, where

74)

y0 is the amount of the drug injected (in milligrams) and t is the elapsed time (in hours). Suppose that 10 milligrams are injected at 10:00 A.M. If a second injection is to be administered when there is 1 milligram of the drug present in the bloodstream, approximately when should the next dose be given? Express your answer to the nearest quarter hour. A) 12:30 P.M B) 5: 30 P.M C) 5:45 P.M D) 3:45 P.M

Solve the equation. 1 log (x + 6) = log (3x) 75) 2 8 3 A) {3}

75) B) {9}

C) {3, 0}

Solve the problem. 76) A city is growing at the rate of 0.8% annually. If there were 3,213,000 residents in the city in 1,994, find how many (to the nearest ten-thousand) were living in that city in 2000. Use y = 3,213,000(2.7)0.008t A) 420,000

B) 3,400,000

C) 8,680,000

D) 3,370,000

Find functions f and g so that f g = H. 1 77) H(x) = 2 x -7 A) f(x) =

77)

1 , g(x) = x2 - 7 x

B) f(x) =

1 x

D) f(x) =

C) f(x) = x2 - 7; g(x) =

1 1 ; g(x) = -9 x x2 1

- 9; g(x) =

1 x

Find the exact value of the logarithmic expression. 1 78) log4 64 A) -3

78)

B) 3

C) -

1 3

Change the logarithmic expression to an equivalent expression involving an exponent. 1 = -2 79) ln e2 A)

1 -2 =e e2

B) -2 e =

1 e2

C) e-2 =

Decide whether the composite functions, f g and g f, are equal to x. 80) f(x) = x , g(x) = x2 A) No, yes

Solve the equation. 81) log x = 3 4 A) {81}

76)

B) No, no

1 e2

C) Yes, no

79) D)

1 e = -2 e2

D) Yes, yes

80)

81) B) {12}

C) {7}

D) {64}

Change the logarithmic expression to an equivalent expression involving an exponent. 16 = -2 82) log 1/4 1 -2 1 2 = 16 = 16 A) B) (-2)1/4 = 16 C) 161/4 = 2 D) 4 4 83) logb 49 =

2 3

83)

A) b2/3= 49

Solve the equation. 84) 4 (7 - 3x) = A)

82)

2 b = 49 3

C) b3/2 = 49

D) 492/3 = b

1 16

1 4

84) B) {4}

C) {-3}

D) {3}

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to two decimal places. 85) log3 25 85) A) 1.10

B) 2.93

C) 3.22

D) 0.34

Solve the problem. 86) The amount of a radioactive substance present, in grams, at time t in months is given by the formula y = 9,000(2)-0.3t. Find the number of grams present in 2 years. If necessary, round to three decimal places. A) 61.211

B) 6.121

C) 593.779

For the given functions f and g, find the requested composite function value. Find (f g)(7). 87) f(x) = 11x2 - 9x, g(x) = 13x - 7; A) 76,860

B) 70,679

C) 39,984

D) 5,937.786

D) 6,181

Decide whether or not the functions are inverses of each other. 1 88) f(x) = 3x + 9, g(x) = x - 3 3 A) Yes

86)

87)

88) B) No

Solve the equation. 89) log (x + 5) = 4 + log (x - 5) 2 2 2 2 A) B) 3 3

89) C) -

17 3

Solve the problem. 90) The function f(x) = 1 + 1.5 ln (x + 1) models the average number of free-throws a basketball player can make consecutively during practice as a function of time, where x is the number of consecutive days the basketball player has practiced for two hours. After how many days of practice can the basketball player make an average of 8 consecutive free throws? A) 404 days B) 105 days C) 107 days D) 402 days

90)

Find the effective rate of interest. 91) 75.07% compounded daily A) 111.685%

B) 75.275%

C) 75.975%

D) 75.193%

Express as a single logarithm. 4 1 92) 4 log m - log n + log j - 6 log k c c c c 5 6

92)

A) log

m 4 j1/6 c n 4/5 k6

B) log

C) log

m 4 n 4/5 c j1/6 k6

D) log

Solve the equation. 93) 3 (10 - 2x) = 81 A) {2}

91)

B) {3}

4m -

4 1 n + j - 6k 5 6

m 4 k6 c j1/6 n 4/5

C) {-3}

93)

D) {4}

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to two decimal places. 94) log5.1 4.1 94) A) 0.61

B) 1.15

C) 0.87

D) 0.80

Solve the equation. 8 x 81 = 95) 3 4,095 A)

1 4

96) e x + 6 = 2 A) {e12}

95) B) {4}

B) {ln 2 - 6}

Solve the problem. 97) The logistic growth model P(t) =

D) -

C) {ln 8}

D) {e2 + 6}

420 represents the population of a species introduced 1 + 51.5e-0.159t

into a new territory after t years. When will the population be 70? A) 13.52 years B) 2.09 years C) 0.94 years

3 13

96)

97)

D) 14.67 years

Solve the equation. 98) log2 (3x - 2) - log2 (x - 5) = 4 A)

1 4

C) {-4}

98) B) {18}

C) {6}

Solve the problem. Round your answer to three decimals. 99) What annual rate of interest is required to triple an investment in 9 years? A) 12.983% B) 6.492% C) 12.207%

38 5

D) 8.006%

99)

Graph the function. 100) f(x) = 4 - ln x

100)

Find the effective rate of interest. 101) 14.2% compounded continuously A) 14.651% B) 15.258%

C) 14.574%

Change the exponential expression to an equivalent expression involving a logarithm. 102) ex = 18 A) log18 x = e

B) logx e = 18

C) ln 18 = x

D) 14.289%

D) ln x = 18

101)

102)

Write as the sum and/or difference of logarithms. Express powers as factors. 1 103) log 1 x3 A) log x3 - log 1 - 3 log x

103)

B) log(x - 1) + log(x2 + x + 1) - 3 log x D) log(x - 1) + log(x2 + 1) - 3 log x

C) log 1 - 3 log 1 - 3 log x

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to three decimal places. 104) log 77.15 104) 6 A) 0.412 B) 12.858 C) 2.425 D) 1.887 The loudness L(x), measured in decibels, of a sound of intensity x, measured in watts per square meter, is defined as x L(x) = 10log ( ), where I0 = 10-12 watt per square meter is the least intense sound that a human ear can detect. I0 Determine the loudness, in decibels, of the sound. 105) A particular Boeing 747 jetliner produces noise at a loudness level of 113 decibels. Find the intensity level (round to the nearest hundredth) in watt per square meter for this noise. A) 0.80 watt per square meter B) 0.10 watt per square meter C) 0.40 watt per square meter D) 0.20 watt per square meter

For the given functions f and g, find the requested composite function value. Find (f f)(0). 106) f(x) = 2x + 4, g(x) = 4x2 + 1; A) 65

B) 6

C) 12

Graph the function. 1 107) f(x) = - log x 2 3

D) 5

105)

106)

107)

Find the domain of the composite function f g. 1 ; g(x) = x - 1 108) f(x) = x - 10

108)

A) {x x 1, x 10} C) {x x 1, x 10, x 101}

B) {x x is any real number} D) {x x 1, x 101}

For the given functions f and g, find the requested composite function. 5 2 , g(x) = ; Find (f g)(x). 109) f(x) = x-2 7x A)

2x - 4 35x

35x 2 + 14x

35x 2 - 14x

109) D)

5x 2 - 14x

Solve the equation. 1 110) 3 -x = 81 A)

1 4

110) C) {4}

B) {-4}

Find the domain of the composite function f g. 111) f(x) = 2 - x; g(x) = 2x - 1 1 3 x A) x| 2 2

1 27

111) B) {x | x 2}

C) {x| x 2}

D) all real numbers

Solve the problem. 112) f(x) = log2(x - 4) and g(x) = log2 (2x + 20). Solve f(x) + g(x) = 6. A) {-64}

112)

B) {6}

C) {64}

D) {-6}

113) pH = -log10[H+ ] Find the [H+] if the pH = 9.4. A) 2.51 × 10-10

113)

B) 3.98 × 10-9

C) 3.98 × 10-10

D) 2.51 × 10-9

Find functions f and g so that f g = H. 114) H(x) = (5 - 2x3 )2

A) f(x) = x3 ; g(x) = (5 - 2x)2

B) f(x) = x2 ; g(x) = 5 - 2x3

C) f(x) = 5 - 2x3 ; g(x) = x2

D) f(x) = (5 - 2x)3 ; g(x) = x2

Solve the problem. 115) The half-life of a radioactive element is 130 days, but your sample will not be useful to you after 80% of the radioactive nuclei originally present have disintegrated. About how many days can you use the sample? A) 302 B) 287 C) 297 D) 312 Use a calculator to evaluate the expression. Round your answer to three decimal places e log 80 + ln 5 116) log 5 + ln 30 A) -2.510

B) 1.654

C) 0.869

115)

116) D) 0.857

Find the exact value of the logarithmic expression. 1 117) log9 729 A) -81

114)

117)

B) 3

C) -3

Express as a single logarithm. 118) 8 log 2 + 10 log 7 c c

D) 81

118) 28 c 7 10

A) log 2 8 7 10 c

B) log

C) log (16 + 70) c

D) log 2 8 · log 7 10 c c

Solve the problem.

119) The function f(x) = 400(0.5)x/70 models the amount in pounds of a particular radioactive material stored in a concrete vault, where x is the number of years since the material was put into the vault. Find the amount of radioactive material in the vault after 150 years. Round to the nearest whole number. A) 429 pounds B) 91 pounds C) 289 pounds D) 93 pounds

119)

The graph of a one-to-one function f is given. Draw the graph of the inverse function f-1 as a dashed line or curve. 120) f(x) = 5x 120)

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator. 121) 10log 18 - log 3

121)

Approximate the value using a calculator. Express answer rounded to three decimal places. 122) e3.55

122)

Use the horizontal line test to determine whether the function is one-to-one. 123)

123)

A) 6

A) 9.650

B) 18

C) log 15

B) 15.154

C) 31.309

A) Yes

B) No 21

D) 1,000,000

D) 34.813

Graph the function. 124) f(x) = 5 x

124)

The Richter scale converts seismographic readings into numbers for measuring the magnitude of an earthquake x according to this function M(x) = log , where x 0 = 10-3 . x0

125) Find the magnitude (to one decimal place) of an earthquake whose seismographic reading is 2000 millimeters at a distance of 100 kilometers from its epicenter. Round the answer to the nearest tenth. A) 6.4 B) 7.3 C) 5.9 D) 6.3

125)

Solve the problem. 126) The Feldmans bought their first house for $13,000. Over the years they moved three times into bigger and bigger houses. Now, 44 years later, they are ready to retire and want a smaller house like the first one they bought. If inflation in property values has averaged 3.1% per year during that time, how much will such a house cost them now? (Round your answer to the nearest dollar.) A) $49,811 B) $3,323 C) $50,854 D) $3,393 127) If 6 -x =

1 , what does 36x equal? 3

A) -9

B) 3

126)

127) C) 9

Graph the function. 128) f(x) = e-0.6x

1 9

128)

Use the horizontal line test to determine whether the function is one-to-one. 129)

A) Yes

129)

B) No

Solve the problem.

130) Suppose that f(x) = 4 x + 5. If f(x) = 1/21, what is x? A) 5 B) 2

C) -5

D) -2

131) The pH of a solution ranges from 0 to 14. An acid has a pH less than 7. Pure water is neutral and has a pH of 7. The pH of a solution is given by pH = - log x where x represents the concentration of the hydrogen ions in the solution in moles per liter. Find the hydrogen ion concentration if the pH = 4.4. A) 2.51 × 10-4 B) 3.98 × 10-4 C) 3.98 × 10-5 D) 2.51 × 10-5 Find the domain of the composite function f g. 20 -7 ; g(x) = 132) f(x) = x+4 x B) {x x 0, x -4, x -5} D) {x x 0, x -4}

Find the exact value of the logarithmic expression. 133) log1/3 9 1 2

131)

132)

A) {x x 0, x -5} C) {x x is any real number}

A) -

130)

133)

1 2

C) 2

D) -2

Solve the problem. 134) In 1990, the population of a country was estimated at 4 million. For any subsequent year the 240 population, P(t) (in millions), can be modeled by the equation P(t) = , where t is 5 + 54.99e-0.0208t

134)

the number of years since 1990. Estimate the year when the population will be 21 million. A) approximately the year 2041 B) approximately the year 2088 C) approximately the year 2093 D) approximately the year 2016

135) The number of books in a small library increases according to the function B = 3,900e0.03t, where t is measured in years. How many books will the library have after 9 years? A) 2,218 B) 7,262 C) 5,109 D) 5,106

135)

Use a graphing calculator to solve the equation. Round your answer to two decimal places. 136) ex = x5 A) {-0.79}

B) {1.30}

C) {2.54}

D) {-0.71}

136)

Solve the problem. 137) The population of a particular country was 22 million in 1982; in 1997, it was 27 million. The exponential growth function A =22ekt describes the population of this country t years after 1982.

137)

Find the amount that results from the investment. 138) $1,000 invested at 12% compounded annually after a period of 4 years A) $1,762.34 B) $573.52 C) $1,573.52

138)

Use the fact that 15 years after 1982 the population increased by 5 million to find k to three decimal places. A) 0.024 B) 0.107 C) 0.014 D) 0.426

D) $1,404.93

Change the logarithmic expression to an equivalent expression involving an exponent. 140) log 9 = 2 3 A) 3 2 = 9 B) 3 9 = 2 C) 2 3 = 9 D) 9 2 = 3 Express as a single logarithm. x2 - 5x - 24 x2 - 4x - 21 - ln + ln (x2 - 16x + 64), 141) ln x-7 x+6

x>0

(x - 8)3(x + 6) (x - 7)2

B) ln

3(x - 8) 2(x - 7)(x + 6)

C) ln

(x - 8)3 (x - 7)2(x + 6)

D) ln

3(x - 8)(x + 6) 2(x - 7)

Solve the problem. 142) Find out how long it takes a $2,600 investment to double if it is invested at 8% compounded r nt monthly. Round to the nearest tenth of a year. Use the formula A = P 1 + . n B) 8.9 yr

C) 9.1 yr

140)

141)

A) ln

A) 8.7 yr

139)

D) 8.5 yr

142)

Graph the function and its inverse on the same Cartesian plane. 143) f(x) = log1/6 x

Find the domain of the function. 144) f(x) = 4 - ln(8x) A) (-4, 8)

B) (- , 4)

(8, )

143)

C) (0, )

Write as the sum and/or difference of logarithms. Express powers as factors. 7x 145) log 3 1 1 A) log 7x B) log 7 + log x 3 3 3 2 2 C) log

7 + log

1 1 log 7 + log x 3 3 2 2

D) (8, )

144)

145)

Evaluate the expression using the values given in the table. 146) (f g)(5)

146)

x 1 5 9 12 f(x) -1 9 3 14 x -5 -1 1 5 g(x) 1 -8 5 9 A) 9

B) 3

Solve the problem. 147) The logistic growth function f(t) =

C) 5

D) Undefined

25,000 models the number of people who have become 1 + 356.1e-1.9t

ill with a particular infection t weeks after its initial outbreak in a particular community. How many people were ill after 3 weeks? A) 25,001 people B) 11,407 people C) 25,357 people D) 210 people

147)

Graph the function. 148) f(x) = 2 - ln(x + 4)

148)

Find functions f and g so that f g = H. 149) H(x) = 7x + 3 A) f(x) = -x ; g(x) = 7x - 3 C) f(x) = x; g(x) = 7x + 3 Solve the problem. 150) The logistic growth model P(t) =

B) f(x) = x ; D) f(x) = - x ;

g(x) = 7x + 3 g(x) = 7x + 3

160 represents the population of a species introduced 1 + 19e-0.187t

into a new territory after t years. What will the population be in 30 years? A) 160 B) 150 C) 151

D) 2,300

149)

150)

Change the exponential expression to an equivalent expression involving a logarithm. 151) 323/5 = 8 A) log

32 =

3 5

B) log

3 5

C) log

32 =

3 5

log

5 = 32 log 32 3

Decide whether the composite functions, f g and g f, are equal to x. 1 152) f(x) = , g(x) = x x A) Yes, yes

B) No, no

C) No, yes

152) D) Yes, no

Solve the equation. 1 153) 3 -x = 81 A) {4}

151)

153) B) {-4}

Graph the function. 154) f(x) = e4x

1 4

1 27

154)

For the given functions f and g, find the requested composite function value. Find (f g)(4). 155) f(x) = 2x + 2, g(x) = 4x2 + 1; A) 22

B) 401

C) 132

D) 16,901

155)

Solve the problem. 156) The formula D = 6e-0.04h can be used to find the number of milligrams D of a certain drug in a patient's bloodstream h hours after the drug has been given. When the number of milligrams reaches 3, the drug is to be given again. What is the time between injections? A) 27.47 hr B) 19.7 hr C) 44.79 hr D) 17.33 hr Find functions f and g so that f g = H. 1 157) H(x) = 5x + 5

157)

A) f(x) =

1 ; g(x) = 5x + 5 x

B) f(x) =

C) f(x) =

1 ; x

D) f(x) = 1;

g(x) = 5x + 5

5x + 5;

g(x) = 1

g(x) =

5+5

Write as the sum and/or difference of logarithms. Express powers as factors. 3 158) ln ey 3 1 1 y 1 1 A) B) ln ey + C) ln y + 3 3 3 3 3

158) D) 3 ln y + 3

Solve the problem. 159) A local bank advertises that it pays interest on savings accounts at the rate of 3% compounded monthly. Find the effective rate. Round answer to two decimal places. A) 3.04% B) 36% C) 3.40% D) 3.44% Use a calculator to evaluate the expression. Round your answer to three decimal places log 4 + log 3 160) ln 4 - ln 9 A) -0.154

156)

B) -3.064

C) -1.331

159)

160) D) 0.301

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to three decimal places. 2.6 161) log 161) 3.3 A) 0.800 B) 1.250 C) 0.788 D) 0.415 Graph the function. 162) f(x) = e3x - 1

162)

Graph the function using a graphing utility and the Change-of-Base Formula.

163) logx - 5 (x + 5)

163)

Find the inverse of the function and state its domain and range . 164) {(-5, 9), (-9, 5), (-8, 4), (8, -4)} A) {(-4, -8), (5, -9), (9, -9), (4, 8)}; D = {(-4, 5, 9, 4}; R = {-8, -9, 8} B) {(9, -5), (5, -9), (4, -8), (-4, 8)} D = {9, 5, 4, -4}; R = {-5, -9, -8, 8} 1 1 1 1 1 1 1 1 D = { -5, -9, -8, 8}, R = , , ,C) -5, , -9, , -8, , 8, 9 5 4 4 9 5 4 4 D) {(-4, -8), (-8, -9), (9, -5), (4, 8)}; D = {-4, -8, 9, 4}; R = {-8, -9, -5, 8} 32

164)

Find functions f and g so that f g = H. 1 165) H(x) = x-2 A) f(x) =

165)

1 1 ; g(x) = x-2 x

C) g(x) =

x ; f(x) =

1 ; g(x) = x-2

D) f(x) = x - 2; g(x) =

1 x

B) f(x) =

1 x-2

Indicate whether the function is one-to-one. 166) {(-10, -16), (14, 17), (16, -4)} A) Yes

166)

B) No

Find a formula for the inverse of the function described below. 167) An organization determines that the cost per person of chartering a bus is given by the formula 300 + 6x C(x) = , x

167)

where x is the number of people in the group and C(x) is in dollars. 300 6 A) C-1(x) = B) C-1(x) = x+6 x - 300

300 + x C) C-1(x) = 6

300 D) C-1(x) = x-6

Solve the problem. 168) The value of a particular investment follows a pattern of exponential growth. In the year 2000, you invested money in a money market account. The value of your investment t years after 2000 is given by the exponential growth model A = 10,000e0.064t. How much did you initially invest in the account? A) $640.00

B) $10,000.00

C) $10,660.92

D) $5,000.00

Evaluate the expression using the graphs of y = f(x) and y = g(x). 169) Evaluate (fg)(-2).

A) 4

B) 0

C) 3

168)

169)

D) -3

Solve the equation. 170) log (4x) = log 5 + log (x - 1) 4 A) B) 5 3

170)

5 C) 9

D) - 5

The Richter scale converts seismographic readings into numbers for measuring the magnitude of an earthquake x according to this function M(x) = log , where x 0 = 10-3 . x0

171) What is the magnitude of an earthquake whose seismographic reading is 0.94 millimeters at a distance of 100 kilometers from its epicenter? Round the answer to four decimal places. A) -3.0269 B) 2.9731 C) -0.0269 D) 0.9731 For the given functions f and g, find the requested composite function value. 172) f(x) = 2x + 9, g(x) = -2/x; Find (g f)(3). 2 43 A) B) - 10 C) 15 3

172)

23 D) 3

Solve the problem. 173) A grocery store normally sells 5 jars of caviar per week. Use the Poisson Distribution P(x) = to find the probability (to three decimals) of selling 4 jars in a week. (x! = x · (x - 1) · (x - 2) · ... · (3)(2)(1)). A) 0.175 B) 0.351 C) 0.702

171)

5 xe-5 x!

173)

D) 0.263

174)

C) Jim's voice is 100 times as intense as Amy's.

D) Jim's voice is 100.1 times as intense as Amy's. Change the logarithmic expression to an equivalent expression involving an exponent. 175) ln x = 9 A) 9 e = x B) ex = 9 C) x9 = e D) e9 = x Change the exponential expression to an equivalent expression involving a logarithm. 176) 6 2 = 36 A) log

36 = 6

B) log

C) log

2 = 36

6=2

D) log

36 = 2

175)

176)

Determine i) the domain of the function, ii) the range of the function, iii) the domain of the inverse, and iv) the range of the inverse. 177) f(x) = 5x + 6 177) 6 ,R= y y 0 ; A) f(x): D = x x 5 6 f-1 (x): D = x x 0 , R = y y 5

B) f(x): D = x x -

6 ,R= y y 0 ; 5

6 f-1 (x): D is all real numbers, R = y y 5

C) f(x): D = x x 0 , R = y y 0 ;

6 f-1 (x): D = x x 0 , R = y y 5

D) f(x): D = x x -

6 , R is all real numbers; 5

6 f-1 (x): D is all real numbers, R = y y 5

Write as the sum and/or difference of logarithms. Express powers as factors. x-5 178) log 6 x2 A) 2 log

B) log

x - log (x - 5) 6 6 C) log (x - 5) + 2 log x 6 6

(x - 5) - 2 log

6 D) log (x - 5) - log x 6 6

178) x

For the given functions f and g, find the requested composite function. x-3 , g(x) = 8x + 3; Find (g f)(x). 179) f(x) = 8 A) x + 6

Find the domain of the function. 180) f(x) = ln(1 - x) A) ( , 1)

B) x -

3 8

B) ( , -1)

179)

C) 8x + 21

D) x

C) (1, )

D) (-1, )

Solve the problem. 181) The value of a particular investment follows a pattern of exponential growth. In the year 2000, you invested money in a money market account. The value of your investment t years after 2000 is given by the exponential growth model A = 2,400e0.064t. When will the account be worth $4,269? A) 2011

B) 2010

C) 2008

B) -0.470

C) -4.899

181)

D) 2009

Use a calculator to evaluate the expression. Round your answer to three decimal places 5 182) log 8 A) 0.204

180)

182) D) -0.204

Find functions f and g so that f g = H. 1 183) H(x) = 2 x -6 A) f(x) = x2 - 6; C) f(x) =

;

183)

1 x

B) f(x) =

g(x) = - 1/6

D) f(x) =

g(x) =

1 ; x 1

g(x) = x2 - 6 ;

For the given functions f and g, find the requested composite function. Find (f g)(x). 184) f(x) = x2 - 7, g(x) = x2 + 2; A) x4 - 3

B) x4 + 4x2 - 3

g(x) = x - 6

C) x4 - 14x2 + 51

D) x4 + 51

184)

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to three decimal places. 185) log 0.011 185) 9 A) 818.182 B) -0.487 C) -2.053 D) -1.959 Find the exact value of the logarithmic expression. 186) log 1 5 1 A) B) 5 5

186) C) 1

Graph the function using a graphing utility and the Change-of-Base Formula. 187) y = log5 x

D) 0

187)

Find a formula for the inverse of the function described below. 188) 32° Fahrenheit = 0° Celsius. A function that converts temperatures in Fahrenheit to those in Celsius 5 is f(x) = (x - 32) . 9 A) f-1 (x) =

9 x + 32 5

B) f-1 (x) = x + 32

C) f-1 (x) =

9 x - 32 5

D) f-1 (x) =

5 (x - 32) 9

Find the present value. Round to the nearest cent. 189) To get $10,500 after11 years at 6% compounded annually A) $5,267.88 B) $5,863.15 C) $4,968.73

D) $5,531.27

190) To get $5600 after 6 years at 9% compounded annually A) $2,260.9 B) $3,639.62 C) $5,962.67 Find the exact value of the logarithmic expression. 191) log2 8 A) 2

Solve the equation. 192) log x = 3 2 A) {9}

188)

D) $3,339.10

189)

190)

191)

B) 3

C) 8

D) 6

192) B) {8}

C) {6}

Find functions f and g so that f g = H. 3 193) H(x) = x +1 3 A) f(x) = x ; g(x) = 1 3 C) f(x) = x ; g(x) = x + 1

D) {1.58}

193) B) f(x) = x + 1 ; g(x) = D) f(x) =

x ; g(x) = x + 1

Determine i) the domain of the function, ii) the range of the function, iii) the domain of the inverse, and iv) the range of the inverse. 3 194) f(x) = 194) x-4

A) f(x): D is all real numbers, R is all real numbers; f-1 (x): D is all real numbers, R is all real numbers B) f(x): D = x x -

3 ,R= y y 4 ; 4

3 f-1 (x): D = x x 4 , R = y y 4

C) f(x): D is all real numbers, R = y y -

3 ; 4

3 f-1 (x): D = x x , R is all real numbers 4

D) f(x): D = {x|x 4}, R = {y 0}; f-1 (x): D = {x|x 0}, R = {y|y 4} Solve the equation. 195) log (x + 4) = log (4x - 2) A) - 2

2 B) 3

C) 2

Decide whether or not the functions are inverses of each other. 196) f(x) = (x - 2)2 , x 2; g(x) = x + 2 A) No

6 D) 5

B) Yes

Change the logarithmic expression to an equivalent expression involving an exponent. 197) log 16 = 4 b A) 16b = 4 B) 164 = b C) 4 b = 16 D) b4 = 16

195)

196)

197)

The loudness L(x), measured in decibels, of a sound of intensity x, measured in watts per square meter, is defined as x L(x) = 10log ( ), where I0 = 10-12 watt per square meter is the least intense sound that a human ear can detect. I0 Determine the loudness, in decibels, of the sound. 198) At a rock concert by The Who, the music registered a loudness level of 120 decibels. The human threshold of pain due to sound averages 130 decibels. Compute the ratio of the intensities associated with these two loudness level to determine by how much the intensity of a sound that crosses the human threshold of pain exceeds that of this particular rock concert. A) The intensity of a sound that crosses the human threshold of pain is 0.1 times as intense as this rock concert. B) The intensity of a sound that crosses the human threshold of pain is 1000 times as intense as this rock concert. C) The intensity of a sound that crosses the human threshold of pain is 10 times as intense as this rock concert. D) The intensity of a sound that crosses the human threshold of pain is 100 times as intense as this rock concert.

Graph the function.

198)

199) f(x) = ex + 5

199)

Solve the problem. 200) Strontium 90 decays at a constant rate of 2.44% per year. Therefore, the equation for the amount P of strontium 90 after t years is P = P0 e-0.0244t. How long will it take for 15 grams of strontium to decay to 5 grams? Round answer to 2 decimal places. A) 40.50 years B) 45.03 years. C) 450.25 years

D) 4.50 years

200)

201) To remodel a bathroom, a contractor charges $25 per hour plus material costs, which amount to $3,950. Therefore, the total cost to remodel the bathroom is given by f(x) = 25x + 3,950 where x is the number of hours the contractor works. Find a formula for f -1 (x). What does f -1 (x) compute? A) f -1 (x) =

x - 158; This computes the number of hours worked if the total cost is x dollars. 25

B) f -1 (x) =

x - 3,950; This computes the total cost if the contractor works x hours. 25

C) f -1 (x) =

x - 3,950; This computes the number of hours worked if the total cost is x dollars. 25

D) f -1 (x) =

x - 158; This computes the total cost if the contractor works x hours. 25

Solve the equation. 202) log (x - 2) = 1 3 A) {5}

201)

202) B) {1}

C) {-1}

D) {3}

Solve the problem.

203) Suppose that f(x) = 2 x. What is f(3)? What point is on the graph of f? A) 8; (3, 2) B) 9; (2, 9) C) 8; (3, 8)

D) 9; (3, 9)

Decide whether or not the functions are inverses of each other. 204) f(x) = x + 9, domain [-9, ); g(x) = x2 + 9, domain (- , ) A) No B) Yes

204)

Decide whether the composite functions, f g and g f, are equal to x. x 205) f(x) = 3x, g(x) = 3 A) No, yes

B) No, no

C) Yes, no

205) D) Yes, yes

Find the domain of the function. 1 206) f(x) = ln x+3 A) (0, )

203)

206) B) (1, )

C) (3, )

D) (-3, )

Solve the problem. 207) An airline charter service charges a fare per person of $250 plus $30 for each unsold seat. The airplane holds 200 passengers. Let x represent the number of unsold seats and write an expression for the total revenue R for a charter flight. A) R(x) = 200(250 + 30x) or 50,000 + 6,000x B) R(x) = x(250 + 30x) or 250x + 30x2

207)

C) R(x) = (200 - x)(250 + 30x) or 50,000 + 5,750x - 30x2 D) R(x) = (200 - x)(250 + 30x) or 50,000 + 6,000x - 30x2

208) The pH of a solution ranges from 0 to 14. An acid has a pH less than 7. Pure water is neutral and has a pH of 7. The pH of a solution is given by pH = - log x where x represents the concentration of the hydrogen ions in the solution in moles per liter. Find the hydrogen ion concentration if the pH = 5. A) 1.61 B) 0.2 C) 105 D) 10-5 40

208)

Approximate the value using a calculator. Express answer rounded to three decimal places. 209) 4 3 A) 32.000

B) 6.928

C) 11.036

D) 9.000

209)

Determine i) the domain of the function, ii) the range of the function, iii) the domain of the inverse, and iv) the range of the inverse. 210) f(x) = 3x + 9 210) A) f(x): D is all real numbers, R = {y|y > 9}; f-1 (x): D is all real numbers, R = {y|y < 9}

B) f(x): D = {x|x > 3}, R = {y|y > 9}; f-1 (x): D = {x|x < 3}, R = {y|y < 9}

C) f(x): D is all real numbers, R is all real numbers; f-1 (x): D is all real numbers, R is all real numbers

D) f(x): D = {x|x > 3}, R is all real numbers; f-1 (x): D = {x|x < 3}, R is all real numbers

Use transformations to graph the function. Determine the domain, range, and horizontal asymptote of the function. 211) f(x) = -2 x+3 + 4 211)

A) domain of f: (- , ); range of f: (- , -4); horizontal asymptote: y = -4

B) domain of f: (- , ); range of f: (-4, ); horizontal asymptote: y = 4

C) domain of f: (- , ); range of f: (- , 4); horizontal asymptote: y = 4

D) domain of f: (- , ); range of f: (- , -4); horizontal asymptote: y = -4

The function f is one-to-one. Find its inverse. 212) f(x) = 6x - 2 x-2 x A) f-1 (x) = B) f-1 (x) = + 2 6 6

x C) f-1 (x) = - 2 6

Express as a single logarithm. 213) 5 log x - log y b b x5 A) log b y C) log

x+2 D) f-1 (x) = 6

213) B) log

5x b y

D) log

b b

x5 ÷ log

(x5 - y)

Solve the problem. 214) The pH of a chemical solution is given by the formula pH = -log10[H+ ]

214)

where [H+ ] is the concentration of hydrogen ions in moles per liter. Find the pH if the [H+] = 3.1 × 10-12.

A) 12.51

B) 11.49

C) 11.51

Find the amount that results from the investment. 215) $12,000 invested at 5% compounded quarterly after a period of 7 years A) $4,991.91 B) $16,991.91 C) $16,885.21 Solve the equation. 216) log (x + 2) + log (x - 4) = 3 3 3 A) {8} B) {-5} 217) 4 1 + 2x = 64 A) {1}

212)

D) 12.49

D) $16,782.13

215)

216)

B) {4}

C) {7}

D) {7, -5}

C) {16}

D) {-1}

217)

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator. log 144 218) e e2 A) e144 B) 12 C) 144 D) e12

218)

Use a graphing calculator to solve the equation. Round your answer to two decimal places. 219) ln(3x) = -x + 3 A) {4.5} B) {0.15} C) {3.15} D) {1.50}

219)

Determine i) the domain of the function, ii) the range of the function, iii) the domain of the inverse, and iv) the range of the inverse. 220) f(x) = 1 + 3x 220) A) f(x): D = x x 0 , R = y y 0 ; 1 f-1 (x): D = x x 0 , R = y y 3

B) f(x): D = x x -

1 ,R= y y 0 ; 3

1 f-1 (x): D is all real numbers, R = y y 3

C) f(x): D = x x -

1 ,R= y y 0 ; 3

1 f-1 (x): D = x x 0 , R = y y 3

D) f(x): D = x x -

1 , R is all real numbers; 3

1 f-1 (x): D is all real numbers, R = y y 3

Approximate the value using a calculator. Express answer rounded to three decimal places. 221) 5.52.75

221)

Solve the problem. 222) f(x) = log5(x + 8) and g(x) = log5 (x - 3).

222)

A) 108.642

B) 11,803.065

C) 260.813

Solve g(x) = 2. What point is on the graph of g? A) {25}, (25, 2) B) {2}, (2, 28)

C) {28}, (28, 2)

Decide whether the composite functions, f g and g f, are equal to x. 223) f(x) = x2 + 2 , g(x) = x - 2 A) No, yes

B) Yes, yes

C) Yes, no

D) 15.125

D) {22}, (22, 2)

D) No, no

Solve the problem. 224) The half-life of plutonium-234 is 9 hours. If 100 milligrams is present now, how much will be present in 3 days? (Round your answer to three decimal places.) A) 9.92 B) 57.435 C) 0.391 D) 79.369

223)

224)

225) During 1991, 200,000 people visited Rave Amusement Park. During 1997, the number had grown to 834,000. If the number of visitors to the park obeys the law of uninhibited growth, find the exponential growth function that models this data. A) f(t) = 200,000e0.238t B) f(t) = 634,000e0.238t

225)

226) The surface area of a balloon is given by S(r) = 4 r2 , where r is the radius of the balloon. If the radius is increasing with time t, as the balloon is being blown up, according to the formula 2 r(t) = t3 , t 0, find the surface area S as a function of the time t. 3

226)

C) f(t) = 634,000e0.248t

A) S(r(t)) =

16 3 t 9

Solve the equation. 227) 8 x - 4 = 164x 12 A) 13

D) f(t) = 200,000e0.248t

B) S(r(t)) =

4 6 t 9

C) S(r(t)) =

12 B) 5

16 6 t 9

4 C) 13

D) S(r(t)) =

16 9 t 9

4 D) 3

227)

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to two decimal places. 256.2 228) log 228) 3 A) 10.10 B) 0.10 C) 0.24 D) 5.05 Solve the equation. 229) log (x + 1) = -3 5 4.362862139e+15 A) 8.549802418e+15 C) -

229)

124 125

1.477743628e+15 2.849934139e+15

126 125

Find the effective rate of interest. 1 230) 6 % compounded monthly 4 A) 6.29%

230) B) 6.25%

C) 6.39%

D) 6.43%

Solve the problem.

1 231) Suppose that f(x) = 2 x. If f(x) = , what is x? 8

A) 2 Solve the equation. 232) 3,1254x - 2 = 1253x 10 A) 11

231)

B) 3

C) -2

D) -3

11 B) 10

11 C) 10

10 D) 11

Find the amount that results from the investment. 233) $1,000 invested at 10% compounded semiannually after a period of 11 years A) $2,785.96 B) $1,925.26 C) $2,853.12 44

D) $2,925.26

232)

233)

Solve the problem. 234) Find the amount in a savings account at the end of 10 years if the amount originally deposited is $1,000 and the interest rate is 7% compounded quarterly. Use: A = P 1 +

234)

r nt where: n

A = final amount P = $1,000 (the initial deposit) r = 7% = 0.07 (the annual rate of interest) n = 4 (the number of times interest is compounded each year) t = 10 (the duration of the deposit in years) A) $40,700.00 B) $1,189.44 C) $2,001.60

D) $2,201.76

235) The number of men dying of AIDS (in thousands) since 1987 is modeled by y = 17.3 + 10.06(ln x), where x represents the number of years after 1987. Use this model to predict the number of AIDS deaths among men in 1994. Express answer rounded to the nearest hundred men. A) 26,000 men B) 37,000 men C) 36,900 men D) 25,800 men Find a formula for the inverse of the function described below. 236) A size 48 dress in Country C is size 12 in Country D. A function that converts dress sizes in x Country C to those in Country D is f(x) = - 12. 2 A) f-1 (x) = 2(x - 12) C) f-1 (x) = x + 12

236)

B) f-1 (x) = 2x + 12 D) f-1 (x) = 2(x + 12)

Find functions f and g so that f g = H. 237) H(x) = 9x + 7 A) f(x) = - x ; g(x) = 9x + 7 C) f(x) = x; g(x) = 9x + 7

B) f(x) = -x ; D) f(x) = x ;

g(x) = 9x - 7 g(x) = 9x + 7

Solve the problem. 238) Which of the two rates would yield the larger amount in 1 year: 4.9% compounded monthly or 4.8% compounded daily? A) 4.9% compounded monthly B) 4.8% compounded daily C) They will yield the same amount. The function f is one-to-one. Find its inverse. 239) f(x) = 4x A) f-1 (x) = -4x

235)

4 B) f-1 (x) = x

x C) f-1 (x) = 4

237)

238)

239) D) f-1 (x) = 4x

Find the inverse function of f. State the domain and range of f. 3x - 2 240) f(x) = x+5

240)

A) f-1 (x) =

x+5 ; domain of f: {x x -5}; range of f: {y y 3x - 2

2 } 3

B) f-1 (x) =

5x + 2 ; domain of f: {x x -5}; range of f: {y y - 3} 3+x

C) f-1 (x) =

5x + 2 ; domain of f: {x x -5}; range of f: {y y 3} 3-x

D) f-1 (x) =

3x + 2 ; domain of f: {x x -5}; range of f: {y y 5} x-5

The function f is one-to-one. Find its inverse. 241) f(x) = (x - 3)3 A) f-1 (x) = C) f-1 (x) =

241) B) f-1 (x) =

x+3 3

D) f-1 (x) =

x-3

Solve the problem. 242) The logistic growth function f(t) =

520 1 + 6.4e-0.22t

3 3

x+3 x + 27

describes the population of a species of butterflies

242)

t months after they are introduced to a non-threatening habitat. What is the limiting size of the butterfly population that the habitat will sustain? A) 6 butterflies B) 70 butterflies C) 1,040 butterflies D) 520 butterflies

Use transformations to graph the function. Determine the domain, range, and horizontal asymptote of the function. 243) f(x) = 5 (x - 2) 243)

A) domain of f: (- , ); range of f:(- , 0) horizontal asymptote: y = 0

B) domain of f: (- , ); range of f:(0, ) horizontal asymptote: y = 0

C) domain of f: (- , ); range of f:(- , 0) horizontal asymptote: y = 0

D) domain of f: (- , ); range of f:(0, ) horizontal asymptote: y = 0

Solve the problem. 244) The bacteria in a 10-liter container double every 3 minutes. After 56 minutes the container is full. How long did it take to fill a quarter of the container? A) 42 min B) 14 min C) 28 min D) 50 min Decide whether or not the functions are inverses of each other. 1 245) f(x) = 6x - 6, g(x) = x + 1 6 A) No

244)

245) B) Yes

Write as the sum and/or difference of logarithms. Express powers as factors. mn 246) log 13 5

246)

1 1 log m + log n - log 5 13 13 13 2 2

1 1 1 log m · log n ÷ log 5 13 13 13 2 2 2

1 1 1 log m + log n - log 5 13 13 13 2 2 2

1 1 log mn - log 5 13 13 2 2

For the given functions f and g, find the requested composite function. Find (f g)(x). 247) f(x) = x + 3, g(x) = 8x - 7; A) 2 2x - 1 B) 2 2x + 1 C) 8 x - 4 47

247) D) 8 x + 3 - 7

Decide whether the composite functions, f g and g f, are equal to x. 248) f(x) = x + 1 , g(x) = x2 A) Yes, no

B) No, yes

C) Yes, yes

D) No, no

Find the inverse of the function and state its domain and range . 249) {(-3, 4), (-1, 5), (0, 2), (2, 6), (5, 7)} A) {(4, -3), (5, -1), (2, 0), (6, 2), (7, 5)} D = {2, 4, 5, 6, 7}; R = {-3, -1, 0, 2, 5} B) {(3, -4), (1, -5), (0, -2), (-2, -6), (-5, -7)}; D = {3, 1, 0, -2, -5}; R = {-7, -6, -5, -4, -2} C) {(-3, -4), (-1, -5), (0, -2), (2, -6), (5, -7)}; D = {-3, -1, 0, 2, 5}; R = {-7, -6, -5, -4, -2} D) {(3, 4), (1, 5), (0, 2), (-2, 6), (-5, 7)}; D = {3, 1, 0, -2, -5}; R = {2, 4, 5, 6, 7} Solve the problem. 250) The logistic growth model P(t) =

1 1 + 13.29e-0.786t

represents the proportion of the total market of a

248)

249)

250)

new product as it penetrates the market t years after introduction. When will the product have 75% of the market? A) 4.69 years B) 2.92 years C) 3.92 years D) 5.69 years

251) How much money needs to be invested now to get $2000 after 4 years at 8% compounded quarterly? Express your answer to the nearest dollar. A) $2746 B) $584 C) $1848 D) $1457

251)

252) Money magazine reports that the percentage of trading days in which the Dasdaq loses or gains 2% or 252) more has been increasing since 1995 indicating more volatility in the Dasdaq. Use a graphing utility to fit an exponential function to the data. Predict the percentage of trading days in 2001 having such swings in value. Year % of trading days 1995, 0 2 1996, 1 5 1997, 2 8 1998, 3 18 1999, 4 23 2000, 5 49 A) y = 1.278e0.611x, 92 days B) y = 2.353e0.610x, 91 days C) y = 1.849e0.531x, 76 days

D) y = 1.669x1.706, 46 days

253) The value of a particular investment follows a pattern of exponential growth. In the year 2000, you invested money in a money market account. The value of your investment t years after 2000 is given by the exponential growth model A = 8,400e0.052t. By what percentage is the account increasing each year? A) 5.8%

B) 5.3%

C) 5.7%

253)

D) 5.5%

254) Between 7:00 AM and 8:00 AM, trains arrive at a subway station at a rate of 5 trains per hour 254) (0.08 trains per minute). The following formula from statistics can be used to determine the probability that a train will arrive within t minutes of 7:00 AM. F(t) = 1 - e-0.08t Determine how many minutes are needed for the probability to reach 20%. A) 16.02 min B) 2.79 min C) 12.36 min

D) 7.05 min

Indicate whether the function is one-to-one. 255) {(-5, -9), (-4, -9), (-3, 3), (-2, 9)} A) Yes

255)

B) No

Suppose that ln 2 = a and ln 5 = b. Use properties of logarithms to write each logarithm in terms of a and b. 256) ln 10 A) ln a + ln b B) a - b C) ab D) a + b Solve the equation. 257) 4 x = 8 1 A) 3

2 B) 3

1 C) 2

3 D) 2

256)

257)

The graph of a one-to-one function f is given. Draw the graph of the inverse function f-1 as a dashed line or curve. 258) f(x) = x + 2 258)

Find the amount that results from the investment. 259) $480 invested at 12% compounded quarterly after a period of 7 years A) $1,098.21 B) $1,061.13 C) $618.21

D) $1,066.22

259)

Solve the problem. 260) pH = -log10[H+ ] Find the pH if the [H+] = 5 × 10-2 . A) 1.3

B) 2.3

260) C) 1.7

D) 2.7

Graph the function. 261) f(x) = 3 ln x

261)

Solve the equation. 262) 3 · 52t - 1 = 75 13 A) 10

1 C) 2

B) {3}

3 D) 2

Find the domain of the function. x+4 263) f(x) = log10 x-7 A) (- , -4)

(7, )

262)

263) B) (- , -4)

C) (7, )

D) (-4, 7)

Graph the function. 264) f(x) = 4 - e-0.39x

264)

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator. 265) ln e 7 A)

B) 49

C) 7

265)

D) e

Use transformations to graph the function. Determine the domain, range, and horizontal asymptote of the function.

266) f(x) = 5 -x + 4

266)

A) domain of f: (- , ); range of f:(5, ) horizontal asymptote: y = 5

B) domain of f: (- , ); range of f:(5, ) horizontal asymptote: y = 5

C) domain of f: (- , ); range of f:(4, ) horizontal asymptote: y = 4

D) domain of f: (- , ); range of f:(4, ) horizontal asymptote: y = 4

Solve the problem. 267) f(x) = log2(x + 9) and g(x) = log2 (x - 2).

267)

Solve f(x) for x = -1. What point is on the graph of f? A) {3}, (-1, 3) B) {3}, (8, 3) C) {3}, (3, -1)

Find the present value. Round to the nearest cent. 268) To get $10,000 after 3 years at 12% compounded monthly A) $8,874.49 B) $11,268.25 C) $3,333.33

D) {17}, (3, 17)

D) $6,989.25

268)

Solve the equation. 269) ln x + 2 = 7 A) {e14 + 2}

B) {e14 - 2}

269)

e7 +2 D) 2

C) {e7 - 2}

The function f is one-to-one. Find its inverse. 7 270) f(x) = 4x + 3 A) f-1 (x) =

7 - 3y 4y

B) f-1 (x) =

270) 7 - 3x 4x

C) f-1 (x) =

4x + 3 7

D) f-1 (x) =

3x - 7 4x

Solve the problem. 271) Conservationists tagged 80 black-nosed rabbits in a national forest in 1990. In 1,993, they tagged 160 black-nosed rabbits in the same range. If the rabbit population follows the exponential law, how many rabbits will be in the range 7 years from 1990? A) 403 B) 108 C) 215 D) 806 Use a graphing calculator to solve the equation. Round your answer to two decimal places. 272) ex - ln x = 3 A) {0.57}

B) {1.27}

Solve the problem. 273) The logistic growth function f(t) =

C) {2.17}

68,000 1 + 3,399.0e-1.5t

D) {1.14}

models the number of people who have

271)

272)

273)

become ill with a particular infection t weeks after its initial outbreak in a particular community. How many people became ill with this infection when the epidemic began? A) 3,400 people B) 20 people C) 3,399 people D) 68,000 people

Solve the equation. 274) 5 x = 24

A) {4.8}

B) {2}

C) {1}

D) {3}

Find the domain of the function. 275) f(x) = log(x + 6) A) (0, )

B) (6, )

C) (1, )

D) (-6, )

274)

275)

Graph the function and its inverse on the same Cartesian plane. 276) f(x) = log5 x

276)

Solve the equation. 5.497558139e+15 x+1 2 x-1 = 277) 1.407374884e+14 5 A) -

3 5

277) 3 5

C) -

3 10

D) -

6 5

Find the domain of the composite function f g. x 6 ; g(x) = 278) f(x) = x+6 x+2

278)

A) {x x -2, x -3} C) {x x 0, x -2, x -3}

B) {x x is any real number} D) {x x -2, x -6}

Write as the sum and/or difference of logarithms. Express powers as factors. (x + 7)(x - 9) 3/5 , x>9 279) ln (x - 1)3 A) 3ln (x + 7) - 5ln (x - 9) B)

279)

9 ln (x - 1) 5

3 9 ln (x2 + 16x - 63) - ln (x - 1) 5 5

C) ln (x + 7) + ln (x - 9) + ln 3 - 9ln (x - 1) - ln 5 3 3 9 D) ln (x + 7) + ln (x - 9) - ln (x - 1) 5 5 5 Suppose that ln 2 = a and ln 5 = b. Use properties of logarithms to write each logarithm in terms of a and b. 5 280) ln 2 A)

ln a ln b

a b

C) a + b

280)

D) b - a

Solve the problem. 281) A mechanic is testing the cooling system of a boat engine. He measures the engine's temperature over 281) time. Use a graphing utility to fit a logistic function to the data. What is the carrying capacity of the cooling system? time, min 5 10 15 20 25 temperature, °F 100 180 270 300 305 314.79 311.63 , 315°F , 312°F A) y = B) y = -1.22x 1 + 7.86e 1 + 8.1e-0.253x C) y =

314.79 1 + 7.86e-0.246x

, 315°F

D) y =

Graph the function. 1 x 282) f(x) = 4

306.53 1 + 7.92e-0.254x

, 307°F

282)

Solve the problem. 283) Sandy manages a ceramics shop and uses a 650°F kiln to fire ceramic greenware. After turning off 283) her kiln, she must wait until its temperature gauge reaches 170°F before opening it and removing the ceramic pieces. If room temperature is 80°F and the gauge reads 550°F in 7 minutes, how long must she wait before opening the kiln? Assume the kiln cools according to Newton's Law of Cooling: U = T + (Uo - T)ekt. (Round your answer to the nearest whole minute.) A) 237 minutes B) 43 minutes

C) 362 minutes

D) 67 minutes

Decide whether the composite functions, f g and g f, are equal to x. 5 284) f(x) = x - 13 , g(x) = x5 + 13 A) No, no B) Yes, yes C) Yes, no

D) No, yes

Find the effective rate of interest. 285) 12.25% compounded monthly A) 12.455% B) 12.962%

D) 13.155%

C) 12.373%

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator. 286) ln e 3 A) 3

B) e

D) 9

284)

285)

286)

Solve the equation. 287) 5 (7 + 3x) =

1 24

A) {6}

287) B) {3}

C) {-3}

1 4.8

Graph the function. 288) f(x) = 4 - e-x

288)

The Richter scale converts seismographic readings into numbers for measuring the magnitude of an earthquake x according to this function M(x) = log , where x 0 = 10-3 . x0

289) What is the magnitude of an earthquake whose seismographic reading is 7.8 millimeters at a distance of 100 kilometers from its epicenter? Round the answer to the nearest tenth. A) 3.9 B) 2.7 C) 2.9 D) 892.1 Solve the equation. 290) log 8 = x 2 A) {3}

289)

290) B) {4}

C) {10}

D) {16}

Find the domain of the composite function f g. 56 -3 ; g(x) = 291) f(x) = x x+8

291)

A) {x x 0, x -8, x -7} C) {x x -8, x 0}

B) {x x -8} D) {x x is any real number}

Decide whether or not the functions are inverses of each other. x-1 292) f(x) = 5x2 + 1, g(x) = 5 A) No C) Yes; No values need to be excluded.

292) B) Yes; Exclude the interval (- , 5) D) Yes; Exclude the interval (- , 1)

Solve the problem. 293) The population P of a predator mammal depends upon the number x of a smaller animal that is its primary food source. The population s of the smaller animal depends upon the amount a of a certain plant that is its primary food source. If P(x) = 2x2 + 2 and s(a) = 3a + 5, what is the

293)

relationship between the predator mammal and the plant food source? A) P(s(a)) = 18a2 + 60a + 52 B) P(s(a)) = 9a 2 + 30a + 27

D) P(s(a)) = 18a2 + 30a + 52

C) P(s(a)) = 6a + 7

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator. 294) log90 10 + log90 9

294)

Graph the function. 295) f(x) = 4 (x - 2) + 1.

295)

A) 90

B) 1

C) 9

D) 10

Solve the problem. 296) A thermometer reading 87°F is placed inside a cold storage room with a constant temperature of 38°F. If the thermometer reads 79°F in 15 minutes, how long before it reaches 60°F? Assume the cooling follows Newton's Law of Cooling: U = T + (Uo - T)ekt. (Round your answer to the nearest whole minute.) A) 67 minutes B) 27 minutes

C) -25 minutes

296)

D) 6 minutes

297) Tracey bought a diamond ring appraised at $1,200 at an antique store. If diamonds have appreciated in value at an annual rate of 12%, what was the value of the ring 9 years ago? (Round your answer to the nearest dollar.) A) $408 B) $3,328 C) $138 D) $433

297)

Solve the equation.

1 x+5 298) ex - 3 = e4

A) -

17 5

298) B)

8 5

C) -

Decide whether or not the functions are inverses of each other. 3 299) f(x) = x3 - 5, g(x) = x + 5 A) Yes B) No

8 3

D) -

23 3

299)

Find the inverse of the function and state its domain and range . 300) {(14, -12), (12, -11), (10, -10), (8, -9)} A) {(-11, -12), (-9, 10), (14, 10), (-11, -10)}; D = {-11, -9, 14}; R = {-12, 10, -10} 1 1 1 1 1 1 1 1 , 12, , 10, , 8, ; D = { 14, 12, 10, 8}, R = ,, ,B) 14, 12 11 10 9 12 11 10 9

300)

C) {(-12, 14), (-11, 12), (-10, 10), (-9, 8)}; D = {-12, -11, -10, -9 }; R = {14, 12, 10, 8} D) {(-11, -12), (-12, 10), (14, 12), (-11, -10)}; D = {(-11, -12, 14}; R = {(-12, 10 12, -10} Determine i) the domain of the function, ii) the range of the function, iii) the domain of the inverse, and iv) the range of the inverse. 3 301) f(x) = 301) 7x - 1

A) f(x): D is all real numbers, R is all real numbers; f-1 (x): D is all real numbers, R is all real numbers 3 ,R= y y -3 ; B) f(x): D = x x 7 3 7

f-1 (x): D = x x - 3 , R = y y

C) f(x): D = x x

1 ,R= y y 0 ; 7

f-1 (x): D = x x 0 , R = y y

D) f(x): D = x x -

1 7

1 ,R= y y 1 ; 7

1 f-1 (x): D = x x 1 , R = y y 7

Write as the sum and/or difference of logarithms. Express powers as factors. 11x 302) log w 4 A) log C) log

w w

11x - log 7x

B) log

D) log

w w

11 + log 11 + log

302) w w

x - log x + log

w w

4 4

Solve the problem. 303) f(x) = 4 x and g(x) = 14.

Find the point of intersection of the graphs of f and g by solving f(x) = g(x). A) (log4 14, 14) B) (14, 14) C) (log4 14, 4)

The function f is one-to-one. Find its inverse. 304) f(x) = 4x + 8 x-8 x+8 A) f(x) = B) f-1 (x) = 4 4

x+4 C) f-1 (x) = 8

303) D) (log4 14, 0)

x-8 D) f-1 (x) = 4

Approximate the value using a calculator. Express answer rounded to three decimal places. 305) e-1.4 A) 0.547

B) -3.806

C) -0.247

D) 0.247

304)

305)

Solve the problem. 306) Khang borrows $2,500 at a rate of 10.5% compounded monthly. Find how much Khang owes at the end of 4 years. Use: A = P 1 +

306)

r nt where: n

A = final amount P = $2,500 (the amount borrowed) r = 10.5% = 0.105 (the annual rate of interest) n = 12 (the number of times interest is compounded each year) t = 4 (the duration of the loan in years) A) $121,050.00 B) $3,797.96 C) $4,177.76

Graph the function. 5 x 307) f(x) = 3

D) $2,588.66

307)

Solve the problem. 308) A fossilized leaf contains 16% of its normal amount of carbon 14. How old is the fossil (to the nearest year)? Use 5600 years as the half-life of carbon 14. A) 35,732 B) 14,779 C) 22,360 D) 1,406 Solve the equation. 309) log11 x2 = 4 A) {2048}

309) B) {2 11, -2 11}

C) {121, -121}

D) {14,641}

Solve the problem. Round your answer to three decimals. 310) How long will it take for an investment to triple in value if it earns 4.75% compounded continuously? A) 26.022 years B) 23.129 years C) 11.564 years D) 14.593 years Decide whether or not the functions are inverses of each other. 1+x 1 , g(x) = 311) f(x) = x x-1 A) Yes

B) No

312)

B) 1

Solve the equation. 313) 4 ln 3x = 28 7 A) ln 3

310)

311)

Find the exact value of the logarithmic expression. 10 312) log 10 A) 10

308)

B) e 7/3

1 2

e7 3

1 10

313) D) {e7 }

Write as the sum and/or difference of logarithms. Express powers as factors. 9

314) log

16 13 s2 r

314)

1 log 16 - 2 log s - 2 log r 13 13 13 9

B) log

1 log 16 - 2 log s - log r 13 13 13 9

D) 9 log

Express as a single logarithm. 4 315) 28 log4 x + log4 (28x6 ) - log4 28 A) log4 x13/4 B) log4 x10/7

16 - log

s - log

16 - 2 log

s - log

315) C) log4 x11/6

D) log4 x13

C) {6}

D) {3, -3}

Solve the equation. 316) 2 x2 - 3= 64 A) { 35, -

316) 35}

Find the domain of the function. 317) f(x) = log9(36 - x2 ) A) (-36, 36)

B) {3}

317) B) ( , -6)

(6, )

C) [-6, 6]

D) (-6, 6)

Solve the problem. 318) f(x) = log3(x + 3) and g(x) = log3 (2x - 4). Solve f(x) = g(x). A) {7}, (7, log3 (3))

318)

B) {7}, (7, log3 (7))

C) {7}, (7, log3 (10))

D) No solution.

Find a formula for the inverse of the function described below. 319) A size 6 dress in Country C is size 44 in Country D. A function that converts dress sizes in Country C to those in Country D is f(x) = x + 38. x x A) f-1 (x) = x + 38 B) f-1 (x) = x - 38 C) f-1 (x) = D) f-1 (x) = 38 -38 Solve the equation. 320) e5x = 7 A)

ln 5 7

B) {5 ln 7}

321) log (4 + x) - log (x - 2) = log 3 1 A) B) {5} 2

ln 7 5

7 e 5

319)

320)

321) C) {-5}

Solve the problem.

322) Suppose that f(x) = 3 x + 1. What is f(5)? What point is on the graph of f? A) 243; (5, 243) B) 244; (5, 244) C) 244; (5, 243)

D) 243; (1, 243)

322)

Find the present value. Round to the nearest cent. 323) To get $2000 after 4 years at 12% compounded semiannually A) $1,271.04 B) $745.18 C) $1,330.11

D) $1,254.82

For the given functions f and g, find the requested composite function value. x-6 , g(x) = x2 + 9; Find (g f)(-2). 324) f(x) = x A)

145 16

B) 13

323)

324)

C) 25

7 13

Solve the problem. 325) In a town whose population is 3000, a disease creates an epidemic. The number of people, N, infected t325) days after the disease has begun is given by the function 3000 N(t) = . Find the number of infected people after 10 days. 1 + 21.2 e - 0.54t A) 2000 people.

B) 2737 people

Find the effective rate of interest. 326) 9.5% compounded quarterly A) 10.405% B) 9.705%

C) 1000 people

D) 142 people

C) 9.623%

D) 9.844%

Suppose that ln 2 = a and ln 5 = b. Use properties of logarithms to write each logarithm in terms of a and b. 327) ln 20 A) 4b B) 2a + b C) 2a + 2b D) a + b Solve the problem. 328) Larry has $1,800 to invest and needs $2,400 in 18 years. What annual rate of return will he need to get in order to accomplish his goal? (Round your answer to two decimals.) A) 1.31% B) 3.31% C) 2.31% D) 1.6% Write as the sum and/or difference of logarithms. Express powers as factors. 14 329) log 15 19 A) log C) log

15 15

14 ÷ log 14 - log

15 15

B) log

D) log

15 15

19 - log 14 + log

327)

328)

329) 15 15

14 14

Change the logarithmic expression to an equivalent expression involving an exponent. 330) log 16 = x 4 A) x4 = 16 B) 4 x = 16 C) 164 = x D) 16x = 4 Solve the equation. 1 x = 4,095 331) 8 A) {4}

326)

330)

331) B) -

1 4

C) {-4}

1 4

Change the logarithmic expression to an equivalent expression involving an exponent. 1 = -3 332) log 5 125 1 3 1 1 =5 A) B) 3 5 = C) 5 -3 = D) 5 125 = 3 125 125 125 Express as a single logarithm. 333) 3 log x + 5 log (x - 6) 6 6 A) 15 log x(x - 6) 6

332)

333) B) log

C) log

x(x - 6)

x(x - 6)15

D) log

x3(x - 6)5

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to two decimal places. 334) log2.5 59 334) A) 23.60

B) 0.22

C) 1.77

D) 4.45

The graph of a one-to-one function f is given. Draw the graph of the inverse function f-1 as a dashed line or curve. 335) f(x) = x3 + 1 335)

Solve the problem. 336) The function D(h) = 9e-0.4h can be used to determine the milligrams D of a certain drug in a patient's bloodstream h hours after the drug has been given. How many milligrams (to two decimals) will be present after 6 hours? A) 6.8 mg B) 0.16 mg C) 0.82 mg D) 99.21 mg

336)

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator. 337) eln 15 A) 14

B) e15

Solve the problem. 338) The logistic growth function f(t) =

C) ln 15

337)

D) 15

46,000 models the number of people who have become 1 + 765.7e-1.7t

338)

ill with a particular infection t weeks after its initial outbreak in a particular community. What is the limiting size of the population that becomes ill? A) 766 people B) 767 people C) 46,000 people D) 92,000 people

Solve the equation. 339) 5 x = 1 1 A) { } 5

339) B) {1}

C) {0}

Solve the problem. 340) A life insurance company uses the following rate table for annual premiums for women for term life 340) insurance. Use a graphing utility to fit an exponential function to the data. Predict the annual premium for a woman aged 70 years. Age 35 40 45 50 55 60 65 Premium $103 $133 $190 $255 $360 $503 $818 A) y = 6.367e0.068x, $743 B) y = 8.94e0.068x, $1044 D) y = 0.0000398x4.06, $1233

C) y = -9306.4 + 2516.3 ln (x), $1723

341) The long jump record, in feet, at a particular school can be modeled by f(x) = 20.2 + 2.5 ln (x + 1) where x is the number of years since records began to be kept at the school. What is the record for the long jump 23 years after record started being kept? Round your answer to the nearest tenth. A) 28.1 ft B) 22.7 ft C) 27.9 ft D) 28.0 ft

341)

The graph of a one-to-one function f is given. Draw the graph of the inverse function f-1 as a dashed line or curve. 7 342) f(x) = 342) x

B) Function is its own inverse

Solve the problem.

343) The size P of a small herbivore population at time t (in years) obeys the function P(t) = 600e0.2t if they have enough food and the predator population stays constant. After how many years will the population reach 2,400? A) 6.93 yrs B) 11.93 yrs C) 37.48 yrs D) 14.45 yrs

Decide whether or not the functions are inverses of each other. 3 2x + 3 , g(x) = 344) f(x) = x+2 x

343)

344)

A) Yes B) No C) Yes; Exclude the value {-2} Solve the problem. 345) The function A = Aoe-0.01155x models the amount in pounds of a particular radioactive material

stored in a concrete vault, where x is the number of years since the material was put into the vault. If 900 pounds of the material are placed in the vault, how much time will need to pass for only 142 pounds to remain? A) 320 years B) 165 years C) 160 years D) 170 years

345)

346) The logistic growth model P(t) =

920 represents the population of a bacterium in a 1 + 25.29e-0.358t

culture tube after t hours. When will the amount of bacteria be 800? A) 8.63 hours B) 14.32 hours C) 8.74 hours

346)

D) 3.05 hours

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to three decimal places. 72.8 347) log 347) 7 A) 0.227 B) 0.423 C) 2.203 D) 4.407 Solve the equation. 348) 3 x = 27 A) {4}

B) {2}

C) {9}

D) {3}

348)

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator. 349) log5 30 · log30 25

349)

The function f is one-to-one. Find its inverse. 350) f(x) = 7x2 - 7, x 0

350)

A) 25

A) f-1 (x) =

B) 5

C) 2

7 x+7

C) f-1 (x) = -

x+7 7

Graph the function. 351) f(x) = log (x + 2) 2

D) 30

B) f-1 (x) =

x+7 7

D) f-1 (x) =

7 x+7

351)

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator. 352) log7 711 A) 77

B) 11

C) 7

352)

D) 1

The function f is one-to-one. Find its inverse. 4x + 3 353) f(x) = 5 A) f-1 (x) =

5 4x - 3

B) f-1 (x) =

353) 5x - 3 4

C) f-1 (x) =

Find the exact value of the logarithmic expression. 354) log 100 10

D) f-1 (x) =

5 4x + 3

354)

A) 20 C)

5x + 3 4

B) 2

7.036874418e+13 7.036874418e+15

D) -2

Graph the function.

355) f(x) = 2 log

355)

Determine whether the given function is exponential or not. If it is exponential, identify the value of the base a. 356) 356) x H(x) 2 -1 0 8 1 14 2 20 3 26 A) Exponential; a = 2 B) Exponential; a = 6 C) Not exponential D) Exponential; a = 8

Find the present value. Round to the nearest cent. 357) To get $6500 after 3 years at 5% compounded quarterly A) $900.19 B) $5,669.80 C) $5,614.94

D) $5,599.81

Use a calculator to evaluate the expression. Round your answer to three decimal places 358) 5 ln 4

357)

358)

0.10

A) -2.526

B) -0.097

C) 2.231

D) 2.526

Approximate the value using a calculator. Express answer rounded to three decimal places. 359) 3 4.3

359)

The function f is one-to-one. Find its inverse. 360) f(x) = (x + 2)3 - 8.

360)

A) 12.900

B) 27.000

A) f-1 (x) = C) f-1 (x) =

3 3

C) 79.507

D) 112.622

x-2+8

B) f-1 (x) =

x+8-2

D) f-1 (x) =

3 3

x+6 x + 10

Solve the problem. 361) f(x) = log2(x + 1) and g(x) = log2 (x - 4).

361)

Solve f(x) = g(x). Do the graphs of f and g intersect? If so, where? A) {5}, (5, log2 (1)) B) {5}, (5, log2 (6))

C) {5}, (5, log2 (5))

D) No solution. No intersection.

Write as the sum and/or difference of logarithms. Express powers as factors. x2 362) log 6 y7 A) 2 log C)

x - 7 log

B) 7 log

2 x log 6 y 7

D) 2 log

6 6

y - 2 log x + 7 log

362) 6 6

x y

Solve the problem. 363) The formula P = 14.7e-0.21x gives the average atmospheric pressure, P, in pounds per square inch, at an altitude x, in miles above sea level. Find the average atmospheric pressure for an altitude of 2.3 miles. Round your answer to the nearest tenth. A) 7.8 lb/in.2 B) 9.1 lb/in.2 C) 8.4 lb/in.2 D) 11.0 lb/in.2 Decide whether the composite functions, f g and g f, are equal to x. 3 364) f(x) = x3 + 2, g(x) = x - 2 A) No, yes B) Yes, yes C) Yes, no

D) No, no

363)

364)

Find the domain of the composite function f g. 3 ; g(x) = x + 5 365) f(x) = x+7

365)

A) {x x -12} C) {x x -7}

B) {x x -7, x -5} D) {x x is any real number}

Solve the problem. 366) f(x) = 4 x + 1 and g(x) = 4 -x + 3 .

Find the point of intersection of the graphs of f and g by solving f(x) = g(x). A) (4, 1) B) (1, 4) C) (1, 16)

Change the exponential expression to an equivalent expression involving a logarithm. 367) 5 2 = x A) log

x=2

B) log

C) log

x=5

Graph the function. 368) f(x) = ex

5=2

366) D) (16, 1)

D) log

2=x

367)

368)

Solve the problem. Round your answer to three decimals. 369) How long will it take for an investment to double in value if it earns 9.5% compounded continuously? A) 7.296 years B) 7.569 years C) 11.564 years D) 3.648 years

369)

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to three decimal places. 266 370) log 370) 5.4 A) 2.425 B) 3.311 C) 0.302 D) 49.259 Solve the problem. 371) If Emery has $1,400 to invest at 7% per year compounded monthly, how long will it be before he has $2,700? If the compounding is continuous, how long will it be? (Round your answers to three decimal places.) A) 91.885 yrs, 9.668 yrs B) 9.41 yrs, 9.383 yrs C) 0.809 yrs, 0.782 yrs D) 0.119 yrs, 0.938 yrs

371)

Determine whether the given function is exponential or not. If it is exponential, identify the value of the base a. 372) 372) x H(x) 11 -1 5 0 1

1 5 11

25 121

1.374389535e+14 1.463449977e+15

11 5

B) Exponential; a =

C) Exponential; a = 5

D) Not exponential

A) Exponential; a =

5 11

Indicate whether the function is one-to-one. 373) {(6, 1), (11, 2), (9, 3), (7, 4)} A) Yes

373)

B) No

For the given functions f and g, find the requested composite function. Find (g f)(x). 374) f(x) = 4x2 + x + , g(x) = 3x - ; A) 12x2 + 9x + 18

B) 4x2 + 9x + 12

C) 12x2 + 9x + 12

D) 4x2 + 3x + 2

Solve the equation. Express irrational answers in exact form and as a decimal rounded to 3 decimal places. 375) ln x + ln (x + 5) = -2 -5 + 2 25 + e-2 2.514 A) B) -5 + 25 + 4e-2 0.054 2 C)

-5 +

25 + 4e-2 2

0.027

-5 -

25 + 4e-2 2

374)

375)

-5.027

Change the logarithmic expression to an equivalent expression involving an exponent. 376) log x = 3 2 A) 2 3 = x B) 2 x = 3 C) 3 2 = x D) x3 = 2

376)

Use a graphing calculator to solve the equation. Round your answer to two decimal places. 377) ex = x2 - 1

377)

Solve the equation. 378) e2x - 1 = (e6 )-x

378)

A) {2.54}

7 A) 3

B) {-0.71}

1 B) 8

C) {0}

D) {-1.15}

C) {0}

1 D) 4

Find the inverse. Determine whether the inverse represents a function. 379) {(6, -1), (1, 0), (-1, 1), (-3, 2)} A) {(-1, 6), (0, 1), (1, -1), (2, -3)}; not a function B) {(0, -1), (-1, -1), (6, 1), (0, 1)}; not a function C) {(-1, 6), (0, 1), (1, -1), (2, -3)}; a function D) {(0, -1), (2, -1), (6, -1), (0, 1)}; a function Find the effective rate of interest. 380) 12% compounded continuously A) 12.374% B) 12.089%

C) 12.451%

379)

D) 12.75%

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator. 381) log4 24 - log4 6 A) 4

B) 24

C) 6

D) 1

380)

381)

The function f is one-to-one. Find its inverse. 6x - 4 382) f(x) = -8x - 4

382)

A) f-1 (x) =

6x - 4 -8x - 4

B) f-1 (x) =

4x - 4 -8x - 6

C) f-1 (x) =

-8x - 6 4x - 4

D) f-1 (x) =

6x + 6 -8x - 4

Change the exponential expression to an equivalent expression involving a logarithm. 383) 12x = 144 A) log

144

B) log

x = 12

C) log

144 = 12

144 = x

D) log

144

12 = x

383)

Solve the problem. 384) After introducing an inhibitor into a culture of luminescent bacteria, a scientist monitors the luminosity384) produced by the culture. Use a graphing utility to fit a logarithmic function to the data. Predict the luminosity after 20 hours. Time, hrs 2 3 4 5 8 10 15 Luminosity 77.4 60.8 54.5 45.8 30.0 24.3 10.5 A) y = 112.97 - 45.97 ln (x), -24.74 B) y = 100.5 - 32.7 ln (x), 2.54 C) y = 107.55 - 41 ln (x), -15.27 D) y = 98.75 - 32.66 ln (x), 0.91 Find the domain of the composite function f g. 385) f(x) = 6x + 24; g(x) = x A) {x x -4 or x 0} C) {x x -4}

B) {x x is any real number} D) {x x 0}

Decide whether or not the functions are inverses of each other. x+6 386) f(x) = 6x - 3, g(x) = 3 A) No

387) 9 2x · 27(3 - x) = 9+

386) B) Yes

Solve the equation.

385)

1 9

87 9 ,

387) 6

B) {10}

C) {-11}

D) {-8}

Suppose that ln 2 = a and ln 5 = b. Use properties of logarithms to write each logarithm in terms of a and b. 388) ln 4 A) 2a B) a 2 C) 4a D) ab Find the domain of the composite function f g. 1 389) f(x) = x + 4; g(x) = x+3

388)

389)

A) {x x -3} C) {x x is any real number}

B) {x x -3, x -4} D) {x x -7} 75

Use the horizontal line test to determine whether the function is one-to-one. 390)

A) Yes

390)

B) No

Express as a single logarithm. 391) log x + log y c c x A) log c y

391) B) log (xy) c

C) log x · log y c c

D) log xy c

Decide whether the composite functions, f g and g f, are equal to x. x-6 , g(x) = 4x + 6 392) f(x) = 4 A) No, no

B) No, yes

C) Yes, yes

Indicate whether the function is one-to-one. 393) {(-9, 2), (-2, 9), (4, 6), (-4, -6)} A) Yes

392) D) Yes, no

B) No

Find functions f and g so that f g = H. 394) H(x) = |4 - 3x2 |

A) f(x) = 4 - 3|x|; g(x) = x2

B) f(x) = |x|; g(x) = 4 - 3x2

C) f(x) = x2 ; g(x) = 4 - 3|x|

8 5 2 log m + log n - log k 9 9 9 9 9 9

1 1 log m + log n - 2 log k 9 9 9 8 5

1 1 log m · log n ÷ 2 log k 9 9 9 8 5

m + 5 log

n - 2 log

394)

D) f(x) = 4 - 3x2 ; g(x) = |x|

Write as the sum and/or difference of logarithms. Express powers as factors. 8 5 m n 395) log 9 k2 A) 8 log

393)

395)

396) log

17 x y

A) log C) log

7 7

396)

17 +

1 log x - log y 7 7 2

B) log

1 log x 7 2

D) log

y - log

17 -

(17 x) - log y 7

17 ·

1 log m ÷ log y 7 7 2

Find the present value. Round to the nearest cent. 397) To get $25,000 after 11 years at 7% compounded semiannually A) $11,728.77 B) $12,139.27 C) $11,877.32

D) $13,271.23

Solve the problem. 398) A thermometer reading 12°C is brought into a room with a constant temperature of 20°C. If the thermometer reads 17°C after 3 minutes, what will it read after being in the room for 9 minutes? Assume the cooling follows Newton's Law of Cooling: U = T + (Uo - T)ekt. (Round your answer to two decimal places.) A) 19.58°C B) 20°C

C) 20.42°C

8x 3 - 12x

8x 3 + 12x

398)

D) 7.63°C

For the given functions f and g, find the requested composite function. 4 3 , g(x) = ; Find (f g)(x). 399) f(x) = x-6 2x A)

397)

399)

4x 3 - 12x

3x - 18 8x

The function f is one-to-one. Find its inverse. 7 400) f(x) = x-8

400)

A) f-1 (x) =

8x + 7 x

B) f-1 (x) =

-8 + 7x x

C) f-1 (x) =

-8 + 7x2 x

D) f-1 (x) =

x -8 + 7x

Find a formula for the inverse of the function described below. 401) A size 12 dress in Country C is size 64 in Country D. A function that converts dress sizes in Country C to those in Country D is f(x) = 2(x + 20). x x x - 20 - 20 + 20 A) f-1 (x) = B) f-1 (x) = C) f-1 (x) = D) f-1 (x) = x - 20 2 2 2 Solve the problem. 402) An oil well off the Gulf Coast is leaking, with the leak spreading oil over the surface of the gulf as a circle. At any time t, in minutes, after the beginning of the leak, the radius of the oil slick on the surface is r(t) = 3t ft. Find the area A of the oil slick as a function of time. A) A(r(t)) = 3 t2 B) A(r(t)) = 9 t C) A(r(t)) = 9t2 D) A(r(t)) = 9 t2

401)

402)

Indicate whether the function is one-to-one. 403) {(20, -18), (-11, -18), (5, -17)} A) Yes

B) No

Graph the function. 1 x ·5 . 404) f(x) = 5

403)

404)

Solve the problem. 405) The logistic growth model P(t) =

1,410 represents the population of a bacterium in a 1 + 27.2e-0.344t

405)

culture tube after t hours. What was the initial amount of bacteria in the population? A) 51 B) 49 C) 55 D) 50

Express as a single logarithm. 406) ( log x - log y) + 3 log z a a a xz 3 x A) log B) log a z3y a y

406) C) log

xz3 y

D) log

3xz y

Solve the problem. 407) Cindy will require $11,000 in 5 years to return to college to get an MBA degree. How much money should she ask her parents for now so that, if she invests it at 9% compounded continuously, she will have enough for school? (Round your answer to the nearest dollar.) A) $7,149 B) $7,014 C) $4,472 D) $17,251 408) If 8 x = 6,what does 8 -2x equal? A) -36

1 C) 12

B) 36

1 D) 36

409) Three bacteria are placed in a petri dish. The population will double every day. The formula for the number of bacteria in the dish on day t is N(t) = 3(3)t

where t is the number of days after the three bacteria are placed in the dish. How many bacteria are in the dish seven days after the three bacteria are placed in the dish? A) 12 B) 2,187 C) 648 D) 54

407)

408)

409)

Graph the function. 410) f(x) = 3ex

410)

Solve the problem. 411) The population of a particular country was 28 million in 1981; in 1989, it was 40 million. The exponential growth function A = 28ekt describes the population of this country t years after 1981.

Use the fact that 8 years after 1981 the population increased by 12 million to find k to three decimal places. A) 0.055 B) 0.311 C) 0.045 D) 0.878

411)

The function f is one-to-one. Find its inverse. 412) f(x) = x + 6 A) f-1 (x) = (x + 6)2

412) B) f-1 (x) =

D) f-1 (x) = x2 + 6, x 0

C) f-1 (x) = x2 - 6, x 0

Solve the equation. 413) 4 + 2 ln x = 9 A)

413)

e5 B) 2

5 2 ln 1

x-6

C) ln

5 2

D) {e 5/2 }

414) log

414)

(x - 3) = 1 - log x 10 10 A) {2} B) {-2}

C) {-5}

D) {5}

The function f is one-to-one. Find its inverse. 415) f(x) = x3 + 8 A) f-1 (x) =

x+8

B) f-1 (x) =

415) 3

C) f-1 (x) =

x-8

D) f-1 (x) =

Use a graphing calculator to solve the equation. Round your answer to two decimal places. 416) log2 x + log3 x = 3 A) {1.53}

417) log4 (x + 2) - log5 (x - 1) = 1 A) {1.75}

B) {4.13}

C) {0.55}

x+8

416)

D) {3.58} 417)

B) {2.00}

C) {2.05}

Solve the problem. Round your answer to three decimals. 418) What annual rate of interest is required to double an investment in 7 years? A) 16.993% B) 5.204% C) 9.902% For the given functions f and g, find the requested composite function value. Find (f g)(4). 419) f(x) = x + 3, g(x) = 5x; A) 6 0.97222222 B) 23 C) 56 0.97222222

D) {-0.69}

D) 10.409%

B) {2.65}

C) {2.27}

For the given functions f and g, find the requested composite function. 421) f(x) = 6x + 9, g(x) = 2x - 1; Find (f g)(x). A) 12x + 15 B) 12x + 8 C) 12x + 17

418)

419) D) 5 7

Use a graphing calculator to solve the equation. Round your answer to two decimal places. 420) e3x = x + 2 A) {0.65}

D) {0.27}

D) 12x + 3

420)

421)

Use the horizontal line test to determine whether the function is one-to-one. 422)

A) Yes

422)

B) No

Solve the equation. 1 2x + 4 = 9 x- 1 423) 3 A) -

1 2

424) 4 (3x - 7 ) = 16 1 A) 4

423) B) - 1

C) -

3 4

D) 3

424) B) {-3}

C) {3}

D) {4}

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator. 425) log3 21 - log3 7 A) 7

B) 1

C) 3

425)

D) 21

Approximate the value using a calculator. Express answer rounded to three decimal places. 426) 4.1 A) 109.223

B) 12.881

C) 36.462

D) 84.162

Write as the sum and/or difference of logarithms. Express powers as factors. 7 (3x) 1 + 4x , x>7 427) ln (x - 7)5 B) 3ln x +

A) ln 3 + ln x - 7ln (1 + 4x) - 5ln (x - 7) C) ln 3 + ln x +

1 ln (1 + 4x) - 5ln (x - 7) 7

426)

427)

4 ln (1 + 4x) - 5ln (x - 7) 7

D) ln 3 + ln x +

1 ln (1 + 4x) - ln 5 - ln (x - 7) 7

Solve the problem. 428) The function A = Aoe-0.0077x models the amount in pounds of a particular radioactive material

stored in a concrete vault, where x is the number of years since the material was put into the vault. If 900 pounds of the material are initially put into the vault, how many pounds will be left after 150 years? A) 283 pounds B) 750 pounds C) 594 pounds D) 270 pounds

428)

Find the exact value of the logarithmic expression. 429) ln e7 A) 1

429)

1 B) 7

C) 7

D) e

Solve the problem. 430) Find a so that the graph of f(x) = loga x contains the point (12, 16). A)

4 3

3 4

430) D)

Suppose that ln 2 = a and ln 5 = b. Use properties of logarithms to write each logarithm in terms of a and b. 7 431) ln 40 3 3 1 1 A) (a + b) B) (a - b) C) (a 3 + b) D) (3a + b) 7 7 7 7 For the given functions f and g, find the requested composite function. x-4 , g(x) = 6x + 4; Find (g f)(x). 432) f(x) = 6 A) x + 8

B) x -

2 3

C) 6x + 20

431)

432) D) x

Graph the function.

433) f(x) = -1 + ex

433)

434) f(x) = -1 + log

434)

The function f is one-to-one. Find its inverse. 435) f(x) = x2 + 4, x 0

435)

A) f-1 (x) = x - 4, x 0 C) f-1 (x) = x - 4, x 4

B) f-1 (x) = x + 4, x -4 D) f-1 (x) = x - 4, x < 0

Graph the function. 436) f(x) = 2 - x - 1

436)

For the given functions f and g, find the requested composite function value. t+ 3 ; Find (f g)(3). 437) f(t) = t4 + 6t2 + 9, g(t) = 3 A) 24

B) 7

C) 49

437) D) 5

The Richter scale converts seismographic readings into numbers for measuring the magnitude of an earthquake x according to this function M(x) = log , where x 0 = 10-3 . x0

438) What is the magnitude of an earthquake whose seismographic reading is 7.6 millimeters at a distance of 100 kilometers from its epicenter?Round the answer to four decimal places. A) 0.20281 B) 3.8808 C) 2.0281 D) 0.38808 Graph the function using a graphing utility and the Change-of-Base Formula. 439) y = log5 (x - 2)

438)

439)

Solve the problem. 440) A cup of coffee is heated to 194° and is then allowed to cool in a room whose air temperature is 72°.

440)

After 11 minutes, the temperature of the cup of coffee is 140°. Find the time needed for the coffee to cool to a temperature of 102°. Assume the cooling follows Newton's Law of Cooling: U = T + (Uo - T)ekt. (Round your answer to one decimal place.) A) 15.1 minutes B) 41.1 minutes

C) 26.4 minutes

D) 29.7 minutes

441) The rabbit population in a forest area grows at the rate of 4% monthly. If there are 300 rabbits in September, find how many rabbits (rounded to the nearest whole number) should be expected by next September. Use y = 300(2.7)0.04t A) 389

B) 470

C) 483

D) 496

Change the exponential expression to an equivalent expression involving a logarithm. 1 442) 5 -2 = 25 A) log

1 = -2 5 25

B) log

-2 =

1 25

C) log

Decide whether or not the functions are inverses of each other. 443) f(x) = (x - 3)2 , x 3; g(x) = x + 3 A) Yes

B) No

441)

1/25

5 = -2

442) D) log

1 =5 -2 25

443)

Solve the problem. 444) The accompanying tables represent a function f that converts seconds to hours and a function g that converts hours to days.

444)

x 86,400 172,800 259,200 345,600 432,000 f(x) 24 48 72 96 120 x 24 48 72 96 120 g(x) 1 2 3 4 5 Express (f -1 g -1 )(x) symbolically.

A) (f -1 g -1 )(x) = 86,400x2

B) (f -1 g -1 )(x) =

x2 86,400

C) (f -1 g -1 )(x) = 86,400x

D) (f -1 g -1 )(x) =

x 86,400

Solve the equation. 445) log (4x + 2) = log (4x + 7) 8 8 A) {5}

445) 9 5

C) {0}

Graph the function. 446) f(x) = e-x

446)

Find the domain of the composite function f g. 4 447) f(x) = x - 4; g(x) = x-6

447)

A) {x 6 < x 7} C) {x x 6, x 4}

B) {x x is any real number} D) {x x 4, x 6}

Find the exact value of the logarithmic expression. 1 448) log9 81 A) 9

448)

B) -2

C) -9

D) 2

Express as a single logarithm. 449) 3 loga (2x + 1) - 2 loga (2x - 1) + 2

449) a 2 (2x + 1)3 (2x - 1)2

A) loga 2(x + 1)

B) loga

C) loga (2x + 3)

D) loga (2x + 1) + 2

Solve the equation. Express irrational answers in exact form and as a decimal rounded to 3 decimal places. 7 x = 81 - x 450) 2 ln

7 + ln 8 2 ln 8

ln 8 7 ln + ln 8 2

Solve the equation. 451) log20 (x2 - x) = 1 A) {1, 20}

ln 56 ln 16

1.602

0.624

D) ln

450)

1.452

7 - ln 8 -0.827 2

451) B) {-4, 5}

C) {-4, -5} 89

D) {4, 5}

452) 2 + log3 (2x + 5) - log3 x = 4 A)

5 4

452) B)

1±

5 7

Solve the problem. 453) The half-life of silicon-32 is 710 years. If 90 grams is present now, how much will be present in 400 years? (Round your answer to three decimal places.) A) 1.813 B) 86.553 C) 0 D) 60.904 Find the domain of the function. 454) f(x) = ln x A) (- , 1)

B) (1, )

C) (- , 0)

Find the domain of the composite function f g. 455) f(x) = 6x + 42; g(x) = x + 2 A) {x x -9} C) {x x 9} Solve the problem. 456) The logistic growth function f(t) =

453)

454)

D) (0, )

455)

B) {x x is any real number} D) {x x -2, x -7}

640 describes the population of a species of butterflies 1 + 8.1e-0.22t

456)

t months after they are introduced to a non-threatening habitat. How many butterflies are expected in the habitat after 12 months? A) 840 butterflies B) 641 butterflies C) 405 butterflies D) 7,680 butterflies

The function f is one-to-one. Find its inverse. 3 457) f(x) = x - 3 A) f-1 (x) = x3 + 9

B) f-1 (x) = x3 + 3

C) f-1 (x) = x + 3

D) f-1 (x) =

457)

x3 + 3

Solve the problem.

1 458) Which of the two rates would yield the larger amount in 1 year: 9% compounded monthly or 9 % 4

458)

compounded annually? 1 A) 9 % compounded annually 4

B) 9% compounded monthly C) They will yield the same amount. Approximate the value using a calculator. Express answer rounded to three decimal places. 459) 5.9731.496 A) 14.494

B) 8.936

C) 43,271.096

D) 11.088

Solve the problem. 460) What principal invested at 8% compounded continuously for 4 years will yield $1190? Round the answer to two decimal places. A) $864.12 B) $1188.62 C) $1638.78 D) $627.48

459)

460)

461) In a Psychology class, the students were tested at the end of the course on a final exam. Then they were461) retested with an equivalent test at subsequent time intervals. Their average scores after t months are given in the table. Time, t ( in months) 1 2 Score, y ( in percentage) 86.2 85.7

3 85.4

4 85.2

5 85.0

Using a graphing utility, fit a logarithmic function y = a + b ln x to the data. Using the function you found, estimate how long will it take for the test scores to fall below 84%. Express your answer to the nearest month. A) 20 months B) 10 months C) 8 months D) 12 months

Use a graphing calculator to solve the equation. Round your answer to two decimal places. 462) ex = -x

462)

Solve the equation. 463) 3 (1 + 2x) = 27

463)

A) {1.05}

A) {-1}

B) {-0.57}

C) {0.57}

D) {-1.05}

B) {1}

C) {3}

D) {9}

Solve the problem. 464) A thermometer reading 36°F is brought into a room with a constant temperature of 70°F. If the thermometer reads 45°F after 4 minutes, what will it read after being in the room for 7 minutes? Assume the cooling follows Newton's Law of Cooling: U = T + (Uo - T)ekt. (Round your answer to two decimal places.) A) 66.05°F B) 89.85°F

Solve the equation. 465) log3 x + log3 (x - 24) = 4 A) {-3, 27}

C) 50.15°F

B) {53}

C) {27}

C) -1

D) 0

For the given functions f and g, find the requested composite function value. Find (f g)(11). 467) f(x) = 8x2 - 10x , g(x) = 11x - 3;

Solve the equation. 468) log5 (x2 - 4x) = 1 A) {5}

D) 30.79°F

465)

Find the exact value of the logarithmic expression. 466) ln e A) e B) 1

A) 100,777

464)

B) 9,435

C) 101,244

D) 110,212

466)

467)

468) B) {1}

C) {-5, 1}

D) {5, -1}

Use the graph of the given one-to-one function to sketch the graph of the inverse function. For convenience, the graph of y = x is also given.

469)

Solve the problem. 470) A nuclear scientist has a sample of 100 mg of a radioactive material which has a half-life in hours. 470) She monitors the amount of radioactive material over a period of a day and obtains the following data. Use a graphing utility to fit an exponential function to the data. Predict the amount of material remaining at 40 hours. Hours 0 5 10 15 20 25 30 . mg 100 68.3 45.2 31.3 21.5 14.6 9.8 A) y = 100e-0.077x, 6.7 mg B) y = 100e-0.077x, 4.6 mg C) y = 92e-0.0686x, 5.9 mg

D) y = 86e-0.071x, 5.0 mg

Find the exact value of the logarithmic expression. 471) ln l A) -1 B) 0

C) e

Find the domain of the composite function f g. 472) f(x) = x; g(x) = 3x + 9 A) {x x 0} C) {x x -3 or x 0}

B) {x x -3} D) {x x is any real number}

D) 1

Solve the problem. 473) How long does it take $1125 to triple if it is invested at 7% interest, compounded quarterly? Round your answer to the nearest tenth. A) 18.1 months B) 18.1 years C) 15.8 years D) 15.8 months Evaluate the expression using the values given in the table. 474) (g f)(1)

471)

472)

473)

474)

x 1 4 8 12 f(x) -1 8 0 12 x -5 -1 1 3 g(x) 1 -8 4 8 A) -8

B) 4

C) 8

For the given functions f and g, find the requested composite function value. Find (f f)(2). 475) f(x) = 2x + 4, g(x) = 4x2 + 5; A) 20

B) 261

C) 46

D) -1

D) 1,769

Solve the problem. 476) The function f(x) = 1 + 1.6 ln (x+1) models the average number of free-throws a basketball player can make consecutively during practice as a function of time, where x is the number of consecutive days the basketball player has practiced for two hours. After 22 days of practice, what is the average number of consecutive free throws the basketball player makes? A) 9 consecutive free throws B) 7 consecutive free throws C) 10 consecutive free throws D) 6 consecutive free throws 477) The formula A = 188e0.038t models the population of a particular city, in thousands, t years after 1998. When will the population of the city reach 332 thousand? A) 2016 B) 2015 C) 2014 D) 2013

475)

476)

477)

Use the horizontal line test to determine whether the function is one-to-one. 478)

A) Yes

478)

B) No

Solve the problem. 479) Find the amount owed at the end of 8 years if $5000 is loaned at a rate of 5% compounded monthly. A) $8060.16 B) $7452.93 C) $9093.60 D) $12,911.25

479)

The Richter scale converts seismographic readings into numbers for measuring the magnitude of an earthquake x according to this function M(x) = log , where x 0 = 10-3 . x0

480) Two earthquakes differ by 0.1 when measured on the Richter scale. How would the seismographic readings differ at a distance of 100 kilometers from the epicenter? A) The earthquake of greater magnitude has a seismographic reading that is 100.1 1.26 times

480)

that of the lesser earthquake.

