/Prealgebra by Valencia College

Competency Exam Information To pass your Prealgebra class you MUST pass the Competency exam AND your class. Questions: Time limit: Calculator: Formulas:

35 multiple-choice None May NOT be used Will NOT be provided

Exam will be taken using WebCT (paper copy can be requested) in the Testing Center during the last week of the term. • Your instructor will give you a time and day by which the first try must be taken. You may choose to take it prior to this assigned day and time. • Requirements for a 2nd try (if you fail the 1st try): o Must be able to pass the class with a 70% or higher class average (including a hypothetical 100% on the final exam). o Must have passed the practice exam a minimum of 3 times since failing the first try. • There is a minimum 24-hour waiting period between tries. If you have any question about the exam, see Mr. Weinsier in the Math Center (4-102). The following review is a list of the type of questions that will be on the exam. It is not a list of the exact questions. ©Valencia Community College – All Rights Reserved

Problem number vs Topic More practice is available on WebCT. 1, 2, 3. Find the perimeter or area of a square, rectangle, or triangle. 4. Find the volume of a rectangular solid. 5, 6, 7. Simplify a numeric expression using order of operations with integers. 8, 9. Simplify a numeric expression with absolute value and integers. 10. Simplify an algebraic expression with integers. 11. Simplify an algebraic expression with fractions. 12. Simplify an algebraic expression with decimals. 13. Evaluate an algebraic expression with integers. 14. Evaluate an algebraic expression with fractions. 15. Evaluate an algebraic expression with decimals. 16,17,18.Solve an equation with integers. 19, 20. Solve an equation with fractions. 21, 22. Solve an equation with decimals. 23. Solve a formula for a variable with assigned values for other variables. 24, 25. Translate a real world word problem using percentages. 26. Translate a real world word problem without percentages. 27. Multiply a monomial with a binomial. 28. Multiply a monomial with a trinomial. 29. Multiply a monomial with a binomial using exponents. 30. Multiply a binomial with a binomial using 1 variable. 31. Multiply a binomial with a binomial using 1 variable and fractions. 32. Multiply a binomial with a binomial using 2 variables. 33. Add polynomials. 34. Subtract polynomials. 35. Add and subtract polynomials.

Suggestions: Before beginning the exam, write down any information that you feel might cause you to make an error on the exam. (Data Dump) Then during the exam you can refer back to this information as a reminder. Work all the problems. Guess, if necessary. Do all rechecking on a clean sheet of scrap paper.

Competency Exam Review: Question #1 Perimeter of a square, rectangle, or triangle 1. What is the perimeter of a square that is 7 inches on each side? a) 49 inches b) 49 sq. inches c) 28 inches d) 28 sq. inches 2. What is the perimeter of a square that is 3 feet on each side? a) 12 feet b) 12 sq. feet c) 9 feet d) 9 sq. feet 3. What is the perimeter of a rectangle that has a length of 8 cm and a width of 5 cm? a) 40 sq. cm b) 40 cm c) 26 cm d) 26 sq. cm 4. What is the perimeter of a rectangle that has a length of 13 inches and a width of 4 inches? a) 34 sq. inches b) 34 inches c) 52 sq. inches d) 52 inches 5. What is the perimeter of a triangle that has one side with a length of 5 inches, a second side of 8 inches, and a third side of 10 inches? a) 23 inches b) 46 inches c) 23 sq. inches d) 46 sq. inches 6. What is the perimeter of a triangle that has one side with a length of 6 cm, a second side of 9 cm, and a third side of 15 cm? a) 30 sq. cm b) 60 cm c) 30 cm d) 60 sq. cm 7. What is the perimeter of a square that is 9 centimeters on each side? 8. What is the perimeter of a rectangle that has a length of 11 meters and a width of 9 meters? 9. What is the perimeter of a triangle that has one side with a length of 7 feet, a second side of 10 feet, and a third side of 12 feet? Challenge questions: 10. What is the perimeter of a rectangle with length of 2 feet and a width of 5 inches? 11. What is the perimeter of a square that is

3 of an inch long on each side? 4

12. What is the perimeter of a rectangle that has a length of 4.6 feet and a width of 3.2 feet? 13. What is the perimeter of a triangle that has one side with a length of 2 second side of 3

1 cm, a 4

1 3 cm, and a third side of 1 cm? 2 5

Competency Exam Review: Question #2 Area of a square or rectangle 1. What is the area of a rectangle that has a length of 6 feet and a width of 4 feet? a) 24 sq. feet b) 20 sq. feet c) 20 feet d) 24 feet 2. What is the area of a rectangle that has a length of 9 meters and a width of 7 meters? a) 63 meters b) 63 sq. meters c) 32 sq. meters d) 32 meters 3. What is the area of a rectangle that has a length of 13 inches and a width of 5 inches? a) 36 inches b) 36 sq. inches c) 65 sq. inches d) 65 inches 4. What is the area of a square that has a side length of 11 inches? a) 44 sq. inches b) 44 inches c) 121 inches d) 121 sq. inches 5. What is the area of a square that has a side length of 12 centimeters? a) 48 cm b) 48 sq. cm c) 144 sq. cm d) 144 cm 6. What is the area of a square that has a side length of 13 feet? a) 169 sq. feet b) 52 sq. feet c) 169 feet d) 52 feet 7. What is the area of a rectangle that has a length of 5 yards and a width of 3 yards? 8. What is the area of a square that has a side length of 10 meters? 9. What is the area of a rectangle that has a length of 17 meters and a width of 11 meters? Challenge questions: 10. What is the area of a rectangle that has a length of 5 yards and a width of 2 feet? 11. What is the area of a square that has a side length of 2

1 feet? 4

12. What is the area of a rectangle that has a length of 6.24 inches and a width of 4.7 inches? 13. What is the area of a square that has a side length of 9.03 meters? 2 3

14. What is the area of a rectangle that has a length of 3 yards and a width of 2

1 4

yards? A4

Competency Exam Review: Question #3 Area of a triangle 1. What is the area of a triangle that has a base of 5 inches and a height of 8 inches? a) 20 inches b) 40 inches c) 20 sq. inches d) 40 sq. inches 2. What is the area of a triangle that has a base of 8 centimeters and a height of 7 centimeters? a) 56 sq. cm b) 28 cm c) 28 sq. cm d) 56 cm 3. What is the area of a triangle that has a base of 9 feet and a height of 10 feet? a) 90 feet b) 45 sq. feet c) 45 feet d) 90 sq. feet 4. What is the area of a triangle that has a base of 6 meters and a height of 8 meters? a) 24 sq. meters b) 48 sq. meters c) 48 meters d) 24 meters 5. What is the area of a triangle that has a base of 2 yards and a height of 3 yards? a) 6 yards b) 3 yards c) 6 sq. yards d) 3 sq. yards 6. What is the area of a triangle that has a base of 20 inches and a height of 11 inches? a) 220 sq. inches b) 110 sq. inches c) 110 inches d) 220 inches 7. What is the area of a triangle that has a base of 9 feet and a height of 7 feet? 8. What is the area of a triangle that has a base of 13 cm and a height of 21cm? 9. What is the area of a triangle that has a base of 28 meters and a height of 17 meters? Challenge questions: 10. What is the area of a triangle that has a base of 2 meters and a height of 46 cm? 11. What is the area of a triangle that has a base of 2.35 inches and a height of 9.8 inches? 12. What is the area of a triangle that has a base of 3 13. What is the area of a triangle that has a base of

2 3 feet and a height of 2 feet? 3 4

3 5 yard and a height of yard? 5 8

Competency Exam Review: Question #4 Volume of a cube or rectangular box 1. What is the volume of a rectangular box that has a length of 6 inches, a width of 9 inches, and a height of 4 inches? a) 216 inches b) 216 sq. inches c) 216 cu. inches d) 19 inches 2. What is the volume of a cube that measures 7 feet on each side? a) 343 cu. feet b) 343 sq. feet c) 343 feet d) 21 feet 3. What is the volume of a rectangular box that has a length of 10 centimeters, a width of 8 centimeters, and a height of 5 centimeters? a) 400 sq. cm b) 23 cm c) 400 cm d) 400 cu. cm 4. What is the volume of a cube that measures 8 inches on each side? a) 512 inches b) 512 sq. inches c) 24 inches d) 512 cu. inches 5. What is the volume of a rectangular box that has a length of 9 feet, a width of 10 feet, and a height of 7 feet? a) 630 feet b) 630 cu. feet c) 630 sq. feet d) 26 feet 6. What is the volume of a cube that measures 11 meters on each side? a) 1331 meters b) 44 meters c) 1331 cu. meters d) 1331 sq. meters 7. What is the volume of a cube that measures 14 meters on each side? 8. What is the volume of a rectangular box that has a length of 23 cm, a width of 15 cm, and a height of 13 cm? 9. What is the volume of a rectangular box that has a length of 6 feet, a width of 7 feet and a height of 8 feet? Challenge questions: 10. What is the volume of a rectangular box that has a length of 2 feet, a width of 2 yards, and a height of 2 inches? 11. What is the volume of a cube that measures 6.4 inches on each side? 12. What is the volume of a rectangular box that has a length of 5.6 feet, a width of 9.3 feet, and a height of 11.9 feet? 1 3

