Algebra spring break math packet by Algebra Works

Name: ______________________ Class: _________________ Date: _________

Algebra Spring Break Math Packet Multiple Choice Identify the choice that best completes the statement or answers the question. ____ ____

1. Evaluate u + xy, for u = 18, x = 10, and y = 8. a. 188 b. 36 c. 98 d. 224 2. When simplifying an expression, you ____ perform operations inside grouping symbols first. a. always b. sometimes c. never Simplify the expression.

____

ÈÍ

˘˙

3. 3 ÍÍÍÍ (15 ! 3 ) 2 ÷ 4 ˙˙˙˙ Î ˚ 108 b. 4. 4(20 + 12) ÷ (4 ! 3) a. 29 b. 5. –4.8 – (–4.9) + 5.7 a. –4 b.

____ ____ ____ ____ ____

____ ____ ____

____

c. 18

d. 9

c. 128

d. 92

–5.8

c. 5.8

d. –15.4

6. (!2) a. –32

b. 16

c. –10

d. 32

7. !5 4 a. 20

b. 125

c. –625

d. 625

8. 1.7m + 6.5n ! 4n + 2.5m ! n a. 4.2m 2 +1.5n b. 4.2m 2 !1.5n

c. 1.5m 2 !4.2n d. 1.5m 2 +4.2n

9. (k 2 ) 4 a. k 6 b. 2k 8 c. k 16 d. k 8 10. A rational number is ____ a real number. a. always b. sometimes c. never 11. Name the set(s) of numbers to which 1.68 belongs. a. rational numbers b. natural numbers, whole numbers, integers, rational numbers c. rational numbers, irrational numbers d. none of the above 12. Which set of numbers is the most reasonable to describe the number of desks in a classroom? a. whole numbers c. rational numbers b. irrational numbers d. integers 13. The opposite of a negative number is ____ negative. a. always b. sometimes c. never

ID: A

Name: ______________________ ____

ID: A

14. Which number line model can you use to simplify –5 + 6? a.

–5 + 6 = 11

–5 + 6 = 1

–5 + 6 = –11

____

–5 + 6 = 11 15. Evaluate || !x ! 2y || for x = –2 and y = 3. 4 b. 8 c. –4 16. Evaluate x(–y + z) for x = 3, y = 3, and z = 1. a. –6 b. 10 c. 12 17. The product of two negative numbers is ____ positive. a. always b. sometimes ÊÁ ˆ˜ 18. If a is a negative number, then a ÁÁÁÁ 1 ˜˜˜˜ is ____ equal to –1. ÁË a ˜¯

d. –8

____ ____ ____

always

sometimes

d. –8 c.

never

Name the property the equation illustrates.

____

19. !2.1 " 1 = !2.1 a. Inverse Property of Multiplication b. Multiplication Property of –1 c. Identity Property of Addition d. Identity Property of Multiplication Solve the equation.

____ ____

20. 11 = –d + 15 a. 11 b. –4 21. Which equation is an identity? a. 11 ! (2v + 3) = !2v ! 8 b. 5w + 8 ! w = 6w ! 2(w ! 4)

c. 4

d. 6

c. 7m ! 2 = 8m + 4 ! m d. 8y + 9 = 8y ! 3

Name: ______________________

ID: A

Solve the proportion.

____

22.

2 11 = 10 x a. 55

b. 2.2

c. 110

d. 1.8

Which number is a solution of the inequality?

____ ____ ____ ____ ____

23. b > 11.3 a. 15

b. 9

c. –14

d. 4

b. 5

c. 2

d. –9

b. 8

c. –1

d. 0

b. 18

c. 2

d. 1

b. 5

24. m > 13

3 a. 3 25. x(7 – x) > 8 a. 2 26. 6 # 6k a. 8 27. 3x ! 15 # 3 a. ! 9 11

6 11

d. 6

Graph the inequality.

____

28. x $ 5 a. b. c. d. Write an inequality for the graph.

____

29. a.

x $ !8

b. x < –8

c. x > –8

d. x < 8

Write an inequality to model the situation.

____

30. Thomas earned $44 or more. a. t > 44 b. t $ 44

c. t < 44

d. t # 44

Name: ______________________

ID: A

Identify the graph of the inequality from the given description.