B) The earthquake of greater magnitude has a seismographic reading that is 100.01 1.02 times that of the lesser earthquake. C) The earthquake of greater magnitude has a seismographic reading that is 100 times that of the lesser earthquake. D) The earthquake of greater magnitude has a seismographic reading that is 10 times that of the lesser earthquake. The function f is one-to-one. Find its inverse. 4 481) f(x) = x A) f-1 (x) =

x 4

Solve the equation. 482) log (x - 3) = 1 5 A) {8} 483) 2 x = A)

B) f-1 (x) =

481) 4 x

C) f-1 (x) = -4x

D) f-1 (x) = 4x

482) B) {4}

C) {-2}

D) {2}

1 8

483) 1 3

B) {-3}

C) {3}

1 4

484) (ex)x · e15 = e8x A) {-3, -5}

B) {3, 5}

C) {3}

For the given functions f and g, find the requested composite function. 485) f(x) = x + , g(x) = 4x + ; Find (g f)(x). A) 20x + 26 B) -20x + 35 C) -20x + 26

D) {5}

D) -20x - 14

484)

485)

Answer Key Testname: CHAPTER 6 1) A 2) B 3) D 4) B 5) A 6) D 7) A 8) C 9) B 10) A 11) B 12) B 13) D 14) A 15) C 16) D 17) B 18) B 19) B 20) B 21) 1999 22) $1643.18 23) $360,351.56 24) p = 25e-0.12q; 9 cassettes 25) 661 students 26) about 3.4 days 1 4 t + 4 t2 27) S(t) = 18

28) 6 years 29) $1252.91 30) 9901 years ln 2 9.90; about 14.9% 31) k = 0.07 32) 9 days 33) 4.84% 34) $6749 35) 26 days 36) $35,766.45 37) -7.26 1200 - 6p + 800 38) C = 40 39) 686 years 40) 5 panes 41) 989 years 42) 6 minutes

43) A = 100 · 4 d; 1,638,400 bacteria 44) 8 or -8 45) 51.37% 96

Answer Key Testname: CHAPTER 6 46) R(x) = 2000000 · 2 x-1 ; $16,000,000 47) about 1.2 hours 48) 43.2 deaths per 100,000 5 8 2 49) logb x + logb y - logb z 3 3 3 50) (f g)(x) = (-1 + 5x)2 ; Domain: all real numbers 51) exponential; y = 252.68 · 1.36x

52) 8.024 hours 53) in about 166.47 years or approximately the year 2158 54) 4 mg; 2 mg 1 55) x(P) = P + 250 2 56) The deceased died approximately 16 hours before the first measurement. 57) 14.18 watts 58) 16.71 F 59) $438.39 60) about 4.6 minutes 61) 2 62) 5 electronic organizers 63) (a) x 0 is one correct answer; another equally correct answer is x 0. (b) For the case x 0, the inverse is f-1 (x) = x + 5. For the case x 0, the inverse is f-1 (x) = -x - 5. 64) 13.9 years W - 1.27 3 ) 65) (a) V(W) = ( 3.34

(b) 0.01 1 4 t 66) V(t) = 3

67) A = 150e0.58t 68) D = 3 L-1 ; 81 distributors 69) D 70) A 71) B 72) D 73) A 74) D 75) A 76) D 77) A 78) A 79) C 80) D 81) D 82) A 83) A 84) D 85) B

Answer Key Testname: CHAPTER 6 86) A 87) A 88) A 89) D 90) B 91) A 92) A 93) B 94) C 95) C 96) B 97) D 98) C 99) C 100) D 101) B 102) C 103) B 104) C 105) D 106) C 107) C 108) D 109) C 110) C 111) A 112) B 113) C 114) B 115) A 116) B 117) C 118) A 119) B 120) B 121) A 122) D 123) B 124) B 125) D 126) A 127) C 128) A 129) A 130) D 131) C 132) A 133) D 134) C 135) C 98

Answer Key Testname: CHAPTER 6 136) B 137) C 138) C 139) B 140) A 141) A 142) A 143) D 144) C 145) D 146) B 147) B 148) A 149) B 150) B 151) B 152) B 153) A 154) C 155) C 156) D 157) A 158) C 159) A 160) C 161) A 162) D 163) D 164) B 165) B 166) A 167) D 168) B 169) C 170) B 171) B 172) A 173) A 174) B 175) D 176) D 177) A 178) B 179) D 180) A 181) D 182) D 183) B 184) B 185) C 99

Answer Key Testname: CHAPTER 6 186) D 187) B 188) A 189) D 190) D 191) B 192) B 193) C 194) D 195) C 196) B 197) D 198) C 199) B 200) B 201) A 202) A 203) C 204) A 205) D 206) D 207) C 208) D 209) C 210) C 211) C 212) D 213) A 214) C 215) B 216) C 217) A 218) B 219) D 220) C 221) A 222) C 223) D 224) C 225) A 226) C 227) A 228) A 229) C 230) D 231) D 232) A 233) D 234) C 235) C 100

Answer Key Testname: CHAPTER 6 236) D 237) D 238) A 239) C 240) C 241) B 242) D 243) B 244) D 245) B 246) C 247) A 248) D 249) A 250) A 251) D 252) B 253) B 254) B 255) B 256) D 257) D 258) B 259) A 260) A 261) C 262) D 263) A 264) D 265) A 266) C 267) A 268) D 269) B 270) B 271) A 272) D 273) B 274) B 275) D 276) D 277) A 278) A 279) D 280) D 281) C 282) B 283) D 284) B 285) B 101

Answer Key Testname: CHAPTER 6 286) C 287) C 288) B 289) A 290) A 291) B 292) D 293) A 294) B 295) C 296) A 297) D 298) A 299) A 300) C 301) C 302) B 303) A 304) D 305) D 306) B 307) C 308) B 309) C 310) B 311) A 312) C 313) C 314) C 315) D 316) D 317) D 318) C 319) B 320) C 321) B 322) B 323) D 324) C 325) B 326) D 327) B 328) D 329) C 330) B 331) C 332) C 333) D 334) D 335) A 102

Answer Key Testname: CHAPTER 6 336) C 337) D 338) C 339) C 340) B 341) A 342) B 343) A 344) B 345) C 346) B 347) D 348) D 349) C 350) B 351) B 352) B 353) B 354) B 355) A 356) C 357) D 358) C 359) D 360) C 361) D 362) A 363) B 364) B 365) A 366) C 367) A 368) B 369) A 370) B 371) B 372) B 373) A 374) C 375) C 376) A 377) D 378) B 379) C 380) D 381) D 382) B 383) C 384) D 385) D 103

Answer Key Testname: CHAPTER 6 386) A 387) C 388) A 389) A 390) A 391) D 392) C 393) A 394) B 395) C 396) A 397) A 398) A 399) A 400) A 401) A 402) D 403) B 404) A 405) D 406) A 407) B 408) D 409) B 410) A 411) C 412) C 413) D 414) D 415) B 416) D 417) B 418) D 419) B 420) D 421) D 422) A 423) A 424) C 425) B 426) D 427) C 428) A 429) C 430) D 431) D 432) D 433) B 434) B 435) C 104

Answer Key Testname: CHAPTER 6 436) C 437) B 438) B 439) D 440) C 441) C 442) A 443) B 444) C 445) D 446) B 447) A 448) B 449) B 450) C 451) B 452) D 453) D 454) D 455) B 456) C 457) B 458) B 459) A 460) A 461) A 462) B 463) B 464) C 465) C 466) B 467) D 468) D 469) C 470) B 471) B 472) B 473) C 474) A 475) A 476) D 477) D 478) B 479) B 480) A 481) B 482) A 483) B 484) B 485) C 105

Chapter 7 Exam Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Match the function to its graph. 1) y = -tan (x + ) A)

Answer the question. 2) Which one of the equations below matches the graph?

A) y = -2 cos 3x

B) y = 2 sin

1 x 3

C) y = -2 sin

1 x 3

D) y = -2 sin 3x

3) Which one of the equations below matches the graph?

A) y = 2 cos

1 x 4

B) y = 4 sin

1 x 2

C) y = 4 cos 2x

D) y = 4 cos

1 x 2

Match the function to its graph. 4) y = -tan x -

Answer the question. 5) Which one of the equations below matches the graph?

A) y = -2 sin

1 x 3

B) y = 2 cos

1 x 3

C) y = 2 sin

1 x 3

D) y = 2 cos 3x

Match the function to its graph. 6) y = -tan x +

Answer the question. 7) Which one of the equations below matches the graph?

A) y = 3 cos

1 x 4

C) y = 3 sin

B) y = -3 sin 4x

Match the function to its graph. 8) y = tan x A)

1 x 4

D) y = 3 cos 4x

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 9) Before exercising, an athlete measures her air flow and obtains 2 a = 0.65 sin t 5

where a is measured in liters per second and t is the time in seconds. If a > 0, the athlete is inhaling; if a < 0, the athlete is exhaling. The time to complete one complete inhalation/exhalation sequence is a respiratory cycle. What is the amplitude? What is the period? What is the respiratory cycle? Graph a over two periods beginning at t = 0.

10) A boy is flying a model airplane while standing on a straight line. The plane, at the end of 10) a twenty-five foot wire, flies in circles around the boy. The directed distance of the plane from the straight line is found to be 3 d = 25 cos t 4 where d is measured in feet and t is the time in seconds. If d > 0, the plane is in front of the boy; if d < 0, the plane is behind him. What is the amplitude? What is the period? Graph d over two periods beginning at t = 0.

11) Is the function f( ) = sin

+ cos

even, odd, or neither?

11)

12) The following data represents the average monthly minimum temperature for a certain city in 12) California. Average Monthly Minimum Month, x Temperature, °F January, 1 49.6 February, 2 50.8 March, 3 55.6 April, 4 57.5 May, 5 60.7 June, 6 63.6 July, 7 65.9 August, 8 65.6 September, 9 64.4 October, 10 62.1 November, 11 54.2 December, 12 50.1 Draw a scatter diagram of the data for one period. Find a sinusoidal function of the form y = A sin ( x - ) + B that fits the data. Draw the sinusoidal function on the scatter diagram. Use a graphing utility to find the sinusoidal function of best fit. Draw the sinusoidal function of best fit on the scatter diagram.

Find the exact value of the indicated trigonometric function of . 1 Find cos and tan . 13) sin = , sec < 0 6

13)

Solve the problem. 14) The following data represents the normal monthly precipitation for a certain city in Arkansas. 14) Normal Monthly Month, x Precipitation, inches January, 1 3.91 February, 2 4.36 March, 3 5.31 April, 4 6.21 May, 5 7.02 June, 6 7.84 July, 7 8.19 August, 8 8.06 September, 9 7.41 October, 10 6.30 November, 11 5.21 December, 12 4.28 Draw a scatter diagram of the data for one period. Find the sinusoidal function of the form y = A sin ( x - ) + B that fits the data. Draw the sinusoidal function on the scatter diagram. Use a graphing utility to find the sinusoidal function of best fit. Draw the sinusoidal function of best fit on the scatter diagram.

15) The following data represents the average percent of possible sunshine for a certain city in Indiana.

15)

Average Percent of Month, x Possible Sunshine January, 1 46 February, 2 51 March, 3 55 April, 4 60 May, 5 68 June, 6 73 July, 7 75 August, 8 74 September, 9 68 October, 10 62 November, 11 41 December, 12 38 Draw a scatter diagram of the data for one period. Find the sinusoidal function of the form y = A sin ( x - ) + B that fits the data. Draw the sinusoidal function on the scatter diagram. Use a graphing utility to find the sinusoidal function of best fit. Draw the sinusoidal function of best fit on the scatter diagram.

16) Wildlife management personnel use predator-prey equations to model the populations of certain predators and their prey in the wild. Suppose the population M of a predator after t months is given by M = 750 + 125 sin

16)

while the population N of its primary prey is given by N = 12,250 + 3050 cos

Calculate both M and N for t = 3, t = 15, and t = 27 months. Explain the answers in terms of reference angles. Without calculating them, what will be the values of M and N for t = 39 months?

17) Salt Lake City, Utah, is due north of Flagstaff, Arizona. Find the distance between Salt Lake City (40°45' north latitude) and Flagstaff (35°16' north latitude). Assume that the radius of the Earth is 3960 miles. Round to nearest whole mile. 8

17)

by 18) The displacement d, in inches, from equilibrium of a weight suspended from a spring is given 18) d = 1 + 2 sin(15t)° where t in time in seconds. Find the displacement when t = 0, 2, 4, 6, 8, 10, and 12 seconds. Do not use a calculator.

19) If cos

1 , find the exact value of (i) sin(90° - ) and (ii) csc ( - ). 6 2

19)

20) The following data represents the normal monthly precipitation for a certain city in California.20) Normal Monthly Month, x Precipitation, inches January, 1 6.06 February, 2 4.45 March, 3 4.38 April, 4 2.08 May, 5 1.27 June, 6 0.56 July, 7 0.17 August, 8 0.46 September, 9 0.91 October, 10 2.24 November, 11 5.21 December, 12 5.51 Draw a scatter diagram of the data for one period. Find a sinusoidal function of the form y = A sin ( x - ) + B that fits the data. Draw the sinusoidal function on the scatter diagram. Use a graphing utility to find the sinusoidal function of best fit. Draw the sinusoidal function of best fit on the scatter diagram.

21) Find the exact value of each of the six trigonometric functions of the angle P.

21)

22) Is the function f( ) = sin

+ tan

even, odd, or neither?

22)

by 23) The four Galilean moons of Jupiter have orbital periods and mean distances from Jupiter given23) the following table.

Io Europa Ganymeade Callisto

Distance (km) 4.214 × 105 6.709 × 105

1.070 × 106 1.883 × 106

Period (Earth hours) 42.460 85.243 171.709 400.536

Find the linear speed of each moon. Which is the fastest (in terms of linear speed)?

24) The current I, in amperes, flowing through an ac (alternating current) circuit at time t, in seconds, 24) is I = 30 sin(50 t) What is the amplitude? What is the period? Graph this function over two periods beginning at t = 0.

25) A study of ice cream consumption over 30 four-week periods in the early 1950s gives rise to the equation C = 0.3520 + 0.0786 sin(0.4806 - 0.1691) where is the number (from 1 to 30) of the four-week period and C is the ice cream consumption in pints per capita. Determine the consumption for the tenth four-week period. Round answer to the nearest 0.001 pint.

25)

Use the definition or identities to find the exact value of the indicated trigonometric function of the acute angle . 2 6 Find sin and tan . 26) cos = 26) 5 A point on the terminal side of angle 27) (5, 12) Find sin .

is given. Find the exact value of the indicated trigonometric function. 27)

Use the definition or identities to find the exact value of the indicated trigonometric function of the acute angle . Find the remaining five trigonometric functions of the acute angle . 28) tan = 2 6 28)

Solve the problem. 29) A mass hangs from a spring which oscillates up and down. The position P of the mass at time t29) is given by P = 4 cos(4t) What is the amplitude? What is the period? Graph this function over two periods beginning at t = 0.

30) A barge is located 200 feet away from the coastline 1200 feet down the coast from a power source at point A. To supply the barge with electricity, a power line will be run from point A to a point B on the coast and then from point B to the barge. If power lines on land coast $3 per foot and power lines under water cost $5 per foot, calculate the total cost of running a power line from point A to the barge when point B is 800 feet down the coast from point A in the direction of the barge. Recalculate the total cost when the distance from A to B is increased in 50-foot increments, until you locate a possible minimum cost. Interpret your solution.

30)

31) The data below represent the average monthly cost of natural gas in an Oregon home. Month Cost

Aug 18.90

Sep 24.24

Oct 44.58

Nov 68.25

Dec 91.92

Jan 109.26

Month Feb Cost 113.60

Mar 106.26

Apr 91.92

May 68.25

Jun 42.58

Jul 24.24

31)

Above is the graph of 47.35 sin x. Make a scatter diagram of the data. Find the sinusoidal function of the form y = A sin ( x - ) + B which fits the data.

32) Wildlife management personnel use predator-prey equations to model the populations of certain predators and their prey in the wild. Suppose the population M of a predator after t months is given by M = 750 + 125 sin

32)

while the population N of its primary prey is given by N = 12,250 + 3050 cos

Find the period for each of these functions.

33) The average daily temperature T of a city in the United States is approximated by 2 T = 55 - 23 cos (t -30) 365

33)

where t is in days, 1 t 365, and t = 1 corresponds to January 1. Find the period of T.

34) Determine the sign of the trigonometric values listed below. (i) sin 250° (ii) tan 330° (iii) cos(-40°)

34)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 35) For what numbers x, 0 x 2 , does sin x = 0? A) 0, , 2

B) 0, 1, 2

3 2

35) D) 0, 1

If A denotes the area of the sector of a circle of radius r formed by the central angle , find the missing quantity. If necessary, round the answer to two decimal places.

36) r = 5 inches,

radians, A = ?

A) 2.62 in2

36)

B) 1.31 in2

C) 6.54 in2

D) 13.08 in2

Solve the problem. 37) For a circle of radius 4 feet, find the arc length s subtended by a central angle of 60°. Round to the nearest hundredth. A) 4.40 ft B) 4.25 ft C) 4.19 ft D) 4.35 ft

37)

Match the given function to its graph. 38) 1) y = sin (x 3) y = sin (x +

2 2

)

2) y = cos (x +

)

4) y = cos (x -

2 2

38)

) )

A) 1C, 2A, 3B, 4D

B) 1B, 2D, 3C, 4A

C) 1A, 2B, 3C, 4D

D) 1A, 2D, 3C, 4B

Solve the problem. 39) If sin

A) -

1 , find csc . 9

1 9

39) B) 9

8 9

D) undefined

Use identities to find the exact value of the indicated trigonometric function of the acute angle . 7 3 , cos = Find cot . 40) sin = 4 4 A)

3 7 7

4 7 7

4 3

7 3

Solve the problem. 41) What is the range of the cotangent function? A) all real numbers B) all real numbers greater than or equal to 1 or less than or equal to -1 C) all real numbers, except integral multiples of (180)° D) all real numbers from -1 to 1, inclusive The point P on the circle x 2 + y2 = r2 that is also on the terminal side of an angle indicated trigonometric function. 42) (-2, -3) Find tan . 13 2 3 A) B) C) 2 3 2

40)

41)

in standard position is given. Find the

42) 13 2

Use a calculator to find the approximate value of the expression. Round the answer to two decimal places. 43) tan 37° A) 0.75 B) 0.60 C) 0.80 D) -0.84

43)

The point P on the circle x 2 + y2 = r2 that is also on the terminal side of an angle indicated trigonometric function. 44) (-3, -4) Find sin . 4 4 3 A) B) C) 5 5 5

44)

in standard position is given. Find the

3 D) 5

Use the even-odd properties to find the exact value of the expression. Do not use a calculator. 45) tan (-30°) 3 3 A) - 3 B) C) 3 D) 3 3 Solve the problem. 46) If f( ) = cos A) -

1 4

and f(a) =

1 , find the exact value of f(-a). 4

3 4

C) -

45)

46) 3 4

1 4

47) For the equation y = -

1 sin(4x + 3 ), identify (i) the amplitude, (ii) the phase shift, and (iii) the 2

period.

A) (i) 2

(ii) 3

1 2

(ii) -

C) (i)

(iii) 3 4

B) (i)

(iii) 4

1 2

D) (i) -

1 2

(ii) -

3 4

(iii)

(ii) -

4 3

(iii) 4

47)

If A denotes the area of the sector of a circle of radius r formed by the central angle , find the missing quantity. If necessary, round the answer to two decimal places. 48) r = 30.7 feet, = 13.721°, A = ? 48) 2 2 2 2 A) 228.7 ft B) 115.85 ft C) 112.85 ft D) 225.7 ft

Find the exact value of the expression if Find [f( )]2 . 49) f( ) = sin 3 A) 4

= 30°. Do not use a calculator. 1 C) 2

B) 1

1 D) 4

Solve the problem. 50) The blade of a windshield wiper sweeps out an angle of 135° in one cycle. The base of the blade is 12 inches from the pivot point and the tip is 32 inches from the pivot point. What area does the wiper cover in one cycle? (Round to the nearest 0.1 square inch.) A) 1041.8 in2 B) 1105.3 in2 C) 1036.7 in2 D) 948.3 in2

49)

50)

Graph the function. 51) y = -2 tan x +

51)

52) y = 2 sec (6x)

52)

The point P on the unit circle that corresponds to a real number t is given. Find the indicated trigonometric function. 3 55 Find cos t. 53) , 53) 8 8 A) -

3 8

55 8

3 8

Convert the angle in degrees to radians. Express the answer as multiple of . 54) 162° 9 10 10 A) B) C) 10 9 11 Graph the function.

D) -

8 D) 9

55 8

54)

55) y = tan x -

55)

Use the even-odd properties to find the exact value of the expression. Do not use a calculator. 56) sec (-30°) 2 3 2 3 A) 2 B) C) D) -2 3 3

56)

Without graphing the function, determine its amplitude or period as requested. 57) y = 4 cos x Find the period. A) 4

57) D) 2

Find the phase shift of the function. 58) y = -4 sin x -

58)

A) -4 units down C)

B) -4 units up

units to the left

Name the quadrant in which the angle lies. 59) cot > 0, sin < 0 A) I B) II

units to the right

C) III

Solve the problem. 60) For what numbers x, 0 x 2 , does cos x = -1? A)

3 C) , 2 2

D) IV

59)

60) D) none

A point on the terminal side of angle is given. Find the exact value of the indicated trigonometric function. 61) (-3, -2) Find sec . 61) 13 3 13 13 2 A) B) C) D) 2 13 3 3 Find the exact value of the expression if f( ) Find . 62) f( ) = sin 5 A) 10 2

= 45°. Do not use a calculator. 62) 2 5

Find the reference angle of the given angle. 63) -60° A) 60° B) 30° Find the exact value of the expression if g( ) Find . 64) g( ) = cos 12 A)

1 24

5 2 2

C) 150°

2 10

D) 120°

63)

= 60°. Do not use a calculator. 64) 3 24

C) 24 3

3 6

Solve the problem. 65) What is the range of the sine function? A) all real numbers greater than or equal to 0 B) all real numbers greater than or equal to 1 or less than or equal to -1 C) all real numbers from -1 to 1, inclusive D) all real numbers Use transformations to graph the function. 66) y = 3 sin ( - x)

65)

66)

Find the reference angle of the given angle. 67) 126° A) 64° B) 46° Solve the problem. 68) Given sin 30° =

C) 54°

D) 36°

1 , use trigonometric identities to find the exact value of csc . 2 6

A) 3 3

3 3

2 3

Find the exact value of the expression if = 45°. Do not use a calculator. 69) f( ) = csc Find f( ). 2 A) B) 2 C) - 2 2

67)

68) D)

2 3 3

69) D) 2

If A denotes the area of the sector of a circle of radius r formed by the central angle , find the missing quantity. If necessary, round the answer to two decimal places.

70) r = 62.4 centimeters, A) 324.5 cm2

radians, A = ?

70)

B) 2,038.8 cm2

C) 1,019.4 cm2

Graph the sinusoidal function. 71) y = -3 cos ( x)

D) 16.3 cm2

71)

Convert the angle to a decimal in degrees. Round the answer to two decimal places. 72) 23°47'37'' A) 23.52° B) 23.84° C) 23.94°

D) 23.79°

Find an equation for the graph. 73)

A) y = 5 cos

1 x 3

72)

73)

B) y = -5 sin

2 x 3

C) y = -5 sin

1 x 3

D) y = -5 sin (3x)

Find the reference angle of the given angle. 74) -517° A) 67° B) 157°

C) 23°

D) 113°

Name the quadrant in which the angle lies. 75) cos > 0, csc < 0 A) I B) II

C) III

D) IV

Find the exact value of the expression. Do not use a calculator. 76) cos 60° + tan 60° 3 3 1+2 3 A) B) 2 3 C) 2 2

74)

75)

76) D)

1+ 3 2

Find the exact value of the expression if Find [g( )]2 . 77) g( ) = cos 3

= 60°. Do not use a calculator. 77)

1 B) 4

3 D) 2

3 C) 4

Use the reference angle to find the exact value of the expression. Do not use a calculator. -3 78) tan 4 A) -1

3 3

78) D) 1

The point P on the unit circle that corresponds to a real number t is given. Find the indicated trigonometric function. 77 2 , Find cot t. 79) 79) 9 9 A) -

9 2

B) -

77 2

2 9

77 9

Solve the problem. 80) What is the y-intercept of y = sin x? A)

80)

B) 1

C) 0

81) John (whose line of sight is 6 ft above horizontal) is trying to estimate the height of a tall oak tree. He first measures the angle of elevation from where he is looking as 35°. He walks 30 feet closer to the tree and finds that the angle of elevation has increased by 12°. Estimate the height of the tree rounded to the nearest whole number. A) 86 ft B) 67 ft C) 90 ft D) 61 ft Without graphing the function, determine its amplitude or period as requested. 1 Find the amplitude. 82) y = 4 cos x 3 A)

4 3

B) 4

C) 6

81)

82) D)

Convert the angle in radians to degrees. Express the answer in decimal form, rounded to two decimal places. 83) 9.07 83) A) 0.16° B) 0.03° C) 519.67° D) 520.32° Graph the function.

84) y = -sec x

84)

The point P on the circle x 2 + y2 = r2 that is also on the terminal side of an angle indicated trigonometric function. 85) (-4, -1) Find csc . A) 17 B) -4 C) -17

in standard position is given. Find the

85) D) - 17

Use the definition or identities to find the exact value of the indicated trigonometric function of the acute angle . Find cos . 86) tan = 3 86) 3 3 1 A) 2 B) C) D) 2 3 2 Solve the problem. 87) If f(x) = sin x and f(a) = A) -

1 6

1 , find the exact value of f(a) + f(a - 4 ) + f(a - 2 ). 9

B) -

1 3

1 6

87) D)

1 3

88) The force acting on a pendulum to bring it to its perpendicular resting point is called the restoring force.88) The restoring force F, in Newtons, acting on a string pendulum is given by the formula F = mg sin where m is the mass in kilograms of the pendulum's bob, g 9.8 meters per second per second is the acceleration due to gravity, and is angle at which the pendulum is displaced from the perpendicular. What is the value of the restoring force when m = 0.8 kilogram and = 45°? If necessary, round the answer to the nearest tenth of a Newton. A) 6.7 N B) 5.3 N C) 5.5 N D) 5.2 N Graph the sinusoidal function. 89) y = 2 sin (3x)

89)

Solve the problem. 90) If f( ) = cot and f(a) = -4, find the exact value of f(a) + f(a + ) + f(a + 3 ). A) -12 + 4 B) -12 C) -4 91) Given cos 30° = A)

3 , use trigonometric identities to find the exact value of sin2 30°. 2

1 2

A point on the terminal side of angle 1 3 Find cot . 92) - , 2 2 A) - 3

D) undefined

B) 3

1 4

90)

91)

D) 1

is given. Find the exact value of the indicated trigonometric function. 92) B) -2

2 3 3

D) -

3 3

Solve the problem. 93) For a circle of radius 4 feet, find the arc length s subtended by a central angle of 30°. Round to the nearest hundredth. A) 2.09 ft B) 6.28 ft C) 376.99 ft D) 4.19 ft Use a coterminal angle to find the exact value of the expression. Do not use a calculator. 94) cot -300° 3 3 A) B) - 3 C) D) 3 2 Find the reference angle of the given angle. 95) 363° A) 87° B) 93°

C) 3°

94) 3

D) 177°

Solve the problem. 96) From the edge of a 1000-foot cliff, the angles of depression to two cars in the valley below are 21° and 28°. How far apart are the cars? Round your answers to the nearest 0.1 ft. A) 714.4 ft B) 724.4 ft C) 724.5 ft D) 713.4 ft

93)

95)

96)

Use a coterminal angle to find the exact value of the expression. Do not use a calculator. 97) csc -360° A) 0 B) -1 C) 1 D) undefined Find an equation for the graph. 98)

98)

A) y = -4 cos (2x)

C) y = 4 cos

B) y = 4 sin (2x)

1 x 2

D) y = 4 cos (2x)

Solve the problem. 99) If tan = -7.7, find the value of tan + tan ( + ) + tan ( + 2 ). A) -21.1 B) -23.1 C) -23.1 + 3

D) undefined

Find the exact value of the indicated trigonometric function of . 4 Find sin . 100) cos = , tan < 0 9 A) -

97)

9 4

B) -

65 9

99)

100)

C) - 65

D) -

65 4

Solve the problem. 101) An experiment in a wind tunnel generates cyclic waves. The following data is collected for 60 seconds:

101)

Time Wind speed (in seconds)(in feet per second) 0 22 15 44 30 66 45 44 60 22 Let V represent the wind speed (velocity) in feet per second and let t represent the time in seconds. Write a sine equation that describes the wave.

A) V = 44 sin (60t - 30) + 22

B) V = 66 sin(60t - 30) + 22

C) V = 66 sin

D) V = 22 sin

+ 22

+ 44

102) The minute hand of a clock is 7 inches long. How far does the tip of the minute hand move in 20 minutes? If necessary, round the answer to two decimal places. A) 15.89 in. B) 14.66 in. C) 12.92 in. D) 17.17 in. Draw the angle. 103) 330° A)

102)

103)

Use the even-odd properties to find the exact value of the expression. Do not use a calculator. 104) cos (-30°) 3 3 1 1 A) B) C) D) 2 2 2 2

104)

Two sides of a right triangle ABC (C is the right angle) are given. Find the indicated trigonometric function of the given angle. Give exact answers with rational denominators. 105) Find sin A when a = 5 and b = 9. 105) 106 9 106 106 5 106 A) B) C) D) 5 106 9 106

Solve the problem. 106) Which of the following trigonometric values are negative? I. sin(-292°) II. tan(-193°) III. cos(-207°) IV. cot 222° A) III only B) I and III C) II, III, and IV

106)

D) II and III

Draw the angle. 107) -120° A)

107)

Find the reference angle of the given angle. 13 108) 12 A)

108) C)

11 12

13 12

Find the exact value of the expression. Do not use a calculator. 109) cot

- cos

109)

2 3-3 2 6

B) -

6 2

C) -

3 6

Without graphing the function, determine its amplitude or period as requested. 110) y = 3 sin 2x Find the amplitude. 3 A) 3 B) C) 2 2

110) D)

Use a calculator to find the approximate value of the expression. Round the answer to two decimal places. 111) cot 0.2039 A) 0.21 B) 0.98 C) 1.02 D) 4.84 Graph the function.

111)

112) y = -cot x -

112)

A point on the terminal side of angle 1 1 Find cos . 113) - , 5 3 A) -

3 34 34

is given. Find the exact value of the indicated trigonometric function. 113) B) -

34 5

5 34 34

34 3

Find the exact value of the expression if = 60°. Do not use a calculator. 114) g( ) = cos Find 7 g( ). 3 7 3 1 A) B) C) 2 2 2

114) D)

7 2

Find the phase shift of the function. 1 115) y = -5 cos x + 4 4 A) C)

115)

units to the right

units to the left

D) 5 units to the right

units to the left

Use identities to find the exact value of the indicated trigonometric function of the acute angle . 2 2 1 , cos = Find tan . 116) sin = 3 3 A)

3 2 4

B) 3

2 4

116)

D) 2 2

Solve the problem. by 117) If friction is ignored, the time t (in seconds) required for a block to slide down an inclined plane is given117) the formula 2a t= g sin cos where a is the length (in feet) of the base and g 32 feet per second per second is the acceleration of gravity. How long does it take a block to slide down an inclined plane with base a = 9 when = 60°? If necessary, round the answer to the nearest tenth of a second. A) 1.4 sec B) 1.1 sec C) 0.3 sec D) 1 sec

Convert the angle in radians to degrees. 118)

118)

A) 36 °

B) 36°

C) 5°

D) 1°

Use a calculator to find the approximate value of the expression. Round the answer to two decimal places. 119) sin 65° A) 0.83 B) 0.94 C) 0.80 D) 0.91 Find the length s. Round the answer to three decimal places. 120)

120)

s 40°

A) 3.351 cm

6 cm

B) 4.608 cm

C) 4.189 cm

119)

D) 3.77 cm

Without graphing the function, determine its amplitude or period as requested. 121) y = cos 3x Find the period. 2 A) 2 B) 1 C) 3 Solve the problem. 122) Given cot = 4 , use trigonometric identities to find the exact value of tan . 17 1 A) B) C) 17 4 4

121) D) 3

122) D) 2

Use Fundamental Identities and/or the Complementary Angle Theorem to find the exact value of the expression. Do not use a calculator.

123) If tan

= 3, find the exact value of cot

A) 4

123)

1 3

C) 2

D) 3

Convert the angle in degrees to radians. Express the answer as multiple of . 124) 6° A)

Graph the function. Show at least one period. 125) y = 4 sin(-2x - )

124) D)

125)

Find the exact value of the expression. Do not use a calculator. 5 126) sin (3 ) + cos 2 A) -1

B) -2

126) C) 0

Graph the function. x 3 + 127) y = csc 5 5

D) 1

127)

The point P on the unit circle that corresponds to a real number t is given. Find the indicated trigonometric function. 21 2 , Find cos t. 128) 128) 5 5 A) -

21 2

B) -

Solve the problem. 129) If cos = -0.5, find the value of cos A) -1.5 B) 0.5

21 5

2 5

+ cos ( + 2 ) + cos ( + 4 ). C) -0.5

D) -

5 21 21

D) -1.5 + 6

Find the area A. Round the answer to three decimal places. 130)

130)

A) 20 yd2

10 yd

129)

B) 3.142 yd2

C) 62.832 yd2

D) 31.416 yd2

Find an equation for the graph. 131)

A) y = 2 sin

1 x 3

131)

B) y = 2 sin (3x)

C) y = 3 sin (2x)

Match the given function to its graph. 132) 1) y = 1 + sin x 2) y = 1 + cos x 3) y = -1 + sin x 4) y = -1 + cos x A

D) y = 3 sin

1 x 2

132) B

A) 1A, 2D, 3C, 4B

B) 1A, 2C, 3D, 4B

C) 1A, 2B, 3C, 4D

D) 1B, 2D, 3C, 4A

Convert the angle in degrees to radians. Express the answer as multiple of . 133) 87° 29 29 29 A) B) C) 30 120 90

29 D) 60

Find the exact value of the indicated trigonometric function of . 7 in quadrant III Find cot . 134) csc = - , 4 A) -

33 7

B) -

7 33 33

134) 33 4

D) -

4 33 33

Use a coterminal angle to find the exact value of the expression. Do not use a calculator. 135) cos 405° 2 2 1 1 A) B) C) D) 2 2 2 2 Match the given function to its graph. 1 1 2) y = cos x 136) 1) y = sin ( x) 3 3 3) y =

1 sin x 3

135)

136)

1 4) y = cos ( x) 3

A) 1A, 2B, 3C, 4D

133)

B) 1A, 2D, 3C, 4B

C) 1B, 2D, 3C, 4A

Graph the function. 36

D) 1A, 2C, 3D, 4B

137) y = 4 tan

1 x 2

137)

If A denotes the area of the sector of a circle of radius r formed by the central angle , find the missing quantity. If necessary, round the answer to two decimal places. 138) r = 12 inches, = 30°, A = ? 138) 2 2 2 2 A) 37.68 in B) 3.14 in C) 6.28 in D) 75.36 in

Solve the problem. 139) Find tan P.

A) tan P =

139)

4 5

B) tan P =

3 5

C) tan P =

3 4

Find the exact value of the expression if = 30°. Do not use a calculator. 140) f( ) = cos Find 11 f( ). 3 11 1 A) B) C) 2 2 2

D) tan P =

4 3

140) D)

11 3 2

Match the given function to its graph. 141) 1) y = -2 sin ( x) 2

1 2) y = -2 sin ( x) 2

3) y = -2 cos (

1 4) y = -2 cos ( x) 2

141)

A) 1B, 2D, 3A, 4C

B) 1C, 2A, 3D, 4B

C) 1A, 2C, 3B, 4D

D) 1A, 2C, 3D, 4B

Use Fundamental Identities and/or the Complementary Angle Theorem to find the exact value of the expression. Do not use a calculator. sec 50° 142) 142) csc 40°

A) 0

B) -1

C) 1

D) undefined

Convert the angle in radians to degrees. 143)

143)

A) 30°

B) 1080°

C) 60°

Name the quadrant in which the angle lies. 144) cot < 0, cos > 0 A) I B) II

C) III

Convert the angle to a decimal in degrees. Round the answer to two decimal places. 145) 106°18'35'' A) 106.27° B) 106.37° C) 106.31°

D) 15°

D) IV

D) 106.32°

Draw the angle. 7 146) 6

144)

145)

146)

Solve the problem. 147) A car is traveling at 37 mph. If its tires have a diameter of 25 inches, how fast are the car's tires turning? Express the answer in revolutions per minute. If necessary, round to two decimal places. A) 490.48 rpm B) 497.48 rpm C) 3,125.76 rpm D) 994.96 rpm 39

147)

148) A weight hangs from a rope 20 feet long. It swings through an angle of 27° each second. How far does the weight travel each second? Round to the nearest 0.1 foot. A) 9.4 feet B) 8.1 feet C) 9.0 feet D) 8.7 feet

148)

149) Given the approximation sin 38° 0.62, use trigonometric identities to find the approximate value of cos 38°. Round the answer to two decimal places. A) 0.78 B) 0.62 C) 1.27 D) 0.79

149)

Use transformations to graph the function. 150) y = -3 cos x

150)

Convert the angle in degrees to radians. Express the answer as multiple of . 151) -135° 3 2 4 A) B) C) 4 3 3

D) -

4 5

Convert the angle in radians to degrees. 11 152) 12 A) 150°

151)

152)

B) 165°

C) 160°

Convert the angle to a decimal in degrees. Round the answer to two decimal places. 153) 29°3'2'' A) 29.11° B) 29.06° C) 29.05°

D) 210°

D) 29.01°

153)

Graph the function. Show at least one period. 154) y = -2 sin 2x +

154)

Solve the problem. 155) A photographer points a camera at a window in a nearby building forming an angle of 42° with the camera platform. If the camera is 52 m from the building, how high above the platform is the window, to the nearest hundredth of a meter? A) 57.75 m B) 1.11 m C) 46.82 m D) 0.9 m Write the equation of a sine function that has the given characteristics. 156) Amplitude: 2 Period: 3 Phase Shift: 2 A) y = 2 sin (2x - 3) C) y = 2 sin 2x +

Solve the problem. 157) If f( ) = sec A) 3

155)

156)

B) y = sin (2x + 3)

3 2

D) y = 2 sin

and f(a) = 3, find the exact value of f(-a). B) -3

1 3

1 x-6 2

D) -

1 3

157)

If s denotes the length of the arc of a circle of radius r subtended by a central angle , find the missing quantity. 158) r = 15.7 inches, = 240°, s = ? 158) A) 66.1 in. B) 66.0 in. C) 65.8 in. D) 65.9 in. Graph the function.

159) y =

1 cot x + 3 4

159)

Solve the problem. 160) A pendulum swings though an angle of 40° each second. If the pendulum is 45 inches long, how far does its tip move each second? If necessary, round the answer to two decimal places. A) 32.71 in. B) 29.57 in. C) 31.42 in. D) 33.85 in. Graph the function. 43

160)

161) y = tan (x + )

161)

Draw the angle. 162) 135° A)

162)

Find an equation for the graph. 163)

A) y = -5 cos (2x)

163)

B) y = -5 cos

1 x 2

C) y = -5 sin

1 x 2

D) y = -5 sin (2x)

Find the exact value of the expression. Do not use a calculator. -5 -8 - sec 164) csc 2 3 A) -1

B) 3

164) C) -3

D) 1

Use the definition or identities to find the exact value of the indicated trigonometric function of the acute angle . 1 Find sec . 165) cos = 165) 2 A) 2

3 3

2 3 3

Solve the problem. 166) A carousel has a radius of 16 feet and takes 31 seconds to make one complete revolution. What is the linear speed of the carousel at its outside edge? If necessary, round the answer to two decimal places. A) 3.24 ft/sec B) 12.17 ft/sec C) 0.52 ft/sec D) 100.53 ft/sec Find the exact value of the expression if = 60°. Do not use a calculator. 167) f( ) = sin Find 8 f( ). 3 1 A) B) C) 4 2 2

167) D) 4 3

Find the exact value of the indicated trigonometric function of . 9 Find csc . 168) cot = - , cos < 0 2 A)

9 85 85

B) -

9 85 85

166)

168)

C) -

85 9

85 2

Find the exact value. Do not use a calculator. 169) sec

169)

3 2

Graph the function.

2 3 3

D) 2

170) y = sec x +

170)

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. 171) cot 720° 171) A) -1 B) 2 C) 2 D) undefined Graph the function. Show at least one period.

172) y = 5 cos 3x +

172)

Solve the problem. 173) For what numbers

is f( ) = sec

not defined?

173)

A) all real numbers C) odd multiples of

B) integral multiples of D) odd multiples of

(180°)

(90°)

174) What is the y-intercept of y = tan x? A) 0

174)

B) 1

D) none

Find the reference angle of the given angle. 5 175) 6 A)

175)

5 6

Find the exact value of the expression. Do not use a calculator. 176) sin2 60° - cos2 45° - sin2 30° A) -

1 2

B) 0

7 6

3 2

176) D) 3

Use the definition or identities to find the exact value of the indicated trigonometric function of the acute angle . 5 Find cos . 177) csc = 177) 4 A)

3 5

5 3

Use transformations to graph the function. 178) y = 3 cos x - 2

3 4

4 5

178)

Solve the problem. 179) Use a calculator to find the value of cos 118°. Round to the nearest hundredth. A) 0.19 B) -0.47 C) -1.88

D) 0.88

Convert the angle in degrees to radians. Express the answer as multiple of . 180) 45° A)

180) D)

179)

Use the definition or identities to find the exact value of the indicated trigonometric function of the acute angle . 3 10 Find csc . 181) sin = 181) 10 A)

1 3

10 3

Write the equation of a sine function that has the given characteristics. 182) Amplitude: 4 Period: 3

D) 3

182)

A) y = sin (3 x) + 4

B) y = 4 sin

2 x 3

C) y = 4 sin (3x)

D) y = 3 sin

1 x 2

Solve the problem. 183) A tree casts a shadow of 26 meters when the angle of elevation of the sun is 24°. Find the height of the tree to the nearest meter. A) 11 m B) 10 m C) 12 m D) 13 m Use a coterminal angle to find the exact value of the expression. Do not use a calculator. 184) sin (26 ) A) 1 B) 0 C) -1 D) undefined

183)

184)

Find the exact value of the expression if = 45°. Do not use a calculator. 185) g( ) = cos Find 12 g( ). A) -12 2 B) 12 2 C) 6 2

185) D) -6 2

Find the exact value of the indicated trigonometric function of . 24 3 , Find cot . < <2 186) cos = 25 2 A)

25 24

7 24

B) -

186)

C) -

24 7

D) -24

Find the length s. Round the answer to three decimal places. 187)

187)

A) 14.006 ft

11 ft

B) 17.278 ft

C) 1.142 ft

D) 8.639 ft

Use the definition or identities to find the exact value of the indicated trigonometric function of the acute angle . 5 Find csc . 188) sec = 188) 3 A)

4 5

3 4

3 5

5 4

The point P on the unit circle that corresponds to a real number t is given. Find the indicated trigonometric function. 7 3 ,Find cot t. 189) 189) 4 4 A) -

3 7 7

7 3

C) -

Graph the function. Show at least one period.

7 3

7 4

190) y = 3 cos -4x +

190)

Solve the problem. 191) Given csc 4 A) 3

= 2 , use trigonometric identities to find the exact value of sec2 . 1 1 B) C) 2 3

1 D) 4

191)

Use the reference angle to find the exact value of the expression. Do not use a calculator. 192) tan 570° 3 3 A) 3 B) C) - 3 D) 3 2

192)

The point P on the unit circle that corresponds to a real number t is given. Find the indicated trigonometric function. 77 2 ,Find sin t. 193) 193) 9 9 A) -

2 9

B) -

9 77 77

9 2

D) -

77 9

Graph the function. 194) y = csc x -

194)

Convert the angle in radians to degrees. 2 195) 3 A) 121°

195)

B) 122°

Solve the problem. 196) For what numbers x, -2 A) -2 , - , 0, , 2

C) 120°

D) 119°

x 2 , does the graph of y = tan x have vertical asymptotes.? 3 3 ,- , , B) 2 2 2 2

C) -2, -1, 0, 1, 2

D) none

Find the phase shift of the function. 197) y = 3 cos (2 x + 3) 3 A) units to the right 2

197)

3 units to the left B) 2

C) 3 units to the right

D) 3 units to the left

Find the area A. Round the answer to three decimal places. 198)

30°

A) 1.309 yd2

5 yd

198)

B) 2.083 yd2

C) 6.545 yd2

D) 13.09 yd2

Find the exact value of the expression. Do not use a calculator. 199) 1 - sin2 30° - sin2 60° A)

1- 3 2

196)

1 4

199) C) 0

D) 1

Solve the problem. 200) An object is traveling around a circle with a radius of 10 meters. If in 15 seconds a central angle of 3 radians is swept out, what is the linear speed of the object? 2 1 A) m/sec B) 2 m/sec C) 3 m/sec D) m/sec 3 3 Use a calculator to find the approximate value of the expression. Round the answer to two decimal places. 3 201) cos 10 A) 1.11

B) 1.00

C) 0.59

200)

201)

D) 0.48

If s denotes the length of the arc of a circle of radius r subtended by a central angle , find the missing quantity. 202) r = 1.91 centimeters, = 5.2 radians, s = ? 202) A) 8.9 cm B) 9.9 cm C) 11.9 cm D) 10.9 cm Find the exact value of the expression if 203) g( ) = sin Find g(2 ). A) 1

= 30°. Do not use a calculator. 3 C) 2

1 B) 2

203) 3

Without graphing the function, determine its amplitude or period as requested. 1 Find the period. 204) y = 3 cos x 4 A)

3 4

C) 3

Find the exact value of the expression if = 45°. Do not use a calculator. 205) f( ) = sin Find 5 f( ). 5 2 2 2 A) B) C) 2 2 2

204) D) 8

205) D)

5 2 2

Solve the problem. by 206) If friction is ignored, the time t (in seconds) required for a block to slide down an inclined plane is given206) the formula 2a t= g sin cos where a is the length (in feet) of the base and g 32 feet per second per second is the acceleration of gravity. How long does it take a block to slide down an inclined plane with base a = 14 when = 45°? If necessary, round the answer to the nearest tenth of a second. A) 1.4 sec B) 0.3 sec C) 1.3 sec D) 1.6 sec

Use the even-odd properties to find the exact value of the expression. Do not use a calculator. 207) sin (-60°) 3 3 1 1 A) B) C) D) 2 2 2 2

207)

Use the definition or identities to find the exact value of the indicated trigonometric function of the acute angle . 3 Find sin . 208) cot = 208) 4 A)

4 3

Solve the problem. 209) If f( ) = cos A)

and f(a) =

3 4

4 5

3 5

5 3

1 , find the exact value of f(a) + f(a + 2 ) + f(a + 4 ). 4

1 4

Graph the sinusoidal function. 210) y = 2 cos ( x)

11 4

209) D)

3 +6 4

210)

A point on the terminal side of angle 211) (-5, -2) Find tan . A) - 1

is given. Find the exact value of the indicated trigonometric function. 2 B) 5

5 C) 2

2 D) 5

Find the exact value of the indicated trigonometric function of . 1 Find cos and tan . 212) sin = , sec < 0 2 A) cos

3 , tan 2

C) cos

3 , tan 2

3 3 3 3

212)

B) cos

3, tan

D) cos

3 , tan 2

10 3 3

3 3

Solve the problem. 213) A twenty-five foot ladder just reaches the top of a house and forms an angle of 41.5° with the wall of the house. How tall is the house? Round your answer to the nearest 0.1 foot. A) 18.7 ft B) 19 ft C) 18.6 ft D) 18.8 ft 214) In a computer simulation, a satellite orbits around Earth at a distance from the Earth's surface of 2.9 x 104 miles. The orbit is circular, and one revolution around Earth takes 10.8 days. Assuming the radius of the Earth is 3960 miles, find the linear speed of the satellite. Express the answer in miles per hour to the nearest whole mile. A) 703 mph B) 799 mph C) 127 mph D) 17,238 mph

211)

213)

214)

Find an equation for the graph. 215)

A) y = 3 cos

1 x 4

215)

C) y = 4 cos

B) y = 4 cos (3x)

1 x 3

D) y = 3 cos (4x)

Use Fundamental Identities and/or the Complementary Angle Theorem to find the exact value of the expression. Do not use a calculator. 216) sin 50° csc 50° 216) A) 1 B) -1 C) 50 D) 0

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. 217) tan 720° 217) 3 A) B) 1 C) 0 D) undefined 3 Find the phase shift of the function. 218) y = 2 sin -3x + A) C)

6 2

218)

units to the left

Name the quadrant in which the angle lies. 219) sin > 0, cos > 0 A) I B) II

6 2

C) III

units to the right units to the right

D) IV

Use a coterminal angle to find the exact value of the expression. Do not use a calculator. 220) cos -660° 3 2 3 1 A) B) C) 2 D) 2 3 2

219)

220)

Two sides of a right triangle ABC (C is the right angle) are given. Find the indicated trigonometric function of the given angle. Give exact answers with rational denominators. 221) Find tan B when a = 3 and b = 2. 221) 3 13 2 13 3 2 A) B) C) D) 13 13 2 3

Use transformations to graph the function. 222) y = 5 sin x + 1

222)

Find the area A. Round the answer to three decimal places. 223)

223)

75°

A) 1.309 m 2

B) 5.236 m 2

C) 2.618 m 2

Solve the problem. 224) For what numbers x, 0 x 2 , does sin x = -1? 3 3 A) , B) 2 2 2

D) 0.833 m 2

224) C)

D) none

Use the definition or identities to find the exact value of the indicated trigonometric function of the acute angle . 3 Find cot . 225) cos = 225) 2 A)

2 3 3

B) 2

3 3

Use Fundamental Identities and/or the Complementary Angle Theorem to find the exact value of the expression. Do not use a calculator. 226) cos 40°sin 50° + sin 40°cos 50° 226) A) 0 B) 2 C) -1 D) 1

Use the even-odd properties to find the exact value of the expression. Do not use a calculator. 227) cos -

227)

A) 1

B) 0

C) -1

D) undefined

A point on the terminal side of angle is given. Find the exact value of the indicated trigonometric function. 228) (-20, 48) Find sin . 228) 12 12 5 5 A) B) C) D) 13 13 13 13 Without graphing the function, determine its amplitude or period as requested. 1 Find the amplitude. 229) y = 5 sin x 2 A)

5 2

C) 5

229) D) 4

The point P on the unit circle that corresponds to a real number t is given. Find the indicated trigonometric function. 3 2 10 Find csc t. 230) , 230) 7 7 A) -

10 6

7 3

C) -

7 10 20

3 7

Find the reference angle of the given angle. 9 231) 8 A)

7 8

231) C)

9 8

Without graphing the function, determine its amplitude or period as requested. 232) y = -4 sin x Find the amplitude. A) -4

B) 4

C) 2

232) D)

Solve the problem. 233) A pick-up truck is fitted with new tires which have a diameter of 40 inches. How fast will the pick-up truck be moving when the wheels are rotating at 320 revolutions per minute? Express the answer in miles per hour rounded to the nearest whole number. A) 6 mph B) 38 mph C) 19 mph D) 43 mph

233)

Two sides of a right triangle ABC (C is the right angle) are given. Find the indicated trigonometric function of the given angle. Give exact answers with rational denominators. 234) Find cot A when b = 3 and c = 10. 234) 91 10 91 3 91 91 A) B) C) D) 3 91 91 10

Draw the angle. 7 235) 4

235)

Solve the problem. 236) The force acting on a pendulum to bring it to its perpendicular resting point is called the restoring force.236) The restoring force F, in Newtons, acting on a string pendulum is given by the formula F = mg sin where m is the mass in kilograms of the pendulum's bob, g 9.8 meters per second per second is the acceleration due to gravity, and is angle at which the pendulum is displaced from the perpendicular. What is the value of the restoring force when m = 0.5 kilogram and = 71°? If necessary, round the answer to the nearest tenth of a Newton. A) 4.4 N B) 1.6 N C) 4.7 N D) 4.6 N 237) For the equation y = period.

A) (i)

1 2

(ii)

C) (i)

1 2

(ii)

1 cos(2x - 2 ), identify (i) the amplitude, (ii) the phase shift, and (iii) the 2

(iii)

B) (i) 2

(ii) 2

(iii) 2

(iii)

D) (i) 2

(ii)

(iii)

Use transformations to graph the function.

237)

238) y = -4 sin (x +

238)

)

Find the exact value of the expression. Do not use a calculator. 239) 1 + cot2 30° - sec2 45° A) 3

B) 2

C) 0

D) 1

239)

Convert the angle to a decimal in degrees. Round the answer to two decimal places. 240) 346°55'8'' A) 346.93° B) 346.92° C) 346.88°

D) 346.98°

Name the quadrant in which the angle lies. 241) sin > 0, cos < 0 A) I B) II

D) IV

C) III

Use a coterminal angle to find the exact value of the expression. Do not use a calculator. 41 242) csc 4 A)

2 2

2 3 3

C) 2

2 4

C) 2 2

Convert the angle to D° M' S'' form. Round the answer to the nearest second. 244) 56.89° A) 56°53'89'' B) 56°53'12'' C) 56°53'24''

243)

3 2 4

D) 56°53'30''

Use a coterminal angle to find the exact value of the expression. Do not use a calculator. 245) sec -690° 2 3 1 A) B) 3 C) D) 3 2

244)

245) 2

Solve the problem. 246) A radio transmission tower is 210 feet tall. How long should a guy wire be if it is to be attached 7 feet from the top and is to make an angle of 23° with the ground? Give your answer to the nearest tenth of a foot. A) 519.5 ft B) 537.5 ft C) 228.1 ft D) 220.5 ft

241)

242)

Use identities to find the exact value of the indicated trigonometric function of the acute angle . 2 2 1 , cos = Find sec . 243) sin = 3 3 A) 3

240)

246)

Draw the angle. 3 247) 4

247)

Find the exact value of the indicated trigonometric function of . 21 , 180°< < 270° Find cos . 248) tan = 20 A) -20

B) -

20 29

248) 21 41 41

Convert the angle to D° M' S'' form. Round the answer to the nearest second. 249) 237.03° A) 237°2'47'' B) 237°1'48'' C) 237°1'3'' Find the exact value of the expression if g( ) Find . 250) g( ) = sin 12 A)

3 24

-20 41 41

D) 237°47'3''

249)

= 30°. Do not use a calculator. 250)

B) 24 3

1 12

1 24

Solve the problem. 251) As part of an experiment to test different liquid fertilizers, a sprinkler has to be set to cover an area of 120 square yards in the shape of a sector of a circle of radius 60 yards. Through what angle should the sprinkler be set to rotate? If necessary, round the answer to two decimal places. A) 12° B) 1.91° C) 2.87° D) 3.82°

251)

Convert the angle in radians to degrees. Express the answer in decimal form, rounded to two decimal places. 252) 6 252) A) 0.04° B) 140.35° C) -0.14° D) 141.39° 65

Use transformations to graph the function. 253) y = 5 cos x

253)

Graph the function. Show at least one period.

254) y = -3 cos(x - )

254)

Graph the function.

255) y = -4 cot (4x)

255)

Solve the problem. 256) For what numbers x, -2

x 2 , does the graph of y = csc x have vertical asymptotes?

A) -2, -1, 0, 1, 2 C) -

B) -2 , - , 0, , 2

3 3 ,- , , 2 2 2 2

D) none

256)

Convert the angle in degrees to radians. Express the answer in decimal form, rounded to two decimal places. 257) -334° 257) A) -5.82 B) -5.8 C) -5.83 D) -5.81 Use the reference angle to find the exact value of the expression. Do not use a calculator. 7 258) tan 6 3 2

C) - 3

258) 3 3

Use Fundamental Identities and/or the Complementary Angle Theorem to find the exact value of the expression. Do not use a calculator. 259) csc2 35° - tan2 55° 259)

A) 2

B) 1

C) -1

D) 0

Without graphing the function, determine its amplitude or period as requested. 9 4 x) Find the amplitude. 260) y = cos (4 5 A)

4 9

9 4

5 2

260) D)

4 5

Use Fundamental Identities and/or the Complementary Angle Theorem to find the exact value of the expression. Do not use a calculator. 261) sec2 40° - tan2 40° 261)

A) 0

B) -1

C) 1

D) 2

Solve the problem. 262) The force acting on a pendulum to bring it to its perpendicular resting point is called the restoring force.262) The restoring force F, in Newtons, acting on a string pendulum is given by the formula F = mg sin where m is the mass in kilograms of the pendulum's bob, g 9.8 meters per second per second is the acceleration due to gravity, and is angle at which the pendulum is displaced from the perpendicular. What is the value of the restoring force when m = 0.6 kilogram and = 60°? If necessary, round the answer to the nearest tenth of a Newton. A) 4.8 N B) 1.8 N C) 5.1 N D) 2.9 N Graph the sinusoidal function.

263) y = 4 sin ( x)

263)

Find the exact value of the expression if = 30°. Do not use a calculator. 264) f( ) = tan Find f( ). 3 A) B) 3 C) 1 3 Graph the sinusoidal function.

264) D)

3 2

265) y =

3 1 cos (- x) 2 4

265)

Find the exact value of the indicated trigonometric function of . 8 in quadrant II Find cos . 266) tan = - , 7 A)

113 8

B) -

7 113 113

C) -

266) 113 7

7 113 113

Solve the problem. 267) For what numbers

is f( ) = csc

A) integral multiples of C) odd multiples of

not defined?

267)

(180°)

B) odd multiples of

(90°)

(180°)

D) all real numbers

268) Two hikers on opposite sides of a canyon each stand precisely 525 meters above the canyon floor. They each sight a landmark on the canyon floor on a line directly between them. The angles of depression from each hiker to the landmark meter are 37° and 21°. How far apart are the hikers? Round your answer to the nearest whole meter. A) 2064 m B) 2063 m C) 1064 m D) 2065 m Without graphing the function, determine its amplitude or period as requested. 269) y = sin 3x Find the period. 2 A) 2 B) 3 C) 3 The point P on the circle x 2 + y2 = r2 that is also on the terminal side of an angle indicated trigonometric function. 270) (3, -2) Find cot . 13 2 3 A) B) C) 3 3 2

268)

269) D) 1

in standard position is given. Find the

270) D)

13 3

Solve the problem. 271) A circle has a radius of 7 centimeters. Find the area of the sector of the circle formed by an angle of 45°. If necessary, round the answer to two decimal places. A) 2.75 cm2 B) 19.24 cm2 C) 38.48 cm2 D) 6.13 cm2

271)

Two sides of a right triangle ABC (C is the right angle) are given. Find the indicated trigonometric function of the given angle. Give exact answers with rational denominators. 272) Find sin B when b = 7 and c = 10. 272) 7 51 51 10 51 7 A) B) C) D) 51 10 51 10

Convert the angle in radians to degrees. 273) -

273)

A) -30 °

B) -1°

C) -30°

Convert the angle to D° M' S'' form. Round the answer to the nearest second. 274) 148.97° A) 148°56'97'' B) 148°58'12'' C) 148°58'97'' Graph the function.

D) 1°

D) 148°59'12''

274)

275) y = 5 csc x +

275)

Solve the problem. 276) An object is traveling around a circle with a radius of 10 centimeters. If in 20 seconds a central angle 1 of radian is swept out, what is the linear speed of the object? 3 A)

1 cm/sec 6

B) 6 radians/sec

1 radians/sec 6

D) 6 cm/sec

276)

Use transformations to graph the function. 277) y = sin ( x)

277)

Graph the function. Show at least one period.

278) y = 5 sin(3x - )

278)

Graph the function.

279) y = 4 sec x -

279)

Draw the angle. 5 280) 3

280)

A point on the terminal side of angle is given. Find the exact value of the indicated trigonometric function. 281) (12, 16) Find sin . 281) 4 4 3 3 A) B) C) D) 5 3 5 4 The point P on the circle x 2 + y2 = r2 that is also on the terminal side of an angle indicated trigonometric function. 282) (-12, -5) Find cos . 12 5 5 A) B) C) 13 13 13

in standard position is given. Find the

12 D) 13

282)

Two sides of a right triangle ABC (C is the right angle) are given. Find the indicated trigonometric function of the given angle. Give exact answers with rational denominators. 283) Find csc B when a = 2 and b = 5. 283) 29 2 29 5 29 29 A) B) C) D) 5 29 29 2

The point P on the unit circle that corresponds to a real number t is given. Find the indicated trigonometric function. 2 21 Find sin t. 284) , 284) 5 5 A)

21 2

21 5

Find the exact value. Do not use a calculator. 285) sin 60° 2 3 A) B) 2 2

2 21 21

2 5

285) C)

1 2

3 3

Two sides of a right triangle ABC (C is the right angle) are given. Find the indicated trigonometric function of the given angle. Give exact answers with rational denominators. 286) Find sec B when a = 9 and b = 5. 286) 9 106 106 5 106 9 106 A) B) C) D) 106 9 106 5

Use transformations to graph the function. 287) y = sin x + 5

287)

Solve the problem. 288) A gear with a radius of 16 centimeters is turning at

point on the outer edge of the gear? 7 cm/sec cm/sec A) B) 112 16

radians/sec. What is the linear speed at a

16 7

cm/sec

D) 112 cm/sec

Use identities to find the exact value of the indicated trigonometric function of the acute angle . 7 3 , cos = Find csc . 289) sin = 4 4 A)

3 7 7

7 3

4 3

290) C) 0

D) none

Find the length s. Round the answer to three decimal places. 291)

291)

60°

A) 4.189 yd

4 yd

289)

4 7 7

Solve the problem. 290) What is the y-intercept of y = cot x? A) 1

288)

B) 3.77 yd

C) 4.608 yd

D) 3.351 yd

A point on the terminal side of angle is given. Find the exact value of the indicated trigonometric function. 292) (18, 24) Find cos . 292) 3 4 3 4 A) B) C) D) 4 5 5 3 The point P on the unit circle that corresponds to a real number t is given. Find the indicated trigonometric function. 65 4 , Find sec t. 293) 293) 9 9 65 4

9 65 65

9 4

4 65 65

Find the exact value of the indicated trigonometric function of . 7 in quadrant IV Find tan . 294) sec = , 4 A) -

7 4

B) -

33 7

294)

C) -

Name the quadrant in which the angle lies. 295) tan > 0, sin < 0 A) I B) II

C) III

D) -

33 4

D) IV

Find the reference angle of the given angle. 42 296) 8 A)

296) C)

Find the exact value of the expression. Do not use a calculator. 5 297) cos (-2 ) + sin 2 A) 1

B) 0

297) C) -2

D) 2

Without graphing the function, determine its amplitude or period as requested. 9 4 x) Find the period. 298) y = sin (8 3 A)

9 4

295)

4 9

8 3

298) D)

3 2

Use a calculator to find the approximate value of the expression. Round the answer to two decimal places. 299) cos 1° A) 0.54 B) -1.00 C) 1.00 D) -0.54

299)

Use the definition or identities to find the exact value of the indicated trigonometric function of the acute angle . 13 Find cot . 300) sec = 300) 12 A)

13 5

12 5

12 13

5 13

Find the exact value. Do not use a calculator. 301) sec

301)

2 2

C) - 2

2 3 3

Find the length s. Round the answer to three decimal places. 302)

A) 6.283 ft

302)

12 ft

B) 22.918 ft

C) 12.566 ft

Graph the function. Show at least one period. 303) y = 4 sin (4 x - 2)

D) 1.571 ft

303)

Solve the problem. 304) Given the approximation sin 29° 0.48, use trigonometric identities to find the approximate value of cot 29°. If necessary, round the answer to two decimal places. A) 1.8 B) 0.55 C) 1.14 D) 0.87

304)

Two sides of a right triangle ABC (C is the right angle) are given. Find the indicated trigonometric function of the given angle. Give exact answers with rational denominators. 305) Find cos A when a = 4 and b = 5. 305) 4 41 5 41 41 41 A) B) C) D) 41 41 4 5

Find the exact value of the expression if = 60°. Do not use a calculator. 306) f( ) = sin Find f( ). 2 3 3 A) B) C) 2 2 3

306) D)

1 2

A point on the terminal side of angle is given. Find the exact value of the indicated trigonometric function. 307) (3, 4) Find csc . 307) 3 4 5 5 A) B) C) D) 4 3 4 3 Solve the problem. 308) A ship in the Atlantic Ocean measures its position to be 30°14' north latitude. Another ship is reported to be due north of the first ship at 41°39' north latitude. Approximately how far apart are the two ships? Round to the nearest mile. Assume that the radius of the Earth is 3960 miles. A) 45,210 mi B) 45,189 mi C) 768 mi D) 789 mi Name the quadrant in which the angle lies. 309) cos < 0, csc < 0 A) I B) II

C) III

D) IV

308)

309)

Use the even-odd properties to find the exact value of the expression. Do not use a calculator. 310) cot -

310)

A) -1

B) - 3

C) 1

Graph the function. 311) y = cot x

D) -

3 3

311)

Use the even-odd properties to find the exact value of the expression. Do not use a calculator. 312) csc -

312)

A) 2

B) -2

Match the given function to its graph. 313) 1) y = sin x 2) y = cos x 3) y = -sin x 4) y = -cos x A

2 3 3

D) -

2 3 3

313) B

A) 1B, 2D, 3C, 4A

B) 1A, 2D, 3C, 4B

C) 1C, 2A, 3B, 4D

D) 1A, 2B, 3C, 4D

If s denotes the length of the arc of a circle of radius r subtended by a central angle , find the missing quantity. 314) s = 2.47 meters, = 1.3 radians, r = ? 314) A) 0.95 m B) 1.5 m C) 0.53 m D) 1.9 m Solve the problem. 315) A surveyor is measuring the distance across a small lake. He has set up his transit on one side of the lake 150 feet from a piling that is directly across from a pier on the other side of the lake. From his transit, the angle between the piling and the pier is 50°. What is the distance between the piling and the pier to the nearest foot? A) 96 ft B) 115 ft C) 126 ft D) 179 ft 316) A wheel of radius 9.5 feet is moving forward at 12 feet per second. How fast is the wheel rotating? A) 0.79 radians/sec B) 1.3 radians/sec C) 0.33 radians/sec D) 3.8 radians/sec 84

315)

316)

Graph the function. 317) y = 2 csc

1 x 4

317)

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. 318) tan 390° 318) 3 3 A) B) C) - 3 D) 3 2 3

Convert the angle in radians to degrees. 29 319) 9 A) 1,160 °

319)

B) 290°

C) 10°

D) 580°

Find an equation for the graph. 320)

A) y = -3 sin (3x)

320)

C) y = 3 cos

B) y = -3 cos (3x)

Find the exact value. Do not use a calculator. 321) tan 45° 3 A) B) 1 2

1 x 3

D) y = -3 cos

1 x 3

321) C)

2 D) 2

Solve the problem. is 322) The current I, in amperes, flowing through a particular ac (alternating current) circuit at time t seconds 322) I = 110 sin (50 t) What is the period and amplitude of the current? 1 second, amplitude = 200 second, amplitude = 50 A) period = B) period = 200 110 C) period = 50 seconds, amplitude =

1 25

D) period =

1 second, amplitude = 110 25

Use the even-odd properties to find the exact value of the expression. Do not use a calculator. 323) sin -

323)

A) -

3 2

C) -

2 2

Two sides of a right triangle ABC (C is the right angle) are given. Find the indicated trigonometric function of the given angle. Give exact answers with rational denominators. 324) Find cot A when a = 7 and c = 10. 324) 10 51 51 7 51 51 A) B) C) D) 51 7 51 10

Use the reference angle to find the exact value of the expression. Do not use a calculator. 4 325) csc 3 A) -

2 3 3

B) - 3

C) -

Graph the function. 326) y = -cot(2x)

1 2

325) D) - 2

326)

Find the area A. Round the answer to three decimal places. 327)

327)

4 7 cm 2 A) 38.485 cm

B) 12.25 cm2

C) 19.242 cm2

D) 2.749 cm2

Solve the problem. 328) What is the domain of the sine function? A) all real numbers, except odd multiples of

328) 2

(90°)

B) all real numbers, except integral multiples of C) all real numbers from -1 to 1, inclusive D) all real numbers

(180°)

329) For what numbers x, 0 x 2 , does cos x = 0? A) 0, 1

3 C) , 2 2

B) 0, , 2

330) For what numbers x, 0 x 2 , does sin x = 1? 3 A) , B) 2 2 2

329) D) 0, 1, 2

330) C) 0, 2

D) none

331) An irrigation sprinkler in a field of lettuce sprays water over a distance of 20 feet as it rotates through an angle of 150°. What area of the field receives water? If necessary, round the answer to two decimal places. A) 26.18 ft2 B) 166.67 ft2 C) 1,047.2 ft2 D) 523.6 ft2

331)

Find the exact value of the expression. Do not use a calculator. 332) sin

- cos

A) 0

332)

B) 1

Use transformations to graph the function.

3-1 2

333) y = cos x - 5

333)

Use a calculator to find the approximate value of the expression. Round the answer to two decimal places. 334) cos 4 A) 1.00 B) 0.65 C) -1.00 D) -0.65

334)

Convert the angle to a decimal in degrees. Round the answer to two decimal places. 335) 21°17'34'' A) 21.29° B) 21.34° C) 21.37°

335)

D) 21.22°

Solve the problem. 336) A rotating beacon is located 11 ft from a wall. If the distance from the beacon to the point on the wall 336) where the beacon is aimed is given by a = 11|sec 2 t|, where t is in seconds, find a when t = 0.31 seconds. Round your answer to the nearest hundredth. A) -29.88 ft B) 24.73 ft C) 29.88 ft D) 19.57 ft 337) Given tan A)

= 2, use trigonometric identities to find the exact value of sec

1 2

5 2

C) 2

337) 5

Write the equation of a sine function that has the given characteristics. 338) Amplitude: 4 Period: Phase Shift: - 5

338)

A) y = 4 sin (2x + 10)

B) y = sin (4x + 5)

C) y = 4 sin (x - 5)

D) y = 4 sin

1 x - 10 2

Find the exact value of the expression if = 30°. Do not use a calculator. 339) g( ) = sin Find 10 g( ). 1 A) B) 5 3 C) 5 2

339) D) -

3 2

Use the reference angle to find the exact value of the expression. Do not use a calculator. -11 340) cot 6 A) -

3 3

C) - 3

340) D)

3 3

Solve the problem. 341) Given the approximation cos 34° 0.83, use trigonometric identities to find the approximate value of csc 34°. If necessary, round the answer to two decimal places. A) 0.56 B) 1.79 C) 0.67 D) 1.21 Write the equation of a sine function that has the given characteristics. 342) Amplitude: 5 Period: 6 Phase Shift: -

C) y = 5 sin

342)

A) y = 5 sin 3x -

1 18

B) y = 5 sin 6x -

1 1 x+ 3 18

D) y = 5 sin

341)

1 1 x3 18

Draw the angle. 343) -150° A)

Graph the function. 344) y = sec (3x)

343)

344)

Find an equation for the graph. 345)

A) y = 2 sin

345)

C) y = 4 sin

B) y = 2 sin (4 x)

D) y = 4 sin (2 x)

Find the phase shift of the function. 346) y = -5 cos (6x + ) A)

346)

units to the left

B) 5 units to the right

C) 6 units to the right

units to the left

Solve the problem. 347) A town's average monthly temperature data is represented in the table below:

Month, x January, 1 February, 2 March, 3 April, 4 May, 5 June, 6 July, 7 August, 8 September, 9 October, 10 November, 11 December, 12

347)

Average Monthly Temperature, °F 32.8 36.8 48.2 61.5 74.7 86.2 89.0 84.2 84.2 61.9 45.6 36.0

Find a sinusoidal function of the form y = A sin ( x - ) + B that fits the data.

A) y = 32.8 sin C) y = 28.1 sin

6 6

xx-

4 2 3

+ 89.0

B) y = 60.9 sin

+ 60.9

D) y = 89.0 sin

Find the reference angle of the given angle. 348) -387° A) 27° B) 63°

6 6

xx-

4 2 3

C) 117°

Find the phase shift of the function. 1 349) y = 4 sin x 4 4 A) C)

4 16

+ 28.1 + 32.8

D) 153°

348)

349)

units to the right

units to the left

units to the right 4

units to the left

If A denotes the area of the sector of a circle of radius r formed by the central angle , find the missing quantity. If necessary, round the answer to two decimal places. 350) r = 13 feet, A = 63 square feet, = ? 350) A) 42.74° B) 610,337.58° C) 305,168.79° D) 21.37°

Find an equation for the graph. 351)

A) y = 3 cos (2 x)

351)

C) y = 3 cos

B) y = 2 cos (3 x)

D) y = 2 cos

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. 352) sin 855° 352) 2 2 1 1 A) B) C) D) 2 2 2 2 Find the exact value of the expression if f( ) Find . 353) f( ) = cos 8 A) 4 3

Solve the problem. 354) If f(x) = cos x and f(a) = A) -

1 4

= 30°. Do not use a calculator. 353) 3 16

C) 16 3

3 4

1 , find the exact value of f(a) + f(a - 2 ) + f(a + 4 ). 12

B) -36

C) -12

354) D) -

1 12

Find the reference angle of the given angle. 7 355) 8 A)

355)

9 8

Name the quadrant in which the angle lies. 356) csc > 0, sec > 0 A) I B) II

C) III

7 8

D) IV

356)

Convert the angle in radians to degrees. Express the answer in decimal form, rounded to two decimal places. 357) 1 357) A) 0.02° B) -0.14° C) 57.3° D) 57.09°

Solve the problem. 358) An object is traveling around a circle with a radius of 20 meters. If in 10 seconds a central angle of 1 radian is swept out, what is the linear speed of the object? 5 A)

2 m/sec 5

1 m/sec 5

1 m/sec 8

1 m/sec 4

Use the reference angle to find the exact value of the expression. Do not use a calculator. 4 359) sin 3 3 2

A) -

B) -1

C) -

1 2

358)

359) 3 2

Use the definition or identities to find the exact value of the indicated trigonometric function of the acute angle . 5 Find tan . 360) sin = 360) 13 A)

12 5

13 12

13 5

5 12

Use a calculator to find the approximate value of the expression. Round the answer to two decimal places. 361) cot

361)

A) 3.08

B) 182.38

C) 3.14

D) 182.44

Use a coterminal angle to find the exact value of the expression. Do not use a calculator. 25 362) cot 3 A)

3 2

Use transformations to graph the function. 363) y = sin (x - )

3 3

362) D) 1

363)

Write the equation of a sine function that has the given characteristics. 364) Amplitude: 2 Period: 4 Phase Shift:

364)

A) y = 2 sin

1 1 x2 8

C) y = 2 sin 4x +

B) y = 2 sin

1 1 x+ 2 8

D) y = 2 sin 2x +

Solve the problem. 365) If sin = 0.7, find sin ( + ). A) 0.7 B) -0.3

C) -0.7

Graph the function.

1 8

D) 0.3

365)

366) y = -cot ( x)

366)

Use transformations to graph the function.

367) y = 4 sin x

367)

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. 11 368) sec 368) 4 A) -

2 3 3

B) -2

2 2

D) - 2

The point P on the unit circle that corresponds to a real number t is given. Find the indicated trigonometric function. 3 7 Find tan t. 369) , 369) 4 4 A)

4 3

7 4

3 7 7

7 3

Convert the angle in degrees to radians. Express the answer in decimal form, rounded to two decimal places. 370) 23° 370) A) 0.38 B) 0.37 C) 0.39 D) 0.4 Match the given function to its graph. 371) 1) y = sin 3x 2) y = 3 cos x 3) y = 3 sin x 4) y = cos 3x A

371) B

A) 1A, 2D, 3C, 4B

B) 1A, 2C, 3D, 4B

C) 1B, 2D, 3C, 4A

D) 1A, 2B, 3C, 4D

Use Fundamental Identities and/or the Complementary Angle Theorem to find the exact value of the expression. Do not use a calculator. 372) If tan2 = 7, find the exact value of sec2 . 372)

A) 8

B) 7

C) 14

D) 6

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. 373) cot 390° 373) 3 3 A) 3 B) C) - 3 D) 3 3 Match the given function to its graph. 374) 1) y = -3 sin (2x)

1 2) y = -3 sin ( x) 2

3) y = 3 cos (2x)

1 4) y = 3 cos ( x) 2

374)

A) 1A, 2C, 3D, 4B

B) 1C, 2A, 3B, 4D

C) 1D, 2B, 3A, 4C

D) 1C, 2A, 3D, 4B

Two sides of a right triangle ABC (C is the right angle) are given. Find the indicated trigonometric function of the given angle. Give exact answers with rational denominators. 375) Find cos A when a = 6 and c = 14. 375) 190 6 95 3 A) B) C) D) 14 14 3 7

376) Find tan A when a = 4 and b = 9. 97 9 A) B) 4 4

376) C)

100

97 9

4 9

Use a calculator to find the approximate value of the expression. Round the answer to two decimal places. 377) sec

377)

A) 1.11

B) 1.00

378) cos 4° A) -0.75

C) 1.07

B) -0.65

D) 1.04

C) 1.00

D) 1.10

Solve the problem. 379) The data below represent the average monthly cost of natural gas in an Oregon home. Month Cost

Aug 21.20

Sep 28.24

Oct 44.73

Nov 67.25

Dec 89.77

Jan 106.26

Month Feb Cost 111.30

Mar 106.26

Apr 89.77

May 67.25

Jun 43.73

Jul 28.24

378)

379)

Above is the graph of 45.05 sin x superimposed over a scatter diagram of the data. Find the sinusoidal function of the form y = A sin ( x - ) + B which best fits the data. 2 2 xx+ 66.25 + 21.20 A) y = 45.05 sin B) y = 45.05 sin 6 3 4 3

C) y = 45.05 sin

+ 66.25

D) y = 45.05 sin

t + 12 + 21.20

Use the reference angle to find the exact value of the expression. Do not use a calculator. 380) csc 1,020° 2 3 1 A) - 2 B) C) D) - 3 3 2 Use transformations to graph the function.

101

380)

381) y = 5 cos ( - x)

381)

102

Solve the problem. by 382) If friction is ignored, the time t (in seconds) required for a block to slide down an inclined plane is given382) the formula 2a t= g sin cos where a is the length (in feet) of the base and g 32 feet per second per second is the acceleration of gravity. How long does it take a block to slide down an inclined plane with base a = 10 when = 61°? If necessary, round the answer to the nearest tenth of a second. A) 1.6 sec B) 1.5 sec C) 1.2 sec D) 0.3 sec

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. 20 383) cos 383) 3 A)

3 2

1 2

D) -

C) III

D) IV

C) -

Name the quadrant in which the angle lies. 384) tan < 0, sin < 0 A) I B) II

The point P on the circle x 2 + y2 = r2 that is also on the terminal side of an angle indicated trigonometric function. 385) (-4, -1) Find sec . 3 17 17 A) - 17 B) C) 17 4

385) D) -

3 2

= 45°. Do not use a calculator. 387)

2 B) 2

B) -

17 4

386)

1 D) 2

C) 2

Use a coterminal angle to find the exact value of the expression. Do not use a calculator. 49 388) sin 6 A) -

384)

in standard position is given. Find the

Solve the problem. 386) What is the range of the cosecant function? A) all real numbers from -1 to 1, inclusive B) all real numbers, except integral multiples of (180)° C) all real numbers greater than or equal to 1 or less than or equal to -1 D) all real numbers Find the exact value of the expression if Find [g( )]2 . 387) g( ) = sin

3 2

1 2

3 2

388) D)

1 2

A point on the terminal side of angle is given. Find the exact value of the indicated trigonometric function. 389) (4, -2) Find sin . 389) 2 5 5 5 A) B) C) D) -2 5 5 2 103

Convert the angle in radians to degrees. 5 390) 12 A) -74°

390)

B) -77°

C) -75°

D) -76°

Solve the problem. 391) The Earth rotates about its pole once every 24 hours. The distance from the pole to a location on Earth 15° north latitude is about 3,825.1 miles. Therefore, a location on Earth at 15° north latitude is spinning on a circle of radius 3,825.1 miles. Compute the linear speed on the surface of the Earth at 15° north latitude. A) 952 mph B) 24,034 mph C) 1,001 mph D) 159 mph

391)

A point on the terminal side of angle is given. Find the exact value of the indicated trigonometric function. 392) (-5, -12) Find cot . 392) 5 12 5 12 A) B) C) D) 13 13 12 5 Use the even-odd properties to find the exact value of the expression. Do not use a calculator. 393) tan A)

393)

3 3 3

B) -

3 3

C) - 3

Graph the sinusoidal function. 1 394) y = -4 sin ( x) 4

394)

104

Use the even-odd properties to find the exact value of the expression. Do not use a calculator. 395) cos (- ) A) -1 B) 0 C) 1 D) undefined 396) sin (-120°) -1 A) 2

395)

396) B)

1 2

3 2

Find the exact value of the expression. Do not use a calculator. 397) csc 60° - cos 45° 4 2-3 3 4 3-3 2 4- 2 A) B) C) 6 6 2

105

D) -

3 2

397) 4- 3 D) 2

Find an equation for the graph. 398)

A) y = cos (4x)

398)

B) y =

1 1 cos x 2 2

C) y =

1 cos (4x) 2

D) y =

1 1 cos x 2 4

Solve the problem. 399) A building 180 feet tall casts a 80 foot long shadow. If a person looks down from the top of the building, what is the measure of the angle between the end of the shadow and the vertical side of the building (to the nearest degree)? (Assume the person's eyes are level with the top of the building.) A) 66° B) 64° C) 24° D) 26° Find an equation for the graph. 400)

A) y = 3 cos (4x)

399)

400)

B) y = 4 cos

1 x 3

C) y = 3 cos

Graph the function. Show at least one period.

106

1 x 4

D) y = 4 cos (3x)

401) y = 4 sin( x + 3)

401)

Find the exact value of the expression. Do not use a calculator. 15 15 - cos 402) tan 4 4 A)

-2 - 2 2

2- 2 2

402) C)

Graph the function. 107

2+ 2 2

-2 + 2 2

403) y = -tan x -

403)

Solve the problem. 404) If csc = 2, find the value of csc + sec(90° - ). If necessary, round the answer to two decimal places. A) 1.58 B) 2 C) 4 D) -0.42

108

404)

Find the exact value. Do not use a calculator. 405) sin

405)

3 2

2 2

1 2

3 3

The point P on the unit circle that corresponds to a real number t is given. Find the indicated trigonometric function. 4 65 Find csc t. 406) , 406) 9 9 A)

65 4

B) -

9 65 65

65 9

D) -

65 9

Use transformations to graph the function. 407) y = cos (

407)

109

Write the equation of a sine function that has the given characteristics. 408) Amplitude: 4 Period: 3 1 A) y = 3 sin x B) y = 4 sin (3x) C) y = sin (3x) + 4 2 Find the exact value of the expression if f( ) Find . 409) f( ) = sin 7 A) 14 3

408) D) y = 4 sin

2 x 3

= 60°. Do not use a calculator. 409) 3 14

3 7

1 14

Find the phase shift of the function. 410) y = -5 sin 2x A)

410)

units to the right

B) 2 units down

C) 5 units up

Use transformations to graph the function.

110

units to the left

411) y = -3 cos (x -

411)

)

Use the reference angle to find the exact value of the expression. Do not use a calculator. 412) sin 495° 2 2 1 1 A) B) C) D) 2 2 2 2

111

412)

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. 10 413) sin 413) 3 A) -1

B) -

1 2

3 2

D) -

3 2

Use transformations to graph the function. 414) y = cos (x -

414)

)

112

Graph the function. 415) y = 2 tan (4x)

415)

Use a calculator to find the approximate value of the expression. Round the answer to two decimal places. 416) csc 58° A) 1.07 B) 1.18 C) 1.01 D) 1.24

113

416)

Find the exact value of the indicated trigonometric function of . 8 Find sec . 417) sin = - , tan > 0 9 A) -

8 17 17

B) -

9 17 17

417) 17 9

C) -

9 8

Use Fundamental Identities and/or the Complementary Angle Theorem to find the exact value of the expression. Do not use a calculator. 418) sin2 65° + cos2 65° 418)

A) 0

B) 2

C) -1

D) 1

Use the reference angle to find the exact value of the expression. Do not use a calculator. 3 419) sec 4 A) -

2 3 3

B) - 2

C) -2

419) 2 2

Convert the angle in radians to degrees. 7 420) 8 A) 206 °

420)

B) 158°

C) 315°

D) 154°

Use the definition or identities to find the exact value of the indicated trigonometric function of the acute angle . 5 Find sin . 421) tan = 421) 12 A)

13 12

5 13

12 13

13 5

If A denotes the area of the sector of a circle of radius r formed by the central angle , find the missing quantity. If necessary, round the answer to two decimal places. 422) = 3 radians, A = 87 square meters, r = ? 422) A) 11.42 m B) 522 m C) 130.5 m D) 7.62 m

Use the reference angle to find the exact value of the expression. Do not use a calculator. 423) cot 930° 3 3 A) B) C) - 3 D) 3 3

423) 3

Convert the angle in degrees to radians. Express the answer as multiple of . 424) -36° A) -

B) -

C) -

Find the exact value. Do not use a calculator. 425) cos 30° 2 3 A) 3 B) 3

424) D) -

425) C)

114

2 2

3 2

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. 13 426) cot 426) 4 A)

3 3

B) 1

D) -1

Use Fundamental Identities and/or the Complementary Angle Theorem to find the exact value of the expression. Do not use a calculator. sin 80° 427) tan 80° 427) cos 80°

A) 80

B) 0

Find the reference angle of the given angle. 428) 88° A) 2° B) 88°

C) 1

D) undefined

C) 92°

D) 178°

428)

If s denotes the length of the arc of a circle of radius r subtended by a central angle , find the missing quantity. 1 429) r = feet, s = 7 feet, = ? 429) 4 A) 28 radians

7 radians 4

7 ° 4

D) 28°

C) III

D) IV

Name the quadrant in which the angle lies. 430) sec < 0, tan < 0 A) I B) II

Use a calculator to find the approximate value of the expression. Round the answer to two decimal places. 431) tan 26° A) 0.49 B) 1.12 C) 0.55 D) 1.18

430)

431)

Use the definition or identities to find the exact value of the indicated trigonometric function of the acute angle . 7 Find sin and cos . 432) tan = 432) 15 A) sin

8 , cos 7

15 8

B) sin

7 , cos 8

C) sin

7 , cos 8

8 15 15

D) sin

15 , cos 8

15 8 =

7 8

Use Fundamental Identities and/or the Complementary Angle Theorem to find the exact value of the expression. Do not use a calculator. cos 10° 433) tan 80° 433) cos 80°

A) 0

B) 2

C) -1

D) 1

If A denotes the area of the sector of a circle of radius r formed by the central angle , find the missing quantity. If necessary, round the answer to two decimal places. 434) = 30°, A = 80 square meters, r = ? 434) A) 17.49 m B) 4.58 m C) 20.93 m D) 83.73 m

115

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. 435) csc 600° 435) 2 3 1 A) B) C) - 2 D) - 3 3 2 Find an equation for the graph. 436)

A) y = -5 sin

1 x 2

436)

C) y = -5 cos

B) y = -5 sin (2x)

Use transformations to graph the function. 437) y = -2 sin x

1 x 2

D) y = -5 cos (2x)

437)

116

Draw the angle. 2 438) 3

438)

117

Find an equation for the graph. 439)

A) y = 2 sin (4x)

439)

C) y = 4 sin

B) y = 4 sin (2x)

1 x 2

D) y = 2 sin

1 x 4

Find the phase shift of the function. 440) y = -4 cos x +

440)

A) -4 units up C)

B) -4 units down

units to the left

units to the right

Find the exact value of the expression. Do not use a calculator. 441) cot 45° - cos 30° 3 2- 3 2 3-3 2 A) B) C) 6 2 6 A point on the terminal side of angle 2 2 ,Find sec . 442) 2 2 A) -

2 2

441) 2- 2 D) 2

is given. Find the exact value of the indicated trigonometric function. 442) B) - 2

118

D) -1

Draw the angle. 443) 60° A)

443)

Solve the problem. 444) The number of hours of sunlight in a day can be modeled by a sinusoidal function. In the northern 444) hemisphere, the longest day of the year occurs at the summer solstice and the shortest day occurs at the winter solstice. In 2000, these dates were June 22 (the 172nd day of the year) and December 21 (the 356th day of the year), respectively. A town experiences 10.96 hours of sunlight at the summer solstice and 8.46 hours of sunlight at the winter solstice. Find a sinusoidal function y = A sin ( x - ) + B that fits the data, where x is the day of the year. (Note: There are 366 days in the year 2000.) 172 2 2 xx+ 9.71 + 9.71 A) y = 10.96 sin B) y = 1.25 sin 356 3 183 3

C) y = 1.25 sin

183

161 366

+ 9.71

D) y = 10.96 sin

445) For what numbers x, 0 x 2 , does cos x = 1? A)

B) 0, 2

Find the exact value of the expression. Do not use a calculator. 446) 3 cot2 45° + 8 sin2 30° A) 7

2 3

+ 8.46

445)

3 C) , 2 2

D) none

C) 3

D) 5

Solve the problem. 447) Given the approximation cos 20° 0.94, use trigonometric identities to find the approximate value of sin 70°. If necessary, round the answer to two decimal places. A) 0.34 B) 1.06 C) 0.94 D) 0.36

119

446)

447)

Find the reference angle of the given angle. 448) -236° A) 56° B) 34°

C) 124°

Graph the function. 1 449) y = sec x 4

D) 146°

448)

449)

120

Solve the problem. 450) To approximate the speed of a river, a circular paddle wheel with radius 0.5 feet is lowered into the water. If the current causes the wheel to rotate at a speed of 13 revolutions per minute, what is the speed of the current? If necessary, round to two decimal places. A) 0.07 mph B) 0.23 mph C) 40.84 mph D) 0.46 mph

450)

If A denotes the area of the sector of a circle of radius r formed by the central angle , find the missing quantity. If necessary, round the answer to two decimal places. 451) r = 5 feet, A = 91 square feet, = ? 451) A) 1,137.5 radians B) 3.64 radians C) 7.28 radians D) 2,275 radians

121

Answer Key Testname: CHAPTER 7 1) C 2) D 3) C 4) B 5) C 6) D 7) A 8) C 9) amplitude = 0.65, period = 5, respiratory cycle = 5 seconds a = 0.65sin

2 t 5

10) amplitude = 25, period = 8/3 d = 25 cos

3 t 4

11) neither

122

Answer Key Testname: CHAPTER 7 12) y = 8.33 sin (0.50x - 2.06) + 57.97

13) cos

35 , tan 6

35 35

14) y = 2.17 sin (0.49x - 1.88) + 6.02

15) y = 15.99 sin (0.57x - 2.29) + 60.62

16) For all 3 values of t, M = 875 and N = 12,250; 2

is the reference angle for the given values of

for t = 39, M = 875 and N = 12,250. 17) 379 mi 18) 1 in.; 2 in.; (1 + 3) in.; 3 in.; (1 + 3) in.; 2 in.; 1 in. 1 (ii) 6 19) (i) 6

20) y = 3.14 sin (0.46x + 1.52) + 3.16

21) sin P =

7 24 7 25 25 24 , cos P = , tan P = , csc P = , sec P = , and cot P = 25 25 24 7 24 7

22) odd

23) 6.24 × 104 kmp; 4.95 × 104 kmp; 3.92 × 104 kmp; 2.95 × 104 kmp; Io 123

Answer Key Testname: CHAPTER 7

24) amplitude = 30, period =

1 25

I = 30sin(50 t)

25) 0.274 pint 1 26) sin = , tan 5 27)

6 12

2 6 ; cos 5

12 13

28) sin

1 ; csc 5

29) amplitude = 4, period =

5 6 ; sec 12

= 5; cot

6 12

P = 4cos(4t)

30) $4636.07; The minimum cost is $4400 when the point is chosen 1050 feet to the right of A.