13. What is the volume of a cube that measures 3 meters on each side?

Competency Exam Review: Question #5 Order of operations with integers 1. Use order of operations to simplify: a) 5 b) 2 c) -3 d) -6 2. Use order of operations to simplify: a) 22 b) 20 c) 5 d) 7 3. Use order of operations to simplify: a) 9 b) 24 c) 36 d) 6 4. Use order of operations to simplify: a) 997 b) 27 c) 3 d) 5 5. Use order of operations to simplify: a) 80 b) 8 c) 60 d) 6 6. Use order of operations to simplify: a) 188 b) 12 c) 92 d) 20

42 − (3 + 4 ⋅ 2) 52 − (3 + 6 ÷ 3) (6 − 4 ÷ 2) ⋅ 32

(8 − 3 ⋅ 2)3 − 3 (12 − 8 ÷ 4) ⋅ 23 (4 + 3 ⋅ 2)2 − 8

7. Use order of operations to simplify:

(4 ⋅ 3 − 2 ⋅ 3 + 8 ÷ 2)3 + 1

8. Use order of operations to simplify:

− (3 + 5 − 5 ⋅ 2) 2

9. Use order of operations to simplify:

32 + 110 − 2 3 − 5

Challenge questions: 10. Use order of operations to simplify:

−52

11. Use order of operations to simplify:

−34 − 43 + ( −2) 5

12. Use order of operations to simplify:

2 − (−23 ) 2 + (−2)3

13. Use order of operations to simplify:

3(5 + 8 − 15)3 3−9

Competency Exam Review: Question #6 Order of operations with integers 1. Use order of operations to simplify: a) 3 b) -27 c) 1 d) -47 2. Use order of operations to simplify: a) 4 b) -16 c) 22 d) 34 3. Use order of operations to simplify: a) -10 b) -14 c) 26 d) 44 4. Use order of operations to simplify: a) 21 b) 5 c) 19 d) -1 5. Use order of operations to simplify: a) 11 b) -7 c) 7 d) -3 6. Use order of operations to simplify: a) 15 b) -9 c) 23 d) -11

−4 ⋅ 6 − (−5) 2 + 2 3 − (2 − 5) 2 + 10

3 ⋅ 5 − (−3)3 + 2 10 − (2 − 4)3 + 3 2 − (7 − 8)5 + 4

3 ⋅ 2 − (−4)2 − (−1)

7. Use order of operations to simplify:

(5 − 9) 2 − (3 − 10) + 23

8. Use order of operations to simplify:

2(5 ⋅ 2 + 8 ÷ 4) (−2)3

9. Use order of operations to simplify:

(12 ÷ 4 ⋅ 3 ÷ 9 + 1) 4 + 1

Challenge questions:

( 5 − 10 + 2 )

2 2

10. Use order of operations to simplify:

32 − 7

11. Use order of operations to simplify:

−34 − 43 8 +1 −5

12. Use order of operations to simplify:

( −2)3 − 23 + 33 (22 )

Competency Exam Review: Question #7 Order of operations with integers 1. Use order of operations to simplify: a) 6 b) -54 c) 54 d) 42

3[8 − 2(5 − 8)]

2. Use order of operations to simplify: a) -2 b) 18 c) 12 d)-8

[5 − 2(3 + 2)] − (−3)

3. Use order of operations to simplify: a) -10 b) -30 c) -4 d) -1

[5 + 3(−2 − 1)] − 6

4. Use order of operations to simplify: a) 60 b) -24 c) 8 d) -4

[8 − 3(4 − 1)]4

5. Use order of operations to simplify: a) 13 b) 1 c) -5 d) 19

10 − [6 − 3(5 − 8)]

6. Use order of operations to simplify: a) 42 b) -26 c) -8 d) 10

[4 + 3(1 − 4)](−2)

7. Use order of operations to simplify:

[ −3 − 8 + ( −2 − 5) ] 2

8. Use order of operations to simplify:

3 + [ −7(5 − 4 − 3) ] 3

9. Use order of operations to simplify:

− [ − ( −3 + 7) − 5]

Challenge questions: 10. Use order of operations to simplify:

⎡⎣ (3 + 4 − 5) 2 − 12 ÷ 4 ⎤⎦ (1 + 3)

11. Use order of operations to simplify:

4 ÷ 2 ⎡⎣5 − 32 (8 ÷ 4) ⎤⎦

12. Use order of operations to simplify:

⎡⎣3(2 + 3) 2 ⎤⎦ ⎡⎣ (6 − 9) 2 (−2) ⎤⎦

13. Use order of operations to simplify:

2 − ⎡⎢ − ( −32 ) ⎤⎥ ⎣ ⎦

Competency Exam Review: Question #8 Absolute value with integers 1. Simplify: a) 12

− −7 − 5 b) -12

c) 2

− 7 +2 2. Simplify: a) -5 b) 9 c) -9 3. Simplify: a) -13 4. Simplify: a) -17

d) 35

d) 5

−9 − (−4) b) -5

c) 5

− −10 + 7 b) -3

c) 17

2− 9 5. Simplify: a) -7 b) 7 c) -11 6. Simplify: a) -10

d) 13

d) 3

d) 11

−3 + − 7 b) 4

c) -4

d) 10

7. Simplify:

− −5 − 3 + 2

8. Simplify:

−4 + −3 − 7 2

9. Simplify:

2 + 3 −4 (−5)

Challenge questions: 10. Simplify:

−52

11. Simplify:

−2 −8 ÷ 42

12. Simplify:

8 − −15 + (−2)3

A10

Competency Exam Review: Question #9 Absolute value with integers − 4+ −3+ 6 1. Simplify: a) -1 b) 5 c) -7 d) 1

4 − −2 + 7 2. Simplify: a) -5 b) 13 c) -1 d) 9 − −3 + 6 + 1 3. Simplify: a) -2 b) -4 c) -8 d) -10 −2 + −5 + 6 4. Simplify: a) -3 b) -1 c) 9 d) 13 2 − −13 + 6 5. Simplify: a) -5 b) 9 c) -17 d) 21 6. Simplify: a) -11

−4 + 3 − 10 b) 9

c) -17

d) 3

7. Simplify:

−2 + −5 − 7 − 4

8. Simplify:

− 2+7−5 2

9. Simplify:

(−8 + 4)(−2) −4 ÷ 4(2)

Challenge questions: 10. Simplify:

−3 25 − 42 − 32

11. Simplify:

−(3 − 8)(−3) (−2 + 5)

12. Simplify:

−2 − (−4 + 3)5 3

A11

Competency Exam Review: Question #10 Simplify expression with integers 1. Simplify: 3 xz − 4 yz + xz − 8 yz b) 4 xz + 12 yz a) 4 x 2 z 2 − 12 y 2 z 2

c) 4 xz − 12 yz

2 x 2 + 3x − x2 − 7 x 2. Simplify: 2 6 4 2 c) x − 4 x a) x − 4 x b) −3x

d) x + 4 x

3. Simplify: 10 a) 4x 4. Simplify: a) xyz

d) −8xyz

−5 x 2 + 3 x 3 + 7 x 2 − x 3

b) −2 x − 2 x 3

c) 2 x + 2 x 3

d) 4x

−5 xy + xz + 7 xy − 2 xz b) 2xy − xz

c) 2xy + xz

d) 2x 2 y 2 − x 2 z 2

9 x y − 4 xy − x y − 6 xy 5. Simplify: a) 8 x 2 y + 10 xy b) −2x 4 y 2 c) 8 x 4 y 2 − 10 x 2 y 2 2

6. Simplify: a) 2x 2 y 6

y 2 − 5 xy + 9 y 2 − 3 xy b) 10 y 2 − 8 xy c) 10 y 2 + 8 xy

7. Simplify:

m 2 + r 2 + 3m 2 − r 2

8. Simplify:

mg 2 + mg − 3mg 2 − 7 mg

9. Simplify:

abc + cba + bac + cab

d) 8 x 2 y − 10 xy

d) 2xy 2

Challenge questions: 10. Simplify:

5 x 2 y − 3 xy 2 − 9 x 2 y 2 + xy 2 − 2 x 2 y

11. Simplify:

−2 st + 5rt − 9 st + rt − rst

12. Simplify:

xyz − 9 x 2 yz − 2 xy 2 z + x 2 yz − xyz

13. Simplify:

12 jk 4 − 3 jk 3 + jk + 8 jk − jk 4 + 8 jk 3

A12

Competency Exam Review: Question #11 Simplify expression with fractions 2 2 x− x 7 3

1. Simplify: a)

1 x 4

b) −

2. Simplify: a) −

1 z 10

a) −

7 z 15

d) 0

c) −

3 z 10

1 2 z 10

c) −

1 xz 12

c) −

1 2 x 15

d) −

1 xz 2

2 3 − x+ x 3 5

b) −

1 x 2

d) −

2 2 x 5

2 1 − xy − xy 3 4

11 2 2 x y 12

6. Simplify:

2 z 3

b) xz

1 x 15

5. Simplify:

4 2 x 21

2 3 xz − xz 3 4

1 2 2 xz 12

4. Simplify:

3 1 − z+ z 5 2

3. Simplify: a) −

8 x 21

b) −

11 xy 12

c) −

3 xy 7

11 xy 12

1 4 z− z 3 5

b) −

7 2 z 15

7. Simplify:

3 2 1 2 z − z 5 8

8. Simplify:

1 5 − mz − mz 4 6

c) −

3 z 2

d) −

17 z 15

A13

Competency Exam Review: Question #12 Simplify expression with decimals 1. Simplify: a) 1.83yz