____

31. x is negative. a.

b. ____

32. x is at least –4.5. a.

Solve the inequality. Then graph your solution.

____

33. c ! 5 $ 6 a. c $ ! 11 b.

____

c $ 11

d. c $ ! 30

34. 4 v < 7 5

____

c. c $ 1

15 28 v< 75

c. v < 3

1 3

d. v < 7

v<!

35. Replace –6v <

with a number that makes the inequalities equivalent. ; v > –0.5

b. 30

c. 6.5

d. –5.5

Name: ______________________

ID: A

Solve the compound inequality. Graph your solution.

____

36. 2x – 2 < –12 or 2x + 3 > 7 a. x < –5 or x > 2 b.

____ ____

c. x < !7 or x > 5

x < –5 or x > 5

d. x < –12 or x > 2

37. A function is ________ a relation. a. always b. sometimes c. never 38. Identify the mapping diagram that represents the relation and determine whether the relation is a function. ÔÏ Ô¸ ÌÔ (!8, !6), (!5, 2), (!8, 1), (7, 3) ˝Ô Ó ˛

The relation is a function.

The relation is not a function

The relation is a function.

The relation is not a function.

The pair of points is on the graph of an inverse variation. Find the missing value.

____

39. (9, 5) and (x, 6) a.

b. 3 1

c. 45

d. 7 1 2

Name: ______________________

ID: A

Find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule.

____

ÊÁ

ˆ˜

40. A(n) = !6 + (n ! 1) ÁÁÁÁ 1 ˜˜˜˜ ÁË 5 ˜¯ a. b.

1 –6, !5 , !4 5 3 4 0, , 1 5 5

c. –6, !5 2 , !4 1 d.

5 5 1 4 5, !5 , 1 5 5

The rate of change is constant in each table. Find the rate of change. Explain what the rate of change means for the situation.

____

41.

a. b. c. d.

Time (hours)

Distance (miles)

260

390

520

650

10; Your car travels for 10 hours. 260; Your car travels 260 miles. 65 ; Your car travels 65 miles every 1 hour. 1 1 ; Your car travels 65 miles every 1 hour. 65

Name: ______________________

ID: A

Match the equation with its graph.

____

42. –7x + 7y = –49 a.

Name: ______________________

ID: A

Is the relationship shown by the data linear? If so, model the data with an equation.

____

43.

a. b. c. d.

–9

–2

–5

–7

–1

–12

–17

4 (x + 9). 5 4 The relationship is linear; y + 9 = ! (x + 2). 5 The relationship is not linear. 5 The relationship is linear; y + 2 = ! (x + 9). 4 The relationship is linear; y + 2 =

Write an equation for the line that is parallel to the given line and that passes through the given point.

____

44. y = 3 x – 9; (–8, –18) 4

3 11 x+ c. y = 3 x – 12 4 2 4 4 b. y = x – 12 d. y = ! 4 x + 12 3 3 45. Find a solution to the following system of equations. !5x + y = !5 !4x + 2y = 2 a. (–8, –15) b. (–2, –15) c. (0, 1)

____

d. (2, 5)

Solve the system using elimination.

____

46. 5x = –25 + 5y

____

10y = 42 + 2x a. (–1, 2) b. (–1, 4) c. (4, –1) d. (5, 10) 47. By what number should you multiply the first equation to solve using elimination? –3x – 2y = 2 –9x + 3y = 24 a. 6 b. –9 c. –3 d. 3

Name: ______________________ ____

____

ID: A

48. Mrs. Huang operates a soybean farm. She buys many supplies in bulk. Often the bulk products need to be custom mixed before Mrs. Huang can use them. To apply herbicide to a large field she must mix a solution of 67% herbicide with a solution of 46% herbicide to form 42 liters of a 55% solution. How much of the 67% solution must she use? a. 23 L b. 18 L c. 34 L d. 35 L 49. Write the following inequality in slope-intercept form. 5x ! 5y # 70 a. y # x ! 14 b. y $ x + 14 c. y $ x ! 14 d. y # x + 14 Write the linear inequality shown in the graph.

____

50.

y # !3x + 4

b. y $ !3x + 4

c. y # !3x ! 4

d. y $ !3x ! 4

x > !3

b. x # !3

c. y > !3

d. y # !3

51.