124

Answer Key Testname: CHAPTER 7 31)

y = 47.35 sin (

2 ) + 66.25 3

32) 12, 12 33) 365 days 34) (i) negative (ii) negative (iii) positive 35) A 36) C 37) C 38) A 39) B 40) A 41) A 42) C 43) A 44) A 45) B 46) D 47) B 48) C 49) D 50) C 51) D 52) A 53) C 54) A 55) D 56) D 57) D 58) D 59) C 60) B 61) D 125

Answer Key Testname: CHAPTER 7 62) D 63) A 64) A 65) C 66) B 67) C 68) D 69) B 70) C 71) A 72) D 73) C 74) C 75) D 76) C 77) B 78) D 79) B 80) B 81) B 82) B 83) C 84) A 85) D 86) D 87) B 88) C 89) C 90) B 91) C 92) D 93) A 94) A 95) C 96) B 97) D 98) D 99) B 100) B 101) D 102) B 103) B 104) B 105) D 106) D 107) B 108) A 109) C 110) A 111) D 126

Answer Key Testname: CHAPTER 7 112) D 113) A 114) D 115) C 116) D 117) B 118) B 119) D 120) C 121) C 122) B 123) D 124) A 125) B 126) C 127) C 128) B 129) A 130) D 131) D 132) D 133) D 134) C 135) A 136) C 137) D 138) A 139) C 140) D 141) A 142) B 143) A 144) D 145) C 146) D 147) B 148) A 149) D 150) B 151) A 152) B 153) C 154) A 155) C 156) A 157) B 158) C 159) B 160) C 161) C 127

Answer Key Testname: CHAPTER 7 162) A 163) C 164) D 165) A 166) A 167) D 168) D 169) D 170) B 171) D 172) D 173) D 174) B 175) D 176) B 177) A 178) D 179) B 180) A 181) B 182) B 183) C 184) B 185) C 186) C 187) D 188) D 189) B 190) C 191) A 192) B 193) A 194) B 195) C 196) B 197) B 198) C 199) C 200) B 201) C 202) B 203) C 204) D 205) D 206) C 207) D 208) B 209) A 210) C 211) B 128

Answer Key Testname: CHAPTER 7 212) A 213) A 214) B 215) C 216) A 217) C 218) B 219) A 220) B 221) D 222) B 223) C 224) B 225) C 226) D 227) B 228) B 229) C 230) C 231) C 232) B 233) B 234) C 235) C 236) D 237) C 238) D 239) B 240) B 241) B 242) D 243) A 244) C 245) A 246) A 247) A 248) B 249) B 250) D 251) D 252) B 253) D 254) D 255) A 256) B 257) C 258) D 259) B 260) B 261) C 129

Answer Key Testname: CHAPTER 7 262) C 263) B 264) A 265) C 266) B 267) A 268) A 269) C 270) C 271) B 272) A 273) C 274) B 275) B 276) A 277) D 278) D 279) B 280) A 281) A 282) D 283) A 284) B 285) B 286) B 287) A 288) C 289) D 290) D 291) A 292) C 293) B 294) D 295) C 296) C 297) D 298) D 299) C 300) B 301) A 302) A 303) C 304) A 305) B 306) B 307) C 308) D 309) C 310) A 311) D 130

Answer Key Testname: CHAPTER 7 312) C 313) C 314) D 315) D 316) B 317) C 318) B 319) D 320) D 321) B 322) D 323) C 324) B 325) A 326) D 327) C 328) D 329) C 330) B 331) D 332) A 333) D 334) D 335) A 336) C 337) B 338) A 339) C 340) B 341) B 342) C 343) C 344) C 345) D 346) D 347) C 348) A 349) B 350) A 351) C 352) D 353) B 354) A 355) A 356) A 357) C 358) A 359) A 360) D 361) A 131

Answer Key Testname: CHAPTER 7 362) A 363) D 364) A 365) C 366) C 367) C 368) D 369) D 370) D 371) C 372) A 373) A 374) A 375) A 376) D 377) A 378) C 379) A 380) C 381) B 382) C 383) C 384) D 385) D 386) C 387) D 388) C 389) B 390) C 391) C 392) C 393) C 394) D 395) B 396) D 397) B 398) C 399) C 400) D 401) C 402) A 403) A 404) C 405) C 406) B 407) D 408) D 409) B 410) A 411) B 132

Answer Key Testname: CHAPTER 7 412) C 413) D 414) B 415) B 416) B 417) B 418) D 419) B 420) B 421) B 422) D 423) D 424) D 425) D 426) B 427) B 428) B 429) A 430) B 431) A 432) B 433) A 434) A 435) A 436) D 437) D 438) C 439) B 440) C 441) B 442) C 443) D 444) C 445) B 446) D 447) C 448) A 449) C 450) D 451) C

133

Chapter 8 Exam Name___________________________________

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Use a calculator to solve the equation on the interval 0 x < 2 . Round the answer to one decimal place if necessary. 1) 6x - 5 sin x = 2 1) Solve the problem. 2) If x = 3 tan , express sin(2 ) as a function of x.

Establish the identity. 3) sin

+x =

2(cos x + sin x)

Solve the problem. 4) Show that cos(sin-1 v - cos-1 v) = 2v

1 - v2

Establish the identity. 5) ln cot u = ln cos u - ln sin u 6)

sin( - ) = cot sin sin

7) 1 -

8) tan

- cot

cos2 u = - sin u 1 - sin u

+ x = -cot x

Solve the problem. 9) An object is propelled upward at an angle , 45° < < 90°, to the horizontal with an initial velocity of v0 feet per second from the base of a plane that makes an angle of 45° with the

horizontal. If air resistance is ignored, the distance R that it travels up the inclined plane is given by the function v0 2 2 R( ) = [sin(2 ) - cos(2 ) - 1]. 32 Show that v0 2 2 R( ) = [sin (cos 16

+ sin ) - 1].

Establish the identity. cot x csc x - 1 = 10) 1 + csc x cot x

10)

11)

1 + csc x = cos x + cot x sec x

11)

12)

cot 2 x 1 - sin x = csc x + 1 sin x

12)

13)

csc x - 1 cot 2 x = csc x + 1 csc 2 x + 2 csc x + 1

13)

Solve the problem. 14) When light travels from one medium to another from air to water, for instance it changes direction. (This is why a pencil, partially submerged in water, looks as though it is bent.) The angle of incidence i is the angle in the first medium; the angle of refraction r is the

14)

second medium. (See illustration.) Each medium has an index of refraction n i and n r, respectively which can be found in tables. Snell's law relates these quantities in the formula n i sin i = n r sin r Solving for r, we obtain ni r = sin-1 n sin i r

Find r for crown glass (n i = 1.52), water(n r = 1.33), and i = 38°.

Establish the identity. 15) sin( - ) cos( + ) = sin

cos

- sin

cos

15)

Use a calculator to solve the equation on the interval 0 x < 2 . Round the answer to one decimal place if necessary. 16) ex = cos x 16) Establish the identity. 1- sec tan + 17) tan 1 - sec

= -2 csc

17)

18) sec 4 x - tan 4 x = sec 2 x + tan 2 x

18)

Use a calculator to solve the equation on the interval 0 x < 2 . Round the answer to one decimal place if necessary. 19) x + 3 sin x = 1 19)

Establish the identity. cos + cos = cot 20) sin - sin

20)

Use a calculator to solve the equation on the interval 0 x < 2 . Round the answer to one decimal place if necessary. 21) cos x + sin x = 2x 21) Establish the identity. sin(8 ) + sin(4 ) = tan(6 ) 22) cos(8 ) + cos(4 )

23) cot

22)

· sec

= csc

23)

= -cos

24)

25) cos(x - y) - cos(x + y) = 2 sin x sin y

25)

1 26) sin3 (3x) = (sin(3x))(1 - cos(6x)) 2

26)

24) sin

27)

cot2 x 1 + sin x = csc x - 1 sin x

28)

sin csc

29)

sin(9 ) + sin(3 ) = cos(3 ) 2 sin(6 )

+ sin + csc

= sin

27)

sin

28)

29)

Solve the problem. 30) Draw a triangle so that tan

30)

= u. The hypotenuse of the triangle with have length

1 + u2 . Use the illustration and the double angle formulas to write sin terms of u.

Establish the identity. 31) 8 csc2 - 6 cot2 = 2 csc2 + 6

and cos

31)

32) 1 +

1 sin3 sin(2 ) = 2 sin

- cos3 - cos

32)

Solve the problem. 33) Given f(x) = 4 sin x (a) Find the intercepts of the graph of f on the interval [- , 3 ]. (b) Graph f(x) = 4 sin x on the interval [- , 3 ]. 4 (c) Solve f(x) = on the interval [- , 3 ]. 2 (d) Determine the values of x such that f(x) < -

33)

4 on the interval [- , 3 ]. 2

Establish the identity. 34)

1 - 2 sec x - 3 sec2 x 1 - 3 sec x = 1 - sec x -tan 2 x

34)

35) sin2 (- ) + cos2 (- ) = 1

35)

Solve the problem. 36) A weight is suspended on a system of spring and oscillates up and down according to 36) P = 0.1[3 cos(8t) - sin(8t)] where P is the position in meters above or below the point of equilibrium (P = 0) and t is time in seconds. Find the time when the weight is at equilibrium. Find all values of t, 0 t 1, rounded to the nearest 0.01 second. 37) Show that sin(sin-1 v - cos-1 v) = 2v2 - 1

37)

Establish the identity. sin x sin x + = 2 tan 2 x 38) csc x - 1 csc x + 1 39) cos

38)

x x 2 - sin = 1 - sin x 2 2

39)

40) csc(u + v) =

csc u csc v cot v + cot u

41) (sec v + tan v)2 =

40)

1 + sin v 1 - sin v

41)

Simplify the trigonometric expression by following the indicated direction. (cot + 1)(cot + 1) - csc2 42) Multiply and simplify: cot Establish the identity. 1 43) cos4 x = (3 + 4 cos(2x) + cos (4x)) 8

42)

43)

Simplify the trigonometric expression by following the indicated direction. cos 1 + sin by 44) Multiply 1 - sin 1 + sin Solve the problem. 45) The seasonal variation in the length of daylight can be represented by a sine function. For example, the daily number of hours of daylight in a certain city in the U.S. can be given by 41 5 2 x + sin h= , where x is the number of days after March 21 ( disregarding leap 4 3 365

44)

45)

year). On what day(s) will there be about 10 hours of daylight?

Establish the identity. sin x sin x + = 2 csc x 46) 1 - cos x 1 + cos x

46)

Use a calculator to solve the equation on the interval 0 x < 2 . Round the answer to one decimal place if necessary. 47) 2x - 3 cos x = 0 47) Establish the identity. 1 48) ln sin2 u + cos(2u) = ln cos u 2

48)

Solve the problem. 49) When light travels from one medium to another from air to water, for instance it changes direction. (This is why a pencil, partially submerged in water, looks as though it is bent.) The angle of incidence i is the angle in the first medium; the angle of refraction r is the

49)

Find r for fused quartz (n i = 1.46), ethyl alcohol (n r = 1.36), and i = 8.5°.

Establish the identity. 5 csc2 x + 4 csc x - 1 5 csc x - 1 = 50) csc x - 1 cot 2 x

50)

Solve the problem. 51) When light travels from one medium to another from air to water, for instance it changes direction. (This is why a pencil, partially submerged in water, looks as though it is bent.) The angle of incidence r is the angle in the first medium; the angle of refraction r is the

Find r for air (n i = 1.0003), methylene iodide (n r = 1.74), and i = 14.7°.

51)

Simplify the trigonometric expression by following the indicated direction. 5 cos2 + 6 cos + 1 52) Factor and simplify: cos2 - 1 Establish the identity. cos u sin u = cos u - sin u 53) 1 + tan u 1 + cot u

53)

Solve the problem. 54) A mass hangs from a spring which oscillates up and down. The position P (in feet) of the mass at time t (in seconds) is given by P = 4 cos (4t). For what values of t, 0 t < , will the position be 2 2 feet? Find the exact values. Do not use a calculator. 55) Wildlife management personnel use predator-prey equations to model the populations of certain predators and their prey in the wild. Suppose the population M of a predator after t months is given by M = 750 + 125 sin

52)

54)

55)

while the population N of its primary prey is given by N = 12,250 + 3050 cos

Find the values of t, 0 t < 12, for which the predator population is 875. Find the values of t, 0 t < 12, for which the prey population is 10,725.

Establish the identity.

56) cos(3x) = cos3 x - 3 sin2 x cos x 57) cos(4 ) = cos4 58) sec

- 6 sin2

cos2

56) + sin4

57)

+ u = -csc u

58)

59) sin3 x cos2 x = sin x (cos2 x - cos4 x)

59)

60) csc2 u - cos u sec u= cot2 u

60)

Solve the problem. 61) The path of a projectile fired at an inclination (in degrees) to the horizontal with an initial 61) velocity v0 is a parabola. The range R of the projectile, that is, the horizontal distance that the projectile travels, is found by using the formula

2 v0 g

sin (2 )

where g is the acceleration due to gravity. Suppose the projectile is fired with an initial velocity of 400 feet per seconds and g = 32 feet per second2 . What angle , 0° < 90°, would you select for the range to be 2500 feet? (There should be two values of .)

Establish the identity. tan v + sec v tan v + sec v = - cos v cot v 62) sec v tan v 63) csc

62)

+ u = sec u

63)

64) csc3 x tan2 x = csc x (1 + tan2 x) 65) sec u + tan u =

64)

cos u 1 - sin u

65)

Use a calculator to solve the equation on the interval 0 x < 2 . Round the answer to one decimal place if necessary. 66) x2 - 3 sin(2x) = 2x 66) Solve the problem. 67) If two sound sources at the same volume are equidistant from a microphone, the pressure on the 67) microphone is given by p = a cos 1 t + a cos 2 t where a,

1 , 2 are constants and t is time. Write p as a product of cosine functions.

Establish the identity. 68) tan2 x = sec2x - sin2 x - cos2 x

68)

Solve the problem. 69) You are flying a kite and want to know its angle of elevation. The string on the kite is 43 meters long and the kite is level with the top of a building that you know is 28 meters high. Use an inverse trigonometric function to find the angle of elevation of the kite. Round to two decimal places.

69)

Use a calculator to solve the equation on the interval 0 x < 2 . Round the answer to one decimal place if necessary. 70) x2 - 4 cos x = 0 70) Establish the identity. csc2 - 2 71) cot(2 )= 2 cot 72)

71)

tan u + cot u 1 = tan u - cot u 2 sin u - cos2 u

73) sec2

u 2 sec u = 2 sec u + 1

74) (cos

+ sin )2 + (cos

72)

73)

- sin )2 = 2(cos2

+ sin2 )

74)

75) cos

75)

= -sin

Solve the problem. 76) A water wheel rotates through the angle , the water level L behind the wheel changes according to the equation L = 1 - sin - 2 cos2 where L is measured in inches. Determine the values of Find the exact values. Do not use a calculator.

for which the water level is zero.

Simplify the trigonometric expression by following the indicated direction. 1 1 + 77) Rewrite over a common denominator: 1 - cos 1 + cos Establish the identity. sin - sin = cot 78) sin + sin 79)

csc + cot tan + sin

= csc

76)

77)

78)

cot

79)

80) cot( - ) = - cot

80)

81) cot3 x = cot x (csc2 x - 1)

81)

82)

sin(9 ) + sin(3 ) tan(6 ) = sin(9 ) - sin(3 ) tan(3 )

82)

83)

cos(4 ) - cos(10 ) = tan(3 ) sin(4 ) + sin(10 )

83)

84) sin(4u) = 2 sin(2u) cos(2u)

84)

1 - cot2 v + 1 = 2 sin2 v 1 + cot2 v

85)

Simplify the trigonometric expression by following the indicated direction. 86) Rewrite in terms of sine and cosine: cot x · tan x

86)

Solve the problem. 87) The formula D = 24 1 -

cos-1 (tan i tan )

can be used to approximate the number of

87)

hours of daylight when the declination of the sun is i° at a location ° north latitude for any date between the vernal equinox and autumnal equinox. To use this formula, cos-1 (tan i tan ) must be expressed in radians. Approximate the number of hours of daylight in Flagstaff, Arizona, (35°13' north latitude) for summer solstice (i = 23.5°).

88) A consumer notes the sinusoidal nature of her monthly power bills. In winter when she uses 88) electricity to heat her home and in summer when she cools her home, the bills are high. In spring and fall, significantly less electricity is used and the bills are much smaller. The following function models this behavior. C = 60 + 40 cos

Here C is the cost of power in dollars for the month t, 1 t 12, with t = 1 corresponding to January. For what values of t, 1 t 12, is the cost exactly $80?

89) The ground movement of an earthquake near a fault line is modeled by the equation 2M d = D tan 12 S

89)

where M is the horizontal movement (in meters) at a distance d (in kilometers) from the earthquake, D is the depth (also in kilometers) below the surface of the center of the earthquake, and S is the total horizontal displacement (also in meters) at the fault line. What is the horizontal movement 5 kilometers from an earthquake centered 3 kilometers below the surface with a total horizontal displacement of 4 meters? Round the answer to the nearest 0.01 meter.

Establish the identity. cot u + csc u - 1 = csc u + cot u 90) cot u - csc u + 1

90)

91) cot 2 x + csc 2 x = 2 csc 2 x - 1

92) cot(x + y) cot(x - y) =

91)

1 - tan2 x tan2 y tan2 x - tan2 y

92)

93) 1 + sec2 x sin2 x = sec2 x

93)

94) csc u - sin u = cos u cot u

94)

95) (1 - cos x)(1 + cos x) = sin2 x

95)

Solve the problem. 96) The formula D = 24 1 -

cos-1 (tan i tan )

can be used to approximate the number of

96)

hours of daylight when the declination of the sun is i° at a location ° north latitude for any date between the vernal equinox and autumnal equinox. To use this formula, cos-1 (tan i tan ) must be expressed in radians. Approximate the number of hours of daylight in Fargo, North Dakota, (46°52'north latitude) for vernal equinox (i = 0°).

Establish the identity. 97) (sec u - tan u)(sec u + tan u) = 1

97)

98) sin(4x) = (4 sin x cos x)(2 cos2 x - 1) 99)

cos( + ) = cot cos sin

98)

- tan

99)

100) tan( - ) = tan

100)

101) cot x sec4 x = cot x + 2 tan x + tan3 x

101)

u csc u + cot u 102) cot2 = 2 csc u - cot u

102)

103)

cos(9 ) - cos(3 ) = - sin(3 ) 2 sin(6 )

103)

Show that the functions f and g are identically equal. sec - 1 tan , g( ) = 0 104) f( ) = tan sec + 1

104)

Establish the identity. sec - 1 tan = 105) tan sec + 1

105)

106)

cos u 1 = cos u - sin u 1 - tan u

106)

107)

1 + cos u 1 - cos u = 4 cot u csc u 1 - cos u 1 + cos u

107)

108)

1 - sin t cos t = cos t 1 + sin t

108)

Show that the functions f and g are identically equal. sin 109) f( ) = csc + cot , g( ) = 1 - cos

109)

Use a calculator to solve the equation on the interval 0 x < 2 . Round the answer to one decimal place if necessary. 110) 7 cos x - ex = 1, x > 0 110) Solve the problem. 111) The path of a projectile fired at an inclination (in degrees) to the horizontal with an initial speed v0 is a parabola. The range R of the projectile, that is, the horizontal distance that the

111)

projectile travels, is found by using the formula

2 v0 g

sin(2 )

where g is the acceleration due to gravity. The maximum height H of the projectile is

2 v0 4g

(1 - cos(2 ))

Find the range R and the maximum height H in terms of g if the projectile is fired with an initial speed of 200 meters per second at an angle of 15° and then at an angle of 22.5°. Do not use a calculator, but simplify the answers.

112) The path of a projectile fired at an inclination (in degrees) to the horizontal with an initial speed v0 is a parabola. The maximum height H of the projectile is given by H=

2 v0 4g

112)

(1 - cos (2 ))

where g is the acceleration due to gravity.

Show that the maximum height H can be written H =

Establish the identity. cos x cos x 2 cos x = 113) sec x - 1 sec x + 1 tan2 x

2 v 0 sin2 2g

113)

114) cot2 x = (csc x - 1)(csc x + 1)

114)

115) tan

115)

116)

· csc

= sec

cos(8 ) - cos(2 ) = - tan(5 ) tan(3 ) cos(8 )+ cos(2 )

116)

Solve the problem. 117) The two equal sides of an isosceles triangle measure three feet. Let the angle between the sides measure . Find the area A of the triangle as a function of

117)

. The answer may

include more than one trigonometric function.

118) If tan

= x + 1 and tan

= x - 1, show that cot( + ) =

2 - x2 2x

Establish the identity. 119) (tan v + 1)2 + (tan v - 1)2 = 2 sec2 v 120) sin [sin

+ sin(5 )] = cos(2 )[cos(2 ) - cos(4 )]

121) tan x -

118)

119) 120)

tan x - 1 1 + tan x

121)

122) csc 4 x - cot 4 x = csc 2 x + cot 2 x

122)

123) cos x +

123)

= -sin x

124) ln 1 + sin u + ln 1 - sin u = 2 ln cos u

124)

sin x + cos x 1 + 2 sin x cos x = sin x - cos x 2 sin 2 x - 1

125)

126) sin(x + y) - sin(x - y) = 2 cos x sin y

126)

125)

Solve the problem. 127) A product of two oscillations with different frequencies such as f(t) = sin(10t) sin(t) is important in acoustics. The result is an oscillation with "oscillating amplitude." (i) Write the product f(t) of the two oscillations as a sum of two cosines and call it g(t). (ii) Using a graphing utility, graph the function g(t) on the interval 0 t 2 . (iii) On the same system as your graph, graph y = sin t and y = -sin t. (iv) The last two functions constitute an "envelope" for the function g(t). For certain values of t, the two cosine functions in g(t) cancel each other out and near-silence occurs; between these values, the two functions combine in varying degrees. The phenomenon is known (and heard) as "beats." For what values of t do the functions cancel each other? Establish the identity. sin3 - cos3 128) sin - cos

= 1 + sin

cos

127)

128)

Solve the problem. 129) Before exercising, an athlete measures her air flow and obtains a = 0.65 sin

2 t where a 5

129)

is measured in liters per second and t is the time in seconds. If a > 0, the athlete is inhaling; if a < 0, the athlete is exhaling. The time to complete one complete inhalation/exhalation sequence is a respiratory cycle. Find the values of t for which the athlete's air flow is zero. Find all values of t for t < 20 seconds.

Establish the identity. 130) cos x +

131) sin x -

132)

3 1 cos x - sin x 2 2

130)

2 (sin x - cos x) 2

131)

tan u - 1 1 - cot u = tan u + 1 1 + cot u

132)

Solve the problem. 133) The average daily temperature T of a city in the United States is approximated by 2 T = 55 - 23 cos (t - 30) 365

133)

where t is in days, 1 t 365, and t = 1 corresponds to January 1. For what range of values of t is the average daily temperature above 70°F? Use a calculator and round answers to the nearest whole number.

Establish the identity. 134) (a tan u + b)2 + (b tan u - a)2 = (a 2 + b2 ) sec2 u 135)

134)

cos(x - y) 1 + tan x tan y = cos(x + y) 1 - tan x tan y

136) sin x +

135)

= cos x

136)

137) (1 + tan2 u)(1 - sin2 u) = 1 138)

1 - cos 1 + cos

sec sec

137)

-1 +1

138)

139) tan u(csc u - sin u) = cos u

139)

140) cos(4u) = 2 cos2 (2u) - 1

140)

141) tan 2 u (1 + cos(2u)) = 1 - cos(2u)

141)

Show that the functions f and g are identically equal. 142) f(x) = csc x · sec x, g(x) = cot x + tan x

142)

Establish the identity. 143) cos x csc x tan x = 1

143)

Use a calculator to solve the equation on the interval 0 x < 2 . Round the answer to one decimal place if necessary. 144) 2x2 - 3x sin x = 2 144) Establish the identity. cos t 1 + sin t + = 2 sec t 145) 1 + sin t cos t

145)

Use a graphing utility to solve the equation on the interval 0° x < 360°. Express the solution(s) rounded to one decimal place. 146) -11 + 24 sin x = 16 cos 2 x 146)

Establish the identity. 147) sec(2 )=

csc2 csc2 - 2

147)

148) (sin x)(tan x cos x - cot x cos x) = 1 - 2 cos 2 x

148)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Express the sum or difference as a product of sines and/or cosines. 7 5 + cos 149) cos 2 2 A) 2 cos(3 ) cos

B) 2 sin(3 ) sin

Use the information given about the angle , 0 150) cot

= -3, sec

10 + 3 10 20

Find cos

B) -

149)

C) 2 sin(3 ) sin

D) 2 cos(3 )

2 , to find the exact value of the indicated trigonometric function. 2

150)

3 + 10 20

3 - 10 20

10 + 3 10 20

D) -

Given that f(x) = sin x, g(x) = cos x, and h(x) = tan x, find the exact value of the composite function. 4 151) f g-1 5 A)

3 5

4 5

1 5

D) -

3 5

151)

Use the information given about the angle , 0 2 , to find the exact value of the indicated trigonometric function. 1 Find cos . 152) sin = , tan > 0 152) 4 2 A)

6 4

8 + 2 15 4

Find the inverse function f-1 of the function f. 153) f(x) = -5 cos(7x) 1 x A) f-1 (x) = cos-1 5 7

4 5 , A) 0, , 3 3

10 4

153)

1 x B) f-1 (x) = - cos-1 7 5

D) f-1 (x) =

C) f-1 (x) = -5 cos-1 (7x)

Solve the equation on the interval 0 154) sin2 + sin = 0

8 - 2 15 4

1 x cos-1 7 5

<2 . 5 B) 0, , , 3 3

2 C) 0, , , 3 3

3 D) 0, , 2

Find the exact solution of the equation. 155) 3 sin-1 x = A)

3 2

155) 2 2

Find the exact value of the expression. 156) sin 285° 2( 3 - 1) A) B) 4 157) cos 2 sin-1 A)

1 2

156) 2( 3 - 1) 4

2( 3 + 1) 4

D) -

5 13

157)

10 13

2 5 + 10 13

C) -

12 13

119 169

Solve the equation. Give a general formula for all the solutions. 158) tan = -1 A)

158)

3 +k 4

154)

+ 2k

3 + 2k 4

Find the exact solution of the equation. 159) sin-1 x = A) {1}

159)

1 2

C) {0}

D) -

1 2

Express the product as a sum containing only sines or cosines. 160) sin(2 ) cos(3 ) 1 1 A) [sin(5 ) - sin ] B) [cos(5 ) - cos ] 2 2 C) sin cos(6 2 )

Find the exact value of the expression. Do not use a calculator. 161) cos [cos-1 (-0.9372)] A) 0.9372

Solve the problem. 162) If sin

1 , 4

B) -0.4686

3 + 15 8

B) -

3 5 +1 8

1 [cos(5 ) + sin ] 2

C) -0.9372

in quadrant II, find the exact value of cos

160)

162)

6 3 - 15 8

D) 0.4686

15 - 4 3 16

Find the exact value of the expression. 3 163) cos tan-1 3 A)

1 2

161)

163) B)

3 2

3 3

Use the information given about the angle , 0 2 , to find the exact value of the indicated trigonometric function. 24 , Find sin . <2 < 164) cos 2 = 164) 25 2 A)

7 5

B) -

Solve the equation on the interval 0 165) 4 sin2 = 1 A) C)

3 6

7 5

C) -

7 2 10

<2 .

2 3

5 7 11 , , 6 6 6

3 6

2 4 5 , , 3 3 3

5 6

165)

Simplify the expression.

166) (1 + cot )(1 - cot ) - csc2 A) 2

B) -2 cot2

C) 0

D) 2 cot2

Use a calculator to find the value of the expression rounded to two decimal places. 3 167) cos-1 7 A) -25.38

B) 115.38

C) -0.44

166)

167) D) 2.01

Find the exact value of the expression. 168) cos-1 cos A) -

168)

2 3

4 3

169) csc-1 (-1) A) -

169) B)

Find the inverse function f-1 of the function f. 170) f(x) = 5 sin x - 7 x+7 A) f-1 (x) = cos 5

3 2

-6 + 4 21 25

Use the information given about the angle , 0 = - 6, cos

Find sin

6+ 5 12

174) sin

A) -

4 3 , < 5 2

171)

-8 - 3 21 25

6 + 4 21 25

172) 3 C) 2

1 D) 2

2 , to find the exact value of the indicated trigonometric function. 2

173)

6 - 30 12

Find sin ( - ).

Find the exact value of the expression. 172) sin 10° cos 50° + cos 10° sin 50° 3 1 A) B) 3 6

173) csc

170)

x+5 D) f-1 (x) = sin-1 7

Find the exact value under the given conditions. 4 3 21 , < < 2 ; cos = 171) sin = - , 5 2 5 -8 + 3 21 25

x+7 B) f-1 (x) = sin-1 5

C) f-1 (x) = 5 sin-1 x - 7

D) -

C) -

6 - 30 12

6- 5 12

Find tan(2 ).

24 7

B) -

174)

7 24

24 7

Solve the equation. Give a general formula for all the solutions. 2 175) cos(2 ) = 2 A)

+k ,

2 +k , 3

7 +k 8 =

4 +k 3

175)

8 4

+ 2k ,

7 + 2k 8

+k ,

3 +k 4

Solve the equation on the interval 0 3 176) sin(4 ) = 2

176)

2 7 7 13 5 19 , , , , , , , 12 6 3 12 6 12 3 12

A) C)

177)

<2 .

3 cot

B) 0,

5 4

D) {0}

-1=0 6

Solve the problem using Snell's Law:

11 6

sin 1 v1 = . sin 2 v2

178) A light beam in air travels at 2.99 × 108 meters per second. If its angle of incidence to a second medium is 83° and its angle of refraction in the second medium is 72°, what is its speed in the second medium (to two decimal places)? A) 2.84 × 108 mps B) 2.87 × 108 mps C) 3.12 × 108 mps D) 2.97 × 108 mps Find the exact value of the expression. 2 179) cos-1 2 A)

177)

179) B)

180) tan-1 1 5 A) 4

178)

3 4

-3 4

2 D) 3

180)

Use the information given about the angle , 0 2 , to find the exact value of the indicated trigonometric function. 5 , Find tan(2 ). < < 181) cos = 181) 13 2 A)

169 119

Solve the equation on the interval 0 182) cos - 1 = 0 A)

169 120

120 119

<2 . 3 C) 2

B) { }

119 120

182) D) {0}

Find the exact value of the expression. 183) cos

sin

1 2

- cos

sin

183)

3 2

C) 1

1 4

184) tan cos-1 A)

4 9

184) B)

9 4

65 4

65 9

Use the information given about the angle , 0 2 , to find the exact value of the indicated trigonometric function. 4 3 Find cos(2 ). < <2 185) sin = - , 185) 5 2 A)

24 25

B) -

24 25

C) -

7 25

Find the exact value of the expression. 1 186) cos sin-1 2 A)

3 2

186) B)

2 2

C) 1

D) 0

Use a calculator to find the value of the expression in radian measure rounded to two decimal places. 4 187) sec-1 3 A) 0.72

B) 48.59

C) 41.41

D) 0.85

Find the domain of the function f and of its inverse function f-1 . 188) f(x) = 3 sin x - 6 A) Domain of f: ( , ) B) Domain of f: [3, 9] Domain of f-1 : [-9, -3] Domain of f-1 : [-9, -3]

C) Domain of f: ( , ) Domain of f-1 : [3, 9]

188)

D) Domain of f: ( , ) Domain of f-1 : ( , )

Find the exact solution of the equation. 189) 4 cos-1 x = A)

187)

189) 3 2

2 2

1 2

Use the information given about the angle , 0 2 , to find the exact value of the indicated trigonometric function. 1 Find sin . 190) cos(2 ) = , 0 < < 190) 4 2 A)

10 - 2 6 4

6 4

Find the exact value under the given conditions. 4 3 12 ; cos = , < 191) tan = , < < 3 2 13 2 A)

33 65

8 - 2 10 4

10 4

Find sin ( + ).

63 65

56 65

191) D)

16 65

Express the sum or difference as a product of sines and/or cosines. 192) sin(2 ) - sin(4 ) A) -2 sin cos(3 ) B) 2 cos(2 ) cos(3 ) C) -2 sin D) 2 sin(3 ) cos

192)

Find the exact solution of the equation. 193) 6 cos-1 x = A)

193) 2 2

3 2

1 2

Use the information given about the angle , 0 2 , to find the exact value of the indicated trigonometric function. 20 3 , Find sin(2 ). < <2 194) cos = 194) 29 2 A)

41 841

840 841

B) -

840 841

D) -

41 841

Write the trigonometric expression as an algebraic expression in u. 195) cos (tan-1 u) A)

u u2 + 1 u2 + 1

u2 + 1 u2 + 1

C) u u2 + 1

195) D)

u2 - 1 u2 - 1

Find the exact value of the expression. 3 196) sin 2 cos-1 2 3 2

A) -

196) 3 2

1 2

Find the exact value of the expression. Do not use a calculator. 4 197) tan-1 tan 7 A)

B) -

197) C)

4 7

D) -

4 7

Simplify the expression. cos + tan 198) 1 + sin A) cos

198) B) sin2

+ sin

C) 1

D) sec

Find the exact value of the expression. 199) cos

1 2

cos

+ sin

sin

199)

1 4

C) 1

3 2

Solve the equation. Give a general formula for all the solutions. 3 200) sin = 2 A)

6 3

200)

5 +k 6

2 + 2k 3

+k ,

+ 2k ,

Use a calculator to solve the equation on the interval 0 201) sin = -0.29 A) {0.29, 3.44} B) {3.44, 5.99}

3 6

2 +k 3

+k ,

+ 2k ,

5 + 2k 6

< 2 . Round the answer to two decimal places. C) {0.29, 1.87}

D) {0.29, 5.99}

Find the exact value of the expression. Do not use a calculator. 4 202) sin-1 sin 7 A)

4 7

202) C)

Solve the equation on the interval [0, 2 ). 203) Suppose f(x) = 6 csc - 2. Solve f(x) = 4. 3 A) B) 2 2

201)

7 4

203) C) {2 }

Express the sum or difference as a product of sines and/or cosines. 204) cos(3 ) - cos(5 ) A) cos(-2 ) B) 2 sin(4 ) sin C) -2 sin(4 ) sin

}

D) -2 cos(4 ) sin

204)

Use the information given about the angle , 0 2 , to find the exact value of the indicated trigonometric function. 3 3 Find sin . < <2 205) sin = - , 205) 5 2 2 A) -

5 5

10 10

Use the Half-angle Formulas to find the exact value of the trigonometric function. 206) sin 22.5° 1 1 1 2- 2 2+ 2 2+ 2 A) B) C) 2 2 2 Solve the equation on the interval 0 207) tan2 = 3

D) -

1 D) 2

30 10

206) 2-

<2 .

4 , 3 3

5 7 11 , , , 6 6 6 6

2 4 5 , , 3 3 3 3

7 6 6

207)

Find the exact value of the expression. 208) cos 20° cos 40° - sin 20° sin 40° 1 A) B) 4

208) 3

3 2

1 2

Write the trigonometric expression as an algebraic expression in u. 209) sin (tan-1 u) A) u u2 + 1

u2 + 1

u u2 - 1 C) u2 - 1

u2 + 1

209) u u2 + 1 D) u2 + 1

Write the trigonometric expression as an algebraic expression containing u and v. 210) cos(sin-1 u - cos-1 v) A) uv + ( 1 - u2 )( 1 - v2 ) C) v 1 - u2 + u 1 - v2

210)

B) uv - ( 1 - u2 )( 1 - v2 ) D) v 1 - u2 - u 1 - v2

Given that f(x) = sin x, g(x) = cos x, and h(x) = tan x, evaluate the given function. The point (x, 3), on the circle 1 x 2 + y2 = 4, also lies on the terminal side of an angle in standard position. The point , y , on the circle x 2 + y2 = 1, also 4 lies on the terminal side of an angle 211) g( + ) 3 - 15 A) 8

in quadrant IV.

-2 2 + B) 6

211)

1+3 5 C) 8

3 + 15 8

Solve the problem. 212) On a Touch-Tone phone, each button produces a unique sound. The sound produced is the sum of two212) tones, given by y = sin (2 lt) and y = sin (2 ht) where l and h are the low and high frequencies (cycles per second) shown on the illustration.

The sound produced is thus given by y = sin (2 lt) + sin (2 ht) Write the sound emitted by touching the 0 key as a product of sines and cosines. A) y = 2 sin(536 t) cos(2,418 t) B) y = 2 sin(268 t) cos(2,150 t) C) y = 2 sin(2,150 t) cos(268 t) D) y = 2 sin(2,418 t) cos(536 t)

Find the exact solution of the equation. 213) 4 cos-1 (5x) =

213)

2 10

1 B) 10

Solve the equation on the interval 0 1 214) 1 - sin = 2

<2 .

11 6

5 2 2

3 10

214) B)

5 6

4 3

2 3

Write the trigonometric expression as an algebraic expression in u. 215) cos (cot-1 u) u2 + 1

u2 + 1

u u2 + 1 B) u2 + 1

215) u2 + 1

u2 - 1

Find the exact value of the expression. tan 55° + tan 95° 216) 1 - tan 55° tan 95° 3 3

A) -

216) C) - 3

B) -2

D) -

1 2

Write the trigonometric expression as an algebraic expression containing u and v. 217) cos(sin-1 u + cos-1 v) A) uv - ( 1 - u2 )( 1 - v2 ) C) uv + ( 1 - u2 )( 1 - v2 )

217)

B) v 1 - u2 + u 1 - v2 D) v 1 - u2 - u 1 - v2

Given that f(x) = sin x, g(x) = cos x, and h(x) = tan x, find the exact value of the composite function. 218) f-1 g A)

218)

D) -

Use a graphing utility to solve the equation on the interval 0° x < 360°. Express the solution(s) rounded to one decimal place. 219) sin2 x - 8 sin x - 4 = 0 219)

A) 28.2°, 151.8°, 208.2°, 331.8° C) No solution

B) 208.2°, 331.8° D) 28.2°, 151.8°

Use the information given about the angle , 0 2 , to find the exact value of the indicated trigonometric function. 5 , Find sin . < <2 220) sin = 220) 5 2 2 A) -

5+2 5 10

B) -

5-2 5 10

5+2 5 10

5-2 5 10

Given that f(x) = sin x, g(x) = cos x, and h(x) = tan x, evaluate the given function. The point (x, 3), on the circle 1 x 2 + y2 = 7, also lies on the terminal side of an angle in quadrant II. The point - , y , on the circle x 2 + y2 = 1, also lies 3 on the terminal side of an angle 221) g(2 ) 4 3 A) 7

in quadrant III.

221) 4 3 D) 7

1 C) 7

1 B) 7

Find the domain of the function f and of its inverse function f-1 . 222) f(x) = 6 sin(2x - 1)

222)

A) Domain of f: [-6, 6] Domain of f-1 : ( , )

B) Domain of f: ( , ) Domain of f-1 : [-6, 6]

C) Domain of f: ( , ) Domain of f-1 : [-2, 2]

D) Domain of f: -

Domain of f-1 : ( , )

Solve the equation on the interval 0 223) 3 sin - cos = -1 A) 0,

<2 . 3 , 2 6

1 1 , 2 2

C) 0,

2 3

7 6

223)

Use the information given about the angle , 0 2 , to find the exact value of the indicated trigonometric function. 1 Find cos(2 ). 224) cos = - , csc < 0 224) 7 A)

-8 3 49

8 3 49

Complete the identity. 225) sin [sin(3 ) + sin 5 )] = ? 1 A) cos [cos(3 ) - cos(5 )] 2 C) cos

47 49

D) -

47 49

225) B) cos

[cos(3 ) - cos(5 )]

[cos(3 ) + cos(5 )]

1 cos 2

[cos(3 ) + cos(5 )]

Find the exact value of the expression. Do not use a calculator. 226) sin-1 sin A) 5

226)

C) -

D) -5

Use the information given about the angle , 0 227) sec

= 4, 0 <

Find cos

10 4

2 , to find the exact value of the indicated trigonometric function.

8-2 4

227)

6 4

8+2 4

Find the exact value of the expression. 11 228) sin 12 24

229)

228) 2+ 4

6+ 4

C) -

1 - tan 80° tan 70° tan 80° + tan 70° 3

230) cos tan-1 A)

229) 3

B) -

3 3

D) -

5 4 - cos-1 12 5

7 13

230) B)

Solve the equation on the interval 0 231) cos2 = 3(1 - sin ) A) {0}

63 65

13 24

52 65

<2 . 231) B)

D) { }

Solve the equation. Give a general formula for all the solutions. 232) sin = 1

232)

+ 2k }

= 0 + 2k }

+ 2k

3 + 2k 2

Find the exact value of the expression. 233) csc-1 -2 A) -

233) B)

Use the information given about the angle , 0 234) sec A)

= 4, 0 < 6 4

Find cos

2 , to find the exact value of the indicated trigonometric function. 2

234)

8 + 2 15 4

10 4

8 - 2 15 4

Use a calculator to solve the equation on the interval 0 235) cos = -0.92 A) {2.74, 3.54} B) {0.40, 2.74} Solve the equation on the interval 0 3 236) cos(2 ) = 2 A) C)

< 2 . Round the answer to two decimal places. C) {2.74, 5.88}

D) {0.40, 3.54}

235)

<2 . 236)

11 13 23 , , 12 12 12

3 2

11 6 6 ,

Use the information given about the angle , 0 2 , to find the exact value of the indicated trigonometric function. 15 3 , Find cos . < <2 237) sin = 237) 17 2 2 A)

5 34 34

4 17

C) -

3 34 34

D) -

5 34 34

Find the exact value of the expression. 1 3 238) sin cos-1 - sin-1 2 2 A)

3 3

238) B) 1

C) 0

2 3 2

Solve the problem. 239) The function I(t) = 40 sin 60 t -

represents the amperes of current produced by an electric

239)

generator as a function of time t, where t is measured in seconds. Find the smallest value of t for which the current is 20 amperes. Round your answer to three decimal places, if necessary. A) 0.017 B) 0.011 C) 0.033 D) 0.008

Find the exact value of the expression. 240) tan(cos-1 1) A)

241) cos2 A)

2 2

240) B) -1

C) 0

3 2

1 4 sin-1 2 5 9 10

Solve the problem using Snell's Law:

241) B)

4 5

16 25

1 5

sin 1 v1 = . sin 2 v2

242) A light beam traveling through air makes an angle of incidence of 47° upon a second medium. The refracted beam makes an angle of refraction of 38°. What is the index of refraction of the material of the second medium? Give the answer to two decimal places. A) 0.84 B) 0.62 C) 0.73 D) 1.19 27

242)

Use the Half-angle Formulas to find the exact value of the trigonometric function. 243) sin 75° 1 1 1 2+ 3 2- 3 2- 3 A) B) C) 2 2 2

243)

1 D) 2

Use a graphing utility to solve the equation on the interval 0° x < 360°. Express the solution(s) rounded to one decimal place. 244) sin2 x - 8 sin x + 16 = 0 244)

A) 208.2°, 331.8° C) 28.2°, 151.8°

B) 28.2°, 151.8°, 208.2°, 331.8° D) No solution

Find the exact value under the given conditions. 12 15 , , < < ; sin = < 245) cos = 13 2 17 2 220 21

A) -

B) -

Find tan( + ).

220 221

20 3

245) D) -

220 171

Solve the problem. 246) Given f(x) = 5 tan x, for what values of x is f(x) > -5 on the interval A) -

, 4 2

B) -

Solve the equation on the interval 0 247) (csc - 2)(cot + 1) = 0 3 5 11 , , , A) 4 6 4 6

, 2 4

C) -

3 5 7 , , 6 4 6 4

248) 2 cos2

- 3 cos 1 A) 0, , 6 6

+1=0

, 4 4

246) D) 0,

<2 .

, ? 2 2

5 B) 0, , 3 3

3 7 11 , , , 6 4 4 6

3 5 5 , , 6 4 6 4

247)

2 C) 0, , 3 3

5 , , 3 2 3

Find the exact value of the expression. 1 4 249) sin2 cos-1 2 5 A)

1 25

249) B)

1 10

1 5

Use a calculator to find the value of the expression rounded to two decimal places. 250) tan-1 (-1.7) A) -1.04

248)

B) -0.53

C) -30.47

9 10

D) -59.53

250)

in quadrant III.

251)

4 3 B) 7

4 3 D) 7

1 C) 7

Use a calculator to find the value of the expression in radian measure rounded to two decimal places. 7 252) sec-1 3 A) -2.01

B) 2.01

C) 1.13

Complete the identity. 253) sin(2 ) sin(4 ) cos(2 ) cos(4 ) = ? A) cos2 (16 ) C)

cos2 (2 ) - cos2 (6 ) 4

Use the information given about the angle , 0 254) cot

= -3, sec

3 - 10 20

Find sin

D) 0.50

sin2 (16 ) 4

cos2 (6 ) + cos2 (2 ) 4

253)

2 , to find the exact value of the indicated trigonometric function. 2

254)

3 + 10 20

B) -

10 - 3 10 20

10 + 3 10 20

Find the exact value of the expression. 3 1 255) tan tan-1 + sin-1 4 2 A)

2 6 5

252)

255) B)

9+4 3 12 - 3 3

2 3 5

2 3 + 2 10 9

Given that f(x) = sin x, g(x) = cos x, and h(x) = tan x, find the exact value of the composite function. 256) f-1 g A)

256)

B) -

D) -

Express the sum or difference as a product of sines and/or cosines. 9 5 + sin 257) sin 2 2 A) 2 cos(7 ) sin

B) 2 sin

7 cos 2

C) 2 sin

257) 7 sin 2

D) 2 sin(7 )

Use the information given about the angle , 0 2 , to find the exact value of the indicated trigonometric function. 1 Find sin . 258) cos = , csc > 0 258) 4 2 A)

6 4

10 4

Solve the equation on the interval 0 259) 3 sin - cos = -1 3 , A) 2 6

8 - 2 15 4

8 + 2 15 4

7 , 2 6

<2 . 2 B) 0, 3

C) 0,

259)

Given that f(x) = sin x, g(x) = cos x, and h(x) = tan x, find the exact value of the composite function. 260) g-1 f

260)

A) -

Solve the equation on the interval 0 261) cos(2 ) = 2 - cos(2 )

<2 . 261)

2 4 , , B) 0, 3 3

A) No solution C)

7 9 15 , , 8 8 8 8 ,

3 5 7 , , 4 4 4 4 ,

Find the exact value of the expression. 3 262) cot-1 3 A) -

262) B) -

Use a calculator to solve the equation on the interval 0 263) tan = 5.7 A) {1.40, 2.97} B) {1.40, 4.89} Find the exact value of the expression. 264) tan-1 (1) 7 A) 4

< 2 . Round the answer to two decimal places. C) {1.40, 1.74}

D) {1.40, 4.54}

264)

5 B) 4

265) sin 15° A)

263)

265) 2( 3 - 1) 4

Solve the equation on the interval 0 266) 2 cos + 2 3 = 3 11 , A) 6 6

2( 3 + 1) 4

2( 3 - 1) 4

C) -

2( 3 + 1) 4

D) -

<2 . 266) B)

Express the sum or difference as a product of sines and/or cosines. 267) cos(5 ) + cos(3 ) A) 2 cos(4 ) sin B) 2 sin(4 ) sin C) 2 cos(4 ) cos

D) 2 cos(4 )

Given that f(x) = sin x, g(x) = cos x, and h(x) = tan x, find the exact value of the composite function. 4 268) h g-1 7 33

33 4

33 7

267)

268)

7 4

Use the information given about the angle , 0 2 , to find the exact value of the indicated trigonometric function. 3 Find cos(2 ). 269) csc = - , tan > 0 269) 2 A)

4 5 9

B) -

1 9

-4 5 9

Write the trigonometric expression as an algebraic expression in u. 270) csc (tan-1 u) A)

u2 + 1

u u2 + 1 B) u2 + 1

u2 + 1

270) u2 + 1

u2 - 1

Solve the problem. 271) The altitude of a projectile in feet (neglecting air resistance) is given by 16 y = (tan )x x2 , 2 v cos2

271)

where x is the horizontal distance covered in feet and v is the initial velocity of the projectile at an angle from the horizontal. Find the firing angle (in degrees) of a projectile fired at an initial velocity of 100 feet per second so that it strikes the ground 312.5 feet from the firing point. A) 50° B) 22.5° C) 45° D) 30°

Find the domain of the function f and of its inverse function f-1 . 272) f(x) = tan(x - 8) + 6

B) Domain of f: x

A) Domain of f: [-8, 8] Domain of f-1 : ( , ) C) Domain of f: x

(2k + 1) 2

(2k + 1) ; k an integer 2

272)

Domain of f-1 : ( , ) + 6; k an integer

D) Domain of f: ( , ) Domain of f-1 : [-7, -5]

Domain of f-1 : ( , )

Use the information given about the angle , 0 2 , to find the exact value of the indicated trigonometric function. 3 5 , csc > 0 Find sin(2 ). 273) sec = 273) 5 A)

1 9

-4 5 9

4 5 9

D) -

1 9

Solve the equation on the interval 0 274) 2 cos + 3 = 2 2 4 , A) 3 3

<2 . 5 11 , B) 6 6

5 7 , C) 6 6

2 5 , D) 3 3

Use the Half-angle Formulas to find the exact value of the trigonometric function. 275) tan 75° A) -2 + 3 B) -2 - 3 C) 2 - 3 Solve the equation on the interval [0, 2 ). 276) Suppose f(x) = cos - 1. Solve f(x) = 0. 3 A) B) } 2 Solve the problem. 277) If cos

1 , 3

Solve the equation on the interval 0 278) cos2 - 1 = 0 A)

C) {0}

1-2 2 1+2 2

277)

15 8

15 - 4 3 16

278)

3 , 2 2

C) {0}

D) {0, }

Find the exact value of the expression. 2 279) sin-1 2 A)

280) tan-1 tan A)

279) B)

C) -

3 5

280) B) -

3 5

C) -

Find the inverse function f-1 of the function f. 281) f(x) = 8 tan(10x - 9)

1 x tan-1 -9 B) f-1 (x) = 10 8

A) f-1 (x) = 8 tan-1 (10x - 9) C) f-1 (x) =

<2 . B)

275) D) 2 +

276)

in quadrant IV, find the exact value of tan

3 + 15 8

274)

1 x tan-1 +9 10 8

D) f-1 (x) =

1 x tan-1 +9 8 10

281)

Find the exact value of the expression. 2 1 282) cos sin-1 + 2 sin-1 3 3 A)

2 3 + 2 10 9

282) B)

2 6 5

2 3 5

7 5+8 2 27

Given that f(x) = sin x, g(x) = cos x, and h(x) = tan x, find the exact value of the composite function. 4 283) g h -1 7 A) -

65 7

7 65 65

C) -

7 65 65

283)

65 4

Use a graphing utility to solve the equation on the interval 0° x < 360°. Express the solution(s) rounded to one decimal place. 284) tan2 x + 5 tan x + 3 = 0 284)

A) 51.8°, 128.2° C) 70.5°, 109.5°, 180.0°

B) 49.8°, 130.2°, 229.8°, 310.2° D) 103.1°, 145.1°, 283.1°, 325.1°

Find the exact value of the expression. 4 285) cot sin-1 9 65 9

285)

B) -

65 4

4 65 65

D) -

9 65 65

Solve the equation. Give a general formula for all the solutions. 286) cos - 1 = 0 A) {

286)

+ 2k }

= 2k }

+ 2k

Find the exact value of the expression. 4 287) cos sin-1 5 A)

1 5

287) B)

3 5

C) -

3 5

Express the product as a sum containing only sines or cosines. 9 288) sin cos 2 2

4 5

288)

1 [cos(10 ) - sin(8 )] 4

1 [sin(5 ) - sin(4 )] 2

1 [cos(5 ) + sin(4 )] 2

1 sin cos(9 ) 4

D) -

Solve the equation on the interval 0 289) 2 cos(2 ) = 3 A)

3 2

11 6

2 - cos

289)

11 13 23 , , , B) 12 12 12 12

290) sin

<2 .

290) B)

Write the trigonometric expression as an algebraic expression in u. 291) tan (csc-1 u) u2 + 1 u2 + 1

u2 - 1 u

291) u2 - 1

u2 - 1 u2 - 1

Use the information given about the angle , 0 2 , to find the exact value of the indicated trigonometric function. 4 3 2 Find cos . 292) cos = , 292) 5 2 2 A) -

3 10 10

B) -

2 5

3 10 10

2 5

Solve the equation. Give a general formula for all the solutions. 293) sin = 0

293)

= 0 + 2k }

=0+k }

+ 2k

Write the trigonometric expression as an algebraic expression in u. 294) tan (sin-1 u) A)

u u2 + 1 u2 + 1

1 - u2 u

Find the exact value under the given conditions. 5 8 , , < < ; sin = < 295) cos = 13 2 17 2 A) -

140 171

294)

u 1 - u2 1 - u2

1 - u2

Find tan( - ).

20 3

C) -

20 3

295) D) -

220 171

Solve the problem. 296) What are the x-intercepts of the graph of f(x) = 2 sin(3x) + 3 on the interval [0, 2 ]? 11 14 17 10 11 16 17 , , , , , , , , , , A) B) 9 9 9 9 9 9 9 9 9 9 9 9 C)

11 19 23 , , 18 18 18

296)

Write the trigonometric expression as an algebraic expression in u. 297) cot (cos-1 u) 1 - u2

1 - u2

297)

u u2 + 1 C) u2 + 1

u 1 - u2 D) 1 - u2

Use the information given about the angle , 0 2 , to find the exact value of the indicated trigonometric function. 3 Find cos . < < 298) cos = - , 298) 5 2 2 A)

30 10

B) -

5 5

Express the product as a sum containing only sines or cosines. 299) cos(5 ) cos(4 ) A) cos2 (20 2 ) C)

1 [cos(9 ) - sin ] 2

5 5

30 10

D) -

299)

1 B) [cos(9 ) - cos ] 2

1 [ cos 2

+ cos(9 )]

Find the exact value of the expression. 2 300) sin 2 sin-1 2 A)

1 2

300) B) 1

D) 0

Use the information given about the angle , 0 2 , to find the exact value of the indicated trigonometric function. 12 , Find sin . < < 301) tan = 301) 5 2 2 A)

3 13 13

Solve the equation on the interval 0 302) 2 cos + 1 = 0 3 , A) 2 2

B) -

2 13 13

D) -

3 13 13

<2 . 5 , 3 3

Use a calculator to solve the equation on the interval 0 303) 7 cot = - 4 A) 2.62, 5.76 B) 2.09, 4.19

3 C) 2

2 4 , D) 3 3

< 2 . Round the answer to two decimal places. C) 2.09, 5.23

D) 2.62, 6.80

Find the exact value of the expression. 7 304) cos-1 sin 6 A)

302)

303)

304) B)

2 3

4 5

Solve the equation on the interval 0 3 305) tan2 = - sec 2 A) C)

3 3

, ,

<2 . 305) B)

3 3

, ,

3 6

Given that f(x) = sin x, g(x) = cos x, and h(x) = tan x, find the exact value of the composite function. 21 306) f h -1 20 A) -

21 29

B) -

20 21

C) -

21 2 4

306)

21 29

Write the trigonometric expression as an algebraic expression containing u and v. 307) sin(tan-1 u + tan-1 v) A) C)

1 - uv u2 + 1 ·

v2 + 1

u+v u2 + 1 ·

v2 + 1

Solve the equation on the interval 0 308) 3 cot2 - 4 csc = 1 7 11 , A) 6 6

307)

u2 + 1 · v2 + 1 1 - uv 1 + uv u2 + 1 ·

v2 + 1

<2 . B)

5 , 6 6

Express the sum or difference as a product of sines and/or cosines. 309) sin(6 ) - sin(4 ) A) -2 sin cos(5 ) B) 2 sin(5 ) cos C) -2 sin(5 ) cos

308)

7 D) 6

D) 2 sin

cos(5 )

309)

Use the information given about the angle , 0 2 , to find the exact value of the indicated trigonometric function. 13 , Find sin . < < 310) sec = 310) 12 2 2 A) -

26 26

B) -

5 26

5 26 26

26 26

in quadrant III.

311)

4 2 B) 9

4 2 C) 7

4 2 D) 7

in quadrant IV.

-2 2 + B) 6

312)

3 - 15 8

15 - 4 3 16

Solve the problem.

313) What are the x-intercepts of the graph of f(x) = 4 cos2 x - 3 on the interval [0, 2 ]? 1 5 A) , B) , 6 6 3 3 C)

5 7 1 , , 6 6 6

313)

2 4 5 , , 3 3 3

Use a calculator to find the value of the expression rounded to two decimal places. 2 314) cos-1 3 A) -0.49

B) 2.06

C) -28.13

314) D) 118.13

Find the exact value of the expression. 1 315) tan cos-1 2 A) -

3 3

315) B) - 3

Solve the equation on the interval 0 316) tan + sec = 1 A) {0}

14 - 24 21 125

C) No solution

5 D) 4

<2 .

Find the exact value under the given conditions. 24 2 , < < ; cos = , 0 < 317) sin = 25 2 5 A)

C) -1

316)

Find cos ( - ).

48 - 7 21 125

48 + 7 21 125

317) D)

-14 + 24 21 125

Use the Half-angle Formulas to find the exact value of the trigonometric function. 318) sin

318)

1 2

C) -

1 2

D) -

1 2

Solve the equation on the interval 0 319) sec2 - 2 = tan2 A)

<2 . 319) B) No solution

Solve the equation. Give a general formula for all the solutions. 2 320) cos = 2 A)

4 4

320)

+ 2k ,

7 + 2k 4

+ 2k ,

5 + 2k 4

Find the exact value of the expression. Do not use a calculator. 321) sin [sin-1 (-0.4)] A) -0.4

B) -2.5

3 4

+ 2k ,

4 + 2k 3

C) -2.5679

321)

D) -0.6

Use the information given about the angle , 0 2 , to find the exact value of the indicated trigonometric function. 1 Find cos . 322) cos = , 0 < < 322) 4 2 2 6 4

8-2 4

10 4

8+2 4

Use the Half-angle Formulas to find the exact value of the trigonometric function. 5 323) sin 12 A) -

1 2

C) -

1 2

323) D)

1 2

Find the exact value of the expression. 4 324) tan 2 cos-1 5 A) -

12 7

324) B)

75 32

Find the exact value under the given conditions. 12 8 , 0 < < ; cos = , 0< 325) sin = 13 2 17 A)

220 221

B) -

C) -

24 7

D) -

96 35

Find cos ( + ).

140 221

21 221

325) D)

171 221

Use the information given about the angle , 0 2 , to find the exact value of the indicated trigonometric function. 3 Find cos(2 ). 326) sin = , 0 < < 326) 5 2 A)

24 25

B) -

7 25

1 5

Solve the equation on the interval 0 2 = 327) cos 2 2 2

<2 . 327)

3 7 , 8 8

3 9 11 , , 8 8 8

3 9 , 8 8 4

5 9 13 , , 4 4 4

Use a calculator to find the value of the expression in radian measure rounded to two decimal places. 328) csc-1 - 8 A) -0.13

B) 1.70

C) -7.18

D) 97.18

Find the exact value of the expression. 13 329) tan 12 A)

3-2

A) C)

9 9

331) 5 2 sin A)

329) 3

B) -2 -

Solve the equation on the interval 0 3 =330) cot 2 3

C) 2 -

D) 2 +

330)

10 16 22 , , 9 9 9

10 9

+ 4 = -1 3

<2 .

328)

9 9

10 9

10 16 , 9 9

11 , 6 6

331) D)

Solve the problem. 332) When granular materials are allowed to fall freely, they form conical (cone-shaped) piles. The naturally occurring angle of slope, measured from the horizontal, at which the loose material comes to rest is called the angle of repose and varies for different materials. The angle of repose is r related to the height h and base radius r of the conical pile by the equation = cot-1 . A certain h

332)

granular material forms a cone-shaped pile with a height of 11 feet and a base diameter of 18.7 feet. What is the height of a pile that has a base diameter of 140 feet? A) 238.00 ft B) 94.71 ft C) 82.35 ft D) 41.18 ft

Solve the equation on the interval 0 333) sin2 = 5(cos + 1) A) {0}

<2 . 333) B) { }

D) No solution

Find the exact value of the expression. 334) tan-1 (- 3) A) -

334) B)

C) -

Find the exact solution of the equation. 335) cos-1 x = 0 A) {1}

B) { }

C) {-1}

335)

D) {0}

Use a calculator to find the value of the expression rounded to two decimal places. 2 336) sin-1 3 A) 28.13

B) 0.49

Solve the equation on the interval 0 337) 6 csc - 3 = 3 3 A) 2

<2 .

C) 61.87

336) D) 1.08

337)

B) { }

C) {2 }

Express the product as a sum containing only sines or cosines. 338) -2 sin(5 ) sin A) cos(6 ) + cos(4 ) B) cos(7 ) + cos(3 ) C) cos(7 ) - cos(3 ) D) cos(6 ) - cos(4 )

338)

Use the information given about the angle , 0 2 , to find the exact value of the indicated trigonometric function. 7 3 , Find cos(2 ). < < 339) tan = 339) 24 2 A)

336 625

Solve the equation on the interval 0 340) 1 + cos = 2 sin2 A)

2 4 , , 3 3

527 625

C) -

527 625

D) -

336 625

<2 . B)

, ,

5 3

Find the exact solution of the equation. 341) 3 tan-1 (2x) = A)

3 6

7 3

11 6

341)

Solve the equation on the interval 0 3 342) tan = 2 3

340)

3 2

3 4

1 D) 4

<2 . 342) B)

4 3

343) 4 cos2x - 3 = 0 5 , A) 3 3 C)

B) 3

5 3

343)

5 1 , , , 6 6 6 6 ,

Use a graphing utility to solve the equation on the interval 0° x < 360°. Express the solution(s) rounded to one decimal place. 344) sin2 x + 8 sin x - 4 = 0 344)

A) 208.2°, 331.8° C) 28.2°, 151.8°

B) 28.2°, 151.8°, 208.2°, 331.8° D) No solution

345) f

in quadrant III.

345)

A) -

6 3

C) -

3 3

Find the exact value of the expression. 346) sec[tan-1 (- 3)] A)

1 2

346) B)

2 3 3

Use a calculator to solve the equation on the interval 0 347) 2 csc = 5 A) {0.41, 2.73} B) {0.20}

C) 2

D) -

2 3 3

< 2 . Round the answer to two decimal places. C) {0.20, 2.94}

Find the exact value of the expression. 348) sin 255° cos 15° - cos 255° sin 15° 3 1 A) B) 2 2

D) {0.41}

347)

348) C)

3 2

17 4

Find the exact value of the expression. Do not use a calculator. 349) cos-1 cos A) -

349)

C) -10

D) 10

Find the exact value of the expression. 8 350) cos tan-1 9 A)

9 145 145

350) B) -

9 145 145

C) -

145 9

145 8

Solve the equation on the interval 0 351) 2 sin2 - 3 sin - 2 = 0 A)

<2 . 7 , , 2 6 6

Find the exact value under the given conditions. 1 1 352) cos = , 0 < < ; sin = - , - < 3 2 2 2 A)

9 3-8 2 5

5 , 3 3

351) 6

Find tan( + ).

9 3+8 2 3

9 3+8 2 5

352) D)

9 3-8 2 3

Given that f(x) = sin x, g(x) = cos x, and h(x) = tan x, find the exact value of the composite function. 3 353) g f-1 5 A) -

3 5

B) -

4 5

353)

1 5

Use a graphing utility to solve the equation on the interval 0° x < 360°. Express the solution(s) rounded to one decimal place. 354) 2 + 13 sin x = 14 cos2 x 354)

A) 34.9°, 214.9°

B) 55.2°, 124.9°

C) 34.9°, 145.2°

D) 214.9°, 325.2°

Find the exact value of the expression. 2 355) sin cos-1 2 A) -

2 2

355) B)

2 2

3 2

D) -

Use a calculator to find the value of the expression rounded to two decimal places. 356) sin-1 (0.3) A) 17.46

Solve the problem. 357) If cos A)

1 , 3

-2 2 + 6

B) 0.30

C) 1.27

in quadrant IV, find the exact value of sin

15 8

15 - 4 3 16

B) 5.74

C) 1.47

D) 72.54

356)

357)

3 3

Use a calculator to find the value of the expression rounded to two decimal places. 358) cos-1 (0.1) A) 84.26

1 2

3 + 15 8

D) 0.10

358)

Given that f(x) = sin x, g(x) = cos x, and h(x) = tan x, find the exact value of the composite function. 2 359) f g-1 9 A)

2 9

77 2

2 77 77

77 9

Express the product as a sum containing only sines or cosines. 360) sin(4 ) sin(8 ) 1 1 A) [cos(12 ) - sin(4 )] B) [cos(4 ) - cos(12 )] 2 2 C)

1 [- cos(4 ) - cos(12 )] 2

Solve the equation on the interval 0 361) tan + sec = 1 A)

360)

D) sin2 (32 2 )

<2 . B) {0}

5 D) 4

C) No solution

Solve the equation. Give a general formula for all the solutions. 362) tan = 3 A)

3 3

A) C)

2 A) 3

Solve the equation on the interval 0 365) cos2 + 2 cos + 1 = 0 A)

3 , 2 2

= sin 3 7 , A) 4 2

3 6

+ 2k ,

+ 2k

<2 .

, 4 3

Find the exact value of the expression. 364) sec-1 (-2)

361)

362)

+ 2k

Solve the equation on the interval 0 363) sin2 - cos2 = 0

359)

4 B) 3

3 5 7 , , , 4 4 4 4

, 4 6

363)

364)

2 C) 3

D) -

<2 . B)

366) cos

365)

7 , 4 4

C) {2 }

5 4

D) { }

7 4

3 5 , 4 4

366)

Use a calculator to solve the equation on the interval 0 367) csc = -7 A) 6.14, 3.28 B) -1.71, 1.43

< 2 . Round the answer to two decimal places. C) 0.14, 3.28

D) -1.71, 8.00

367)

Use a graphing utility to solve the equation on the interval 0° x < 360°. Express the solution(s) rounded to one decimal place. 368) cos2 x + cos x - 1 = 0 368)

A) 49.8°, 130.2°, 229.8°, 310.2° C) 51.8°, 308.2°

B) 70.5°, 109.5°, 180.0° D) 103.2°, 145.2°, 283.2°, 325.2°

Find the exact value of the expression. 369) sin-1 (0.5) A)

7 D) 3

2 5 C) 5

5 2 D) 2

370) sin(tan-1 2)

369)

370)

A) 5 2

B) 2 5

in quadrant III.

371)

4 2 9

C) -

4 2 7

Express the product as a sum containing only sines or cosines. 5 cos 372) cos 2 2 1 cos2 (5 ) 4

1 [cos(3 ) - sin(2 )] 2

1 [cos(2 ) + cos(3 )] 2

1 [cos(6 ) - sin(4 )] 4

<2 . 2 4 , , B) 0, 3 3

9 8

D) No solution

4 2 7

372)

Solve the equation on the interval 0 373) sin(2 ) + sin = 0 3 5 7 , , , A) 4 4 4 4

373)

374) 4 sin2

-3=0 2 , 3 3

A) C)

2 4 5 , , 3 3 3

374)

5 7 11 , , , 6 6 6 6

5 6

Use the Half-angle Formulas to find the exact value of the trigonometric function. 5 375) cos 12 A) -

1 2

C) -

1 2

375) D)

1 2

Find the exact value of the expression. 3 376) cot-1 3 A)

376) B)

Solve the equation on the interval 0 377) 3 cot2 - 4 csc = 1 7 11 , A) 6 6

<2 . B)

377)

5 , 6 6

378) h

in quadrant III.

378)

A) -

2 2

C) -

Find the domain of the function f and of its inverse function f-1 . 379) f(x) = 7 sin(9x)

379)

A) Domain of f: ( , ) Domain of f-1 : [2, 16]

B) Domain of f: ( , ) Domain of f-1 : [-7, 7]

C) Domain of f: ( , ) Domain of f-1 : [-9, 9]

D) Domain of f: -

1 1 , 9 9

Domain of f-1 : ( , )

Solve the problem. 380) If sin

1 , 4

in quadrant II, find the exact value of sin

3 - 15 8

1+3 5 8

380)

3 15 - 4 3 16

1-3 5 8

381) When granular materials are allowed to fall freely, they form conical (cone-shaped) piles. The naturally occurring angle of slope, measured from the horizontal, at which the loose material comes to rest is called the angle of repose and varies for different materials. The angle of repose is r related to the height h and base radius r of the conical pile by the equation = cot-1 . Find the h

381)

angle of repose for a granular material which forms a cone-shaped pile with a height of 18 feet and a base diameter of 50.4 feet. A) = 35.54° B) = 54.46° C) = 70.35° D) = 19.65°

Find the exact value of the expression. 2 3 382) sec-1 3 A) -

382) B)

C) -

Find the inverse function f-1 of the function f. 383) f(x) = cos(x - 7) - 8 A) f-1 (x) = cos-1(x - 7) - 8

383)

<2 .

7 9 15 , , 8 8 8

Use the information given about the angle , 0 385) tan A)

= 2, cos

Find sin

5+ 5 10

2 +k , 3

3 5 7 , , 4 4 4

2 , to find the exact value of the indicated trigonometric function. 2

385)

5- 5 10

C) -

Solve the equation. Give a general formula for all the solutions. 386) 2 cos + 1 = 0 3 = + 2k , = + 2k A) B) 2 2 C)

384)

2 4 , , B) 0, 3 3

A) No solution C)

B) f-1 (x) = cos-1(x + 7) + 8 D) f-1 (x) = cos-1(x - 8) - 7

C) f-1 (x) = cos-1(x + 8) + 7 Solve the equation on the interval 0 384) 2 cos(2 ) = 1

4 +k 3

1 - 5 10

2 = + 2k , 3 =

3 +k 2

D) -

4 = + 2k 3

1 + 5 10

386)

Solve the equation on the interval 0 387) csc(3 ) = 0 2 4 , , A) 0, 3 3 C)

<2 .

387) B) No solution

3 5 7 , , 4 4 4 4 ,

9 8 8 ,

Use the Half-angle Formulas to find the exact value of the trigonometric function. 388) sin 165° 1 1 1 2+ 3 2- 3 2- 3 A) B) C) 2 2 2 Find the exact value of the expression. 389) cot 195° A) - 3 + 2 B)

-6 - 4 21 25

Solve the problem using Snell's Law:

389) 3-2

Find the exact value under the given conditions. 4 3 2 21 ; tan = , < 390) sin = - , < < 5 2 21 2 A)

388)

1 D) 2

C) - 3 - 2

Find cos ( + ).

8 - 3 21 25

3+2

6 - 4 21 25

390) D)

8 + 3 21 25

sin 1 v1 = . sin 2 v2

391) A ray of light near the horizon with an angle of incidence of 76° enters a pool of water and strikes a fish's eye. If the index of refraction is 1.33, what is the angle of refraction (to two decimal places)? A) 43.15° B) 43.38° C) 46.62° D) 46.85° Find the exact value of the expression. 392) sin 10° cos 110° + cos 10° sin 110° 3 1 A) B) 2 6 393)

392) C) -

3 2

D) -

1 2

tan 175° - tan 55° 1 + tan 175° tan 55°

A) - 3

393) B) -2

Use a calculator to solve the equation on the interval 0 394) cos = 0.89 A) {0.47, 2.04} B) {0.47, 5.81} Solve the equation on the interval 0 395) 2 sin2 = 3(cos + 1) 5 11 , A) 0, 6 6

391)

C) -

1 2

D) -

3 3

< 2 . Round the answer to two decimal places. C) {0.47, 3.62}

D) 0.47, 2.67

2 5 , C) 0, 3 3

2 4 , , D) 3 3

394)

<2 . 5 7 , , B) 6 6

395)

Find the exact solution of the equation. 396) 2 cos-1 x = A) {0}

396)

B) {1}

Express the product as a sum containing only sines or cosines. 397) sin(8 ) sin(5 ) 1 1 A) [ cos(3 ) - cos(13 )] B) [sin(13 ) + cos(3 )] 2 2 C) sin2 (40 2 )

397)

1 [cos(13 ) - cos(3 )] 2

Write the trigonometric expression as an algebraic expression in u. 398) cos (sin-1 u) u2 + 1

u2 - 1

398) 1 - u2

u2 + 1 u

Find the exact value of the expression. 3 399) sin-1 2 A)

399) B)

Solve the equation. Give a general formula for all the solutions. 2 3 400) csc = 3 3 A) {

+ 6k ,

= 2 + 6k }

+ 6k ,

+ 6k

7 , 4 4

Solve the equation on the interval 0 401) 2 cos2 - 1 = 0 A) C)

9 3

+ 2k ,

18 9

+ 2k + 2k

<2 .

5 , 3 3 4

400)

3 5 7 , , 4 4 4

Use a calculator to solve the equation on the interval 0 402) 7 tan - 5 = 0 A) 0.62, 2.52 B) 0.62, 3.76

401)

2 4 5 , , 3 3 3

< 2 . Round the answer to two decimal places. C) 0.95, 4.09

D) 0.62, 5.66

402)

Solve the problem. 403) A weight suspended from a spring is vibrating vertically with up being the positive direction. The 3 t function f(t) = 10 sin represents the distance in centimeters of the weight from its rest 4 4

403)

position as a function of time t, where t is measured in seconds. Find the smallest positive value of t for which the displacement of the weight above its rest position is 5 cm. Round answer to three decimal places, if necessary. A) 0.556 B) 2.293 C) 1.586 D) 0.222

Find the inverse function f-1 of the function f. 404) f(x) = - sin(x + 7) - 4 A) f-1 (x) = -sin-1 (x + 4) - 7

404) B) f-1 (x) = -sin-1 (x + 7) - 4 D) f-1 (x) = sin-1 (x + 4) - 7

C) f-1 (x) = -sin-1 (x - 4) + 7 405) f(x) = 8 cos x + 9

x-9 A) f-1 (x) = cos-1 8

x+9 B) f-1 (x) = cos-1 8

C) f-1 (x) = 8 cos-1 x + 9

D) f-1 (x) = sin

405)

x-9 8

Use the Half-angle Formulas to find the exact value of the trigonometric function. 406) cos A)

406)

8 1 2

1 2

Find the exact value of the expression. 3 407) sin 2 cos-1 5 A)

24 25

407) B) -

24 25

12 25

D) -

12 25

Write the trigonometric expression as an algebraic expression in u. 408) sec (sin-1 u) A)

1 - u2

u2 - 1

408) 1 - u2

1 - u2

u2 - 1 u

Use the information given about the angle , 0 2 , to find the exact value of the indicated trigonometric function. 5 , Find cos . < <2 409) sin = 409) 5 2 2 A) -

5+2 5 10

5-2 5 10

C) -

5-2 5 10

5+2 5 10

Given that f(x) = sin x, g(x) = cos x, and h(x) = tan x, find the exact value of the composite function. 410) g-1 f A) -

410)

6 6

C) -

Use a calculator to solve the equation on the interval 0 411) 6 sin + 5 = 0 A) 2.56, 3.73 B) 2.16, 5.30

< 2 . Round the answer to two decimal places. C) 2.56, 5.70

D) 4.13, 5.30

Given that f(x) = sin x, g(x) = cos x, and h(x) = tan x, find the exact value of the composite function. 24 412) h g-1 25 A) -

7 24

25 24

C) -24

D) -

411)

412)

24 7

Use a graphing utility to solve the equation on the interval 0° x < 360°. Express the solution(s) rounded to one decimal place. 413) 3 cos2 x + 2 cos x = 1 413)

A) 103.2°, 145.2°, 283.2°, 325.2° C) 70.5°, 180.0°, 289.5°

B) 51.8°, 128.2° D) 49.8°, 130.2°, 229.8°, 310.2°

Find the exact value of the expression. Do not use a calculator. 414) tan [tan-1 (-0.4)] A) -0.4

B) -2.5

C) -2.3652

414)

D) -0.6

Find the exact value of the expression. 5 2 5 2 cos sin - sin 415) cos 18 9 18 9 A) -1

416)

415)

B) 1

2 2

D) 0

tan 65° - tan (-55°) 1 + tan 65° tan (-55°)

A) -

3 3

416) B) -

1 2

C) - 3

D) -2

Express the sum or difference as a product of sines and/or cosines. 417) sin(4 ) - sin(2 ) A) 2 sin cos(3 ) B) 2 sin(3 ) cos C) sin(3 ) cos

D) sin

Solve the equation on the interval [0, 2 ). 418) Suppose f(x) = 2 cos + 1. Solve f(x) = 0. 3 3 , A) B) 2 2 2

2 4 , D) 3 3

5 , 3 3

cos(3 )

417)

418)

Use the Half-angle Formulas to find the exact value of the trigonometric function. 419) tan

419)

A) 1 +

B) -1 +

C) 1 -

D) -1 -

Find the exact solution of the equation. 420) -4 tan-1 x = A) {-1}

420)

C) {1}

Use the Half-angle Formulas to find the exact value of the trigonometric function. 421) cos 165° 1 1 1 2+ 3 2+ 3 2- 3 A) B) C) 2 2 2 Express the product as a sum containing only sines or cosines. 422) sin(8 ) cos(5 ) A) sin cos(40 2) C)

1 [cos(13 ) - cos(3 )] 2

D) {0}

1 D) 2

421) 2-

422)

1 B) [sin(13 ) + sin(3 )] 2

1 [sin(13 ) + cos(3 )] 2

Use a calculator to find the value of the expression in radian measure rounded to two decimal places. 10 423) cot-1 17 A) -59.53

B) -0.53

C) -30.47

D) -1.04

Find the exact value of the expression. 4 3 424) cos tan-1 - sin-1 3 5 A)

2 6 5

424) B)

2 3 5

24 25

D) 1

425) cos-1 (1) A)

425) B) -

Use the information given about the angle , 0 426) tan A)

= 3,

423)

10 + 1 3

Find tan

D) 0

2 , to find the exact value of the indicated trigonometric function. 2

426)

10 - 1 -3

10 + 1 -3

10 - 1 3

in quadrant IV.

427)

3 - 15 8

3 + 15 8

15 - 4 3 16

Find the domain of the function f and of its inverse function f-1 . 428) f(x) = -6 cos(10x)

A) Domain of f: ( , ) Domain of f-1 : [4, 16] C) Domain of f: -

428)

B) Domain of f: ( , ) Domain of f-1 : [-10, 10]

1 1 , 10 10

D) Domain of f: ( , ) Domain of f-1 : [-6, 6]

Domain of f-1 : ( , )

Find the exact value of the expression. 429) cos[tan-1 (-1)] A) -

2 2

430) sec sin-1 -

429) B)

2 2

1 2

D) -

3 2

430)

A) 2

2 2

C) 1

Find the inverse function f-1 of the function f. 431) f(x) = -2 cos(10x + 5) 1 x -5 A) f-1 (x) = cos-1 2 10

C) f-1 (x) = -

D) 0

431) B) f-1 (x) = -2 cos-1 (10x + 5)

1 x cos-1 +5 10 2

D) f-1 (x) =

Use a calculator to solve the equation on the interval 0 432) sin = 0.42 A) {0.43, 2.71} B) {0.43, 2.00}

1 x cos-1 -5 10 2

< 2 . Round the answer to two decimal places. C) {0.43, 5.85}

D) {0.43, 3.58}

Find the exact value of the expression. 4 433) sec 2 tan-1 3 A)

24 7

432)

433) B) -

7 25

C) -

25 7

D) -

12 7

7 6

434) cos-1 cos A)

434) B)

Solve the equation on the interval 0 435) 2 3 sin(4 ) = 3

7 6

C) -

5 6

<2 .

A) {0} C) 0,

435)

5 , 4 4

2 7 7 13 5 19 , , , , , , , 12 6 3 12 6 12 3 12

Find the domain of the function f and of its inverse function f-1 . 436) f(x) = cos(x - 3) + 4 A) Domain of f: ( , ) B) Domain of f: ( , ) -1 Domain of f : [3, 5] Domain of f-1 : [-5, -3]

C) Domain of f: ( , ) Domain of f-1 : ( , )

436)

D) Domain of f: [-3, 3] Domain of f-1 : ( , )

Find the exact value of the expression. 2 437) tan sin-1 2 A)

437) B) 2

C) 1

Use the Half-angle Formulas to find the exact value of the trigonometric function. 438) cos 22.5° 1 1 1 2- 2 2+ 2 2- 2 A) B) C) 2 2 2 Find the exact solution of the equation. 439) 7 sin-1 x - 4 = 5 sin-1 x - 5 A) {-1}

Solve the equation on the interval 0 440) csc5 - 4 csc = 0 A) C)

441) sin2

3 5 , , 4 6 6

- cos2 + cos 5 7 , A) 0, 6 6

D) {0}

<2 .

3 5 , , , 4 4 3 6 4

1 2

438)

439)

1 C) 2

B) {1}

2 2

2 4 , , B) 0, 3 3

5 5 , , 4 3 3

2 4 , C) 0, 3 3

440)

3 5 7 , , , 4 4 4 4

5 D) 0, , 3 3

441)

442) sec

=- 2 ,

442) B)

6 6

11 6

, ,

11 6

Find the domain of the function f and of its inverse function f-1 . 443) f(x) = 4 tan x + 6 (2k + 1) ; k an integer A) Domain of f: x B) Domain of f: x 2 Domain of f-1 : [2, 10]

C) Domain of f: ( , ) Domain of f-1 : x

= 2, cos

445) sin

3 , 5

Find cos

B) -

2 , to find the exact value of the indicated trigonometric function. 2

16 65

B) -

Solve the equation on the interval 0 447) sec2 - 2 = tan2 A)

445)

5 5

10 10

Find cos ( + ).

33 65

C) -

56 65

63 65

447) C)

v2 + 1

1 + uv u2 + 1 ·

446)

<2 .

1 - uv u2 + 1 ·

30 10

D) -

Write the trigonometric expression as an algebraic expression containing u and v. 448) sin(tan-1 u - tan-1 v) A)

5- 5 10

B) No solution

5- 5 10

C) -

Find the exact value under the given conditions. 5 3 4 , < < 2 ; tan = - , < 446) sin = 13 2 3 2 A) -

444)

1 + 5 10

Find sin

5 5

A) -

D) Domain of f: ( , ) Domain of f-1 : [2, 10]

(2k + 1) ; k an integer 2

1 - 5 10

443)

Domain of f-1 : ( , )

Use the information given about the angle , 0 444) tan

(2k + 1) ; k an integer 2

v2 + 1

u-v u2 + 1 ·

v2 + 1

u2 + 1 · v2 + 1 1 - uv

448)

Use the information given about the angle , 0 2 , to find the exact value of the indicated trigonometric function. 7 3 , Find tan(2 ). < < 449) tan = 449) 24 2 A)

336 527

B) -

336 527

C) -

Find the exact value of the expression. 450) sin 200° cos 80° - cos 200° sin 80° 3 10 A) B) 2 3

527 336

450) 3 C) 2

1 D) 2

8 451) csc tan-1 3

3 73 73

451)

B) -

3 73 73

73 3

73 8

D) -

Use the information given about the angle , 0 2 , to find the exact value of the indicated trigonometric function. 12 , Find cos . < < 452) tan = 452) 5 2 2 A) -

2 13 13

B) -

3 13 13

2 13 13

Find the exact value of the expression. tan 5° + tan 25° 453) 1 - tan 5° tan 25° A) 2

453) B)

3 3

Express the product as a sum containing only sines or cosines. 454) cos(3 ) cos(7 ) A) cos2 (13 2 ) C)

1 [cos(4 ) + cos(10 )] 2

1 2

1 B) [cos(10 ) - cos(4 )] 2

D) Domain of f: ( , ) Domain of f-1 : [-6, 6]

454)

1 [cos(10 ) - sin(4 )] 2

Find the domain of the function f and of its inverse function f-1 . 455) f(x) = -6 cos(10x + 9) A) Domain of f: ( , ) B) Domain of f: ( , ) Domain of f-1 : ( , ) Domain of f-1 : [-10, 10]

C) Domain of f: [-6, 6] Domain of f-1 : ( , )

455)

Find the exact value under the given conditions. 3 21 , 0< < < ; cos = 456) sin = , 5 2 29 A)

24 145

Find sin ( - ).

143 145

C) -

17 145

456) D)

144 145

Solve the equation. Give a general formula for all the solutions. 457) cos = 0

457)

=0+k }

= 0 + 2k }

+ 2k

Find the exact solution of the equation. 458) -3 sin-1 (2x) = 3 4

458) 3 C) 4

1 B) 4

2 4

Find the exact value of the expression. 459) cot[sin-1 (-1)] A) 0

459) B) -

Solve the problem using Snell's Law:

3 2

C) -1

D) -

2 2

sin 1 v1 = . sin 2 v2

460) The index of refraction of light passing from air into a second medium is 1.56. If the angle of incidence is 81°, what is the angle of refraction (to two decimal places)? A) 50.72° B) 37.31° C) 39.28° D) 52.69° Use a calculator to find the value of the expression rounded to two decimal places. 2 461) sin-1 7 A) 16.60

B) 0.29

C) 73.40

461) D) 1.28

Find the exact value of the expression. 2 3 462) csc-1 3 A)

462) B)

C) -

D) -

463) tan 345° A) 2 +

460)

463) 3

2+ 3 4

C) -2 -

2- 3 4

464) csc tan-1 A)

3 3

464)

1 2

C) 2

2 3 3

Find the exact value of the expression. Do not use a calculator. 465) tan-1 tan A) -

465)

B) 8

D) -8

466) f

in quadrant III.

466)

2+ 7 14

2- 7 14

7-2 7 14

C) -

2( 3 - 1) 4

7+2 7 14

2( 3 - 1) 4

Find the exact value of the expression. 467) cos 285° A) - 2( 3 + 1)

Solve the equation on the interval 0 468) cot 2 A) C)

467) B) - 2( 3 - 1)

<2 .

468)

3 7 , 8 8 4

5 9 13 , , and 4 4 4

469) tan(2 ) - tan 5 , A) 4 4

3 8

3 7 11 15 , , , and 8 8 8 8

469) B) {0, }

C) {0}

2 7 7 13 5 , , , , , , 12 6 3 12 6 12 3

Use the information given about the angle , 0 2 , to find the exact value of the indicated trigonometric function. 5 , Find cos(2 ). < < 470) cos = 470) 13 2 A)

120 169

B) -

119 169

D) -

120 169

471) cos

3 , sin 5

30 10

Find cos

B) -

471)

30 10

5 5

Find the inverse function f-1 of the function f. 472) f(x) = 6 tan(7x)

A) f-1 (x) = 6 tan-1 (7x)

B) f-1 (x) =

1 x tan-1 6 7

1 x tan-1 7 6

D) f-1 (x) =

1 6 tan(7x)

C) f-1 (x) =

5 5

D) -

472)

Find the exact solution of the equation. 473) sin-1 x =

473)

A) {-1}

B) {0}

Find the exact value of the expression. Do not use a calculator. 474) sin [sin-1 (-0.3)] A) -2.7

B) 0.3

C) {1}

D) { }

C) -0.3

D) 2.7

474)

3 475) cos-1 cos 5

A) -

3 5

475) B)

2 5

C) -

2 5

3 5

Find the exact value of the expression. 24 476) cot cos-1 25 A)

25 24

476) B) -24

C) -

7 24

Use the Half-angle Formulas to find the exact value of the trigonometric function. 477) tan 165° A) 2 - 3 B) 2 + 3 C) -2 + 3

D) -

24 7

477) D) -2 -

Use the information given about the angle , 0 2 , to find the exact value of the indicated trigonometric function. 5 , 0< < Find sin(2 ). 478) cos = 478) 5 2 A)

4 5

1 5

3 5

Express the sum or difference as a product of sines and/or cosines. 479) sin(8 ) - sin(2 ) A) 2 sin(3 ) cos(5 ) B) 2 cos(2 ) cos(5 ) C) 2 sin(3 ) D) 2 sin(5 ) cos(3 )

2 5

479)

Use the Half-angle Formulas to find the exact value of the trigonometric function. 480) sin

480)

1 2

Find the exact value of the expression. 481) sin

481)

12 2( 3 - 1) 4

2( 3 - 1)

Solve the problem using Snell's Law:

C) - 2( 3 - 1)

2( 3 - 1) 4

D) -

sin 1 v1 = . sin 2 v2

482) A light beam in air travels at 2.99 × 108 meters per second. If its angle of incidence to a second medium is 39° and its angle of refraction in the second medium is 30°, what is its speed in the second medium (to two decimal places)? A) 3.76 × 108 mps B) 1.49 × 108 mps C) 2.38 × 108 mps D) 1.88 × 108 mps

482)

Use the information given about the angle , 0 2 , to find the exact value of the indicated trigonometric function. 1 Find sin . 483) sin = , 0 < < 483) 4 2 2 8 - 2 15 4

484) cos A)

1 , 0< 4 8-2 4

10 4

Find sin

6 4

484)

10 4

8 + 2 15 4

6 4

8+2 4

Find the exact value of the expression. 2 485) sin cos-1 3 A)

2 5 5

486) cos-1

2 2

11 6

485) B)

5 2

5 3

2 3

486) B)

1 1 487) cos sin-1 - tan-1 3 2

4 10 + 15

487) B)

2 3+4 3 5

2 3+1 5

2 6 5

Write the trigonometric expression as an algebraic expression in u. 488) sin (csc-1 u) u2 - 1

Solve the equation on the interval 0 489) sec = cos A) {0}

u2 + 1

488)

1 u

D) u

<2 . B)

7 , 4 4

489)

3 , 2 2

D) {0, }

Write the trigonometric expression as an algebraic expression containing u and v. 490) cos(tan-1 u + tan-1 v) u+v

u2 + 1 ·

1 + uv

u2 + 1 ·

v2 + 1

<2 .