(1.6 y)(0.23z ) b) 0.368yz

c) 3.68yz

(0.8 x)(0.41x) 2. Simplify: 2 a) 0.328x b) 0.328x

c) 1.21x

(23.4 z )(0.6 x) 3. Simplify: a) 0.24xz b) 1.404xz

c) 14.04xz

d) 1.83 + yz

d) 1.21x

d) 24xz

(3.7 y)(0.62 y) 4. Simplify: a) 2.294y b) 4.32 y 2 c) 4.32y

d) 2.294 y 2

(3.14 z )(0.8 z ) 5. Simplify: 2 a) 2.512z b) 2.512z

c) 3.94z

d) 3.94z

(5.3 y )(9.2 z ) 6. Simplify: a) 14.5yz b) 1.45yz

c) 48.76 yz

7. Simplify:

(4.6a)(6.4c)

8. Simplify:

(0.34r )(7.8k )

9. Simplify:

(12.3m)(7.73t )

d) 487.6yz

Challenge questions: (4.4a) (0.7 y ) (0.26 z ) 10. Simplify: 11. Simplify:

(−0.9d ) (0.09 f )

12. Simplify:

(9.8h) (13.6h)

13. Simplify:

(−10.4 j ) (−6.28k )

14. Simplify:

(25.3m)2

15. Simplify:

(−2.8r )3

A14

Competency Exam Review: Question #13 Evaluate expression with integers 1. Evaluate the following expression for x = -4 and y = 3: a) -28 b) 28 c) -4 d) 4 2. Evaluate the following expression for x = -5 and y = -2: a) 65 b) -65 c) -85 d) 77 3. Evaluate the following expression for x = -4 and y = -3: a) 4 b) 20 c) -4 d) -20

4. Evaluate the following expression for x = -4 and y = -2: a) 24

b) 12

c) -12

x 2 − xy x (3 x − y ) 2x − xy 3x 2 y

d) -24

5. Evaluate the following expression for x = 3 and y = -4: a) -2 b) 14 c) -7 d) 25 6. Evaluate the following expression for x = 2 and y = -4: a) 12 b) -4 c) -12 d) 4 7. Evaluate the following expression for r = 5 and t = 3: 8. Evaluate the following expression for x = -6 and y = -2: 9. Evaluate the following expression for h = -5 and j = 4:

x2 − y 2 ( x − y )( x + y ) (rt )(r − t )

(2 x 2 ) y (3h − j + 4)(hj )

Challenge questions: 10. Evaluate the following expression for x = 6 and y = -3:

( x 2 − y )( x + y 2 )

11. Evaluate the following expression for w = -7 and z = -7:

( w + wz + 3z ) 2

(−4 x − y 2 )2 −3xy

−cg 3 + (cg )2 A15

Competency Exam Review: Question #14 Evaluate expression with fractions 1. Evaluate the following expression for x = 1/2 and y = 2/3: a) 1/12 b) 7/24 c) 1/24 d) 1/4

x 2 ( y − x)

2. Evaluate the following expression for x = 1/2 and y = 3/4: a) 15/64 b) 3/4 c) 3/8 d) 3/64

y ( y − x)2

3. Evaluate the following expression for x = 2/3 and y = 1/2: a) 7/36 b) 4/3 c) 3/5 d) 1/9

( x − y )( x + y )

4. Evaluate the following expression for x = 3/4 and y = 1/4: a) 2 b) 5/4 c) 7/8 d) 11/4

2 x2 − y

5. Evaluate the following expression for x = 2/3 and y = 1/2: a) 7/36 b) 1/3 c) 3/5 d) 2

x2 − y2

6. Evaluate the following expression for x = 1/2 and y = 2/3: a) 11/18 b) 67/36 c) 19/36 d) 5/6

( y − x) 2 + x

7. Evaluate the following expression for x = 3/5 and y = 2/3:

( x − 2 y )2

8. Evaluate the following expression for x = 1/3 and y = 2/3:

−x − 3y2

9. Evaluate the following expression for j = 3/4 and m = 2/5:

2 jm − ( jm) 2

Challenge questions: 10. Evaluate the following expression for x = 1/2 and y = 2/5:

( x − y )2 + ( y − x)2

11. Evaluate the following expression for c = 2/3 and d = 3/4:

−c ( d 2 − 3c )

12. Evaluate the following expression for t = 1/2 and m = 2/3:

−(tm 2 ) (t 2 − m)

13. Evaluate the following expression for a = 1/4 and k = 1/3:

a + 2k k − 2a

A16

Competency Exam Review: Question #15 Evaluate expression with decimals (10 − x 2 ) y

1. Evaluate the following expression for x = 2.4 and y = 0.3: a) 1.272 b) 1.56 c) 5.5 d) 14.28 2. Evaluate the following expression for x = 0.2 and y = 3.4: a) 223.2 b) 1.512 c) 0.56 d) 2.304

x( y 2 − 4)

3. Evaluate the following expression for x = 2.3 and y = 0.14: ( x − y )(2 + x ) a) 5.4 b) 9.632 c) 9.288 d) 5.6 4. Evaluate the following expression for x = 0.8 and y = 1.6: a) 0.704 b) 0.96 c) 9.92 d) 7.04 5. Evaluate the following expression for x = 1.2 and y = 0.4: a) 18

b) 11.1

c) 1.08

(0.4)( y 2 − x) 3x 2 y

d) 10.8

6. Evaluate the following expression for x = 1.5 and y = 0.6: a) 0.01323 b) 13.23 c) 1.323 d) 1.26 7. Evaluate the following expression for x = 1.3 and y = 0.8: 8. Evaluate the following expression for m = 0.35 and y = 3.4: 9. Evaluate the following expression for q = 1.5 and w = 0.6:

(0.3)( x + y)2 2xy 2 − 3.34 2.2m −

0.1y 2

q2 − w2

Challenge questions: 10. Evaluate the following expression for x = 0.12 and y = 0.5:

−( x + y)2

11. Evaluate the following expression for g = 1.5 and h = 0.6:

−0.23(2h − g )2

12. Evaluate the following expression for k = 5.1 and z = 0.3:

2k − z 2 z

−0.2 g (3m − g ) A17

Competency Exam Review: Question #16 Solve equation with integers 1. Solve for y: a) y = 11/3

−3 y + 7 = 4 b) y = 1 c) y = -1

d) y = -11/3

2. Solve for y: a) y = -9/2

5 − 4 y = 13 b) y = 13 c) y = -2

d) y = 2

3. Solve for x: a) x = 3

−3 x + 8 x = 15 b) x = 10 c) x = 15/11

d) x = -3

4. Solve for z: a) z = 2

4 z − 9 = −17 b) z = -2 c) z = -13/2

d) z = 17/5

5. Solve for y: a) y = 4

10 − 2 y = 2 b) y = /4 c) y = -6

6. Solve for x: a) x = 5/3

d) y = 6

5 x − 10 x = 25 b) x = 5 c) x = -20

d) x = -5

7. Solve for x:

−4 x + 5 = 9

8. Solve for m:

9m − 4 = 10

9. Solve for t:

−6t − t = 9

Challenge questions: 10. Solve for y:

6y + 2y − 4 = 7

11. Solve for x:

−12 − 5 = 2 x + 7 x − 4

12. Solve for z:

−8 z + 20 z = −7 − 11

13. Solve for w:

−12 + 7 = − w − w

14. Solve for m:

−3m + m − 4 = 5 − 9 − 2

15. Solve for g:

12 − (−6) − 4 = −2 g − 5g + g

A18

Competency Exam Review: Question #17 Solve equation with integers 1. Solve for x: a) x = –4/3

4x +1 = x − 3 b) x = –2/3 c) x = –4/5

2. Solve for x: a) x = 1/2

−3x + 7 = x − 5 b) x = -1/2 c) x = -3

d) x = -2/5

d) x = 3

3. Solve for y: a) y = 1

−6 + 5 y = 2 y + 9 b) y = 5 c) y = 3/7

d) y = -11

4. Solve for z: a) z = 3

−2 z + 9 = 4 z − 3 b) z = 6 c) z = -6

d) z = 2

5. Solve for y: a) y = 2

10 − 3 y = 3 y − 2 b) y = -4/3 c) y = 0

d) undefined

6. Solve for z: a) z = -3

−7 + 4 z = −2 z − 1 b) z = -4/3 c) z = 1

d) z = -4

7. Solve for x:

5 − 3x = 7 x − 9

8. Solve for p:

−p +9 = 5p −5

9. Solve for f:

9 f − 4 = 12 − f

Challenge questions: 4 z + 3 z − 6 = 10 − z 10. Solve for z: 11. Solve for w:

9w − 12 + 8 = −2w + 3 − w

12. Solve for c:

7 + c − 5c = −c + 2c − 12

13. Solve for x:

−7 + 5 x − 11 = 2 x + 3 − 8 x

14. Solve for z:

−4 z − 7 z + z = 12 − (−4) − 20

15. Solve for t:

−5t − 5 + 11t − 9 = 8 − 8t + 7 + t

A19

Competency Exam Review: Question #18 Solve equation with integers 1. Solve for x: a) x = 1/2 2. Solve for x: a) x = 17/3 3. Solve for x: a) x = 19/2 4. Solve for x: a) x = 11/6 5. Solve for x: a) x = 22/3

3(2 x + 5) = 2(4 x − 1) b) x = 13/2

c) x = 17/2

d) x = 3

6(4 − 2 x) = 2(3x + 5) b) x = 7/9

c) x = 17/9

d) x = 7/3

4(5 x − 1) = 3(6 x + 5) b) x = 11/2

c) x = 1/2

d) x = 11/38

2(7 x − 2) = 5(3 − 4 x) b) x = -19/34

c) x = -11/6

d) x = 19/34

7( x + 4) = 2(5 x − 3) b) x = 34/3

c) x = 22/17

2(8 x − 1) = 6(5 − x) 6. Solve for x: 14 a) x = /11 b) x = 16/11 c) x = 16/5 7. Solve for y:

3(2 y − 5) = 4( y + 2)

8. Solve for n:

4(3n − 4) = 5(2 − n)

9. Solve for p:

6( p − 3) = 2(5 + 2 p )

d) x = 2

d) x = 14/5

Challenge questions: 10. Solve for x: −3(2 x − 5) = 7(−5 − x) 11. Solve for d:

−4(2d + 5d ) + 2 = 3d

12. Solve for q:

3q(−5 − 9 + 7) = −(−2q + 4)

13. Solve for y:

−(3 y − 4 y + 7) = 2( y + 3 − 10)

14. Solve for w:

−2(3w + 7) − 3w + 4 = (− w + 5)(−3)

A20

Competency Exam Review: Question #19 Solve equation with fractions 1. Solve for z: a) z = 1/15 2. Solve for x: a) x = 1/10 3. Solve for y: a) y = 20/9 4. Solve for z: a) z = 37/20 5. Solve for x: a) x = 8/15 6. Solve for z: a) z = 5/4

3 2 z− = 5 3 b) z = 3 c) z = 5/8

d) z = 19/15

2 1 = 5 2 b) x = 9/10 c) x = 3/7

d) x = 1/3

3 5 +y= 4 3 b) y = -2 c) y = 11/12

d) y = 29/12

3 5 +z= 5 4 13 b) z = /20

c) z = 25/12

4 2 = 3 5 b) x = 3/10 c) x = -14/15

d) z = 3/4

x−

3 5 = 2 6 b) z = 5/9 c) z = 7/3

d) x = 26/15

z−

d) z = -2/3

1 1 = 2 6

7. Solve for x:

x−

8. Solve for k:

4 2 +k = 5 7

9. Solve for p:

3 1 = +p 8 5

A21

Competency Exam Review: Question #20 Solving equation with fractions 1. Solve for y: a) y = 4/5 2. Solve for z: a) z = -11/15 3. Solve for x: a) x = 3/14 4. Solve for y: a) y = 5/6 5. Solve for x: a) x = 7/6 6. Solve for z: a) z = -22/35

1 3 y= 5 5

b) y = 2/5

c) y = 3/25

d) y = 3

3 3 z= 4 5

b) z = 29/15

c) z = 4/5

d) z = 9/20

3 2 x= 4 7

b) x = 8/21

c) x = -13/28

d) x = 29/28

2 5 y= 3 4

b) y = 15/8

c) y = 23/12

d) y = 7/12

1 4 x= 6 3

b) x = 8

c) x = 2/9

d) x = 3/2

6 4 z= 5 7

b) z = 62/35

7. Solve for y:

2 4 y= 5 5

8. Solve for g:

2 5 = g 3 6

9. Solve for f:

1 3 f = 8 7

c) z = 24/35

d) z = 10/21

Challenge questions: 10. Solve for t:

2 5 − t= 5 7

11. Solve for z:

1 3 z+2= 4 2

A22

Competency Exam Review: Question #21 Solve equation with decimals 3.24 = 0.4 x + 5.5 1. Solve for x: a) x = 0.904 b) x = -2.66 c) x = -5.65

d) x = 2.6

4.56 = 0.2 y + 6 2. Solve for y: a) y = -7.2 b) y = 16.8 c) y = 25.44

d) y = 0.288

5.6 = 0.02 z + 7.38 3. Solve for z: a) z = 0.2596 b) z = 649 c) z = 0.0356

d) z = -89

0.3x − x = 14.07 4. Solve for x: a) x = -20.1 b) x = 45.9 c) x = -9.849

d) x = -46.9

y − 0.4 y = 48.3 5. Solve for y: a) y = 48.9 b) y = 47.7 c) y = 80.5

d) y = -120.75

1.6 z − 2 z = 20.1 6. Solve for z: a) z = 20.5 b) z = 8.45 c) z = 10.5625 7. Solve for w:

0.4w + 3.5 = 0.33

8. Solve for x:

0.8 x − 4.12 = 7.5

9. Solve for q:

2.2q − q = 6

d) z = -50.25

Challenge questions: 10. Solve for q: −0.5q + 1.4 = q − 0.4 11. Solve for r:

1.1r − 2r = 7 − 4.3

12. Solve for m:

4 − 2.1m = −1.3m + 10.2

13. Solve for y:

3.2 y − y − 0.11 = 2 y + 3.3

14. Solve for a:

a − 1.5a − 0.2 = 5.8 − 9 + 0.1a

15. Solve for z:

1.6 z − 2 z = 20.1

A23

Competency Exam Review: Question #22 Solve equation with decimals 1. Solve for x:

x = 2.07 1.2

a) x = 2.484

2. Solve for y: a) y = 1.77

3. Solve for z:

b) x = 1.725

a) x = 5.72

5. Solve for y: a) y = 4.3

6. Solve for z:

b) y = 1.53

c) y = 13.75

d) y = 0.198

z = 4.07 0.16 b) z = 0.6512

c) z = 3.91

d) z = 4.23

x = 5.8 0.08 b) x = 5.88

c) x = 72.5

d) x = 0.464

c) y = 7.42

d) y = 4.62

y = 6.02 1.4 b) y = 8.428

z = 2.04 0.012

a) z = 0.02448

b) z = 170

7. Solve for q:

q = 3.6 0.07

8. Solve for h:

h = 8.02 12.7

9. Solve for w:

5.6 =

A24

d) x = 3.27

y = 1.65 0.12

a) z = 25.4375

4. Solve for x:

c) x = 0.87

c) z = 2.028

d) z = 2.052

w 1.034

Competency Exam Review: Question #23 Solve a formula with given values 1. The formula for the perimeter of a rectangle is: P = 2L + 2W Solve for ‘L’ when P = 30 and W = 6. a) L = 36 b) L = 21 c) L = 9 d) L = 2 2. The formula for the perimeter of a rectangle is: P = 2L + 2W Solve for ‘W’ when P = 23 and L = 7. a) W = 4.5 b) W = 2 c) W = 18.5 d) W = 18 3. The formula for the area of a triangle is: A = Solve for ‘b’ when A = 17 and h = 8. a) b = 26 b) b = 2.375 c) b = 4.25

d) b = 68

4. The formula for the area of a triangle is: A = Solve for ‘h’ when A = 23 and b = 4. a) h = 52 b) h = 40 c) h = 11.5

bh 2

d) h = 69

5. The formula for the volume of a rectangular box is: V = LWH Solve for ‘W’ when V =162, L = 4, and H = 3. a) W = 1944 b) W = 13.5 c) W = 162 d) W = 121.5 6. The formula for the volume of a rectangular box is: V = LWH Solve for ‘H’ when V =174, L = 2, and W = 6. a) H = 2088 b) H = 14.5 c) H = 43.5 d) H = 162 7. The formula for the perimeter of a rectangle is: P = 2L + 2W Solve for ‘W’ when P = 45 and L = 10. 8. The formula for the area of a triangle is:

bh 2

Solve for ‘h’ when A = 25 and b = 10. 9. The formula for the volume of a rectangular box is: Solve for ‘H’ when V =135, L = 5, and W = 3.