Name: ______________________

ID: A

Find a solution of the system of linear inequalities.

____

52. y < 3x + 12 y # 5x + 7 a. (1, 2)

b. (0, –1)

c. (2, 17)

d. (–2, –5)

Solve the system of linear inequalities by graphing.

____

53. y $ x + 4 2x + y $ !4

____ ____

54. Which number is written in scientific notation? a. 7.8 " 10 !5 b. 3.4 " 100 2 c. 55. Which list shows the numbers in order from least a. 5.4 " 10 4 , 5.4 " 10 3 , 4.5 " 10 4 c. 3 4 4 b. 5.4 " 10 , 4.5 " 10 , 5.4 " 10 d.

0.84 " 10 to greatest?

d. !5 " 10 !12

5.4 " 10 , 5.4 " 10 , 4.5 " 10 4.5 " 10 , 5.4 " 10 , 5.4 " 10

Name: ______________________

ID: A

Simplify the product.

____

56. 7a 3 (5a 6 – 2b 3 ) a. 12a 9 – 9a 3 b 6 b. 35a 9 – 14ab6

c. 35a 9 – 14a 3 b 3 d. 12a 1 8 – 9a 3 b 6

Find the product.

____

57. (2n + 2)(2n – 2) a. 4n 2 – 4 b. 4n 2 – 4n – 4

c. 4n 2 + 2n – 4 d. 4n 2 + 4n – 4

Factor the expression.

____

58. w2 + 18w + 77 a. (w – 7)(w + 11) b. (w – 7)(w – 11) 59. 6x2 + 5x + 1 a. (3x – 1)(2x – 1) b. (3x + 1)(2x – 1) 60. k2 – 16h 2 a. (k + 4h)(k + 4h) b. (k – 4h 2 )(k + 4) 61. Is a.

____ ____

____ ____ ____

c. (w + 7)(w + 11) d. (w + 1)(w + 77) c. (3x – 1)(2x + 1) d. (3x + 1)(2x + 1) c. h 2 (k + 4)(k – 4) d. (k + 4h)(k – 4h)

5 rational or irrational? 8 rational

b. irrational

a is ________ rational if a and b are integers and b % 0. b a. always b. sometimes c. never 63. Which of the quadratic functions has the widest graph? a. y = 1 x 2 b. y = !4x 2 c. y = 0.3x 2 d. y = ! 4 x 2 3 5

62. The expression

64. If |m | > |n |, then the graph of y = mx 2 is ________ narrower than y = nx 2 . a. always b. sometimes c. never 65. A parabola ________ has an axis of symmetry. a. always b. sometimes c. never 66. The quadratic equation x 2 + a = 0, where a > 0, ________ has at least one real number solution. a. always b. sometimes c. never

Name: ______________________

ID: A

Solve the equation by factoring.

____

____ ____

67. 3z 2 + 3z ! 6 = 0 a. z = 1 or z = –2 b. z = 1 or z = 2

68. The expression ax 2 ! bx = 0 ________ has the solution x = 0. a. always b. sometimes c. 69. For which discriminant is the graph possible?

a. ____

c. z = 3 or z = –2 d. z = 3 or z = 2

b ! 4ac = !4

b ! 4ac = 3

never

b ! 4ac = 0

70. The equation x 2 + n = 0 ____ has at least one real number solution when n > 0. a. always b. sometimes c. never

Short Answer 71. a. Write an equation to show how the amount of money in a jar of nickels is related to the number of nickels in the jar. b. If the jar contains 40 nickels, how much money is this?

72. A class writes the equation n + n + 1 + n + 2 = 87 to solve the following problem. The sum of 3 consecutive odd integers is 87. Find the three integers. What error did they make?

73. Write four solutions to the inequality 1 > x . 3

74. Eduardo solved –4x > 120 by adding 4 to each side of the inequality. What mistake did he make? 75. What number would you add to each side of the inequality to solve 13 < 4n – 14.4?