3 2 , , , 2 2 3 3

1 - uv

v2 + 1

Solve the equation on the interval 0 491) 2 sin2 = sin

u2 + 1 · v2 + 1 1 - uv

v2 + 1

490)

491)

5 B) 0, , , 6 6

2 3

5 6

Find the exact value of the expression. 3 492) csc cos-1 2 A) 2

492) B)

2 2

Find the exact value under the given conditions. 7 21 , , < < ; sin = 493) cos = 25 2 5 A)

-48 + 7 21 125

3 2

-14 - 24 21 125

1 2

2 3 3

Find cos ( + ).

14 + 24 21 125

Use the Half-angle Formulas to find the exact value of the trigonometric function. 494) cos 75° 1 1 1 2- 3 2- 3 2+ 3 A) B) C) 2 2 2 Express the sum or difference as a product of sines and/or cosines. 495) sin(8 ) + sin(2 ) A) 2 cos(5 ) sin(3 ) B) 2 sin(10 ) C) 2 sin(5 ) sin(3 ) D) 2 sin(5 ) cos(3 )

493) D)

48 - 7 21 125

1 D) 2

494) 2+

495)

Find the exact value of the expression. 7 496) cos-1 cos 6 A)

496) B)

4 5

5 6

Find the exact solution of the equation. 497) 9 cos-1 x - = 7 cos-1 x 1 A) 2

497)

B) {1}

C) {0}

Complete the identity. 498) 1 - cos(2 ) + cos(8 ) - cos(10 ) = ? A) 4 cos cos(4 ) sin(5 ) C) 4 sin cos(4 ) sin(5 )

D) {-1}

B) 4 cos D) 4 sin

498)

cos(4 ) cos(5 ) sin(4 ) sin(5 )

Use the information given about the angle , 0 2 , to find the exact value of the indicated trigonometric function. 4 3 Find sin(2 ). < <2 499) sin = - , 499) 5 2 A)

24 25

B) -

Find the exact value of the expression. 500) cot-1 3 A)

24 25

C) -

7 25

500)

2 3

Use the information given about the angle , 0 2 , to find the exact value of the indicated trigonometric function. 29 , Find cos(2 ). < < 501) csc = 501) 20 2 A) -

840 841

502) cos(2 ) = A)

1 , 0< 4

Solve the equation on the interval 0 503) cos2 - sin2 = 1 + sin

C) -

840 841

502)

8-2 5 2

10 4

6 4

<2 .

7 11 , A) 0, , 6 6

C) 0,

41 841

Find cos .

8 - 2 10 4

41 841

4 5 , B) 0, , 3 3

5 , 6

7 11 , , 6 2 6

503)

in quadrant IV.

504)

1-3 5 B) 3 + 15

3 + 15 C) 1-3 5

3 - 15 D) 1+3 5

Find the exact value of the expression. 5 505) sin-1 sin 7 A)

505) B)

7 5

5 7

Use a graphing utility to solve the equation on the interval 0° x < 360°. Express the solution(s) rounded to one decimal place. 506) 7 cot2 x - 5 = 0 506)

A) 70.5°, 109.5°, 180.0° C) 51.8°, 128.2°

B) 49.8°, 130.2°, 229.8°, 310.2° D) 103.2°, 145.2°, 283.2°, 325.2°

507) g

in quadrant III.

507)

2 2+ 7 14

A) -

7+2 7 14

Use the information given about the angle , 0 508) csc

= - 6, cos 6 + 30 12

A) -

509) cos

A) -

3 , 5

5 5

Find cos

3 2

7-2 7 14

2- 7 14

2 , to find the exact value of the indicated trigonometric function. 2

508)

6+ 5 12

Find cos

6+ 5 12

6 - 30 12

D) -

509)

30 10

C) -

30 10

Express the sum or difference as a product of sines and/or cosines. 510) cos(10 ) - cos(4 ) A) -2 cos(7 ) sin(3 ) B) 2 cos(7 ) cos(3 ) C) -2 sin(7 ) sin(3 ) D) 2 cos(3 )

5 5

510)

Find the exact value of the expression. 12 511) cos 2 tan-1 5 A) -

3 13

B) -

Solve the equation on the interval 0 512) cot = 2 cos A) 0,

144 169

C) -

+ sin

119 169

10 13

512)

B) 0,

3 , , , 6 2 6 2

513) B)

C) -

Solve the equation. Give a general formula for all the solutions. 514) cos = 1 3 = + 2k A) B) 2 C)

<2 .

3 , , , 3 2 3 2

513) cos

511)

+ 2k

514) = 0 + 2k }

+ 2k }

Find the exact value of the expression. 2 1 515) sin sin-1 + cos-1 3 3 A)

2 3 5

515) B)

2 6 5

2 + 2 10 9

2 3 + 2 10 9

Use the information given about the angle , 0 2 , to find the exact value of the indicated trigonometric function. 12 3 , Find sin(2 ). < < 516) tan = 516) 5 2 A) -

517) sin A)

119 169 2 6 , tan 5

B) -

-4 6 25

120 169

119 169

Find sin(2 ).

517)

4 6 25

C) -

23 25

Find the exact value of the expression. 7 518) sin-1 sin 6 A) -

518) B)

5 6

7 6

519) sec sin-1 A)

8 9

519)

9 17 17

17 9

C) -

8 17 17

9 8

D) -

Use a graphing utility to solve the equation on the interval 0° x < 360°. Express the solution(s) rounded to one decimal place. 520) sin2 x + 8 sin x + 16 = 0 520)

A) No solution C) 208.2°, 331.8°

B) 28.2°, 151.8° D) 28.2°, 151.8°, 208.2°, 331.8°

Express the product as a sum containing only sines or cosines. 521) 2 cos(7 ) cos A) cos(8 ) + cos(6 ) B) cos(14 ) + cos(2 ) C) cos(8 ) + sin(6 ) D) cos(10 ) + sin(4 )

521)

Find the exact solution of the equation. 522) -sin-1 (4x) =

522)

A) {0}

2 8

C) -

2 8

D) -

2 2

Use the information given about the angle , 0 2 , to find the exact value of the indicated trigonometric function. 5 Find cos . 523) csc = - , tan > 0 523) 2 2 5 + 21 10

A) -

Solve the equation on the interval 0 524) tan(2 ) = -1 A) C)

8 8

, ,

50 + 10 21 10

C) -

50 - 10 21 10

11 15 , , , 8 8 8 8

<2 .

11 13 , 8 8

21 10

524)

Answer Key Testname: CHAPTER 8 1) 1.1 2) sin (2 ) = 2 sin 3) sin

+ x = sin

cos

x · x2 + 9

=2·

cos x + sin x cos

3 6x = 2 x +9 x2 + 9

2 (cos x + sin x).

1 - v2 · v + v ·

4) cos(sin-1 v - cos-1v) = cos(sin-1 v) cos( cos-1 v) + sin (sin-1 v) sin( cos-1 v) = cos u = ln cos u - ln sin u 5) ln cot u = ln sin u 6)

sin( - ) sin = sin sin

7) 1 -

cos - cos sin sin

sin

sin cos sin sin

cos sin sin sin

cos sin

= cot

1 - v2 = 2v

- cot

cos2 u 1 - sin2u (1 - sin u)(1 + sin u) =1=1= 1 - (1 + sin u) = - sin u 1 - sin u 1 - sin u 1 - sin u

sin (( /2) + x) sin ( /2) cos x + sin x cos ( /2) 1 · cos x + sin x · 0 = = = -cot x. 2 cos (( /2) + x) cos ( /2) cos x - sin ( /2) sin x 0 · cos x - 1 · sin x v0 2 2 v0 2 2 v0 2 2 [sin(2 ) - cos(2 ) - 1] = [2 sin cos - (1 - 2 sin2 ) - 1] = [2 sin cos 9) R( ) = 32 32 32 v0 2 2 v0 2 2 [sin (cos + sin ) - 1]. · 2 [sin (cos + sin ) - 1)] = 32 16

8) tan

+x =

10)

cot x cot x cot x csc 2 x - 1 (csc x + 1)(csc x - 1) csc x - 1 = = = = . 1 + csc x (1+ csc x) cot x (1+ csc x) cot x (1+ csc x) cot x cot x

11)

1 + csc x 1 cos x (sin x + 1) cos x sin x cos x = cos x 1 + = = + = cos x + cot x. sec x sin x sinx sin x sin x

12)

cot 2 x csc2 x - 1 (csc x + 1)(csc x - 1) 1 sin x 1 - sin x = = = csc x - 1 = = . csc x + 1 csc x + 1 csc x + 1 sin x sin x sin x

13)

csc x - 1 csc x + 1 = csc x + 1 csc x + 1

16) 0

1- sec tan

tan 1 - sec

2sec tan

2 cos

= ·

+ 2 sin2

- 2] =

csc x - 1 csc 2 x - 1 cot 2 x = = . csc x + 1 2 2 csc x + 2 csc x + 1 csc x + 2 csc x + 1

14) r = 44.72° 15) sin( - ) cos ( + ) = (sin cos - cos sin )(cos cos - sin sin ) = sin cos cos2 - sin2 cos sin - cos2 sin cos + cos sin sin2 = sin cos (cos2 + sin2 ) - sin cos (sin2 + cos2 ) = sin cos - sin 17)

1 - v2

cos sin

(1 - sec )2 + tan2 tan (1 - sec ) =-

2 sin

1 - 2 sec + sec2 + tan2 tan (1 - sec )

cos 2 sec2 - 2 sec 2sec ( sec - 1) = =tan (1 - sec ) tan (1 - sec )

= - 2 csc

18) sec 4 x - tan 4 x = (sec 2 x + tan 2 x)(sec 2 x - tan 2 x) = (sec 2 x + tan 2 x)(1) = sec 2 x + tan 2 x. 19) 0.3 + 2 cos cos cos 2 2 2 cos + cos = = = cot 20) + sin - sin 2 2 sin cos sin 2 2 2 21) 0.7 65

Answer Key Testname: CHAPTER 8

22)

sin (8 ) + sin (4 ) 2 sin (6 ) cos (2 ) sin (6 ) = = = tan (6 ) cos (8 ) + cos (4 ) 2 cos (6 ) cos (2 ) cos (6 )

23) cot

· sec

24) sin

= sin

cos sin

1 cos

cos

- cos

1 sin

= csc 2

sin

= (-1) · cos

- 0 · sin

= - cos

25) cos (x - y) - cos (x + y) = cos x cos y + sin x sin y - ( cos x cos y - sin x sin y) = 2 sin x sin y. 1 - cos(6x) 1 (sin(3x)) = (sin(3x))(1 - cos(6x)). 26) sin3 (3x) = (sin2 (3x))(sin(3x)) = 2 2 27)

cot2 x csc2 x -1 (csc x - 1)(csc x +1) 1 + sin x = = = csc x +1 = . csc x - 1 csc x - 1 csc x -1 sin x

28)

sin csc

29)

sin (9 ) + sin (3 ) 2 sin (6 ) cos (3 ) = = cos (3 ) 2 sin (6 ) 2 sin (6 )

30) sin

+ sin + csc

1 + u2

sin 1 sin

; cos

+ sin 1 + sin

sin + sin sin + sin sin sin

= (sin

+ sin ) ·

sin sin sin + sin

= sin

sin

1 - u2 1 + u2

31) 8 csc2 - 6 cot2 = 2 csc2 + 6 csc2 - 6 cot2 = 2 csc2 + 6 (csc2 - cot2 ) = 2 csc2 + 6 sin3 - cos3 1 = sin2 + sin cos + cos2 = 1 + sin cos = 1 + sin(2 ) 32) sin - cos 2 33) (a) - , 0, 2 , 3 (b)

(d) x -

34)

<x<-

4 4

<x<

1 - 2 sec x - 3 sec2 x (1 - 3 sec x) (1 + sec x) (1 - 3 sec x) (1 + sec x) 1 - 3 sec x = = = . (1 + sec x)(1 - sec x) 1 - sec x 1- sec2 x - tan2 x

35) sin2 (- ) + cos2 (- ) = (-sin )2 + (cos )2 = sin2

+ cos2 = 1

Answer Key Testname: CHAPTER 8 36) 0.16, 0.55, 0.94 37) sin(sin-1 v - cos-1 v) = sin(sin-1 v) cos( cos-1 v) - cos (sin-1 v) sin( cos-1 v) = v · v -

1 - v2 ·

2v2 - 1 sin x sin x (csc x + 1) sin x + (csc x - 1) sin x 1 + sin x + 1 - sin x + = = = 2 tan2 x. 38) csc x - 1 csc x + 1 csc2 x - 1 cot2 t

39) cos -2

x x 2 - sin = 2 2

1 - cos x 2

1 + cos x 2 1 - cos x = -2 2 2

1 - cos x 2

1 - v2 = v2 - (1 - v2 ) =

1 + cos x 1 + cos x + =1-2 2 2

1 - cos2 x =1 4

sin2 x sin x =1-2 = 1 - sin x 4 2

40) csc(u + v) =

1 sin u sin v

1 1 · sin u sin v

1 1 = = = sin(u + v) sin u cos v + cos u sin v sin u cos v + cos u sin v sin u cos v cos u sin v + sin u sin v sin u sin v sin u sin v

csc u csc v cot v + cot u

41) (sec v + tan v)2 = sec2 v + 2 sec v tan v + tan2 v =

1 2 sin v sin2v 1 + 2 sin v + sin2 v (1 + sin v)2 + + = = = cos2 v cos2 v cos2 v cos2 v 1 - sin2 v

(1 + sin v)2 1 + sin v = (1 - sin v)(1 + sin v) 1 - sin v

42) 2

1 + cos(2x) 43) cos4 x = cos2 x cos2 x = 2

1 1 1 1 + cos(4x) 1 (1 + cos(2x))2 = (1+ 2 cos(2x) + cos2 (2x)) = 1 + 2 cos(2x) + = 4 4 4 2 8

( 3 + 4 cos(2x) + cos(4x)). 1 + sin 44) cos

45) 191 days after March 21 and 356 days after March 21 (i.e., September 28 and March 12) sin x sin x sin x[(1 + cos x)+(1 - cos x)] 2 sin x 2 sin x + = = = = 2 csc x. 46) 1 - cos x 1 + cos x (1 - cos x)(1 + cos x) 2 1 - cos x sin2 x 47) 0.9 1 1 1 48) ln sin2 u + cos(2u) = ln sin2 u + (cos2 u - sin2 u) = ln cos2 u = ln cos u 2 2 2 49) r = 9.13° 5 csc2 x + 4 csc x - 1 (5 csc x - 1) (csc x + 1) (5 csc x - 1) (csc x + 1) 5 csc x - 1 = = = . 50) (csc x - 1) (csc x + 1) csc x - 1 cot2 x csc2 x - 1 51) r = 8.39° 5 cos + 1 52) cos - 1 53)

cos u sin u = 1 + tan u 1 + cot u

cos u sin u cos2 u sin2 u cos2 u - sin2 u = = = sin u cos u cos u + sin u sin u + cos u cos u + sin u 1+ 1+ cos u sin u

(cos u - sin u)(cos u + sin u) = cos u - sin u cos u + sin u

Answer Key Testname: CHAPTER 8

54) t =

7 9 15 , , , 16 16 16 16

55) M = 875, t = 3; N = 10,725, t = 4, 8

56) cos(3x) = cos(2x + x) = cos(2x) cos x - sin(2x) sin x = (cos2 x - sin2 x) cos x - 2 sin x cos x sin x = cos3 x - sin2 x cos x - 2 sin2 x cos x = cos3 x - 3 sin2 x cos x. 57) cos(4 ) = cos[2(2 )] = cos2(2 ) - sin2 (2 ) = (cos2 - sin2 )2 - (2 sin cos )2 = cos4

- 2 sin2

cos2

+ sin4 - 4 sin2 cos2 = cos4 - 6 sin2 cos2 + sin4 1 1 +u = = = -csc u. 58) sec 2 cos ( /2) cos u - sin ( /2) sin u 0 · cos u - 1 · sin u

59) sin3 x cos2 x = sin x (1 - cos2 x) (cos2 x) = sin x (cos2 x - cos4 x). 1 = csc2 u - 1 = cot2 u 60) csc2 u - cos u sec u = csc2 u - cos u · cos u 61) 15°, 75° 62)

tan v + sec v tan v + sec v tan v sec v sin v 1 cos v 1 sin2 v - 1 = +1-1= · cos v · = sin v = =sec v tan v sec v tan v cos v cos v sin v sin v sin v cos2 v cos v = - cos v · = - cos v cot v sin v sin v

63) csc

1 1 = = sec u. sin ( /2) cos u + cos ( /2) sin u 1 · cos u + 0 · sin u

+u =

64) csc3 x tan2 x = csc x tan2 x (1 + cot2 x) = csc x (1 + tan2 x). 65) sec u + tan u =

1 sin u 1 + sin u 1 + sin u 1 - sin u 1 - sin2 u cos2 u cos u + = = · = = = cos u cos u cos u cos u 1 - sin u cos u(1 - sin u) cos u(1 - sin u) 1 - sin u

66) 0, 1.7 67) p = 2a cos (

1+ 2

t) cos (

68) tan2 x = sec2 x - 1 = sec2 x - (sin2 x + cos2 x) = sec2 x - sin2 x - cos2 x. 69) 40.63° 70) -1.2, 1.2 1 -2 sin2 cos(2 ) 1 - 2 sin2 csc2 - 2 = = = 71) cot(2 ) = sin(2 ) 2 sin cos 2 cos 2 cot sin

72)

sin u cos u + cos u sin u

sin2 u + cos2 u cos u sin u

tan u + cot u sin2 u + cos2 u 1 = = = = tan u - cot u sin u cos u 2 2 2 2 2 sin u - cos u sin u - cos u sin u - cos2 u cos u sin u cos u sin u

73) sec2

u = 2

74) (cos

+ sin )2 + (cos

75) cos

u cos2 2

= cos

2 2 sec u = 1 + cos u sec u + 1

- sin )2 = cos2 + 2 cos cos

+ sin

sin

= 0 · cos

+ sin2 + cos2 - 2 cos - 1 · sin

= - sin

sin

+ sin2

= 2(cos2

+ sin2 )

Answer Key Testname: CHAPTER 8

76)

77)

2 sin2

78)

79)

sin sin

7 11 , 6 6

- sin + sin

csc + cot tan + sin

80) cot( - ) =

2 sin

+ 2

1 sin

sin cos

cos

+ 2

cos

cos sin

+ sin

cos( - ) cos = sin( - ) sin

cos cos

sin

cos

1 + cos sin sin

+ sin cos

+ sin - cos

cos

sin sin

cos

+ 2

sin

+ 2

1 + cos sin

= tan

cot

+ 2

cos 1 = sin (1 + cos ) sin

(-1) · cos + 0 · sin 0 · cos - (-1) · sin

- cos sin

cos sin

= csc

cot

= - cot

81) cot3 x = cot x cot2 x = cot x (csc2 x - 1). sin (9 ) + sin (3 ) 2 sin (6 ) cos (3 ) sin (6 ) cos (3 ) tan (6 ) = = · = 82) sin (9 ) - sin (3 ) 2 sin (3 ) cos (6 ) cos (6 ) sin (3 ) tan (3 ) 83)

cos (4 ) - cos (10 ) sin (3 ) -2 sin (7 ) sin (-3 ) - [-sin (3 )] = = = = tan (3 ). sin (4 ) + sin (10 ) 2 sin (7 ) cos (-3 ) cos (3 ) cos (3 )

84) sin(4u) = sin [2(2u)] = 2 sin(2u) cos(2u).

85)

1 - cot2 v 1 - cot2 v 1 cot2 v +1= +1= + 1 = sin2 v 2 2 2 1 + cot v csc v csc v csc2v

cos2 v sin2v 1 sin2 v

+ 1 = sin2 v - cos2 v + (sin2 v + cos2 v) = 2 sin2 v

86) 1 87) 14.38 hr 88) t = 0, 2, 6, 8, 12 89) 1.38 m cot u + csc u - 1 cot u + (csc u - 1) cot u + (csc u - 1) cot u + (csc u - 1) = = · = 90) cot u - csc u + 1 cot u - (csc u - 1) cot u - (csc u - 1) cot u + (csc u - 1) cot2 u + 2 cot u(csc u - 1) + (csc2 u - 2 csc u + 1) csc2 u - 1 + 2 cot u(csc u - 1) + (csc2 u - 2 csc u + 1) = = cot2 u - (csc2 u - 2 csc u + 1) csc2 u - 1 - (csc2 u - 2 csc u + 1) 2csc2 u - 2 csc u + 2 cot u(csc u - 1) 2 csc u(csc u - 1) + 2 cot u(csc u - 1) 2(csc u + cot u)(csc u - 1) = = = csc u + cot u 2 (csc u - 1) 2 (csc u - 1) -2 + 2 csc u

91) cot 2 x + csc 2 x = csc 2 x - 1 + csc 2 x = 2 csc 2 x - 1. 92) cot ( x + y) cot (x - y) =

1 - tan x tan y 1 + tan x tan y 1 - tan2 x tan2 y · = . tan x + tan y tan x - tan y tan2 x - tan2 y

sin2 x = 1 + tan2 x = sec2 x. 93) 1 + sec2 x sin2 x = 1 + cos2 x

94) csc u - sin u =

1 1 - sin2 u cos2 u cos u - sin u = = = cos u · = cos u cot u sin u sin u sin u sin u

95) (1 - cos x)(1 + cos x) = 1 - cos2 x = sin2 x 69

Answer Key Testname: CHAPTER 8 96) 12 hr

97) (sec u - tan u)(sec u + tan u) = sec2 u - tan2 u = 1 98) sin(4x) = 2 sin(2x) cos(2x) = (4 sin x cos x)(2 cos2 x - 1). 99)

cos( + ) cos = cos sin

cos - sin cos sin

cos cos cos sin

sin cos

sin sin

cos sin

sin cos

= cot

- tan

tan - 0 = tan 1 + tan · 0 101) cot x sec4 x = cot x (1 + tan 2 x)2 = cot x (1 + 2 tan2 x + tan4 x) = cot x + 2 tan x + tan3 x.

100) tan ( - ) =

102) cot2

103)

u = 2

u tan2 2

1 + cos u csc u + cot u = 1 - cos u csc u - cot u

cos (9 ) - cos (3 ) -2 sin (6 ) sin (3 ) = = - sin (3 ) 2 sin (6 ) 2 sin (6 )

104) f( ) = 105)

tan - tan 1 + tan tan

sin

sec - 1 tan (sec = tan sec + 1

sec - 1 sec - 1 sec = · tan tan sec

- 1)(sec + 1)- tan2 tan (sec + 1)

(sec2 - 1)- tan2 tan (sec + 1)

sec2 - 1 tan2 +1 = = + 1 tan (sec + 1) tan (sec 1 cos u

+ 1)

tan2 - tan2 = 0 = g( ) tan (sec + 1)

tan sec + 1

106)

cos u cos u = · cos u - sin u cos u - sin u

107)

1 + cos u 1 - cos u (1 + cos u)2 - (1 - cos u)2 1 + 2 cos u + cos2 u - (1 - 2 cos u + cos2 u) 4 cos u 4 cos u = = = = · 1 - cos u 1 + cos u 2 2 2 sin u 1 - cos u 1 - cos u sin u

1 cos u

1 1 = sin u 1 - tan u 1cos u

1 = 4 cot u csc u sin u

108)

1 - sin t 1 + sin t = cos t 1 + sin t

109) g( ) =

sin 1 - cos

1 - sin t cos 2 t cos t = = . cos t cos t (1 + sin t) 1 + sin t

sin 1 - cos

1 + cos 1 + cos

sin (1 + cos ) sin (1 + cos ) 1 + cos = = sin 1 - cos2 sin2

= f( ) 110) 1

111)

= 15°: R =

;

= 22.5°: R =

20,000( 2) 5000(2 , H= g g

2 v0

112) H = 113)

20,000 5000(2 , H= g g

(1 - cos(2 )) =

(1 - (1 - 2 sin2 )) =

2 v0 4g

(2 sin2 ) =

2 v 0 sin2 2g

cos x cos x cos x (sec x + 1) - cos x ( sec x - 1 ) 1 + cos x - 1 + cos x = = = sec x - 1 sec x + 1 sec2 x - 1 tan 2 x 2 cos x . tan2 x

1 sin

cos sin

= csc

+ cot

Answer Key Testname: CHAPTER 8 114) cot2 x = csc2 x - 1 = (csc x - 1)(csc x + 1). sin 1 1 · = = sec 115) tan · csc = cos sin cos 116)

cos (8 ) - cos (2 ) -2 sin (5 ) sin (3 ) sin (5 ) sin(3 ) = =· = - tan (5 ) tan (3 ) cos (8 ) + cos (2 ) 2 cos (5 ) cos (3 ) cos (5 ) cos(3 )

117) A = 9 sin

cos

118) cot( + ) =

2 1

tan( + )

1 - tan tan tan + tan

1 - (x + 1)(x - 1) 1 - (x2 - 1) 2 - x2 = = (x + 1) + (x - 1) 2x 2x

119) (tan v + 1)2 + (tan v - 1)2 = tan2 v + 2 tan v + 1 + tan2 v - 2 tan v + 1 = 2(tan2v + 1) = 2 sec2 v 1 120) sin [sin + sin(5 )] = sin [2 sin(3 ) cos(2 )] = 2 cos(2 )[sin sin(3 )] = 2 cos(2 ) (cos(2 ) - cos(4 )) = cos(2 2 )[cos(2 ) - cos(4 )] tan x - tan /4 tan x - 1 . = = 121) tan x 4 1 + (tan x)(tan /4) 1 + tan x

122) csc 4 x - cot 4 x = (csc 2 x + cot 2 x)(csc 2 x - cot 2 x) = (csc 2 x + cot 2 x)(1) = csc 2 x + cot 2 x. 123) cos x +

= cos x cos

- sin x sin

= (cos x)(0) - (sin x)(1) = - sin x.

124) ln 1 + sin u + ln 1 - sin u = ln ( 1 + sin u · 1 - sin u ) = ln 1 - sin2 u = ln cos2 u = 2 ln cos u sin x + cos x sin x + cos x sin x + cos x sin 2 x + 2 cos x sin x + cos 2 x = = = 125) sin x - cos x sin x + cos x sin x - cos x sin 2 x - cos 2 x 1 + 2 cos x sin x 1 + 2 sin x cos x = . 2 2 sin x + sin x - 1 2 sin 2 x - 1

126) sin (x + y) - sin (x - y) = sin x cos y + cos x sin y - sin x cos y + cos x sin y = 2 cos x sin y. 1 1 127) (i) g(t) = cos(9t) - cos(11t) 2 2 (ii), (iii)

(iv) t =

128)

n , n any integer 10

sin3 - cos3 sin - cos

(sin

- cos )(sin2 + sin sin - cos

cos + cos2 )

= sin2 + sin

129) t = 0, 2.5, 5, 7.5, 10, 12.5, 15, 17.5 130) cos x + 131) sin x -

6 4

= cos x cos = sin x cos

6 4

3 1 cos x - sin x. 2 2

cos x =

2 (sin x - cos x). 2

- sin x sin - sin

cos + cos2 = 1 + sin

cos

Answer Key Testname: CHAPTER 8

132)

1 -1 cot u

tan u - 1 = tan u + 1

1 +1 cot u

1 - cot u cot u

1 + cot u cot u

1 - cot u 1 + cot u

133) 163 t 262

134) (a tan u + b)2 + (b tan u - a)2 = a 2 tan2 u + 2ab tan u + b2 + b2 tan2 u - 2ab tan u + a 2 = (a2 + b2 )(tan2 u + 1) = (a 2 + b2 ) sec2 u 135)

cos (x - y) cos x cos y + sin x sin y 1/(cos x cos y) cos x cos y + sin x sin y = = · = cos (x + y) cos x cos y - sin x sin y 1/(cos x cos y) cos x cos y - sin x sin y 1 + tan x tan y . 1 - tan x tan y

136) sin x +

= sin x cos

+ sin

cos x = (sin x)(0) + (1)(cos x) = cos x.

137) (1 + tan2 u)(1 - sin2 u) = sec2 u · cos2 u =

138)

1 - cos 1 + cos

1 sec

1 1+ sec

sec - 1 sec sec + 1 sec

1 · cos2 u = 1 cos2 u

sec sec

-1 +1

139) tan u(csc u - sin u) = tan u · csc u - tan u · sin u =

sin u 1 sin u 1 sin2 u 1 - sin2 u cos2 u · · sin u = = = = cos u sin u cos u cos u cos u cos u cos u

cos u

140) cos(4u) = cos[2(2u)] = 2 cos2 (2u) - 1 1 - cos(2u) (1 + cos(2u)) = 1 - cos(2u) 141) tan 2 u (1 + cos(2u)) = 1 + cos(2u) 142) g(x) = cot x + tan x =

cos x sin x cos2 x + sin2 x 1 1 1 + = = = · = csc x · sec x = f(x) sin x cos x sin x cos x sin x cos x sin x cos x

143) cos x csc x tan x = (cos x)

1 sinx

sin x = 1. cos x

144) 1.9 145)

cos t 1 + sin t cos2 t + 1 + 2 sin t + sin 2 t 2 + 2 sin t 2 + = = = = 2 sec t. 1 + sin t cos t cos t (1 + sin t) cos t (1 + sin t) cos t

146) 48.6°, 131.4° 147) sec(2 ) =

1 1 = cos(2 ) 1 - 2 sin2

1 sin2 1 sin2

148) (sin x)(tan x cos x + cot x cos x) = sin x 149) A 150) D 151) A 152) B 153) D

-2

csc2 csc2 - 2

sin x cos x cos 2 x = sin 2 x - cos 2 x = (1 - cos 2 x)- cos 2 x = 1 - 2 cos 2 x. cos x sin x

Answer Key Testname: CHAPTER 8 154) D 155) A 156) B 157) D 158) C 159) B 160) A 161) C 162) B 163) B 164) D 165) C 166) B 167) D 168) C 169) D 170) B 171) D 172) C 173) B 174) D 175) A 176) A 177) C 178) B 179) B 180) B 181) D 182) D 183) A 184) C 185) C 186) A 187) A 188) A 189) C 190) B 191) A 192) A 193) C 194) B 195) B 196) B 197) B 198) D 199) D 200) C 201) B 202) B 203) B 73

Answer Key Testname: CHAPTER 8 204) B 205) C 206) D 207) C 208) D 209) D 210) C 211) C 212) D 213) A 214) B 215) B 216) A 217) D 218) A 219) B 220) D 221) C 222) B 223) A 224) D 225) C 226) B 227) A 228) A 229) B 230) B 231) C 232) C 233) A 234) C 235) A 236) A 237) D 238) C 239) B 240) C 241) B 242) D 243) D 244) D 245) A 246) A 247) C 248) B 249) B 250) A 251) D 252) B 253) C 74

Answer Key Testname: CHAPTER 8 254) C 255) B 256) B 257) B 258) A 259) C 260) D 261) C 262) D 263) D 264) C 265) A 266) D 267) C 268) B 269) C 270) C 271) C 272) C 273) B 274) A 275) D 276) C 277) B 278) D 279) B 280) C 281) C 282) D 283) B 284) D 285) B 286) B 287) B 288) B 289) B 290) B 291) D 292) A 293) B 294) C 295) A 296) B 297) D 298) C 299) D 300) B 301) A 302) D 303) C 75

Answer Key Testname: CHAPTER 8 304) C 305) B 306) A 307) C 308) B 309) D 310) C 311) D 312) C 313) C 314) B 315) B 316) A 317) D 318) A 319) B 320) C 321) A 322) C 323) D 324) C 325) B 326) C 327) C 328) A 329) C 330) D 331) D 332) C 333) B 334) A 335) A 336) B 337) D 338) D 339) B 340) B 341) B 342) C 343) B 344) C 345) B 346) C 347) A 348) B 349) B 350) A 351) A 352) A 353) C 76

Answer Key Testname: CHAPTER 8 354) C 355) B 356) B 357) A 358) C 359) D 360) B 361) B 362) C 363) B 364) C 365) D 366) B 367) A 368) C 369) A 370) C 371) B 372) C 373) B 374) C 375) D 376) D 377) B 378) C 379) B 380) B 381) A 382) B 383) C 384) C 385) A 386) B 387) B 388) B 389) D 390) D 391) D 392) A 393) A 394) B 395) D 396) A 397) A 398) C 399) D 400) A 401) C 402) B 403) A 77

Answer Key Testname: CHAPTER 8 404) A 405) A 406) C 407) B 408) C 409) A 410) B 411) D 412) A 413) C 414) A 415) D 416) C 417) A 418) D 419) C 420) A 421) A 422) B 423) D 424) C 425) D 426) C 427) C 428) D 429) B 430) A 431) D 432) A 433) C 434) D 435) D 436) A 437) C 438) D 439) A 440) B 441) C 442) C 443) B 444) C 445) C 446) A 447) B 448) B 449) A 450) C 451) D 452) A 453) B 78

Answer Key Testname: CHAPTER 8 454) C 455) D 456) B 457) A 458) C 459) A 460) C 461) B 462) D 463) C 464) D 465) A 466) D 467) D 468) D 469) B 470) B 471) C 472) C 473) C 474) C 475) D 476) D 477) C 478) A 479) A 480) D 481) A 482) C 483) A 484) C 485) C 486) B 487) A 488) C 489) D 490) D 491) B 492) A 493) C 494) A 495) D 496) D 497) C 498) C 499) B 500) C 501) B 502) C 503) A 79

Answer Key Testname: CHAPTER 8 504) C 505) B 506) B 507) C 508) A 509) A 510) C 511) C 512) D 513) A 514) B 515) C 516) C 517) A 518) A 519) A 520) A 521) A 522) C 523) C 524) B

Chapter 9 Exam Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) Island A is 150 miles from island B. A ship captain travels 250 miles from island A and then finds that he is off course and 160 miles from island B. What angle, in degrees, must he turn through to head straight for island B? Round the answer to two decimal places. (Hint: Be careful to properly identify which angle is the turning angle.) A) 55.08° B) 110.17° C) 34.92° D) 145.08° SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 2) An object of mass m attached to a coiled spring with damping factor b is pulled down a distance 2) a from its rest position and then released. Assume the positive direction of the motion is up and the period of the first oscillation is T. Write an equation that relates the distance d of the object from its rest position after t seconds. m = 15 g; a = 11 cm; b = 0.7 g/sec; T = 3 sec

3) A square wave is built up from sinusoidal curves of varying periods and amplitudes. Graph the following function, which can be used to approximate the square wave. 4 1 f(x) = sin( x) + sin(3 x) 0 x 4 3

A better approximation to the square wave is given by 4 1 1 f(x) = sin( x) + sin(3 x) + sin(5 x) 0 x 4 3 5

Graph this function and compare the result to the previous graph. Adding another term will improve the approximation even more. Write this new function with four terms.

4) In 1838, the German mathematician and astronomer Friedrich Wilhelm Bessel was the first person to calculate the distance to a star other than the Sun. He accomplished this by first determining the parallax of the star, 61 Cygni, at 0.314 arc seconds (Parallax is the change in position of the star measured against background stars as Earth orbits the Sun. See illustration.) If the distance from Earth to the Sun is about 150,000,000 km and = 0.314 seconds =

0.314 0.314 minutes = degrees 60 60 · 60

determine the distance d from Earth to 61 Cygni using Bessel's figures.

5) Two surveyors 180 meters apart on the same side of a river measure their respective angles to a point between them on the other side of the river and obtain 54° and 68°. How far from the point (line-of-sight distance) is each surveyor? Round your answer to the nearest 0.1 meter.

6) An object is suspended from a coiled spring. It is pulled downward and released. The position 6) P above or below its rest position after t seconds is given by P = -e-x/2 cos x Find all values of t (0 t < 4 ) for which the object is at the rest position and graph the equation for 0 t < 4 .

7) Yosemite Falls in California consists of three sections: Upper Yosemite Fall (by itself one of the ten highest waterfalls in the world), the Middle Cascade, and Lower Yosemite Fall. From a footbridge across the creek 2500 feet from the falls, the angles of elevation to the top and bottom of Upper Yosemite Fall are 45.74° and 24.42°, respectively. How high is the total series of three falls? How high is Upper Yosemite Fall? Round your answers to the nearest foot.

8) Find the area of the shaded portion ( see illustration) of a circle of radius 25 cm, formed by a central angle of 115°. Round your answer to the nearest square cm.

[Hint: Subtract the area of the triangle from the area of the sector of the circle to obtain the area of the shaded portion.]

9) A pier 1250 meters long extends at an angle from the shoreline. A surveyor walks to a point 1500 meters down the shoreline from the pier and measures the angle formed by the ends of the pier. If is found to be 53°. What acute angle (correct to the nearest 0.1°) does the pier form with the shoreline? Is there more than one possibility? If so, how can we know which is the correct one?

10) Penrose tiles are formed from a rhombus WXYZ with sides of length 1 and interior angles 10) 72° and 108°. (Refer to the illustration.) A point O is chosen on the diagonal 1 unit from Y. Line segments OX and OZ are drawn to the other vertices. The two resulting tiles are called a kite (figure OXYZ) and a dart (figure OXWZ). Find the area of the kite tile and the dart tile, correct to the nearest 0.01.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the triangle. 11)

11)

70°

40°

A) B = 75°, a = 2.74, c = 4 C) B = 70°, a = 2.74, c = 4

B) B = 70°, a = 4, c = 2.74 D) B = 65°, a = 4, c = 2.74

Solve the problem. 12) The distance from home plate to dead center field in a certain baseball stadium is 407 feet. A baseball diamond is a square with a distance from home plate to first base of 90 feet. How far is it from first base to dead center field? A) 349.2 ft B) 474.9 ft C) 384.5 ft D) 332.1 ft 13) Two hikers on opposite sides of a canyon each stand precisely 525 meters above the canyon floor. They each sight a landmark on the canyon floor on a line directly between them. The angles of depression from each hiker to the landmark meter are 37° and 21°. How far apart are the hikers? Round your answer to the nearest whole meter. A) 1064 m B) 2065 m C) 2063 m D) 2064 m Solve the triangle. 14) b = 3, c = 5, A = 95° A) a = 6.05, B = 55.4°, C = 29.6° C) a = 6.05, B = 29.6°, C = 55.4°

B) a = 5.05, B = 55.4°, C = 29.6° D) a = 7.05, B = 29.6°, C = 55.4°

Solve the problem. 15) Two points A and B are on opposite sides of a building. A surveyor selects a third point C to place a transit. Point C is 46 feet from point A and 69 feet from point B. The angle ACB is 45°. How far apart are points A and B? A) 95.5 ft B) 68.1 ft C) 106.6 ft D) 48.9 ft

12)

13)

14)

15)

Two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve any triangle(s) that results. 16) A = 30°, a = 5, b = 10 16) A) B = 90°, C = 60°, c = 8.7 B) B = 60°, C = 60°, c = 8.7 C) B = 60°, C = 90°, c = 8.7 D) no triangle

Solve the problem. 17) A tree casts a shadow of 26 meters when the angle of elevation of the sun is 24°. Find the height of the tree to the nearest meter. A) 11 m B) 13 m C) 12 m D) 10 m

17)

18) A plane takes off from an airport on the bearing S29°W. It continues for 20 minutes then changes to bearing S52°W and flies for 2 hours 20 minutes on this course then lands at a second airport. If the plane' s speed is 420 mph, how far from the first airport is the second airport? Round your answer correct to the nearest mile. A) 1011 mi B) 1010 mi C) 1111 mi D) 1110 mi

18)

19) A twenty-five foot ladder just reaches the top of a house and forms an angle of 41.5° with the wall of the house. How tall is the house? Round your answer to the nearest 0.1 foot. A) 18.6 ft B) 18.8 ft C) 19 ft D) 18.7 ft

19)

Find the area of the triangle. If necessary, round the answer to two decimal places. 20)

A) 54.54

20)

21) a = 4, b = 5, c = 7 A) 16.01

B) 13.23

C) 628.45

D) 107.78

B) 10.01

C) 9.80

D) 3.46

Solve the problem. 22) A radio transmission tower is 190 feet tall. How long should a guy wire be if it is to be attached 15 feet from the top and is to make an angle of 20° with the ground? Give your answer to the nearest tenth of a foot. A) 555.5 ft B) 511.7 ft C) 186.2 ft D) 202.2 ft 23) John (whose line of sight is 6 ft above horizontal) is trying to estimate the height of a tall oak tree. He first measures the angle of elevation from where he is standing as 35°. He walks 30 feet closer to the tree and finds that the angle of elevation has increased by 12°. Estimate the height of the tree rounded to the nearest whole number. A) 61 ft B) 86 ft C) 90 ft D) 67 ft Find the area of the triangle. If necessary, round the answer to two decimal places. 24)

A) 13.16

110°

C) 4.05

22)

23)

24)

B) 1.2

21)

D) 3.29

Two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve any triangle(s) that results. 25) B = 41°, a = 4, b = 3 25) A) one triangle B) two triangles A1 = 61°, C1 = 78°, c1 = 4.5; A = 29°, C = 110°, c = 5.7 A2 = 119°, C2 = 20°, c2 = 1.6 D) no triangle

C) two triangles A1 = 61°, C1 = 78°, c1 = 0.1;

A2 = 119°, C2 = 20°, c2 = 0.1

Solve the problem. 26) A plane flying a straight course observes a mountain at a bearing of 34.1° to the right of its course. At that time the plane is 10 kilometers from the mountain. A short time later, the bearing to the mountain becomes 44.1°. How far is the plane from the mountain when the second bearing is taken (to the nearest tenth of a km)? A) 13.7 km B) 12.4 km C) 5.4 km D) 8.1 km

26)

The displacement d (in meters) of an object at time t (in seconds) is given. Describe the motion of the object. What is the maximum displacement from its resting position, the time required for one oscillation, and the frequency? 27) d = 2 - 5 cos ( t) 27) 1 oscillation/sec A) simple harmonic; 5 m; 2 sec; 2

B) simple harmonic; 5 m;

1 sec; 2 oscillations/sec 2

C) simple harmonic; -5 m; 2 sec;

1 oscillation/sec 2

D) simple harmonic; 2 m; 2 sec;

1 oscillation/sec 2

28) d = -2 sin (3t)

2 A) simple harmonic; 2 m; 3

3 sec; oscillations/sec 2

B) simple harmonic; -2 m;

2 3

sec;

3 oscillations/sec 2

C) simple harmonic; 2 m;

3 2 sec; 2 3

oscillations/sec

D) simple harmonic; -2 m; 3

sec;

28)

oscillations/sec

Solve the problem. 29) A ship at sea, the Admiral, spots two other ships, the Barstow and the Cauldrew and measures the angle between them at be 45°. They radio the Barstow and by comparing known landmarks, the distance between the the Admiral and the Barstow is found to be 323 meters. The Barstow reports an angle of 59° between the Admiral and the Cauldrew. To the nearest meter, what is the distance between the Barstow and the Cauldrew? A) 81 m B) 49 m C) 235 m D) 266 m

29)

Find the area of the triangle. If necessary, round the answer to two decimal places. 30) A = 23°, b = 9, c = 2 A) 3.50 B) 3.51 C) 3.52

D) 3.53

Solve the triangle. 31)

31)

25°

100°

A) C = 55°, a = 11.63, c = 13.98 C) C = 50°, a = 11.63, c = 13.98

B) C = 55°, a = 13.98, c = 11.63 D) C = 60°, a = 13.98, c = 11.63

32) a = 70, b = 9, C = 105° A) c = 78.65, A = 66.1°, B = 8.9° C) c = 72.85, A = 68.1°, B = 6.9°

B) c = 75.75, A = 70.1°, B = 4.9° D) no triangle

Find the area of the triangle. If necessary, round the answer to two decimal places. 33) a = 6, b = 6, c = 7 A) 17.06 B) 21.14 C) 18.25 Solve the triangle. 34) a = 6, b = 8, C = 70° A) c = 6.3, A = 28.6°, B = 81.4° C) c = 9, A = 52.8°, B = 57.2°

D) 15.54

B) c = 8.2, A = 43.5°, B = 66.5° D) c = 10, A = 56.9°, B = 53.1°

Find the area of the triangle. If necessary, round the answer to two decimal places. 35)

A) 8.18

30)

32)

33)

34)

35)

B) 37.47

C) 2.81

Solve the triangle. 36) a = 9, b = 6, c = 5 A) A = 38.9°, B = 31.6°, C = 109.5° C) A = 38.9°, B = 109.5°, C = 31.6°

D) 154.49

B) A = 109.5°, B = 38.9°, C = 31.6° D) A = 109.5°, B = 31.6°, C = 38.9°

37) b = 2, c = 3, A = 95° A) a = 3.75, B = 32.1°, C = 52.9° C) a = 2.75, B = 52.9°, C = 32.1°

B) a = 3.75, B = 52.9°, C = 32.1° D) a = 4.75, B = 32.1°, C = 52.9°

36)

37)

38)

3 25°

9 A) b = 5.41, A = 143.6°, C = 11.4° C) b = 7.41, A = 11.4°, C = 143.6°

B) b = 6.41, A = 11.4°, C = 143.6° D) b = 6.41, A = 143.6°, C = 11.4°

Find the area of the triangle. If necessary, round the answer to two decimal places. 39) a = 14, b = 32, c = 26 A) 181.99 B) 5280.01 C) 177.99

D) 3219.69

Solve the problem. 40) A guy wire to the top of a tower makes an angle of 69° with the level ground. At a point 26 feet farther from the base of the tower and in line with the base of the wire, the angle of elevation to the top of the tower is 20°. What is the length of the guy wire? A) 70.97 ft B) 9.53 ft C) 32.16 ft D) 11.78 ft 41) It is 4.7 km from Lighthouse A to Port B. The bearing of the port from the lighthouse is N73°E. A ship has sailed due west from the port and its bearing from the lighthouse is N31°E. How far has the ship sailed from the port? Round your answer to the nearest 0.1 km. A) 3.5 km B) 3.1 km C) 2.7 km D) 3.7 km Solve the triangle. 42) B = 60°, C = 70°, a = 4 A) A = 50°, b = 5.52, c = 4.91 C) A = 50°, b = 4.52, c = 4.91

B) A = 50°, b = 5.91, c = 4.52 D) A = 50°, b = 4.91, c = 4.52

39)

40)

41)

42)

Solve the problem. by: 43) The distance d (in meters) of the bob of a pendulum from its rest position at time t (in seconds) is given43) d = -9e-0.6t/60 cos

2 2 0.36 t 7 3600

What is the maximum displacement of the bob after the first oscillation? A) about 0.13 m B) about 8.91 m C) about 5.18 m

D) about 8.39 m

Solve the right triangle using the information given. Round answers to two decimal places, if necessary.

44) b = 7, A = 35°; Find a, c, and B. A) a = 5.9 B) a = 5.9 c = 9.54 c = 8.54 B = 55° B = 55°

C) a = 4.9 c = 8.54 B = 55°

D) a = 4.9 c = 9.54 B =55°

Solve the triangle. 45)

44)

45)

4 A) A = 125.1°, B = 24.1°, C = 30.8° C) A = 30.8°, B = 24.1°, C = 125.1°

B) A = 30.8°, B = 125.1°, C = 24.1° D) A = 125.1°, B = 30.8°, C = 24.1°

Two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve any triangle(s) that results. 46) B = 16°, b = 5.8, a = 10.52 46) A) two triangles B) one triangle A1 = 30°, C1 = 134°, c1 = 15.1; A = 150°, C = 14°, c = 5.1 A2 = 150°, C2 = 14°, c2 = 5.1 C) one triangle A = 30°, C = 134°, c = 15.1

D) no triangle

Solve the triangle. 47) a = 6, c = 8, B = 126° A) b = 12.5, A = 23°, C = 31° C) b = 15.4, A = 25°, C = 29°

B) b = 18.3, A = 21°, C = 33° D) no triangle

Solve the problem. 48) A ladder leans against a building that has a wall slanting away from the ladder at an angle of 96° with the ground. If the bottom of the ladder is 23 feet from the base of the wall and it reaches a point 52 feet up the wall, how tall is the ladder to the nearest foot? A) 60 ft B) 59 ft C) 61 ft D) 58 ft

47)

48)

Graph the damped vibration curve for 0 t 2 . 49) d(t) = e-t/ cos (2t)

49)

Solve the triangle. 50) A = 30°, B = 100°, a = 5 A) C = 50°, b = 7.66, c = 8.85 C) C = 50°, b = 7.66, c = 9.85

B) C = 50°, b = 10.85, c = 7.66 D) C = 50°, b = 9.85, c = 7.66

Use the method of adding y-coordinates to graph the function.

50)

51) g(x) = cos x - cos (2x)

51)

Solve the triangle. 52)

52)

6 A) A = 55.8°, B = 82.8°, C = 41.4° C) A = 55.8°, B = 41.4°, C = 82.8°

B) A = 41.4°, B = 55.8°, C = 82.8° D) A = 41.4°, B = 82.8°, C = 55.8°

Find the area of the triangle. If necessary, round the answer to two decimal places. 53) A = 30°, b = 12, c = 7 A) 36.37 B) 19 C) 38.37

D) 21

53)

Solve the right triangle using the information given. Round answers to two decimal places, if necessary.

54) a = 7, b = 3; Find c, A, and B. A) c = 7.62 B) c = 7.62 A = 66.8° A = 67.8° B = 23.2° B = 22.2°

C) c = 6.32 A = 66.8° B = 23.2°

Find the area of the triangle. If necessary, round the answer to two decimal places. 55) a = 12, b = 15, C = 52° A) 35.46 B) 141.84 C) 70.92

D) c = 6.32 A = 67.8° B = 22.2°

D) 88.80

54)

55)

Two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve any triangle(s) that results. 56) C = 35°, a = 18.7, c = 16.1 56) A) two triangles B) one triangle A1 = 103°, B1 = 42°, b1 = 27.4; A = 42°, B = 103°, b = 27.4 A2 = 7°, B2 = 138°, b2 = 3.4 C) two triangles A1 = 42°, B1 = 103°, b1 = 27.4;

D) no triangle

A2 = 138°, B2 = 7°, b2 = 3.4

An object attached to a coiled spring is pulled down a distance a from its rest position and then released. Assuming that the motion is simple harmonic with period T, write an equation that relates the displacement d of the object from its rest position after t seconds. Also assume that the positive direction of the motion is up. 57) a = 11; T = 6 seconds 57) 1 1 t t A) d = -11 sin B) d = -11 cos 3 3

C) d = -11 cos

1 6

D) d = -6 cos

2 11

Solve the right triangle using the information given. Round answers to two decimal places, if necessary.

58) b = 3, B = 40°; Find a, c, and A. A) a = 3.58 B) a = 3.58 c = 5.67 c = 4.67 A = 60° A = 60°

C) a = 3.58 c = 4.67 A = 50°

D) a = 3.58 c = 5.67 A = 50°

Solve the problem. 59) A famous golfer tees off on a straight 390 yard par 4 and slices his drive to the right. The drive goes 270 yards from the tee. Using a 7-iron on his second shot, he hits the ball 180 yards and it lands inches from the hole. How many degrees (to the nearest degree) to the right of the line from the tee to the hole did he slice his drive? A) 119° B) 37° C) 52° D) 24° 60) A room in the shape of a triangle has sides of length 8 yd, 10 yd, and 14 yd. If carpeting costs $17.50 a square yard and padding costs $2.25 a square yard, how much to the nearest dollar will it cost to carpet the room, assuming that there is no waste? A) $745 B) $686 C) $774 D) $754

58)

59)

60)

Two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve any triangle(s) that results. 61) a = 7, b = 9, B = 49° 61) A) two triangles B) one triangle A1 = 76.01°, C1 = 54.99°, c1 = 7.60 or A = 35.94°, C = 95.06°, c = 11.88 A2 = 103.99°, C2 = 27.01, c2 = 12.14 C) one triangle A = 76.01°, C = 54.99°, c = 7.60

D) no triangle

Solve the problem. 62) Two tracking stations are on the equator 139 miles apart. A weather balloon is located on a bearing of N 35°E from the western station and on a bearing of N 19°E from the eastern station. How far is the balloon from the western station? Round to the nearest mile. A) 486 mi B) 408 mi C) 399 mi D) 477 mi 14

62)

Solve the triangle. 63) a = 3, c = 2, B = 90° A) b = 2.61, A = 33.8°, C = 56.2° C) b = 4.61, A = 56.2°, C = 33.8°

B) b = 3.61, A = 33.8°, C = 56.2° D) b = 3.61, A = 56.2°, C = 33.8°

Find the area of the triangle. If necessary, round the answer to two decimal places. 64) A = 83°, b = 9, c = 6 A) 27.01 B) 53.60 C) 26.80 65) a = 14, b = 13, c = 15 A) 84

B) 87

C) 93

D) 3.29

D) 90

Solve the problem. 66) Two sailboats leave a harbor in the Bahamas at the same time. The first sails at 24 mph in a direction 330°. The second sails at 28 mph in a direction 210°. Assuming that both boats maintain speed and heading, after 3 hours, how far apart are the boats? A) 130.4 mi B) 86.1 mi C) 100.6 mi D) 135.2 mi Find the area of the triangle. If necessary, round the answer to two decimal places. 67)

63)

64)

65)

66)

67)

1 10°

A) 2.43

B) 1.22

C) 0.61

D) 3.45

Solve the triangle. 68)

68)

110°

A) c = 4.14, A = 43°, B = 27° C) c = 4.14, A = 27°, B = 43°

B) c = 3.14, A =43°, B = 27° D) c = 5.14, A = 27°, B = 43°

Two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve any triangle(s) that results. 69) b = 5, c = 7, B = 75° 69) A) one triangle B) one triangle C = 39°, A = 66°, a = 16 C = 37°, A = 68°, a = 14 C) one triangle D) no triangle B = 38°, A = 67°, a = 12

A) d = 5 cos

B) d = -5 cos

C) d = -5 cos (10t)

D) d = 5 cos (10t)

Solve the problem. 71) A rocket tracking station has two telescopes A and B placed 2.6 miles apart. The telescopes lock onto a rocket and transmit their angles of elevation to a computer after a rocket launch. What is the distance to the rocket from telescope B at the moment when both tracking stations are directly east of the rocket telescope A reports an angle of elevation of 21° and telescope B reports an angle of elevation of 47°? A) 4.34 mi B) 5.31 mi C) 1.27 mi D) 2.13 mi

71)

The displacement d (in meters) of an object at time t (in seconds) is given. Describe the motion of the object. What is the maximum displacement from its resting position, the time required for one oscillation, and the frequency? 72) d = 5 sin (5t) 72) 5 oscillations/sec A) simple harmonic; 5 m; 5 sec;

B) simple harmonic; 5 m;

2 5

sec;

5 oscillations/sec 2

C) simple harmonic; -5 m;

2 5

sec;

5 oscillations/sec 2

D) simple harmonic; 5 m;

5 2 sec; 2 5

oscillations/sec

Solve the problem. 73) A flagpole is perpendicular to the horizontal but is on a slope that rises 10° from the horizontal. The pole casts a 43-foot shadow down the slope and angle of elevation of the sun measured from the slope is 36°. How tall is the pole? Round your answer to the nearest 0.1 foot. A) 36.2 ft B) 33.5 ft C) 35.4 ft D) 36.4 ft

73)

Two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve any triangle(s) that results. 74) a = 6, b = 4, B = 10° 74) A) one triangle B) one triangle A = 15.1°, C = 154.9°, c = 9.77 A = 164.9°, C = 5.1°, c = 2.05

C) two triangles A1 = 15.1°, C1 = 154.9°, c1 = 9.77 or

D) no triangle

A2 = 164.9°, C2 = 5.1°, c2 = 2.05

75) B = 42°, b = 7, a = 25 A) one triangle A = 38°, C = 99°, c = 29 C) one triangle A = 40°, C = 97°, c = 32

B) one triangle A = 41°, C = 98°, c = 33.5 D) no triangle

75)

76) B = 96°, b = 5, a = 25 A) one triangle A = 48°, C = 36°, c = 30 C) one triangle A = 47°, C = 36°, c = 32

B) one triangle A = 49°, C = 36°, c = 34 D) no triangle

76)

77) d = -9 sin

A) simple harmonic; 9 m;

77) 1 sec; 4 oscillations/sec 4

B) simple harmonic; -9 m; 4 sec;

1 oscillation/sec 4

C) simple harmonic; 9 m; 2 sec;

1 oscillation/sec 2

D) simple harmonic; 9 m; 4 sec;

1 oscillation/sec 4

Solve the problem. 78) From the edge of a 1000-foot cliff, the angles of depression to two cars in the valley below are 21° and 28°. How far apart are the cars? Round your answers to the nearest 0.1 ft. A) 714.4 ft B) 713.4 ft C) 724.4 ft D) 724.5 ft 79) A box has dimensions 2" × 3" × 4". (See illustration.)

78)

79)

Determine the angle formed by the diagonal of the 2" × 3" side and the diagonal of the 3" × 4" side. Round your answer to the nearest degree. A) 60° B) 62° C) 50° D) 65°

Two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve any triangle(s) that results. 80) A = 85°, a = 2, b = 4 80) A) one triangle B) one triangle A = 43°, C = 52°, c = 6 B = 44°, C = 51°, c = 10 C) one triangle D) no triangle B = 42°, C = 53°, c = 8

Solve the problem. 81) Find the area of the Bermuda Triangle if the sides of the triangle have the approximate lengths 846 miles, 922 miles, and 1,314 miles. A) 1,551,715 sq mi B) 512,411 sq mi C) 387,929 sq mi D) 492,017 sq mi

81)

82) A ship sailing parallel to shore sights a lighthouse at an angle of 12° from its direction of travel. After traveling 5 miles farther, the angle is 22°. At that time, how far is the ship from the lighthouse? A) 10.79 mi B) 2.78 mi C) 5.99 mi D) 5 mi Use the method of adding y-coordinates to graph the function. 83) f(x) = x - sin x

83)

82)

Solve the right triangle using the information given. Round answers to two decimal places, if necessary.

84) a = 2, c = 6; Find b, A, and B. A) b = 6.32 B) b = 5.66 A = 20.47° A = 19.47° B = 69.53° B = 70.53°

C) b = 5.66 A = 70.53° B = 19.47°

D) b = 6.32 A = 19.47° B = 70.53°

Solve the problem. 85) A surveyor standing 67 meters from the base of a building measures the angle to the top of the building and finds it to be 39°. The surveyor then measures the angle to the top of the radio tower on the building and finds that it is 50°. How tall is the radio tower? A) 25.59 m B) 9.16 m C) 13.02 m D) 9 m Solve the triangle. 86) a = 19, b = 16, c = 11 A) A = 57.3°, B = 87.4°, C = 35.3° C) A = 35.3°, B = 57.3°, C = 87.4°

B) A = 87.4°, B = 35.3°, C = 57.3° D) A = 87.4°, B = 57.3°, C = 35.3°

Solve the problem. 87) A sailboat leaves port on a bearing of S72°W. After sailing for two hours at 12 knots, the boat turns 90° toward the south. After sailing for three hours at 9 knots on this course, what is the bearing to the ship from port? Round your answer to the nearest 0.1°. A) N23.6°E B) N24.6°E C) S23.6°W D) S24.6°W

84)

85)

86)

87)

88) A photographer points a camera at a window in a nearby building forming an angle of 42° with the camera platform. If the camera is 52 m from the building, how high above the platform is the window, to the nearest hundredth of a meter? A) 0.9 m B) 1.11 m C) 57.75 m D) 46.82 m

88)

89) To find the distance AB across a river, a distance BC of 918 m is laid off on one side of the river. It is found that B = 110.6° and C = 15.1°. Find AB. Round to the nearest meter. A) 294 m B) 237 m C) 240 m D) 297 m

89)

The displacement d (in meters) of an object at time t (in seconds) is given. Describe the motion of the object. What is the maximum displacement from its resting position, the time required for one oscillation, and the frequency? 90) d = 5 cos (3t) 90) 2 3 sec; oscillations/sec A) simple harmonic; 5 m; 3 2

B) simple harmonic; -5 m;

2 3

sec;

3 oscillations/sec 2

C) simple harmonic; 5 m;

3 2 sec; 2 3

oscillations/sec

D) simple harmonic; 5 m; 3

sec;

oscillations/sec

Solve the triangle. 91) b = 7, c = 9, A = 113° A) a = 13.4, B = 29°, C = 38° C) a = 16.3, B = 31°, C = 36°

B) a = 19.2, B = 27°, C = 40° D) no triangle

Solve the problem. 92) Given a triangle with a = 9, b = 11, A = 31°, what is (are) the possible length(s) of c? Round your answer to two decimal places. A) 16.42 or 2.44 B) 14.21 C) 16.42 or 3.41 D) 6.61

91)

92)

93) A new homeowner has a triangular-shaped back yard. Two of the three sides measure 65 ft and 80 ft and form an included angle of 125°. The owner wants to approximate the area of the yard, so that he can determine the amount of fertilizer and grass seed to be purchased. Find the area of the yard rounded to the nearest square foot. A) 4260 sq. ft B) 2130 sq. ft C) 2129 sq. ft D) 5200 sq. ft

93)

94) A famous golfer tees off on a long, straight 475 yard par 4 and slices his drive 17° to the right of the line from tee to the hole. If the drive went 288 yards, how many yards will the golfer's second shot have to be to reach the hole? A) 421.6 yd B) 662.9 yd C) 216.6 yd D) 755.1 yd

94)

An object attached to a coiled spring is pulled down a distance a from its rest position and then released. Assuming that the motion is simple harmonic with period T, write an equation that relates the displacement d of the object from its rest position after t seconds. Also assume that the positive direction of the motion is up. 95) a = 10; T = 4 seconds 95) 1 1 t t A) d = -10 sin B) d = -4 cos 2 5

C) d = -10 cos

1 t 2

D) d = -10 cos

1 2

Solve the problem. 96) Two points A and B are on opposite sides of a building. A surveyor selects a third point C to place a transit. Point C is 50 feet from point A and 65 feet from point B. The angle ACB is 47°. How far apart are points A and B? A) 67.1 ft B) 47.9 ft C) 94.6 ft D) 105.6 ft

96)

97) An airplane is sighted at the same time by two ground observers who are 3 miles apart and both directly west of the airplane. They report the angles of elevation as 11° and 21°. How high is the airplane? A) 1.18 mi B) 1.08 mi C) 0.57 mi D) 2.22 mi

97)

98) A building 160 feet tall casts a 80 foot long shadow. If a person looks down from the top of the building, what is the measure of the angle between the end of the shadow and the vertical side of the building (to the nearest degree)? (Assume the person's eyes are level with the top of the building.) A) 27° B) 63° C) 30° D) 60°

98)

99) A straight trail with a uniform inclination of 11° leads from a lodge at an elevation of 500 feet to a mountain lake at an elevation of 10,000 feet. What is the length of the trail (to the nearest foot)? A) 10,187 ft B) 9,678 ft C) 49,788 ft D) 52,408 ft

99)

Solve the triangle. 100) a = 9, b = 14, c = 15 A) A = 34°, B = 66.1°, C = 79.9° C) A = 38°, B = 64.1°, C = 77.9°

B) A = 36°, B = 66.1°, C = 77.9° D) no triangle

Solve the problem. 101) In flying the 78 miles from Champaign to Peoria, a student pilot sets a heading that is 10° off course and maintains an average speed of 140 miles per hour. After 15 minutes, the instructor notices the course error and tells the student to correct his heading. Through what angle will the plane move to correct the heading and how many miles away is Peoria when the plane turns? A) 17.9°; 67.97 mi B) 162.1°; 67.97 mi C) 162.1°; 43.95 mi D) 17.9°; 43.95 mi 102) A painter needs to cover a triangular region 63 meters by 66 meters by 71 meters. A can of paint covers 70 square meters. How many cans will be needed? A) 28 cans B) 14 cans C) 3 cans D) 311 cans

100)

101)

102)

An object attached to a coiled spring is pulled down a distance a from its rest position and then released. Assuming that the motion is simple harmonic with period T, write an equation that relates the displacement d of the object from its rest position after t seconds. Also assume that the positive direction of the motion is up. 103) a = 8; T = 4 seconds 103) 1 1 t t A) d = -4 cos B) d = -8 sin 4 2

C) d = -8 cos

1 2

D) d = -8 cos

1 4

Solve the problem. 104) A surveyor is measuring the distance across a small lake. He has set up his transit on one side of the lake 150 feet from a piling that is directly across from a pier on the other side of the lake. From his transit, the angle between the piling and the pier is 70°. What is the distance between the piling and the pier to the nearest foot? A) 141 ft B) 412 ft C) 51 ft D) 55 ft

104)

Solve the triangle. 105) a = 9, b = 9, c = 8 A) A = 63.6°, B = 63.6°, C = 52.8° C) A = 63.6°, B = 52.8°, C = 63.6°

B) A = 52.8°, B = 63.6°, C = 63.6° D) A = 64.6°, B = 64.6°, C = 50.8°

Solve the problem. 106) A forest ranger at Lookout A sights a fire directly north of her position. Another ranger at Lookout B, exactly 2 kilometers directly west of A, sights the same fire at a bearing of N41.2°E. How far is the fire from Lookout A? Round your answer to the nearest 0.01 km. A) 2.28 km B) 2.32 km C) 2.25 km D) 2.18 km

105)

106)

Answer Key Testname: CHAPTER 9 1) D 2) d = -11e-0.7t/30 cos

2 2 0.49 t 3 900

f(x) =

sin( x) +

1 1 1 sin(3 x) + sin(5 x) + sin (7 x) 3 5 7

4) 9.85 × 1013 km (More recent observations have refined this value to about 1.08 × 1014 km.) 5) 196.8 m, 171.7 m 3 5 7 ; ; 6) t = ; 2 2 2 2

7) 2565 ft; 1430 ft 8) 344 sq. cm 9) 53.6° or 20.4°; yes; direct observation 10) 0.59 sq. units; 0.36 sq. units 11) C 12) A 13) D 14) C 15) D 16) A 17) C 18) D 19) D 20) A 21) C 23

Answer Key Testname: CHAPTER 9 22) B 23) D 24) D 25) B 26) D 27) A 28) A 29) C 30) C 31) B 32) C 33) A 34) B 35) A 36) B 37) A 38) B 39) C 40) D 41) D 42) C 43) D 44) C 45) D 46) A 47) A 48) B 49) B 50) D 51) A 52) C 53) D 54) A 55) C 56) C 57) B 58) C 59) D 60) C 61) B 62) D 63) D 64) C 65) A 66) D 67) C 68) C 69) D 70) B 71) D 24

Answer Key Testname: CHAPTER 9 72) B 73) D 74) C 75) D 76) D 77) D 78) C 79) A 80) D 81) C 82) C 83) C 84) B 85) A 86) D 87) C 88) D 89) A 90) A 91) A 92) A 93) B 94) C 95) C 96) B 97) A 98) A 99) C 100) B 101) D 102) A 103) C 104) B 105) A 106) A

Chapter 10 Exam Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Match the graph to one of the polar equations. 1)

A) r = 2 cos

B) r sin

C) r = 2 sin

Solve the problem. 2) Which of the following vectors is parallel to v = -10i - 8j? A) w = 4i + 4j B) w = 20i + 16j C) w = 3i - 5j

D) r = 1

D) w = -20i + 25j

Match the graph to one of the polar equations. 3)

A) r = 4 cos

B) r = 4 sin

C) r sin

Solve the problem. 4) Which of the following vectors is orthogonal to 20i - 8j? A) w = 15i - 6j B) w = 20i + 4j C) w = 4i + 3j

D) r = 2

D) w = -10i - 25j

The polar equation of the graph is either r = a + b cos equations. 5)

A) r = 3 + 4 cos

or r = a + b sin , a > 0, b > 0. Match the graph to one of the

B) r = 4 + 3 cos

C) r = 4 + 3 sin

D) r = 3 + 4 sin

A) r = 4 + 3 sin

B) r = 4 + 3 cos

C) r = 3 + 4 sin

D) r = 3 + 4 cos

Match the graph to one of the polar equations. 7)

A) r = 4 cos

B) r = 4 sin

C) r sin

D) r = 2

The polar equation of the graph is either r = a + b cos equations. 8)

A) r = 4 + 3 cos

or r = a + b sin , a > 0, b > 0. Match the graph to one of the

B) r = 3 + 4 cos

C) r = 4 + 3 sin

D) r = 3 + 4 sin

Match the graph to one of the polar equations. 9)

A) r = 2 + sin

B) r = 2 + cos

C) r = 4 cos

Solve the problem. 10) Which of the following vectors is parallel to v = 9i + 5j? 15 25 15 25 i+ j ij A) w = 45i - 25j B) w = C) w = 2 6 2 6

D) r = 4 sin

3 5 D) w = i + j 2 6

10)

Match the graph to one of the polar equations. 11)

A) r = -4 sin

B) r = -4 cos

The polar equation of the graph is either r = a + b cos equations. 12)

A) r = 4 + 2 cos

11)

C) r = -2

D) r sin

= -2

or r = a + b sin , a > 0, b > 0. Match the graph to one of the

12)

B) r = 4 + 2 sin

C) r = 2 + 4 cos

D) r = 2 + 4 sin

Match the graph to one of the polar equations. 13)

A) r = 6 cos

13)

B) r = 3 + sin

C) r = 6 sin

D) r = 3 + cos

14)

B) r = -

C) r =

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 15) Two forces, F1 of magnitude 35 newtons (N) and F2 of magnitude 55 newtons, act on an

15)

object at angles of 45° and -60° (respectively) with the positive x-axis. Find the direction and magnitude of the resultant force; that is, find F1 + F2 . Round the direction and magnitude to two decimal places.

16) Plot the point 4, (a) r > 0, (b) r < 0, (c) r > 0

-2 0 2

and find other polar coordinates (r, ) of the point for which:

16)

<0 <2 <4

17) A truck pushes a load of 45 tons up a hill with an inclination of 35°. Express the force vector F in terms of i and j. Round the components of F to two decimal places.

17)

18) Plot the point 4, (a) r > 0, (b) r < 0, (c) r > 0

-2 0 2

and find other polar coordinates (r, ) of the point for which:

18)

<0 <2 <4

19) Two forces, F1 of magnitude 60 newtons (N) and F2 of magnitude 70 newtons, act on an

19)

object at angles of 40° and 130° (respectively) with the positive x-axis. Find the direction and magnitude of the resultant force; that is, find F1 + F2 . Round the direction and magnitude to two decimal places.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. The rectangular coordinates of a point are given. Find polar coordinates for the point. 20) (0, -4) A) 4,

C) 4, -

B) (4, 0)

Plot the point given in polar coordinates. 21) (-2, 45°)

20) D) (4, )

21)

The polar coordinates of a point are given. Find the rectangular coordinates of the point. 22) (7.7, 5.5) Round the rectangular coordinates to two decimal places. A) (7.66, -0.74) B) (5.46, -5.43) C) (7.66, 0.74) D) (5.46, 5.43)

22)

Find the quantity if v = 5i - 7j and w = 3i + 2j. 23) v + w A) 74 + 13 B) 39

23) C) 2 6 +

Identify and graph the polar equation. 24) r = 2

24)

logarithmic spiral

The polar coordinates of a point are given. Find the rectangular coordinates of the point. 4 25) 5, 3 A)

5 3 5 , 2 2

B) -

5 5 3 , 2 2

C) -

Plot the point given in polar coordinates. 26) (5, 30°)

5 3 5 ,2 2

25) D)

5 5 3 ,2 2

26)

Plot the complex number in the complex plane. 27) -6 - 4i

27)

The letters x and y represent rectangular coordinates. Write the equation using polar coordinates (r, ). 28) 2xy = 3 A) 2r cos sin = 3 B) r2 sin 2 = 3 C) r2 cos

sin

D) r2 sin 2 = 6

28)

Decompose v into two vectors v1 and v2 , where v1 is parallel to w and v2 is orthogonal to w.

29) v = -3i - 5j,

w = 3i + j 21 7 8 24 i - j, v2 = - i j A) v1 = 5 5 5 5 C) v1 = -

21 7 9 23 i - j, v2 = - i j B) v1 = 5 5 5 5

14 14 5 31 ij, v2 = i j 3 9 3 9

D) v1 = -

29)

21 7 6 18 i - j, v2 = i j 5 5 5 5

State whether the vectors are parallel, orthogonal, or neither. 30) v = 3i + 4j, w = 4i - 3j A) Parallel B) Orthogonal

C) Neither

30)

Use the figure below. Determine whether the given statement is true or false.

31) H + I + J = B A) True

B) False

Identify and graph the polar equation. 32) r = 2 + 2 cos

31)

32)

cardioid

Find the dot product v · w. 33) v = 14i - 9j, w = 10i + 15j A) 5 B) 275

C) -135

D) 140

Write the expression in the standard form a + bi. 34) 2(cos 15° + i sin 15°) 3 A) 3 2 + 3 2i

33)

34) C) 4 2 + 4 2i

B) 4 + 4i

Plot the point given in polar coordinates. 35) (2, -135°)

D) 3 + 3i

35)

36) 2, -

36)

Find the angle between v and w. Round your answer to one decimal place, if necessary. 37) v = 4i, w=j A) 270° B) 0° C) 90° D) 180°

37)

Use the figure below. Determine whether the given statement is true or false.

38) A + B + C + D + E = 0 A) True

B) False

38)

Write the complex number in polar form. Express the argument in degrees, rounded to the nearest tenth, if necessary. 39) 3 + i 39) A) 4(cos 30° + i sin 30°) B) 2(cos 60° + i sin 60°) C) 2(cos 30° + i sin 30°) D) 4(cos 60° + i sin 60°)

Solve the problem. 40) If v = -10i + j and w = -7i + j, find v + w . A) 151 B) 325

40) C)

293

D) 3

41) A box of supplies that weighs 1500 kilograms is suspended by two cables as shown in the figure. To two 41) decimal places, what is the tension in the two cables?

A) Tension in right cable: 723.54 kg; tension in left cable: 776.46 kg B) Tension in right cable: 776.46 kg; tension in left cable: 1098.08 kg C) Tension in right cable: 776.46 kg; tension in left cable: 723.54 kg D) Tension in right cable: 1098.08 kg; tension in left cable: 776.46 kg Find zw or

z as specified. Leave your answer in polar form. w

42) z = 8 cos w = 3 cos Find

2 6

+ i sin + i sin

42)

2 6

z . w

8 cos + i sin 3 12 12

B) 5 cos

8 cos + i sin 3 3 3

D) 5 cos

12 3

+ i sin + i sin

12 3

Use the vectors in the figure below to graph the following vector.

43) z - v

43)

Write the complex number in rectangular form. 44) 9(cos 180° + i sin 180°) A) 9i B) 9

C) -9

D) -9i

44)

Graph the polar equation. 0 45) r = ,

45)

Write the complex number in rectangular form. 11 11 + i sin 46) 4 cos 6 6 A) -2 3 - 2i

46)

B) 2 3 - 2i

C) 2 + 2 3i

D) 2 - 2 3i

Write the vector v in the form ai + bj, given its magnitude v and the angle it makes with the positive x-axis. 47) v = 5, = 240° 47) 5 5 3 5 5 3 j j A) v = 5 i + B) v = 5 - i 2 2 2 2 C) v = 5 -

2 2 ij 2 2

D) v = 5 -

5 3 5 i- j 2 2

Test the equation for symmetry with respect to the given axis, line, or pole. 48) r2 = sin(2 ); the pole

48)

Write the expression in the standard form a + bi. 49) 2(cos 75° + i sin 75°) 3

49)

A) Symmetric with respect to the pole B) May or may not be symmetric with respect to the pole

A) 4 2 - 4 2i

B) -4 - 4 2i

C) 4 2 + 4 2i

D) -4 2 - 4 2i

Test the equation for symmetry with respect to the given axis, line, or pole. 50) r = 3 + 6 sin ; the polar axis A) Symmetric with respect to the polar axis B) May or may not be symmetric with respect to the polar axis Solve the problem. 51) If u = -8i - 2j and v = 6i + 7j, find u + v. A) 14i + 5j B) -14i - 3j Find zw or

C) -2i + 5j

50)

D) -3i + 5j

51)

z as specified. Leave your answer in polar form. w

52) z = 5(cos 35° + i sin 35°) w = 2(cos 40° + i sin 40°) Find zw. A) 10(cos 50.9° + i sin 50.9°) C) 7(cos 75° + i sin 75°)

52)

B) 7(cos 50.9° + i sin 50.9°) D) 10(cos 75° + i sin 75°)

Find the angle between v and w. Round your answer to one decimal place, if necessary. 53) v = -5i + 7j, w = -6i - 4j A) 110.8° B) 90.9° C) 88.2° D) 20.7° Find the unit vector having the same direction as v. 54) v = -12i - 5j 5 12 i+ j A) u = -156i - 65j B) u = 13 13

C) u = -

13 13 ij 12 5

D) u = -

53)

12 5 ij 13 13

Solve the problem. Round your answer to the nearest tenth. 55) A wagon is pulled horizontally by exerting a force of 60 pounds on the handle at an angle of 25° to the horizontal. How much work is done in moving the wagon 50 feet?" . A) 2110.8 ft-lb B) 2718.9 ft-lb C) 1267.9 ft-lb D) 1617.4 ft-lb

54)

55)

The polar coordinates of a point are given. Find the rectangular coordinates of the point. 2 56) -5, 3 A) -

5 -5 3 , 2 2

B) -

5 5 3 , 2 2

5 -5 3 , 2 2

56) D)

5 5 3 , 2 2

Use the vectors in the figure below to graph the following vector.

57) u + z

57)

Find the unit vector having the same direction as v. 58) v = -3j A) u = -3j

B) u = -j

C) u = 9j

D) u = -

1 j 3

58)

The rectangular coordinates of a point are given. Find polar coordinates for the point. 59) (100, -30) Round the polar coordinates to two decimal places, with in degrees. A) (104.40, -106.70°) B) (104.40, 106.70°) C) (104.40, 16.70°) D) (104.40, -16.70°)

59)

Use the figure below. Determine whether the given statement is true or false.

60) A + H = F A) True

60)

B) False

The letters x and y represent rectangular coordinates. Write the equation using polar coordinates (r, ). 61) y = 5 A) r sin = 5 B) sin cos = 5 C) r = 5 D) r cos = 5

61)

Match the point in polar coordinates with either A, B, C, or D on the graph. 62) -3,

62)

A) A

B) B

C) C

D) D

The letters x and y represent rectangular coordinates. Write the equation using polar coordinates (r, ). 63) y = x A) r = sin B) r = cos C) sin = cos D) sin = - cos Find zw or

63)

z as specified. Leave your answer in polar form. w

64) z = 10(cos 30° + i sin 30°) w = 5(cos 10° + i sin 10°) z Find . w

64)

A) 2(cos 20° + i sin 20°) C) 5(cos 20° + i sin 20°)

B) 2(cos 3° + i sin 3°) D) 5(cos 3° + i sin 3°)

Plot the point given in polar coordinates. 5 65) 5, 3

65)

Write the expression in the standard form a + bi. 66) 2(cos 105° + i sin 105°) 3 A) -4 2 - 4 2i

66)

B) 4 2 - 4 2i

C) 4 - 4 2i

Graph the polar equation. 22

D) -4 2 + 4 2i

67) r = tan , -

67)

Find the quantity if v = 5i - 7j and w = 3i + 2j. 68) v + w A) 2 6 + 13 B) 74 +

68) 13

Find zw or

z as specified. Leave your answer in polar form. w

69) z = 1 + i w= 3-i Find zw. 2 (cos 15° + i sin 15°) A) 2

69)

B) 2 2(cos 15° + i sin 15°)

C) 2 2(cos 345° + i sin 345°)

D) 2 2(cos 75° + i sin 75°)

Write the expression in the standard form a + bi. 70) (1 - i)10 A) 32

B) -32 + 32i

C) -32i

Find the unit vector having the same direction as v. 71) v = -3i - 4j 5 5 A) u = - i - j B) u = -15i - 20j 3 4

C) u = -

Graph the polar equation. 72) r = sin tan

D) 32 - 32i

3 4 i- j 5 5

D) u =

4 3 i+ j 5 5

70)

71)

72)

The letters r and represent polar coordinates. Write the equation using rectangular coordinates (x, y). 73) r = 1 + 2 sin A) x2 + y2 = x2 + y2 + 2x B) x2 + y2 = x2 + y2 + 2y C) x2 + y2 =

x2 + y2 + 2y

D) x2 + y2 =

x2 + y2 + 2x

Decompose v into two vectors v1 and v2 , where v1 is parallel to w and v2 is orthogonal to w.

74) v = i + 9j,

w=i+j

A) v1 = 10i + 10j, v2 = -8i + 8j C) v1 =

Find zw or

73)

74)

B) v1 = 5i + 5j, v2 = 4i - 4j

11 11 9 7 i+ j, v2 = - i + j 2 2 2 2

D) v1 = 5i + 5j), v2 = -4i + 4j

z as specified. Leave your answer in polar form. w

75) z =

3 cos

7 7 + i sin 4 4

6 cos

9 9 + i sin 4 4

Find

z . w

75)

2 3 3 cos + i sin 2 2 2

C) 3 2 cos

+ i sin

B) 3 2 cos

Find the quantity if v = 5i - 7j and w = 3i + 2j. 76) v - w A) 85 B) 74 -

3 3 + i sin 2 2

2 cos + i sin 2 2 2

76) 13

Find the unit vector having the same direction as v. 77) v = 4i 1 A) u = i B) u = i 4

D) 2 6 -

77) C) u = 4i

D) u = 16i

Write the complex number in polar form. Express the argument in degrees, rounded to the nearest tenth, if necessary. 78) -12 + 16i 78) A) 20(cos 126.9° + i sin 126.9°) B) 20(cos 306.9° + i sin 306.9°) C) 20(cos 53.1° + i sin 53.1°) D) 20(cos 233.1° + i sin 233.1°) The polar coordinates of a point are given. Find the rectangular coordinates of the point. 79) (-5, 120°) 5 5 3 5 -5 3 5 5 3 5 -5 3 A) - , B) - , C) , D) , 2 2 2 2 2 2 2 2 Solve the problem. 80) If v = 3i - 4j, find v . A) 5

B) 25

C) 5

D) 7

Find the dot product v · w. 81) v = i - j, w = -i + j A) 0

B) -1

C) 1

D) -2

79)

80)

81)

Write the complex number in polar form. Express the argument in degrees, rounded to the nearest tenth, if necessary. 82) -4 82) A) 4(cos 0° + i sin 0°) B) 4(cos 90° + i sin 90°) C) 4(cos 180° + i sin 180°) D) 4(cos 270° + i sin 270°) Use the figure below. Determine whether the given statement is true or false.

83) C + D + G + I + J = 0 A) True

B) False

83)

The vector v has initial position P and terminal point Q. Write v in the form ai + bj; that is, find its position vector. 84) P = (0, 0); Q = (3, 5) 84) A) v = 3i + 5j B) v = -5i - 3j C) v = -3i - 5j D) v = 5i + 5j Plot the complex number in the complex plane. 85) -7 + 5i

85)

Find zw or

z as specified. Leave your answer in polar form. w

86) z = 10(cos 45° + i sin 45°) w = 5(cos 15° + i sin 15°) Find zw. A) 50(cos 30° + i sin 30°) C) 5(cos 60° + i sin 60°)

86)

B) 5(cos 30° + i sin 30°) D) 50(cos 60° + i sin 60°)

State whether the vectors are parallel, orthogonal, or neither. w = i - 4j 87) v = i + 2j, A) Parallel B) Orthogonal Test the equation for symmetry with respect to the given axis, line, or pole. 88) r = 3 - 3 sin ; polar axis A) Symmetric with respect to the polar axis B) May or may not be symmetric with respect to the polar axis

C) Neither

87)

88)

Find zw or

z as specified. Leave your answer in polar form. w

89) z = 2 + 2i w= 3-i Find zw.

89)

A) 4 2 cos C) 4 cos

23 23 + i sin 12 12

B) 4 cos

23 23 + i sin 12 12

D) 4 2 cos

+ i sin 12

+ i sin

Find all the complex roots. Leave your answers in polar form with the argument in degrees. 90) The complex cube roots of -8i A) 8(cos 90° + i sin 90°), 8(cos 210° + i sin 210°), 8(cos 330° + i sin 330°) B) 512(cos 90° + i sin 90°), 512(cos 210° + i sin 210°), 512(cos 330° + i sin 330°) C) 2(cos 180° + i sin 180°), 2(cos 300° + i sin 300°), 2(cos 60° + i sin 60°) D) 2(cos 90° + i sin 90°), 2(cos 210° + i sin 210°), 2(cos 330° + i sin 330°) Plot the point given in polar coordinates. 7 91) 3, 6

90)

91)

Transform the polar equation to an equation in rectangular coordinates. Then identify and graph the equation. 92) r sec = -6 92)

(x + 3)2 + y2 = 9; circle, radius 3 center (-3, 0) in rectangular coordinates

y = -6; horizontal line 6 units below the pole

x = -6; vertical line 6 units to the left of the pole

x2 + (y + 3)2 = 9; circle, radius 3, center at (0, -3) in rectangular coordinates

Identify and graph the polar equation. 93) r = 4 - 5 sin

93)

limacon without inner loop

limacon with inner loop

limacon without inner loop

limacon with inner loop

The letters x and y represent rectangular coordinates. Write the equation using polar coordinates (r, ). 94) x2 + y2 - 4x = 0 A) r sin2 = 4 cos C) r cos2 = 4 sin

94)

B) r = 4 cos D) r = 4 sin

Solve the problem. Round your answer to the nearest tenth. 95) Find the work done by a force of 4 pounds acting in the direction of 37° to the horizontal in moving an object 2 feet from (0, 0) to (2, 0). A) 4.8 ft-lb B) 6.4 ft-lb C) 12.8 ft-lb D) 6.8 ft-lb

95)

Plot the complex number in the complex plane. 96) 3 - i

96)

The letters r and 97) r = cos

represent polar coordinates. Write the equation using rectangular coordinates (x, y).

A) x2 + y2 = x

B) (x + y)2 = x

C) (x + y)2 = y

Plot the point given in polar coordinates.

D) x2 + y2 = y

97)

98) 2,

3 4

98)

The letters x and y represent rectangular coordinates. Write the equation using polar coordinates (r, ). 99) x2 = 4y A) r cos2 = 4 sin C) r sin2 = 4 cos

B) 4 cos2 D) 4 sin2

= r sin = r cos

99)

Plot the complex number in the complex plane. 100) 5i

100)

Solve the problem. 101) If v = -2i + 2j, find v . A) 2

B) 2 2

C) 4

D) 8

102) If v = -i - j, find v . A) 1

B) 0

C) 2

101)

102)

The rectangular coordinates of a point are given. Find polar coordinates for the point. 103) (- 3, -1) A) 2, -

B) 2,

Find the dot product v · w. 104) v = 13i + 8j, w = 9i - 4j A) 117 105) v = 6i - 3j, A) 0

w = 8i + j

C) 2, -

B) 85

C) 149

B) 51

C) -18

Plot the point given in polar coordinates. 106) (-2, -135°)

103) D) 2,

D) -32

D) 45

104)

105)

106)

The letters x and y represent rectangular coordinates. Write the equation using polar coordinates (r, ). 107) y2 = 16x A) sin2

C) r sin2

B) sin2 = 16r2 cos D) r2 sin2 = 16 cos

= 16r cos = 16 cos

Find all the complex roots. Leave your answers in polar form with the argument in degrees. 108) The complex fifth roots of 3 + i A) 32(cos 6° + i sin 6°), 32(cos 78° + i sin 78°), 32(cos 150° + i sin 150°), 32(cos 222° + i sin 222°), 32(cos 294° + i sin 294°) B) 32(cos 30° + i sin 30°), 32(cos 102° + i sin 102°), 32(cos 174° + i sin 174°), 32(cos 246° + i sin 246°), 32(cos 318° + i sin 318°) 5 5 5 5 C) 2(cos 30° + i sin 30°), 2(cos 102° + i sin 102°), 2(cos 174° + i sin 174°), 2(cos 246° + i sin 5 246°), 2(cos 318° + i sin 318°) 5 5 5 5 D) 2(cos 6° + i sin 6°), 2(cos 78° + i sin 78°), 2(cos 150° + i sin 150°), 2(cos 222° + i sin 5 222°), 2(cos 294° + i sin 294°)

107)

108)

Solve the problem. 109) If P = (9, 3) and Q = (x, 57), find all numbers x such that the vector represented by PQ has length 90. A) {-81, -63} B) {-81, 81} C) {-63, 90} D) {-63, 81} The letters r and 110) r =

109)

represent polar coordinates. Write the equation using rectangular coordinates (x, y).