V = LWH

A25

Competency Exam Review: Question #24 Translate a word problem using a percentage 1. Nashali found a dress she really liked that originally sold for $78. The dress was discounted 30%. Using ‘P’ as the amount she will have to pay for the dress (excluding sales tax), write an algebraic equation that describes this transaction. a) P = (0.30)(78) b) P = 78 ÷ 0.30 c) P = 78 ÷ 0.70 d) P = 78 – (0.30)(78) 2. At Target Richard found a CD player that originally sold for $148. A sign indicated that the player was discounted 45%. Using ‘P’ as the amount he will have to pay for the CD player (excluding sales tax), write an algebraic equation that describes this transaction. a) P = (0.45)(148) b) P = 148 – (0.45)(148) c) P = 148 ÷ 0.45 d) P = 148 ÷ 0.55 3. Maria bought a pair of slacks that originally sold for $50. A sign indicated that the slacks were discounted 60%. Using ‘P’ as the amount she will have to pay for the slacks (excluding sales tax), write an algebraic equation that describes this transaction.. a) P = 50 – (0.60)(50) b) P = 50 + (0.60)(50) c) P = (0.60)(50) d) P = 50 ÷ (0.60) 4. Best Buy is selling a television for $1250.00. Sales tax in Orange County is 6%. Using ‘P’ as the amount I will have to pay for the television (including sales tax), write an algebraic equation that describes this transaction. a) P = (0.06)(1250) b) P = 1250 ÷ 0.06 c) P = 1250 + (0.06)(1250) d) P = 1250(0.94) 5. My car cost $7500.00. Sales tax on the car is 8%. Using ‘P’ to represent the total amount paid for the car (including sales tax), write an algebraic equation that describes this transaction. a) P = 7500 ÷ (0.08) b) P = 7500 + (7500)(0.08) c) P = (0.08)(7500) d) P = 7500(0.92) 6. The Rug King is selling silk rugs for $2350. Sales tax in Seminole County is 7%. Using ‘P’ as the amount you will have to pay for the rug (including sales tax), write an algebraic equation that describes this transaction. a) P = 2350 ÷ 0.07 b) P = (0.07)(2350) c) P = 2350(0.93) d) P = 2350 + (0.07)(2350) A26

Competency Exam Review: Question #25 Translate a word problem using a percentage 1. Richard put $550 into his savings account, which pays 4% per year simple interest and left it there for 3 years. Using ‘A’ as the total amount that will be in the bank at the end of the 3 years, write an algebraic equation that describes this transaction. a) A = (550)(0.04)(3) b) A = 550 + (0.04)(3) c) A = 550 + (550)(0.04)(3) d) A = 550 – 550(0.04)(3) 2. Mandy put $2500 into her savings account, which pays 3% per year simple interest and left it there for 4 years. Using ‘A’ as the total amount that will be in the bank at the end of the 4 years, write an algebraic equation that describes this transaction. a) A = 2500(0.03)(4) b) A = 2500 + (0.03)(4) c) A = 2500 – 2500(0.03)(4) d) A = 2500 + 2500(0.03)(4) 3. Jeremy put $1200 into his savings account, which pays 5% per year simple interest and left it there for 2 years. Using ‘A’ as the total amount that will be in the bank at the end of the 2 years, write an algebraic equation that describes this transaction. a) A = 1200 + 1200(0.05)(2) b) A = 1200(0.05)(2) c) A = 1200 – 1200(0.05)(2) d) A = 1200 + (0.05)(2) 4. Juan took Brooke out for dinner at the Outback. The bill was $40.00. Juan left a 15% tip. Using ‘T’ as the total of the bill and the tip, write an algebraic equation that describes this transaction. a) T = 40(0.15) b) T = 40 ÷ 0.15 c) T = 40 + 40(0.15) d) T = 40 – 40(0.15) 5. Susan and Brian went out for dinner at Olive Garden. The bill was $35. Susan left a 20% tip. Using ‘T’ as the total of the bill and the tip, write an algebraic equation that describes this transaction. a) T = 35 + 35(0.20) b) T = 35(0.20) c) T = 35 ÷ (0.20) d) T = 35 – 35(0.20) 6. Donald and Rose went out for dinner at Disney. The bill was $130. Donald, a big spender, left a 25% tip. Using ‘T’ as the total of the bill and the tip, write an algebraic equation that describes this transaction. a) T = 130(0.25) b) T = 130 + 130(0.25) c) T = 130 – 130(0.25) d) T = 130 ÷ 0.25

A27

Competency Exam Review: Question #26 Translate a word problem with no percentage 1. Jon decided to rent an apartment with three other friends. Jon agreed to pay the security deposit of $150 in addition to his share of the first month’s rent. All four of them agreed to contribute equally toward the monthly rent. Using ‘R’ as the total rent due each month, translate this problem into an algebraic expression that will show how much Jon will pay for the first month. R R + 150 + 150 a) 4R + 150 b) c) d) R + 150 4 4 2. Alfred decided to rent an apartment with two other friends, Alfred agreed to pay the security deposit of $125 in addition to his share of the first month’s rent. All three of them agreed to contribute equally toward the monthly rent. Using ‘R’ as the total rent due each month, translate this problem into an algebraic expression that will show how much Alfred will pay for the first month. R R + 125 + 125 c) 3 R + 125 a) b) d) R + 125 3 3

3. When Marcie bought her car, she gave the dealership $500 as a down payment. Her monthly payments will be $225. Using ‘M’ as the number of months needed to pay off the car, translate this problem into an algebraic expression that will show how much Marcie will pay for the car. c) 225M − 500 d) 500 − 225M a) 500 + 225M b) 225M 4. When Xiao bought his car, he gave the dealership $1500 as a down payment. He will pay off his car after 48 months. Using ‘M’ as the monthly payment, translate this problem into an algebraic expression that will show how much Xiao will pay for the car. b) 1500 + 48M c) 1500 − 48M d) 48M − 1500 a) 48M 5. Keisha is investing her money in an IRA. Initially she will be putting in $775. Using ‘C’ as the additional amount invested each month, translate this problem into an algebraic expression that will show how much Keisha invested for the entire year. a) 775 + C b) 775 − 12C c) 775C d) 775 + 12C 6. Gretchen is investing her money in an IRA. Each month she will contribute $200. Using ‘V’ as the amount initially invested, translate this problem into an algebraic expression that will show how much Gretchen invested for the entire year. c) 200 − 12V d) 200V a) V + 200(12) b) 200 + 12V

A28

Competency Exam Review: Question #27 Multiply a monomial and a binomial 1. Multiply and simplify where possible: a) 20x2 – 2 b) 20x – 8 c) 12x

4 x(5 x − 2) d) 20x2 – 8x

2. Multiply and simplify where possible: a) 21y – 15 b) 9y + 2 c) 21y2 – 15y

3 y (7 y − 5) d) 7y

5 x(8 z − 3) 3. Multiply and simplify where possible: a) 40xz – 15 b) 40xz – 15x c) 13xz + 2 d) 25xz 4. Multiply and simplify where possible: a) 6yz – 14y b) 6yz – 14 c) 5yz – 5

2 y (3z − 7) d) -8yz

5. Multiply and simplify where possible: a) 14 – 6x b) 14x + 6x2 c) 9x + 5x2

2 x(7 + 3x) d) 20x

6. Multiply and simplify where possible: a) 45xy b) 14xy c) 25x + 20xy

5 x(5 + 4 y ) d) 10x + 9xy

7. Multiply and simplify where possible:

8 y (2 y − 9)

8. Multiply and simplify where possible:

10 g (5 + 3m)

9. Multiply and simplify where possible:

(3 f + 8h)2h

Challenge questions: 10. Multiply and simplify where possible:

−5 g (2t − 13)

11. Multiply and simplify where possible:

−3h(−2v + 11)

12. Multiply and simplify where possible:

(6d − 5c) (−4)

13. Multiply and simplify where possible:

2 ⎛4 1⎞ x⎜ x + ⎟ 5 ⎝5 2⎠

14. Multiply and simplify where possible:

3.5m(0.23h − 0.7)

A29

Competency Exam Review: Question #28 Multiply a monomial and a trinomial 2 z (3 z 2 + 7 z − 10) 1. Multiply and simplify where possible: a) 6z3 + 14z2 – 20z b) 6z2 + 14z – 20 d) 10z3 c) 5z3 + 9z2 – 12z 3x(5x − 4 y + 9 z) 2. Multiply and simplify where possible: 2 a) 30xyz b) 15x – 12xy + 27xz c) 8x – xy + 12xz d) 15x – 12xy + 17xz 2 x (7 z 2 + z − 4) 3. Multiply and simplify where possible: b) 16xz – 8x a) 8xz2 2 d) 9xz2 + 3xz – 2x c) 14xz + 2xz – 8x

5x(3 y + 4 z − 11) 4. Multiply and simplify where possible: a) 15y + 20z –55x b) -4xyz c) 8xy + 9xz – 6x d) 15xy + 20xz – 55x 4 x ( y 2 − 8 x + 3) 5. Multiply and simplify where possible: a) 4xy2 – 32x2 + 12x b) 5xy2 – 4x2 + 7x c) 4xy – 20x d) 4xy2 – 32x + 12

3xy(2z + 5x − 9) 6. Multiply and simplify where possible: 2 b) -6xyz a) 5xyz + 8x y – 6xy c) 6xyz + 15xy – 27xy d) 6xyz + 15x2y – 27xy 7. Multiply and simplify where possible:

2 y(4 x + 5 y + 2 z)

8. Multiply and simplify where possible:

2cd (5x − 3d + 8)

9. Multiply and simplify where possible:

(2 x + 5 y − 7) (4 x 2 )

Challenge questions: 10. Multiply and simplify where possible:

−3z(−2 y + 3xz − yz)

11. Multiply and simplify where possible:

−6 a 2 ( − az − 5a 2 z + 7)