Name: ______________________

ID: A

76. Graph the points on the same coordinate plane. A(4, 4), B(3, –1), C(–4, –1)

Use the vertical line test to determine whether the relation is a function. Ï ¸ 77. ÔÔÌ (!1, !2), (3, !1), (!5, 2), (!3, !5) ÔÔ˝ Ó

Name: ______________________

ID: A

Ï ¸ 78. ÔÌÔ (4, 0), (4, !5), (4, !2), (2, !4) Ô˝Ô Ó

79. Model the function rule y = 3x + 0 with a table of values and a graph. x –1 0 1

Name: ______________________

ID: A

80. Elaine is in the business of repairing home computers. She charges a base fee of $45 for each visit and $25 per hour for her labor. The total cost c(x) for a home visit and x hours of labor is modeled by the function rule c(x) = 45 + 25x. Use the function rule to make a table of values and a graph. x 0 1 2 3

c(x)

For the data in the table, tell whether y varies directly with x. If it does, write an equation for the direct variation.

81. x 2 3 4 5

y –6.6 –9.9 –13.2 –16.5

Is the equation a direct variation? If it is, find the constant of variation.

82. x ! 6y = 0 83. 5x = y

Name: ______________________

ID: A

84. A biologist records the number of microbes growing in a culture at the times listed in the table. If the microbes continue to multiply at this rate, how many will there be at 6 P.M. on the second day? Time of Observation Day 1, 12:00 noon Day 1, 6:00 P.M. Day 2, 12:00 midnight Day 2, 6:00 A.M.

Number of Microbes 12,000 18,000 27,000 40,500

85. Suppose you have $20.00 to buy cold cuts for a class picnic. Ham costs $3.99 per pound and turkey costs $4.99 per pound. The equation 3.99x + 4.99y = 20 models this situation. What does the x-intercept of the graph of the equation tell you about the amount of meat you can buy?

86. Graph the following linear inequalities on the same coordinate plane. What figure does the solution to all three inequalities make? y # !5 y $ 2x + 5 y $ !2x + 5

Name: ______________________

ID: A

87. Graph the following equation. y # |x ! 2 | ! 2

Name: ______________________

ID: A

88. A local citizen wants to fence a rectangular community garden. The length of the garden should be at least 110 ft, and the distance around should be no more than 380 ft. a. Write a system of inequalities that models the possible dimensions of the garden. b. Graph the system to show all possible solutions.

Name: ______________________

ID: A

89. You have a gift certificate to a book store worth $90. Each paperback books is $9 and each hardcover books is $12. You must spend at least $25 in order to use the gift certificate. Write and graph a system of inequalities to model the number of each kind of books you can buy. Let x = the number of paperback books and y = the number of hardback books.

90. Write 32x 5 y 5 with only one exponent. Use parentheses. 91. Solve the equation. Show your work. 16

= 4

92. Suppose you are playing a game with two number cubes. Let A represent rolling 2, 3, or 4, and B represent rolling 1, 5, or 6. The probability of A is a. b.

1 1 and the probability of B is . 2 2

2 ÊÁ 1 1 ˆ˜˜˜ Á Á Simplify ÁÁ A + B ˜˜ ÁË 2 2 ˜¯ What is the probability that one number cube shows 2, 3, or 4, and the other shows 1, 5, or 6?

Name: ______________________

ID: A

93. Factor the following trinomial. w1 8 â&#x20AC;&#x201C; 9w9 y5 + 14y1 0

94. Factor the following expression. 198q 3 r2 â&#x20AC;&#x201C; 184q 2 r2 + 18qr2

95. Find a pair of factors for each number by using the difference of two squares. a. b. c.

45 77 112

96. Make a table of values and graph the quadratic function y = 3 x 2 . 4

3 2 x 4

(x, y)

Name: ______________________

ID: A

97. An architect is designing an archway. The shape of the arch is described by the three inequalities given. Make a graph of the arch. 3 2 3 2 y $ ! x + 12; y # ! x + 10; y # 0 4 4

98. Solve 1 x 2 + 1 = 0 by graphing the related function. 2

99. The formula h = !16t 2 + vt models the height of a model rocket, where h is the height in meters, t is the time in seconds and v is the initial vertical velocity in meters per second. If the model rocket is fired at an initial vertical velocity of 80 meters per second, will the rocket ever reach a height of 88 meters? Justify your answer.

100. For the equation !2x 2 + x + j = 0, find all the values of j such that the equation has two real number solutions. Show your work.