5 1 + cos

A) x2 = 10y - 25

110) B) x2 = 25 - 10y

C) y2 = 10x - 25

D) y2 = 25 - 10x

Write the vector v in the form ai + bj, given its magnitude v and the angle it makes with the positive x-axis. 111) v = 15, = 30° 111) 2 2 1 3 i+ j j A) v = 15 B) v = 15 i + 2 2 2 2 C) v = 15

3 1 i+ j 2 2

D) v = 15 -

3 1 i+ j 2 2

Find all the complex roots. Leave your answers in polar form with the argument in degrees. 112) The complex fifth roots of -2i 5 5 5 5 A) 2(cos 45° + i sin 45°), 2(cos 117° + i sin 117°), 2(cos 189° + i sin 189°), 2(cos 261° + i sin 5 261°), 2(cos 333° + i sin 333°) 4 4 4 4 B) 2(cos 54° + i sin 54°), 2(cos 126° + i sin 126°), 2(cos 198° + i sin 198°), 2(cos 270° + i sin 4 270°), 2(cos 342° + i sin 342°) C) 32(cos 54° + i sin 54°), 32(cos 126° + i sin 126°), 32(cos 198° + i sin 198°), 32(cos 270° + i sin 270°), 32(cos 342° + i sin 342°) 5 5 5 5 D) 2(cos 54° + i sin 54°), 2(cos 126° + i sin 126°), 2(cos 198° + i sin 198°), 2(cos 270° + i sin 5 270°), 2(cos 342° + i sin 342°) Solve the problem. 113) If v = 3i + 2j, what is 8v ? A) -4 52

112)

113) B) 4 20

C) 4 52

D) i 320

Test the equation for symmetry with respect to the given axis, line, or pole. 114) r = -4 sin ; the pole A) Symmetric with respect to the pole B) May or may not be symmetric with respect to the pole

114)

The rectangular coordinates of a point are given. Find polar coordinates for the point. 115) (0.6, -1.1) Round the polar coordinates to two decimal places, with in degrees. A) (1.25, 57.93°) B) (1.25, -57.93°) C) (1.25, -61.39°) D) (1.25, 61.39°)

115)

The letters r and represent polar coordinates. Write the equation using rectangular coordinates (x, y). 116) r sin = 10 A) y = 10x B) x = 10 C) x = 10y D) y = 10

116)

State whether the vectors are parallel, orthogonal, or neither. 117) v = 3i + j, w = i - 3j A) Parallel B) Orthogonal

117)

C) Neither

Find the angle between v and w. Round your answer to one decimal place, if necessary. 118) v = -2i + 9j, w = 4i + 2j A) 76.0° B) 28.0° C) 38.0° D) 86.0°

118)

The letters r and represent polar coordinates. Write the equation using rectangular coordinates (x, y). 119) r = 10 sin A) x2 + y2 = 10y B) x2 + y2 = 10x C) x2 + y2 = 10x D) x2 + y2 = 10y Identify and graph the polar equation. 120) r = 4 + 3 sin

120)

119)

limacon without inner loop

limacon with inner loop

limacon without inner loop

Write the complex number in polar form. Express the argument in degrees, rounded to the nearest tenth, if necessary. 121) -5 - 5i 121) A) 25(cos 225° + i sin 225°) B) 5 2(cos 225° + i sin 225°) C) 5 2(cos 230° + i sin 230°) D) 25(cos 230° + i sin 230°) 38

Match the point in polar coordinates with either A, B, C, or D on the graph. 122) -3, -

122)

A) A

B) B

C) C

D) D

Transform the polar equation to an equation in rectangular coordinates. Then identify and graph the equation. 123) r = 6 cos 123)

(x + 3)2 + y2 = 9; circle, radius 3, center at (-3, 0) in rectangular coordinates

x2 + (y - 3)2 = 9; circle, radius 3, center at (0, 3) in rectangular coordinates

(x - 3)2 + y2 = 9; circle, radius 3, center at (3, 0) in rectangular coordinates

x2 + (y + 3)2 = 9; circle, radius 3, center at (0, -3) in rectangular coordinates

Write the complex number in rectangular form. 124) 4(cos 300° + i sin 300°) A) -2 + 2 3i B) -2 3 - 2i

124) C) 2 - 2 3i

D) 2 3 - 2i

The letters x and y represent rectangular coordinates. Write the equation using polar coordinates (r, ). 125) x2 + 4y2 = 4 A) r2 (4 cos2 + sin2 ) = 4 C) 4 cos2 + sin2 = 4r

B) cos2 + 4 sin2 = 4r D) r2 (cos2 + 4 sin2 ) = 4

125)

Use the figure below. Determine whether the given statement is true or false.

126) G + H = F A) True Find the dot product v · w. 127) v = 5i, w=j A) 5

126)

B) False

127) B)

C) 6

D) 0

The rectangular coordinates of a point are given. Find polar coordinates for the point. 128) (-2, 0) A) 2,

B) (2, )

C) (-2, )

Graph the polar equation.

128) D) 2,

129) r =

4 1 - 4 sin

129)

State whether the vectors are parallel, orthogonal, or neither. 130) v = 3i - j, w = 6i - 2j A) Parallel B) Orthogonal Plot the point given in polar coordinates.

C) Neither

130)

131) (2, 45°)

131)

Solve the problem. 132) An SUV weighing 4,600 pounds is parked on a street which has an incline of 14°. Find the force required to keep the SUV from rolling down the hill and the force of the SUV perpendicular to the hill. Round the forces to the nearest hundredth. A) 1,421.48 lb and 4,374.86 lb B) 1,112.84 lb and 4,463.36 lb C) 798.78 lb and 4,530.12 lb D) 556.42 lb and 2,231.68 lb Plot the point given in polar coordinates. 42

132)

133) (2, 0°)

133)

Test the equation for symmetry with respect to the given axis, line, or pole. 134) r = -2 cos ; the polar axis A) Symmetric with respect to the polar axis B) May or may not be symmetric with respect to the polar axis Graph the polar equation.

134)

135) r =

4 4 - 2 cos

135)

Write the vector v in the form ai + bj, given its magnitude v and the angle it makes with the positive x-axis. 136) v = 3, = 135° 136) 3 3 3 3 3 3 j i- j A) v = 3 - i + B) v = 3 2 2 2 2 C) v = 3 -

2 2 i+ j 2 2

137) v = 5, = 270° A) v = -5j

D) v = 3

B) v = -5i + 5j)

2 2 ij 2 2

C) v = -5i

D) v = -5i - 5j

137)

Solve the problem. 138) Find a so that the vectors v = i + aj and w = 5i + 4j are orthogonal. 4 5 5 A) B) C) 5 4 4

138)

4 D) 5

Decompose v into two vectors v1 and v2 , where v1 is parallel to w and v2 is orthogonal to w.

139) v = 2i - 5j,

w = -3i - j 3 1 21 49 ij, v2 = ij A) v1 = 10 10 10 10 C) v1 =

3 1 13 39 ij, v2 = ij B) v1 = 10 10 10 10

1 1 5 44 i - j, v2 = i j 3 9 3 9

D) v1 =

3 1 17 49 ij, v = ij 10 10 2 10 10

Write the expression in the standard form a + bi. 4 5 5 + i sin 140) 3 cos 6 6 A) -

9 9 3 i + 2 2

B) -

140)

9 3 9 + i 2 2

C) -

9 3 9 - i 2 2

D) -

9 9 3 i 2 2

The letters r and represent polar coordinates. Write the equation using rectangular coordinates (x, y). 141) r(1 - 2 cos ) = 1 A) x2 + y2 = 1 + 2x B) x2 + y2 = 2 + x C) x2 + y2 = (2 + x)2

Find zw or

139)

141)

D) x2 + y2 = (1 + 2x)2

z as specified. Leave your answer in polar form. w

142) z = 8 cos w = 3 cos

6 2

Find zw.

A) 12 cos C) 12 cos

+ i sin + i sin

142)

6 2

2 2 + i sin 3 3

B) 24 cos

+ i sin

D) 24 cos

+ i sin

2 2 + i sin 3 3

Test the equation for symmetry with respect to the given axis, line, or pole. 143) r = 4 + 4 cos ; the line

143)

A) May or may not be symmetric with respect to the line B) Symmetric with respect to the line

The polar coordinates of a point are given. Find the rectangular coordinates of the point. 144) (4, 70°) Round the rectangular coordinates to two decimal places. A) (4.01, 1.59) B) (3.76, 1.37) C) (1.59, 4.01) D) (1.37, 3.76) Graph the polar equation. 45

144)

145) r =

2 1 - sin

145)

Solve the problem. 146) Find a vector v whose magnitude is 14 and whose component in the i direction is four times the component in the j direction. 21 7 21 7 10 i + 10 j or v= 10 i 10 j A) v = 5 5 5 5 B) v =

7 5

10 i -

21 5

10 j

v=-

7 5

10 i +

21 5

10 j

C) v =

7 5

10 i +

21 5

10 j

v=-

7 5

10 i -

21 5

10 j

D) v =

21 5

10 i +

7 5

10 j

v=-

21 5

10 i -

7 5

10 j

146)

The vector v has initial position P and terminal point Q. Write v in the form ai + bj; that is, find its position vector. 147) P = (-3, -1); Q = (5, 2) 147) A) v = 5i + 6j B) v = 6i + 5j C) v = 3i + 8j D) v = 8i + 3j Test the equation for symmetry with respect to the given axis, line, or pole. 148) r = 3 sin(3 ); the line

148)

A) May or may not be symmetric with respect to the line B) Symmetric with respect to the line

Write the complex number in rectangular form. 149) 3 cos A)

+ i sin

149)

3 3 3 i + 2 2

3+i

Solve the problem. 150) If v = 3i - 5j and w = -7i + 4j, find 3v - 4w. A) 17i - 10j B) 37i - 31j Find zw or

3 3 i + 6 6

C) -4i - j

3 3 3 i + 2 2

D) -19i + j

150)

z as specified. Leave your answer in polar form. w

151) z = 5(cos 200° + i sin 200°) w = 4(cos 50° + i sin 50°) z Find . w

151)

4 (cos 40° + i sin 40°) 5

5 (cos 40° + i sin 40°) 4

5 (cos 150° + i sin 150°) 4

4 (cos 150° + i sin 150°) 5

Graph the polar equation.

152) r =

2 1 - cos

152)

Write the complex number in polar form. Express the argument in degrees, rounded to the nearest tenth, if necessary. 153) 5i 153) A) 5(cos 270° + i sin 270°) B) 5(cos 180° + i sin 180°) C) 5(cos 0° + i sin 0°) D) 5(cos 90° + i sin 90°) Graph the polar equation.

154) r = csc

- 4, 0 <

154)

The letters x and y represent rectangular coordinates. Write the equation using polar coordinates (r, ). 155) 2x + 3y = 6 A) 2 sin + 3 cos = 6r B) r(2 cos + 3 sin ) = 6 C) 2 cos + 3 sin = 6r D) r(2 sin + 3 cos ) = 6

155)

Find zw or

z as specified. Leave your answer in polar form. w

156) z = 6 cos

3 3 + i sin 2 2

w = 12 cos Find

156)

5 5 + i sin 6 6

z . w

1 cos + i sin 6 3 3

1 cos + i sin 2 3 3

1 2 2 cos + i sin 6 3 3

1 2 2 cos + i sin 2 3 3

Decompose v into two vectors v1 and v2 , where v1 is parallel to w and v2 is orthogonal to w.

157) v = i + 5j,

w = 3i + j 12 4 7 21 i + j, v2 = - i + j A) v1 = 5 5 5 5 C) v1 =

12 4 1 21 i + j, v2 = i + j B) v1 = 5 5 5 5

12 4 8 26 i + j, v2 = i + j 5 5 5 5

D) v1 =

157)

8 8 5 37 i + j, v2 = - i + j 3 9 3 9

The polar coordinates of a point are given. Find the rectangular coordinates of the point. 158) (-3, -135°) -3 2 -3 2 -3 2 3 2 3 2 3 2 3 2 -3 2 , , , , A) B) C) D) 2 2 2 2 2 2 2 2

158)

Transform the polar equation to an equation in rectangular coordinates. Then identify and graph the equation. 159) r = 6 159)

x2 + y - 3 2 = 9; circle, radius 3, center at 0, 3 in rectangular coordinates

x = 6; vertical line 6 units to the right of the pole

x2 + y2 = 36; circle, radius 6, center at pole

x - 3 2 + y2 = 9; circle, radius 3, center at 3, 0 in rectangular coordinates

Solve the problem. 160) If u = 3i - 2j and v = -8i + 7j, find u - v. A) 10i + 5j B) -5i + 5j

C) 11i - 9j

160)

D) 9i + 5j

The rectangular coordinates of a point are given. Find polar coordinates for the point. 161) (4, -4) A) 4 2,

Solve the problem. 162) If w = 8i + 2j, find 4w. A) 32i + 2j

B) -4 2, -

C) 4 2, -

B) 32i + 8j

C) 12i + 2j

Plot the point given in polar coordinates.

161) D) -4 2,

D) 12i + 6j

162)

163) -3, -

163)

Solve the problem. Round your answer to the nearest tenth. 164) A person is pulling a freight cart with a force of 59 pounds. How much work is done in moving the cart 60 feet if the cart's handle makes an angle of 31° with the ground? A) 3,181.7 ft-lb B) 1,823.2 ft-lb C) 182.3 ft-lb D) 3,034.4 ft-lb

164)

Transform the polar equation to an equation in rectangular coordinates. Then identify and graph the equation. 165) r sin = 3 165)

y = -3; horizontal line 3 units below the pole

x = 3; vertical line 3 units to the right of the pole

y = 3; horizontal line 3 units above the pole

x = -3; vertical line 3 units to the left of the pole

Plot the point given in polar coordinates.

166) -2,

9 4

166)

State whether the vectors are parallel, orthogonal, or neither. 167) v = 4i - 2j, w = 4i + 2j A) Orthogonal B) Parallel Identify and graph the polar equation.

C) Neither

167)

168) r2 = 2 sin(2 )

168)

rose with four petals

lemniscate

rose with four petals

Find zw or

z as specified. Leave your answer in polar form. w

169) z = 10(cos 45° + i sin 45°) w = 5(cos 15° + i sin 15°) z Find . w

169)

1 (cos 30° + i sin 30°) 2

B) 2(cos 45° + i sin 45°)

1 (cos 45° + i sin 45°) 2

D) 2(cos 30° + i sin 30°)

Match the point in polar coordinates with either A, B, C, or D on the graph. 170) -3,

170)

A) A

B) B

C) C

D) D

Plot the complex number in the complex plane. 171) 2 + i

171)

The polar coordinates of a point are given. Find the rectangular coordinates of the point. 3 172) 9, 4 A)

-9 2 9 2 , 2 2

-9 2 -9 2 , 2 2

9 2 -9 2 , 2 2

172) D)

9 2 9 2 , 2 2

Find all the complex roots. Leave your answers in polar form with the argument in degrees. 173) The complex fourth roots of -16 4 4 4 4 A) 2(cos 45° + i sin 45°), 2(cos 135° + i sin 135°), 2(cos 225° + i sin 225°), 2(cos 315° + i sin 315°) B) 2(cos 45° + i sin 45°), 2(cos 135° + i sin 135°), 2(cos 225° + i sin 225°), 2(cos 315° + i sin 315°) C) 2(cos 90° + i sin 90°), 2(cos 180° + i sin 180°), 2(cos 270° + i sin 270°), 2(cos 360° + i sin 360°) D) 16(cos 45° + i sin 45°), 16(cos 135° + i sin 135°), 16(cos 225° + i sin 225°), 16(cos 315° + i sin 315°)

Test the equation for symmetry with respect to the given axis, line, or pole. 174) r = 6 + 2 cos ; the pole A) Symmetric with respect to the pole B) May or may not be symmetric with respect to the pole The letters r and 175) r = 5

174)

represent polar coordinates. Write the equation using rectangular coordinates (x, y). B) x2 - y2 = 25

A) x + y = 25

C) x + y = 5

D) x2 + y2 = 25

Solve the problem. 176) A tightrope walker located at a certain point deflects the rope as indicated in the figure. If the weight of the tightrope walker is 115 pounds, how much tension is in each part of the rope? Round your answers to the nearest tenth. 4.7°

173)

175)

176)

3.9°

115 pounds

A) tension in the left part: 647.9 lb; tension in the right part: 721.5 lb C) tension in the left part: -84.9 lb; tension in the right part: -94.6 lb

B) tension in the left part: -88.4 lb; tension in the right part: 108.2 lb D) tension in the left part: 300.6 lb; tension in the right part: -367.9 lb

The letters x and y represent rectangular coordinates. Write the equation using polar coordinates (r, ). 177) xy = 1 A) 2r2 sin cos = 1 B) r sin 2 = 2 C) 2r sin

cos

177)

D) r2 sin 2 = 2

State whether the vectors are parallel, orthogonal, or neither. 178) v = 3i + 2j, w = 6i + 4j A) Orthogonal B) Parallel

C) Neither

178)

Find zw or

z as specified. Leave your answer in polar form. w

179) z = 6 cos

3 3 + i sin 2 2

w = 12 cos

179)

5 5 + i sin 6 6

Find zw.

A) 36 cos C) 36 cos

6 3

+ i sin + i sin

B) 72 cos

D) 72 cos

6 3

+ i sin + i sin

6 3

Write the expression in the standard form a + bi. 3 3 4 + i sin 180) 2 cos 4 4 A) 4 Find zw or

180)

B) -4i

C) -4

D) 4i

z as specified. Leave your answer in polar form. w

181) z = 1 - i w = 1 - 3i z Find . w

181)

2 (cos 15° + i sin 15°) 2

1 (cos 15° + i sin 15°) 2

1 (cos 75° + i sin 75°) 2

2 (cos 75° + i sin 75°) 2

The rectangular coordinates of a point are given. Find polar coordinates for the point. 182) (-2, 2.5) Round the polar coordinates to two decimal places, with in radians. A) (3.2, -0.67) B) (3.2, 0.67) C) (3.2, 2.25) D) (-3.2, 0.67) Plot the point given in polar coordinates. 183) (2, 360°)

182)

183)

Write the expression in the standard form a + bi. 184) ( 3 + i)5 A) 9 3 + 5i

184)

B) 16 - 16 3i

C) -16 3 + 16i

Graph the polar equation. 4 185) r = 4 - 2 sin

D) 16 3 - 16i

185)

Solve the problem. 186) A woman walks 100 yards eastward along a straight shoreline and then swims 30 yards southward into the ocean on a line that is perpendicular to the shoreline. Using her starting point as the pole and the east direction as the polar axis, give her current position in polar coordinates. Round the coordinates to the nearest hundredth. Express in degrees. A) (104.40, -88.28°) B) (11.40, -16.70°) C) (104.40, -16.70°) D) (11.40, -88.28°) The polar coordinates of a point are given. Find the rectangular coordinates of the point. 187) (2, -360°) A) (0, -2) B) (0, 2) C) (-2, 0) D) (2, 0) Plot the point given in polar coordinates.

186)

187)

188) 2,

-3 4

188)

Solve the problem. 189) At a state fair truck pull, two pickup trucks are attached to the back end of a monster truck as illustrated in the figure. One of the pickups pulls with a force of 1,200 pounds and the other pulls with a force of 3,200 pounds with an angle of 45° between them. With how much force must the monster truck pull in order to remain unmoved? HINT: Find the resultant force of the two trucks. Round your answer to the nearest tenth.

189)

1,200 lb 45°

3,200 lb

A) The truck must pull with a force of 3,958.6 lb. B) The truck must pull with a force of 2,193.0 lb. C) The truck must pull with a force of 2,499.9 lb. D) The truck must pull with a force of 4,136.5 lb. Match the point in polar coordinates with either A, B, C, or D on the graph. 190) 3,

190)

A) A

B) B

C) C

D) D

The polar coordinates of a point are given. Find the rectangular coordinates of the point. 3 191) -3, 4 A)

-3 2 3 2 , 2 2

3 2 3 2 , 2 2

3 2 -3 2 , 2 2

191) D)

-3 2 -3 2 , 2 2

Write the complex number in rectangular form. 192) 8 cos A)

+ i sin

1 3 i + 4 4

192)

B) 4 + 4 3i

3 1 + i 4 4

D) 4 3 + 4i

Match the point in polar coordinates with either A, B, C, or D on the graph. 193) 3, -

A) A Find zw or

193)

B) B

C) C

D) D

z as specified. Leave your answer in polar form. w

194) z = 10(cos 30° + i sin 30°) w = 5(cos 10° + i sin 10°) Find zw. A) 15(cos 300° + i sin 300°) C) 50(cos 300° + i sin 300°)

194)

B) 50(cos 40° + i sin 40°) D) 15(cos 40° + i sin 40°)

Plot the point given in polar coordinates. -3 195) -2, 4

195)

Solve the problem. 196) A fire truck is en route to an address that is 6 blocks east and 11 blocks south of the fire station. Using the fire station as the pole and the east direction as the polar axis, express the fire truck's destination in polar coordinates. Round the coordinates to the nearest hundredth. Express in degrees. A) (4.12, -61.39°) B) (12.53, -61.39°) C) (4.12, -28.61°) D) (12.53, -28.61°) Find zw or

196)

z as specified. Leave your answer in polar form. w

197) z = 1 + i w = 1 - 3i z Find . w

197)

2 (cos 15° + i sin 15°) 2

2 (cos 105° + i sin 105°) 2

1 (cos 105° + i sin 105°) 2

1 (cos 15° + i sin 15°) 2

Identify and graph the polar equation.

198) r = 4 sin(2 )

198)

rose with four petals

rose with two petals

lemniscate

Write the expression in the standard form a + bi. 199) (1 + i)20 A) -1024i

circle

B) 1024i

C) 1024

D) -1024

199)

Solve the problem. 200) Two forces of magnitude 25 pounds and 40 pounds act on an object. The force of 40 lb acts along the positive x-axis, and the force of 25 lb acts at an angle of 80° with the positive x-axis. Find the direction and magnitude of the resultant force. Round the direction and magnitude to the nearest whole number. A) Direction: 4°; magnitude: 65 lb B) Direction: 51°; magnitude: 51 lb C) Direction: 29°; magnitude: 51 lb D) Direction: 40°; magnitude: 47 lb Write the complex number in rectangular form. 201) 6(cos 330° + i sin 330°) A) 3 3 + 3i B) -3 3 + 3i

200)

201) C) -3 3 - 3i

D) 3 3 - 3i

Test the equation for symmetry with respect to the given axis, line, or pole. 202) r = 6 + 2 sin ; the line

202)

A) Symmetric with respect to the line

B) May or may not be symmetric with respect to the line

The polar coordinates of a point are given. Find the rectangular coordinates of the point. 2 203) 3, 3 A)

3 3 3 , 2 2

B) -

3 -3 3 , 2 2

Find the quantity if v = 5i - 7j and w = 3i + 2j. 204) v - w A) 2 6 - 13 B) 85

203)

C) -

3 3 3 , 2 2

3 -3 3 , 2 2

74 -

204)

Use the vectors in the figure below to graph the following vector.

205) v - w

205)

Match the point in polar coordinates with either A, B, C, or D on the graph. 206) -3, -

206)

A) A

B) B

C) C

D) D

Write the expression in the standard form a + bi. 1 3 10 i 207) - 2 2 A) -

1 3 i 2 2

207)

1 3 i + 2 2

C) -

1 3 i + 2 2

1 3 i 2 2

Transform the polar equation to an equation in rectangular coordinates. Then identify and graph the equation. 208) r = 2 sin 208)

x2 + (y - 1)2 = 1; circle, radius 1, center at (0, 1) in rectangular coordinates

x2 + (y + 1)2 = 1; circle, radius 1, center at (0, -1) in rectangular coordinates

(x - 1)2 + y2 = 1; circle, radius 1, center at (1, 0) in rectangular coordinates

(x + 1)2 + y2 = 1; circle, radius 1, center at (-1, 0) in rectangular coordinates

Find the unit vector having the same direction as v. 209) v = -3i + j 10 i + 10j A) u = 3 C) u = -3 10i +

209) 3 10 10 ij B) u = 10 10

10j

D) u = -

3 10 10 i+ j 10 10

Transform the polar equation to an equation in rectangular coordinates. Then identify and graph the equation. 210)

210)

3x; line through the pole making

an angle of

y=-

with the polar axis

3 x; line through the pole making 3

an angle of

with the polar axis

y=-

; horizontal line

units

below the pole

2 3

center at

+ y2 = 3

2 9

; circle, radius

, 0 in rectangular coordinates

Match the point in polar coordinates with either A, B, C, or D on the graph. 5 211) 3, 3

A) A

B) B

C) C

211)

D) D

Use the vectors in the figure below to graph the following vector.

212) 3w

212)

The letters r and represent polar coordinates. Write the equation using rectangular coordinates (x, y). 213) r = 2(sin - cos ) A) x2 + y2 = 2x - 2y B) 2x2 + 2y2 = y - x C) x2 + y2 = 2y - 2x

D) 2x2 + 2y2 = x - y

213)

Graph the polar equation. 214) r = 1 + cos

214)

Find the dot product v · w. 215) v = i + 2j, w = 6i - j A) 4

B) -4

C) 8

D) 0

215)

Match the point in polar coordinates with either A, B, C, or D on the graph. 216) -3,

216)

A) A

B) B

C) C

D) D

Solve the problem. Round your answer to the nearest tenth. 217) Find the work done by a force of 200 pounds acting in the direction -i + 2j in moving an object 75 feet from (0, 0) to (-75, 0). A) 8944.9 ft-lb B) 13,416.1 ft-lb C) 15,000.0 ft-lb D) 6708.2 ft-lb Graph the polar equation. 3 218) r =

217)

218)

Write the expression in the standard form a + bi. 219) (- 3 + i)6 A) -64 3 + 64i

219)

B) 64 - 64 3i

C) 64i

D) -64

Write the vector v in the form ai + bj, given its magnitude v and the angle 220) v = 3, = 180° A) v = -3i - 3j B) v = -3j C) v = -3i

it makes with the positive x-axis. 220) D) v = 3j

The letters x and y represent rectangular coordinates. Write the equation using polar coordinates (r, ). 221) x = -3 A) r sin = 3 B) r sin = -3 C) r cos = 3 D) r cos = -3

221)

Test the equation for symmetry with respect to the given axis, line, or pole. 222) r = -4 cos ; the line

222)

A) May or may not be symmetric with respect to the line B) Symmetric with respect to the line

Solve the problem. 223) An audio speaker that weighs 50 pounds hangs from the ceiling of a restaurant from two cables as shown 223) in the figure. To two decimal places, what is the tension in the two cables?

A) Tension in right cable: 35.90 lb; tension in left cable: 41.59 lb B) Tension in right cable: 41.59 lb; tension in left cable: 35.90 lb C) Tension in right cable: 14.10 lb; tension in left cable: 41.59 lb D) Tension in right cable: 35.90 lb; tension in left cable: 14.10 lb The polar coordinates of a point are given. Find the rectangular coordinates of the point. 224) (400, 130°) Round the rectangular coordinates to two decimal places. A) (-257.12, 306.42) B) (306.42, 257.12) C) (-257.12, -306.42) D) (306.42, -257.12)

224)

Use the vectors in the figure below to graph the following vector.

225) 2u - z - w

225)

The vector v has initial position P and terminal point Q. Write v in the form ai + bj; that is, find its position vector. 226) P = (2, 2); Q = (-6, -4) 226) A) v = 8i + 6j B) v = -8i - 6j C) v = -6i - 8j D) v = 6i + 8j

Answer Key Testname: CHAPTER 10 1) A 2) B 3) D 4) D 5) B 6) C 7) B 8) B 9) B 10) D 11) D 12) B 13) B 14) D 15) Direction: -23.65°; magnitude: 57.04 N 16)

4, -

11 6

(b) -4,

7 6

(a)

(c)

13 6

17) 36.86i + 25.81j

Answer Key Testname: CHAPTER 10 18)

4, -

7 6

(b) -4,

11 6

(a)

(c)

17 6

19) Direction: 89.40°; magnitude: 92.20 N 20) C 21) A 22) B 23) D 24) A 25) B 26) C 27) D 28) B 29) D 30) B 31) A 32) B 33) A 34) C 35) B 36) C 37) C 38) A 39) C 40) C 41) D 42) C 43) B 44) C 45) A 46) B 80

Answer Key Testname: CHAPTER 10 47) B 48) A 49) D 50) B 51) C 52) D 53) C 54) D 55) B 56) C 57) B 58) B 59) D 60) A 61) A 62) D 63) C 64) A 65) D 66) B 67) C 68) B 69) B 70) C 71) C 72) A 73) C 74) D 75) A 76) B 77) A 78) A 79) D 80) C 81) D 82) C 83) B 84) A 85) B 86) D 87) C 88) B 89) D 90) D 91) C 92) A 93) D 94) B 95) B 96) A 81

Answer Key Testname: CHAPTER 10 97) A 98) D 99) A 100) C 101) B 102) D 103) C 104) B 105) D 106) C 107) C 108) D 109) D 110) D 111) C 112) D 113) C 114) B 115) C 116) D 117) B 118) A 119) D 120) D 121) B 122) B 123) C 124) C 125) D 126) B 127) D 128) B 129) C 130) A 131) B 132) B 133) B 134) A 135) D 136) C 137) A 138) C 139) D 140) D 141) D 142) D 143) A 144) D 145) C 146) D 82

Answer Key Testname: CHAPTER 10 147) D 148) B 149) A 150) B 151) C 152) D 153) D 154) A 155) B 156) D 157) A 158) A 159) C 160) C 161) C 162) B 163) D 164) D 165) C 166) A 167) C 168) C 169) D 170) A 171) D 172) A 173) B 174) B 175) D 176) C 177) D 178) B 179) D 180) C 181) A 182) C 183) D 184) C 185) D 186) C 187) D 188) C 189) D 190) A 191) C 192) D 193) D 194) B 195) C 196) B 83

Answer Key Testname: CHAPTER 10 197) B 198) A 199) D 200) C 201) D 202) A 203) C 204) B 205) D 206) A 207) A 208) B 209) D 210) A 211) B 212) A 213) C 214) C 215) A 216) B 217) D 218) C 219) D 220) C 221) D 222) A 223) A 224) A 225) A 226) B

Chapter 11 Exam Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Match the equation to the graph. 1) (x + 1)2 = 5(y - 2) A)

x2 y2 =1 16 4

Match the equation to its graph. 3) y2 = -10x A)

Match the graph to its equation. 4)

A) -

y2 x2 + =1 25 49

x2 y2 + =1 25 49

y2 x2 =1 25 49

Match the equation to its graph. 5) x2 = 7y A)

Match the equation to the graph. y2 x2 =1 6) 16 4

Match the equation to its graph. 7) y2 = 15x A)

8) x2 = -6y A)

Match the equation to the graph. 9) (y + 2)2 = 8(x + 1) A)

10) (y + 2)2 = -7(x + 2) A)

10)

Match the graph to its equation. 11)

y2 x2 + =1 9 16

11)

x2 y2 =1 16 9

y2 x2 =1 9 16

x2 y2 + =1 9 16

Match the equation to the graph. 12) (x + 1)2 = -6(y + 1) A)

12)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 13) A race track is in the shape of an ellipse 80 feet long and 60 feet wide. What is the width 32 feet from the center? 14) A hall 130 feet in length was designed as a whispering gallery. If the ceiling is 25 feet high at the center, how far from the center are the foci located? The parametric equations of four curves are given. Graph each of them, indicating the orientation. 3 t 15) C1 : x = 7sin t, y = 7 - 7cos2 t; 2 2

13)

14)

15)

C2 : x = ln t, y = ln t2 ; e-4 t e3 C3 : x = t2 - 8, y = t - 3; -4 t 4 C4 : x = t - 5, y = t + 2; -4 t 7

Solve the problem. 16) A satellite dish is shaped like a paraboloid of revolution. The signals that emanate from a satellite strike the surface of the dish and are reflected to a single point, where the receiver is located. If the dish is 8 feet across at its opening and is 2 feet deep at its center, at what position should the receiver be placed?

16)

17) A sealed-beam headlight is in the shape of a paraboloid of revolution. The bulb, which is placed at the focus, is 3 centimeters from the vertex. If the depth is to be 6 centimeters, what is the diameter of the headlight at its opening?

17)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Name the conic. 18)

A) parabola

18)

B) ellipse

C) hyperbola

D) circle

Graph the hyperbola. 19) 36y2 - 4x2 = 144

19)

Find an equation of the parabola described. 20) Focus at (13, 0); directrix the line x = -13 A) x2 = 52y B) y2 = 52x

C) y2 = -52x

D) y2 = 13x

20)

Write an equation for the parabola. 21)

A) y2 = -12x

21)

B) y2 = 12x

C) x2 = 12y

D) x2 = -12y

Find parametric equations for the rectangular equation. 22) y = 3x2 + 6

22)

A) y = t; x = 3t2 + 6; 0 t < C) x = t; y = 3t2 + 6; 0 t <

B) x =

t; y = 3t + 6; t 0

D) x = t2 ; y = 3t + 6; 0 t <

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola. x2 y2 =1 23) 36 144 A) center at (0, 0) transverse axis is x-axis vertices at (-6, 0) and (6, 0) foci at (-12, 0) and (12, 0) asymptotes of y = - 2x and y = 2x C) center at (0, 0) transverse axis is x-axis vertices at (-12, 0) and (12, 0) foci at (- 3 20, 0) and (3 20, 0) asymptotes of y = - 2x and y = 2x

B) center at (0, 0) transverse axis is y-axis vertices at (0, -6) and (0, 6) foci at (- 3 20, 0) and (3 20, 0) asymptotes of y = - 2x and y = 2x D) center at (0, 0) transverse axis is x-axis vertices at (-6, 0) and (6, 0) foci at (- 3 20, 0) and (3 20, 0) asymptotes of y = - 2x and y = 2x

Identify the equation without completing the square. 24) y2 - 3x2 + 8x + 3y + 4 = 0 A) parabola

23)

B) ellipse

C) hyperbola

Solve the problem.

D) not a conic

24)

25) Rachel's bus leaves at 2:25 PM and accelerates at the rate of 3 meters per second per second. Rachel, 25) who can run 8 meters per second, arrives at the bus station 5 seconds after the bus has left. Find parametric equations that describe the motions of the bus and Rachel as a function of time, and simulate the motion of the bus and Rachel by simultaneously graphing these equations.

A) Bus: x1 =

3 2 t , y1 = 1; 2

B) Bus: x1 = 3t2 , y1 = 1;

Rachel: x2 = 8(t - 5), y2 = 3

C) Bus: x1 =

3 2 t , y1 = 1; 2

D) Bus: x1 = 3t2 , y1 = 1;

Rachel: x2 = 4(t - 5), y2 = 3

Rachel: x2 = 8(t + 5), y2 = 3

Graph the equation. 26) 9(x - 1)2 + 4(y - 2)2 = 36

26)

Find a rectangular equation for the plane curve defined by the parametric equations. 27) x = t3 + 1, y = t3 - 20; -2 t 2

B) y = x3; for x in -3 x 1 D) y = - x2 ; for x in -4 x 4

A) y = - x - 21; for x in -7 x 9 C) y = x - 21; for x in -7 x 9

Solve the problem. 28) A reflecting telescope contains a mirror shaped like a paraboloid of revolution. If the mirror is 16 inches across at its opening and is 3 feet deep, where will the light be concentrated? A) 0.6 in. from the vertex B) 5.3 in. from the vertex C) 0.4 in. from the vertex D) 0.3 in. from the vertex

27)

28)

Graph the hyperbola. (x + 1)2 (y + 1)2 =1 29) 4 9

29)

30) (y - 1)2 - 9(x + 4)2 = 9

30)

Write an equation for the graph. 31)

31)

(x - 1)2 (y - 2)2 + =1 16 9

(x - 2)2 (y - 1)2 + =1 9 16

(x + 2)2 (y + 1)2 + =1 16 9

(x - 2)2 (y - 1)2 + =1 16 9

Solve the problem. 32) An experimental model for a suspension bridge is built in the shape of a parabolic arch. In one section, cable runs from the top of one tower down to the roadway, just touching it there, and up again to the top of a second tower. The towers are both 6.25 inches tall and stand 50 inches apart. At some point along the road from the lowest point of the cable, the cable is 1 inches above the roadway. Find the distance between that point and the base of the nearest tower. A) 15.2 in. B) 9.8 in. C) 10.2 in. D) 15 in. Identify the equation without applying a rotation of axes. 33) 2x2 + 10xy + 25y2 + 3x - 4y + 7 = 0 A) parabola

B) hyperbola

C) ellipse

Find an equation for the parabola described. 34) Vertex at (2, 7); focus at (2, 4) A) (x - 2)2 = -12(y - 7)

D) not a conic

B) (y - 7)2 = -8(x - 2) D) (y - 7)2 = 8(x - 2)

C) (x - 2)2 = 12(y - 7)

Find the center, foci, and vertices of the ellipse. 35) 36x2 + 4y2 = 144 A) center at (0, 0) foci at (- 4 2, 0) and (4 2, 0) vertices at (-6, 0), (6, 0) C) center at (0, 0) foci at (0, - 4 2) and (0, 4 2) vertices at (0, -6), (0, 6)

B) center at (0, 0) foci at (0, -6) and (0, 6) vertices at (0, -36), (0, 36) D) center at (0, 0) foci at (0, 6) and (2, 0) vertices at (0, 36) and (4, 0)

32)

33)

34)

35)

Find an equation for the ellipse described. 36) Center at (0, 0); focus at (0, -2); vertex at (0, 8) x2 y2 x2 y2 + =1 + =1 A) B) 64 60 4 60

y2 + =1 C) 4 64

Find a rectangular equation for the plane curve defined by the parametric equations. 37) x = 5 cos t, y = -2 sin t; 0 t 2 1 1 x A) 4x2 - 25y2 = 1; x B) 4x2 + 25y2 = 1; 2 5 C) 4x2 + 25y2 = 100; -5 x 5

y2 + =1 D) 60 64

1 5

36)

37)

D) 4x2 - 25y2 = 100; x 5

Find the vertex, focus, and directrix of the parabola. Graph the equation. 38) y2 = 8x

A) vertex: (0, 0) focus: (-2, 0) directrix: x = 2

B) vertex: (0, 0) focus: (0, 2) directrix: y = -2

38)

C) vertex: (0, 0) focus: (0, 2) directrix: y = -2

D) vertex: (0, 0) focus: (2, 0) directrix: x = -2

Graph the equation. 39) x2 = 6y

39)

Graph the curve whose parametric equations are given. 40) x = 3t, y = t + 4; -2 t 3

40)

Find an equation for the hyperbola described. Graph the equation.

41) Center at (0, 0); vertex at (0, 6); focus at (0, 2 10)

41)

x2 y2 =1 4 36

y2 x2 =1 36 4

x2 y2 =1 36 4

y2 x2 =1 4 36

Find a polar equation for the conic. A focus is at the pole. 42) e = 2; directrix is perpendicular to the polar axis 4 to the right of the pole 8 8 8 A) r = B) r = C) r = 1 - 2 sin 1 + 2 cos 1 + 2 sin

8 D) r = 1 - 2 cos

Solve the problem. 43) A spotlight has a parabolic cross section that is 6 ft wide at the opening and 2.5 ft deep at the vertex. How far from the vertex is the focus? Round answer to two decimal places. A) 0.21 ft B) 0.90 ft C) 0.26 ft D) 0.52 ft 22

42)

43)

Graph the equation. 44) (y + 1)2 = -6(x + 1)

44)

Discuss the equation and graph it. 2 45) r = 2 - 2 cos

45)

A) directrix perpendicular to polar axis 1 right of pole 1 focus (0, 0), vertex , 0 2

B) directrix parallel to polar axis 1 below pole 1 3 focus (0, 0), vertex , 2 2

C) directrix perpendicular to polar axis 1 left of pole 1 focus (0, 0), vertex , 2

D) directrix parallel to polar axis 1 above pole 1 focus (0, 0), vertex , 2 2

Identify the equation without applying a rotation of axes. 46) 8x2 - 9xy + 4y2 - 2x - 4y + 3 = 0 A) hyperbola

B) parabola

C) ellipse

D) not a conic

Solve the problem. 47) A bridge is built in the shape of a semielliptical arch. It has a span of 92 feet. The height of the arch 25 feet from the center is to be 8 feet. Find the height of the arch at its center. A) 14.72 ft B) 8.31 ft C) 25.39 ft D) 9.53 ft Find the vertex, focus, and directrix of the parabola with the given equation. 48) (x + 2)2 = 20(y + 4) A) vertex: (-2, -4) focus: (-2, -9) directrix: x = 1 C) vertex: (-4, -2) focus: (-4, 3) directrix: y = -7

B) vertex: (2, 4) focus: (2, 9) directrix: y = -1 D) vertex: (-2, -4) focus: (-2, 1) directrix: y = -9

46)

47)

48)

Find an equation of the parabola described. 49) Directrix the line y = 3; vertex at (0, 0) A) x = 3y2

1 2 y B) x = 12

C) y = -12x2

Rotate the axes so that the new equation contains no xy-term. Graph the new equation. 50) x2 + 2xy + y2 - 8x + 8y = 0

1 2 x D) y = 12

49)

50)

51) 5x2 - 6xy + 5y2 - 8 = 0

51)

Graph the hyperbola. (y + 1)2 (x - 2)2 =1 52) 4 16

52)

Solve the problem. 53) A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 162 feet and a maximum height of 30 feet. Find the height of the arch at 25 feet from its center. A) 0.7 ft B) 11.4 ft C) 56.3 ft D) 27.1 ft

53)

Graph the ellipse and locate the foci. x2 y2 + =1 54) 16 9

54)

A) foci at (4, 0) and (-4, 0)

B) foci at ( 7, 0) and (- 7, 0)

C) foci at ( 25, 0) and (- 25, 0)

D) foci at (0,

7) and (0, - 7)

Use a graphing utility to graph the curve defined by the given parametric equations. 55) x = 3 cos t, y = 2 sin t; 0 t 2

Identify the equation without applying a rotation of axes. 56) 4x2 - 3xy + 2y2 - 2x + 4y + 1 = 0 A) hyperbola

B) parabola

C) ellipse

55)

D) not a conic

56)

Rotate the axes so that the new equation contains no xy-term. Graph the new equation. 57) 31x2 + 10 3xy + 21y2 -144 = 0

57)

Graph the curve whose parametric equations are given. 58) x = -sec t, y = tan t; -

<t<

58)

Find an equation for the ellipse described. 59) Foci at (±2, 0); x-intercepts are ±7 x2 y2 x2 y2 + =1 + =1 A) B) 4 49 45 49

x2 y2 + =1 C) 49 45

x2 y2 + =1 D) 4 45

Solve the problem. 60) An arch for a bridge over a highway is in the form of a semiellipse. The top of the arch is 35 feet above ground (the major axis). What should the span of the bridge be (the length of its minor axis) if the height 31 feet from the center is to be 15 feet above ground? A) 68.62 ft B) 64.62 ft C) 144.67 ft D) 34.31 ft

59)

60)

Name the conic. 61)

A) parabola

61)

B) ellipse

C) circle

Find an equation for the ellipse described. 62) Focus at (0, -3); vertices at (0, ±4) x2 y2 x2 y2 + =1 + =1 A) B) 16 7 7 16

y2 + =1 C) 9 16

D) hyperbola

y2 + =1 D) 9 7

62)

Graph the equation. 63) (x + 1)2 = 7(y - 1)

63)

Graph the curve whose parametric equations are given.

64) x = 3 cos t, y = - 3 sin t;

3 2

64)

Solve the problem. 65) A satellite following the hyperbolic path shown in the picture turns rapidly at (0, 6) and then 65) 12 moves closer and closer to the line y = x as it gets farther from the tracking station at the origin. Find 5 the equation that describes the path of the rocket if the center of the hyperbola is at (0, 0).

(0, 6)

12 x 5

x2 y2 =1 36 24 2 5

y2 x2 =1 36 25 4

Find an equation for the hyperbola described. 66) Vertices at (0, ±6); asymptotes at y = ± A)

y2 x2 =1 36 25

y2 x2 =1 25 36 4

x2 y2 =1 24 2 36 5

3 x 5

66)

y2 x2 =1 100 36

y2 x2 =1 36 100

y2 x2 =1 25 9

Graph the hyperbola. 67) (x + 2)2 - 4(y + 1)2 = 4

67)

Solve the problem. 68) The position of a projectile fired with an initial velocity v0 feet per second and at an angle

to the

horizontal at the end of t seconds is given by the parametric equations x = (v0 cos )t,

y = (v0 sin )t - 16t2 . Suppose the initial velocity is 8 feet per second. Obtain the rectangular equation of the trajectory and identify the curve. 1 x2 + (tan )x; ellipse A) y = 4 cos2

C) y = -

1 x2 4 cos2

B) y = -

+ (tan )x; parabola

D) y =

1 x2 4 cos2

+ (cot )x; hyperbola + (cot )x; parabola

68)

Identify the equation without completing the square. 69) 3x2 + 4y2 + 4x + 3y = 0 A) parabola

B) hyperbola

C) ellipse

D) not a conic

70) 4x2 - 3x + y - 1 = 0 A) ellipse

B) parabola

C) hyperbola

D) not a conic

Find a polar equation for the conic. A focus is at the pole. 71) e = 1; directrix is parallel to the polar axis 1 above the pole 1 1 1 A) r = B) r = C) r = 1 - sin 1 + cos 1 + sin

1 D) r = 1 - cos

Identify the conic that the polar equation represents. Also, give the position of the directrix. 2 72) r = 1 - 2 cos

69)

70)

71)

72)

A) ellipse, directrix perpendicular to the polar axis 1 right of the pole B) ellipse, directrix perpendicular to the polar axis 1 left of the pole C) hyperbola, directrix perpendicular to the polar axis 1 left of the pole D) hyperbola, directrix perpendicular to the polar axis 1 right of the pole Find the vertex, focus, and directrix of the parabola. Graph the equation. 73) x2 = 16y

A) vertex: (0, 0) focus: (-4, 0) directrix: x = 4

B) vertex: (0, 0) focus: (0, -4) directrix: y = 4

73)

C) vertex: (0, 0) focus: (4, 0) directrix: x = -4

D) vertex: (0, 0) focus: (0, 4) directrix: y = -4

Rotate the axes so that the new equation contains no xy-term. Discuss the new equation. 74) x2 + xy + y2 - 3y - 6 = 0 A)

= 45° 2 y' = -18x'

= 45°

2 2 2

x' -

parabola vertex at (0, 0) 9 focus at (- , 0) 2

y' +

3 2 2 2 15

74)

ellipse center at (

2 3 2 , ) 2 2

major axis is y'-axis 2 3 2 2 9 2 vertices at ( ,) and ( , ) 2 2 2 2

= 45° x'2 y'2 =1 6 8

= 45° x'2 y'2 + =1 3 4 ellipse center at (0, 0) major axis is y'-axis vertices at (0, ±2)

hyperbola center at (0, 0) transverse axis is the x'-axis vertices at (± 6, 0)

Solve the problem. 75) Car A (travelling north at 70 mph) and car B (traveling west at 50 mph) are heading toward the 75) same intersection. Car A is 6 miles from the intersection when car B is 7 miles from the intersection. . Find a formula for the distance between the cars as a function of time, using the parametric equations that describe the motion of cars A and B. Using a graphing utility, find the minimum distance between the cars. When are the cars closest?

7 mi

car B 50 mph

6 mi car A 70 mph

A) d = B) d = C) d = D) d =

(70t - 6)2 + (7 - 50t)2 ; 528.12 mi; 6.24 min (70t - 6)2 + (7 - 50t)2 ; 2.21 mi; 0.10 min (70t + 6)2 + (7 - 50t)2 ; 2.21 mi; 6.24 h (70t - 6)2 + (7 - 50t)2 ; 2.21 mi; 6.24 min

Graph the hyperbola. 76) 9y2 = 4x2 + 36

76)

Find an equation of the parabola described and state the two points that define the latus rectum. 77) Focus at (0, 4); directrix the line y = -4 A) y2 = 4x; latus rectum: (9, 2) and (-9, 2) B) x2 = 16y; latus rectum: (8, 4) and (-8, 4) C) x2 = 16y; latus rectum: (4, 8) and (-4, 8)

D) x2 = 4y; latus rectum: (2, 4) and (-2, 4)

77)

Write an equation for the parabola. 78)

A) y2 = 12x

78)

B) x2 = 12y

C) y2 = -12x

D) x2 = -12y

Find the center, foci, and vertices of the ellipse. (x + 2)2 (y - 2)2 + =1 79) 36 9

79)

A) center at (-2, 2) foci at (- 3 3, 2), (3 3, 2) vertices at (6, 2), (-6, 2) C) center at (-2, 2) foci at (-2 + 3 3, -2), (-2 - 3 3, -2) vertices at (6, 2), (-6, 2)

B) center at (-2, 2) foci at (-2 + 3 3, 2), (-2 - 3 3, 2) vertices at (-8, 2), (4, 2) D) center at (2, -2) foci at (2 + 3 3, -2), (2 - 3 3, -2) vertices at (-8, 2), (4, 2)

Solve the problem. 80) Two recording devices are set 3,600 feet apart, with the device at point A to the west of the device at point B. At a point on a line between the devices, 400 feet from point B, a small amount of explosive is detonated. The recording devices record the time the sound reaches each one. How far directly north of site B should a second explosion be done so that the measured time difference recorded by the devices is the same as that for the first detonation? A) 1,754.99 ft B) 914.29 ft C) 1,842.8 ft D) 4,963.87 ft

80)

Graph the equation. 81) 9(x + 2)2 + 16(y - 1)2 = 144

81)

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola. 82) (x - 4)2 - 25(y - 2)2 = 25 A) center at (4, 2) transverse axis is parallel to x-axis vertices at (-1, 2) and (9, 2) foci at (4 - 26, 2) and (4 + 26, 2) 1 1 asymptotes of y - 2 = - (x - 4) and y - 2 = (x - 4) 5 5

82)

B) center at (2, 4) transverse axis is parallel to x-axis vertices at (-3, 4) and (7, 4) foci at (2 - 26, 4) and (2 + 26, 4) 1 1 asymptotes of y - 4 = - (x - 2) and y - 4 = (x - 2) 5 5 C) center at (4, 2) transverse axis is parallel to x-axis vertices at (3, 2) and (5, 2) foci at (4 - 26, 2) and (4 + 26, 2) asymptotes of y - 2 = - 5(x - 4) and y - 2 = 5(x - 4) D) center at (4, 2) transverse axis is parallel to y-axis vertices at (4, -3) and (4, 7), foci at (4, 2 - 26) and (4, 2 + 26), asymptotes of y + 2 = - 5(x + 4) and y + 2 = 5(x + 4) Find the center, foci, and vertices of the ellipse. 83) 4x2 + 5y2 - 56x + 50y + 301 = 0

83)

(x - 7)2 (y + 5)2 + =1 A) 5 4

center: (7, -5); foci: (8, -5), (6, -5); vertices: (9.2, -5), (4.8, -5) (x - 7)2 (y + 5)2 + =1 B) 5 4 center: (-7, 5); foci: (-6, 5), (-8, 5); vertices: (-9.2, 5), (-4.8, 5) (x - 7)2 (y + 5)2 + =1 C) 4 5 center: (7, -5); foci: (8, -5), (6, -5); vertices: (9.2, -5), (4.8, -5) (x - 7)2 (y + 5)2 + =1 D) 4 5 center: (-7, 5); foci: (-6, 5), (-8, 5); vertices: (-9.2, 5), (-4.8, 5)

Graph the equation. (x + 2)2 (y + 1)2 + =1 84) 4 16

84)

Find an equation for the ellipse described. 85) Center (0, 0); major axis horizontal with length 20; length of minor axis is 14 x2 y2 x2 y2 x2 y2 + =1 + =1 + =1 A) B) C) 400 196 49 100 20 49

y2 + =1 D) 100 49

85)

Graph the ellipse and locate the foci. 86) 9x2 + 4y2 = 36

A) foci at (0,

86)

B) foci at ( 5, 0) and (- 5, 0)

5) and (0, - 5)

C) foci at (2 3, 0) and (-2 3, 0)

D) foci at ( 13, 0) and (- 13, 0)

Use a graphing utility to graph the curve defined by the given parametric equations. 87) x = 2t2 , y = t + 2; - < t <

87)

Find the vertex, focus, and directrix of the parabola with the given equation. 88) (y + 2)2 = 20(x - 4) A) vertex: (4, -2) focus: (-1, -2) directrix: x = 9

B) vertex: (-2, 4) focus: (3, 4) directrix: x = -7

C) vertex: (4, -2) focus: (9, -2) directrix: x = -1

D) vertex: (-4, 2) focus: (1, 2) directrix: x = -9

Solve the problem. 89) A baseball pitcher throws a baseball with an initial speed of 126 feet per second at an angle of 20° to the horizontal. The ball leaves the pitcher's hand at a height of 5 feet. Find parametric equations that describe the motion of the ball as a function of time. How long is the ball in the air? When is the ball at its maximum height? What is the maximum height of the ball? A) x = 118.4t, y = -16t2 + 43.09t + 5 B) x = 118.4t, y = -16t2 + 43.09t + 5 2.572 sec, 1.347 sec, 4.985 feet C) x = 118.4t, y = -16t2 + 43.09t + 5

5.609 sec, 1.347 sec, 29.012 feet

90) The orbit of a planet around a sun is an ellipse with the sun at one focus. The aphelion of a planet is its greatest distance from the sun, its perihelion is its shortest distance, and its mean distance is the length of the semimajor axis of the elliptical orbit. If a planet has a perihelion of 328.4 million miles and a mean distance of 331 million miles, write an equation for the orbit of the planet around the sun. x2 y2 x2 y2 + =1 + =1 A) B) 2 2 2 331 330.99 331.01 3312 x2

3312

328.42

89)

5.143 sec, 1.347 sec, 237.094 feet D) x = 118.4t, y = -16t2 + 43.09t + 5

2.805 sec, 1.347 sec, 34.012 feet

88)

3312

Find the vertex, focus, and directrix of the parabola. Graph the equation. 91) y2 + 10y = 4x + 3

90)

y2 =1 2.62

91)

A) vertex: (-7, -5) focus: (-6, -5) directrix: x = -8

B) vertex: (-7, -5) focus: (-7, -4) directrix: y = -6

C) vertex: (-7, -5) focus: (-7, -6) directrix: y = -4

D) vertex: (-7, -5) focus: (-8, -5) directrix: x = -6

Find a rectangular equation for the plane curve defined by the parametric equations. 92) x = 2t, y = t + 1; -2 t 3 1 A) y = -2x + 1; for x in - < x < B) y = x + 1; for x in -4 x 6 2 C) y =

1 x - 1; for x in - < x < 2

D) y = x2 + 1; for x in -2 x 2

92)

Rotate the axes so that the new equation contains no xy-term. Discuss the new equation. 93) xy +16 = 0 A) = 45° B) = 36.9° x'2 y'2 y'2 x'2 + =1 + =1 4 2 32 32

93)

ellipse center at (0, 0) major axis is the x'-axis vertices at (±2, 0) D) = 45° y'2 = -32x'

ellipse center at (0, 0) major axis is y'-axis vertices at (0, ±4 2) C) = 45° y'2 x'2 =1 32 32

parabola vertex at (0, 0) focus at (-8, 0)

hyperbola center at (0, 0) transverse axis is y'-axis vertices at (0, ±4 2)

Solve the problem. 94) An experimental model for a suspension bridge is built in the shape of a parabolic arch. In one section, cable runs from the top of one tower down to the roadway, just touching it there, and up again to the top of a second tower. The towers are both 16 inches tall and stand 80 inches apart. Find the vertical distance from the roadway to the cable at a point on the road 20 inches from the lowest point of the cable. A) 3.8 in. B) 4 in. C) 4.2 in. D) 16 in.

94)

Rotate the axes so that the new equation contains no xy-term. Graph the new equation. 95) 17x2 - 12xy + 8y2 - 68x + 24y -12 = 0

95)

Find a polar equation for the conic. A focus is at the pole. 2 96) e = ; directrix is perpendicular to the polar axis 2 to the left of the pole 3 A) r =

4 3 - 2 cos

B) r =

6 3 - 2 cos

C) r =

4 3 + 2 cos

96) D) r =

6 3 + 2 cos

Rotate the axes so that the new equation contains no xy-term. Discuss the new equation. 97) x2 + 2xy + y2 - 8x + 8y = 0 A)

= 36.9° x'2 y'2 + =1 4 2

ellipse center (0, 0) major axis is x'-axis vertices at (±2, 0) C) = 36.9° x'2 y'2 + =1 4 4

ellipse center (0, 0) major axis is x'-axis vertices at (±2, 0)

Identify the equation without applying a rotation of axes. 98) x2 + 6xy + 9y2 + 4x - 3y + 2 = 0 A) parabola

B) ellipse

Find an equation for the ellipse described. 99) Focus at (-2, 0); vertices at (±5, 0) x2 y2 x2 y2 + =1 + =1 A) B) 21 25 4 25

97)

= 45° 2 x' = -4 2y' parabola vertex at (0, 0) focus at (0, - 2)

= 45°

y'2 = -4 2x' parabola vertex at (0, 0) focus at (- 2, 0)

C) hyperbola

D) not a conic

x2 y2 + =1 C) 4 21

x2 y2 + =1 D) 25 21

98)

99)

Graph the equation. 100) y2 = 6x

100)

Find an equation for the ellipse described. Graph the equation. 101) Vertices at (5, -4) and (5, 8); length of minor axis is 6

101)

(x - 5)2 (y - 2)2 + =1 9 36

(x + 5)2 (y + 2)2 + =1 36 9

(x - 5)2 (y - 2)2 + =1 36 9

(x + 5)2 (y + 2)2 + =1 9 36

Identify the equation without completing the square. 102) 4x2 + 2y2 + 3x + 2 = 0 A) hyperbola

B) parabola

C) ellipse

Find an equation for the ellipse described. 103) Center at (0, 0); focus at (-6, 0); vertex at (8, 0) x2 y2 x2 y2 + =1 + =1 A) B) 36 28 28 64

y2 + =1 C) 36 64

Find an equation for the ellipse described. Graph the equation.

D) not a conic

y2 + =1 D) 64 28

102)

103)

104) Foci at (-1, 2) and (5, 2); length of major axis is 10

104)

(x - 3)2 (x + 2)2 + =1 25 16

(x + 3)2 (y + 2)2 + =1 25 16

(y + 3)2 (x - 2)2 + =1 25 16

(x - 2)2 (y - 2)2 + =1 25 16

Graph the equation. (x - 2)2 (y + 1)2 + =1 105) 16 9

105)

Solve the problem. 106) A searchlight is shaped like a paraboloid of revolution. If the light source is located 2 feet from the base along the axis of symmetry and the opening is 10 feet across, how deep should the searchlight be? A) 0.2 ft B) 3.1 ft C) 12.5 ft D) 6.3 ft 107) A reflecting telescope has a mirror shaped like a paraboloid of revolution. If the distance of the vertex to the focus is 30 feet and the distance across the top of the mirror is 50 inches, how deep is the mirror in the center? 125 125 125 in. in. in. A) B) 9 in. C) D) 24 288 3456

106)

107)

Graph the hyperbola. 108) 16x2 - 4y2 = 64

108)

Find the parametric equations that define the curve shown. 109)

109)

A) x = -2t - 3, y = t + 2; 0 t 3 C) x = 2t - 3, y = -t + 2; 0 t 3

B) x = -2t - 3, y = -t + 2; 0 t 2 D) x = 2t - 3, y = -t + 2; 0 t 2

Identify the equation without applying a rotation of axes. 110) x2 - 4xy - 3y2 - 2x + 3y + 10 = 0 A) parabola

B) hyperbola

C) ellipse

D) not a conic

Find the asymptotes of the hyperbola. 111) x2 - y2 + 6x - 4y + 1 = 0

111)

1 1 A) y + 2 = (x + 3) and y + 2 = - (x + 3) 2 2

B) y - 3 = (x - 2) and y - 3 = - (x - 2)

C) y + 3 = (x + 2) and y + 3 = - (x + 2)

D) y + 2 = (x + 3) and y + 2 = - (x + 3)

Solve the problem. 112) A comet follows the hyperbolic path described by

110)

x2 y2 = 1, where x and y are in millions. If the 6 23

112)

sun is the focus of the path, how close to the sun is the vertex of the path?

A) 2.4 million

B) 5.4 million

Identify the equation without completing the square. 113) 4y2 - 2x + 4y = 0 A) ellipse

B) hyperbola

C) 3.0 million

D) 29 million

C) parabola

D) not a conic

113)

Find an equation for the ellipse described. 114) Center at (0, 0); focus at (0, 7); vertex at (0, 8) x2 y2 x2 y2 + =1 + =1 A) B) 49 15 64 15

y2 + =1 C) 49 64

y2 + =1 D) 15 64

Identify the conic that the polar equation represents. Also, give the position of the directrix. 6 115) r = 12 - 4 sin A) ellipse, directrix perpendicular to the polar axis B) ellipse, directrix parallel to the polar axis

3 below the pole 2

C) ellipse, directrix perpendicular to the polar axis D) ellipse, directrix parallel to the polar axis

3 right of the pole 2

3 left of the pole 2

3 above the pole 2

114)

115)

Graph the equation. 116) (x + 2)2 = -8(y - 1)

116)

Find a rectangular equation for the plane curve defined by the parametric equations. 117) x = 4 tan t, y = 3 sec t; 0 t 2 y2 x2 y2 x2 + = 1; for x in - < x < = 1; for x in - < x < A) B) 9 16 9 16 C) y = x2 - 9; for x in -3 x 3

D) y = 3 1 +

x2 ; for x in - < x < 16

117)

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola. 118) x2 - 4y2 + 8x + 32y - 52 = 0 A) center at (-4, 4) transverse axis is parallel to y-axis vertices at (-4, 2) and (-4, 6) foci at (-4, 4 - 5) and (-4, 4 + 5) asymptotes of y + 4 = - 2(x - 4) and y + 4 = 2(x - 4) B) center at (4, -4) transverse axis is parallel to x-axis vertices at (2, -4) and (6, -4) foci at (4 - 5, -4) and (4 + 5, -4) 1 1 asymptotes of y + 4 = - (x - 4) and y + 4 = (x - 4) 2 2

118)

C) center at (-4, 4) transverse axis is parallel to x-axis vertices at (-5, 4) and (-3, 4) foci at (-4 - 5, 4) and (-4 + 5, 4) asymptotes of y - 4 = - 2(x + 4) and y - 4 = 2(x + 4) D) center at (-4, 4) transverse axis is parallel to x-axis vertices at (-6, 4) and (-2, 4) foci at (-4 - 5, 4) and (-4 + 5, 4) 1 1 asymptotes of y - 4 = - (x + 4) and y - 4 = (x + 4) 2 2 Find the vertex, focus, and directrix of the parabola. Graph the equation. 119) x2 - 10x = 12y - 61

119)

A) vertex: (5, 3) focus: (8, 3) directrix: x = 2

B) vertex: (5, 3) focus: (2, 3) directrix: x = 8

C) vertex: (5, 3) focus: (5, 6) directrix: y = 0

D) vertex: (5, 3) focus: (5, 0) directrix: y = 6

120) (y + 3)2 = (x - 3)

120)

A) vertex: (3, -3) focus: (3, -5) directrix: y = -1

B) vertex: (3, -3) focus: (1, -3) directrix: x = 5

C) vertex: (-3, 3) focus: (-3, 1) directrix: y = 5

D) vertex: (3, -3) focus: (1, -3) directrix: x = 5

Find an equation for the ellipse described. 121) Center at (0, 0); focus at (-6, 0); vertex at (8, 0) x2 y2 x2 y2 + =1 + =1 A) B) 36 64 36 28

y2 + =1 C) 28 64

y2 + =1 D) 64 28

121)

Rotate the axes so that the new equation contains no xy-term. Graph the new equation. 122) x2 + xy + y2 - 3y - 6 = 0

122)

Graph the curve whose parametric equations are given. 123) x = 7 sin t, y = 7 cos t; 0 t 2

123)

Find parametric equations for the rectangular equation. 124) y = x4 - 5 A) x = t, y = t4 - 5; 0 t < C) x = t2 , y = t2 - 5; 0 t <

B) x = t, y = t2 - 5; 0 t < D) x = t2 , y = t4 - 5; 0 t <

124)

Solve the problem. 125) Find parametric equations for an object that moves along the ellipse

x2 y2 + = 1 with the motion 9 9

125)

described. The motion begins at (0, 3), is clockwise, and requires 1 second for a complete revolution.

A) x = 3 sin ( C) x = 3 sin (

t), y = 3 cos (

t), 0 t 1

B) x = 3 cos (

t), y = 3 sin (

t), 0 t 1

1 1 t), y = 3 cos ( t), 0 t 1 2 2

D) x = 3 sin (

t), y = -3 cos (

t), 0 t 1

Find the vertex, focus, and directrix of the parabola with the given equation. 126) (y + 2)2 = -12(x + 1)

126)

Rotate the axes so that the new equation contains no xy-term. Discuss the new equation. 127) 24xy - 7y2 + 36 = 0

127)

A) vertex: (-2, -1) focus: (-5, -1) directrix: x = 1 C) vertex: (-1, -2) focus: (-4, -2) directrix: x = 2

B) vertex: (-1, -2) focus: (2, -2) directrix: x = -4 D) vertex: (1, 2) focus: (-2, 2) directrix: x = 4

= 36.9° y'2 4x'2 =1 4 9

hyperbola center at (0, 0) transverse axis is the y'-axis vertices at (0, ±2)

= 53.1° y'2 4x'2 =1 4 9

hyperbola center at (0, 0) transverse axis is the y'-axis vertices at (0, ±2)

= 36.9°

4y'2 x'2 =1 9 4

= 36.9° y'2 x'2 =1 9 16 hyperbola center at (0, 0) transverse axis is the y'-axis vertices at (0, ±3)

hyperbola center at (0, 0) transverse axis is the y'-axis 3 vertices at (0, ± ) 2

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola. 128) 144y2 - 4x2 = 576 A) center at (0, 0) transverse axis is x-axis vertices: (-12, 0), (12, 0) foci: (- 2 37, 0) , (2 37, 0) 1 1 asymptotes of y = - x and y = x 6 6

B) center at (0, 0) transverse axis is y-axis vertices: (0, -2), (0, 2) foci: (- 2 37, 0) , (2 37, 0) 1 1 asymptotes of y = - x and y = x 6 6

C) center at (0, 0) transverse axis is x-axis vertices: (-2, 0), (2, 0) foci: (-12, 0), (12, 0) 1 1 asymptotes of y = - x and y = x 6 6

D) center at (0, 0) transverse axis is y-axis vertices at (0, -2) and (0, 2) foci at (0, - 2 37) and (0, 2 37) 1 1 asymptotes of y = - x and y = x 6 6

Discuss the equation and graph it. 3 129) r = 2 + 4 sin

128)

129)

A) hyperbola, directrix perpendicular to 3 the polar axis unit right of the pole 4 1 3 vertices ( , 0), (- , ) 2 2

B) ellipse, directrix perpendicular to 3 the polar axis unit left of the pole 2 3 1 vertices ( , 0), ( , ) 2 2

C) ellipse, directrix parallel to 3 the polar axis unit below the pole 2 3 1 3 vertices ( , ), ( , ) 2 2 2 2

D) hyperbola; directrix parallel to 3 the polar axis unit above the pole 4 1 3 3 vertices ( , ), (- , ) 2 2 2 2

Solve the problem.

130) The roof of a building is in the shape of the hyperbola y2 - x2 = 26, where x and y are in meters. Determine the distance, w, the outside walls are apart, if the height of each wall is 12 m.

A) 118 m

B) 10.85 m

C) 21.7 m

D) 13 m

130)

Graph the curve whose parametric equations are given. 131) x = t, y = 2t + 3; 0 t 4

131)

Rotate the axes so that the new equation contains no xy-term. Graph the new equation. 132) 24xy - 7y2 + 36 = 0

132)

Find an equation of the parabola described. 133) Focus at (3, 0); vertex at (0, 0) A) x2 = 3y B) x2 = 12y

C) y2 = 12x

Find the center, foci, and vertices of the ellipse. 134) 16x2 + 49y2 = 784 A) center at (0, 0) foci at (0, - 33) and (0, 33) vertices at (0, -7), (0, 7) C) center at (0, 0) foci at (0, -4) and (0, 4) vertices at (0, -16), (0, 16)

D) y2 = 3x

B) center at (0, 0) foci at (-7, 0) and (7, 0) vertices at (-49, 0), (49, 0) D) center at (0, 0) foci at (- 33, 0) and ( 33, 0) vertices at (-7, 0), (7, 0)

133)

134)

Name the conic. 135)

135)

A) ellipse

B) hyperbola

C) parabola

Rotate the axes so that the new equation contains no xy-term. Discuss the new equation. 136) 17x2 - 12xy + 8y2 - 68x + 24y -12 = 0 A)

= 26.6° x'2 y'2 + =1 4 16

ellipse center at (0, 0) major axis is y'-axis vertices at (0, ±4) B) = 63.4° x'2 y'2 =1 16 4 hyperbola center at (0, 0) transverse axis is the x'-axis vertices at (±4, 0) C) = 63.4° x'2 = -16y'

parabola vertex at (0, 0) focus at (0, -4) D) = 63.4° 2 5 2 4 5 2 x' y' + 5 5 + =1 16 4 ellipse center at (

2 5 4 5 ,) 5 5

major axis is x'-axis 2 5 4 5 2 5 4 5 vertices at (4 + ,) and (-4 + ,) 5 5 5 5

D) circle

136)

Find an equation for the hyperbola described. 137) Vertices at (0, ±10); asymptotes at y = ± A)

y2 x2 =1 100 64

5 x 8

137)

y2 x2 =1 100 256

y2 x2 =1 64 25

y2 x2 =1 256 100

Rotate the axes so that the new equation contains no xy-term. Graph the new equation. 138) xy +16 = 0

Find a rectangular equation for the plane curve defined by the parametric equations. 139) x = 2t - 1, y = t2 + 7; -4 t 4 1 A) y = - x + 30; for x in -6 x 4 2

C) y =

138)

1 B) y = x2 + 1; for x in -6 x 4 2

1 2 1 29 x + x+ ; for x in -9 x 7 4 2 4

D) y = x2 + 1; for x in -2 x 2

139)

Find the center, foci, and vertices of the ellipse. x2 y2 + =1 140) 81 16

140)

A) center at (0, 0) foci at (- 65, 0) and ( 65, 0) vertices at (-9, 0), (9, 0) C) center at (0, 0) foci at (0, - 65) and (0, 65) vertices at (0, -9), (0, 9)

B) center at (0, 0) foci at (-9, 0) and (9, 0) vertices at (-81, 0), (81, 0) D) center at (0, 0) foci at (0, -4) and (0, 4) vertices at (0, -16), (0, 16)

Graph the hyperbola. 141) 4x2 = 9y2 + 36

141)

Discuss the equation and graph it.

142) r =

3 3 - sin

142)

A) directrix perpendicular to polar axis 3 right of pole 3 center - , 0 8 vertices

3 , 2

B) directrix perpendicular to polar axis 3 left of pole 3 center , 0 8

3 ,0 4

vertices

C) directrix parallel to polar axis 3 below pole 3 center , 8 2 vertices

3 , 4

3 ,0 2

D) directrix parallel to polar axis 3 above pole 3 center - , 8 2

3 3 3 , , , 2 2 4 2

vertices -

3 3 3 3 , , , 4 2 2 2

Find an equation for the ellipse described. 143) Center (0, 0); major axis vertical with length 10; length of minor axis is 6 x2 y2 x2 y2 x2 y2 + =1 + =1 + =1 A) B) C) 25 9 36 100 9 25 Rotate the axes so that the new equation contains no xy-term. Discuss the new equation. 144) 31x2 + 10 3xy + 21y2 -144 = 0 A)

= 30° x'2 y'2 + =1 4 9

ellipse center at (0, 0) major axis is y'-axis vertices at (0, ±3) C) = 36.9° x'2 y'2 + =1 9 4

ellipse center at (0, 0) major axis is x'-axis vertices at (±3, 0)

Find an equation for the parabola described. 145) Vertex at (6, -3); focus at (9, -3) A) (x + 6)2 = -24(y - 3)

= 45° 2 y' = -4 2x' parabola vertex at (0, 0) focus at (- 2, 0)

y2 + =1 D) 6 25

143)

144)

= 45°

x'2 = -4 2y' parabola vertex at (0, 0) focus at (0, - 2)

B) (y + 3)2 = 12(x - 6) D) (y + 3)2 = -12(x - 6)

C) (x + 6)2 = 24(y - 3)

145)

Graph the equation. 146) y2 = -5x

146)

Graph the ellipse and locate the foci. 147) 4x2 + 9y2 = 36

147)

A) foci at ( 13, 0) and (- 13, 0)

B) foci at (2 3, 0) and (-2 3, 0)

C) foci at (0,

D) foci at ( 5, 0) and (- 5, 0)

5) and (0, - 5)

Find an equation for the hyperbola described. 148) Vertices at (±5, 0); foci at (±11, 0) x2 y2 x2 y2 =1 =1 A) B) 96 25 25 121

x2 y2 =1 C) 25 96

Find the vertex, focus, and directrix of the parabola with the given equation. 149) (x + 1)2 = -20(y + 3) A) vertex: (-3, -1) focus: (-3, -6) directrix: y = 4 C) vertex: (-1, -3) focus: (-1, 2) directrix: x = -8

B) vertex: (-1, -3) focus: (-1, -8) directrix: y = 2 D) vertex: (1, 3) focus: (1, -2) directrix: y = 8

x2 y2 =1 D) 121 25

148)

149)

Rotate the axes so that the new equation contains no xy-term. Discuss the new equation. 150) 5x2 - 6xy + 5y2 - 8 = 0 A)

= 45° x'2 + y'2 = 1 4

= 45° 2 x' = -4y'

parabola vertex at (0, 0) focus at (0, -1)

ellipse center at (0, 0) major axis is the x'-axis vertices at (±2, 0) C) = 45° x'2 - y'2 = 1 4

hyperbola center at (0, 0) transverse axis is the x'-axis vertices at (±2, 0)

= 45°

y'2 = -4x' parabola vertex at (0, 0) focus at (-1, 0)

Find parametric equations for the rectangular equation. 151) y = 3x - 2

151)

A) x = t, y = 3t - 2; 0 t <

B) x = t, y = 3t2 - 2; 0 t <

t 2 ,y=t- ;0 t< 3 3

D) y = 3t, 3x = t + 2; 0 t <

C) x =

150)

Graph the hyperbola. x2 y2 =1 152) 9 4

152)

Find an equation for the ellipse described. 153) Center at (0, 0); focus at (0, 2); vertex at (0, -8) x2 y2 x2 y2 + =1 + =1 A) B) 60 64 4 60

y2 + =1 C) 64 60

y2 + =1 D) 4 64

154) Center at (0, 0); focus at (4, 0); vertex at (7, 0) x2 y2 x2 y2 + =1 + =1 A) B) 49 33 33 49

x2 y2 + =1 C) 16 49

x2 y2 + =1 D) 16 33

153)

154)

155) Center at (6, 6); focus at (12, 6); vertex at (14, 6) (x + 6)2 (y + 6)2 + =1 A) 64 28 C)

(x - 6)2 (y - 6)2 + =1 B) 64 28

(x - 6)2 (y + 6)2 + =2 121 10

(x + 6)2 (y - 6)2 =1 36 22

Find an equation for the ellipse described. Graph the equation. 156) Foci at (2, 4) and (-8, 4); vertex at (-9, 4)

156)

(x - 4)2 (y + 3)2 + =1 36 11

(x + 3)2 (y - 4)2 + =1 36 11

(x - 4)2 (y + 3)2 + =1 11 36

(x + 3)2 (y - 4)2 + =1 11 36

155)

Find the center, foci, and vertices of the ellipse. 157) 36x2 + y2 - 288x + 540 = 0

157)

x2 + (y - 4)2 = 1 A) 36

center: (4, 0); foci: (4, 6 0.97222222), (4, -6 0.97222222); vertices:(4, 6), (4, -6) x2 + (y - 6)2 = 1 B) 16 center: (6, 0); foci: (6, (6, -4) y2 =1 C) (x - 6)2 + 16

15), (6, -6 0.97222222); vertices:(6, 4),

center: (6, 0); foci: (6, y2 =1 D) (x - 4)2 + 36

15), (6, - 15); vertices:(6, 4), (6, -4)

center: (4, 0); foci: (4, 6 0.97222222), (4, -6 0.97222222); vertices:(4, 6), (4, -6)

Find an equation of the parabola described. 158) Vertex at (0, 0); axis of symmetry the x-axis; containing the point (8, 9) 81 81 81 x x y A) y2 = B) y2 = C) x2 = 32 8 8 Find an equation for the parabola described. 159) Vertex at (8, -2); focus at (8, -6) A) (y - 2)2 = 8(x + 8)

D) x2 =

81 y 32

159)

B) (x - 8)2 = -16(y + 2) D) (y - 2)2 = -8(x + 8)

C) (x - 8)2 = 16(y + 2)

160) Vertex at (4, 7); focus at (5, 7) A) (y - 7)2 = -4(x - 4)

160)

B) (x - 7)2 = 8(y - 7) D) (y - 7)2 = 4(x - 4)

C) (x - 7)2 = -8(y - 7)

Find an equation of the parabola described. 161) Focus at (0, -4); directrix the line y = 4 A) x2 = -16y B) x2 = 16y

C) y2 = -16x

Find an equation for the ellipse described. Graph the equation. 162) Center at (-5, 4); focus at (-8, 4); contains the point (-10, 4)

158)

D) y2 = -4x

161)

162)

(x + 4)2 (y - 5)2 + =1 16 25

(x + 5)2 (y - 4)2 + =1 25 16

(x + 5)2 (y - 4)2 + =1 16 25

(x + 4)2 (y - 5)2 + =1 25 16

Solve the problem. 163) An experimental model for a suspension bridge is built in the shape of a parabolic arch. In one section, cable runs from the top of one tower down to the roadway, just touching it there, and up again to the top of a second tower. The towers stand 50 inches apart. At a point between the towers and 12.5 inches along the road from the base of one tower, the cable is 1.56 inches above the roadway. Find the height of the towers. A) 6.25 in. B) 8.25 in. C) 5.75 in. D) 6.75 in. Convert the polar equation to a rectangular equation. 16 sec 164) r = 4 sec + 1

163)

164)

A) 17x2 + 16y2 - 32x - 256 = 0 C) 16x2 + 15y2 + 32y - 256 = 0

B) 15x2 + 16y2 + 32x - 256 = 0 D) 16x2 + 16y2 + 32x - 256 = 0

Graph the curve whose parametric equations are given. 165) x = t3 + 1, y = t3 - 15; -2 t 2

165)

Determine the appropriate rotation formulas to use so that the new equation contains no xy-term. 166) x2 + 2xy + y2 - 8x + 8y = 0 A) x =

1 3 3 1 x' y' and y = x' + y' 2 2 2 2

B) x =

2 2 (x' - y') and y = (x' + y') 2 2

C) x = -y' and y = x' D) x =

2+ 2

x' -

y' and y =

x' +

2+ 2

166)

Find the parametric equations that define the curve shown. 167)

A) x = -5sin ( B) x = 5sin ( C) x = 8sin ( D) x = 8sin (

2 2 2

(t - 1)), y = 8 cos (

(t - 1)), y = -8 cos ( (t - 1)), y = -5 cos ( (t - 1)), y = -5 cos (

2 2 2 2

167)

(t - 1)); 0 t 3 (t - 1)); 0 t 4 (t - 1)); 0 t 3 (t - 1)); 0 t 4

Find the asymptotes of the hyperbola. 168) y2 - x2 = 9

168)

1 1 A) y = x and y = - x 9 9

C) y =

B) y = x and y = - x

1 1 x and y = - x 3 3

D) y = 3x and y = - 3x

Determine the appropriate rotation formulas to use so that the new equation contains no xy-term. 169) 3x2 + 6xy + 3y2 - 8x + 8y = 0 A) x = -y' and y = x' 2 2 (x' - y') and y = (x' + y') B) x = 2 2 C) x = D) x =

169)

1 3 3 1 x' y' and y = x' + y' 2 2 2 2

2+ 2

x' -

y' and y =

x' +

2+ 2

Convert the polar equation to a rectangular equation. 8 170) r = 2 + cos

170)

A) 3x2 + 4y2 + 16x - 64 = 0 C) 4x2 + 4y2 + 16x - 64 = 0

B) 4x2 + 3y2 + 16y - 64 = 0 D) 5x2 + 4y2 - 16x - 64 = 0

Find the center, foci, and vertices of the ellipse. 171) 36(x - 3)2 + 25(y + 1)2 = 900 A) center at (-1, 3) foci at (-1, 3 - 11), (-1, 3 + vertices at (-1, 5), (-1, -7) C) center at (3, -1) foci at (3, -1 - 11), (3, -1 + vertices at (3, 5), (3, -7)

B) center at (-3, -1) foci at (-3, -1 - 11), (-3, -1 + 11) vertices at (-3, 5), (-3, -7) D) center at (4, -1) foci at (4, -1 - 11), (4, -1 + 11) vertices at (4, 5), (4, -7)

11)

Find the vertex, focus, and directrix of the parabola. Graph the equation. 172) (x + 1)2 = -4(y - 2)

A) vertex: (-1, 2) focus: (1, 2) directrix: x = -3

B) vertex: (1, -2) focus: (1, 0) directrix: y = -4

C) vertex: (-1, 2) focus: (-1, 4) directrix: y = 0

D) vertex: (1, -2) focus: (3, -2) directrix: x = -1

171)

172)

Find an equation for the hyperbola described. 173) center at (4, 9); focus at (0, 9); vertex at (3, 9) (x - 4)2 - (y - 9)2 = 1 A) 15 C)

173)

(y - 9)2 =1 B) (x - 4)2 15

(x - 9)2 - (y - 4)2 = 1 15

D) (x - 9)2 -

(y - 4)2 =1 15

Solve the problem. 174) A baseball player hit a baseball with an initial speed of 190 feet per second at an angle of 40° to the horizontal. The ball was hit at a height of 5 feet off the ground. Find parametric equations that describe the motion of the ball as a function of time. How long is the ball in the air? When is the ball at its maximum height? What is the distance the ball traveled? A) x = 145.54t, y = -16t2 + 122.17t + 5 B) x = 145.54t, y = -16t2 + 122.17t + 5 7.594 sec, 3.818 sec, 1,105.231 feet

15.353 sec, 3.818 sec, 2,234.476 feet D) x = 145.54t, y = -16t2 + 122.17t + 5

C) x = 145.54t, y = -16t2 + 122.17t + 5 7.676 sec, 3.818 sec, 1,117.165 feet

7.676 sec, 3.818 sec, 1,880.513 feet

Write an equation for the hyperbola. 175)

x2 y2 =1 25 16

174)

175)

x2 y2 =1 16 25

y2 x2 =1 25 16

Find the asymptotes of the hyperbola. x2 y2 =1 176) 25 16

y2 x2 =1 16 25

176)

A) y =

16 16 x and y = x 25 25

B) y =

5 5 x and y = - x 4 4

C) y =

4 4 x and y = - x 5 5

D) y =

25 25 x and y = x 16 16

Find the center, foci, and vertices of the ellipse. x2 y2 + =1 177) 4 36

177)

A) center at (0, 0) foci at (0, -6) and (0, 6) vertices at (0, -36), (0, 36) C) center at (0, 0) foci at (- 4 2, 0) and (4 2, 0) vertices at (-6, 0), (6, 0)

B) center at (0, 0) foci at (0, - 4 2) and (0, 4 2) vertices at (0, -6), (0, 6) D) center at (0, 0) foci at (0, 6) and (2, 0) vertices at (0, 36), (4, 0)

Find an equation for the hyperbola described. 1 9 6 178) Vertices ( , -3) and (- , -3); asymptotes y + 3 = ± (x + 2) 2 2 5

178)

4(x - 2)2 (y - 3)2 =1 25 9

4(x + 2)2 (y + 3)2 =1 25 9

(y + 3)2 4(x + 2)2 =1 9 25

(x + 2)2 4(y + 3)2 =1 9 25

Name the conic. 179)

A) parabola

179)

B) hyperbola

C) circle

D) ellipse

Solve the problem. 180) Ron throws a ball straight up with an initial speed of 60 feet per second from a height of 6 feet. Find parametric equations that describe the motion of the ball as a function of time. How long is the ball in the air? When is the ball at its maximum height? What is the maximum height of the ball? A) x = 0, y = -16t2 + 60t + 6 B) x = 0, y = -16t2 + 60t + 6 7.294 sec, 1.875 sec, 431.63 feet C) x = 0, y = -16t2 + 60t + 6

3.847 sec, 1.875 sec, 62.25 feet D) x = 0, y = -16t2 + 60t + 6

3.647 sec, 1.875 sec, 6.01 feet

7.695 sec, 1.875 sec, 56.25 feet

Convert the polar equation to a rectangular equation. 12 181) r = 3 - 3 cos A) x2 = -8y + 16

180)

181)

B) x2 = 8y + 16

C) y2 = -8x + 16 87

D) y2 = 8x + 16

Find an equation for the hyperbola described. 182) Vertices at (±9, 0); foci at (±11, 0) x2 y2 x2 y2 =1 =1 A) B) 40 81 121 81

y2 =1 C) 81 40

y2 =1 D) 81 121

Identify the conic that the polar equation represents. Also, give the position of the directrix. 4 183) r = 2 + 2 sin

182)

183)

A) hyperbola, directrix perpendicular to the polar axis 2 right of the pole B) parabola, directrix parallel to the polar axis 2 above the pole C) hyperbola, directrix parallel to the polar axis 2 above the pole D) parabola, directrix perpendicular to the polar axis 2 right of the pole Find an equation for the ellipse described. 184) Foci at (0, ±4); y-intercepts are ±8 x2 y2 x2 y2 + =1 + =1 A) B) 64 48 48 64

x2 y2 + =1 16 48

x2 y2 + =1 16 64

184)

Graph the equation. 185) (y - 2)2 = 8(x - 1)

185)

186) x2 = -16y

186)

Solve the problem.

187) The roof of a building is in the shape of the hyperbola y2 - x2 = 41, where x and y are in meters. Refer to the figure and determine the height h of the outside walls.

a=b=8m A) 33 m

B) 10.2 m

C) 23 m

D) 105 m

187)

Find two sets of parametric equations for the given rectangular equation. 188) y = 3x + 9 t t A) x = t, y = 3t + 9; x = t, y = + 9 B) x = 3t, y = t + 9; x = , y = t + 9 3 3 C) x = t, y = 3t + 9; x =

t ,y=t+9 3

188)

D) x = t, y = 3t + 9; x = 3t, y = t + 9

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola. (x - 1)2 (y - 2)2 =1 189) 4 36

189)

A) center at (2, 1) transverse axis is parallel to x-axis vertices at (0, 1) and (4, 1) foci at (2 - 2 10, 1) and (2 + 2 10, 1) asymptotes of y - 1 = - 3(x - 2) and y - 1 = 3(x - 2) B) center at (1, 2) transverse axis is parallel to x-axis vertices at (-5, 2) and (7, 2) foci at (1 - 2 10, 2) and (1 + 2 10, 2) 1 1 asymptotes of y - 2 = - (x - 1) and y - 2 = (x - 1) 3 3 C) center at (1, 2) transverse axis is parallel to y-axis vertices at (1, 0) and (1, 4) foci at (1, 2 - 2 10) and (1, 2 + 2 10) 1 1 asymptotes of y + 2 = - (x + 1) and y + 2 = (x + 1) 3 3 D) center at (1, 2) transverse axis is parallel to x-axis vertices at (-1, 2) and (3, 2) foci at (1 - 2 10, 2) and (1 + 2 10, 2) asymptotes of y - 2 = - 3(x - 1) and y - 2 = 3(x - 1) Determine the appropriate rotation formulas to use so that the new equation contains no xy-term. 190) 13x2 - 6xy + 7y2 - 8x + 8y = 0 A) x =

x' -

2+ 2

y' and y =

2+ 2

x' +

190)

B) x = -y' and y = x' 2 2 (x' - y') and y = (x' + y') C) x = 2 2 D) x =

1 3 3 1 x' y' and y = x' + y' 2 2 2 2

Convert the polar equation to a rectangular equation. 4 sec 191) r = sec + 2

191)

A) 3y2 - x2 + 16 = 0 C) 3x2 - y2 + 16 = 0

B) 3y2 - x2 -16y + 16 = 0 D) 3x2 - y2 -16x + 16 = 0 91

Identify the equation without applying a rotation of axes. 192) 3x2 - 10xy + 4y2 - 2x + 2y - 7 = 0 A) parabola

B) hyperbola

C) ellipse

Graph the curve whose parametric equations are given. 193) x = t2 , y = t + 5; 0 t 4

D) not a conic

192)

193)

Graph the ellipse and locate the foci. x2 y2 + =1 194) 4 9

194)

A) foci at ( 5, 0) and (- 5, 0)

B) foci at (2 3, 0) and (-2 3, 0)

C) foci at ( 13, 0) and (- 13, 0)

D) foci at (0,

5) and (0, - 5)

Graph the curve whose parametric equations are given. 195) x = 4 tan t, y = 5 sec t; 0 t 2

195)

Use a graphing utility to graph the curve defined by the given parametric equations. 196) x = t + 2, y = 3t - 1; 0 t 3

Find a rectangular equation for the plane curve defined by the parametric equations. 197) x = 4 sin t, y = 4 cos t; 0 t 2 A) y = x2 - 9; for x in -2 x 2 B) y2 - x2 = 16; for x in - < x < C) y = a 2 - x2 = 16; for x in - < x < D) x2 + y2 = 16; for x in -4 x 4

196)

197)

Graph the curve whose parametric equations are given. 198) x = 2t - 1, y = t2 + 6; -4 t 4

198)

Find an equation for the hyperbola described. Graph the equation.

199) Center at (0, 0); focus at ( 58, 0); vertex at (7, 0)

199)

x2 y2 =1 49 9

y2 x2 =1 49 9

y2 x2 =1 9 49

x2 y2 =1 9 49

Solve the problem. 200) Car A (travelling north at 50 mph) and car B (traveling west at 40 mph) are heading toward the same intersection. Car A is 4 miles from the intersection when car B is 5 miles from the intersection. Find parametric equations that describe the motion of cars A and B.

5 mi

200)

car B 40 mph

4 mi car A 50 mph

A) Car A: x = 40t - 5, y = 0; Car B: x = 0, y = 4 - 50t B) Car A: x = 0, y = 50t - 4; Car B: x = 5 - 40t, y = 0 C) Car A: x = 0, y = 40t - 5; Car B: x = 50t - 4, y = 0 D) Car A: x = -50t + 4, y = 0; Car B: x = 5 - 40t, y = 0 Find an equation for the ellipse described. Graph the equation. 201) Foci at (2, 7) and (2, 1); length of major axis is 10

201)

(x - 4)2 (y + 2)2 + =1 16 25

(x - 4)2 (y + 2)2 + =1 25 16

(y - 4)2 (x - 2)2 + =1 25 16

(y - 4)2 (x + 2)2 + =1 25 16

Find an equation for the ellipse described. 202) Vertices at (-8, 4) and (12, 4); focus at (10, 4) (x - 4)2 (y - 2)2 + =1 A) 81 35 C)

(x + 2)2 (y + 4)2 + =1 64 36

(x - 2)2 (y - 4)2 + =1 100 36

(x - 2)2 (y + 4)2 =1 144 44

Identify the conic that the polar equation represents. Also, give the position of the directrix. 6 203) r = 3 - 4 cos A) ellipse, directrix is perpendicular to the polar axis at a distance

3 units to the right of the pole 2

B) hyperbola, directrix is perpendicular to the polar axis at a distance 3 units to the right of the pole 3 C) hyperbola, directrix is perpendicular to the polar axis at a distance units to the left of the 2 pole D) ellipse, directrix is perpendicular to the polar axis at a distance 3 units to the left of the pole

202)

203)

Solve the problem. 204) Rachel's bus leaves at 6:15 PM and accelerates at the rate of 4 meters per second per second. Rachel, who can run 5 meters per second, arrives at the bus station 6 seconds after the bus has left. Find parametric equations that describe the motions of the bus and Rachel as a function of time. Determine algebraically whether Rachel will catch the bus. If so, when? 5 A) Bus: x1 = 4t2 , y1 = 1; Rachel: x2 = (t - 6), y2 = 3 2

204)

Rachel will catch the bus at 6:19 PM B) Bus: x1 = 2t2 , y1 = 1; Rachel: x2 = 5(t - 6), y2 = 3 Rachel will catch the bus at 6:20 PM

C) Bus: x1 = 2t2 , y1 = 1; Rachel: x2 = 5(t - 6), y2 = 3

Rachel won't catch the bus. D) Bus: x1 = 2t2 , y1 = 1; Rachel: x2 = 5(t + 6), y2 = 3 Rachel won't catch the bus.