12. Multiply and simplify where possible:

3 ⎛2 3 1⎞ x⎜ z + x − ⎟ 5 ⎝5 4 3⎠

A30

Competency Exam Review: Question #29 Multiply a monomial and a binomial with exponents

xy (3 x 3 + 7 yz )

1. Multiply and simplify where possible: a) 4 x 4 y + 8 xy 2 z

b) 3x y + 7 yz

c) 3x y + 7 xy z

d) 3x y + 7 y z

x 2 (4 x 3 − 7 y 2 )

2. Multiply and simplify where possible: a) −3x y 5

4 x6 − 7 x 2 y 2

b) 5 x − 6 x y

d) 4 x − 7 x y

3. Multiply and simplify where possible: b) 3 x 2 y 3 + 6 x 3 yz a) 2 x 2 y 3 + 5 x 3 yz c) 2 x 2 y 2 + 5 x 2 yz d) 7 x 3 y 3 z

x 2 y (2 y 2 + 5 xz )

x 4. Multiply and simplify where possible: b) x 2 z 2 − 9 x 2 yz 2 a) −8x 3 yz 3 d) 2 x 3 z 2 − 8 x 2 yz 3 c) x 3 z 2 − 9 x 2 yz 3

z ( x − 9 yz)

2 2

xy 5. Multiply and simplify where possible: 2 3 2 3 2 3 2 3 b) 9 xy z + 2 x y a) 10 xy z + 3 x y 2 3 3 c) 11x y z d) 9 xy 2 z 3 + 2 xy 2

(9 z 3 + 2 xy )

xy (6 x − 3 y z ) 6. Multiply and simplify where possible: b) 7 x 3 y − 2 xy 4 z a) 6 x 3 y − 3 xy 4 z d) 3 x 3 y 4 z c) 6 x 2 y − 3 xy 3 z 2

7. Multiply and simplify where possible:

3k 2 ( 2 h 2 k 3 − 5 km 4 )

8. Multiply and simplify where possible:

(3x

9. Multiply and simplify where possible:

− 5 gh 2 ( 4 gh + 7 g 2 h )

y 2 + xyz )( 5 x 2 yz 3 )

A31

Competency Exam Review: Question #30 Multiply a binomial with a binomial using 1 variable (2 y + 3)(7 y − 5) 1. Multiply and simplify where possible: 2 a) 14y + 11y – 15 b) 9y – 2 2 c) 14y – 15 d) 14y2 – 31y – 15 (4 x − 3)(6 x − 7) 2. Multiply and simplify where possible: 2 a) 10x – 10 b) 10x – 46x – 10 2 c) 24x + 21 d) 24x2 – 46x + 21 (5 z + 7)(7 z − 1) 3. Multiply and simplify where possible: 2 2 a) 12z + 44z + 4 b) 35z – 7 2 c) 35z + 44z – 7 d) 12z2 + 18z + 6 (4 y − 3)(2 y + 5) 4. Multiply and simplify where possible: 2 a) 8y + 14y – 15 b) 6y – 2 2 c) 8y – 15 d) 6y2 + 8y + 2 (9 x − 2)(2 x − 9) 5. Multiply and simplify where possible: 2 a) 11x – 11 b) 18x – 85x + 18 2 c) 18x – 18 d) 11x2 – 22x – 11 (4 z + 5)(5 z + 4) 6. Multiply and simplify where possible: 2 2 a) 9z + 9 b) 20z + 20 2 c) 9z + 18z + 9 d) 20z2 + 41z + 20 7. Multiply and simplify where possible:

(2 z + 7)(5 z + 1)

8. Multiply and simplify where possible:

(6 g − 5)(2 g + 7)

9. Multiply and simplify where possible:

(8 − h)(8h + 5)

Challenge questions: 10. Multiply and simplify where possible:

(−3 p + 1) (−5 p − 1)

11. Multiply and simplify where possible:

⎛2 ⎞⎛ 1 ⎞ ⎜ h + 12 ⎟ ⎜ h + 3 ⎟ ⎝3 ⎠⎝ 4 ⎠

12. Multiply and simplify where possible:

(1.4 g + 3) (2.4 g + 1)

A32

Competency Exam Review: Question #31 Multiply a binomial with a binomial using fractions 3 ⎞⎛ 3⎞ ⎛ ⎜ z + ⎟⎜ z − ⎟ 4 ⎠⎝ 4⎠ ⎝ 9 2 d) z − 16

1. Multiply and simplify where possible: 2 a) z −

3 4

2 c) z −

b) 2z

2 3

2 ⎞⎛ 2⎞ ⎛ ⎜ x + ⎟⎜ x − ⎟ 5 ⎠⎝ 5⎠ ⎝

2. Multiply and simplify where possible: 2 a) x −

2 5

2 b) x −

4 25

4 5

2 c) x −

4 ⎞⎛ 4⎞ ⎛ y − y + ⎜ ⎟⎜ ⎟ 5 ⎠⎝ 5⎠ ⎝

3. Multiply and simplify where possible: 2 a) y −

16 25

2 b) y −

4 5

2 d) 2 y −

c) 2y

4. Multiply and simplify where possible: 2 a) x −

2 3

b) 2x

2 c) x −

4 9

2 b) y −

8 7

2 c) y −

4 7

2 a) z −

4 49

2 b) z −

4 7

2 c) z −

2 7

7. Multiply and simplify where possible:

4 3

4 ⎞⎛ 4⎞ ⎛ ⎜ y − ⎟⎜ y + ⎟ 7 ⎠⎝ 7⎠ ⎝

2 d) y −

6. Multiply and simplify where possible:

8 5

2 ⎞⎛ 2⎞ ⎛ ⎜ x + ⎟⎜ x − ⎟ 3 ⎠⎝ 3⎠ ⎝

2 d) x −

5. Multiply and simplify where possible: a) 2y

d) 2x

16 49

2 ⎞⎛ 2⎞ ⎛ z z + − ⎜ ⎟⎜ ⎟ 7 ⎠⎝ 7⎠ ⎝ d) 2z

1 ⎞⎛ 1⎞ ⎛ ⎜ w + ⎟⎜ w − ⎟ 5 ⎠⎝ 5⎠ ⎝

A33

Competency Exam Review: Question #32 Multiply a binomial with a binomial using 2 variables ( x − 2 y)(3x + 5 y) 1. Multiply and simplify where possible: a) 3x + 11xy – 10y b) 4x + 3y 2 2 c) 3x – xy – 10y d) 3x2 – 10y2 (2 x − 3 y )(3x + 5 y) 2. Multiply and simplify where possible: 2 2 a) 6x + xy – 15y b) 3x + 2y c) 6x + xy – 15y d) 6x2 – 15y2 (5 x − z )(2 x − 7 z ) 3. Multiply and simplify where possible: a) 10x – 37xz + 7z b) 10x2 + 7z2 c) 7x – 8y d) 10x2 – 37xz + 7z2 (5 x + 2 z )( x − 3z ) 4. Multiply and simplify where possible: 2 2 2 a) 5x – 6z b) 5x – 13xz – 6z2 c) 5x – 13xz – 6z d) 6x – z (3 y − 2 z )(3 y − z ) 5. Multiply and simplify where possible: 2 2 2 2 a) 9y – 9yz + 2z b) 9y + 2z c) 6y – 3z d) 9y – 9yz + 2z (4 y + z )(2 y − 7 z ) 6. Multiply and simplify where possible: a) 6y – 6z b) 8y – 26yz – 7z 2 2 c) 8y – 7z d) 8y2 – 26yz – 7z2 7. Multiply and simplify where possible:

(3q + 5w) (2q − 3w)

8. Multiply and simplify where possible:

(t − 7 y)(5t + y)

9. Multiply and simplify where possible:

(3z − 5a)(5 z − 3a)

Challenge questions: 10. Multiply and simplify where possible:

(2 y + 3m) (5m + 4 y)

11. Multiply and simplify where possible:

(− g + 4t ) (3g − t )

12. Multiply and simplify where possible:

(−4k − j ) (−6 j − 7k )

A34

Competency Exam Review: Question #33 Addition of polynomials (5 y 2 + 2 y − 7) + (9 y − 8) 1. Simplify: a) 5y2 + 18y + 56 b) 5y2 + 11y –15

c) 5y2 – 11y + 15

d) 5y2 + 7y – 1

(2 x 2 − 5 x + 4) + (4 x 2 − 7) 2. Simplify: a) 6x2 – 5x – 3 b) 6x2 – 5x – 11 c) 6x2 – 5x + 3

d) 6x2 + 5x – 3

(2 z − 5) + (8 z 2 − z + 7) 3. Simplify: a) 8z2 – z – 12 b) 8z2 + 2z + 2

d) 8z2 + z + 2

c) 8z2 – 2z + 12

(6 x 2 − 3 x − 7) + (3 x 2 + 5) 4. Simplify: a) 9x2 – 3x – 2 b) 9x2 – 3x – 12 c) 3x2 – 3x – 2 (7 y 2 − 2 y ) + ( y 2 − 6 y + 1) 5. Simplify: a) 7y2 + 8y + 1 b) 8y2 + 8y + 1 c) 8y2 – 8y + 1 ( z 2 + 8 z − 5) + (5 z − 8) 6. Simplify: a) z2 + 13z + 13 b) z2 + 13z – 13