Find an equation of the parabola described. 205) Focus at (5, 0); vertex at (0, 0) A) x2 = 20y B) y2 = 20x

C) y = 20x2

D) x = 20y2

Write an equation for the hyperbola. 206)

x2 y2 =1 4 9

205)

206)

y2 x2 =1 9 4

100

x2 y2 =1 9 4

y2 x2 =1 4 9

Graph the hyperbola. y2 x2 =1 207) 9 4

207)

Solve the problem. 208) An arch in the form of a semiellipse is 52 ft wide at the base and has a height of 20 ft. How wide is the arch at a height of 12 ft above the base? A) 20.8 ft B) 17.7 ft C) 35.5 ft D) 41.6 ft Find the asymptotes of the hyperbola. (x + 3)2 (y + 4)2 =1 209) 4 9 A) y =

209)

3 3 (x + 3) and y = - (x + 3) 2 2

C) y + 4 =

208)

3 3 (x + 3) and y + 4 = - (x + 3) 2 2

101

B) y + 4 =

2 2 (x + 3) and y + 4 = - (x + 3) 3 3

D) y + 3 =

3 3 (x + 4) and y + 3 = - (x + 4) 2 2

Identify the equation without completing the square. 210) 2x2 - 3y2 + 2x + 3y + 1 = 0 A) ellipse

B) hyperbola

C) parabola

D) not a conic

210)

Graph the function. 211) y = -

9 - 4x2

211)

102

Answer Key Testname: CHAPTER 11 1) A 2) B 3) D 4) B 5) C 6) C 7) A 8) C 9) D 10) D 11) A 12) D 13) 36 ft 14) 60 ft 15)

16) The receiver should be located 2 feet from the base of the dish, along its axis of symmetry. 17) about 17 cm 18) B 19) A 20) B 21) B 22) C 103

Answer Key Testname: CHAPTER 11 23) D 24) C 25) A 26) D 27) C 28) C 29) A 30) D 31) D 32) D 33) C 34) A 35) C 36) D 37) C 38) D 39) B 40) C 41) B 42) B 43) B 44) A 45) C 46) C 47) D 48) D 49) D 50) B 51) B 52) D 53) D 54) B 55) B 56) C 57) B 58) C 59) C 60) A 61) A 62) B 63) B 64) B 65) B 66) C 67) B 68) C 69) C 70) B 71) C 72) C 104

Answer Key Testname: CHAPTER 11 73) D 74) B 75) D 76) A 77) B 78) B 79) B 80) B 81) C 82) A 83) A 84) C 85) D 86) A 87) A 88) C 89) C 90) A 91) A 92) B 93) C 94) B 95) B 96) A 97) B 98) C 99) D 100) C 101) A 102) C 103) D 104) D 105) B 106) B 107) C 108) A 109) C 110) B 111) D 112) C 113) C 114) D 115) B 116) D 117) B 118) D 119) C 120) B 121) D 122) A 105

Answer Key Testname: CHAPTER 11 123) D 124) A 125) A 126) C 127) C 128) D 129) D 130) C 131) D 132) A 133) C 134) D 135) D 136) D 137) B 138) A 139) C 140) A 141) C 142) C 143) C 144) A 145) B 146) A 147) D 148) C 149) B 150) A 151) A 152) C 153) A 154) A 155) B 156) B 157) D 158) B 159) B 160) D 161) A 162) B 163) A 164) B 165) C 166) B 167) D 168) B 169) B 170) A 171) C 172) C 106

Answer Key Testname: CHAPTER 11 173) B 174) C 175) D 176) C 177) B 178) B 179) B 180) B 181) D 182) C 183) B 184) B 185) B 186) D 187) B 188) C 189) D 190) A 191) D 192) B 193) C 194) D 195) B 196) C 197) D 198) B 199) A 200) B 201) C 202) B 203) C 204) C 205) B 206) C 207) A 208) D 209) C 210) B 211) B

107

Chapter 12 Exam Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use the properties of determinants to find the value of the second determinant, given the value of the first. s t u 32 - s 16 - t 64 - u . 1) Given v w x = 3, find the value of v w x 4 2 8 4 2 8 A) -3 B) -24 C) 24 D) 3 Solve the system of equations. If the system has no solution, say that it is inconsistent. 2) x - 4y = -10 2x - 8y = -17 A) x = 4, y = 2; (4, 2) B) x = 2, y = 3; (2, 3) C) x = 2, y = 4; (2, 4) D) inconsistent

Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. 3x - 2y + z = -7 3) x + y - 2z = 12 3) 3x + y - z = 10 A) x = 1, y = 3, z = -4; (1, 3, -4)

B) x = 2, y = 3, z = -7; (2, 3, -7)

C) x = 1, y = -3, z = -16; (1, -3, -16)

D) x = 5, y =

13 13 , z = -3; 5, , -3 2 2

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the linear programming problem. 4) The Jillson's have up to $75,000 to invest. They decide that they want to have at least $25,000 invested in stable bonds yielding 6% and that no more than $45,000 should be invested in more volatile bonds yielding 12%. How much should they invest in each type of bond to maximize income if the amount in the more volatile bond should not exceed the amount in the more stable bond? What is the maximum income? Solve the problem. 5) The perimeter of a parking lot is 500 yards. Find the dimensions of the lot if the length is 50 yards more than three times the width. 6) Lexie wants to have an income of $9000 per year from investments. To that end she is going to invest $90,000 in three different accounts. These accounts pay 7%, 10%, and 14% simple interest. If she wants to have $10,000 more in the account paying 7% simple interest than she has in the account paying 14% simple interest, how much should go into each account?

7) A company manufactures three types of wooden chairs at two different locations. In one week,7) the main location produces 18 Kitui chairs, 12 Goa chairs, and 6 Santa Fe chairs while the secondary location produces 10 Kitui chairs, 3 Goa chairs, and 5 Santa Fe chairs. (a) Find a 2 by 3 matrix representing the above data. (b) If each Kitui chair requires 25 board-feet of wood, a Goa chair requires 29 board-feet of wood, and a Santa Fe requires 30 board-feet of wood, find a 3 by 1 matrix representing the amount of material. (c) Multiply the 2 by 3 matrix found in part a and the 3 by 1 matrix found in part b to get a 2 by 1 matrix showing the week's usage of material at both locations. 8) A tea shop owner is mixing a blend of two teas, one of which costs $6.50 per pound, the other costing $4.00 per pound. The owner wants to have 20 pounds of a mixture that will sell for $5.50 per pound. How much of each type of tea should be used? Solve the problem using matrices. 9) A company manufactures three types of wooden chairs: the Kitui, the Goa, and the Santa Fe. To make a Kitui chair requires 1 hour of cutting time, 1.5 hours of assembly time, and 1 hour of finishing time. A Goa chair requires 1.5 hours of cutting time, 2.5 hours of assembly time and 2 hours of finishing time. A Santa Fe chair requires 1.5 hours of cutting time, 3 hours of assembly time, and 3 hours of finishing time. If 41 hours of cutting time, 70 hours of assembly time, and 58 hours of finishing time were used one week, how many of each type of chair were produced? Solve the problem. 10) Jaya has $16,000 to invest. She invests part of it in an account paying 6% simple interest and the rest in an account paying 7% simple interest. If her annual income is $1080, how much does she have invested in each account? Compute the product. 11) -2 1 1 -1 0 -1

10)

11)

Graph the equations of the system. Then solve the system to find the points of intersection. 12) x2 + y2 = 36

12)

x2 - y2 = 36

Solve the problem using matrices. 13) Melody has $45,000 to invest and wishes to receive an annual income of $4290 from this money. She has chosen investments that pay 5%, 8%, and 12% simple interest. Melody wants to have the amount invested at 12% to be double the amount invested at 8%. How much should she invest at each rate? Solve the problem. 14) The difference of two numbers is 5 and the difference of their squares is 55. Find the numbers. Set up the linear programming problem. 15) Charlene baby-sits for $4 per hour. She also works as a tutor for $7 per hour. Because of school, her parents only allow her to work 13 hours per week. How many hours can Charlene tutor and baby-sit and still make at least $50 per week? (a) Let x = hours spent baby-sitting and let y = hours spent tutoring. Write a system of inequalities for this situation. (b) Graph the solution set.

13)

14)

15)

Write the partial fraction decomposition of the rational expression. x2 - 56 16) x4 + 5x2 - 36 Solve the linear programming problem. 17) An artist is creating a mosaic that cannot be larger than the space allotted which is 4 feet tall and 6 feet wide. The mosaic must be at least 3 feet tall and 5 feet wide. The tiles in the mosaic have words written on them and the artist wants the words to all be horizontal in the final mosaic. The word tiles come in two sizes: The smaller tiles are 4 inches tall and 4 inches wide, while the large tiles are 6 inches tall and 12 inches wide. If the small tiles cost $3.50 each and the larger tiles cost $4.50 each, how many of each should be used to minimize the cost? What is the minimum cost? Graph the equations of the system. Then solve the system to find the points of intersection. 18)

16)

17)

18)

y = x y =6-x

Set up the linear programming problem. 19) Eric's Carpentry manufactures two types of bookshelves that are 4 feet tall and 3 feet wide, a basic 19) model and a deluxe model. Each basic bookshelf requires 1.5 hours for assembly and 1 hour for finishing; each deluxe model requires 2.5 hours for assembly and 1 hour for finishing. Two assemblers and one finisher are employed by the company, and each works 40 hours per week. (a) Using x to denote the number of basic bookcases and y to denote the number of deluxe bookcases, write a system of linear inequalities that describes the possible number of each model of bookcase that can be manufactured in a week. (b) Graph the system and label the corner points. Solve the problem. 20) To raise money, a group of three friends is each trying to sell 100 candles. Each friend has a package containing the same number of tapers, votives, and tealights. The tapers sell for $6.00 each, the votives sell for $1.50 each, and the tealights sell for $0.75 each. Maya sold all of the candles to raise $431.25, Lorrin sold all of the tapers and tealights to raise $378.75, while Sara sold all the votives, all the tealights, and half of the tapers to raise $251.25. How many of each type of candle did each package contain?

20)

Show that the matrix has no inverse. 21) 3 15 6 -3 -1 1 -1 7 4

21)

Solve the problem using matrices. 22) The perimeter of a picture frame is 11 feet. If three times the height is equal to eight times the width, what are the dimensions of the frame?

22)

Solve the problem.

23) Find real numbers a, b, and c such that the graph of the function y = ax2 + bx + c contains the points (1, 2), (2, 11), and (-3, -14).

Solve the linear programming problem. 24) Your computer supply store sells two types of laser printers. The first type, A, has a cost of $86 and you make a $45 profit on each one. The second type, B, has a cost of $130 and you make a $35 profit on each one. You expect to sell at least 100 laser printers this month and you need to make at least $3850 profit on them. How many of what type of printer should you order if you want to minimize your cost? Graph the equations of the system. Then solve the system to find the points of intersection. 25) (x + 3)2 + (y + 1)2 = 4 y2 + 2y - x - 6 = 0

23)

24)

25)

Set up the linear programming problem. 26) The Jillson's have up to $75,000 to invest. They decide that they want to have at least $40,000 26) invested in stable bonds yielding 6% and that no more than $20,000 should be invested in more volatile bonds yielding 12%. (a) Using x to denote the amount of money invested in the stable bonds and y the amount invested in the more volatile bonds, write a system of linear inequalities that describes the possible amounts of each investment. (b) Graph the system and label the corner points.

Solve the problem.

27) Find real numbers a, b, and c such that the graph of the function y = ax2 + bx + c contains the points (1, 1), (2, 4), and (-3, 29).

27)

28) A boat on a river goes 77 miles downstream in 2 hours and 45 minutes. The return trip takes 3 hours and 30 minutes. If the boat's speed is the same in each direction, find the speed of the boat and the speed of the current.

28)

Show that the matrix has no inverse. 29) 4 -10 -2 5

29)

Solve the problem.

30) The matrix 922 represents one week's usage of wood (in board-feet) at two locations of a 30) 435 company that manufactures chairs. Due to differences in transportation costs, the first location pays $0.89 per board-foot and the second location pays $0.94 per board-foot. (a) Find a 1 by 2 matrix representing the cost of the wood. (b) Multiply the given matrix and the matrix found in part a to determine the total cost of wood for that week. 31) A health shop owner made trail mix containing dried fruit, nuts, and carob chips. The dried fruit sells for $5.50 per pound, the nuts sell for $7.50 per pound, and the carob chips sell for $8.50 per pound. The shop owner mixed 50 pounds of the trail mix and sells it for $6.70 per pound. If the amount of nuts is five pounds more than the amount of carob ships, how much of each item was used for the trail mix?

31)

Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. -5x + 2z = 13 32) 32) x + 3y - 2z = -15 4x + 5y - z = -18 Solve the linear programming problem. 33) The Fiedler family has up to $130,000 to invest. They decide that they want to have at least $40,000 invested in stable bonds yielding 5.5% and that no more than $60,000 should be invested in more volatile bonds yielding 11%. How much should they invest in each type of bond to maximize income if the amount in the stable bond should not exceed the amount in the more volatile bond? What is the maximum income? 34) Joely's Tea Shop, a store that specializes in tea blends, has available 45 pounds of A grade tea and 70 pounds of B grade tea. These will be blended into 1 pound packages as follows: A breakfast blend that contains one third of a pound of A grade tea and two thirds of a pound of B grade tea and an afternoon tea that contains one half pound of A grade tea and one half pound of B grade tea. If Joely makes a profit of $1.50 on each pound of the breakfast blend and $2.00 profit on each pound of the afternoon blend, how many pounds of each blend should she make to maximize profits? What is the maximum profit? Solve the problem. 35) Craig, Jenni, and Jade go to a store having a sale on workout gear. Craig buys three pairs of socks, two T-shirts, and one pair of shorts for $35.90. Jenni buys four pairs of socks, three T-shirts, and three pairs of shorts for $71.35. Jade buys one pair of socks, four T-shirts, and 2 pairs of shorts for $59.30. What is the price of each item? Graph the equations of the system. Then solve the system to find the points of intersection. 36) y = x2 - 12x + 36

33)

34)

35)

36)

y = -x + 8

Solve the system using the inverse matrix method. 37) 4x + 2z = -20 x - y - 5z = 5 -3x - 2y - z = 12

37)

Solve the problem. 38) A store has a sale on workout gear. Mark bought three pairs of shorts and three T-shirts for $70.35 (before tax). Later, he went back and bought two more pairs of shorts and four more T-shirts for $63.90 (before tax). How much did the shorts and T-shirts cost? Solve the linear programming problem. 39) Eric's Carpentry manufactures two types of bookshelves that are 4 feet tall and 3 feet wide, a basic model and a deluxe model. Each basic bookshelf requires 1.5 hours for assembly and 1 hour for finishing; each deluxe model requires 2.5 hours for assembly and 1 hour for finishing. Two assemblers and one finisher are employed by the company, and each works 40 hours per week. Eric can sell more basic models than deluxe models, so he wants the number of basic models produced to be 50% more than the number of deluxe models produced. If he makes $50 profit on the basic models and $65 profit on the deluxe models, how many should he make to maximize the profit? What is the maximum profit? Graph the equations of the system. Then solve the system to find the points of intersection. 40) x2 + y2 = 100

38)

39)

40)

y = x2 - 10

Use the given matrices to compute the given expression. 41) If A = 7 -5 and B = -9 -3 , find -5A + 4B. 2 -8 -8 1

41)

Solve the problem. 42) A coffee store has available 75 pounds of A grade coffee and 120 pounds of B grade coffee. 42) These will be blended into 1 pound packages as follow: an economy blend that contains 4 ounces of A grade coffee and 12 ounces of B grade coffee and a superior blend that contains 8 ounces of A grade coffee and 8 ounces of B grade coffee. Using x to denote the number of packages of the economy blend and y to denote the number of packages of the superior blend, write a system of linear inequalities that describes the possible number of packages of each blend. Graph the system and label the corner points.

Solve the problem using matrices.

43) Find real numbers a, b, and c such that the graph of the function y = ax2 + bx + c contains the points (-2, -4), (1, -1), and (3, -19).

Solve the problem. 44) Meisha has $25,000 that she wants to invest. She invests it in accounts paying 12%, 7%, and 6% simple interest. The account paying 12% is a higher-risk account, so she wants the amount in that account to be half of the amount she has in the account paying 6% simple interest. If her annual interest is $1945, how much is invested at each rate?

43)

44)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the system of equations by elimination. 45) 3 1 x + y = 11 5 2

45)

6x + 2y = 116 A) x = -2, y = 20; (-2, 20) C) x = -20, y = 6; (-20, 6)

B) x = 20, y = -2; (20, -2) D) x = -20, y = 5; (-20, 5)

Use the properties of determinants to find the value of the second determinant, given the value of the first. x y z x y z 46) u v w = -97 u v w = ? 1 -3 3 3 -9 9 A) 97 B) -97 C) -291 D) 291

46)

Solve the system of equations using Cramer's Rule if it is applicable. If Cramer's Rule is not applicable, say so. 47) 6x + 6y = 18 47) 5x + y = -9 A) x = -6, y = -3; (-6, -3) B) x = -3, y = 6; (-3, 6) C) x = 3, y = -6; (3, -6) D) x = 6, y = -3; (6, -3) Solve the system of equations. If the system has no solution, say that it is inconsistent. 48) x + y = -1 x + y = -2 A) x = 0, y = 0; (0, 0) B) x = 0, y = -3; (0, -3) C) x = -1, y = -2; (-1, -2) D) inconsistent

48)

Determine whether the system corresponding to the given augmented matrix is consistent or inconsistent. If it is consistent, give the solution. 49) 49) 1001 1 0 1 0 9 -9 0 0 1 -9 0 0000 0 A) consistent; x1 = 9, x2 = -9, x3 = -1, x4 = -9; (9, -9, -1, -9)

B) consistent; x1 = 1 - x4 , x2 = -9 - 9x4 , x3 = 9x4, x4 any real number

or {(x, y, z)|x1 = 1 - x4 , x2 = -9 - 9x4 , x3 = 9x4 , x4 any real number}

C) consistent; x1 = 1 + x4 , x2 = -9 + 9x4 , x3 = -9x4 , x4 any real number

or {(x, y, z)|x1 = 1 + x4 , x2 = -9 + 9x4 , x3 = -9x4 , x4 any real number}

D) inconsistent

Each matrix is nonsingular. Find the inverse of the matrix. Be sure to check your answer. 50) 5 3 3 2 1 1 3 -3 2 2 2 3 2 -3 A) B) C) D) 1 1 3 5 -3 5 -3 3 5 5 Solve the system using the inverse matrix method. 51) 2x + 4y - 5z = -8 x + 5y + 2z = -1 3x + 3y + 3z = 15 A) x = 2, y = 5, z = 2; (2, 5, 2) C) x = 5, y = -2, z = 2; (5, -2, 2)

50)

51)

B) x = 5, y = 2, z = -2; (5, 2, -2) D) x = -5, y = -2, z = -2; (-5, -2, -2)

Solve the system of equations by substitution. 52) 2x + 9y = -8 1 13 x+ y= 3 3

52)

A) x = -5, y = 2; (-5, 2) C) x = 5, y = -2; (5, -2)

B) x = -5, y = -2; ( -5, -2) D) x = 5, y = 2; (5, 2)

Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. 3x - 7y - z = -31 53) 53) x + 7y + 6z = 112 2x + y + z = 34 A) x = 9, y = 9, z = 7; (9, 9, 7) B) inconsistent C) x = -9, y = 7, z = 18; (-9, 7, 18) D) x = 9, y = 7, z = 9; (9, 7, 9) Solve the system of equations using substitution. 54) x2 - y2 = 39

54)

x - y = 3 A) x = -8, y = 5 or (-8, 5) C) x = 8, y = 5 or (8, 5)

B) x = -8, y = -5 or (-8, -5) D) x = 8, y = -5 or (8, -5)

Solve the problem using matrices. 55) A ceramics workshop makes wreaths, trees, and sleighs for sale at Christmas. A wreath takes 3 hours to prepare, 2 hours to paint, and 8 hours to fire. A tree takes 15 hours to prepare, 3 hours to paint, and 4 hours to fire. A sleigh takes 4 hours to prepare, 13 hours to paint, and 7 hours to fire. If the workshop has 95 hours for prep time, 56 hours for painting, and 102 hours for firing, how many of each can be made? A) 10 wreaths; 5 trees; 3 sleighs B) 9 wreaths; 4 trees; 2 sleighs C) 4 wreaths; 2 trees; 9 sleighs D) 2 wreaths; 9 trees; 4 sleighs Graph the region indicated by graphing the system of inequalities. Label all points of intersection. 56) y x2 - 8 y -x2

55)

56)

A) O(0, 0), A(0, -8)

B) O(0, 0), A(0, -8)

C) O(0, 0), A(0, -8)

D) O(0, 0), A(0, -8)

Write the system of equations associated with the augmented matrix. Do not solve. 57) 1 0 0 0 -3 0 1 0 0 -5 0 0 1 0 -9 0 0 0 1 0 A) B) C) x1 = 6 x1 = 3 x1 = -3 x2 = 4

x2 = 5

x2 = -5

x4 = 4

x4 = 0

x3 = 0

x3 = 9

57)

x3 = -9

Write the partial fraction decomposition of the rational expression. -3x2 - 6x - 5 58) (x + 2)(x + 1)2 A)

2 5 -2 + + x + 2 x + 1 (x + 1)2

2 -5 -2 + + x + 2 x + 1 (x + 1)2

-5 -2 -2 + + x + 2 x + 1 (x + 1)2

5 2 2 + + x + 2 x + 1 (x + 1)2

x1 = 0

x2 = -8

x3 = -12 x4 = 3

58)

Solve the system of equations. [Hint: Let u =

59)

1 1 1 1 and v = , and solve for u and v. Then let x = , and y = .] x y u v

59)

2 4 + =7 x y 1 2 - =4 x y

A) x = -8, y = C) x =

4 4 ; -8, 15 15

B) x = -

15 1 15 1 ,y=- ; ,4 8 4 8

D) x =

Graph the system of inequalities. 60) 2x + 3y 6 x-y 3 x 1

1 15 1 15 ,y= ; - , 8 4 8 4

4 4 , y = -8; , -8 15 15

60)

Find the value of the determinant. 61) 1 2 5 2 5 5 1 2 5 A) 1

61)

B) -20

C) 110

Write the system of equations associated with the augmented matrix. Do not solve. 62) 7 4 6 14 6 8 7x + 4y = 6 7x + 4y = - 6 4x + 7y = 6 A) 6x + 14y = 8 B) 14x + 6y = - 8 C) 14x + 6y = 8

D) 0

62) 7x + 4y = 6 D) 14x + 6y = 8

Perform the indicated operation(s), whenever possible. 7 -4 8 -2 -6 -1 63) Let A = -6 5 -1 and B = -7 -4 3 . Find A - B. -3 -9 -5 0 6 -3 9 2 9 A) 1 9 2 3 15 -4

5 -10 7 B) -13 1 -8 -3 -3 2

63)

9 2 9 C) 1 9 -4 3 15 2

Graph the system of inequalities. 64) 3x + y < 9 3x + y > -1

5 -10 7 D) -13 1 2 -3 -3 -8

64)

C) No solution

Solve the system of equations by elimination. 65) 5x - 2y = -1 x + 4y = 35 A) x = 3, y = 9; (3, 9) C) x = 3, y = 8; (3, 8) Find the value of the determinant. 66) 2 1 33 A) -7

65)

B) x = 2, y = 8; (2, 8) D) x = 2, y = 9; (2, 9)

66) B) -3

C) 3

Write the augmented matrix for the system. 67) 3.2x + 0.2y = -15.4 0.8x - 0.4y = -5.2 A) 3.2 0.2 -15.4 -5.2 0.8 -0.4 C) 3.2 -15.4 0.2 0.8 -5.2 -0.4

D) 9

67)

-15.4 0.2 -5.2 -0.4

3.2 0.8

3.2 0.8 -0.4 0.2

-15.4 -5.2

Compute the product. 68) 7 -9 9 -7 -6 9 -7 -2 -6 9 6 -6 -4 3 -7 1 5 -9

68)

-49 54 81 -63 -12 36 -4 15 63 7 -9 9 -7 -2 -6 1 5 -9 C) -7 -6 9 9 6 -6 -4 3 -7

-166 -69 54 55 12 -9 74 -3 42

-166 55 74 -69 55 -3 54 -9 42

Write the system of equations associated with the augmented matrix. Do not solve. 2 8 9 -2 69) 4 0 2 4 8 9 0 2 2x + 8y + 9z = -2 2x + 8y + 9z = -2 2x - 8y + 9z = -2 A) 4x B) C) 4x 4x + 2z = 4 + 2z = 4 + 2z = -4 = 2 + 9z = 2 = -2 8x + 9y 8x 8x + 9y Perform the row operation(s) on the given augmented matrix. 70) R2 = -3r1 + r2 4 -4 1 2 -5 0 3 -3 -1 5 -2 -1 A) 4 -4 1 2 -17 12 0 -9 -1 5 -2 -1 C) -17 12 0 -9 -5 0 3 -3 -1 5 -2 -1

70)

19 -4 -8 11 -5 0 3 -3 -1 5 -2 -1

4 -4 1 2 7 -12 6 3 -1 5 -2 -1

Write the partial fraction decomposition of the rational expression. -18x + 90 71) (x + 4)2 (x2 + 2) A)

12x - 3 -3x + 3 + (x + 4)2 x2 + 2

3 9 -3 + + x + 4 (x + 4)2 x2 + 2

3 12 -3x - 3 + + x + 4 (x + 4)2 x2 + 2

3 9 -3x + 3 + + x + 4 (x + 4)2 x2 + 2

69)

71)

Tell whether the given rational expression is proper or improper. x3 - 11x + 28 72) x2 - 9x + 20 A) improper

72)

B) proper

Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. 7x - y - 8z = 4 73) 73) 4x + 9z = 21 7y + z = 64 A) x = 3, y = 1, z = 9; (3, 1, 9) B) x = 3, y = 9, z = 1; (3, 9, 1) C) inconsistent D) x = -3, y = 9, z = 6; (-3, 9, 6) Graph the system of inequalities. 74) 2x - y -4 x + 3y -9

74)

The graph of two equations along with the points of intersection are given. Substitute the points of intersection into the systems of equations. Are the points of intersection solutions to the system of equations (Y/N)? 75) 75)

x2 + y2 = 52 2y+3x = 0 A) Yes

B) No

An objective function and a system of linear inequalities representing constraints are given. Graph the system of inequalities representing the constraints. Find the value of the objective function at each corner of the graphed region. Use these values to determine the maximum value of the objective function and the values of x and y for which the maximum occurs. z = 6x + 7y 76) Objective Function 76) Constraints x 0 y 0 2x + 3y 12 2x + y 8 A) maximum 24; at (4, 0) B) maximum 32; at (2, 3) C) maximum 52; at (4, 4) D) maximum 32; at (3, 2)

Solve the system of equations by elimination. 77) 2x + 4y = -14 10x + 2y = 56 A) x = -2, y = 7; (-2, 7) C) x = -7, y = 7; (-7, 7)

77)

B) x = 10, y = -10; (10, -10) D) x = 7, y = -7; (7, -7)

Solve the linear programming problem. 78) Two kinds of crated cargo, A and B, are to be shipped by truck. The weight and volume of each type are 78) given in the following table:

Volume Weight

A B 50 cubic feet 10 cubic feet 200 pounds 360 pounds

The shipping company charges $75 per crate for cargo A and $100 per crate for cargo B. The truck has a maximum load limit of 7,200 pounds and 1,000 cubic feet. How many of each type of cargo should be shipped to maximize profit for the shipping company? A) 20 crates of cargo A and 0 crates of cargo B B) 18 crates of cargo A and 10 crates of cargo B C) 0 crates of cargo A and 20 crates of cargo B D) 10 crates of cargo A and 18 crates of cargo B

Perform the indicated operation(s), whenever possible. 79) Let A = -1 0 and B = -1 4 . Find A - B. 43 31 A) B) 0 -4 -2 4 74 1 2 Find the value of the determinant. 2 2 4 80) 6 3 4 2 3 3 A) 190

79)

0 4 -1 -2

80) B) 22

C) -10

D) -22

Write the partial fraction decomposition of the rational expression. x+2 81) x3 - 2x2 + x

81)

2 3 -2 + + x x - 1 (x - 1)2

2 5 -2 + + x x - 1 (x - 1)2

2 3 -2 + + x x - 1 (x - 1)2

Solve the system of equations by elimination. 82) 7 x - y = 10 12

82)

5 x + 2y = 11 9

A) x = -18, y = C) x = 18, y =

[-1]

1 1 ; -18, 2 2

B) x = -16, y = -

1 1 ; 18, 2 2

D) x = 16, y =

1 1 ; -16, 2 2

1 1 ; 16, 2 2

Solve the system of equations. 83) x + y + z = -5 x - y + 3z = -17 3x + y + z = -7 A) x = -5, y = 1, z = -1; (-5, 1, -1) C) x = -1, y = 1, z = -5; (-1, 1, -5)

83)

B) x = -5, y = -1, z = 1; (-5, -1, 1) D) inconsistent

Solve for x.

x -4 -1 84) -2 2 0 = 10 -1 -2 8 A) 2

84) B) -2

C) 1

D) 5

Each matrix is nonsingular. Find the inverse of the matrix. Be sure to check your answer. 85) -4 -3 0 4 A) B) C) D) 1 3 1 3 1 3 4 16 4 16 4 16 0 -

1 4

Solve the system of equations by elimination. 86) 3x - 5y = -12 6x + 8y = -24 A) x = 0, y = -4; (0, -4) C) x = 4, y = 0; (4, 0)

1 4

85)

0 -

1 3 4 16

86) B) x = -4, y = 0; (-4, 0) D) x = 0, y = 4; (0, 4)

Solve the system of equations. 87) 7x + 7y + z = 1 x + 8y + 8z = 8 9x + y + 9z = 9 A) x = 0, y = 1, z = 0; (0, 1, 0) C) x = 0, y = 0, z = 1; (0, 0, 1)

87)

B) x = 1, y = -1, z = 1; (1, -1, 1) D) x = -1, y = 1, z = 1; (-1, 1, 1)

Find the value of the determinant. -2 5 4 88) 3 -2 1 1 6 -3 A) -12

1 4

88)

B) 130

C) 80

D) -90

Find the maximum or minimum value of the given objective function of a linear programming problem. The figure illustrates the graph of feasible points.

89) z = 8x + 9y. Find minimum. A) minimum: 61 B) minimum: 50

C) minimum: 51

D) no minimum

Perform the row operation(s) on the given augmented matrix. 90) (a) R2 = -2r1 + r2

89)

90)

(b) R 3 = -2r1 + r3 (c) R3 = 2r2 + r3 1 -3 -5 2 2 -5 2 5 2 -5 4 6

1 -3 -5 2 A) 0 1 12 1 0 -21 -2 4

1 -3 -5 2 B) 0 1 12 1 0 -9 18 4

1 -3 -5 2 C) 0 1 12 1 0 3 38 4

1 -3 -5 2 D) 0 11 12 1 0 12 26 3

Solve the system of equations using substitution. 91) x2 + y2 = 61

91)

x + y = 11 A) x = 6, y = -5; x = 5, y = -6 or (6, -5), (5, -6) C) x = -6, y = -5; x = -5, y = -6 or (-6, -5), (-5, -6)

B) x = -6, y = 5; x = -5, y = 6 or (-6, 5), (-5, 6) D) x = 6, y = 5; x = 5, y = 6 or (6, 5), (5, 6)

Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. 92) 92) 3x + 5y - 2w =-13 2x + 7z - w = -1 4y + 3z + 3w= 1 -x + 2y + 4z = -5 3 3 3 3 A) x = , y = -2, z = 0, w = ; , -2, 0, 4 4 4 4 B) x = -1, y = -

20 2 20 2 , z = 0, w = ; -1, , 0, 13 5 13 5

C) x = 1, y = -2, z = 0, w = 3; (1, -2, 0, 3) 4 13 5 4 13 5 , z = 0, w = ; , , 0, D) x = , y = 3 20 2 3 20 2

Perform the indicated operation(s), whenever possible. 93) Let A = [6 4] and B = -2 . Find A + B. 9 A) B) 4 [4 13] 13 Perform the indicated operations and simplify. 94) 2 5 -4 1 Let A = 1 0 , B = 0 2 , and C = 2 -1 -1 -5 A)

26 6 2 9 10 12

16 0 9

Find the value of the determinant. 95) 2 0 0 3 9 7 9 5 8 A) -74

93)

D) not defined 6 -2 4 9

94) 5 2 4 . Find BC + 5 . 3 1 -2 0

-14 -10 -16 2 1 0 -10 8 1

21 6 2 4 10 12

16 0 4

-19 -10 -16 2 -4 0 -10 8 -4

95)

B) 214

C) 74

D) 79

Each matrix is nonsingular. Find the inverse of the matrix. Be sure to check your answer. 96) 2 -1 0 -1 1 -2 1 0 -1 1 -2 2 1 -1 2 1 -1 2 1 -1 2 A) 3 -2 -4 B) -2 -1 -4 C) -3 -2 4 D) -3 -2 -4 -1 -1 2 -1 -1 1 -1 1 1 -1 -1 1

96)

Graph the inequality. 97) x - y < -4

97)

Solve the system of equations. If the system has no solution, say that it is inconsistent. 98) x + 3y = 1 -4x - 12y = -4 A) x = 0, y = 0; (0, 0) x 1 B) y = - + , where x is any real number 3 3 or {(x, y) | y = -

x 1 + , where x is any real number} 3 3

C) x = 1, y = 0; (1, 0) D) inconsistent 23

98)

Graph the inequality. 99) 5x + y 2

99)

Solve the system of equations by substitution. 100) 5x + 3y = 80 2x + y = 30 A) x = 10, y = 0; (10, 0) C) x = 10, y = 10; (10, 10)

100)

B) x = 0, y = 10; (0, 10) D) x = 0, y = 0; (0, 10)

Solve the system using the inverse matrix method. 101) -5x + 3y = 8 2x - 4y = -20 A) x = 6, y = 2; (6, 2) C) x = 2, y = 6; (2, 6)

101)

B) x = -2, y = -6; (-2, -6) D) x = -6, y = -2; (-6, -2)

Use the given matrices to compute the given expression. -1 -8 5 -3 6 3 102) Let A = 7 1 9 and B = -4 3 -1 . Find 2A + 4B. 7 -9 3 65 2 -4 3 13 A) -2 4 -4 88 5

-5 -10 13 B) 10 5 17 20 -13 8

102)

-4 -2 8 3 48 13 -4 5

-14 8 22 -2 14 14 38 2 14

Solve the system of equations using substitution. 103) y = (x + 5)2 + 1

103)

2x - y + 10 = 0 A) x = 0, y = 10; x = 0, y = 26 or (0, 10), (0, 26) C) x = -4, y = 2; x = 4, y = 18 or (-4, 2), (4, 18)

104)

B) x = -5, y = 0 or (-5, 0) D) x = -4, y = 2 or (-4, 2)

104)

xy = 1 3x - y = 2

B) x = 1 , y = 1; x = -3, y = -

A) x = -1 , y = 1; x = 3, y = -3 or (-1, 1), (3, -3)

or 1, 1 , -3, -

C) x = 1 , y = 1; x = or 1, 1 , -

1 , y = -3 3

D) x = -

1 , -3 3

Graph the system of inequalities.

1 3

1 1 , y = -3 or - , -3 3 3

105) 2x + y > 2 2x + y < 1

105)

A) No solution

Write the partial fraction decomposition of the rational expression. 3x3 - 4x2 + 7x - 12 106) (x2 + 4)3 A) C)

x2 + 4

3x - 4 -5x + 4 + (x2 + 4)2 (x2 + 4)3

3x + 4 -5x - 4 + 2 (x2 + 4) (x2 + 4)3

3x - 4 -5x + 4 + (x2 + 4)2 (x2 + 4)3

x+1 3x - 4 -5x + 4 + + 2 x2 + 4 (x2 + 4) (x2 + 4)3

106)

Set up the linear programming problem. 107) Mrs. White wants to crochet hats and afghans for a church fundraising bazaar. She needs 6 hours to make a hat and 2 hours to make an afghan, and she has no more than 38 hours available. She has material for no more than 11 items, and she wants to make at least two afghans. Let x = the number of hats she makes and y = the number of afghans she makes. Write a system of inequalities that describes these constraints. A) 6x + 2y 38 B) 2x + 6y 38 C) 6x + 2y 38 D) 6x + 2y 38 x + y 11 x + y 11 x + y 11 x + y 11 y 2 x 2 y 2 x 2 Solve the linear programming problem. 108) Maximize and minimize z = 11x - 18y subject to: x 0, y 0, 4x + 5y 30, 4x + 3y 20, A) maximum: -76.25; minimum: -108 C) maximum: 55; minimum: 0

x 5, y 8. B) maximum: 55; minimum: -108 D) maximum: -108; minimum: 0

107)

108)

Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. 7x - 9y + 6z = -87 109) -35x + 45y - 30z = 435 109) 14x - 18y + 12z = -174 A) x = 14, y = 18, z = 12; (14, 18, 12) B) inconsistent C) x = -6, y = 9, z = 6; (-6, 9, 6) 9 6 87 , y is any real number, z is any real number D) x = y - z 7 7 7 or (x, y, z) | x =

9 6 87 y- z, y is any real number, z is any real number 7 7 7

Solve the system of equations by substitution. 110) 3x + y = 13 2x - 7y = 24 A) x = -5, y = -2; (-5, -2) C) x = -5, y = 2; (-5, 2)

110)

B) x = 5, y = 2; (5, 2) D) x = 5, y = -2; (5, -2)

Solve using elimination. 111) 2x2 + xy - y2 = 3

111)

x2 + 2xy + y2 = 3 2 3 3 2 3 3 ,y=; x=,y= A) x = 3 3 3 3 or

C) x = or

B) x =

2 3 3 2 3 3 ,, , 3 3 3 3

-2 1 2 3 1 ,y= ; x= ,y=3 3 3 3

D) x =

1 -2 1 2 3 , , ,3 3 3 3

-2 1 2 3 1 , y= - ; x = ,y= 3 3 3 3 1 2 3 1 -2 ,- , , 3 3 3 3 2 3 3 2 3 3 ,y= ; x=,y=3 3 3 3 2 3 3 2 3 3 , , ,3 3 3 3

Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. 3x + y = 3 112) 112) 6x + 4y = 0 A) inconsistent B) x = -3, y = -2; (-3, -2) C) x = 2, y = -3; (2, -3) D) x = -3, y = 2; (-3, 2) Determine whether the system corresponding to the given augmented matrix is consistent or inconsistent. If it is consistent, give the solution. 113) 113) 1 0 0 -7 0 1 0 3 0 0 0 1 A) consistent; x = 7, y = -3; (7, -3) B) consistent; x = -7, y = 3, z = 1; (-7, 3, 1) C) consistent; x = -7, y = 3; (-7, 3) D) inconsistent

Solve the problem. 114) The Paperback Trader is a book store that takes in used paperbacks for 20% of their cover price and sells them for 50% of their cover price. Pat brings in a stack of 13 paperback books to trade and gets $13.67 credit. Some of the books had a cover price of $5.95, the rest $4.95. She wants to get some Tom Clancy books having a cover price of $5.95. How many $5.95 books did she bring in and how many Clancy books can she get without paying any additional cash? A) 4 $5.95 books, 4 Clancy books B) 4 $5.95 books, 2 Clancy books C) 4 $5.95 books, 5 Clancy books D) 9 $5.95 books, 2 Clancy books

114)

Find the maximum or minimum value of the given objective function of a linear programming problem. The figure illustrates the graph of feasible points.

115) z = -6x - y. Find maximum. A) maximum: -17 B) maximum: -26

C) maximum: -21

D) no maximum

Solve the problem. 116) A movie theater charges $8.00 for adults and $5.00 for children. If there were 40 people altogether and the theater collected $272.00 at the end of the day, how many of them were adults? A) 29 adults B) 24 adults C) 16 adults D) 10 adults

115)

116)

Perform the row operation(s) on the given augmented matrix. 117) R 3 = 4r1 + r3 -7 -5 -1 -10 6 -2 9 5 28 -6 6 18 -7 -5 -1 -10 A) 6 -2 9 5 0 -26 2 -22 -7 -5 -1 -10 C) 6 -2 9 5 0 16 2 -22

117)

-7 -5 -1 -10 B) 6 -2 9 5 0 16 10 -22 -7 -5 -1 -10 D) 6 -2 9 5 0 -26 10 -22

Solve the system of equations. If the system has no solution, say that it is inconsistent. 118) 3x - 5y = -1 3x - 5y = 8 8 -1 8 -1 ,y= ; , A) x = B) x = 3, y = 5; (3, 5) 5 3 5 3 C) x = -1, y = 8; (-1, 8)

118)

D) inconsistent

Each matrix is nonsingular. Find the inverse of the matrix. Be sure to check your answer. 119) 1 0 0 -8 1 0 0 9 1 A) B) C) D) 1 0 0 1 0 0 1 00 1 9 72 -8 1 0 9 -1 0 8 10 0 1 1 -72 -9 1 72 -8 1 0 0 9 0 0 1

119)

Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. x - y + 3z = 10 120) 5x 120) + z=3 x + 4y + z = -1 A) x = 3, y = 0, z = -1; (3, 0, -1) B) x = 3, y = -1, z = 0; (3, -1, 0) C) x = 0, y = 3, z = -1; (0, 3, -1) D) x = 0, y = -1, z = 3; (0, -1, 3) Solve the system of equations using substitution. 121) y=x- 5 y2 = -20x

121)

A) x = -5, y = -10; x = 5, y = 0 or (-5, -10), (5, 0) B) x = -5, y = -10 or (-5, -10) C) x = -5, y = -10; x = -5, y = 10 or (-5, -10), (-5, 10) D) x = -5, y = -10; x = -5, y = 10; x = 5, y = 0 or (-5, -10), (-5, 10), (5, 0)

Perform the row operation(s) on the given augmented matrix. 122) (a) R2 = -3r1 + r2

122)

(b) R 3 = -2r1 + r3 (c) R3 = 4r2 + r3 1 -3 -5 -2 3 -5 -4 5 2 5 4 6

1 -3 -5 -2 A) 0 14 19 4 0 67 90 26

1 -3 -5 -2 B) 0 -8 -9 3 0 -21 -22 -2

1 -3 -5 -2 C) 0 4 11 11 0 27 58 54

1 -3 -5 -2 D) 0 4 11 11 0 15 25 21

Use the properties of determinants to find the value of the second determinant, given the value of the first. xy z 1 1 -1 123) u v w = -12 -3u -3v -3w = ? 1 1 -1 x- 1 y- 1 z+ 1 A) 12 B) 36 C) -12 D) -36 Write the partial fraction decomposition of the rational expression. 2x2 - 2x + 5 124) (x - 1)3 A)

2 2 5 + x-1 2 (x - 1) (x - 1)3

2 x+2 x2 + 5 + + x-1 (x - 1)2 (x - 1)3

2 2 5 + + x-1 2 (x - 1) (x - 1)3

2 2 + x-1 (x - 1)2

Each matrix is nonsingular. Find the inverse of the matrix. Be sure to check your answer. 125) -5 -1 6 0 5 1 1 1 0 0 0 0 6 6 6 6 A) B) C) D) 1 5 5 5 -1 -1 -1 1 6 6 6 6

123)

124)

125)

Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. x - y + 2z + w = 1 126) y + z = 5 126) z-w =2 A) x = 0 - 4w, y = 3 - w, z = 2 + w, where w is any real number B) x = -4, y = 2, z = 3, w = 1; (-4, 2, 3, 1) C) inconsistent D) x = 0, y = 3, z = 2, w = 0; (0, 3, 2, 0)

Solve the system of equations. If the system has no solution, say that it is inconsistent. 127) 6x - 2y = 2 -24x + 8y = -6 A) x = 6, y = 2; (6, 2) C) x =

B) x = 4, y = 3; (4, 3)

9 3 9 3 ,y=- ;( ,- ) 2 2 2 2

Compute the product. 128) 3 -2 1 30 0 4 -3 -2 1 A) 9 -6 -6 8 3 -5

127)

D) inconsistent

128)

90 04

9 -6 3 -6 8 -5

D) not defined

Verify that the values of the variables listed are solutions of the system of equations. 129) x + y = -2 x-y=8 x = -3, y = -5 A) solution

129)

B) not a solution

Each matrix is nonsingular. Find the inverse of the matrix. Be sure to check your answer. 108 130) 1 2 3 253 9 -40 16 112 -1 -1 2 -1 0 -8 A) 0 2 -5 B) -3 13 -5 C) -1 -2 -3 D) 0 2 5 -1 -2 -5 -3 8 2 3 5 -2 833 Use the given matrices to compute the given expression. 131) Let B = -1 2 5 -3 . Find -3B. A) 3 2 5 -3 B) 3 -6 -15 9

130)

131) C) -3 6 15 -9

D) -3 0 3 -5

Graph the inequality. 132) y + 6 < x

132)

Solve the system of equations. 133) -x + y + 2z = 0 x + 2y + z = 6 -2x - y + z = -6 A) x = z + 2, and y = 2 - z, where z is any real number or {(x, y, z) |x = z + 2, and y = 2 - z, where z is any real number} B) x = z + 2, and y = z - 2, where z is any real number or {(x, y, z) |x = z + 2, and y = z - 2, where z is any real number} C) x = 2 - z, and y = z + 2, where z is any real number or {(x, y, z) |x = 2 - z, and y = z + 2, where z is any real number} D) inconsistent

133)

Solve the linear programming problem. 134) An airline with two types of airplanes, P1 and P2 , has contracted with a tour group to provide

134)

transportation for a minimum of 400 first class, 750 tourist class, and 1500 economy class passengers. For a certain trip, airplane P1 costs $10,000 to operate and can accommodate 20 first

class, 50 tourist class, and 110 economy class passengers. Airplane P2 costs $8500 to operate and can accommodate 18 first class, 30 tourist class, and 44 economy class passengers. How many of each type of airplane should be used in order to minimize the operating cost? A) 11 P1 planes and 7 P2 planes B) 9 P1 planes and 13 P2 planes

C) 5 P1 planes and 17 P2 planes

D) 7 P1 planes and 11 P2 planes

Write the augmented matrix for the system. 135) 8x + 12y - 2z + w = 9 7y + z = 11 x - y - 6z = 4 5x - 5y + 9z = -7 A)

8 0 1 5

12 7 1 5

2 1 6 9

1 9 0 11 0 4 0 -7

8 12 -2 1 9

0 7 1 0 11

1 -1 -6 0 4

9 -5 9 0 -7

135)

8 0 1 5

12 7 -1 -5

-2 1 -6 9

9 6 4 -7

8 0 1 5

12 7 -1 -5

-2 1 -6 9

1 9 0 11 0 4 0 -7

Use a graphing utility to solve the system of equations. Express the solution rounded to two decimal places. 136) 136) 3 2 x +y =2 x2 y = 4 A) x = 2.14, y = -1.37 or (2.14, -1.37) C) x = 1.37, y = 2.14 or (1.37, 2.14)

B) x = 2.14, y = 1.37 or (2.14, 1.37) D) x = -1.37, y = 2.14 or (-1.37, 2.14)

Solve the problem. 137) A rectangular piece of tin has an area of 630 square inches. A square of 5 inches is cut from each corner, and an open box is made by turning up the ends and sides. If the volume of the box is 1,100 cubic inches, what were the original dimensions of the piece of tin? A) 26 in. by 35 in. B) 16 in. by 25 in. C) 21 in. by 30 in. D) 11 in. by 15 in. Perform the row operation(s) on the given augmented matrix. 1 138) R1 = r1 3 3 15 -3 5 1 -3 1 5 -1 5 1 A) -1 3 3

B) 1 5 -1 5 1 -3

138)

Solve the system of equations. 139) x - y + 3z = -5 + z= 0 5x x + 3y + z = 15 A) x = 0, y = 5, z = 0; (0, 5, 0) C) x = 0, y = 0, z = 5; (0, 0, 5)

137)

1 5 -1 6 6 -4

1 5 -3 5 1 -3

139)

B) x = 0, y = 5, z = -5; (0, 5, -5) D) inconsistent

Solve the problem. 140) A flat rectangular piece of aluminum has a perimeter of 58 inches. The length is 5 inches longer than the width. Find the width. A) 12 in. B) 22 in. C) 29 in. D) 17 in.

140)

Encode or decode the given message, as requested, numbering the letters of the alphabet 1 through 26 in their usual order. 1 0 -2 141) Use the coding matrix A = 1 2 3 to encode the message COME_HERE. 141) 11 1 35 5 19 27 -21 -23 -11 -5 -7 -21 3 A) 15 0 18 B) -14 -30 39 C) 72 29 56 D) 28 69 44 13 8 5 8 11 -13 31 13 28 13 33 26 Solve the system of equations using Cramer's Rule if it is applicable. If Cramer's Rule is not applicable, say so. 142) 3x + 3y = 33 142) 2x - 3y = 12 A) x = 9, y = 2; (9, 2) B) x = -9, y = -2; (-9, -2) C) x = 2, y = 9; (2, 9) D) x = -2, y = 9; (-2, 9)

An objective function and a system of linear inequalities representing constraints are given. Graph the system of inequalities representing the constraints. Find the value of the objective function at each corner of the graphed region. Use these values to determine the maximum value of the objective function and the values of x and y for which the maximum occurs. z = 7x + 6y 143) Objective Function 143) Constraints x 0 y 0 3x + y 21 x + y 10 x + 2y 12 A) maximum 60; at (6, 3) B) maximum 65.5; at (5.5, 4.5) C) maximum 68; at (8, 2) D) maximum 66; at (6, 4)

Solve the problem. 144) A person at the top of a 600 foot tall building drops a yellow ball. The height of the yellow ball is given by the equation h = -16t2 + 600 where h is measured in feet and t is the number of seconds

144)

since the yellow ball was dropped. A second person, in the same building but on a lower floor that is 292 feet from the ground, drops a white ball 3.5 seconds after the yellow ball was dropped. The height of the white ball is given by the equation h = -16(t - 3.5)2 + 292 where h is measured in feet and t is the number of seconds since the yellow ball was dropped. Find the time that the balls are the same distance above the ground and find this distance. A) 5 sec; 200 ft B) 4.5 sec; 276 ft C) 3.5 sec; 404 ft D) 4 sec; 344 ft

Graph the system of inequalities. 145) 9x + y 9 9x + y 0

145)

B) No solution

Solve the system of equations. 146) 3x + 5y + z = 11 5x - 3y - z = 27 4x + y + 4z = 23 A) x = 5, y = 1, z = -1; (5, 1, -1) C) x = 1, y = -1, z = 5; (1, -1, 5)

146)

B) x = 5, y = -1, z = 1; (5, -1, 1) D) inconsistent

Solve the problem. 147) An 8-cylinder Crown Victoria gives 18 miles per gallon in city driving and 21 miles per gallon in highway driving. A 300-mile trip required 15.5 gallons of gasoline. How many whole miles were driven in the city? A) 168 mi B) 153 mi C) 147 mi D) 132 mi

147)

Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. -3x - 5y - z = -25 148) 148) x - 6y + 6z = 27 6x + y + z = 26 A) x = 3, y = 6, z = 2; (3, 6, 2) B) x = -3, y = 2, z = 6; (-3, 2, 6) C) inconsistent D) x = 3, y = 2, z = 6; (3, 2, 6) Use the given matrices to compute the given expression. 149) If A = 2 -1 and B = 5 -3 , find -2A + 4B. 7 9 4 7 A) B) 16 -10 -24 -18 -30 -34 2 10

149) C)

D) -3 -6 3 5

7 4 11 13

Write the augmented matrix for the system. 150) 3x +8y +9z = 94 5x +7y +3z = 89 4x +7y -2z = 65 8x +5y +7z = 4 A) B) 3 5 4 5 3 8 9 94 8 7 7 4 5 7 3 89 9 3 -2 5 4 7 -2 65 94 89 65 8 8 5 7 4

150)

3 8 9 4 5 7 3 65 4 7 -2 89 8 5 7 94

3 5 4 8 8 7 7 5 9 3 -2 5 94 89 65 4

Solve the system of equations using Cramer's Rule if it is applicable. If Cramer's Rule is not applicable, say so. 5x - 2y - z = 29 151) x + 6y - 4z = 34 151) 6x + y + z = 54 A) x = 9, y = 3, z = 1; (9, 3, 1) B) x = 5, y = 1, z = 5; (5, 1, 5) C) x = 8, y = 5, z = 1; (8, 5, 1) D) x = 8, y = -5, z = -1; (8, -5, -1) Find the value of the determinant. 2 4 -2 152) 3 3 4 3 -2 -5 A) -64

152) B) 28

C) 124

D) -124

Write the partial fraction decomposition of the rational expression. 3x3 + 4x2 153) (x2 + 5)2

154)

3x - 4 -15x + 20 + x2 + 5 (x2 + 5)2

3x + 4 15x + 20 + x2 + 5 (x2 + 5)2

3x + 4 -15x - 20 + x2 + 5 (x2 + 5)2

3x + 4 15x - 20 + x2 + 5 (x2 + 5)2

153)

154)

x2 + 5x + 6

3 2 + x+3 x+2

3 -2 + x+3 x+2

Graph the system of inequalities.

2 -3 + x+3 x+2

155) 2x + 3y 6 x-y 3

155)

156) y x2 x+y>2

156)

157) x2 + y2 100 y - x2 > 0

157)

Solve the system of equations by substitution. 158) 3x + 2y = -6 = -12 3x A) x = -4, y = 3; (-4, 3) C) x = 3, y = -4; (3, -4)

158)

B) x = -3, y = 0; (-4, 0) D) x = -4, y = -3; (-4, -3)

Solve the problem. 159) State University has a College of Arts & Sciences, a College of Business, and a College of Engineering. The 159) percentage of students in each category are given by the following matrix.

Arts & Sciences Business Engineering

Freshman 60% 20% 20%

Sophomore Junior 50% 40% 70% 40% 30% 10% 10% 30% 20%

Senior

The student population is distributed by class and age as given in the following matrix.

Freshman Sophomore Junior Senior

Female 440 550 890 630

Male 770 750 680 480

How many female students are in the College of Business? How many male students are in the College of Arts & Sciences? A) 706 students; 529 students B) 536 students; 706 students C) 1,336 students; 638 students D) 638 students; 1,445 students

Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. 160) 160) x+ y+ z- w= 6 2x - y + 3z + 4w = -4 4x + 2y - z - w = -13 -x - 2y + 4z + 3w = 12 1 1 1 1 1 1 1 1 A) x = - , y = , z = , w = - ; - , , , 4 3 5 2 4 3 5 2 B) x = -4, y = 3, z = 5, w = -2; (-4, 3, 5, -2) C) x = 4, y = -3, z = -5, w = 2; (4, -3, -5, 2) 1 1 1 1 1 1 1 1 D) x = , y = - , z = - , w = ; , - , - , 4 3 5 2 4 3 5 2

Write a system of linear inequalities that has the given graph. 161)

x 8 y 8 x+y 3

y x x y x+y

161)

0 0 8 8 3

y x y x+y

0 0 8 3

y x x x+y

Each matrix is nonsingular. Find the inverse of the matrix. Be sure to check your answer. 162) -6 -1 6 0 A) B) C) D) 1 1 1 -1-1 0 0 -1 6 6 6 1 0 6 1 -1 -1-1 -1 0 Solve the system of equations. 163) x-y+z=0 x+y+z=4 x + y - z = -4 A) x = -2, y = 2, z = 4; (-2, 2, 4) C) x = -2, y = 4, z = 2; (-2, 4, 2)

0 0 8 3

162)

163)

B) x = 2, y = 4, z = -2; (2, 4, -2) D) inconsistent

Perform the indicated operation(s), whenever possible. 164) Let A = -5 5 , B = -6 -9 and C = 1 -7 . Find A + B - C. -7 -6 -4 -2 -1 -6 A) B) C) 2 7 0 21 -10 -11 -12 -14 -4 -10 -2 2 Graph the inequality.

164)

-12 3 -10 -2

165) x > -8

165)

Solve the system of equations using substitution. 166) -2x - y = -56 y = x2 + 8

166)

A) x = 8, y = 72; x = -6, y = 44 or (8, 72), (-6, 44) C) x = -8, y = 72; x = 6, y = 44 or (-8, 72), (6, 44)

B) x = -8, y = 56; x = 6, y = 28 or (-8, 56), (6, 28) D) x = 8, y = 72; x = 6, y = 44 or (8, 72), (6, 44)

Perform the indicated operation(s), whenever possible. 167) 7 -8 5 2 8 1 Let A = 14 -10 -1 and B = 5 0 -4 . Find A - B. -6 7 -6 5 6 3 A) B) C) 5 0 4 5 16 4 5 -16 4 9 -10 3 9 -10 3 9 -10 3 1 -1 -3 11 1 9 11 -1 9 Write the augmented matrix for the system. 168) = 0 3x - y -3x + y - 6 = 0 A) B) 3 -1 0 3 -3 -3 1 - 6 -1 1

167)

9 0 6 19 -10 -5 -1 13 -3

168)

0 6

3 -3 -1 1

6 0

3 -1 -3 1

0 6

Solve the system of equations using Cramer's Rule if it is applicable. If Cramer's Rule is not applicable, say so. 8 4x + 2y = 7 169) 7x - 7y = 7 A) not applicable C) x = -

169)

11 32 11 32 ,y= ; , B) x = 21 21 21 21

11 10 11 10 ,y=; ,21 21 21 21

D) x =

11 10 11 10 ,y=; ,21 21 21 21

Write a system of linear inequalities that has the given graph. 170)

x 4 y+ x 9

y x x y+ x

170)

0 0 9 4

y x x y+ x

0 0 4 9

y 0 x 0 x 4 y+ x 9

Graph the inequality. 171) x2 + y2 > 49

171)

Solve the problem. 172) A right triangle has an area of 16 square inches. The square of the hypotenuse is 80. Find the lengths of the legs of the triangle. Round your answer to the nearest inch. A) 16 in. and 64 in. B) 4 in. and 8 in. C) 8 in. and 4 in. D) 2 in. and 16 in.

172)

Write the partial fraction decomposition of the rational expression. 7x3 - 2 173) x2 (x + 1)3 A)

6 2 6 3 9 + + + x x2 x + 1 (x + 1)2 (x + 1)3

6 2 6 3 9 + x x2 x + 1 (x + 1)2 (x + 1)3

6 6 3 9 + x x + 1 (x + 1)2 (x + 1)3

2 6 3 9 + 2 x 1 2 + x (x + 1) (x + 1)3

Use the properties of determinants to find the value of the second determinant, given the value of the first. xy z x+ 2 y+ 4 z- 6 174) u v w = 18 2u - 1 2v - 2 2w + 3 = ? -3 1 2 -3 1 2 A) 36 B) -36 C) 18 D) -18

173)

174)

Graph the inequality. 175) y x - 6

175)

Solve the system of equations. 176) 4x + 4y + z = 10 4x - 5y - z = -21 4x + y + 4z = 7 A) x = -1, y = 2, z = 3; (-1, 2, 3) C) x = 2, y = 3, z = -1; (2, 3, -1)

176)

B) x = -1, y = 3, z = 2; (-1, 3, 2) D) inconsistent

Graph the inequality. 177) -2x - 3y -6

177)

Perform the row operation(s) on the given augmented matrix. 178) R2 = 3r1 + r2 1 7 10 -3 9 -2 A) 3 21 30 0 30 28

7 10 B) 1 0 -12 -32

178)

Graph the system of inequalities.

3 21 30 -3 9 -2

D) 1 7 10 0 30 28

179) -x + 5y < 15 x 4

179)

Solve the system of equations using substitution. 180) x2 + y2 = 61

180)

x - y = 1 A) x = -6, y = 5; x = -5, y = 6 or (-6, 5), (-5, 6) C) x = 6, y = -5; x = 5, y = -6 or (6, -5), (5, -6)

B) x = 6, y = 5; x = -5, y = -6 or (6, 5), (-5, -6) D) x = -6, y = -5; x = -5, y = -6 or (-6, -5), (-5, -6)

Solve the linear programming problem. 181) A candy company has 125 pounds of cashews and 155 pounds of peanuts which they combine into two different mixes. The deluxe mix has half cashews and half peanuts and sells for $6 per pound. The economy mix has one third cashews and two thirds peanuts and sells for $5.70 per pound. How many pounds of each mix should be prepared for maximum revenue? A) 95 deluxe, 30 economy B) 285 deluxe, 60 economy C) 125 deluxe, 0 economy D) 190 deluxe, 90 economy Solve the problem. 182) A tour group split into two groups when waiting in line for food at a fast food counter. The first group bought 8 slices of pizza and 5 soft drinks for $38.89. The second group bought 5 slices of pizza and 4 soft drinks for $25.61. How much does one slice of pizza cost? A) $1.99 per slice of pizza B) $3.43 per slice of pizza C) $3.93 per slice of pizza D) $1.49 per slice of pizza Graph the inequality. 183) xy 7

181)

182)

183)

Each matrix is nonsingular. Find the inverse of the matrix. Be sure to check your answer. 184) 2 1 1 -5 A) B) C) D) 5 1 5 1 2 1 11 11 11 11 11 11 1 2 11 11

1 11

2 11

1 5 11 11

184)

5 1 11 11 1 11

2 11

Write the partial fraction decomposition of the rational expression. 2x - 5 185) x2 - 5x - 6 A)

17 3 x+6 x-1

1 1 + x-6 x+1

Solve the system of equations by substitution. 186) x+ y=0 2x + 3y = -7 A) x = 7, y = -7; (7, -7) C) x = -6, y = 6; (-6, 6)

9 1 + x+2 x-3

185) D)

1 1 + x-3 x-2

186)

B) x = 6, y = -6; (6, -6) D) x = -7, y = 7; (-7, 7)

Solve the linear programming problem. 187) A doctor has told a patient to take vitamin pills. The patient needs at least 12 units of vitamin A and at least 8 units of vitamin D. The red vitamin pills cost 20¢ each and contain 3 units of A and 1 unit of D. The blue vitamin pills cost 35¢ each and contain 2 units of A and 2 units of D. To avoid indigestion, the patient should take no more than 6 red pills and no more than 9 blue pills. How many pills should the patient take each day to minimize costs? A) 6 red and 1 blue B) 0 red and 9 blue C) 6 red and 9 blue D) 2 red and 3 blue

187)

Solve the system of equations. 188) x + y + z = -8 x - y + 3z = -2 3x + y + z = -14 A) x = -1, y = -4, z = -3; (-1, -4, -3) C) x = -1, y = -3, z = -4; (-1, -3, -4)

188)

B) x = -3, y = -4, z = -1; (-3, -4, -1) D) inconsistent

Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. x-y=1 189) x + y = 4 189) 5 3 5 3 A) x = , y = ; , B) x = 5, y = 3; 5, 3 2 2 2 2 D) x = -

C) inconsistent

Solve the system of equations by elimination. 190) x + y = -1 x - y = 13 A) x = 6, y = -7; (6, -7) C) x = 1, y = -7; (1, -7)

3 11 3 11 ,y= ; - , 2 2 2 2

190)

B) x = 1, y = 6; (1, 6) D) x = 6, y = 7; (6, 7)

Graph the system of inequalities. 191) 4x + 3y 12 x y

191)

Determine whether the system corresponding to the given augmented matrix is consistent or inconsistent. If it is consistent, give the solution. 192) 192) 1 4 5 12 0 35 5 0 0 1 -2 A) consistent; x = 2, y = -2, z = 5; (2, -2, 5) B) consistent; x = -2, y = 5, z = 2; (-2, 5, 2) C) consistent; x = 2, y = 5, z = -2; (2, 5, -2) D) inconsistent

Write the partial fraction decomposition of the rational expression. 3x + 6 193) (x - 8)2 A)

1 x + 30 + x-8 (x - 8)2

3 30 + x-8 (x - 8)2

3 x + 30 + x-8 (x - 8)2

3 48 + x-8 (x - 8)2

Graph the system of inequalities.

193)

194) x2 + y2 36 -6x + 4y -24

194)

Perform the indicated operation(s), whenever possible. 195) 5 -8 0 0 8 3 Let A = 10 -10 -3 and B = 5 0 -4 . Find A + B. -6 6 -3 5 3 9 A) B) C) 15 16 3 5 03 15 16 3 15 -10 1 5 -10 1 5 -10 -7 -1 9 6 1 96 1 96

195)

5 0 3 15 -10 -7 -1 9 6

Compute the product. 196) 2 -8 -3 2 1 6 1 -1 0 1 6 1 A) -24 10 4 9 -5 12 2 -1 1

196)

4 10 -24 12 -5 9 1 -1 2

Solve the system using the inverse matrix method. 197) x + 3y = -8 21x + 6y = 3 A) x = -3, y = 1; (-3, 1) C) x = -1, y = 3; (-1, 3)

9 -1 4 -24 -5 1 2 10 12

D) not defined

197)

B) x = 1, y = -3; (1, -3) D) x = 3, y = -1; (3, -1)

Write the partial fraction decomposition of the rational expression. 3x - 2 198) x3 - 1 A)

1 3 x-1 3

(x - 1)2

1 7 x+ 3 3

(x2 + x + 1)

(x - 1)3

Solve the system of equations by elimination. 199) 5x + 3y = 80 2x + y = 30 A) x = 0, y = 10; (0, 10) C) x = 0, y = 0; (0, 0) Compute the product. 200) 1 2 0 -3 1 0 1 5 -1 0 1 -1 A) 1 5 -4 9

198)

3 x-1 1 2 x-1

-3(x - 7)

x2 + x + 1 5 2 x+1

199)

B) x = 10, y = 10; (10, 10) D) x = 10, y = 0; (10, 0)

200)

1 -4 5 9

0 10 0 -1 0 0

10 -5 1 5 -1 0 -5 -2 0

An objective function and a system of linear inequalities representing constraints are given. Graph the system of inequalities representing the constraints. Find the value of the objective function at each corner of the graphed region. Use these values to determine the maximum value of the objective function and the values of x and y for which the maximum occurs. z = 9x + 9y 201) Objective Function 201) Constraints x 0 0 y 5 2x + 3y 12 2x + 3y 20 A) maximum: 63; at (2, 5) B) maximum: 54; at (6, 0) C) maximum: -36; at (4, 0) D) maximum: 90; at (10, 0)

Write the partial fraction decomposition of the rational expression. 3x2 - x - 10 202) x(x + 1)(x - 1) A)

10 3 -4 + + x x+1 x-1

10 -3 -4 + + x x+1 x-1

10 4 -3 + + x x+1 x-1

10 3 -4 + + x x+1 x-1

202)

Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. 5x + y =2 203) -4x - y + z - w = 3 203) z +w=8 A) x = - 3 - 2w, y = 17 + 10w, z = 8 - w, where w is any real number B) inconsistent C) x = - 3 + 2w, y = 17 - 10w, z = 8 - w, where w is any real number D) x = 17 - 10w, y = - 3 + 2w, z = 8 - w, where w is any real number Graph the system of linear inequalities. Tell whether the graph is bounded or unbounded, and label the corner points. 204) 204) x 0 y 0 x+y 4 x + 2y 8

A) bounded; corner points (0, 0), (0, 4), (4, 0)

B) bounded; corner points (4, 0), (0, 4), (8, 0)

C) unbounded; corner points (0, 4), (8, 0)

D) unbounded; corner points (0, 4), (4, 0)

x2 + y2 = 25 2y + x = 5 A) No

B) Yes

206)

x2 = y -1 y = -3x + 5

A) Yes

B) No

Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. 207) 6x - 8y = -6 207) -6x + 8y = -9 A) x =6, y =6; (6, 6) B) inconsistent C) x =6, y =-9; (6, -9) D) x =-6, y =-9; (-6, -9)

Compute the product. 208)

208) -9 6 8

-9 -5 -3 -5 4 1

-9 -5 -3 -5 4 1 -9 6 8

C) 27 77

D) not defined

27 77

Solve the system of equations by substitution. 209) 1 2 x + y = 32 2 3

209)

1 5 x - y = 40 4 9

A) x = 100, y = -27; (100, -27) C) x = -100, y = 27; (-100, 27)

B) x = 100, y = 27; (100, 27) D) x = -100, y = -27; (-100, -27)

Use the properties of determinants to find the value of the second determinant, given the value of the first. xy z u vw 210) u v w = 26 -2 -6 4 = ? 1 3 -2 x y z A) 26 B) -26 C) -52 D) 52 Each matrix is nonsingular. Find the inverse of the matrix. Be sure to check your answer. 1 3 2 211) 1 3 3 2 7 8 1 1 1 1 1 1 3 2 3 2 A) 1

1 3

1 B) 1 - 3

1 3

1 2

1 7

1 8

1 7

1 8

1 2

-1 -3 -2 C) -1 -3 -3 -2 -7 -8

210)

211)

-3 10 -3 2 -4 1 -1 1 0

Solve the system of equations using Cramer's Rule if it is applicable. If Cramer's Rule is not applicable, say so. x + 2y = 10 1 x - y = -12 212) 212) 4 68 53 68 53 ,y= ; , 3 3 3 3

A) x = - 28, y = 5; - 28, 5

B) x =

C) not applicable

D) x = -

Graph the system of inequalities.

28 29 28 29 ,y= ; , 3 3 3 3

213) 2x + 3y 6 x-y 3 y 2

213)

Solve the problem. 214) A retired couple has $160,000 to invest to obtain annual income. They want some of it invested in safe Certificates of Deposit yielding 6%. The rest they want to invest in AA bonds yielding 11% per year. How much should they invest in each to realize exactly $15,100 per year? A) $100,000 at 6% and $60,000 at 11% B) $110,000 at 11% and $50,000 at 6% C) $110,000 at 6% and $50,000 at 11% D) $120,000 at 11% and $40,000 at 6% 60

214)

Verify that the values of the variables listed are solutions of the system of equations. 215) x+ y+ z=1 x - y + 4z = 14 5x + y + z = -19 x = 5, y = 1, z = -5 A) solution

B) not a solution

Each matrix is nonsingular. Find the inverse of the matrix. Be sure to check your answer. 216) 4 2 5 -2 A) B) C) D) 5 2 2 1 1 1 18 9 9 9 9 9 1 9

1 9

215)

5 1 18 9

5 2 18 9

216)

1 9

5 2 18 9

Solve the problem. 217) The sum of the squares of two numbers is 85. The difference of the two numbers is -11. Find the two numbers. A) -9 and -2 or 2 and 9 B) -9 and 2 C) -9 and 2 or -2 and 9 D) -2 and 9 Graph the system of inequalities. 218) 2x + 3y 6 x-y 3 x 1

217)

218)

Solve the system of equations using substitution. 219) x2 + y2 = 169

219)

x + y = 17 A) x = -12, y = -5; x = -5, y = -12 or (-12, -5), (-5, -12) C) x = -12, y = 5; x = -5, y = 12 or (-12, 5), (-5, 12)

B) x = 12, y = -5; x = 5, y = -12 or (12, -5), (5, -12) D) x = 12, y = 5; x = 5, y = 12 or (12, 5), (5, 12)

Solve the system of equations using Cramer's Rule if it is applicable. If Cramer's Rule is not applicable, say so. 5x - 3y + 7z = 38 220) -9x + 4y - 6z = -48 220) -8x - 3y - 3z = -90 A) x = 6, y = 9, z = 5; (6, 9, 5) B) x = 9, y = 5, z = 9; (9, 5, 9) C) x = 7, y = 7, z = 5; (7, 7, 5) D) x = 6, y = -9, z = -5; (6, -9, -5)

Set up the linear programming problem. 221) A dietitian needs to purchase food for patients. She can purchase an ounce of chicken for $0.25 and an 221) ounce of potatoes for $0.02. The dietician is bound by the following constraints. · Each ounce of chicken contains 13 grams of protein and 24 grams of carbohydrates. · Each ounce of potatoes contains 5 grams of protein and 35 grams of carbohydrates. · The minimum daily requirements for the patients under the dietitian's care are 45 grams of protein and 58 grams of carbohydrates. Let x = the number of ounces of chicken and y = the number of ounces of potatoes purchased per patient. Write a system of inequalities that describes these constraints. A) B) 13x + 5y 45 13x + 5y 58 24x + 35y 58 24x + 35y 45 C) D) 13x + 24x 45 13x + 24y 45 5y + 35y 58 5x + 35y 58 Use a graphing utility to solve the system of equations. Express the solution rounded to two decimal places. 222) 222) 3 2 3x + y = 6 x4y = 2

A) x = 1.18, y = 1.03; x = 1.07, y = 1.52; x = -0.91, y = 2.88 or (1.18, 1.03), (1.07, 1.52), (-0.91,2.88) B) x = 1.81, y = 0.28; x = 0.20, y = 2.45; x = -0.20, y = -2.45 or (1.81, 0.28), (0.20, 2.45), (-0.20, -2.45) C) x = 1.99, y = 0.13; x = 1.04, y = 1.70; x = -0.91, y = 2.95 or (1.99, 0.13), (1.04, 1.70), (-0.91, 2.95) D) No real solution exists. Graph the system of inequalities. 223) x2 + y2 25

223)

x+y>1

Each matrix is nonsingular. Find the inverse of the matrix. Be sure to check your answer. 224) -5 a -7 a a 1 a 7 a 1 2 2 2 2 2 2 A) 7 a B) a C) D) 5 7 a 2 2 2 2 2 2 Graph the system of inequalities. 225) 2x + 3y 6 x- y 3 y 2

224)

a a 2 2 7 5 2 2

225)

226) x2 + y2 81 -3x + 5y -15

226)

227) 2x + 3y 6 x-y 3 x 1

227)

Write a system of linear inequalities that has the given graph. 228)

y x y y+ x

0 0 2 8

228)

y 2 y x y+ x 8

x y y y+ x

0 2 x 8

y x y y y+ x

0 0 2 x 8

Set up the linear programming problem. 229) A steel company produces two types of machine dies, part A and part B. The company makes a $2.00 profit on each part A that it produces and a $6.00 profit on each part B that it produces. Let x = the number of part A produced in a week and y = the number of part B produced in a week. Write the objective function that describes the total weekly profit. A) z = 6x + 2y B) z = 8(x + y) C) z = 2x + 6y D) z =2(x - 6) + 6(y - 2) Write the partial fraction decomposition of the rational expression. 4x2 + 2x - 24 230) x(x + 4)(x + 2) A)

3 4 -3 + + x x+4 x+2

4 3 -3 + + x x+4 x+2

5 2 -3 + + x x+4 x+2

x+4 3 + 2 x +2 x +4

Graph the system of inequalities. 231) x + 2y 2 x-y 0

229)

230)

231)

Graph the inequality. 232) y -2x + 1

232)

Solve the problem. 233) Find the dimensions of a rectangle whose perimeter is 42 feet and whose area is 90 square feet. A) 5 ft by 16 ft B) 5 ft by 14 ft C) 7 ft by 14 ft D) 6 ft by 15 ft Solve the system using the inverse matrix method. 234) -3x + 9y = 9 3x + 2y = 13 A) x = -3, y = -2; (-3, -2) C) x = -2, y = -3; (-2, -3)

233)

234)

B) x = 3, y = 2; (3, 2) D) x = 2, y = 3; (2, 3)

Solve the problem. 235) The area of a garden is 1,080 square feet, and the length of its diagonal is 51 feet. Find the dimensions of the garden. A) 72 ft by 15 ft B) 24 ft by 45 ft C) 120 ft by 9 ft D) 8 ft by 135 ft

235)

Solve the system of equations using Cramer's Rule if it is applicable. If Cramer's Rule is not applicable, say so. 236) 236) x - y + 5z = 1 + z =0 4x -x + y - 5z = -4 A) not applicable B) x = 5, y = -1, z = 0; (5, -1, 0) C) x = 0, y = -1, z = 0; (0, -1, 0) D) x = 0, y = 0, z = -1; (0, 0, -1)

Graph the inequality. 237) 3x + 4y 12

237)

Find the maximum or minimum value of the given objective function of a linear programming problem. The figure illustrates the graph of feasible points.

238) z = x + 5y + 8. Find minimum. A) minimum: 27 B) minimum: 35

C) minimum: 22

D) no minimum

238)

Write the partial fraction decomposition of the rational expression. 12x2 + 162x + 384 239) (x + 8)(x + 2)(x + 11) A) C)

8 2 2 + + x + 8 x + 2 x + 11

B) -

8 2 2 + + x + 8 x + 2 x + 11

239) 8 2 2 x + 8 x + 2 x + 11

8 2 2 + x + 8 x + 2 x + 11

Use a graphing utility to find the inverse, if it exists, of the matrix. Round answers to two decimal places. 240) 3 28 -16 5 -14 15 34 25 2 A) B) 0.03 0.02 0.02 0.01 -0.02 -0.01 0.02 -0.04 0.01 0.02 -0.03 0.01 0.02 0.02 0.00 0.02 0.02 0.01 C) D) 0.03 0.02 0.03 0.02 -0.02 -0.01 0.02 -0.04 0.02 0.02 -0.03 0.01 0.02 0.02 0.01 0.02 0.02 0.01 Solve for x. 241)

5 -3 1 -2 -2 x = 28 8 2 -1 A) 2

240)

241)

B) -1

C) 0

D) 1

Graph the inequality. 242) -2x - 5y 10

242)

Solve using elimination. 243) 4x2 - 4y2 = 84

243)

3x2 + 2y2 = 83 A) x = 5, y = -2; x = 5, y = 2 or (5, -2), (5, 2) B) x = 5, y = 2; x = -5, y = 2 ; x = 5, y = -2; x = -5, y = -2 or (5, 2), (-5, 2), (5, -2), (-5, -2) C) x = -5, y = -2; x = -2, y = -5 or (-5, -2), (-2, -5) D) x = 5, y = 2; x = 2, y = 5; x = -5, y = -2; x = -2, y = -5 or (5, 2), (2, 5), (-5, -2), (-2, -5)

244)

3x2 + 2y2 = 89

x2 - 2y2 = -21 A) x = - 17, y = 19; x = - 17, y = - 19 or (- 17, 19), (- 17, - 19) B) x = 17, y = 19; x = , 17, y = - 19 ; or ( 17, 19), ( 17, - 19) C) x = 19, y = 17; x = - 19, y = 17; x = , 19, y = - 17 ; x = or ( 17, 19), (- 17, 19), ( 17, - 19), (- 17, - 19) D) x = 17, y = 19; x = - 17, y = 19; x = , 17, y = - 19 ; x = or ( 17, 19), (- 17, 19), ( 17, - 19), (- 17, - 19)

Use the given matrices to compute the given expression. 245) Let A = 3 3 and B = 0 4 . Find 4A + B. 26 -1 6 A) B) 12 16 12 7 1 12 7 12

19, y = -

17, y = -

245) C)

12 28 4 48

12 16 7 30

Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. 246) 246) x + y - z + w = -5 3x - y + 3z - 2w = 7 -2x + 2y + z - w = 16 -x - 2y - 3z + 3w = -22 1 1 1 1 1 1 1 1 A) x = , y = - , z = - , w = - ; , - , - , 2 3 4 2 2 3 4 2 B) x = -2, y = -3, z = 5, w =

1 1 ; -2, -3, 5, 2 2

C) x = 2, y = -3, z = -4, w = -2; (2, -3, -4, -2) D) x = -2, y = 3, z = 4, w = -2; (-2, 3, 4, -2) Solve the problem. 247) The equation of the line passing through the distinct points (x1 , y1 ) and (x2 , y2 ) is given by

247)

x y 1 x1 y1 1 = 0. Find the equation of the line passing through the points (3, 5) and (-1, 4). x2 y2 1

A) x + 4y + 17 = 0

B) -x + 4y - 17 = 0

C) x + 7y + 17 = 0

D) x - 4y + 17 = 0

Perform the indicated operations and simplify. 248) 0 -1 -6 0 Let A = 2 0 , B = 1 1 , and C = -3 1 2 . Find C(A - B). 0 -3 -1 3 6 3 2 A) 20 11 3 -7

3 -7 20 11

C) -17 10 -3 -1

248)

D) -22 3 12 -3

Solve the system of equations using substitution. 249) xy = 72 x + y = 17 A) x = 9, y = 8; x = 8, y = 9 or (9, 8), (8, 9) C) x = 9, y = -8; x = 8, y = -9 or (9, -8), (8, -9)

249)

B) x = -9, y = -8; x = -8, y = -9 or (-9, -8), (-8, -9) D) x = -9, y = 8; x = -8, y = 9 or (-9, 8), (-8, 9)

Verify that the values of the variables listed are solutions of the system of equations. 250) x+y=1 x - y = -11 x = -5, y = 6 A) solution

250)

B) not a solution

Solve the system of equations using Cramer's Rule if it is applicable. If Cramer's Rule is not applicable, say so. 251) 4x - 7y = 5 251) 2x + 5y = -3 2 11 2 11 ,y= ; , 17 17 17 17

B) x =

23 11 23 11 ,y=; ,3 3 3 3

2 11 2 11 ,y=; ,17 17 17 17

D) x =

2 1 2 1 ,y= ; , 3 3 3 3

A) x = C) x =

Solve the system of equations. 252) x + 2y + 4z = 14 2y + 4z = 10 z=3 A) x = 4, y = -1, z = 3; (4, -1, 3) C) x = 4, y = 3, z = -1; (4, 3, -1)

252)

B) x = 3, y = -1, z = 4; (3, -1, 4) D) inconsistent

Verify that the values of the variables listed are solutions of the system of equations. 253) x - y + 4z = -8 4x + z = -3 x + 4y + z = -19 x = 0, y = -4, z = -3 A) solution

B) not a solution

253)

Solve the system using the inverse matrix method. 254) x + 2y + 3z = -7 x+y+z = 6 x - 2z = -3

254)

12 3 -2 4 -1 The inverse of 1 1 1 is 3 -5 2 . -1 2 -1 1 0 -2

A) x = 41, y = -57, z = 22; (41, -57, 22) C) x = 35, y = -64, z = 22; (35, -64, 22)

B) x = -7, y = 0, z = 0; (-7, 0, 0) D) x = 7, y = 3, z = 2; (7, 3, 2)

Graph the inequality. 255) y -4

255)

Perform the indicated operation(s), whenever possible. 256) 72 -1 4 Let A = 0 4 and B = 17 4 . Find A - B. 9 -4 42 A) B) 3 -3 -8 2 -17 0 7 0 -5 6 5 -6

256)

1 5 7 8 13 0

1 2 7 0 5 -2

Solve the system of equations using substitution. 257) xy = 20 x+y= 9 A) x = 10, y = 2; x = 2, y =10 or (10, 2), (2, 10) C) x = 6, y = 3; x = 3, y = 6 or (6, 3), (3, 6)

257)

B) x = 20, y = 1; x = 1, y = 20 or (20, 1), (1, 20) D) x = 5, y = 4; x = 4, y = 5 or (5, 4), (4, 5)

Encode or decode the given message, as requested, numbering the letters of the alphabet 1 through 26 in their usual order. 258) Use the coding matrix A = 1 -4 and its inverse A-1 = 9 4 to decode the cryptogram -7 -8 . 258) 21 16 21 -2 9 A) ABLE B) ALAS C) ACTS D) ARMS Write the partial fraction decomposition of the rational expression. x 259) (x - 2)(x - 3) A)

2 -3 + x-2 x-3

3 -2 + x-2 x-3

259)

-2 -3 + x-2 x-3

2 -3 + x-2 x-3

Compute the product. 260) 1 3 -3 30 4

30 -3 1 04

3 -9 0 0 0 16

260)

C) -6 -9 9 16

D) not defined -9 -6 16 9

Write the augmented matrix for the system. 6x +9z = -6 261) 4y -2z = 16 2x +8y +6z = 16 6 0 9 -6 A) 0 4 -2 16 2 8 6 16

261)

6 9 0 -6 B) 4 -2 0 16 2 8 6 16

60 9 C) 0 4 -2 28 6

6 0 2 -6 D) 0 4 8 16 9 -2 6 16

Solve the linear programming problem. 262) A vineyard produces two special wines, a white and a red. A bottle of the white wine requires 14 pounds of grapes and 1 hour of processing time. A bottle of red wine requires 25 pounds of grapes and 2 hours of processing time. The vineyard has on hand 2,198 pounds of grapes and can allot 160 hours of processing time to the production of these wines. A bottle of the white wine sells for $11.00, while a bottle of the red wine sells for $20.00. How many bottles of each type should the vineyard produce in order to maximize gross sales? A) 42 bottles of white and 59 bottles of red B) 132 bottles of white and 14 bottles of red C) 14 bottles of white and 132 bottles of red D) 76 bottles of white and 42 bottles of red

262)

Solve the system of equations by substitution. 263) x + 5y = 5 5x - 7y = -7 A) x = 0, y = 1; (0, 1) C) x = 1, y = 0; (1, 0)

263)

B) x = 0, y = 0; (0, 0) D) x = 1, y = 1; (1, 1)

Solve the linear programming problem. 264) Minimize z = 19x + 13y + 21 subject to: x 0, y 0, x + y 1. A) minimum: 40 B) minimum: 34

264) C) minimum: 21

D) minimum: 53

Compute the product. 265)

7 5 1 [1 -6 -6] -3 -2 6 -6 2 -6 A) 7 -30 -6 -3 12 -36 -6 -12 36

265)

1 -6 -6 7 5 1 -3 -2 6 -6 2 -6

61 5 1

D) 61 5 1

Write the partial fraction decomposition of the rational expression. 5x3 + 18x - 3 266) (x2 + 3)2 A)

5x 3x + 3 + x2 + 3 (x2 + 3)2

5x + 1 3x - 3 + x2 + 3 (x2 + 3)2

5x 3x - 3 + x2 + 3 (x2 + 3)2

5x -3x - 3 + x2 + 3 (x2 + 3)2

Solve the problem using matrices. 267) Ron attends a cocktail party (with his graphing calculator in his pocket). He wants to limit his food intake to 122 g protein, 118 g fat, and 159 g carbohydrate. According to the health conscious hostess, the marinated mushroom caps have 3 g protein, 5 g fat, and 9 g carbohydrate; the spicy meatballs have 14 g protein, 7 g fat, and 15 g carbohydrate; and the deviled eggs have 13 g protein, 15 g fat, and 6 g carbohydrate. How many of each snack can he eat to obtain his goal? A) 4 mushrooms, 3 meatballs, 9 eggs B) 9 mushrooms, 4 meatballs, 3 eggs C) 3 mushrooms, 9 meatballs, 4 eggs D) 10 mushrooms, 5 meatballs, 4 eggs Each matrix is nonsingular. Find the inverse of the matrix. Be sure to check your answer. 100 268) -1 1 0 111 1 -1 1 1 0 0 111 -1 0 0 A) 0 1 -1 B) 1 1 0 C) 0 1 1 D) -1 -1 0 -2 -1 1 -1 -1 -1 0 0 1 001

266)

267)

268)

Use the given matrices to compute the given expression. 269) Let A = -1 2 and B = 1 0 . Find 3A + 4B. A) -3 4 B) 1 6

269) C) -1 4

D) 2 2

Solve the system of equations by substitution. 270) 1 4 x- y=5 5

270)

x + 8y = -4 A) x = 0, y = 4; (0, 4) C) x = 0, y = -4; (0, -4)

B) x = -4, y = 0; (-4, 0) D) x = 4, y = 0; (4, 0)

Use the properties of determinants to find the value of the second determinant, given the value of the first. x y z x y z-x 271) u v w = 31 u v w-u =? 1 -1 3 1 -1 2 A) 0 B) -31 C) 31 D) Cannot determine

271)

Determine whether the system corresponding to the given augmented matrix is consistent or inconsistent. If it is consistent, give the solution. 272) 272) 1 0 -4 6 0 1 8 -2 000 0 A) consistent; x = 6, y = -2, z = -4; (6, -2, -4) B) consistent; x = 6 + 4z, y = -2 - 8z, z any real number or {(x, y, z)|x = 6 + 4z, y = -2 - 8z, z any real number} C) consistent; x = 6 - 4z, y = -2 + 8z, z any real number or {(x, y, z)|x = 6 - 4z, y = -2 + 8z, z any real number} D) inconsistent

Solve the problem. 273) A person with no more than $7,000 to invest plans to place the money in two investments, telecommunications and pharmaceuticals. The telecommunications investment is to be no more than 3 times the pharmaceuticals investment. Write a system of inequalities to describe the situation. Let x = amount to be invested in telecommunications and y = amount to be invested in pharmaceuticals. A) x + y 7,000 B) x + y = 7,000 C) x + y 7,000 D) x + y = 7,000 x 3y y 3x 3x y x 3y x 0 x 0 x 0 x 0 y 0 y 0 y 0 y 0

273)

Solve the system of equations using Cramer's Rule if it is applicable. If Cramer's Rule is not applicable, say so. 2x + 3y = 27 274) 274) 4x + 5y = 49 A) x = -6, y = -5; (-6, -5) B) x = -5, y = 6; (-5, 6) C) x = 5, y = 6; (5, 6) D) x = 6, y = 5; (6, 5)

Solve the problem. 275) A man is planting a section of garden with tomatoes and cucumbers. The available area of the section is 100 square feet. He wants the area planted with tomatoes to be more than 30% of the area planted with cucumbers. Write a system of inequalities to describe the situation. Let x = amount to be planted in tomatoes and y = amount to be planted in cucumbers. A) x + y 100 B) x + y 100 C) x + y 100 D) x + y = 100 x > 0.30y x > 30y x < 0.30y x 0.30y x 0 x 0 x 0 x 0 y 0 y 0 y 0 y 0 Perform the row operation(s) on the given augmented matrix. 276) (a) R2 = 3r1 + r2

275)

276)

(b) R 3 = -2r1 + r3 (c) R3 = 4r2 + r3

1 2 -3 4 -3 -5 8 -10 2 0 -1 4 A) 1 2 -3 4 0 1 1 -2 0 0 1 4

Solve the problem.

x 277) Given that a 2

A) 0

y b 4

1 2 -3 0 1 -1 0 0 1

4 2 4

1 2 -3 - 4 0 1 -1 2 0 0 1 4

z 2 4 c = 3, find the value of the determinant 3a 3b 5 x-2 y-4

B) 6

C) 9

Perform the indicated operation(s), whenever possible. 278) 3 -5 Let A = -2 and B = 5 . Find A + B. -4 5 A) B) 3 -5 -2 -2 5 3 -4 5 1

1 2 -3 -4 0 1 -1 2 0 0 1 -4

5 . 3c z-5

277)

D) -9

278)

[-2 3 1]

2 1 2

An objective function and a system of linear inequalities representing constraints are given. Graph the system of inequalities representing the constraints. Find the value of the objective function at each corner of the graphed region. Use these values to determine the maximum value of the objective function and the values of x and y for which the maximum occurs. z = 6x - 4y 279) Objective Function 279) Constraints x 0 0 y 5 x-y 6 x + 2y 12 A) maximum: 36; at (6, 0) B) maximum: 40; at (8, 2) C) maximum: -20; at (0, 5) D) maximum: -8; at (2, 5)

Solve the system of equations using Cramer's Rule if it is applicable. If Cramer's Rule is not applicable, say so. 9x - 8y = 9 280) 36x - 32y = 18 280) 3 27 3 27 ; ,A) x = 4, y = 2; (4, 2) B) x = , y = 5 40 5 40 C) x = 9, y = 18; (9, 18)

Compute the product. 281) 0 -2 6 -1 3 12 1 -3 2 A) 3 -7 0 2 -8 10

D) not applicable

281)

C) not defined

3 2 -7 -8 0 10

Graph the system of inequalities. 282) x + 7y 7 x + 7y 0

0 -6 18 1 -6 4

282)

B) No solution

Solve the system of equations using substitution. 283) y = x2 - 3

283)

x2 + y2 = 5 A) x = 1, y = -2; x = 4, y = 13 or (1, -2), (4, 13) B) x = -1, y = -2; x = 1, y = -2 or (-1, -2), (1, -2) C) x = -2, y = 1; x = -1, y = -2; x = 1, y = -2; x = 2, y = 1 or (-2, 1), (-1, -2), (1, -2), (2, 1) D) x = -2, y = 1; x = 2, y = 1 or (-2, 1), (2, 1)

Write a system of linear inequalities that has the given graph. 284)

x y y y

0 7 x-3 3-x

y x y y

284)

0 7 x-3 3-x

x y y y y

0 0 7 x-3 3-x

y y y y

0 7 x-3 3-x

Write the augmented matrix for the system. 285) 5 2 3 x+ y=2 11 2

285)

8 1 1 x- y= 11 2 2

5 2

2 3 - 0 11 2

8 1 1 11 2 2

5 2

2 3 11 2

8 1 11 2

1 2

5 2

2 3 11 2

8 1 11 2

1 2

5 2

2 3 11 2

8 1 11 2

1 2

Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. 286) 6x + 4y = -6 286) 5x = -15 A) x = -3, y = -3; (-3, -3) B) x = -3, y = 3; (-3, 3) C) x = 3, y = -3; (3, -3) D) inconsistent Solve the problem using matrices.

287) Find the function f(x) = ax3 + bx2 + cx + d for which f(0) = -2, f(1) = 5, f(-1) = 3, f(2) = 4. 8 5 A) f(x) = 10x3 - 18x2 - 13x + 6 B) f(x) = x3 + 4x2 + x - 2 3 3 C) f(x) = -

10 3 13 x + 6x2 + x-2 3 3

287)

D) f(x) = -8x3 +12x2 + 5x - 6

Solve the linear programming problem. 288) Maximize and minimize z = 8x + 7y subject to: x 0, y 0, 2x + 3y 6, x 10, y 5. A) maximum: 80; minimum: 21 C) maximum: 115; minimum: 80

288) B) maximum: 115; minimum: 14 D) maximum: 35; minimum: 21

Tell whether the given rational expression is proper or improper. If improper, rewrite it as the sum of a polynomial and a proper rational expression. x-2 289) 289) x2 + 3

A) improper; C) improper;

(x +

x-2 3)(x -

B) improper;

2 2 + x+ 3 x- 3

2 2 x+ 3 x- 3

D) proper

Perform the indicated operation(s), whenever possible. 6 10 - 4 -4 6 7 290) Let A = 3 -5 12 and B = -5 6 - 8 . Find A - B. 7 -11 14 3 11 7 10 A) -8 -4

4 11 22

-11 -20 -7

-10 -4 -2 -11 4 -22

3 4 7

2 16 3 C) -2 1 4 10 0 21

290)

-10 -4 8 -11 4 -22

11 20 7

Solve the system of equations. If the system has no solution, say that it is inconsistent. 291) 3x + y = 8 -9x - 3y = -24 A) y = 3x + 8, where x is any real number or {(x, y) | y = 3x + 8, where x is any real number} B) x = -3y + 8, where y is any real number or {(x, y) |x = -3y + 8, where y is any real number} C) y = -3x + 8, where x is any real number or {(x, y) | y = -3x + 8, where x is any real number} D) inconsistent

291)

Graph the system of linear inequalities. Tell whether the graph is bounded or unbounded, and label the corner points. 292) 292) x 0 y 0 x+y 4 x+y 1

A) bounded; corner points (4, 0), (0, 4),(0, 1), (1, 0)

B) unbounded; corner points (0, 0), (0, 1), (1, 0)

C) no solution

D) unbounded; corner points (4, 0), (0, 4)

Solve the problem. 293) Determinants are used to show that three points lie on the same line (are collinear). If x1 y1 1

293)

x2 y2 1 = 0, x3 y3 1

then the points (x1 , y1 ), (x2 , y2 ), and (x3 , y3 ) are collinear. If the determinant does not equal 0, then the points are not collinear. Are the points (9, -5), (0, 10), and (27, -34) collinear? A) Yes B) No

294) The final grade for an algebra course is determined by grades on the midterm and final exam. The grades 294) for four students and two possible grading systems are modeled by the following matrices.

Student 1 Student 2 Student 3 Student 4

Midterm Final 73 79 44 62 82 90 98 96

System System 1 2 Midterm 0.4 0.5 Final 0.6 0.5 Find the final course score for Student 3 for both grading System 1 and System 2. A) System 1: 77.8; System 2: 94.2 B) System 1: 48.6; System 2: 53 C) System 1: 76.6; System 2: 76 D) System 1: 86.8; System 2: 86

295) The Family Fine Arts Center charges $22 per adult and $15 per senior citizen for its performances. On a recent weekend evening when 543 people paid admission, the total receipts were $9,517. How many who paid were senior citizens? A) 286 senior citizens B) 347 senior citizens C) 257 senior citizens D) 196 senior citizens

295)

Graph the inequality. 296) y x2 + 3

296)

Solve the problem. 297) The Family Arts Center charges $25 for adults, $15 for senior citizens, and $6 for children under 12 for their live performances on Sunday afternoon. This past Sunday, the paid revenue was $12,435 for 839 tickets sold. There were 49 more children than adults. How many children attended? A) 208 children B) 291 children C) 340 children D) 330 children Graph the system of inequalities.

297)

298) y - x 5 x+y 3 y - 3x -1

298)

Solve the system of equations using substitution. 299) y = x2 - 10x + 25

299)

x+y=7 A) x = 3, y = 10; x = 6, y = 1 or (3, 10), (6, 1) C) x = 5, y = 2 or (5, 2)

B) x = 3, y = 4; x = 6, y = 1 or (3, 4), (6, 1) D) x = -3, y = 10; x = -6, y = 13 or (-3, 10), (-6, 13)

Perform the indicated operation(s), whenever possible. 300) Let A = -5 1 and B = 6 2 . Find A + B. 25 1 -2 A) B) 1 -3 10 -4 -7

300)

13 33

34 -1 3

Solve the problem. 301) An application of Kirchoff's Rules to the circuit shown results in the following system of equations:

301)

I2 + I3 = I1 20 + 40 - 10I1 - 10I2 = 0 40 - 10I1 - 5I3 = 0

Find the currents I1 , I2 , and I3.

20 V

40 V 5

A) I1 = 4.5, I2 = 3.5, and I3 = 1

B) I1 = 3.5, I2 = 2.5, and I3 = 1 D) I1 = 2.5, I2 = 1.5, and I3 = 1

C) I1 = 5.5, I2 = 4.5, and I3 = 1

Solve the system of equations using substitution. 302) y = 6x2 - 5x

302)

y = 2x + 3 1 A) x = - , y = 2; x = 1, y = 5 2 or -

C) x = or

B) x =

1 , 2 , (1, 5) 2

1 11 3 ,y= ; x=- ,y=0 3 3 2

D) x =

1 11 3 , , - ,0 3 3 2

3 1 7 , y = 6; x = - , y = 2 3 3 3 1 7 , 6 ), - , 2 3 3 1 10 ,y= ; x = 1, y = 5 6 3 1 10 , , (1, 5) 6 3

Solve the system of equations by substitution. 303) 5x - 2y = -1 x + 4y = 35 A) x = 3, y = 9; (3, 9) C) x = 3, y = 8; (3, 8)

303)

B) x = 2, y = 8; (2, 8) D) x = 2, y = 9; (2, 9)

Write the partial fraction decomposition of the rational expression. x+1 304) (x - 2)2 (x + 4) A)

12 x-2 -1 x-2

(x - 2)2 1 x 4 (x - 2)2

-12

x+4 1 4

x+4

304) 1 12

x-2

1 2 (x - 2)2

1 2

(x - 2)2 +

1 12

x+4

1 12

x+4

Write the augmented matrix for the system. 8x +8y +6z = 52 305) 4x +7y -2z = 28 -2x +5y +2z = 22 A)

88 6 4 7 -2 -2 5 2

305)

8 8 6 52 4 7 -2 28 -2 5 2 22

52 6 8 8 C) 28 -2 7 4 22 2 5 -2

Solve the system of equations. 306) x+ y+ z=7 x - y + 2z = 7 5x + y + z = 11 A) x = 4, y = 1, z = 2; (4, 1, 2) C) x = 1, y = 4, z = 2; (1, 4, 2)

8 4 -2 52 D) 8 7 5 28 6 -2 2 22

306)

B) x = 4, y = 2, z = 1; (4, 2, 1) D) x = 1, y = 2, z = 4; (1, 2, 4)

Solve using elimination. 307) 2x2 + y2 = 17

307)

3x2 - 2y2 = -6 A) x = 2, y = 3; x = 2, y = -3; x = -2, y = 3; x = -2, y = -3 or (2, 3), (2, -3), (-2, 3), (-2, -3) B) x = 2, y = -3; x = -2, y = 3 or (2, -3), (-2, 3) C) x = 1, y = 3; x = -1, y= -3 or (1, 3), (-1, -3)

D) x= 1, y = 3; x = 1, y = -3; x = -1, y = 3; x = -1, y = -3 or (1, 3), (1, -3), (-2, 3), (-2, -3)

Solve the linear programming problem. 308) A summer camp wants to hire counselors and aides to fill its staffing needs at minimum cost. The average monthly salary of a counselor is $2400 and the average monthly salary of an aide is $1100. The camp can accommodate up to 45 staff members and needs at least 30 to run properly. They must have at least 10 aides, and may have up to 3 aides for every 2 counselors. How many counselors and how many aides should the camp hire to minimize cost? A) 12 counselors and 18 aides B) 35 counselors and 10 aides C) 27 counselors and 18 aides D) 18 counselors and 12 aides Write the partial fraction decomposition of the rational expression. 5x - 26 309) (x + 2)(x - 4) A)

6 1 x+2 x-4

5 26 x+2 x-4

1 6 x-4 x+2

308)

309) D)

6 1 + x+2 x-4

Solve the problem. 310) Determinants are used to show that three points lie on the same line (are collinear). If x1 y1 1

310)

x2 y2 1 = 0, x3 y3 1

then the points (x1 , y1 ), (x2 , y2 ), and (x3 , y3 ) are collinear. If the determinant does not equal 0, then the points are not collinear. Are the points (-8, 8), (0, 2), and (-24, 20) collinear? A) Yes B) No

Solve the system using the inverse matrix method. 311) -2x - 6y = -2 2x - y = -5 A) x = 1, y = -2; (1, -2) C) x = -1, y = 2; (-1, 2)

311)

B) x = 2, y = -1; (2, -1) D) x = -2, y = 1; (-2, 1)

Solve the problem. 312) A ceramics workshop makes wreaths, trees, and sleighs for sale at Christmas. A wreath takes 3 hours to prepare, 2 hours to paint, and 10 hours to fire. A tree takes 14 hours to prepare, 3 hours to paint, and 4 hours to fire. A sleigh takes 4 hours to prepare, 17 hours to paint, and 7 hours to fire. If the workshop has 117 hours for preparation time, 83 hours for painting, and 115 hours for firing, how many of each can be made? A) 3 wreaths, 7 trees, 6 sleighs B) 6 wreaths, 3 trees, 7 sleighs C) 8 wreaths, 7 trees, 4 sleighs D) 7 wreaths, 6 trees, 3 sleighs

312)

Determine whether the system corresponding to the given augmented matrix is consistent or inconsistent. If it is consistent, give the solution. 313) 313) 1 0 0 0 0 1 0 0 0 0 0 -8 A) consistent; x = 0, y = -8; (0, -8) B) consistent; x = 0, y = 0; (0, 0) C) consistent; z = -8; (-9) D) inconsistent

Solve the system of equations. 314) x + 4y - z = 3 x + 5y - 2z = 5 3x + 12y - 3z = 9 A) x = 3z + 5, and y = z - 2, where z is any real number or {(x, y, z) |x = 3z + 5, and y = z - 2, where z is any real number} B) x = z - 2, and y = -3z - 5, where z is any real number or {(x, y, z) |x = z - 2, and y = -3z - 5, where z is any real number} C) x = -3z - 5, and y = z + 2, where z is any real number or {(x, y, z) |x = -3z - 5, and y = z + 2, where z is any real number} D) inconsistent Solve the system using the inverse matrix method. 315) x + 2y + 3z = 5 x + y + z = 12 2x + 2y + z = 3

314)

315)

123 -1 4 -1 The inverse of 1 1 1 is 1 -5 2 . 221 0 2 -1

A) x = 7, y = -34, z = 26; (7, -34, 26) C) x = 56, y = 71, z = 27; (56, 71, 27)

B) x = 40, y = -49, z = 21; (40, -49, 21) D) x = 20, y = -24, z = 3; (20, -24, 3)

Graph the inequality. 316) x + y < -3

316)

Encode or decode the given message, as requested, numbering the letters of the alphabet 1 through 26 in their usual order. 111 -1 -1 1 317) Use the coding matrix A = -1 1 2 and its inverse A-1 = 5 2 -3 to decode the cryptogram 317) 123 -3 -1 2 37 16 35 38 20 4 . 82 40 60 A) STAY_CALM B) LOOK_DOWN C) GOOD_LUCK D) HELP_THEM

Compute the product. 318) -9 2 4

318)

6 0 -3

B) -66

-54 0 -12

C) 210

D) -54 0 -12

Write the partial fraction decomposition of the rational expression. x2 - 111 319) x4 - x2 - 72

319)

1 1 7 + + x + 3 x - 3 x2 + 8

1 1 7 + x + 3 x - 3 x2 + 8

1 1 7 x + 3 x - 3 x2 + 8

Solve the system of equations using substitution. 320) 3y - x = 10 x2 + y2 - 100 = 0 A) x = 0, y = or 0,

320)

10 16 ; x = 6, y = 3 3

10 16 , 6, 3 3

B) x = -10, y = 0; x = 8, y = 6 or (-10, 0), (8, 6) C) x = 10, y = 0; x = -10, y = 0; x = 8, y = 6 or (10, 0), (-10, 0), (8, 6) 10 10 16 ; x = 0, y = ; x = 6, y = D) x = 0, y = 3 3 3 or 0,

321)

10 10 16 , 0, , 6, 3 3 3

321)

xy - x2 = -20 x - 2y = 3

A) x = 5, y = 1; x = -8, y = or (5, 1), -8, -

B) x = -5, y = -1; x = 8, y =

11 2

C) x = -5, y = -1; x = or (-5, -1), -

11 2

or (-5, -1), 8, 11 ,y=8 2

11 2

D) x = 5, y = 1; x = -

11 ,8 2

or (5, 1), -

11 2

11 , -8 2

11 , y = -8 2

322)

xy = 72 x2 + y2 = 145

A) x = 8, y = 9; x = 9, y = 8; x = 8, y = -9; x = 9, y = -8 or (8, 9), (9, 8), (8, -9), (9, -8) B) x = 8, y = 9; x = -8, y = -9; x = 8, y = -9; x = -8, y = 9 or (8, 9), (-8, -9), (8, -9), (-8, 9) C) x = -8, y = -9; x = -9, y = -8; x = -8, y = 9; x = -9, y = 8 or (-8, -9), (-9, -8), (-8, 9), (-9, 8) D) x = 8, y = -8; x = -8, y = -9; x = 9, y = 8; x = -9, y = -8 or (8, -8), (-8, -9), (9, 8), (-9, -8)

Encode or decode the given message, as requested, numbering the letters of the alphabet 1 through 26 in their usual order. 323) Use the coding matrix A = 2 1 and its inverse A-1 = 3 -1 to decode the cryptogram 9 6 . 323) 53 25 17 -5 2 A) CURB B) CARE C) DARE D) BEAD Solve the system of equations. 324) 2x - y + 5z = -7 x + y - 2z = -2 x - y + 4z = -4 A) x = 3z + 1, and y = z - 3, where z is any real number or {(x, y, z) |x = 3z + 1, and y = z - 3, where z is any real number} B) x = -3 - z, and y = 3z + 1, where z is any real number or {(x, y, z) |x = -3 - z, and y = 3z + 1, where z is any real number} C) x = z + 3, and y = 3z + 1, where z is any real number or {(x, y, z) |x = z + 3, and y = 3z + 1, where z is any real number} D) inconsistent Compute the product. 325) -1 3 -2 0 -1 3 42 A) -1 9 -10 6 Find the value of the determinant. 326) 2 6 64 A) 44

324)

325)

2 -6 -3 3

20 -4 6

9 -1 6 -10

326) B) -12

C) -28

D) 28

Solve the problem. 327) The perimeter of a rectangle is 44 inches and its area is 105 square inches. What are its dimensions? A) 8 in. by 14 in. B) 6 in. by 16 in. C) 7 in. by 15 in. D) 6 in. by 14 in.

327)

Solve the system of equations using substitution. 328) ln x = 3ln y 3 x = 27y

328)

A) x = 3, y = 9 or ( 3, 9) C) x = 9, y = 3 or (9, 3)

B) x = 3 3, y = 3 or (3 3, 3) D) x = 3, y = 3 3 or ( 3, 3 3)

Solve the system of equations by elimination. 329) 6x + 3y = 51 2x - 6y = 38 A) x = 10, y = -3; (10, -3) C) x = -3, y = 10; (-3, 10)

329) B) x = -10, y = 3; (-10, 3) D) x = 3, y = -10; (3, -10)

Perform the indicated operation(s), whenever possible. 330) 5 -8 2 8 Let A = -1 4 and B = 7 2 . Find A + B. -9 8 3 -8 A) B) 70 70 -6 4 66 -6 0 -6 0

330)

74 66 -6 0

Each matrix is nonsingular. Find the inverse of the matrix. Be sure to check your answer. 331) 0 1 3 -4 A) B) C) D) 1 1 0 4 1 0 3 4 1 3 3 3 3 4 0 -1 1 3 Graph the system of inequalities. 332) x2 + y2 16

3 -16 -8 2 -12 11

331)

4 1 3 3 1 0

332)

x2 + y2 9

B) no solution

Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. 333) 2x + 4y = 12 333) 3x + 5y = 13 A) x = -4, y = 5; (-4, 5) B) inconsistent C) x = 5, y = -4; (5, -4) D) x = -4, y = -5; (-4, -5) 334)

334)

3x + 5y + 2w = -12 2x + 6z - w = -5 -2y + 3z - 3w =-3 -x + 2y + 4z + w = -2 A) x = 1, y = 3, z = 0, w = -3; (1, 3, 0, -3) C) x = -1, y = 3, z = 0, w = -3; (-1, 3, 0, -3)

B) x = -1, y = -3, z = 0, w = 3; (-1, -3, 0, 3) D) x = 1, y = -3, z = 0, w = 3; (1, -3, 0, 3)

Set up the linear programming problem. 335) A steel company produces two types of machine dies, part A and part B and is bound by the following 335) constraints: · Part A requires 1 hour of casting time and 10 hours of firing time. · Part B requires 4 hours of casting time and 3 hours of firing time. · The maximum number of hours per week available for casting and firing are 100 and 70, respectively. · The cost to the company is $0.75 per part A and $3.00 per part B. Total weekly costs cannot exceed $45.00. Let x = the number of part A produced in a week and y = the number of part B produced in a week. Write a system of three inequalities that describes these constraints. A) B) x + 10y 100 x + 10y 100 4x + 3y 70 4x + 3y 70 0.75x + 3y 45 0.75x + 3y 45 C) D) x + 4y 100 x + 4y 100 10x + 3y 70 10x + 3y 70 3x + 0.75y 45 0.75x + 3y 45 Solve the system of equations. If the system has no solution, say that it is inconsistent. 336) 9x - 2y = 3 27x - 6y = 15 1 9 1 9 A) x = , y = - ; , B) x = 3, y = 15; (3, 15) 2 4 2 4 C) x = 3, y = 5; (3, 5)

336)

D) inconsistent

Solve the system of equations using substitution. 337) y = x2 - 6x + 9

337)

y = -x2 - 6x + 11 A) x = 1, y = 4; x = -1, y = 16 or (1, 4), (-1, 16) C) x = 1, y = 4; x = 0, y = 9 or (1, 4), (0, 9)

B) x = -1, y = 16; x = 1, y = 4 or (-1, 16), (1, 4) D) x = -1, y = 16; x = 0, y = 9 or (-1, 16), (0, 9)

Solve the problem. 338) Three shrimp boats supply the shrimp wholesalers on Hilton Head with fresh catch. The Annabelle takes 50% of its catch to Hudson's, 20% to Captain J's, and 30% to Mainstreet. The Curly Q takes 40% of its catch to Hudson's, 40% to Captain J's, and 20% to Mainstreet. The SloJoe takes 30% of its catch to Hudson's, 40% to Captain J's, and 30% to Mainstreet. One week Hudson's received 238.3 pounds of shrimp, Captain J's received 206 pounds, and Mainstreet received 158.7 pounds. How many pounds of shrimp did each boat catch? A) Annabelle 176 lbs, Curly Q 222 lbs, SloJoe 205 lbs B) Annabelle 205 lbs, Curly Q 222 lbs, SloJoe 176 lbs C) Annabelle 222 lbs, Curly Q 205 lbs, SloJoe 176 lbs D) Annabelle 205 lbs, Curly Q 176 lbs, SloJoe 222 lbs Graph the system of inequalities.

338)

339) -x + 2y -6 3x + 2y > -18

339)

100

An objective function and a system of linear inequalities representing constraints are given. Graph the system of inequalities representing the constraints. Find the value of the objective function at each corner of the graphed region. Use these values to determine the maximum value of the objective function and the values of x and y for which the maximum occurs. z = 7x - 11y 340) Objective Function 340) Constraints 0 x 5 0 y 8 4x + 5y 30 4x + 3y 20 A) maximum: 35; at (5, 0) B) maximum: -66; at (0, 6) C) maximum: -46.25; at (1.25, 5) D) maximum: 0; at (0, 0)

Verify that the values of the variables listed are solutions of the system of equations. 341) 2x + y = 5 3x + 2y = 8 x = 2, y = -1 A) solution

Solve for x. 342) x 1 2 1 x -2 = 3x 0 1 2 1 A) 0 or 2

341)

B) not a solution

342)

1 2

C) -

Graph the system of inequalities. 343) x2 + y 4

1 2

D) 0 or

1 2

343)

x2 - y 3

101

Solve the system of equations by substitution. 344) 6x + y = 0 -6x + y = -12 A) x = 1, y = 12; (1, 12) C) x = -1, y = -6; (-1, -6)

344)

B) x = 1, y = -6; (1, -6) D) x = -1, y = 6; (-1, 6)

Write the partial fraction decomposition of the rational expression. 10x + 2 345) x3 - 1 A)

4 2 -4 + + x-1 x+1 x-1

4 -4x + 2 + x - 1 x2 + x + 1

4x + 2 -4 + x - 1 x2 + x + 1

4 2x - 4 + x - 1 x2 + x + 1

Solve the problem. 346) In a 1-mile race, the winner crosses the finish line 10 feet ahead of the second-place runner and 27 feet ahead of the third-place runner. Assuming that each runner maintains a constant speed throughout the race, by how many feet does the second-place runner beat the third-place runner? (5280 feet in 1 mile.) A) 7.01 ft B) 17.03 ft C) -10.05 ft D) -17.09 ft

102

345)

346)

Solve the system of equations by substitution. 347) x + 7y = -2 3x + y = 34 A) x = 12, y = -2; (12, -2) C) x = 7, y = 12; (7, 12)

347)

B) x = -2, y = 3; (-2, 3) D) x = 3, y = 7; (3, 7)

Encode or decode the given message, as requested, numbering the letters of the alphabet 1 through 26 in their usual order. 348) Use the coding matrix A = 3 7 to encode the message LIFE. 348) 25 A) -3 -5 B) 78 62 C) 99 53 D) 54 28 3 3 54 43 69 37 129 67 Find the maximum or minimum value of the given objective function of a linear programming problem. The figure illustrates the graph of feasible points.

349) z = -x - 8y. Find maximum. A) maximum: -42 B) maximum: -34

C) maximum: -27

D) maximum: -20

349)

An objective function and a system of linear inequalities representing constraints are given. Graph the system of inequalities representing the constraints. Find the value of the objective function at each corner of the graphed region. Use these values to determine the maximum value of the objective function and the values of x and y for which the maximum occurs. z = 3x + 2y 350) Objective Function 350) Constraints 0 x 10 0 y 5 3x + 2y 6 A) maximum: 6; at (0, 3) B) maximum: 10; at (0, 5) C) maximum: 40; at (10, 5) D) maximum: 30; at (10, 0)

Solve the system of equations by elimination. 351) 8x + 48y = 48 5x - 6y = -6 A) x = 1, y = 1; (1, 1) C) x = 1, y = 0; (1, 0)

351)

B) x = 0, y = 1; (0, 1) D) x = 0, y = 0; (0, 0)

103

Solve the problem using matrices. 352) An application of Kirchoff's Rules to the circuit shown results in the following system of equations:

352)

I2 + I3 = I1 28 + 56 - 14I1 - 14I2 = 0 56 - 14I1 - 7I3 = 0

Find the currents I1 , I2 , and I3.

28 V

56 V 7

A) I1 = 4.5, I2 = 3.5, and I3 = 1

B) I1 = 2.5, I2 = 1.5, and I3 = 1

C) I1 = 3.5, I2 = 2.5, and I3 = 1

D) I1 = 5.5, I2 = 4.5, and I3 = 1

Solve the linear programming problem. 353) A doctor has told a sick patient to take vitamin pills. The patient needs at least 6 units of vitamin A and at least 6 units of vitamin B. The red vitamin pills cost 10¢ each and contain 1 unit of A and 2 units of B. The blue vitamin pills cost 25¢ each and contain 2 units of A and 1 unit of B. To avoid indigestion, the patient should take no more than 4 red pills and no more than 7 blue pills. How many pills should the patient take each day to minimize costs? A) 4 red and 7 blue B) 0 red and 6 blue C) 2 red and 2 blue D) 4 red and 1 blue

104

353)

Perform the row operation(s) on the given augmented matrix.

354) (a) R3 = -2r1 + r3 (b) R 4 = 3r1 + r4

354)

1 1 -1 1 4 0 -1 2 -2 0 3 0 -3 -5 2 -1 4 0 1 -5 A) 1 1 -1 1 4 0 -1 2 -2 0 1 -2 -1 -7 -6 -1 4 0 1 -5 C) 1 1 -1 1 4 0 -1 2 -2 0 1 -2 -1 -7 -6 2 7 -3 4 7

1 1 -1 1 4 0 -1 2 -2 0 5 2 -5 -3 10 2 7 -3 4 7 1 1 -1 1 0 -1 2 -2 1 -2 -1 -7 2 7 -3 4

4 0 0 4

Set up the linear programming problem. 355) The liquid portion of a diet is to provide at least 300 calories, 36 units of vitamin A, and 90 units of vitamin C daily. A cup of dietary drink X provides 60 calories, 12 units of vitamin A, and 10 units of vitamin C. A cup of dietary drink Y provides 60 calories, 6 units of vitamin A, and 30 units of vitamin C. Set up a system of linear inequalities that describes the minimum daily requirements for calories and vitamins. Let x = number of cups of dietary drink X, and y = number of cups of dietary drink Y. Write all the constraints as a system of linear inequalities. A) B) 60x + 60y 300 60x + 60y 300 12x + 6y 36 12x + 6y > 36 10x + 30y 90 10x + 30y 90 x 0 y 0 C) D) 60x + 60y > 300 60x + 60y 300 12x + 6y > 36 12x + 6y 36 10x + 30y > 90 10x + 30y 90 x>0 y>0 Use the given matrices to compute the given expression. 4 356) Let C = -2 . Find 1/2 C. 8 A) B) 2 4 -2 -1 8 8

355)

356) C)

105

8 -4 16

2 -1 4

Use a graphing utility to solve the system of equations. Express the solution rounded to two decimal places. y = x-4/3 357) y = ex A) x = 1.14, y = 0.81 or (1.14, 0.81) C) x = 0.48, y = 1.63 or (0.48, 1.63)

B) x = 0.22, y = 0.98 or (0.22, 0.98) D) x = 0.64, y = 1.89 or (0.64, 1.89)

Solve the problem. 358) The diagonal of the floor of a rectangular office cubicle is 2 ft longer than the length of the cubicle and 5 ft longer than twice the width. Find the dimensions of the cubicle. Round to the nearest tenth, if necessary. A) width = 2 ft, length = 9 ft B) width = 3.9 ft, length = 9.7 ft C) width = 4 ft, length = 11 ft D) width = 9.7 ft, length = 22.4 ft Write the system of equations associated with the augmented matrix. Do not solve. -8 6 -4 -6 359) -6 7 0 -2 -4 0 9 -9 A) B) -8x + 6y - 4z = -6 -8x + 6y - 4z = -6 -6x + 7y = -2 -6x + 7y - 2z = 0 -4x + 9y = -9 -4x + 9y - 9z = 0 C) D) -8x + 6y - 4z = -6 -8x + 6y - 4z = -6 -6x + 7y = -2 -6x + 7z = -2 -4x + 9z = -9 -4x + 9y = -9 Graph the system of inequalities. 360) y < -x + 5 y > 5x - 3

357)

358)

359)

360)

106

Solve the problem. 361) The sum of the squares of two numbers is 100. The sum of the two numbers is 2. Find the two numbers. A) -6 and 8 B) -6 and 8 or -8 and 6 C) -8 and -6 or 6 and 8 D) -8 and 6

361)

Solve the system of equations using Cramer's Rule if it is applicable. If Cramer's Rule is not applicable, say so. -3x + 8z = -8 362) -3x + 4y - 8z = -16 362) -6x - 8y = -96 A) x = 6, y = 2, z = 6; (6, 2, 6) B) x = 8, y = 6, z = 2; (8, 6, 2) C) x = 9, y = 4, z = 2; (9, 4, 2) D) x = 8, y = -6, z = -2; (8, -6, -2)

107

Solve the system of equations using substitution. 363) 8x2 + 10y2 = 90 y=x+3

A) x = 0, y = 3; x = or 0, 3 ,

363)

10 19 ,y= 3 3

B) x = 0, y = 3; x = -

10 19 , 3 3

C) x = 0, y = -3; x = or 0, -3 , -

or 0, 3 , 10 1 ,y=3 3

10 1 ,3 3

D) x = 0, y = -3; x =

10 1 ,3 3

or 0, -3 ,

10 1 ,y=3 3

10 19 ,y= 3 3

10 19 , 3 3

2x2 = y + 5 y = -6x - 1

A) Yes

B) No

Solve the problem using matrices. 365) The table below shows the number of birds for three selected years after an endangered species protection 365) program was started. x (Number of years after 1980) y (Number of birds)

1 37

2 57

3 85

Use the quadratic function y = ax2 + bx + c to model the data. Solve the system of linear equations involving a, b, and c using matrices. Find the equation that models the data. A) y = 5x2 + 16x + 20 B) y = 6x2 - 8x + 28

C) y = 8x2 - 24x + 21

D) y = 4x2 + 8x + 25

Graph the system of inequalities.

108

366) xy < 9 y x2 - 4

366)

Tell whether the given rational expression is proper or improper. If improper, rewrite it as the sum of a polynomial and a proper rational expression. x 367) 367) 8-x 8 8-x

B) proper

8 8-x

D) improper; 1 +

A) improper; -1 + C) improper; 1 -

109

8 8-x

Write the partial fraction decomposition of the rational expression. 9x2 + 16x + 22 368) (x + 3)(x2 + 2) A)

5 4x + 4 + x + 3 x2 + 2

5 4 + x + 3 x2 + 2

5 4 4 + + x + 3 x + 2 (x + 2)2

5 4x - 4 + x + 3 x2 + 2

Each matrix is nonsingular. Find the inverse of the matrix. Be sure to check your answer. 111 369) 2 1 1 223 1 -1 1 1 1 1 1 1 1 1 1 1 -1 1 0 -1 -1 -1 2 2 A) 4 -1 -1 B) C) D) -2 -1 -1 1 1 1 1 1 1 -2 0 1 -2 -2 -3 2 2 3 2 2 3 Solve the problem using matrices. 370) There were approximately 100 vehicles sold at a particular dealership last month. The dealer tracks sales by age group for marketing purposes. The number of 36- to 59-year-old buyers and the number of buyers 60 and older combined exceeds the number of buyers 35 and younger by 30. If the number of buyers in the oldest group is doubled, it is 35 less than the number of users in the middle group. Find the number of buyers in each of the three age groups. A) 35, 35 and younger; 55, 36-59 year olds; 10, 60 and older B) 10, 35 and younger; 55, 36-59 year olds; 35, 60 and older C) 29, 35 and younger; 57, 36-59 year olds; 14, 60 and older D) 37, 35 and younger; 52, 36-59 year olds; 11, 60 and older Use the properties of determinants to find the value of the second determinant, given the value of the first. xy z 1 3 -2 371) u v w = 23 uv w =? 1 3 -2 xy z A) 0 B) 23 C) -23 D) Cannot determine Solve the system of equations using substitution. 372) x + y = 13 x2 + y2 = -12y + 149

368)

369)

370)

371)

372)

A) x = -5, y = 18; x = -2, y = 15 or (-5, 18), (-2, 15) C) x = 18, y = -5; x = 15, y = -2 or (18, -5), (15, -2)

B) x = 8, y = 5; x = 11, y = 2 or (8, 5), (11, 2) D) x = 5, y = 8; x = 2, y = 11 or (5, 8), (2, 11)

110

Solve using elimination. 373) x 2 + y2 = 9

373)

x 2 - y2 = 9 A) x = -3, y = 0; x = -3, y = 3 or (-3, 0), (-3, 3) B) x = 3, y = 0; x = -3, y = 0 or (3, 0), (-3, 0) C) x = 3, y = 0; x = 3, y = 3 or (3, 0), (3, 3) D) x = 3, y = 3; x = -3, y = 3 or (3, 3), (-3, 3)

Write the partial fraction decomposition of the rational expression. 5x2 + 7x + 18 374) x3 + 2x2 + 4x + 8 A)

3 2 3 + + x + 2 x + 4 (x + 4)2

3 2 + x + 2 x2 + 4

3 2x + 3 + x + 4 x2 + 2

3 2x + 3 + x + 2 x2 + 4

Solve the linear programming problem. 375) The Acme Class Ring Company designs and sells two types of rings: the VIP and the SST. They can produce up to 24 rings each day using up to 60 total man-hours of labor. It takes 3 man-hours to make one VIP ring and 2 man-hours to make one SST ring. How many of each type of ring should be made daily to maximize the company's profit, if the profit on a VIP ring is $40 and on an SST ring is $35? A) 16 VIP and 8 SST B) 12 VIP and 12 SST C) 18 VIP and 6 SST D) 14 VIP and 10 SST Graph the inequality. 376) x + 5y -6

374)

375)

376)

111

Use a graphing utility to solve the system of equations. Round answers to two decimal places. 377) 25x + 61y -12z = 15 18x - 12y + 7z = -3 3x + 4y - z = 12 A) x =-22.55, y = 4.56, z = -6.06; (-22.55, 4.56, -6.06) B) x = 4.56, y = -6.06, z = -22.55; (4.56, -6.06, -22.55) C) x = 4.56, y = -22.55, z = -6.06; (4.56, -22.55, -6.06) D) x = -22.55, y = -6.06, z = 4.56; (-22.55, -6.06, 4.56)

112

377)

Graph the inequality. 378) x2 + y2 16

378)

113

Solve the system using the inverse matrix method. 379) x + 2y + 3z = -9 x + y + z = 11 -x + y + 2z = 9 The inverse of

379)

123 1 -1 -1 1 1 1 is -3 5 2 . -1 1 2 2 -3 -1

A) x = -29, y = 100, z = -60; (-29, 100, -60) C) x = 11, y = 46, z = 24; (11, 46, 24)

B) x = -9, y = 44, z = -18; (-9, 44, -18) D) x = -24, y = 37, z = 22; (-24, 37, 22)

Write the partial fraction decomposition of the rational expression. x-8 380) (x - 4)(x - 5) A)

4 -3 + x-4 x-5

3 -4 + x-4 x-5

Use the given matrices to compute the given expression. 1 -1 381) Let C = -3 and D = 3 . Find C - 4D. -2 2 A) B) -5 -3 15 9 -10 4

380)

4 -3 + x-4 x-5

4 3 + x-4 x-5

381) C)

5 -6 4

Write the system of equations associated with the augmented matrix. Do not solve. 382) 2 7 3 2 2 28 A) B) C) 2x + 7y = 3 3x + 7y = -2 2x + 28y = -7 2x + 2y = 28 28x + 2y = -2 7x + 3y = -2

5 -15 10

382)

2x + 2y = 3 7x + 2y = 28

Solve the problem. 383) Ron attends a cocktail party (with his graphing calculator in his pocket). He wants to limit his food intake to 109 g protein, 103 g fat, and 153 g carbohydrate. According to the health conscious hostess, the marinated mushroom caps have 3 g protein, 5 g fat, and 9 g carbohydrate; the spicy meatballs have 14 g protein, 7 g fat, and 15 g carbohydrate; and the deviled eggs have 13 g protein, 15 g fat, and 6 g carbohydrate. How many of each snack can he eat to obtain his goal? A) 2 mushrooms, 9 meatballs, 4 eggs B) 9 mushrooms, 4 meatballs, 2 eggs C) 4 mushrooms, 2 meatballs, 9 eggs D) 10 mushrooms, 5 meatballs, 3 eggs Write the augmented matrix for the system. 384) 2x + 7y = 31 4y = 20 A) 2 7 31 4 20 0

383)

384)

B) 4 0 20 27 7

C) 31 7 2 20 0 4 114

D) 2 7 31 0 4 20

Find the maximum or minimum value of the given objective function of a linear programming problem. The figure illustrates the graph of the feasible points. 385) z = 4x + 5y. Find maximum and minimum. 385)

A) maximum value: 59; minimum value: 10 C) maximum value: 29; minimum value: 10

B) maximum value: 59; minimum value: 8 D) maximum value: 29; minimum value: 8

Graph the system of inequalities. 386) y > -3 x 2

386)

115

Write the system of equations associated with the augmented matrix. Do not solve. 387) 5 3 5 3 8 -5 5x + 3y = 0 5x + 3y = 5 3x + 5y = 5 A) 3x + 8y = 0 B) 8x + 3y = -5 C) 3x + 8y = -5

387) D)

5x + 3y = 5 3x + 8y = -5

Use a graphing utility to solve the system of equations. Express the solution rounded to two decimal places. x2 + y2 = 25 388) y = -ln x A) x = 4.76, y = -1.52; x = 0.01, y = 5.00 or (4.76, -1.52), (0.01, 5.00) C) x = 5.12, y = 3.67; x = -0.76, y = 2.05 or (5.12, 3.67), (-0.76, 2.05)

B) x = 5.12, y = -3.67; x = 0.76, y = 2.05 or (5.12, -3.67), (0.76, 2.05) D) x = -4.76, y = 1.52; x = -0.01, y = 5.00 or (-4.76, 1.52), (-0.01, 5.00)

Solve the system of equations. 389) x - y + 5z = -23 + z = -5 5x x + 5y + z = -15 A) x = -5, y = 0, z = -2; (-5, 0, -2) C) x = 0, y = -2, z = -5; (0, -2, -5)

388)

389)

B) x = -5, y = -2, z = 0; (-5, -2, 0) D) inconsistent

Graph the system of inequalities. 390) y > x2

390)

4x + 2y 8

116

Each matrix is nonsingular. Find the inverse of the matrix. Be sure to check your answer. 391) 3 -3 1 -2 2 -1 -4 5 -2 A) B) C) D) 1 -1 0 1 -1 1 1 -3 1 1 -1 1 -2 -3 0 -2 -3 0 0 -2 1 0 -2 1 -2 -3 0 -2 -3 0 0 -2 -1 0 -2 1 Solve the system of equations. If the system has no solution, say that it is inconsistent. 392) x + y + z = -2 x - y + 3z = -12 4x + 4y + 4z = -5 A) x = -3, y = 2, z = -1; (-3, 2, -1) B) x = -3, y = -1, z = 2; (-3, -1, 2) C) x = -1, y = 2, z = -3; (-1, 2, -3) D) inconsistent

117

391)

392)

An objective function and a system of linear inequalities representing constraints are given. Graph the system of inequalities representing the constraints. Find the value of the objective function at each corner of the graphed region. Use these values to determine the maximum value of the objective function and the values of x and y for which the maximum occurs. z = 3x + 5y 393) Objective Function 393) Constraints x 0 y 0 2x + y 15 x - 3y -3 A) maximum 75; at (0, 15) B) maximum 33; at (6, 3) C) maximum 22.5; at (7.5, 0) D) maximum 38; at (6, 4)

Each matrix is nonsingular. Find the inverse of the matrix. Be sure to check your answer. 394) 100 110 111 1 00 1 0 -1 1 00 1 0 0 A) -1 1 0 B) -1 1 0 C) 1 1 1 D) -1 -1 0 0 -1 1 0 -1 1 0 -1 1 0 1 1 Graph the system of inequalities. 395) y > x2

394)

395)

2x + 3y 6

118

Verify that the values of the variables listed are solutions of the system of equations. 396) 2x + y = 10 4x + 2y = 20 x = 3, y = 4 A) solution

396)

B) not a solution

Each matrix is nonsingular. Find the inverse of the matrix. Be sure to check your answer. 397) 10 1 -1 0 A) 0 1 B) 0 -1 C) 0 1 D) 0 -1 1 10 1 10 -1 10 -1 10 Solve the system of equations by substitution. 398) x + y = -8 x - y = 11 A) x = 8, y = -9.5; (8, -9.5) C) x = 1.5, y = -9.5; (1.5, -9.5)

398)

B) x = 8, y = 1.5; (8, 1.5) D) x = 1.5, y = 9.5; (1.5, 9.5)

Solve for x. 399)

5 9 =8 -2 x A) 2

397)

399)

B) -2

C) -5

Graph the system of inequalities.

119

D) -4

400) y < x + 1 5x + 9y > 45

400)

Solve the system of equations by elimination. 401) 4x + 7y = 17 4x + 2y = 42 A) x = -13, y = 4; ( -13, 4) C) x = 13, y = -5; (13, -5)

401)

B) x = -5, y = 13; (-5, 13) D) x = -13, y = 7; (-13, 7)

120

Solve the system of equations. If the system has no solution, say that it is inconsistent. 402) x - y + 5z = 1 + z= 0 5x -x + y - 5z = -4 A) x = 0, y = 0, z = -1; (0, 0, -1) B) x = 0, y = -1, z = 0; (0, -1, 0) C) x = 5, y = -1, z = 0; (5, -1, 0) D) inconsistent

402)

Find the maximum or minimum value of the given objective function of a linear programming problem. The figure illustrates the graph of feasible points.

403) z = x + 9y. Find maximum. A) maximum: 38 B) maximum: 22

C) maximum: 30

D) maximum: 47

Solve the problem. 404) The area of a rectangular piece of cardboard shown is 855 square inches. The cardboard is used to make an open box by cutting a 5-inch square from each corner and turning up the sides. If the box is to have a volume of 1,575 cubic inches, find the dimensions of the cardboard that must be used.

A) 14 in. by 40 in.

B) 19 in. by 45 in.

C) 9 in. by 30 in.

x+1 5x - 3 + 2 x + 2 (x2 + 2)2

1 -x - 3 + 2 x + 2 (x2 + 2)2

1 5x - 3 + 2 x + 2 (x2 + 2)2

5x - 3 -1 + 2 x + 2 (x2 + 2)2

Set up the linear programming problem. 406) A dietitian needs to purchase food for patients. She can purchase an ounce of chicken for $0.35 and an ounce of potatoes for $0.03. Let x = the number of ounces of chicken and y = the number of ounces of potatoes purchased per patient. Write the objective function that describes the total cost per patient per meal. A) z = 0.03x + 0.35y B) z = 35x + 3y C) z = 3y + 35y D) z = 0.35x + 0.03y 121

404)

D) 24 in. by 50 in.

Write the partial fraction decomposition of the rational expression. x2 + 5x - 1 405) (x2 + 2)2 A)

403)

405)

406)

Solve the system of equations. If the system has no solution, say that it is inconsistent. 407) x y + =4 2 3

407)

x y + =2 4 6

A) x = -1, y = B) y = -

15 15 ; -1, 2 2

3 x + 12, where x is any real number 2

or {(x, y) | y = -

3 x + 12, where x is any real number} 2

C) x = 0, y = 12; (0, 12) D) inconsistent Find the value of the determinant. 408) 12 -7 -4 3 A) 8

408) B) 4

C) 64

122

D) -8

Graph the inequality. 409) x - y > -5

409)

Solve the problem. 410) A system for tracking ships indicated that a ship lies on a hyperbolic path described by 6x2 - y2 = 29. The process is repeated and the ship is found to lie on a hyperbolic path described by y2 - 2x2 = 7. If it is known that the ship is located in the first quadrant of the coordinate system, determine its exact location. A) (-5, -3) B) (3, 5) C) (5, 3) D) (-3, -5)

123

410)

Write the partial fraction decomposition of the rational expression. 125 - 19x 411) 3 x - 10x2 + 25x

411)

5 6 -5 + + x x - 5 (x - 5)2

5 12 -5 + + x x - 5 (x - 5)2

5 6 -5 + + x x - 5 (x - 5)2

Encode or decode the given message, as requested, numbering the letters of the alphabet 1 through 26 in their usual order. 412) Use the coding matrix A = -1 -3 to encode the message CARE. 412) 2 5 A) -6 -33 B) -1 -8 C) -57 -16 D) 18 105 11 61 96 27 -4 -29 -7 -4 Perform the row operation(s) on the given augmented matrix. 413) R2 = -2r2 + r1

413)

2 4 6 -8 1 2 3 6 4 6 7 1

2 4 6 -8 A) -4 -8 -12 6 4 6 7 1 2 4 6 -8 C) 0 0 0 0 4 6 7 1

2 4 6 -8 B) -4 -8 -12 -20 4 6 7 1 2 4 6 -8 D) 0 0 0 -20 4 6 7 1

Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. 3x - 4y = 12 1 414) x + y = 414) 4 A) x =

13 45 13 45 ,y=; ,7 28 7 28

B) inconsistent

C) x =

11 37 11 37 ,y=; ,7 28 7 28

D) x = - 13, y =

Compute the product. 415) 9 2 4 -3 7 8 7 -9 -1 456 4 2 -6 A) 54 -53 -67 95 -25 -25

53 53 ; - 13, 4 4

415)

-3 7 8 4 5 6 9 5 6 7 -9 -1 4 4 -6

124

-27 14 32 28 -45 -6 16 10 -36

54 95 -53 -25 -67 -25

Write the augmented matrix for the system. 6x + 7y = 38 416) 4x + 6y = 28 A) 6 7 38 4 6 28

416)

B) 6 7 28 6 4 38

C) 38 7 6 28 4 6

D) 6 4 38 7 6 28

Solve the linear programming problem. 417) Mrs. White wants to crochet beach hats and baby afghans for a church fund-raising bazaar. She needs 8 hours to make a hat and 3 hours to make an afghan and she has 59 hours available. She wants to make no more than 13 items and no more than 12 afghans. The bazaar will sell the hats for $13 each and the afghans for $7 each. How many of each should she make to maximize the income for the bazaar? What is the maximum income? A) 4 hats, 9 afghans, $115 B) 12 hats, 1 afghans, $163 C) 6 hats, 7 afghans, $127 D) 9 hats, 4 afghans, $145 Solve the system of equations using substitution. 418) x2 + y2 = 4

417)

418)

x + y =2 A) x = 0, y = 2; x = 2, y = 0 or (0, 2), (2, 0) C) x = 0, y = -2; x = -2, y = 0 or (0, -2), (-2, 0)

B) x = 2, y = -2; x = -2, y = -2 or (2,-2), (-2, -2) D) x = 0, y = 0; x = 2, y = -2 or (0, 0), (2, -2)

Solve using elimination. 419) x2 + y2 = 130

419)

x2 - y2 = 32 A) x = -9, y = -7; x = -7, y = -9 or (-9, -7), (-7, -9) B) x = 9, y = 7; x = 7, y = 9; x = -9, y = -7; x = -7, y = -9 or (9, 7), (7, -9), (-9, -7), (-7, -9) C) x = 9, y = 7; x = -9, y = 7; x = 9, y = -7; x = -9, y = -7 or (9, 7), (-9, 7), (9, -7), (-9, -7) D) x = 9, y = -7; x = 9, y = 7 or (9, -7), (9, 7)

Perform the indicated operations and simplify. 420) Let A =

3 -4 , B = 5 -2 8 , and C = -2 5 1 0 -3

32 19 40 -15 31 -37

7 -9 3 -5 -1 6

0 1 . Find AB + BC. 2

B) -10 -19 12 -15 31 -25

C) 32 7 50 5 -23 -37

125

420)

D) 68 3 8 -2

31 -5

Solve the system using the inverse matrix method. 421) bx + 5y = 7 b 0 bx + 4y = 9 17 17 , y = -2; , -2 A) x = b b C) x = -2, y =

421)

17 17 ; -2, b b

B) x =

-17 -17 , y = -2; , -2 b b

D) x =

-17 -17 , y = 2; ,2 b b

Tell whether the given rational expression is proper or improper. x2 - 8x + 15 422) (x2 - 13x + 40)(x + 5) A) proper

422)

B) improper

Solve the problem. 423) The equation of a line passing through two distinct points (x1 , y1 ) and (x2 , y2 ) is given by

423)

x y 1 x2 y2 1 = 0. Use the determinant to write an equation for the line passing through (9, 6) x3 y3 1

and (-7, 3). Express the line's equation in standard form. A) 3x + 9y - 42 = 0 B) -3x + 16y + 69 = 0 C) 3x - 16y + 69 = 0 D) 6x - 7y + 27 = 0

Set up the linear programming problem. 424) An office manager is buying used filing cabinets. Small file cabinets cost $6 each and large file cabinets cost $8 each, and the manager cannot spend more than $102 on file cabinets. A small cabinet takes up 7 square feet of floor space and a large cabinet takes up 10 square feet, and the office has no more than 123 square feet of floor space available for file cabinets. The manager must buy at least 7 file cabinets in order to get free delivery. Let x = the number of small file cabinets bought and y = the number of large file cabinets bought. Write a system of inequalities that describes these constraints. A) 6x + 8y 102 B) 6x + 8y 102 C) 6x + 8y 102 D) 6x + 8y 102 7x + 10y 123 10x + 7y 123 7x + 10y 123 7x + 10y 123 x+y 7 x 7 x+y 7 y 7 Write the partial fraction decomposition of the rational expression. 10x - 28 425) x2 - 5x + 6 A)

3 7 + x-3 x-2

Solve for x. 426) 8 x = 32 2 5 A) -3

2 -8 + x-3 x-2

2 8 + x+3 x+2

424)

425) D)

2 8 + x-3 x-2

426) B) 4

C) -4

126

D) 3

Solve using elimination. 427) x2 + y2 = 64

427)

x2 y2 + =1 64 9

A) x = 0, y= -8; x = 0, y = 8 or (0, -8), (0, 8) C) x = -8, y= 0; x = 8, y = 0 or (-8, 0), (8, 0)

B) x = 0, y= -3; x = 0, y = 3 or (0, -3), (0, 3) D) No real solution exists.

Graph the inequality. 428) y > x2 - 5

428)

127

Each matrix is nonsingular. Find the inverse of the matrix. Be sure to check your answer. 429) -2 4 4 -4 1 1 1 1 1 1 1 1 2 4 2 2 2 4 2 2 A) B) 1 1 C) 1 1 D) 1 1 1 1 2 4 2 4 2 4 2 4

429)

Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. x+y + z= 7 430) x - y + 3z = -1 430) 2x + y + z = 12 A) x = -1, y = 5, z = 3; (-1, 5, 3) B) x = 5, y = 3, z = -1; (5, 3, -1) C) x = -1, y = 3, z = 5; (-1, 3, 5) D) x = 5, y = -1, z = 3; (5, -1, 3) x + 3y - 2z - w = 10 431) 4x + y + z + 2w = 20 -3x - y - 3z - 2w = -21 x - y - 3z -2w = -9 A) x = 3 + w, y = 4 - 2w, z = 2 + 2w, where w is any real number B) x = 10, y = 20, z = -21, w = -9; (10, 20, -21, -9) C) x = 2, y = 6, z = -2, w = 3; (2, 6, -2, 3) D) x = 3, y = 4, z = 2, w = 1; (3, 4, 2, 1)

Solve the problem using matrices. 432) Jenny receives $1270 per year from three different investments totaling $20,000. One of the investments pays 6%, the second one pays 8%, and the third one pays 5%. If the money invested at 8% is $1500 less than the amount invested at 5%, how much money has Jenny invested in the investment that pays 6%? A) $1500 B) $4500 C) $8500 D) $10,000 Solve the system of equations. 433) 2x + 4y - 2z = 0 =1 3x + 5y A) x = 2 - 5z, and y = 3z - 1, where z is any real number or {(x, y, z) |x = 2 - 5z, and y = 3z - 1, where z is any real number} 1 B) x = 1 - 5z, and y = 3z - , where z is any real number 2 or (x, y, z) |x = 1 - 5z, and y = 3z -

1 , where z is any real number 2

C) x = -2 - 7z, and y = -3z -1, where z is any real number or {(x, y, z) |x = -2 - 7z, and y = -3z -1, where z is any real number} D) x = 2 + 7z, and y = -3z - 1, where z is any real number or {(x, y, z) |x = 2 + 7z, and y = -3z - 1, where z is any real number}

128

431)

432)

433)

Solve the problem. 434) The area of a triangle with vertices (x1 , y1 ), (x2 , y2 ), and (x3 , y3) is

434)

x1 y1 1 1 Area = ± x y 1 , 2 2 2 x3 y3 1 where the symbol ± indicates that the appropriate sign should be chosen to yield a positive area. Use this formula to find the area of a triangle whose vertices are (3, 6), (9, -2), and (-4, -8). A) 8 B) 140 C) 70 D) 16

Use the given matrices to compute the given expression. 435) Let A = -3 3 . Find 4A. 02 A) B) 17 -12 12 46 0 2 Find the value of the determinant. 436) 4 -3 5 8 A) 17

435) C)

-12 3 02

-12 12 0 8

436) B) 47

C) -52

Graph the system of inequalities. 437) 2x + 3y 6 x-y 3 y 2

D) -47

437)

129

Write the system of equations associated with the augmented matrix. Do not solve. 1006 438) 0 1 0 1 0019 x = -6 x=6 x = -3 A) y = -1 B) y = 1 C) y = -8 z = -9 z=9 z=0 Write the partial fraction decomposition of the rational expression. 10x + 2 439) (x - 1)(x2 + x + 1) A)

4 2 -4 + + x-1 x+1 x-1

4 -4x + 2 + x - 1 x2 + x + 1

4x + 2 -4 + x - 1 x2 + x + 1

4 2x - 4 + x - 1 x2 + x + 1

130

438) x=0 D) y = 7 z = 15

439)

Solve the system of equations. 440) x-y+z=8 x+y+z=6 x + y - z = -12 A) x = 2, y = -1, z = -9; (2, -1, -9) C) x = -2, y = -1, z = -9; (-2, -1, -9)

440)

B) x = 2, y = -1, z = 9; (2, -1, 9) D) x = -2, y = -1, z = 9; (-2, -1, 9)

131

Answer Key Testname: CHAPTER 12 1) D 2) D 3) A 4) $37,500 in the stable bonds and $37,500 in the volatile bonds; maximum income $6750 5) 200 yd by 50 yd 6) $40,000 at 7%, $20,000 at 10%, $30,000 at 14% 25 (b) 29 (c) 978 7) (a) 18 12 6 10 3 5 487 30 8) 12 lbs of the $6.50/lb tea; 8 lbs of the $4.00/lb tea 9) 14 Kitui chairs, 10 Goa chairs, 8 Santa Fe chairs 10) $4000 at 6%; $12,000 at 7% 11) -2 2 0 1 -1 0 -1 1 0 12)

(6, 0), (-6, 0) 13) $9000 at 5%, $12,000 at 8%, and $24,000 at 12% 14) 8 and 3

132

Answer Key Testname: CHAPTER 12 15) (a) x 0 y 0 4x + 7y 50 x + y 13 (b)

16)

1 1 5 + x + 2 x - 2 x2 + 9

17) 0 small tile, 6 large tiles; minimum cost $27 18)

(4, 2)

133

Answer Key Testname: CHAPTER 12 19) (a) 1.5x + 2.5y x+ y x y (b)

80 40 0 0

20) 60 tapers, 35 votives, 25 tealights 3 15 6 1 0 0 -3 -1 1 0 1 0 21) -1 7 4 0 0 1 1 3

0 0

1 5 2 1 1 1 0 0 1 2 14 14 0 12 6 1 0 1 3

1 00 1 52 3 -3 -1 1 -1 7 4 0 1 0 0 01

1 00 1 5 2 3 0 14 7 -1 7 4 1 1 0 0 01

1 3

0 0 1 5 2 1 1 1 0 0 1 14 14 2 0 0 0 - 11 - 6 1 21 7

22) 1.5 ft by 4 ft 23) a = 1, b = 6, c = -5 24) order 100 type A printers

134

1 00 3

1 5 2 0 14 7 1 1 0 0 12 6 1 0 1 3

Answer Key Testname: CHAPTER 12 25)

(-3, 1), (-3, -3), (-4, -1 + 26) (a) x + y 75,000 x 40,000 y 20,000 x 0 y 0 (b)

3), (-4, -1 -

27) a = 2, b = -3, c = 2 28) boat: 25 mph; current: 3 mph 4 -10 1 0 29) -2 5 0 1

5 1 10 2 4 -2

5 01

1 0 5 4 12 1 1 0 0 2

(b) $1229.48 30) (a) 0.89 0.94 31) fruit: 25 lbs; nuts: 15 lbs; carob chips: 10 lbs 32) x = -1, y = -2, z = 4 33) $60,000 in the stable bonds and $60,000 in the volatile bonds; maximum income $9900 34) 75 packages of the breakfast blend, 40 packages of the afternoon blend; maximum profit $192.50 35) socks: $2.50 per pair; T-shirts: $7.95 each; shorts: $12.50 per pair

135

Answer Key Testname: CHAPTER 12 36)

(7, 1), (4, 4) 37) x = -4, y = 1, z = -2; (-4, 1, 2) 38) shorts: $14.95; T-shirts: $8.50 39) 24 basic models, 16 deluxe models; maximum profit $2240 40)

41)

(0, -10), ( 19, 9), (- 19, 9)

-71 13 48 -37

136

Answer Key Testname: CHAPTER 12 42)

x 0 y 0 3x + 2y 480 x + 2y 300

43) a = -2 , b = -1, c = 2 44) $6500 at 12%, $5500 at 7%, $13,000 at 6% 45) B 46) C 47) B 48) D 49) B 50) C 51) C 52) C 53) D 54) C 55) B 56) B 57) C 58) B 59) D 60) D 61) D 62) D 63) A 64) B 65) C 66) C 67) A 68) B 69) A 70) A 71) D 72) A 73) B 74) A 137

Answer Key Testname: CHAPTER 12 75) A 76) D 77) D 78) B 79) B 80) B 81) D 82) C 83) C 84) D 85) C 86) B 87) C 88) B 89) B 90) C 91) D 92) C 93) D 94) B 95) C 96) D 97) C 98) B 99) B 100) C 101) C 102) D 103) D 104) C 105) A 106) B 107) A 108) B 109) D 110) D 111) D 112) C 113) D 114) A 115) A 116) B 117) A 118) D 119) C 120) D 121) B 122) C 123) D 124) C 138

Answer Key Testname: CHAPTER 12 125) C 126) A 127) D 128) D 129) B 130) B 131) B 132) A 133) A 134) B 135) D 136) D 137) C 138) B 139) A 140) A 141) C 142) A 143) B 144) B 145) D 146) B 147) B 148) D 149) A 150) B 151) C 152) C 153) C 154) B 155) C 156) B 157) A 158) A 159) D 160) B 161) B 162) B 163) A 164) D 165) A 166) C 167) C 168) D 169) D 170) D 171) C 172) B 173) B 174) A 139

Answer Key Testname: CHAPTER 12 175) A 176) B 177) C 178) D 179) D 180) B 181) D 182) C 183) D 184) A 185) B 186) A 187) D 188) B 189) A 190) A 191) D 192) C 193) B 194) A 195) D 196) D 197) B 198) A 199) B 200) B 201) D 202) B 203) C 204) C 205) A 206) A 207) B 208) C 209) A 210) C 211) D 212) D 213) D 214) B 215) B 216) D 217) C 218) A 219) D 220) A 221) A 222) A 223) A 224) D 140

Answer Key Testname: CHAPTER 12 225) B 226) C 227) A 228) C 229) C 230) B 231) A 232) D 233) D 234) B 235) B 236) A 237) B 238) C 239) C 240) C 241) C 242) C 243) B 244) D 245) D 246) D 247) D 248) C 249) A 250) A 251) C 252) A 253) A 254) A 255) B 256) B 257) D 258) A 259) B 260) B 261) A 262) B 263) A 264) B 265) D 266) C 267) B 268) B 269) B 270) B 271) C 272) B 273) A 274) D 141

Answer Key Testname: CHAPTER 12 275) A 276) B 277) D 278) B 279) B 280) D 281) A 282) D 283) C 284) D 285) B 286) B 287) C 288) B 289) D 290) D 291) C 292) A 293) B 294) D 295) B 296) D 297) C 298) A 299) B 300) C 301) B 302) B 303) C 304) B 305) B 306) D 307) A 308) A 309) A 310) A 311) D 312) D 313) D 314) C 315) B 316) C 317) C 318) B 319) C 320) B 321) A 322) D 323) D 324) B 142

Answer Key Testname: CHAPTER 12 325) A 326) C 327) C 328) B 329) A 330) A 331) D 332) C 333) A 334) B 335) D 336) D 337) B 338) A 339) D 340) A 341) B 342) D 343) D 344) B 345) B 346) B 347) A 348) C 349) D 350) C 351) B 352) C 353) D 354) C 355) B 356) D 357) D 358) D 359) C 360) B 361) A 362) B 363) B 364) B 365) D 366) A 367) A 368) A 369) A 370) A 371) C 372) B 373) B 374) D 143

Answer Key Testname: CHAPTER 12 375) B 376) B 377) B 378) C 379) A 380) A 381) D 382) A 383) B 384) D 385) B 386) D 387) D 388) A 389) C 390) A 391) B 392) D 393) B 394) A 395) A 396) A 397) B 398) C 399) B 400) D 401) C 402) D 403) D 404) B 405) C 406) D 407) B 408) A 409) C 410) B 411) B 412) A 413) D 414) A 415) A 416) A 417) A 418) A 419) C 420) C 421) A 422) A 423) C 424) C 144

Answer Key Testname: CHAPTER 12 425) D 426) B 427) C 428) D 429) B 430) B 431) D 432) A 433) A 434) C 435) D 436) B 437) B 438) B 439) B 440) D

145

Chapter 13 Exam Name___________________________________

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n. n 1) 3 + 8 + 13 + ... + (5n - 2) = (5n + 1) 1) 2 Solve.

2) Karen has a balance of $1000 on a department store credit card that charges 1.5% interest per month on any unpaid balance. She can afford to pay $150 toward the balance each month. Her balance each month, after making a $150 payment, is given by the recursively defined sequence B0 = $1000

Bn = 1.015Bn-1 - 150

Determine Karen's balance after making the first payment. That is, determine B1 .

Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n. 3) Show that the formula 3) 2 + 4 + 6 + 8 + ... + 2n = n 2 + n + 3 obeys Condition II of the Principle of Mathematical Induction. That is, show that if the formula is true for some natural number k, it is also true for the next natural number k + 1. Then show that the formula is false for n = 1.

Solve.

4) Show that the statement "n 2 - n + 3 is a prime number" is true for n = 1, but is not true for n = 3.

5) You deposit $150 each 6 months into an annuity with an annual interest rate of 13.5%, compounded semiannually. a) What is the balance after 20 years? b) What is the balance after 40 years?

Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n. 6n - 1 6) 1 + 6 + 62 + ... + 6 n - 1 = 6) 5 Solve.

7) Jake bought a truck by taking out a loan for $26,500 at 0.25% interest per month. Jake's 7) regular monthly payment is $567, but he decides to pay an extra $75 toward the balance each month. His balance each month, after making his payment, is given by the recursively defined sequence B0 = $26,500 Bn = 1.0025Bn-1 - 642 Determine Jake's balance after making the first payment. That is, determine B1 .

8) Lexington Reservoir has 300 million gallons of water. About 0.07% of the water is lost to 8) evaporation every week. About 150,000 gallons of water enter the reservoir every week. The amount of water in the reservoir at the end of each week is given by the recursively defined sequence w0 = 300

wn = (0.9993)wn-1 + 0.15

Determine the amount of water in the reservoir at the beginning of the second week. That is, determine w2 .

Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n. n(n + 1) 9) 1 · 1 + 2 · 1 + 3 · 1 + . . . + n = 9) 2 10) 6 + 12 + 18 + ... + 6n = 3n(n + 1)

11) 2 + 2 ·

Solve.

1 1 2 +2· + ... + 2 · 2 2

10)

1 n-1 = 2

211-

1 n 2 1 2

12) Maria deposited $1500 in an independent retirement account at her bank. She earns 0.5% 12) interest per month on the balance. Each month, she deposits $100 in the account. Her balance each month after making a $100 deposit, is given by the recursively defined sequence B0 = $1500

Bn = 1.005Bn-1 + 100

If she made the initial deposit on September 30, and makes each monthly deposit on the last day of the month, how much money will be in the account at the end of the year for Maria to count as a deduction for that year's federal income taxes? That is, determine B3 .

Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n. 1 1 1 1 1 1 + ... + =113) + + + 13) 2 4 8 16 n 2 2n 14) Use the Principle of Mathematical Induction to show that the statement "5 is a factor of 7 n - 2 n " is true for all natural numbers. (Hint: 7 k+1 - 2 k+1 = 7(7 k - 2 k) + 5 · 2 k) 15) 5 + 10 + 15 + ... + 5n =

5n(n + 1) 2

16) 1 · 2 + 2 · 3 + 3 · 4 + . . . + n(n + 1) =

14)

15)

n(n + 1)(n + 2) 3

16)

Solve.

17) A wildlife refuge currently has 100 deer in it. A local wildlife society decides to add an additional 17) 2 deer each month. It is already known that the deer population is growing 12% per year. The size of the population is given by the recursively defined sequence p0 = 100

pn = 1.01pn-1 + 2

How many deer are in the wildlife refuge at the end of the second month? That is, what is p2 ?

Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n. n(6n2 - 3n - 1) 18) 1 2 + 42 + 72 + . . . + (3n - 2)2 = 18) 2 19) 1 -

Solve.

1 2

1 1 1 ... 1= 3 n+1 n+1

19)

20) 25 n = 2 5n

20)

21) Christine contributes $100 each month to her 401(k). To the nearest dollar, what will be the value of Christine's 401(k) in 20 years if the per annum rate of return is assumed to be 10% compounded monthly.

21)

Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n. 22) n 2 - n + 2 is divisible by 2 22) Solve.

23) Initially, a pendulum swings through an arc of 3 feet. On each successive swing, the length of the arc is 0.8 of the previous length. After 10 swings, what total length will the pendulum have swung (to the nearest tenth of a foot)?

23)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 24) During a five-year period, a company doubles its profits each year. If the profits at the end of the fifth year are $240,000, then what are the profits for each of the first four years? A) $15,000, $30,000, $45,000, $60,000 B) $16,000, $32,000, $64,000, $126,000 C) $15,000, $30,000, $60,000, $120,000 D) $15,000, $30,000, $60,000, $150,000 Expand the expression using the Binomial Theorem. 25) (2x - 1)4 A) -16x4 + 32 x3 + 24x2 + 8x + 1

D) 16x4 - 32x3 + 24x2 - 8x + 1

Use the Binomial Theorem to find the indicated coefficient or term. 26) The 7th term in the expansion of (4x + 2y)10 A) 1,720,320x4 y7

25)

B) (4x2 - 2x + 1)4

C) 16x3 - 32x2 + 24x - 8

24)

B) 3,440,640x4 y6

C) 860,160x6 y4

D) 1,720,320x6 y4

26)

An arithmetic sequence is given. Find the common difference and write out the first four terms. 27) {4n + 5} A) d = 4; 9, 13, 17, 21 B) d = 5; 9, 13, 17, 21 C) d = 4; 4, 9, 13, 17 D) d = 5; 4, 9, 13, 17 Find the nth term {a n} of the geometric sequence. When given, r is the common ratio.

28) 8, 24, 72, 216, 648, ... A) a n = 8 · 3 n-1

C) a n = a 1 + 3 n

B) a n = 8 · 3n

Write out the sum. n-1 (3k + 7) 29) k=0 A) 10 + 13 + 16 + ... + (3n + 4) C) 10 + 13 +16+ ... + (3n + 7)

D) a n = 8 · 3 n

27)

28)

29) B) 7 + 10 + 13 + ... + (3n + 4) D) 7 + 10 + 13 + ... + (3n + 7)

Use a graphing utility to find the sum of the geometric sequence. Round answer to two decimal places, if necessary. 1 2 2 2 2 3 ... 2 13 + + + 30) + + 30) 5 5 5 5 5 A) 6553.4

B) 3276.4

C) 6553.2

D) 3276.6

Expand the expression using the Binomial Theorem. 31) (3x + 2)5

31)

A) 243x5 + 240x4 + 720x3 + 720x2 + 240x + 32

B) 243x5 + 810x4 + 1,080x3 + 720x2 + 240x + 32 C) (9x2 + 12x + 4)5

D) 243x5 + 162x4 + 108x3 + 72x2 + 48x + 32 Solve.

32) Use the Binomial Theorem to approximate (1.01)5 = (1 + 10-2)5 to 7 decimal places. A) 1.0510101 B) 1.050101 C) 1.0550505 D) 1.0550101

32)

33) A local civic theater has 22 seats in the first row and 21 rows in all. Each successive row contains 3 additional seats. How many seats are in the civic theater? A) 790 seats B) 1070 seats C) 1010 seats D) 1092 seats

33)

Use the Binomial Theorem to find the indicated coefficient or term. 34) The 7th term in the expansion of (x + 3y)10 A) 153,090x6 y4

Solve.

B) 51,030x6 y4

C) 51,030x4 y7

D) 153,090x4 y6

35) A brick staircase has a total of 12 steps The bottom step requires 106 bricks. Each successive step requires 5 less bricks than the prior one. How many bricks are required to build the staircase? A) 912 bricks B) 1,602 bricks C) 942 bricks D) 1,884 bricks

34)

35)

36) Suppose you just received a job offer with a starting salary of $37,000 per year and a guaranteed raise of $1500 per year. How many years will it be before you've made a total (or aggregate) salary of $1,025,000? A) 25 years B) 20 years C) 18 years D) 21 years

36)

37) As Sunee improves her algebra skills, she takes 0.9 times as long to complete each homework assignment as she took to complete the preceeding assignment. If it took her 60 minutes to complete her first assignment, find how long it took her to complete the fifth assignment. Find the total time she took to complete her first five homework assignments. (Round to the nearest minute.) A) 35 min; 246 min B) 35 min; 206 min C) 39 min; 206 min D) 39 min; 246 min

37)

Use the Binomial Theorem to find the indicated coefficient or term. 38) The 5th term in the expansion of (5x + 3)5 A) 3,375x2

Solve.

B) 1,215

C) 2,025x

39) Joytown has a present population of 40,000 and the population is increasing by 2.5% each year. How long will it take for the population to double? Round your answer to the nearest year. A) 40 years B) 28 years C) 29 years D) 41 years

39)

40) A theater has 22 rows with 26 seats in the first row, 31 in the second row, 36 in the third row, and so forth. How many seats are in the theater? A) 3,564 seats B) 1,727 seats C) 1,782 seats D) 3,454 seats

40)

Find the indicated term using the given information. 41) a 19 = -43 , a 12 = -22 ; a 6 A) -7

Solve.

38) D) 675x

41)

B) -3

C) -4

D) 11

42) Laura invests $225 each quarter in a fixed-interest mutual fund paying annual interest of 5.5% compounded quarterly. How much will her account have in it at the end of 8 years? A) $2,187 B) $8,968 C) $26,902 D) $9,097

42)

Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given. 43) a = 7; r = 7 43) n/2-1 n-1/2 A) a 5 = 7 7, a n = 7 B) a 5 = 2,401 7, a n = 7 C) a 5 = 16,807, a n = 7 n

D) a 5 = 49 7, a n = 7 n/2

Use a graphing utility to find the sum of the geometric sequence. Round answer to two decimal places, if necessary. 44) -5 - 15 - 45 - 135 - 405 - ... - 5 · 3 8 44) A) -49,225

Solve.

B) -49,168

C) -49,203

D) -49,205

45) A bicycle wheel rotates 300 times in a minute as long as the rider is pedaling. If the rider stops pedaling, the wheel starts to slow down. Each minute it will rotate only 3/4 as many times as in the preceding minute. How many times will the wheel rotate in the 4th minute after the rider's feet leave the pedals? Round your answer to the nearest unit. A) 5 times B) 127 times C) 0 times D) 95 times 5

45)

Find the nth term {a n} of the geometric sequence. When given, r is the common ratio.

46) 2, 1,

1 1 , , ... 2 4

A) a n =

1 (2)n-1 2

46) B) a n = 2

1 n-1 4

C) a n = 2 · 2 n-1

Express the sum using summation notation. 47) 3 + 12 + 27 + . . . + 75 5 5 3k2 3k2 A) B) k=0 k =1 Solve.

32k

k=1

D) a n = 2

1 n-1 2

47) k2

k =1

48) Lonnie deposits $200 each month into an account paying annual interest of 5% compounded monthly. How much will his account have in it at the end of 5 years? A) $13,447 B) $13,601 C) $1,105 D) $13,730

Evaluate the factorial expression. 5! 49) 7! A) 2!

49) B)

1 42

Write out the sum. n-1 1 50) 3k + 1 k=0 1 1 1 1 + ... + A) + + 3 9 27 3n C)

1 2!

D) 42

50)

1 1 1 1 + + + ... + 3 9 27 3n + 1

B) 1 +

1 1 1 + + ... + 3 9 3n

D) 0 +

1 1 1 + + ... + 3 9 3n

Evaluate the factorial expression. 10! 51) 5!5! A) 504

51) B) 126

C) 30,240

D) 252

The given pattern continues. Write down the nth term of the sequence {a n} suggested by the pattern.

52) 3 , 9 , 27 , 81 , 243 , ... A) a n = 3 n-1 + 2

52)

B) a n = 3 + 6 (n - 1)

D) a n = 3 n

C) a n = 6 n Solve.

48)

53) Looking ahead to retirement, you sign up for automatic savings in a fixed-income 401K plan that pays 5.5% per year compounded annually. You plan to invest $2,000 at the end of each year for the next 30 years. How much will your account have in it at the end of 30 years? A) $146,169 B) $146,641 C) $144,871 D) $143,328

53)

Evaluate the factorial expression. 4! 54) 3! A) 1

54) B)

Evaluate the expression. 129 55) 3 129! A) 126!

4 3

C) 4!

55) B) 2,097,024

C) 126

Find the indicated term of the geometric sequence. 56) 7th term of 0.6, 0.06, 0.006, . . . A) 0.00000001 B) 0.00000006 Solve.

D) 4

D) 349,504

C) 0.000006

D) 0.0000006

56)

57) A new piece of equipment cost a company $53,000. Each year, for tax purposes, the company depreciates the value by 25%.What value should the company give the equipment after 8 years? A) $7,075 B) $1 C) $5,306 D) $3

57)

58) A pendulum bob swings through an arc 80 inches long on its first swing. Each swing thereafter, it swings only 87% as far as on the previous swing. What is the length of the arc after 12 swings? Round your answer to two decimal places, if necessary. A) 765.6 inches B) 17.29 inches C) 13.09 inches D) 15.04 inches

58)

Express the sum using summation notation. 3 11 3 10 39 34 + + + ... + 59) 73 74 75 7 10 A)

8 k=1

3 12 - k 72+k

Find the sum. 5 2 60) (4)k 3 k=1 2,710 A) 3

8 k=1

59) 3 12 - k 7k

8 k=1

3-k 72+k

4 k=1

3 12 + k 72+k

60) B)

2,728 3

2,773 3

2,701 3

A geometric sequence is given. Find the common ratio and write out the first four terms. 1 n-1 61) {sn } = 4 2 1 n-1 1 A) a n = 4 B) a n = (4)n-1 4 2 1 1 1 ; s1 = 4, s2 = 1, s3 = , s4 = 4 4 16 n-1 1 C) a n = 4 2 r=

1 ; s = 4, s2 = 8, s3 = 16, s4 = 32 2 1

D) a n = 4 · (2)n-1

r = 2; s1 = 4, s2 = 8, s3 = 16, s4 = 32

1 1 ; s = 4, s2 = 2, s3 = 1, s4 = 2 1 2

Find the sum of the sequence. 62) 5 9k k=2 A) 126

61)

62)

B) 63

C) 81

D) 45

Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given. 63) a = 7; r = 2 63) n-1 n-1 A) a 5 = 224; a n = 7 · (2) B) a 5 = 112; a n = 7 · (2) C) a 5 = 224; a n = 7 · (2)n

D) a 5 = 112; a n = 7 · (2)n

Determine whether the infinite geometric series converges or diverges. If it converges, find its sum. 2 64) -6 - 2 - - ... 3 A) Converges; 3

B) Converges; -

C) Converges; - 9

D) Diverges

Find the sum of the sequence. 65) 4 1 k 3 k=1 20 A) 81

26 3

65)

B) -

20 81

40 81

D) -

16 81

The given pattern continues. Write down the nth term of the sequence {a n} suggested by the pattern.

66) -1 , 1 , 3 , 5 , 7 , ... A) a n = n + 2

64)

C) a n = -1 ( 2 )n-1

B) a n = 3 n - 2

D) a n = 2 n - 3

66)

An arithmetic sequence is given. Find the common difference and write out the first four terms. 1 n + 67) 9 3 A) d =

1 1 4 7 10 ; , , , 3 9 9 9 9

B) d =

1 1 4 7 10 ; , , , 9 9 9 9 9

C) d =

1 4 7 10 13 ; , , , 3 9 9 9 9

D) d =

1 4 7 10 13 ; , , , 9 9 9 9 9

67)

Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. 68) {2n - 5} 68) A) Arithmetic; d = -5 B) Arithmetic; d = 2 C) Geometric; r = 2 D) Neither

Determine whether the infinite geometric series converges or diverges. If it converges, find its sum. 69) 7 + 14 + 28 + 56 + ... A) Converges; B) Converges; 105 C) Converges; 112 D) Diverges An arithmetic sequence is given. Find the common difference and write out the first four terms. 70) {7 - 3n} A) d = -3; 4, 3 , 0 , -3 B) d = -3; -3, -6, -9, -12 C) d = -3; 4, 1, -2, -5 D) d = 3; 4, 7 , 10 , 13

70)

Express the sum using summation notation. 1 1 3 7 71) + + + ... + 3 2 5 8 A)

14 k=1

B) k k+ 2

n k=1

71) C) k k+ 2

14 k=2

D) k k+ 1

14 k=0

k k+ 2

Find the nth term {a n} of the geometric sequence. When given, r is the common ratio.

72) 8, -24, 72, -216, 648, ... A) a n = 8 · (-3)n

69)

B) a n = 8 · (-3)n-1

C) a n = 8 · (-3)n

Write out the sum. n (4k + 6) 73) k=1 A) 10 + 14 + 18 + ... + (4n + 6) C) 6 +10 + 14 + ... + (4n + 6)

D) a n = a 1 - 3n

72)

73) B) 1 + 2 + 3 + ... + n D) 4n + 6

Expand the expression using the Binomial Theorem. 74) (x5 + 5y)4

74)

A) x20 + 20x15y + 150x10y2 + 500x5 y3 + 625y4 B) x20 + 15x15y + 150x10y2 + 375x5 y3 + 625y4 C) x9 + 20x8 y +30x7 y2 + 20x5 y3 + 5y4 D) x9 + 15x8 y + 150x7 y2 + 375x5 y3 + 625y4 9

Use a graphing utility to find the sum of the geometric sequence. Round answer to two decimal places, if necessary. 75) 3 + 6 + 12 + 24 + 48 + ... + 3 · 2 7 75) A) 767

B) 802

C) 765

D) 745

Find the nth term and the indicated term of the arithmetic sequence whose initial term, a, and common difference, d, are given. 76) a = 94; d = -5 76) a n = ?; a 8 = ?

A) a n = 99 - 5n; a 8 = 24

B) a n = 99 - 5n; a 8 = 59

C) a n = 94 - 5n; a 8 = 59

D) a n = 94 - 5n; a 8 = 24

Expand the expression using the Binomial Theorem. 77) (fx + gy)5

77)

A) f5x5 + 5f3 g2 x3 y2 + 5fg4 xy4 + g5 y5 B) f5x5 + 5f4 gx4 y + 10f3 g2 x3 y2 + 10f2 g3 x2 y3 + 5fg4 xy4 + g5 y5 C) f5x5 + g5 y5 D) f5x5 + 5fgx4 y + 10f3 g2 x3 y2 + 10f2 g3 x2 y3 + 5fgxy4 + g5 y5

Find the first term, the common difference, and give a recursive formula for the arithmetic sequence. 78) 6th term is 38; 15th term is -34 A) a 1 = 86, d = 8, a n = a n-1 + 8 B) a 1 = 78, d = -8, a n = a n-1 - 8

78)

Write out the sum. n (k + 9)2 79) k=1

79)

C) a 1 = 78, d = 8, a n = a n-1 + 8

D) a 1 = 86, d = -8, a n = a n-1 - 8

A) 100 + 121 + 144 + ... + (n + 9)2

B) 10 + 11 + 12 + ... + (n + 9)2 D) (n + 9)2

C) 1 + 2 + 3 + ... + n Expand the expression using the Binomial Theorem. 80) (x + 2)5 A) x5 + 10x4 + 40x3 + 80x2 + 80x + 2

B) x5 + 10x4 + 80x3 + 160x2 + 80x + 2

C) x5 + 10x4 + 80x3 + 160x2 + 80x + 32

80)

D) x5 + 10x4 + 40x3 + 80x2 + 80x + 32

The sequence is defined recursively. Write the first four terms. an - 1 81) a 1 = -2; an = n+1

81)

A) a 1 = -2, a 2 = - 1, a 3 = -

1 1 , a4 = 3 12

B) a 1 = -2, a 2 = -

C) a 1 = -2, a 2 = -2, a 3 = -

2 1 ,a =3 4 6

D) a 1 = -2, a 2 = -2, a 3 = - 1, a 4 = -

2 1 1 , a3 = - , a4 = 3 6 30 1 3

Determine whether the infinite geometric series converges or diverges. If it converges, find its sum. 82) 72 + 12 + 2 + ... 5.066549581e+15 A) Converges; 3.518437209e+14

C) Converges;

B) Converges; 86

7.599824371e+14 8.796093022e+12

Find the sum. 10 (3.4n + 8.75) 83) n=1 A) 274.5

D) Diverges

83) B) 42.75

C) 192.4

D) 231.75

Express the sum using summation notation. 22 23 2n + + ... + 84) 2 + 2 3 n A)

n k=0

2k k

82)

n k=1

84) 2k k

n k=0

2k k

n k=1

2k k

Find the nth term and the indicated term of the arithmetic sequence whose initial term, a, and common difference, d, are given. 85) a = -2; d = 10 85) a n = ?; a 9 = ?

A) a n = -2 + 10n; a 9 = 78

B) a n = -12 + 10n; a 9 = 138

C) a n = -12 - 10n; a 9 = 78

D) a n = -12 + 10n; a 9 = 78

Write out the first five terms of the sequence. 86) {sn } = {2(4n - 2)}

86)

A) s1 = 4, s2 = 8, s3 = 12, s4 = 16, s5 = 20

B) s1 = 2, s2 = 6, s3 = 10, s4 = 14, s5 = 18

C) s1 = -4, s2 = 4, s3 = 12, s4 = 20, s5 = 28

Solve.

D) s1 = 4, s2 = 12, s3 = 20, s4 = 28, s5 = 36

87) A ball is dropped from a height of 25 feet. Each time it strikes the ground, it bounces up to 0.7 of the 87) previous height. The total distance the ball has traveled before the second bounce is 25 + 2(25 · 0.7) feet, and the total distance the ball has traveled before bounce n + 1 is n 25 + 50 0.7k feet. k=1 Use facts about infinite geometric series to calculate the total distance the ball has traveled by the time it has stopped bouncing. 2 3 2 1 A) 141 feet B) 144 feet C) 141 feet D) 140 feet 3 5 5 3

The given pattern continues. Write down the nth term of the sequence {a n} suggested by the pattern.

88) 4, -8, 12, -16, ... A) a n = (-1)n + 1 · 4n

B) a n = (-1)n · 4

C) a n = (-1)n · 4n

D) a n = (-1)n + 1 · 4 11

88)

Solve.

89) A particular substance decays in such a way that it loses half its weight each day. How much of the substance is left after 10 days if it starts out at 256 grams? 1 1 A) gram B) 2 grams C) 4 grams D) gram 2 4

89)

The given pattern continues. Write down the nth term of the sequence {a n} suggested by the pattern.

90) 1,

1 1 1 , , , ... 2 4 8

A) a n =

90)

1 2

B) a n =

C) a n =

D) a n =

2n - 1

1 2+n

Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. 91) 1, -3, 9, -27, 81, ... 91) A) Geometric; r = -3 B) Arithmetic; d = -4 C) Geometric; r = 3 D) Neither

Find the sum. 36 (3n + 8) 92) n=1 A) 2,232

92) B) 2,286

C) 2,502

D) 2,376

The given pattern continues. Write down the nth term of the sequence {a n} suggested by the pattern.

93)

1 1 1 1 , , , , ... 1 ·3 2 ·4 3 ·5 4 ·6

A) a n =

1 n(n + 2)

93) B) a n =

1 2n

C) a n =

1 n · 2n

D) n(n + 2)

Determine whether the infinite geometric series converges or diverges. If it converges, find its sum. 5 5 5 +... 94) 5 - + 4 16 64 A) Converges; -

5 4

C) Converges;

B) Converges; 4

15 4

A geometric sequence is given. Find the common ratio and write out the first four terms. 5n 95) {dn } = 20 A) r = 5; d1 =

1 5 25 125 ,d = ,d = , d4 = 4 2 4 3 4 4

B) r = 5; d1 =

5 25 125 5.497558139e+15 ,d = ,d = , d4 = 4 2 4 3 4 3.518437209e+13

C) r =

5 5 25 125 5.497558139e+15 ;d = ,d = ,d = , d4 = 4 1 4 2 4 3 4 3.518437209e+13

D) r =

5 1 5 25 125 ;d = ,d = ,d = , d4 = 4 1 4 2 4 3 4 4

94)

D) Diverges

95)

Solve.

96) Jennifer takes a job with a starting salary of $27,000 for the first year with an annual increase of 4% beginning in the second year. What is Jennifer's salary, to the nearest dollar, in the eighth year? A) $37,738 B) $34,106 C) $35,530 D) $36,465

96)

Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given. 97) a = 5; r = -5 97) n-1 n A) a 5 = 3,125; a n = 5 · (-5) B) a 5 = -625; a n = 5 · (-5) C) a 5 = 3,125; a n = 5 · (-5)n

D) a 5 = -625; a n = 5 · (-5)n-1

Find the indicated term using the given information. 167 59 , a 18 = ; a5 98) a 45 = 4 4 A) -9

98)

7 4

C) 1

11 4

Find the nth term and the indicated term of the arithmetic sequence whose initial term, a, and common difference, d, are given. 99) a = 2; d = 4 99) a n = ?; a 13 = ?