7. Simplify:

(2 g 2 + 5 g − 3) + (4 g − 7)

8. Simplify:

( m − 2) + (4m 2 − 5m + 6)

9. Simplify:

(7 p 2 − 8 p − 5) + ( p 2 − 8)

c) z2 + 3z – 13

d) 9x2 – 3x + 12

d) 7y2 – 8y + 1

d) z2 + 3z – 13

Challenge questions: ( −2 z 2 + 8 z − 1) + (−4 z 2 − 9 z ) 10. Simplify:

11. Simplify:

(3a 2 + 5c − 2) + (−5a 2 + 9c )

12. Simplify:

(8 x 2 + 3 z 2 − 1) + (5 z 2 + 2 x 2 − 7)

13. Simplify:

( xy 2 + 2 xy − 3) + (4 x 2 y − 8 xy )

14. Simplify:

( −4 w2 + 8wz − 5 z 2 ) + (−5 z 2 − zw − 3)

A35

Competency Exam Review: Question #34 Subtraction of polynomials (9 x 2 + 3 x + 5) − (2 x 2 − 8 x + 1) 1. Simplify: a) 7x2 – 5x + 6 b) 7x2 + 11x + 4 c) 7x2 – 5x + 4 d) 11x2 – 5x + 6 (4 y 2 − 2 y + 7) − (6 y 2 − 8 y + 5) 2. Simplify: a) -2y2 + 6y + 2 b) 10y2 – 10y + 12 c) -2y2 – 10y + 12 d) -2y2 – 6y – 12 (7 z 2 − z − 5) − (6 z 2 + 8 z − 2) 3. Simplify: a) 13z2 + 7z – 7 b) z2 – 9z – 3 c) z2 – 9z + 7 d) z2 + 7z – 7 (3 x 2 + 4 x − 5) − (7 x 2 − x + 3) 4. Simplify: a) -4x2 + 5x – 8 b) 10x2 + 3x – 2 c) -4x2 + 3x – 2 d) -4x2 – 5x – 8 (10 y 2 + 2 y − 5) − (2 y 2 + 8 y − 3) 5. Simplify: a) 12y2 – 6y – 2 b) 8y2 + 10y – 8 c) 8y2 – 6y – 8 d) 8y2 – 6y – 2 ( z 2 − 3 z + 1) − (7 z 2 − 8 z + 5) 6. Simplify: a) -6z2 – 11z + 6 b) -6z2 + 5z – 4 c) -6z2 – 11z – 4 d) -7z2 + 5z – 4

7. Simplify:

(2 g 2 + 5 g − 1) − (8 g 2 − g + 9)

8. Simplify:

(7 p 2 − 2 p + 10) − (7 p 2 + 9 p − 4)

9. Simplify:

(6 x 2 + 5 x − 4) − ( x 2 − x + 1)

Challenge questions: 10. Simplify:

( −6 z 2 − 3 z − 2) − (−5 z 2 − 8 z − 3)

11. Simplify:

( xh 2 − 3h − x + 4) − (−2h 2 x − 8h + x)

A36

Competency Exam Review: Question #35 Addition and Subtraction of polynomials ( z 2 + 3) + (4 z − 7) − (5 z 2 + z − 9) 1. Simplify: a) -4z2 + 5z + 5 b) -4z2 + 3z + 5 c) -4z2 + 5z – 13 d) -6z2 + 3z – 13 (4 x 2 − 5) − (8 x 2 + 2 x − 5) + (6 x − 1) 2. Simplify: a) -4x2 + 8x – 6 b) 12x2 + 4x – 1 c) -4x2 + 4x – 1 d) -4x2 + 8x – 1

( x − 3 y) + (4 x + 5 y − 7) − (5x − 6 − 9 y) 3. Simplify: a) 11y – 1 b) -7y – 13 c) 10x + 11y – 1 d) 10x – 7y – 13 (4 y + 3z − 1) + (4 z − 5) − (8 y + z − 3) 4. Simplify: a) -4y + 8z – 9 b) 12y + 6z – 3 c) -4y + 6z – 3 d) -4y + 8z + 9 (2 y + 9) − (5 y 2 − 6 y − 1) + ( y 2 − 4) 5. Simplify: a) -4y2 + 8y – 5 b) -4y2 + 8y + 6 c) 6y2 – 4y – 5 d) -4y2 – 4y + 4

( x − 5z) + (3z + 2) − (5x − 6 − z) 6. Simplify: a) -4x – z + 8 b) -4x – 3z – 4 c) 9x – z + 8 d) -4x – 2z – 4 7. Simplify:

(3 y + z) + (4 z − 2) − (5 y + 7 − 6 z)

8. Simplify:

( g − 7h − 2) + (h − 2) − (3g + 7 − 2h)

9. Simplify:

(9t − 8) − (5t − 6 − w) + (3w + t )

Challenge questions: (−2h − 5 j + 3) − (−3 j ) − 2h + (7h − 1 − j ) 10. Simplify:

11. Simplify:

(2am − 9d + 4) + 3d − (2ma − 5 − 6d ) + (−4)

12. Simplify:

4 p − (−5t − 5 p) + (3 p + 2 − t ) − (−2t + 3 − p)

A37

Competency Exam Review Answers: Q #1 1. C 2. A 3. C 4. B 5. A 6. C 7. 36 centimeters 8. 40 meters 9. 29 feet 10. 58 inches 11. 3 inches 12. 15.6 feet 13. 7

7 centimeters 20

Q #2 1. A 2. B 3. C 4. D 5. C 6. A 7. 15 sq. yards 8. 100 sq. meters 9. 187 sq. meters 10. 30 sq. feet 1 11. 5 sq. feet 16 12. 29.328 sq. inches 13. 81.5409 sq. inches 14. 8 1 sq. yards 4 Q #3 1. C 2. C 3. B 4. A 5. D 6. B 7. 31.5 sq. feet 8. 136.5 sq. centimeters 9. 238 sq. meters 10. 4600 sq. centimeters 11. 11.515 sq. inches 12. 5 1 sq. feet

Q #4 1. C 2. A 3. D 4. D 5. B 6. C 7. 2744 cu. meters 8. 4485 cu. centimeters 9. 336 cu. feet 10. 3456 cu. inches 11. 262.144 cu. inches 12. 619.752 cu. feet 1 cu. meters 13. 37 27 Q #5 1. A 2. B 3. C 4. D 5. A 6. C 7. 31 8. -4 9. -3 10. -25 11. -177 12. -70 13. 4 Q #6 1. D 2. A 3. D 4. A 5. C 6. B 7. 31 8. -192 9. 17 10. 1 2

11. 30 12. 92

Q #7 1. D 2. A 3. A 4. D 5. C 6. D 7. -36 8. 45 9. 9 10. 4 11. -26 12. -1350 13. -6561

Q #10 1. C 2. A 3. C 4. B 5. D 6. B 7. 4m 2 8. −2mg 2 − 6mg 9. 4abc 10. 3x 2 y − 2 xy 2 − 9 x 2 y 2 11. −11st + 6rt − rst 12. −8 x 2 yz − 2 xy 2 z

Q #8 1. B 2. A 3. D 4. B 5. A 6. B 7. -6 8. -15 9. -58 10. 25 11. -1 12. 15

13. 11 jk 4 + 5 jk 3 + 9 jk

Q #9 1. A 2. C 3. A 4. B 5. A 6. D 7. 6 8. -8 9. 16 10. -57 11. 45 12. 7

Q #11 1. B 2. A 3. C 4. A 5. B 6. A

19 2 z 40 13 8. − mz 12 7.

Q #12 1. B 2. A 3. C 4. D 5. B 6. C 7. 29.44ac 8. 2.652kr 9. 95.079mt 10. 0.8008ayz 11. −0.081df

12. 133.28h 2 13. 65.312 jk 14. 640.09m 2 15. −21.952r 3

24 3 sq. yard 13. 16

14. 117.714 sq. feet

A38

Q #13 1. B 2. A 3. D 4. D 5. C 6. C 7. 30 8. -144 9. 300 10. 585 11. 441

12. −

3 10

13. -48 Q #14 1. C 2. D 3. A 4. C 5. A 6. C

121 225 5 8. − 3 7.