A) a n = -2 - 4n; a 13 = 50

B) a n = 2 + 4n; a 13 = 50 D) a n = -2 + 4n; a 13 = 50

C) a n = -2 + 4n; a 13 = 22

Solve. 100) A small business owner made $30,000 the first year he owned his store and made an additional 9% over the previous year in each subsequent year. Find how much he made during his fourth year of business. Find his total earnings during the first four years. (Round to the nearest cent, if necessary.) A) $38,850.87; $137,193.87 B) $390,963.00; $792,033.00 C) $21.87; $32,964.87 D) $205,770.00; $401,070.00 The sequence is defined recursively. Write the first four terms. 101) a 1 = 6; a n = 6a n-1 A) a 1 =

6, a2 =

B) a 1 =

6, a2 =

6, a 3 =

6, a 4 =

C) a 1 =

6 6, a 3 = 6 6 6, a 4 = 6, a2 = 6, a 3 = 6 6, a 4 = 36

D) a 1 =

6, a2 = 6 6, a 3 = 36 6, a 4 = 216 6

6 6 6 6 6

100)

101)

Express the sum using summation notation. 3 9 27 ... 3 13 + - + (-1)(13 + 1) 102) 4 16 64 4 A)

B) (-1)(k+1)

k=1 14

102)

3 k 4

D) (-1)(k+1)

k=1

3 k 4

k=1 13

3 k 4

(-1)(k+1)

k=1

Find the indicated term using the given information. 103) a = -10 , d = 3 ; a8 A) -34

3 k 4

103)

B) 14

C) -31

D) 11

Determine whether the infinite geometric series converges or diverges. If it converges, find its sum. 1 1 1 + +... 104) 1 + + 5 25 125 A) Converges;

5 4

B) Converges;

1 5

C) Converges;

The sequence is defined recursively. Write the first four terms. 105) a 1 = -9; an = n - a n - 1 A) a 1 = -9, a 2 = -18, a 3 = 9, a 4 = -27

C) a 1 = -10, a 2 = -7, a 3 = -9, a 4 = -6

6 5

104)

D) Diverges

105) B) a 1 = -9, a 2 = -7, a 3 = 10, a 4 = -6

D) a 1 = -9, a 2 = 11, a 3 = -8, a 4 = 12

Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given. 106) a = -3; r = -2 106) n-1 n A) a 5 = -48; a n = -3 · (-2) B) a 5 = 24; a n = -3 · (-2) C) a 5 = 24; a n = -3 · (-2)n-1

Find the sum of the sequence. 107) 11 7 k=1 A) 4

107)

B) 11

Solve. 108) For the geometric sequence 2, 1, A) a n =

1 1-n 2

D) a 5 = -48; a n = -3 · (-2)n

C) 77

D) 7

1 1 , , ... , find a n . 2 4

108)

B) a n = 2 n-2

C) a n =

1 n-2 2

D) a n = 2 1-n

The sequence is defined recursively. Write the first four terms. 109) a 1 = 2; a n = 3a n-1 - 1 A) a 1 = 2, a 2 = 6, a 3 = 18, a 4 = 54 C) a 1 = 2, a 2 = 7, a 3 = 22, a 4 = 67

Find the sum of the sequence. 110) 6 (2k - 3) k=3 A) 24

109) B) a 1 = 2, a 2 = 5, a 3 = 14, a 4 = 41

D) a 1 = 2, a 2 = 5, a 3 = 17, a 4 = 53

110)

B) 27

C) 21

D) 15

Expand the expression using the Binomial Theorem. 111) (x + 1)6

111)

A) x6 + 6x5 +30x4 + 120x3 + 30x2 + 6x + 1 B) x6 + 6x5 + 30x4 + 120x3 + 360x2 + 720x + 720 C) x6 + 6x5 +15x4 + 20x3 + 15x2 + 6x + 1 D) x6 + 6x5 + 15x4 + 20x3 + 15x2 + 6x + 6

112) (g - 2h)3 A) g3 - 6g2 h + 12gh2 - 8h3

B) g3 - 6h2 g + 12hg2 - 8h3 D) g3 - 8h3

C) g3 - 3g2 h + 6gh2 - 2h3

Determine whether the infinite geometric series converges or diverges. If it converges, find its sum. 113) 4

112)

113)

2 k-1 3

k=1 A) Converges; 16

Find the sum. 114) 2 + 4 + 6 + ... + 1,572 A) 619,369

B) Converges; 12

C) Converges; 4

D) Diverges

B) 618,582

C) 617,796

D) 617,010

Expand the expression using the Binomial Theorem. 115) (2x + y)6

114)

115)

A) 2x6 + 12x5 y + 30x4 y2 + 40x3 y3 + 12xy5 + y6

B) 64x6 + 192x5 y + 240x4 y2 + 160x3 y3 + 240x2 y4 + 192xy5 + 64y6 C) 64x6 + 192x5 y + 240x4 y2 + 160x3 y3 + 60x2 y4 + 12xy5 + y6

D) 64x6 + 192x5 y + 480x4 y2 + 960x3 y3 + 1440x2 y4 + 12xy5 + y6 Use the Binomial Theorem to find the indicated coefficient or term. 116) The 10th term in the expansion of (x - 2y)14 A) -1,025,024x9 y5

B) 512,512x9 y5

C) 512,512x5 y10

D) -1,025,024x5 y9

116)

The sequence is defined recursively. Write the first four terms. 117) a 1 = y; a n = a n-1 + U

117)

A) a 1 = U, a 2 = U + y, a 3 = U + 2y, a 4 = U + 3y B) a 1 = y, a 2 = y - U, a 3 = y - 2U, a 4 = y - 3U C) a 1 = y, a 2 = y + U, a 3 = y + 2U, a 4 = y + 3U

D) a 1 = y, a 2 = U, a 3 = 2U, a4 = 3U

Write out the sum. n 2 k 118) 3 k=0 2 4 2.251799814e+15 2 n + ... + A) + + 3 9 7.599824371e+15 3

118) 2 4 2 n + + ... + 3 9 3 2 4 2 n D) 0 + + + ... + 3 9 3

B) 1 +

C) 0 + 1 + 2 + 3 + ... + n

Determine whether the sequence is arithmetic. 119) 2, 4, 6, 10, 12, ... A) Arithmetic Write out the sum. n k3 120) 5 k=1 A) 5 + 40 + 135 + ... + C)

119)

B) Not arithmetic

120) n3 5

B) 1 + 2 + 3 + ... + n

n3 5

1 8 1.519964874e+15 n3 + + + ... + 5 5 2.814749767e+14 5

Expand the expression using the Binomial Theorem. 121) (w - s)6

121)

A) w6 - 8w5 s + 17w4 s2 - 22w3 s3 + 17w2 s4 - 8ws5 + s6 B) w6 - s6

C) w6 - 6w5 s + 15w4 s2 - 20w3 s3 + 15w2 s4 - 6ws5 + s6 D) w6 - 6w5 s - 30w4 s2 + 120w3 s3 + 360w2 s4 - 720ws5 - 720s6 Evaluate the expression. 8 122) 0 A) 0

B) 2

C) 1

Determine whether the sequence is arithmetic. 123) 2, -1, -4, -7, -10, ... A) Arithmetic

B) Not arithmetic

D) 40,320

122)

123)

Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. 2 124) 1 - n 124) 5

A) Arithmetic; d = -

2 5

B) Arithmetic; d =1

C) Geometric; r = -

2 5

D) Neither

Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given. 1 125) a = 9; r = 125) 5 7.91648372e+13 1 n 9.89560465e+12 1 n ; a =9· ; a =9· A) a 5 = B) a 5 = 5.497558139e+15 n 5 3.435973837e+15 n 5 7.91648372e+13 1 n-1 9.89560465e+12 1 n-1 ; a =9· ; a =9· C) a 5 = D) a 5 = 5.497558139e+15 n 5 3.435973837e+15 n 5 Find the sum of the sequence. 126) 5 (k2 + 10) k=3 A) 105

B) 42

C) 80

D) 54

Find the sum. 127) 1 + 2 + 3 + ... + 112 A) 6328

B) 12,656

C) 6216

D) 12,544

126)

Determine whether the sequence is arithmetic. 128) 5, -15, 45, -135, 405, ... A) Arithmetic

B) Not arithmetic

Write out the first five terms of the sequence. 129) {sn } = {2 n }

127)

128)

129)

A) s1 = 1, s2 = 4, s3 = 9, s4 = 16, s5 = 24

B) s1 = 1, s2 = 2, s3 = 4, s4 = 8, s5 = 16

C) s1 = 2, s2 = 4, s3 = 8, s4 = 16, s5 = 32

D) s1 = 4, s2 = 8, s3 = 16, s4 = 32, s5 = 64

Solve. 130) A hockey player signs a contract with a starting salary of $880,000 per year and an annual increase of 5% beginning in the second year. What will the athlete's salary be, to the nearest dollar, in the eighth year? A) $1,240,409 B) $1,237,009 C) $1,238,748 D) $1,238,248

130)

Write out the first five terms of the sequence. n 131) {sn } = 2 n +2

131)

A) s1 =

1 1 3 2 5 ,s = ,s = ,s = ,s = 2 2 3 3 8 4 5 5 12

B) s1 =

1 1 3 2 5 ,s = ,s = ,s = ,s = 3 2 3 3 11 4 9 5 27

C) s1 =

1 1 3 2 5 ,s = ,s = ,s = ,s = 4 2 3 3 8 4 5 5 12

D) s1 =

1 1 3 2 5 ,s = ,s = ,s = ,s = 3 2 3 3 8 4 5 5 12

Solve. 132) For the geometric sequence 64, 16, 4, 1, ... , find a n . 1 n 1 n-4 A) a n = B) a n = 4 4

132) C) a n = 4 n-4

D) a n = 4 n

Write out the sum. n 5 k+1 133)

133)

k=1

A) 5 2 + 5 3 + 5 4 + ... + 5 n+1 C) 5 + 5 2 + 5 3 + ... + 5 n

B) 5 2 + 5 3 + 5 4 + ... + 5 n D) 5 + 5 2 + 5 3 + ... + 5 n+1

Evaluate the expression. 10 134) 1 A) 1

134) B) 10!

C) 10

Expand the expression using the Binomial Theorem. 135) (3x2 + 2)3 A) 27x6 + 54x4 + 36x2 + 8 C) (9x4 + 12x2 + 4)3

Find the sum of the sequence. 136) 5 (k + 3) k=1 A) 8

10 9

135)

B) 27x3 + 54x2 + 36x + 8 D) 81x8 + 27x6 + 54x4 + 36x2 + 8

136)

B) 12

C) 30

D) 22

Express the sum using summation notation. 1 u u2 un-1 + + ... + 137) + x 2x 3x nx A)

n k=0

<b>k kx

n k=0

137) uk-1 kx

n k=1

uk-1 kx

n k=1

uk kx

Find the sum. 138) n

138) 5 · 7 k-1

k=1

A) -

5 (1 - 7 n-1 ) 6

B) - 5 (1 - 7 n )

C) -

5 (1 - 7 n ) 6

D) - 30 (1 - 7 n )

A geometric sequence is given. Find the common ratio and write out the first four terms. 139) {sn } = {2 n } A) r = 2; s1 = 2, s2 = 4, s3 = 8, s4 = 16

B) r = 2n; s1 = 2, s2 = 4, s3 = 8, s4 = 16 D) r = 2n; s1 = 2, s2 = 4, s3 = 6, s4 = 8

C) r = 2; s1 = 2, s2 = 4, s3 = 6, s4 = 8

Find the sum. 3 2 k+1 140) 3 k=1 2.25619786e+15 A) 2.40463193e+15 C)

139)

140)

4.011018418e+15 2.849934139e+15

3.859285813e+15 1.202315965e+15

2.051088964e+14 2.186029027e+14

Find the nth term {a n} of the geometric sequence. When given, r is the common ratio.

141) a = -2; r =

1 4

141) 1 n-1 4 1 n

A) a n = -2 -

B) a n = -2

C) a n = -2

D) a n =

1 n-1 4

1 (-2)n-1 4

Determine whether the infinite geometric series converges or diverges. If it converges, find its sum. 1 142) 2 + 1 + + ... 2 A) Converges; 4

B) Converges; 1

C) Converges; 2

D) Diverges

Find the first term, the common difference, and give a recursive formula for the arithmetic sequence. 143) 6th term is -10; 15th term is -46 A) a 1 = 10, d = 4, a n = a n-1 + 4 B) a 1 = -30, d = 4, a n = a n-1 + 4 C) a 1 = -10, d = -4, a n = a n-1 - 4

142)

143)

D) a 1 = 10, d = -4, a n = a n-1 - 4

Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. 144) {10n/5 } 144)

A) Geometric; r = 101/5 C) Arithmetic; d = 101/5

B) Geometric; r = 10 D) Neither

Express the sum using summation notation. 145) 2 + 4 + 6 + ... + 10 A)

k=0

k=1

Find the sum of the sequence. 146) 16 (2k + 7) k=1 A) 53

2k2

k=1

B) 384

C) 400

B) 2835

k=1

C) -945

D) 272

D) 945

Evaluate the expression. 6 148) 3 A) 10

146)

Use the Binomial Theorem to find the indicated coefficient or term. 147) The coefficient of x8 in the expansion of (x2 - 3)7 A) -2835

145)

147)

148) B) 120

C) 20

D) 40

Write out the first five terms of the sequence. (-1)n 149) {cn } = (n + 4)(n + 2)

149)

A) c1 = -

1 1 1 1 1 ,c = ,c =,c = ,c =8 2 10 3 12 4 14 5 16

B) c1 = -

1 1 1 1 1 ,c = ,c =,c = ,c =15 2 24 3 35 4 48 5 63

C) c1 =

1 1 1 1 1 ,c =,c = ,c =,c = 8 2 10 3 12 4 14 5 16

D) c1 =

1 1 1 1 1 ,c =,c = ,c =,c = 15 2 24 3 35 4 48 5 63

The sequence is defined recursively. Write the first four terms. 150) a 1 = 2, a 2 = 5; an = a n-2 - 3a n-1 A) a 1 = 2, a 2 = 5, a 3 = -13, a 4 = 44 C) a 1 = 2, a 2 = 5, a 3 = 17, a 4 = -46

150) B) a 1 = 2, a 2 = 5, a 3 = -1, a 4 = -16

D) a 1 = 2, a 2 = 5, a 3 = 1, a 4 = 2

Expand the expression using the Binomial Theorem. 151) (5x - 2y)3 A) 125x3 - 50x2 y + 20xy2 - 8y3

B) 25x3 y - 10x2 y2 + 4xy3

C) 25x3 y - 20x2 y2 + 4xy3

D) 125x3 - 150x2 y + 60xy2 - 8y3

151)

The given pattern continues. Write down the nth term of the sequence {a n} suggested by the pattern.

152)

1 1 1 1 1 , , , , , ... 1 4 9 16 25

A) a n =

1 3n - 2

Find the sum. 153) (-6) + (-1) + 4 + 9 + ... + 39 A) 160

152) B) a n =

1 n-1 2

C) a n =

B) 170

1 n2

D) a n =

C) 165

1 n-1 n

D) 330

153)

Find the nth term {a n} of the geometric sequence. When given, r is the common ratio.

154) 2, 1,

1 1 1 , , , ... 2 4 8

A) a n = 2 · C) a n = 2 ·

154)

1 n+1 2 1 n-1

B) a n = 2 · D) a n = 2 ·

1 n 2 1 n-1 4

Find the indicated term using the given information. 1 155) a = 3 , d = - ; a 31 2 25 2

A) -

155)

B) 18

Expand the expression using the Binomial Theorem. 156) (x2 - 5y)4

A) x8 - 20x6 y + 150x4 y2 - 500x2 y3 + 625y4 C) x8 - 5x6 y + 150x4 y2 - 250x2 y3 + 625y4

37 2

D) - 12

B) x8 - 20x6 y + 150x4 y2 + 20x2 y3 + 625y4 D) x4 - 20x3 y + 150x2 y2 - 500xy3 + 625y4

Evaluate the factorial expression. 9! 157) 7! 2! A) 36

156)

157) B) 0

C) 1

D) 9

Solve. 158) A pendulum bob swings through an arc 80 inches long on its first swing. Each swing thereafter, it swings only 70% as far as on the previous swing. How far will it swing altogether before coming to a complete stop? A) 133 inches B) 267 inches C) 114 inches D) 229 inches

158)

Find the sum. 159)

1 3 3 2 3 3 ... 3 n-1 + + + + + 7 7 7 7 7

A) -

1 (1 - 3 n ) 7

159) B) -

1 (1 - 3 n ) 14

D) -

2 (1 - 3 n ) 7

Evaluate the factorial expression. 4! 160) 2! A) 12

160) B) 4

4 2

D) 2!

Solve. 161) After being struck with a hammer, a gong vibrates 20 vibrations in the first second and in each 2 second thereafter makes as many vibrations as in the previous second. Find how many 3 vibrations the gong makes before it stops vibrating. A) 60 vibrations B) 70 vibrations

Write out the sum. n (k + 1) 162) k=1 A) n + 1 C) 1 + 2 + 3 + ... + n

C) 25 vibrations

161)

D) 30 vibrations

162) B) 2 + 3 + 4 + ... + (n + 1) D) 1 + 2 + 3 + ... + (n + 1)

Find the indicated term of the sequence. 163) The ninth term of the arithmetic sequence 30, 25, 20, ... A) 70 B) -10 C) -40

D) -15

164) The twelfth term of the arithmetic sequence 0, 8, 16, ... A) 77 B) 88 C) 96

D) 104

163)

164)

Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. 165) 2, 4, 7,11, ... 165) A) Geometric; r = 2 B) Geometric; r = 4 C) Arithmetic; d = 2 D) Neither

Find the indicated term using the given information. 166) a 20 = 42 , a 14 = 24 ; a 1 A) -15

166)

B) -9

C) 3

D) -12

Express the sum using summation notation. 10 20 30 10n ... + + + 167) e e2 e3 en A)

n k=0

10 + k ek

n k=1

167) 10k ek

n k=0

10k ek

n k=1

10 + k ek

Use a graphing utility to find the sum of the geometric sequence. Round answer to two decimal places, if necessary. 168) 7 - 21 + 63 - 189 + 567 - ... + 7 · (-3)10 168) A) 310,007

B) 310,016

C) 310,003

D) 310,009

Find the indicated term of the sequence. 169) The twenty-third term of the arithmetic sequence 7 , 2 , -3 , ... A) 122 B) -108 C) -103

169)

D) 117

A geometric sequence is given. Find the common ratio and write out the first four terms. 4 n 170) {tn } = 3 A) r =

4 4 4 4 4 n; t1 = , t2 = , t3 = , t4 = 3 3 3 3 3

B) r =

4 4 16 1.801439851e+16 9.007199255e+15 ;t = ,t = ,t = ,t = 3 1 3 2 9 3 7.599824371e+15 4 2.849934139e+15

C) r =

4 4 4 4 4 ;t = ,t = ,t = ,t = 3 1 3 2 3 3 3 4 3

D) r =

4 4 16 1.801439851e+16 9.007199255e+15 n; t1 = , t2 = ,t = ,t = 3 3 9 3 7.599824371e+15 4 2.849934139e+15

170)

Solve the problem. 171) The population of a town is increasing by 500 inhabitants each year. If its population at the beginning of 1990 was 23,430, what was its population at the beginning of 1998? A) 27,430 inhabitants B) 187,300 inhabitants C) 374,600 inhabitants D) 26,930 inhabitants Find the indicated term of the geometric sequence. 1 1 172) 5th term of 1, , , ... 3 9 A) a 5 =

1 81

B) a 5 =

171)

172)

1 729

C) a 5 =

1 3

D) a 5 =

1 27

Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. 4 n 173) 173) 3

A) Arithmetic; d =

4 3

B) Geometric; r =

C) Geometric; r =

4 3

D) Neither

Determine whether the sequence is arithmetic. 174) 2, 6, 10, 14, 18, ... A) Arithmetic

3 4

B) Not arithmetic

Write out the first five terms of the sequence. 175) {sn } = {3n - 3}

174)

175)

A) s1 = 0, s2 = -3, s3 = -6, s4 = -9, s5 = -12

B) s1 = 0, s2 = 3, s3 = 6, s4 = 9, s5 = 12

C) s1 = 0, s2 = 1, s3 = 2, s4 = 3, s5 = 4

D) s1 = 6, s2 = 9, s3 = 12, s4 = 15, s5 = 18

176) {sn } = {n2 - n}

176)

A) s1 = 0, s2 = 2, s3 = 6, s4 = 12, s5 = 20

B) s1 = 0, s2 = 3, s3 = 8, s4 = 15, s5 = 24

C) s1 = 2, s2 = 6, s3 = 12, s4 = 20, s5 = 30

D) s1 = 1, s2 = 4, s3 = 9, s4 = 16, s5 = 25

Determine whether the infinite geometric series converges or diverges. If it converges, find its sum. 1 177) 4 - 1 + - ... 4 A) Converges; 4

B) Converges;

16 5

C) Converges; - 1

D) Diverges

Solve. 178) Given that a1 = -4, a 2 = -4 and a n+2 = a n+1 - 4a n , what is the fifth term of this recursively defined sequence? A) a 5 = -308

B) a 5 = 28

C) a 5 = -20

177)

178)

D) a 5 = 764

Find the nth term and the indicated term of the arithmetic sequence whose initial term, a, and common difference, d, are given. 179) a = 9; d = -2 179) a n = ?; a 16 = ?

A) a n = 11 - 2n; a 16 = -7

B) a n = 11 + 2n; a 16 = -21

C) a n = 11 - 2n; a 16 = -21

D) a n = 9 - 2n; a 16 = -21

Solve.

180) The number of students in a school in year n is estimated by the model a n = 5n 2 + 12n + 88. About how many students are in the school in each of the first three years? A) 117, 144, 181 B) 110, 132, 169 C) 105, 132, 169

Find the sum. 46 (-4n - 6) 181) n=1 A) -4,508

D) 105, 132, 154

181) B) -4,324

C) -4,485

The sequence is defined recursively. Write the first four terms. 182) a 1 = 3; a n = a n-1 - 3 A) a 1 = 3, a 2 = 6 , a 3 = 9 , a 4 = 12

C) a 1 = 3, a 2 = 2 , a 3 = -1 , a 4 = -4

Evaluate the expression. 6 183) 6 A) 720

180)

D) -4,600

182) B) a 1 = 3, a 2 = 0, a 3 = -3, a 4 = -6

D) a 1 = -3, a 2 = -6, a 3 = -9, a 4 = -12

B) 1

Find the indicated term of the geometric sequence. 184) 5th term of -1, 2, -4, ... A) a 5 = 32 B) a 5 = 16

C) 0

D) 2

C) a 5 = -32

D) a 5 = -16

183)

184)

Solve. 185) A ping-pong ball is dropped from a height of 9 ft and always rebounds

1 of the distance fallen. 3

Find the total sum of the rebound heights of the ball. A) 3 ft B) 4.5 ft C) 6 ft

185)

D) 13.5 ft

Find the nth term {a n} of the geometric sequence. When given, r is the common ratio. 1 1 1 , - , , ... 2 4 8 1 n-1 A) a n = 2 · 4

186) 2, - 1,

C) a n = 2 · -

186) B) a n = 2 · -

1 n 2

D) a n = 2 · -

1 n-1 2 1 n+1 2

The sequence is defined recursively. Write the first four terms. 1 187) a 1 = 135; a n+1 = (a n ) 3 A) a 1 = 135, a 2 = 45, a 3 = 15, a 4 = 5

B) a 1 = 135, a 2 = 405, a 3 = 1215, a 4 = 3645

C) a 1 = 135, a 2 = 67.5, a 3 = 33.75, a 4 = 16.875

Find the sum. 25 (-2n + 1) 188) n=1 A) -625

187) D) a 1 = 135, a 2 = 105, a 3 = 75, a 4 = 45

188) B) -550

C) -462.5

D) -600

Use the Binomial Theorem to find the indicated coefficient or term. 189) The 5th term in the expansion of (4x - 3y)10

189)

Find the indicated term using the given information. 190) a = 1 , d = 5 ; a 47

190)

A) -23,224,320x6 y5 C) 17,418,240x4 y6

A) 236

B) -23,224,320x4 y6 D) 69,672,960x6 y4

B) -229

C) 231

D) -234

Find the sum. 191) 5 + 10 + 15 + ... + 540

191)

A) 29430 C)

B) 28890

2.041140258e+15 6.871947674e+10

4.007719883e+15 1.374389535e+11

A geometric sequence is given. Find the common ratio and write out the first four terms. 192) {sn } = {3 2n } A) r = 9; s1 = 6, s2 = 12, s3 = 18, s4 = 24

B) r = 6; s1 = 6, s2 = 12, s3 = 18, s4 = 24

C) r = 3; s1 = 9, s2 = 81, s3 = 729, s4 = 6,561

D) r = 9; s1 = 9, s2 = 81, s3 = 729, s4 = 6,561

192)

Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. 193) {2n 2 } 193)

A) Arithmetic; d = 2

B) Geometric; r =

C) Geometric; r = 2

D) Neither

2 2

Write out the first five terms of the sequence. 2n 194) {cn } = n

194)

A) c1 = 1, c2 = 2, c3 = 4, c4 = 8, c5 = 16 C) c1 = 2, c2 = 2, c3 =

8 32 , c4 = 4, c5 = 3 5

Solve. 195) Find the 10th term of the geometric sequence A) 19683

B) c1 = 2, c2 = 4, c3 = 8, c4 = 16, c5 = 32 D) c1 = 0, c2 = 2, c3 = 2, c4 =

1 , 1, 3, ... 3

B) 6561

195)

C) 177,147

Expand the expression using the Binomial Theorem. 196) (2x + 5)3 A) 8x3 + 60x2 + 149x + 125

D) 2187

196)

B) 8x3 + 60x2 + 60x + 125

C) 4x2 + 20x + 25

197) x -

8 ,c =4 3 5

D) 4x6 + 10x3 + 15,625

3 4 x

197)

A) x4 - 12x5/2 + 54x C) x4 -

108 81 + x x2

B) x4 +

81 x2

D) x4 - 12x3/2 + 54x -

108 81 + x x2

Use the Binomial Theorem to find the indicated coefficient or term. 198) The 3rd term in the expansion of (9x + 6)3 A) 1,458x2

B) 36

C) 972x

198) D) 1,944x

Write out the first five terms of the sequence. n+3 199) {sn } = (-1)n - 1 2n - 1 A) s1 = 4, s2 =

199)

5 6 8 , s3 = , s4 = 1, s5 = 3 5 9

B) s1 = 4, s2 = -

5 6 8 , s3 = , s4 = - 1, s5 = 3 5 9

5 6 8 , s = - , s4 = 1, s5 = 3 3 5 9

D) s1 = -4, s2 =

5 6 8 , s = , s = - 1, s5 = 3 3 5 4 9

C) s1 = -4, s2 =

200) {sn } = {n - 5}

200)

A) s1 = -4, s2 = -3, s3 = -2, s4 = -1, s5 = 0

B) s1 = -5, s2 = -4, s3 = -3, s4 = -2, s5 = -1 D) s1 = 0, s2 = 1, s3 = 2, s4 = 3, s5 = 4

C) s1 = 5, s2 = 10, s3 = 15, s4 = 20, s5 = 25

Find the first term, the common difference, and give a recursive formula for the arithmetic sequence. 201) 7th term is 27; 16th term is 81 A) a 1 = -15, d = 6, a n = a n-1 - 6 B) a 1 = -9, d = 6, a n = a n-1 + 6 C) a 1 = -9, d = 6, a n = a n-1 - 6

D) a 1 = -15, d = 6, a n = a n-1 + 6

Express the sum using summation notation. 202) 2 2 + 3 2 + 4 2 + ... + 8 2 A)

k=2

k=1

k=3

Find the indicated term using the given information. 203) -14 , -19 , -24 , ... ; a 21 A) 91

D) ( k - 1)2

202) n

k=2

203)

B) 86

C) -114

D) -119

Write out the first five terms of the sequence. 3n 204) {sn } = 4n + 1 A) s1 =

201)

204)

9 1.519964874e+15 2.849934139e+15 8.549802418e+15 , s2 = , s3 = , s4 = ,s = 17 3.659174697e+15 9.042383627e+15 3.606398139e+16 5

6.412351813e+15 3.603759311e+16

B) s1 =

3 2 9 12 5 ,s = ,s = ,s = ,s = 5 2 3 3 13 4 17 5 7

C) s1 =

3 9 1.519964874e+15 2.849934139e+15 8.549802418e+15 ,s = ,s = ,s = ,s = 5 2 17 3 3.659174697e+15 4 9.042383627e+15 5 3.606398139e+16

D) s1 =

2 9 12 5 18 ,s = ,s = ,s = ,s = 3 2 13 3 17 4 7 5 25

Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. 205) 3, 5, 7, 11, 13, ... 205) A) Geometric; r = 2 B) Arithmetic; d = 4 C) Arithmetic; d = 2 D) Neither

Use the Binomial Theorem to find the indicated coefficient or term. 206) The coefficient of x in the expansion of (2x + 4)5 A) 1,280

B) 2,560

C) 5,120

D) 640

206)

Use a graphing utility to find the sum of the geometric sequence. Round answer to two decimal places, if necessary. 207) 207) 5 4(2)k k=1 A) 120 B) 24 C) 340 D) 248 Find the sum of the sequence. 208) 8 k k=1 A) 8

208)

B) 56

Find the indicated term of the sequence. 209) The eighteenth term of the arithmetic sequence 5 A) -97 3 B) -103 3

C) 36

3, -1 3, -7 3, ... C) 113 3

D) 7

209) D) 107 3

Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. 210) {5n 2 - 4} 210)

A) Geometric; r = 5 C) Arithmetic; d = -4

B) Arithmetic; d = 5 D) Neither

Determine whether the infinite geometric series converges or diverges. If it converges, find its sum. 1 211) 32 + 8 + 2 + + . . . 2 A) Converges;

128 3

C) Converges; -

B) Converges; 42

32 3

D) Diverges

Solve. 212) To save for retirement, you decide to deposit $1,750 into an IRA at the end of each year for the next 30 years. If the interest rate is 9% per year compounded annually, find the value of the IRA after 30 years. (Round to the nearest dollar.) A) $217,237 B) $238,538 C) $21,468 D) $11,756,391 Find the sum. 46 (2n - 8) 213) n=1 A) 1,932

211)

212)

213) B) 2,093

C) 1,794

D) 1,748

Solve. 214) Jack decided to put $600 into an IRA account every 3 months at a rate of 6% compounded quarterly. Find a recursive formula that represents his balance at the end of each quarter. How long will it be before the value of the account is $100,000? What will be the balance in 30 years when Jack retires? 0.6 )B(n - 1) + 600; 7 years; $4 million A) B0 = 600 Bn = (1 + 4 B) B0 = 600 Bn = (1 +

0.06 )B(n - 1) + 600; 18 years; $151,860 3

C) B0 = 600 Bn = (1 +

0.06 )B(n - 1) + 600; 21 years; $202,355 4

D) B0 = 600 Bn = (1 +

0.06 )B + 600; 10 years; $6.8 million 12 (n - 1)

Determine whether the sequence is arithmetic. 215) 4, 12, 36, 108, 972, ... A) Arithmetic

215)

B) Not arithmetic

Find the nth term {a n} of the geometric sequence. When given, r is the common ratio.

216) a = -2; r = 3

A) a n = -2 · -3 n-1

B) a n = -2 · 3n

C) a n = 3 · -2n-1

D) a n = -2 · 3n-1

Solve. 217) After working for 25 years you would like to have $800,000 in an annuity for early retirement. If the annual interest rate is 7.5%, compounded monthly, what will your monthly deposit need to be? A) $1146.98 B) $911.93 C) $3088.48 D) $2666.67 Find the sum of the sequence. 218) 4 k(k + 12) k=2 A) 150

B) 54

C) 137

219) 4 , 10 , 16 , 22 , 28 , ...

217)

D) 92

B) a n = 6 n - 1

C) a n = 2 ( 3 n - 1 )

D) a n = 4 ( 6 )n-1

Evaluate the expression. 6 220) 2 A) 1

216)

218)

The given pattern continues. Write down the nth term of the sequence {a n} suggested by the pattern.

A) a n = 2 n - 6

214)

219)

220) B) 6

C) 0

D) 15

Find the sum of the sequence. 221) 4 (-1)k · -6k k=1 A) -12

221)

B) 1,296

C) 60

D) -60

Write out the first five terms of the sequence. 2n + 5 222) {cn } = 2n

222)

A) c1 =

7 9 11 13 3 , c2 = , c3 = , c4 = , c5 = 2 4 6 8 2

B) c1 =

7 9 11 13 15 , c2 = , c3 = , c4 = , c5 = 2 2 9 2 2

C) c1 =

9 11 13 3 17 ,c = ,c = ,c = ,c = 4 2 6 3 8 4 2 5 12

D) c1 =

9 11 13 15 17 ,c = ,c = ,c = ,c = 2 2 2 3 2 4 2 5 2

A geometric sequence is given. Find the common ratio and write out the first four terms. 5n 223) {un } = 2n - 1 A) r =

5 5 25 125 5.497558139e+15 ;u = ,u = ,u = , u4 = 2 1 2 2 4 3 8 1.407374884e+14

B) r =

5 25 125 5.497558139e+15 ; u1 = 5, u2 = , u3 = , u4 = 2 2 4 7.036874418e+13

C) r = 5; u1 = 5, u2 =

25 125 5.497558139e+15 , u3 = , u4 = 2 4 7.036874418e+13

D) r = 5; u1 = 5, u2 =

25 125 5.497558139e+15 ,u = , u4 = 2 3 2 1.759218604e+13

The sequence is defined recursively. Write the first four terms. 224) a 1 = 4; a n = 4a n-1 A) a 1 = 12, a 1 = 48, a 2 = 192, a4 = 384 C) a 1 = 4, a 2 = 16, a3 = 64, a 4 = 256

223)

224) B) a 1 = 4, a 1 = 15, a2 = 14, a 4 = 13 D) a 1 = 4, a 1 = 18, a2 = 66, a 4 = 258

Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given. 225) a = 2; r = 4 225) A) a 5 = 2,048 5 , a n = 2 · 4n n B) a 5 = 2 + 16 , an = 2 + 4 (n-1) C) a 5 = 512 4 , a n = 2 · 4 n-1 n-1

D) a 5 = 512 , a n = 2 · 4 n-1

Determine whether the sequence is arithmetic. 226) 2, -3, -8, -13, -18, ... A) Arithmetic

B) Not arithmetic

Find the sum. 227) -3 + 1 + 5 + 9 + 13 + ... + (4n - 7) A) n(4n - 7) B) n(4n + 7)

C) n(2n + 5)

226)

D) n(2n - 5)

227)

Express the sum using summation notation. 228) 4 2 + 8 3 + 124 + ... + 329 A)

k=1 8

4k2k - 1

(4k)k

k=1

k=1 8

228) 2(k - 1)k + 1 (4k)k + 1

k=1

Solve.

229) Use the Binomial Theorem to approximate (0.98)6 = (1 - 2(10-2 ))6 to 5 decimal places. A) 0.85841 B) 0.88548 C) 0.88854 D) 0.88584

Expand the expression using the Binomial Theorem. 230) ( x + 2)4 A) x2 + 4 2x3/2 + 12x + 8 2x1/2 + 4 C) x2 + 4

Find the sum of the sequence. 231) 4 3k k=1 A) 30

B) x2 + 4 2x1/2 + 12x + 8 2x1/2 + 16 D) x2 + 2 2x3/2 + 6x + 4 2x1/2 + 4

229)

230)

231)

B) 39

C) 120

D) 84

Use a graphing utility to find the sum of the geometric sequence. Round answer to two decimal places, if necessary. 232) 232) 12 1 · (-2)k-1 8 k=1 A) -170.87 B) -171.37 C) -170.62 D) -169.75 Find the first term, the common difference, and give a recursive formula for the arithmetic sequence. 233) 7th term is -28; 16th term is -82 A) a 1 = 14, d = -6, a n = a n-1 - 6 B) a 1 = 8, d = 6, a n = a n-1 + 6 C) a 1 = 8, d = -6, a n = a n-1 - 6

D) a 1 = 14, d = 6, a n = a n-1 + 6

Use the Binomial Theorem to find the indicated coefficient or term. 234) The coefficient of x in the expansion of (9x + 8)3 A) 1,728

B) 64

Find the indicated term of the geometric sequence. 235) 8th term of 1, 3, 9, ... A) a 8 = 6,561 B) a 8 = 2,187

C) 1,944

D) 3,456

C) a 8 = 19,683

D) a 8 = 9

Use the Binomial Theorem to find the indicated coefficient or term. 236) The coefficient of x4 in the expansion of (3x + 4)6 A) 34,560

233)

B) 19,440

C) 11,664

D) 23,328

234)

235)

236)

Evaluate the factorial expression. 237) 5! A) 20 238)

B) 9

C) 120

D) 10

3!5! 5!

237)

238) 21 20

B) 1

1 20

D) 6

Determine whether the infinite geometric series converges or diverges. If it converges, find its sum. 239) k=1

1 k- 1 ·5 2

A) Converges;

239) 5 2

Find the sum. 240) 1 + 3 + 5 + ... + 697 A) 122,150

B) Converges;

C) Converges; 25

D) Diverges

B) 122,500

C) 121,104

D) 121,801

Find the nth term {a n} of the geometric sequence. When given, r is the common ratio.

241) -8, -24, -72, -216, -648, ... A) a n = -8 · 3n

B) a n = -8 · 3n-1

C) a n = -8 · 3n

D) a n = a 1 + 3 n

The given pattern continues. Write down the nth term of the sequence {a n} suggested by the pattern.

242) 0, 2, 6, 12, 20, ...

A) a n = 2n - 2

B) a n = n2 - n

C) a n = 2n-1 - 1

B) 6

C) 3

241)

242)

D) a n = 4n - 6

Use the Binomial Theorem to find the indicated coefficient or term. 1 1 3 243) The coefficient of in the expansion of 2x + x x A) 9

240)

243) D) 2

Use a graphing utility to find the sum of the geometric sequence. Round answer to two decimal places, if necessary. 244) 244) 5 2(-4)k k=1 A) 24 B) -5,140 C) 248 D) -1,640 Evaluate the expression. 10 245) 3 A) 60

B) 120

C) 604,800

D) 3

245)

Answer Key Testname: CHAPTER 13 1) First we show that the statement is true when n = 1. (1) For n = 1, we get 3 = (5(1) + 1) = 3. 2 This is a true statement and Condition I is satisfied. Next, we assume the statement holds for some k. That is, k 3 + 8 + 13 + ... + (5k - 2) = (5k + 1) is true for some positive integer k. 2 We need to show that the statement holds for k + 1. That is, we need to show that k+ 1 3 + 8 + 13 + ... + (5(k + 1) - 2) = (5(k + 1) + 1). 2 So we assume that 3 + 8 + 13 + ... + (5k - 2) = equation. 3 + 8 + 13 + ... + (5k - 2) + 5(k + 1) - 2 =

k (5k + 1) is true and add the next term, 5(k + 1) - 2, to both sides of the 2

k (5k + 1) + 5(k + 1) - 2 2

1 [k(5k + 1) + 10(k + 1) - 4] 2

1 (5k2 + k + 10k + 10 - 4) 2

1 (5k2 + 11k + 6) 2

1 (k + 1)(5k + 6) 2

k+ 1 (5k + 5 + 1) 2

k+ 1 (5(k + 1) + 1) 2

Condition II is satisfied. As a result, the statement is true for all natural numbers n. 2) $865 3) Assume the statement is true for some natural number k. Then 2 + 4 + 6 + 8 + ... + 2k + 2(k + 1) = (k2 + k + 3) + 2(k +1)

So the statement is true for k + 1.

= (k2 + 3k +2) + 3 = (k + 2)(k + 1) + 3 = ((k + 1) + 1)(k + 1) + 3 = (k + 1)2 + (k + 1) + 3

However, when n = 1, the left side of the statement is 2n = 2(1) = 2, and the right side of the statement is n 2 + n + 3 = 1 2 + 1 + 3 = 5, so the formula is false for n = 1.

4) When n = 1, n 2 - n + 3 = 1 2 - 1 + 3 = 3, which is a prime number, so the statement is true when n = 1. When n = 3, n 2 - n + 3 = 3 2 - 3 + 3 = 9, which is not a prime number, so the statement is not true for n = 3. 5) a) $28,081.98 b) $411,032.84

Answer Key Testname: CHAPTER 13 6) First, we show that the statement is true when n = 1. 6 (1) - 1 5 = = 1. For n = 1, we get 1 (or 6 [(1) - 1]) = 5 5 This is a true statement and Condition I is satisfied. Next, we assume the statement holds for some k. That is, 6k - 1 1 + 6 + 62 + ... + 6 k - 1 = is true for some positive integer k. 5 We need to show that the statement holds for k + 1. That is, we need to show that 6k + 1 - 1 1 + 6 + 62 + ... + 6 k = . 5 So we assume that 1 + 6 + 6 2 + ... + 6 k - 1 =

1 + 6 + 6 2 + ... + 6 k - 1 + 6 k =

6k - 1 is true and add the next term, 6k, to both sides of the equation. 5

6k - 1 + 6k 5

6k - 1 + 5 · 6k 5

6 · 6k - 1 5

6k + 1 - 1 . 5

Condition II is satisfied. As a result, the statement is true for all natural numbers n. 7) $25,924.25 8) 299,880 gallons

Answer Key Testname: CHAPTER 13 9) First we show that the statement is true when n = 1. (1)(1 + 1) For n = 1, we get 1 = = 1. 2 This is a true statement and Condition I is satisfied. Next, we assume the statement holds for some k. That is, k(k + 1) 1 ·1 + 2 ·1 + 3 ·1 + . . . + k = is true for some positive integer k. 2 We need to show that the statement holds for k + 1. That is, we need to show that (k + 1)(k + 2) 1 · 1 + 2 · 1 + 3 · 1 + . . . + (k + 1) = . 2 So we assume that 1 · 1 + 2 · 1 + 3 · 1 + . . . + k = equation. 1 · 1 + 2 · 1 + 3 · 1 + . . . + k + (k + 1) =

k(k + 1) is true and add the next term, (k + 1), to both sides of the 2

k(k + 1) + (k + 1) 2 =

[k(k + 1) + 2(k + 1)] 2

(k + 1)(k + 2) 2

Condition II is satisfied. As a result, the statement is true for all natural numbers n. 10) First we show that the statement is true when n = 1. For n = 1, we get 6 = 3(1)(1 + 1) = 6. This is a true statement and Condition I is satisfied.

Next, we assume the statement holds for some k. That is, 6 + 12 + 18 + ... + 6k = 3k(k + 1) is true for some positive integer k. We need to show that the statement holds for k + 1. That is, we need to show that 6 + 12 + 18 + ... + 6(k + 1) = 3(k + 1)(k + 2). So we assume that 6 + 12 + 18 + ... + 6k = 3k(k + 1) is true and add the next term, 6(k + 1), to both sides of the equation. 6 + 12 + 18 + ... + 6k + 6(k + 1) = 3k(k + 1) + 6(k + 1) = (k + 1)(3k + 6) = 3(k + 1)(k + 2) Condition II is satisfied. As a result, the statement is true for all natural numbers n. 11) First we show that the statement is true when n = 1. 1 1 212 For n = 1, we get 3 = = 3. 1 12 This is a true statement and Condition I is satisfied. Next, we assume the statement holds for some k. That is, 1 k 2 12 1 1 2 1 k- 1 2+2· +2· is true for some positive integer k. + ... + 2 · = 2 2 2 1 12 We need to show that the statement holds for k + 1. That is, we need to show that

Answer Key Testname: CHAPTER 13

2+2·

1 1 2 +2· + ... + 2 · 2 2

So we assume that 2 + 2 ·

1 +2· 2

1 (k + 1) - 1 = 2

21-

1 k+ 1 2

1 2

1 2 1 k-1 + ... + 2 · = 2 2

1 1 2 +2· + ... + 2 · 2 2

1 k- 1 1 (k + 1) - 1 +2· = 2 2

2 1-

1 k 2

1 12 1 k 2

21=

1 12 1 k 2

21=

121-

1 2

+2·

1 (k + 1) - 1 2

1 k 2

2 +

1 k + 2

1 2

1 2 1 k 2

121-

1 k 1 12 2

121-

is true and add the next term, 2 ·

1 2

to both sides of the equation. 2+2·

1 k 2

21-

1 k+ 1 2

1 2

1 k+ 1 2 1-

1 2

Condition II is satisfied. As a result, the statement is true for all natural numbers n. 12) $1824.12

1 (k + 1) - 1 , 2

Answer Key Testname: CHAPTER 13

13) When n = 1, the left side of the statement is statement is 1 -

1 1 1 = = , and the right side of the n 1 2 2 2

1 1 1 1 =1= 1 - = , so the statement is true when n = 1. 2 2 2n 21

Assume the statement is true for some natural number k. Then, 1 1 1 1 1 1 1 1 1 1 1 + + + + ... + + = 1+ =1=11. 2 4 8 16 2 2 k 2 k+1 2k 2 k+1 2k 2 k+1 So the statement is true for k + 1. Conditions I and II are satisfied; by the Principle of Mathematical Induction, the statement is true for all natural numbers. 14) When n = 1, 7 n - 2n = 7 1 - 2 1 = 5, so the statement is true when n = 1. Assume the statement is true for some natural

number k. That is, 7 k - 2 k = 5m for some integer m. Then, 7 k+1 - 2 k+1 = 7(7 k - 2 k) + 5 · 2 k = 7(5m) + 5 · 2 k = 5(7m + 2 k).

So the statement is true for k + 1. Conditions I and II are satisfied; by the Principle of Mathematical Induction, the statement is true for all natural numbers. 15) First, we show the statement is true when n = 1. 5(1)((1) + 1) For n = 1, we get 5 = = 5. 2 This is a true statement and Condition I is satisfied. Next, we assume the statement holds for some k. That is, 5k(k + 1) 5 + 10 + 15 + ... + 5k = is true for some positive integer k. 2 We need to show that the statement holds for k + 1. That is, we need to show that 5(k + 1)(k + 2) 5 + 10 + 15 + ... + 5(k + 1) = . 2 So we assume that 5 + 10 + 15 + ... + 5k =

5 + 10 + 15 + ... + 5k + 5(k + 1) =

5k(k + 1) is true and add the next term, 5(k + 1), to both sides of the equation. 2

5k(k + 1) + 5(k + 1) 2

= 5(

k(k + 1) + k + 1) 2

= 5(

k(k + 1) 2(k + 1) + ) 2 2

=5·

k(k + 1) + 2(k + 1) 2

=5·

(k + 1)(k + 2) 2

5(k + 1)(k + 2) . 2

Condition II is satisfied. As a result, the statement is true for all natural numbers n.

Answer Key Testname: CHAPTER 13 16) First we show that the statement is true when n = 1. 1(1 + 1)(1 + 2) For n = 1, we get 2 = = 2. 3 This is a true statement and Condition I is satisfied. Next, we assume the statement holds for some k. That is, k(k + 1)(k + 2) 1 · 2 + 2 · 3 + 3 · 4 + . . . + k(k + 1) = is true for some positive integer k. 3 We need to show that the statement holds for k + 1. That is, we need to show that (k + 1)(k + 2)(k + 3) 1 · 2 + 2 · 3 + 3 · 4 + . . . + (k + 1)(k + 2) = . 3 So we assume that 1 · 2 + 2 · 3 + 3 · 4 + . . . + k(k + 1) = sides of the equation.

k(k + 1)(k + 2) is true and add the next term, (k + 1)(k + 2), to both 3

1 · 2 + 2 · 3 + 3 · 4 + . . . + k(k + 1) + (k + 1)(k + 2) =

k(k + 1)(k + 2) + (k + 1)(k + 2) 3

k(k + 1)(k + 2) 3(k + 1)(k + 2) + 3 3

k(k + 1)(k + 2) + 3(k + 1)(k + 2) 3

(k + 1)(k + 2)(k + 3) 3

Condition II is satisfied. As a result, the statement is true for all natural numbers n. 17) 106 deer

Answer Key Testname: CHAPTER 13 18) First we show that the statement is true when n = 1. 1(6 · 12 - 3 · 1 - 1) = 1. For n = 1, we get 1 = 2 This is a true statement and Condition I is satisfied. Next, we assume the statement holds for some k. That is, k(6k2 - 3k - 1) 1 2 + 42 + 72 + . . . + (3k - 2)2 = is true for some positive integer k. 2 We need to show that the statement holds for k + 1. That is, we need to show that (k + 1)(6(k + 1)2 - 3(k + 1) - 1) 1 2 + 42 + 72 + . . . + (3(k + 1) - 2)2 = . 2 So we assume that 1 2 + 42 + 72 + . . . + (3k - 2)2 = sides of the equation. 1 2 + 42 + 72 + . . . + (3k - 2)2 + (3(k + 1) - 2)2 =

Simplify the expression

k(6k2 - 3k - 1) is true and add the next term, (3(k + 1) - 2)2 , to both 2

k(6k2 - 3k - 1) + (3(k + 1) - 2)2 2

k(6k2 - 3k - 1) + (3k + 1)2 2

k(6k2 - 3k - 1) 2(9k2 + 6k + 1) + 2 2

6k3 - 3k2 - k + 18k2 + 12k + 2 2

6k3 + 15k2 + 11k + 2 2

(k + 1)(6(k + 1)2 - 3(k + 1) - 1) to verify: 2

(k + 1)(6(k + 1)2 - 3(k + 1) - 1) (k + 1)(6(k2 + 2k + 1) - 3k -3 - 1) = 2 2 =

(k + 1)(6k2 + 12k + 6 - 3k - 4) 2

(k + 1)(6k2 + 9k + 2) 2

6k3 + 15k2 + 11k + 2 2

Condition II is satisfied. As a result, the statement is true for all natural numbers n.

Answer Key Testname: CHAPTER 13 19) First we show that the statement is true when n = 1. 1 1 1 For n = 1, we get = = . 2 1+1 2 This is a true statement and Condition I is satisfied. Next, we assume the statement holds for some k. That is, 1 1 1 1 = 11... 1is true for some positive integer k. 2 3 k+ 1 k+ 1 We need to show that the statement holds for k + 1. That is, we need to show that 1 1 1 1 11... 1. = 2 3 k+ 2 k+ 2 So we assume that 1 -

1 2

the equation. 1 1 1 11... 12 3 k+ 1

1 1 1 1 ... 1is true and multiply the next term, 1 , to both sides of = 3 k+ 1 k+ 1 k+ 2 1-

1 1 1 1= k+ 2 k+ 1 k+ 2 =

1 1 k + 1 (k + 1)(k + 2)

k+ 2 1 (k + 1)(k + 2) (k + 1)(k + 2)

k+2- 1 (k + 1)(k + 2)

k+ 1 (k + 1)(k + 2)

1 (k + 2)

Condition II is satisfied. As a result, the statement is true for all natural numbers n. 20) First we show that the statement is true when n = 1. For n = 1, we get 2 5 = 2 (5·1) = 2 5 This is a true statement and Condition I is satisfied.

Next, we assume the statement holds for some k. That is, 25 k = 2 5k is true for some positive integer k.

We need to show that the statement holds for k + 1. That is, we need to show that 25 (k + 1) = 2 (5(k + 1)). So we assume that 2 5 k = 2 5k is true and multiply the next term, 2 5 (k + 1), to both sides of the equation. 25 k 2 5 (k + 1) = 2 5k 2 5 (k + 1) 25 (k + (k + 1)) = 2 5k 2 5(k + 1) 25 (2k + 1) = 2 (5k + 5k + 5))

2 (5(2k + 1)) = 2 (5(2k + 1)) Condition II is satisfied. As a result, the statement is true for all natural numbers n. 21) $75,937

Answer Key Testname: CHAPTER 13 22) First, we show that the statement is true when n = 1. For n = 1, n 2 - n + 2 = (1)2 - (1) + 2 = 2. This is a true statement and Condition I is satisfied.

Next, we assume the statement holds for some k. That is, k2 - k + 2 is divisible by 2 is true for some positive integer k.

We need to show that the statement holds for k + 1. That is, we need to show that (k + 1)2 - (k + 1) + 2 is divisible by 2. So we assume k2 - k + 2 is divisible by 2 and look at the expression for n = k + 1. (k + 1)2 - (k + 1) + 2 = k2 + 2k + 1 - k - 1 + 2 = (k2 - k + 2) + 2k

Since k2 - k + 2 is divisible by 2, then k2 - k + 2 = 2m for some integer m. Hence, (k + 1)2 - (k + 1) + 2 = (k2 - k + 2) + 2k = 2m + 2k = 2(m + k).

Condition II is satisfied. As a result, the statement is true for all natural numbers n. 23) approximately 13.4 feet 24) C 25) D 26) B 27) A 28) A 29) B 30) D 31) B 32) A 33) D 34) D 35) C 36) B 37) D 38) C 39) B 40) B 41) C 42) B 43) D 44) D 45) D 46) D 47) B 48) B 49) B 50) A 51) D

Answer Key Testname: CHAPTER 13 52) D 53) C 54) D 55) D 56) D 57) C 58) B 59) A 60) B 61) C 62) A 63) B 64) C 65) B 66) D 67) C 68) B 69) D 70) C 71) A 72) B 73) A 74) A 75) C 76) B 77) B 78) B 79) A 80) D 81) B 82) C 83) A 84) D 85) D 86) D 87) A 88) A 89) D 90) C 91) A 92) B 93) A 94) B 95) A 96) C 97) A 98) B 99) D 100) A 101) B 42

Answer Key Testname: CHAPTER 13 102) D 103) D 104) A 105) D 106) A 107) C 108) C 109) B 110) A 111) C 112) A 113) B 114) B 115) C 116) D 117) C 118) B 119) B 120) D 121) C 122) C 123) A 124) A 125) C 126) C 127) A 128) B 129) C 130) D 131) B 132) B 133) A 134) C 135) A 136) C 137) C 138) C 139) A 140) A 141) B 142) A 143) D 144) A 145) D 146) B 147) C 148) C 149) B 150) A 151) D 43

Answer Key Testname: CHAPTER 13 152) C 153) C 154) C 155) D 156) A 157) A 158) B 159) B 160) A 161) A 162) B 163) B 164) B 165) D 166) A 167) B 168) D 169) C 170) B 171) A 172) A 173) C 174) A 175) B 176) A 177) B 178) C 179) C 180) C 181) D 182) B 183) B 184) D 185) B 186) B 187) A 188) A 189) D 190) C 191) A 192) D 193) D 194) C 195) B 196) A 197) A 198) C 199) B 200) A 201) B 44

Answer Key Testname: CHAPTER 13 202) A 203) C 204) C 205) D 206) B 207) D 208) C 209) A 210) D 211) A 212) B 213) C 214) C 215) B 216) D 217) B 218) C 219) C 220) D 221) A 222) A 223) B 224) C 225) C 226) A 227) D 228) D 229) D 230) A 231) C 232) C 233) C 234) A 235) B 236) B 237) C 238) D 239) D 240) D 241) B 242) B 243) B 244) D 245) B

Chapter 14 Exam Name___________________________________

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Construct a probability model for the experiment. 1) Spinner I has 3 sections of equal area, numbered 1, 2, and 3. Spinner II has 3 sections of equal 1) area, labeled Red, Yellow, and Green. Spin Spinner I twice, then Spinner II. What is the probability of getting a 2, followed by a 1, followed by Yellow or Red? 2) Rolling a 6-sided fair die once and tossing a fair coin once. Solve the problem. 3) A die is weighted so that an even-numbered face is three times as likely to occur as an odd-numbered face. What probability should be assigned to each face? Construct a probability model for the experiment. 4) Tossing two fair coins once

5) Spinner I has 4 sections of equal area, numbered 1, 2, 3, and 4, and Spinner II has 4 sections of 5) equal area, labeled Red, Yellow, Green, and Blue. Spin Spinner I and then spin Spinner II. What is the probability of getting a 1 or 3 followed by Red? 6) Rolling a 6-sided fair die once

Solve the problem. 7) How many different 11-letter words (real or imaginary) can be formed from the letters of the word MISSISSIPPI? Leave your answer in factorial form.

Construct a probability model for the experiment. 8) Tossing a fair coin twice given that the coin is weighted so that heads is three times as likely as tails to occur.

9) Tossing one fair coin three times

10) Spinner I has 4 sections of equal area, numbered 1, 2, 3, and 4. Spinner II has 3 sections of equal 10) area, labeled Red, Yellow, and Green. Spinner III has 2 sections of equal area labeled A and B. Spin Spinner I, then Spinner II, then Spinner III. What is the probability of getting a 2, followed by Yellow or Green, followed by B? Solve the problem. 11) A twelve-sided die is weighted so that only the numbers 1 through 7 will appear and they will occur with the same probability. What probability should be assigned to each face? Construct a probability model for the experiment. 12) Rolling a 6-sided fair die twice

11)

12)

Solve the problem. 13) A coin is weighted so that heads is 11 times as likely as tails to occur. What probability should be assigned to heads? to tails?

13)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the value of the permutation. 14) P(5, 1) A) 5

B) 2.5

C) 48

D) 120

Solve the problem. 15) In a student survey, 92 students indicated that they speak Spanish, 31 students indicated that they speak French, 10 students indicated that they speak both Spanish and French, and 138 students indicated that they speak neither. How many students participated in the survey? A) 261 B) 113 C) 241 D) 251 16) A group of 9 friends goes bowling. How many different possibilities are there for the order in which they play if the youngest person is to bowl first? A) 8 B) 9 C) 40,320 D) 362,880 Write down all the subsets of the given set. 17) {2, , 9, } A) {2}, { }, {9}, { }, {2, }, {2, 9}, {2, }, { , 9}, { , }, {9, }, {2, , 9}, {2, , }, {2, 9, }, { , 9, }, {2, , 9, } B) {2}, { }, {9}, { }, {2, }, {2, 9}, {2, }, { , 9}, { , }, {9, }, {2, , 9}, {2, , }, {2, 9, }, { , 9, }, C) {2}, { }, {9}, { }, {2, }, {2, 9}, {2, }, { , 9}, { , }, {9, }, {2, , 9}, {2, , }, {2, 9, }, { , 9, }, {2, , 9, }, D) {2}, { }, {9}, { }, {2, }, {2, 9}, {2, }, { , 9}, { , }, {9, }, {2, , }, {2, 9, }, { , 9, }, {2, , 9, }, Solve the problem. 18) A lottery game has balls numbered 1 through 21. What is the probability of selecting an even numbered ball or a 11? 10 3 10 11 A) B) C) D) 11 7 21 21

14)

15)

16)

17)

18)

19) In a survey about the number of siblings of college students, the following probability table was constructed:

19)

Number of Siblings Probability 0 0.26 1 0.33 2 0.19 3 0.12 4 or more 0.10 What is the probability that a student has at least 2 siblings? A) 0.22 B) 0.59 C) 0.78

D) 0.41

20) How many arrangements of answers are possible in a multiple-choice test with 10 questions, each of which has 4 possible answers? A) 1,048,576 B) 5,040 C) 151,200 D) 210

20)

21) List all the combinations of 6 objects a, b, c, d, e, and f taken 2 at a time. What is C(6, 2)? 21) A) aa, ab, ac, ad, ae, af, ba, bb, bc, bd, be, bf, ca, cb, cc, cd, ce, cf, da, db, dc, dd, de, df, ea, eb, ec, ed, ee, ef, fa, fb, fc, fd, fe, ff C(6, 2) = 36 B) ab, ac, ad, ae, af, bc, bd, be, bf, cd, ce, cf, de, df, ef C(6, 2) = 15 C) ab, ac, ad, ae, af, ba, bc, bd, be, bf, ca, cb, cd, ce, cf, da, db, dc, de, df, ea, eb, ec, ed, ef, fa, fb, fc, fd, fe C(6, 2) = 30 D) ab, ac, ad, ae, bc, bd, be, cd, ce, cf, de, df C(6, 2) = 12 22) How many 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0? No digit can be used more than once. A) 604,800 B) 720 C) 120 D) 1,209,600

22)

23) Find the probability of having 4 girls in a 4-child family. 1 1 1 A) B) C) 8 4 32

23)

1 16

24) The table below shows the results of a consumer survey of annual incomes in 100 households.

24)

Income Number of households $0 - 14,999 9 $15,000 - 24,999 20 $25,000 - 34,999 30 $35,000 - 44,999 26 $45,000 or more 15 What is the probability that a household has an annual income less than $25,000? A) 0.2 B) 0.29 C) 0.71 D) 0.59

25) If n(A) = 20, n(A B) = 58, and n(A B) = 16, find n(B). A) 53 B) 38 C) 55

D) 54

25)

26) A bag contains 6 red marbles, 2 blue marbles, and 1 green marble. What is the probability of choosing a marble that is not blue when one marble is drawn from the bag? 7 9 2 A) B) C) 7 D) 9 7 9

26)

27) List all the combinations of 4 objects 1, 2, 3, and 4 taken 3 at a time. What is C(4, 3)? 27) A) 123, 124, 134, 234 C(4, 3) = 4 B) 111, 112, 113, 114, 121, 122, 123, 124, 131, 132, 133, 134, 141, 142, 143, 144, 211, 212, 213, 214, 221, 222, 223, 224, 231, 232, 233, 234, 241, 242, 243, 244, 311, 312, 313, 314, 321, 322, 323, 324, 331, 332, 333, 334, 341, 342, 343, 344, 411, 412, 413, 414, 421, 422, 423, 424, 431, 432, 433, 434, 441, 442, 443, 444 C(4, 3) = 64 C) 123, 124, 132, 134, 142, 143, 213, 214, 231, 234, 241, 243, 312, 314, 321, 324, 341, 342, 412, 413, 421, 423, 431, 432 C(4, 3) = 24 D) 123, 124, 134, 234, 321, 432 C(4, 3) = 6 28) Each of ten tickets is marked with a different number from 1 to 10 and put in a box. If you draw a ticket from the box, what is the probability that you will draw 7, 8, or 1? 1 1 1 3 A) B) C) D) 7 10 8 10

28)

29) Given that P(A) = 0.54, P(B) = 0.26, and P(A B) = 0.19, find P(A B). A) 0.42 B) 0.61 C) 0.99

29)

D) 0.8

30) In a survey of 138 vacationers in a popular beach resort town, 53 indicated they would consider buying a home there, 42 would consider buying a beach villa, 51 would consider buying a lot, 23 would consider both a home and a villa, 18 would consider both a home and a lot, 16 would consider both a villa and a lot, and 8 would consider all three. How many vacationers would not consider any of the three? How many would consider only a home? A) 41; 20 B) 49; 35 C) 41; 11 D) 41; 25

30)

31) Given that P(A) = 0.34 and P(B) = 0.27, find P(A B) if A and B are mutually exclusive. A) 0.0918 B) 0 C) 0.5182 D) 0.61

31)

Find the value of the permutation. 32) P(3, 0) A) 6

B) 1

C) 12

D) 2

Solve the problem. 33) In the city of Gloomville, the probability of rain on New Year's Day is 56%. What is the probability that next New Year's Day it will not rain in Gloomville? A) 56% B) 31.36% C) -56% D) 44%

32)

33)

34) Among a group of 71 investors, 20 owned shares of Stock A, 27 owned shares of Stock B, 36 owned shares of Stock C, 12 owned shares of both Stock A and Stock B, 10 owned shares of Stock A and Stock C, 13 owned shares of Stock B and Stock C, and 8 owned shares of all three. How many investors did not have shares in any of the three? How many owned shares of either Stock A or Stock C but not Stock B? A) 15; 35 B) 15; 27 C) 15; 29 D) 23; 27

34)

35) The psychology lab at a college is staffed by 10 male doctoral students, 6 female doctoral students, 12 male undergraduates, and 11 female undergraduates. If a person is selected at random from the group, find the probability that the selected person is an undergraduate or a female. 29 6 17 23 A) B) C) D) 39 13 39 39

35)

36) A restaurant offers a choice of 4 salads, 7 main courses, and 3 desserts. How many possible 3-course meals are there? A) 168 possible meals B) 28 possible meals C) 14 possible meals D) 84 possible meals

36)

37) In how many ways can 5 people each have different birth months? A) 792 B) 60 C) 95,040

37)

D) 248,832

38) How many 7-symbol codes can be formed using 5 different symbols? Repeated symbols are allowed. A) 78,125 B) 21 C) 2,520 D) 42 Find the value of the combination. 39) C(7, 7) A) 0.5

B) 1,260

C) 1

D) 5,040

Solve the problem. 40) How many different 10-letter words (real or imaginary) can be formed from the letters in the word ACCOUNTING? A) 90,720 B) 1,814,400 C) 907,200 D) 3,628,800

38)

39)

40)

41) Lisa has 4 skirts, 6 blouses, and 3 jackets. How many 3-piece outfits can she put together assuming any piece goes with any other? A) 144 possible outfits B) 24 possible outfits C) 13 possible outfits D) 72 possible outfits

41)

42) In survey of 50 households, 25 responded that they have an HDTV television, 35 responded that they had a multimedia personal computer and 15 responded they had both. How many households had neither an HDTV television nor a multimedia personal computer? A) 25 B) 35 C) 15 D) 5

42)

Write down all the subsets of the given set. 43) {a} A) a B) , {a}

C) {a}

D) {a, b}

43)

Solve the problem. 44) A spinner has regions numbered 1 through 21. What is the probability that the spinner will stop on an even number or a multiple of 3? 1 2 10 A) B) C) 17 D) 3 3 9 45) Given that P(A) = 0.41, P(B) = 0.58, and P(A B) = 0.73, find P(A B). A) 0.2378 B) 0.26 C) 0.99

D) 0.47

44)

45)

46) A bag contains 15 balls numbered 1 through 15. What is the probability of selecting a ball that has an even number when one ball is drawn from the bag? 2 15 7 A) B) 7 C) D) 15 7 15

46)

47) The following data represent the marital status of females 18 years and older in a certain U.S. city.

47)

Marital Status Number (in thousands) Married 307 Widowed 60 Divorced 55 Never married 112 Determine the number of females 18 years old and older who are married or widowed. A) 307,000 B) 362,000 C) 367,000 D) 422,000

48) During July in Jacksonville, Florida, it is not uncommon to have afternoon thunderstorms. On average, 11.1 days have afternoon thunderstorms. What is the probability that a randomly selected day in July will not have a thunderstorm? Round to two decimal places, if necessary. A) 0.64 B) 0.63 C) 0.89 D) 0.36 Write down all the subsets of the given set. 49) {p, q, r} A) , {p}, {q}, {r}, {p, q}, {p, r}, {q, r} B) , {p}, {q}, {r}, {p, q}, {p, r}, {q, r}, {p, p}, {q, q}, {r, r}, {p, q, r} C) {p}, {q}, {r}, {p, q}, {p, r}, {q, r}, {p, q, r} D) , {p}, {q}, {r}, {p, q}, {p, r}, {q, r}, {p, q, r}

49)

Solve the problem. 50) In a survey about the number of siblings of college students, the following probability table was constructed: Number of Siblings Probability 0 0.24 1 0.31 2 0.20 3 0.11 4 or more 0.14 What is the probability that a student has at most 2 siblings? A) 0.25 B) 0.55 C) 0.45

48)

D) 0.75

50)

Use the information given in the figure. 51)

5 1 18

How many are in B or C? A) 49

51)

21 2

B) 41

C) 3

D) 50

Solve the problem. 52) From 9 names on a ballot, a committee of 5 will be elected to attend a political national convention. How many different committees are possible? A) 126 B) 3,024 C) 7,560 D) 15,120 53) Given that P(A) = 0.82, P(A B) = 0.95, and P(A B) = 0.24, find P(B). A) 0.58 B) 0.37 C) 0.13

D) 0.61

54) In a survey about the number of siblings of college students, the following probability table was constructed:

52)

53)

54)

Number of Siblings Probability 0 0.26 1 0.32 2 0.20 3 0.11 4 or more 0.11 What is the probability that a student has 1, 2, or 3 siblings? A) 0.89 B) 0.63 C) 0.31

Write down all the subsets of the given set. 55) {2, 4, 10, 12} A) {2}, {4}, {10}, {12}, {2, 4}, {2, 10}, {2, 12}, {4, 10}, {4, 12}, {10, 12}, {2, 4, 10}, {2, 4, 12}, {2, 10, 12}, {4, 10, 12}, B) {2}, {4}, {10}, {12}, {2, 4}, {2, 10}, {2, 12}, {4, 10}, {4, 12}, {10, 12}, {2, 4, 10}, {2, 4, 12}, {2, 10, 12}, {4, 10, 12}, {2, 4, 10, 12}, C) {2}, {4}, {10}, {12}, {2, 4}, {2, 10}, {2, 12}, {4, 10}, {4, 12}, {2, 4, 10}, {2, 4, 12}, {2, 10, 12}, {4, 10, 12}, {2, 4, 10, 12}, D) {2}, {4}, {10}, {12}, {2, 4}, {2, 10}, {2, 12}, {4, 10}, {4, 12}, {10, 12}, {2, 4, 10}, {2, 4, 12}, {2, 10, 12}, {4, 10, 12}, {2, 4, 10, 12}

D) 0.52

55)

Solve the problem. 56) How many different vertical arrangements are there of 8 flags if 4 are white, 3 are blue, and 1 is red? A) 70 B) 19 C) 12 D) 280 57) Find the probability of getting 2 tails when 3 fair coins are tossed. 3 2 1 A) B) C) 8 3 4 Find the value of the combination. 58) C(10, 4) A) 2,520

B) 1,440

C) 210

1 D) 2

D) 151,200

Solve the problem. 59) A hot dog stand sells hot dogs with cheese, relish, chili, tomato, onion, mustard, or ketchup. How many different hot dogs can be concocted using any 4 of the extras? A) 210 B) 35 C) 420 D) 840 Use the information given in the figure. 60)

5 1 21

57)

58)

59)

60)

26 4

How many are in A or B or C? A) 96 B) 92

Find the value of the permutation. 61) P(9, 1) A) 362,880

56)

C) 15

B) 1

C) 9

D) 1

D) 40,320

Solve the problem. 62) Given that P(A) = 0.63 and P(B) = 0.13, find P(A B) if A and B are mutually exclusive. A) 0.76 B) 0.0819 C) 0 D) 0.6781 63) How many 5-card poker hands consisting of three 3's and two cards that are not 3's are possible in a 52-card deck? A) 4512 B) 2652 C) 5304 D) 2256

61)

62)

63)

Determine whether the following is a probability model. 64) Outcome Probability Red 0.15 Blue 0.18 Green 0.27 White 0.25 A) Yes

64)

B) No

Solve the problem. 65) How many different license plates can be made using 3 letters followed by 2 digits selected from the digits 0 through 9, if digits may be repeated but letters may not be repeated? A) 1,581,840 B) 1,560,000 C) 1,757,600 D) 38.6904762 Determine whether the following is a probability model. 66) Outcome Probability Golfing 0.11 Skiing 0.15 Swimming 0.06 Biking 0.21 Hiking 0.47 A) Yes

65)

66)

B) No

Solve the problem. 67) What is the probability that the arrow will land on an odd number? Assume that all sectors have equal 67) area.

2 5

3 5

C) 1

D) 0

Use the information given in the figure. 68)

5 2 18

68)

15 1

How many are in B and C? A) 46 B) 34

C) 3 9

D) 2

69)

3 4 27

30 4

How many are in B but not in A? A) 37 B) 40

C) 33

D) 30

Solve the problem. 70) The faculty at a college consists of 96 full-time teachers and 48 part-time teachers. Of the 96 full-time teachers, 45 are female. Of the 48 part-time teachers, 25 are female. Find the probability that a randomly selected teacher is male or works part-time. 11 23 61 19 A) B) C) D) 16 144 72 36 71) If n(A) = 44, n(B) = 34, and n(A B) = 73, find n(A B). A) 68 B) 5 C) 78

D) 10

72) In how many ways can 9 people be lined up? A) 181,440 B) 1

D) 9

C) 362,880

70)

71)

72)

73) A 6-sided die is rolled. What is the probability of rolling a number less than 6? 5 1 1 5 A) B) C) D) 7 6 3 6

73)

74) Two 6-sided dice are rolled. What is the probability the sum of the two numbers on the dice will be 3? 17 1 1 A) B) C) D) 2 18 18 2

74)

75) Suppose that the sample space is S = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 and that outcomes are equally likely. Compute the probability of the event E = 2, 10 . 1 1 2 A) B) C) D) 2 5 10 9

75)

76) How many different license plates can be made using 3 letters followed by 2 digits selected from the digits 0 through 9, if letters and digits may be repeated? A) 1,757,600 B) 260 C) 6 D) 36

76)

77) How many ways are there to choose a soccer team consisting of 3 forwards, 4 midfield players, and 3 defensive players, if the players are chosen from 7 forwards, 8 midfield players, and 5 defensive players? A) 115 B) 184,756 C) 21,168,000 D) 24,500 Determine whether the following is a probability model. 78) Outcome Probability Red 0.15 Blue 0.27 Green 0.33 White 0.50 A) Yes

77)

78)

B) No

Solve the problem. 79) How many 3-letter codes can be formed using the letters A, B, C, D, E, F, G, H, and I. Repeated letters are allowed. A) 729 B) 19,683 C) 504 D) 84 80) In a survey about the number of siblings of college students, the following probability table was constructed:

79)

80)

Number of Siblings Probability 0 0.25 1 0.30 2 0.21 3 0.11 4 or more 0.13 What is the probability that a student 3 or more siblings? A) 0.13 B) 0.24 C) 0.76

D) 0.11

81) How many different 4-letter codes are there if only the letters A, B, C, D, E, F, G, H, and I can be used and no letter can be used more than once? A) 6,561 B) 4 C) 126 D) 3,024 Use the information given in the figure. 82)

5 4 24

How many are in set A? A) 31

81)

82)

16 3

B) 35

C) 38 11

D) 22

83)

3 5 24

How many are not in C? A) 62

30 11

B) 65

C) 54

D) 63

Solve the problem. 84) A bag contains 2 red marbles, 9 blue marbles, and 6 green marbles. If one marble is selected at random, determine the probability that it is blue. 6 9 9 2 A) B) C) D) 17 11 17 17

84)

85) An exam consists of 9 multiple-choice questions and 6 essay questions. If the student must answer 5 of the multiple-choice questions and 4 of the essay questions, in how many ways can the questions be chosen? A) 5,443,200 B) 1,080 C) 1890 D) 261,273,600

85)

86) How many 7-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 if the first digit cannot be 0? Repeated digits are allowed. A) 4,782,969 B) 9,000,000 C) 1,360,800 D) 181,440

86)

87) If n(B) = 12, n(A B) = 3, and n(A B) = 21, find n(A). A) 14 B) 10 C) 12

87)

Find the value of the permutation. 88) P(5, 5) A) 60

B) 120

C) 2

D) 9

D) 1

Solve the problem. 89) Suppose that the sample space is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and that outcomes are equally likely. Compute the probability of the event E: "a number divisible by 3". 1 3 2 A) 3 B) C) D) 3 10 5

88)

89)

Use the information given in the figure. 90)

3 2 27

90)

16 12

How many are in A and B and C? A) 2 B) 62

C) 70

D) 8

Solve the problem. 91) In a probability model, which of the following numbers could be the probability of an outcome: 1 1 5 0, 0.2, -0.01, - , , , 1, 1.5 3 2 4 B) 0.2,

A) 0, 0.2, -0.01, 1, 1.5 C) 0, 0.2,

1 , 1 2

91)

1 , 1 2

D) 0, 0.2, -0.01, -

1 1 , , 1 3 2

92) In a survey about the number of siblings of college students, the following probability table was constructed:

92)

Number of Siblings Probability 0 0.23 1 0.34 2 0.21 3 0.10 4 or more 0.12 What is the probability that a student has less than 2 siblings? A) 0.21 B) 0.78 C) 0.57

Determine whether the following is a probability model. 93) Outcome Probability Red -0.19 Blue 0.22 Green 0.29 White 0.30 A) Yes

D) 0.22

93)

B) No

Solve the problem. 94) If n(A B) = 62, n(A B) = 10, and n(A) = n(B), find n(A). A) 36 B) 5 C) 26

D) 31

94)

95) A bag contains 5 red marbles, 4 blue marbles, and 1 green marble. What is the probability of choosing a marble that is red or green when one marble is drawn from the bag? 3 5 2 A) B) C) 6 D) 5 3 5

95)

96) A committee is to be formed consisting of 3 men and 2 women. If the committee members are to be chosen from 12 men and 10 women, how many different committees are possible? A) 265 B) 26,334 C) 9,900 D) 118,800

96)

97) In a survey of 53 hospital patients, 24 said they were satisfied with the nursing care, 20 said they were satisfied with the medical treatment, and 5 said they were satisfied with both. How many patients were satisfied with neither? How many were satisfied with only the medical treatment? A) 14; 15 B) 19; 15 C) 14; 20 D) 19; 20

97)

Determine whether the following is a probability model. 98) Outcome Probability Red 0.19 Blue 0.26 Green 0.33 White 0.22 A) Yes 99)

98)

B) No 99)

Outcome Probability Jim 0 Tom 0 Bill 1 Carl 0 A) Yes

B) No

Solve the problem. 100) 7 different books are to be arranged on a shelf. How many different arrangements are possible? A) 7 B) 5,040 C) 720 D) 2,520

100)

101) List all the ordered arrangements of 4 objects 1, 2, 3, and 4 choosing 3 at a time without repetition. 101) What is P(4, 3)? A) 111, 112, 113, 114, 121, 122, 123, 124, 131, 132, 133, 134, 141, 142, 143, 144, 211, 212, 213, 214, 221, 222, 223, 224, 231, 232, 233, 234, 241, 242, 243, 244, 311, 312, 313, 314, 321, 322, 323, 324, 331, 332, 333, 334, 341, 342, 343, 344, 411, 412, 413, 414, 421, 422, 423, 424, 431, 432, 433, 434, 441, 442, 443, 444 P(4, 3) = 64 B) 123, 124, 132, 134, 142, 143, 213, 214, 231, 234, 241, 243, 312, 314, 321, 324, 341, 342, 412, 413, 421, 423, 431, 432 P(4, 3) = 24 C) 123, 124, 134, 234 P(4, 3) = 4 D) 123, 124, 132, 142, 143, 213, 214, 231, 241, 243, 312, 314, 321, 341, 342, 412, 413, 421, 423, 431 P(4, 3) = 20

102) In a survey of 391 computer buyers, 178 put price as a main consideration, 216 put performance as a main consideration, and 55 listed both price and performance. How many computer buyers listed other considerations? How many looked only for performance? A) 107; 216 B) 52; 161 C) 123; 161 D) 52; 216

102)

103) If n(A) = 29, n(B) = 50, and n(A B) = 18, find n(A B). A) 79 B) 61 C) 97

103)

D) 43

104) A certain mathematics test consists of 20 questions. Goldie decides to answer the questions without reading them. In how many ways can Goldie fill in the answer sheet if the possible answers are true and false? A) 190 B) 1,048,576 C) 400 D) 40

104)

105) Suppose that the sample space is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and that outcomes are equally likely. Compute the probability of the event E = {1, 2, 4, 5, 7, 9, 10}. 4 7 7 A) B) 7 C) D) 5 10 9

105)

106) List all the ordered arrangements of 6 objects a, b, c, d, e, and f choosing 2 at a time without 106) repetition. What is P(6, 2)? A) ab, ac, ad, ae, af, ba, bc, bd, be, bf, ca, cb, cd, ce, cf, da, db, dc, de, df, ea, eb, ec, ed, ef, fa, fb, fc, fd, fe P(6, 2) = 30 B) aa, ab, ac, ad, ae, af, ba, bb, bc, bd, be, bf, ca, cb, cc, cd, ce, cf, da, db, dc, dd, de, df, ea, eb, ec, ed, ee, ef, fa, fb, fc, fd, fe, ff P(6, 2) = 36 C) ab, ac, ad, ae, af, ba, bc, bd, be, bf, ca, cb, cd, ce, cf, da, db, dc, de, df, ea, eb, ec, ed, ef P(6, 2) = 25 D) ab, ac, ad, ae, af, bc, bd, be, bf, cd, ce, cf, de, df, ef P(6, 2) = 15 107) A man has 4 shirts and 5 ties. How many different shirt and tie arrangements can he wear? A) 16 B) 25 C) 20 D) 40

107)

108) How many different license plates can be made using 3 letters followed by 2 digits selected from the digits 0 through 9, if neither letters nor digits may be repeated? A) 1,404,000 B) 1,757,600 C) 1,123,200 D) 117,000

108)

109) The table below shows the results of a consumer survey of annual incomes in 100 households.

109)

Income Number of households $0 - 14,999 5 $15,000 - 24,999 22 $25,000 - 34,999 29 $35,000 - 44,999 30 $45,000 or more 14 What is the probability that a household has an annual income between $15,000 and $44,999 inclusive? A) 0.81 B) 0.51 C) 0.52 D) 0.29

110) What is the probability that at least 2 people have the same birth month in a group of 6 people? A) 0.788 B) 0.223 C) 0.777 D) 0.212

110)

111) Sam estimates that if he leaves his car parked outside his office all day on a weekday, the chance that he will get a parking ticket is 25%. If Sam leaves his car parked outside his office all day next Tuesday, what is the chance that he will not get a parking ticket? A) 6.25% B) 75% C) 25% D) -25%

111)

112) Mary finds 8 fish at a pet store that she would like to buy, but she can afford only 5 of them. In how many ways can she make her selection? How many ways can she make her selection if he decides that one of the fish is a must? A) 6,720; 840 B) 336; 210 C) 56; 35 D) 3,360; 420

112)

113) A student must choose 1 of 5 mathematics electives, 1 of 6 science electives, and 1 of 8 programming electives. How many possible course selections are there? A) 30 course selections B) 240 course selections C) 19 course selections D) 480 course selections

113)

114) A survey of 2,512 credit card users indicated that 1,098 had bought books online, 1,255 had bought music online, 434 had bought pet supplies online, 102 had bought both books and music, 219 had bought both books and pet supplies, 148 had bought both music and pet supplies, and 79 had bought all three. How many credit card users did not buy any of the three? How many bought either books or pet supplies but not music? A) 194; 1,002 B) 115; 1,142 C) 115; 1,002 D) 115; 1,081

114)

115) An environmental organization has 24 members. Each member will be placed on exactly 1 of 4 teams. Each team will work on a different issue. The first team has 8 members, the second has 6, the third has 3, and the fourth has 7. In how many ways can these teams be formed? A) 4.947307485 × 1012 B) 7.067582122 × 1011

115)

116) The table below shows the results of a consumer survey of annual incomes in 100 households.

116)

C) 6.934494901 × 1019

D) 6.204484017 × 1023

Income Number of households $0 - 14,999 8 $15,000 - 24,999 24 $25,000 - 34,999 28 $35,000 - 44,999 30 $45,000 or more 10 What is the probability that a household has an annual income of $25,000 or more? A) 0.28 B) 0.6 C) 0.4 D) 0.68

Answer Key Testname: CHAPTER 14

1) S = {11 Red, 11 Yellow, 11 Green, 12 Red, 12 Yellow, 12 Green, 13 Red, 13 Yellow, 13 Green, 21 Red, 21 Yellow, 21 Green, 22 Red, 22 Yellow, 22 Green, 23 Red, 23 Yellow, 23 Green, 31 Red, 31 Yellow, 31 Green, 32 Red, 32 Yellow, 32 Green, 33 Red, 33 Yellow, 3 Green }; 1 Each outcome has a probability of . 27 The probability of getting a 2, followed by a 1, followed by Yellow or Red is

2 . 27

2) S = {1H, 2H, 3H, 4H, 5H, 6H, 1T, 2T, 3T, 4T, 5T, 6T}; each outcome has a probability of 3) The faces numbered 1, 3, 5 will each have probability 1/12. The faces numbered 2, 4, 6 will each have probability 1/4. 4) S = {HH, HT, TH, TT}; each outcome has the probability of

1 12

1 4

5) S = {1 Red, 1 Yellow, 1 Green, 1 Blue, 2 Red, 2 Yellow, 2 Green, 2 Blue, 3 Red, 3 Yellow, 3 Green, 3 Blue, 4 Red, 4 1 Yellow, 4 Green, 4 Blue}; each outcome has a probability of 16 The probability of getting a 1 or 3 followed by Red is

1 8

6) S = {1, 2, 3, 4, 5, 6}; each outcome has the probability of 7)

1 6

11! 4!4!2!

8) S = {HH, HT, TH, TT} Outcome Probability HH 9/16 HT 3/16 TH 3/16 TT 1/16

9) S = {HHH, HTH, HHT, HTT, THH, TTH, THT, TTT}; each outcome has the probability of

1 8

10) S = {1 Red A, 1 Red B, 1 Yellow A, 1 Yellow B, 1 Green A, 1 Green B, 2 Red A, 2 Red B, 2 Yellow A, 2 Yellow B, 2 Green A, 2 Green B, 3 Red A, 3 Red B, 3 Yellow A, 3 Yellow B, 3 Green A, 3 Green B, 4 Red A, 4 Red B, 4 Yellow A, 4 Yellow B, 4 Green A, 4 Green B}; 1 Each outcome has a probability of . 24 The probability of getting a 2, followed by Yellow or Green, followed by B is

11) The faces numbered 1 through 7 will each have the probability

1 12

1 ; faces numbered higher than 7 will each have 7

probability 0. 12) S = {11, 12, 13, 14, 15, 16, 21, 22, 23, 24, 25, 26, 31, 32, 33, 34, 35, 36, 41, 42, 43, 44, 45, 46, 51, 52, 53, 54, 55, 56, 61, 62, 63, 1 64, 65, 66}; each outcome has a probability of 36

13) P(H) =

11 1 ; P(T) = 12 12

Answer Key Testname: CHAPTER 14 14) A 15) D 16) C 17) C 18) D 19) D 20) A 21) B 22) B 23) D 24) B 25) D 26) A 27) A 28) D 29) B 30) A 31) D 32) B 33) D 34) C 35) A 36) D 37) C 38) A 39) C 40) C 41) D 42) D 43) B 44) B 45) B 46) D 47) C 48) A 49) D 50) D 51) D 52) A 53) B 54) B 55) B 56) D 57) A 58) C 59) B 60) B 61) C 62) C 63) A 18

Answer Key Testname: CHAPTER 14 64) B 65) B 66) A 67) B 68) C 69) C 70) A 71) B 72) C 73) D 74) B 75) A 76) A 77) D 78) B 79) A 80) B 81) D 82) B 83) B 84) C 85) C 86) B 87) C 88) B 89) C 90) A 91) C 92) C 93) B 94) A 95) A 96) C 97) A 98) A 99) A 100) B 101) B 102) B 103) B 104) B 105) C 106) A 107) C 108) A 109) A 110) C 111) B 112) C 113) B 19

Answer Key Testname: CHAPTER 14 114) B 115) B 116) D

Chapter 15 Exam Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use a graphing utility to solve the system of linear equations and give the solution of the system. 9x + 3y - z = 15 1) x + 7y - 6z = -18 7x + y + z = 21 A)

5 59 ,y=,z=9 3 20

x = 1, y = 5, z = 9

5 11 ,y=,z=9 2 2

x = 9, y = 5, z = 1

Select a setting so that the given points will lie within the viewing rectangle. 2) (-3, 0), (0, 60), (5, -40) A) X min = -1 B) X min = -4 C) X min = -50 X max = 6 X max = 6 X max = 70 X scl = 1 X scl = 1 X scl = 10 Y min = -50 Y min = -50 Y min = -4 Y max = 70 Y max = 70 Y max = 6 Y scl = 10 Y scl = 10 Y scl = 1

D) X min = -4 X max = 6 X scl = 1 Y min = -10 Y max = 70 Y scl = 10

For the equation, create a table, -3 x 3, and list points on the graph. 3) y = x + 4 A) B)

(-3, -7), (-2, -6), (-1, -5), (0, -4), (1, -3), (2, -2), (3, -1)

(-3, 7), (-2, 6), (-1, 5), (0, 4), (1, 3), (2, 2), (3, 1)

(-3, -1), (-2, -2), (-1, -3), (0, -4), (1, -5), (2, -6), (3, -7)

(-3, 1), (-2, 2), (-1, 3), (0, 4), (1, 5), (2, 6), (3, 7)

Use a graphing utility to graph the polar equation. 4) r cos = 2 A)

Use a graphing utility to graph the inequality. 5) 2x + y - 3 0 A)

For the equation, create a table, -3 x 3, and list points on the graph. 6) y = x2 + 2 A)

(-3, 11), (-2, 6), (-1, 3), (0, 2), (1, 3), (2, 6), (3, 11)

(-3, 10), (-2, 5), (-1, 2), (0, 1), (1, 2), (2, 5), (3, 10)

(-3, -1), (-2, 0), (-1, 1), (0, 2), (1, 3), (2, 4), (3, 5)

(-3, 7), (-2, 2), (-1, -1), (0, -2), (1, -1), (2, 2), (3, 7)

Use a graphing utility to graph the inequality. 7) 2x + y - 3 0 A)

Use a graphing utility to graph the parametric equation. 8) x = t2 + 2, y = 2t - 1, -3 t 3 A)

For the equation, create a table, -3 x 3, and list points on the graph. 9) 2x + 3y = 6 A) B)

(-3, 8), (-2, 7.33), (-1, 6.67), (0, 6), (1, 5.33), (2, 4.67), (3, 4)

(-3, 0), (-2, 0.67), (-1, 1.33), (0, 2), (1, 2.67), (2, 3.33), (3, 4)

(-3, 4), (-2, 3.33), (-1, 2.67), (0, 2), (1, 1.33), (2, 0.67), (3, 0)

(-3, 8), (-2, 6), (-1, 4), (0, 2), (1, 0), (2, -2), (3, -4)

Use ZERO (or ROOT) to find the solutions to the equation. Round to two decimal places. 10) x2 + 5x - 7 = 0

10)

Determine the viewing window used. 11)

11)

A) x = 1.02, -6.3

B) x = 1.02, -6.26

C) x = 0.98, -6.26

D) x = 1.14, -6.14

Use INTERSECT to find the solution to the equation. Round to two decimal places, if necessary. 12) 2(x - 5) = 5(x - 6) A) x = -6.67 B) x = -3.33 C) x = 6.67 D) x = 3.33

12)

Determine the coordinates of the points shown. Tell in which quadrant the point lies. Assume the coordinates are integers. 13) 13)

A) (-6, -8); quadrant IV C) (-6, -8); quadrant III

B) (-6, -4); quadrant III D) (-6, -4); quadrant IV

Use ZERO (or ROOT) to approximate the smaller of the two x-intercepts of the equation. Express the answer rounded to two decimal places. 14) y = x2 + 5x + 2 14)

A) 4.56

B) -0.44

C) -4.56

D) 0.44

Determine the viewing window used. 15)

15)

Use ZERO (or ROOT) to approximate the positive x-intercepts of the equation. Round to two decimal places. 16) y = x3 + 3.3x2 - 5.2x - 6.3 16) A) 0.86

B) 1.75

C) 1.57

D) 4.18

Determine the coordinates of the points shown. Tell in which quadrant the point lies. Assume the coordinates are integers. 17) 17)

A) (2, -2); quadrant III C) (2, -1); quadrant IV

B) (2, -2); quadrant IV D) (2, -1); quadrant III

Graph the equation using the indicated viewing window. 18) 2x + 3y = 6; X min = -10 X max = 10 X scl = 2 Y min = -8 Y max = 8 Y scl = 2 A)

18)

Determine the coordinates of the points shown. Tell in which quadrant the point lies. Assume the coordinates are integers. 19) 19)

A) (1, 3); quadrant I C) (1, 6); quadrant I

B) (1, 3); quadrant II D) (1, 6); quadrant II

Graph the equation using the indicated viewing window. 20) y = x2 + 2;

20)

X min = -5 X max = 5 X scl = 1 Y min = -20 Y max = 20 Y scl = 5 A)

Determine the coordinates of the points shown. Tell in which quadrant the point lies. Assume the coordinates are integers. 21) 21)

A) (-4, 6); quadrant II C) (-4, 6); quadrant I

B) (-4, 3); quadrant I D) (-4, 3); quadrant II

Determine the viewing window used. 22)

22)

Use ZERO (or ROOT) to approximate the positive x-intercepts of the equation. Round to two decimal places. 23) y = x3 + 3x2 - 5x - 7 23) A) 1.91

B) 1.83

24) y = x4 + 1.5x3 - 8.31x2 - 3.27x + 8.39 A) 0.87 and 2.21 B) 1.19 and 3.44 Graph the equation using the indicated viewing window. 25) y = x + 4; X min = -5 X max = 5 X scl = 1 Y min = -4 Y max = 4 Y scl = 1

C) 3.83

D) 1.76

C) 0.94 and 2.18

D) 8.39

24)

25)

Determine whether the given viewing rectangle will result in a square screen. 26) X min = -2 X max = 16 X scl = 1 Y min = -7 Y max = 11 Y scl = 3 A) Yes B) No Determine the viewing window used. 27)

26)

27)

Answer Key Testname: CHAPTER 15 1) B 2) B 3) D 4) A 5) A 6) A 7) C 8) C 9) B 10) D 11) B 12) C 13) C 14) C 15) C 16) B 17) C 18) C 19) C 20) A 21) A 22) A 23) B 24) C 25) A 26) B 27) D