9. 51 100 10. 1 50 11. 23 24 12. 5 54 13. − 11 2

Q #15 1. A 2. B 3. C 4. A 5. D 6. C 7. -1.676 8. 0.6 9. 1.89 10. -0.3844 11. -0.0207 12. 33.7 13. -0.05472

Q #16 1. B 2. C 3. A 4. B 5. A 6. D 7. x = −1

14 9 9 9. t = − 7 11 10. y = 8 13 11. x = − 9 3 12. z = − 2 5 13. w = 2 14. m = 1 7 15. g = − 3

8. m =

Q #17 1. A 2. D 3. B 4. D 5. A 6. C

7 5 7 8. p = 3 8 9. f = 5 10. z = 2 7 11. w = 12 19 12. c = 5 7. x =

Q #18 1. C 2. B 3. A 4. D 5. B 6. B

23 2 26 8. n = 17 9. p = 14 10. x = −50 2 11. d = 31 4 12. q = 23 13. y = 7 5 14. w = 12 7. y =

Q #19 1. D 2. A 3. C 4. B 5. D 6. C

7. x =

2 3

18 35 7 9. p = 40 2 10. h = 15

8. k = −

Q #20 1. D 2. C 3. B 4. B 5. B 6. D 7. y = 2

4 5 24 9. f = 7 25 10. t = − 14 11. z = −2

8. g =

Q #21 1. C 2. A 3. D 4. A 5. C 6. D 7. w = −7.925 8. x = 14.525 9. q = 5 10. q = 1.2 11. r = −3 12. m = −7.75 13. y = 17.05 14. a = 5 15. z = −50.25 Q #22 1. A 2. D 3. B 4. D 5. B 6. A 7. q = 0.252 8. h = 101.854 9. w = 5.7904

13. x = 21

11 14. z = 2 5 29 15. t = 13

A39

Q #23 1. C 2. A 3. C 4. C 5. B 6. B 7. w = 12.5 8. h = 5 9. H = 9 Q #24 1. D 2. B 3. A 4. C 5. B 6. D Q #25 1. C 2. D 3. A 4. C 5. A 6. B Q #26 1. C 2. B 3. A 4. B 5. D 6. A Q #27 1. D 2. C 3. B 4. A 5. B 6. C 7. 16 y 2 − 72 y 8. 50 g + 30 gm

9. 6 fh + 16h 2 10. −10 gt + 65 g 11. 6hv − 33h 12. −24d + 20c

Q #28 1. A 2. B 3. C 4. D 5. A 6. D 7. 8 xy + 10 y 2 + 4 yz

8. 10cdx − 6cd 2 + 16cd 9. 8 x3 + 20 x 2 y − 28 x 2 10. 6 yz − 9 xz 2 + 3 yz 2 11. 6a3 z + 30a 4 z − 42a 2 12.

6 9 2 1 xz + x − x 25 20 5

Q #29 1. C 2. D 3. A 4. C 5. B 6. A 7. 6h 2 k 5 − 15k 3 m 4 8. 15 x5 y 3 z 3 + 5 x3 y 2 z 4

9. −20 g 2 h3 − 35 g 3 h3 Q #30 1. A 2. D 3. C 4. A 5. B 6. D 7. 10 z 2 + 37 z + 7 8. 12 g 2 + 32 g − 35

7. w2 −

1 25

Q #32 1. C 2. A 3. D 4. B 5. A 6. D 7. 6q 2 + qw − 15w2

8. 5t 2 − 34ty − 7 y 2 9. 15a 2 − 34 az + 15 z 2 10. 15m 2 + 22my + 8 y 2 11. −3 g 2 + 13 gt − 4t 2 12. 6 j 2 + 31 jk + 28k 2 Q #33 1. B 2. A 3. D 4. A 5. C 6. B 7. 2 g 2 + 9 g − 10

Q #34 1. B 2. A 3. B 4. A 5. D 6. B 7. −6 g 2 + 6 g − 10 8. −11 p + 14

9. 5 x 2 + 6 x − 5 10. − z 2 + 5 z + 1 11. 3h 2 x + 5h − 2 x + 4 Q #35 1. B 2. C 3. A 4. C 5. B 6. A 7. −2 y + 11z − 9 8. −2 g − 4h − 11 9. 5t + 4w − 2 10. 3h − 3 j + 2 11. 5 12. 13 p + 6t − 1

8. 4m 2 − 4m + 4 9. 8 p 2 − 8 p − 13

9. −8h 2 + 59h + 40 10. 15 p 2 − 2 p − 1

1 2 h + 5h + 36 6 12. 3.36 g 2 + 8.6 g + 3 11.

Q #31 1. D 2. B 3. A 4. C 5. D 6. A

10. 11. 12. 13. 14.

−6 z 2 − z − 1 −2a 2 + 14c − 2 10 x 2 + 8 z 2 − 8 4 x 2 y + xy 2 − 6 xy − 3 −4w2 + 7wz −10 z 2 − 3

8 2 1 x + x 25 5 14. 0.805hm − 2.45m 13.

A40

Competency Exam Practice #1: 1. What is the perimeter of a rectangle that has a length of 9 cm and a width of 7 cm? a) 32 sq. cm b) 32 cm c) 63 cm d) 63 sq. cm 2. What is the area of a square that has a side length of 6 centimeters? a) 24 cm b) 24 sq. cm c) 36 sq. cm d) 36 cm 3. What is the area of a triangle that has a base of 8 inches and a height of 10 inches? a) 40 inches b) 80 inches c) 40 sq. inches d) 80 sq. inches 4. What is the volume of a cube that measures 5 meters on each side? a) 125 meters b) 15 meters c) 125 cu. meters d) 125 sq. meters 5. Use order of operations to simplify: a) 3 b) 1723 c) 43 d) 1

(10 − 4 ⋅ 2)3 − 5

6. Use order of operations to simplify: a) 6 b) -18 c) -2 d) -26

−3 ⋅ 5 − ( −4) 2 + 5

7. Use order of operations to simplify: a) 2 b) -13 c) -5 d) -18

−4 − [5 − 2(8 − 10)]

8. Simplify: −7 − (−10) a) -3 b) 3 c) -17

d) 17

−8 + −9 + 2 9. Simplify: a) -1 b) 3 c) 15 d) 1

10.

11.

7 x 2 y − 2 xy − x 2 y − 9 xy Simplify: a) 6 x 2 y + 11xy b) −5x 4 y 2 c) 6 x 4 y 2 − 11x 2 y 2 Simplify: a) −

1 z 10

d) 6 x 2 y − 11xy

3 1 − z+ z 5 2

2 z 3

c) −

3 z 10

1 2 z 10

A41

12. Simplify: a) 1.83yz

(1.6 y)(0.23z ) b) 0.368yz

d) 1.83 + yz

c) 3.68yz

13.

Evaluate the following expression for x = -3 and y = -4: a) 7 b) -7 c) 25 d) 2

14.

Evaluate the following expression for x = 3/4 and y = 1/4: a) 2 b) 5/4 c) 7/8 d) 11/4

15.

Evaluate the following expression for x = 0.2 and y = 3.4: a) 223.2 b) 1.512 c) 0.56 d) 2.304

16.

Solve for x: −4 − x = 20 a) x = 24 b) x = -16 c) x = 16

17. Solve for x: a) x = 1/2

−3x + 7 = x − 5 b) x = -1/2 c) x = -3

a) y = 20/9 20. Solve for z: a) z = -22/35

a) x = 5.72

A42

x( y 2 − 4)

d) x = 3

3 5 +y= 4 3 b) y = -2 c) y = 11/12

d) x = 14/5

d) y = 29/12

6 4 z= 5 7

b) z = 62/35

c) z = 24/35

d) z = 10/21

21. Solve for z: 5.6 = 0.02 z + 7.38 a) z = 0.2596 b) z = 649 c) z = 0.0356

22. Solve for x:

2x2 − y

d) x = -24

18. Solve for x: 2(8 x − 1) = 6(5 − x) a) x = 14/11 b) x = 16/11 c) x = 16/5 19. Solve for y:

x2 − y 2

d) z = -89

x = 5.8 0.08 b) x = 5.88

c) x = 72.5

d) x = 0.464

23. The formula for the perimeter of a rectangle is: Solve for ‘W’ when P = 20 and L = 8. a) W = 8 b) W = 2 c) W = 18 d) W = 4

P = 2L + 2W

24. Best Buy is selling a television for $1250.00. Sales tax in Orange County is 6%. Using ‘P’ as the amount I will have to pay for the television (including sales tax), write an algebraic equation that describes this transaction. a) P = (0.06)(1250) b) P = 1250 ÷ 0.06 c) P = 1250 + (0.06)(1250) d) P = 1250(0.94) 25. Jeremy put $825 into his savings account, which pays 4% per year simple interest and left it there for 2 years. Using ‘A’ as the total amount that will be in the bank at the end of the 2 years, write an algebraic equation that describes this transaction. a) A = 825 + 825(0.04)(2) b) A = 825(0.04)(2) c) A = 825 – 825(0.04)(2) d) A = 825 + (0.04)(2) 26. Keisha is investing her money in an IRA. Initially she will be putting in $775. Using ‘C’ as the additional amount invested each month, translate this problem into an algebraic expression that will show how much Keisha invested for the entire year. a) 775 + C b) 775 − 12C c) 775C d) 775 + 12C 27. Multiply and simplify where possible: a) 20x2 – 2 b) 20x – 8 c) 12x

4 x(5 x − 2) d) 20x2 – 8x

5x(3 y + 4 z − 11) 28. Multiply and simplify where possible: a) 15y + 20z –55x b) -4xyz c) 8xy + 9xz – 6x d) 15xy + 20xz – 55x

xy (6 x − 3 y z ) 29. Multiply and simplify where possible: 3 4 3 4 b) 7 x y − 2 xy z a) 6 x y − 3 xy z 2 3 d) 3 x 3 y 4 z c) 6 x y − 3 xy z 2

30. Multiply and simplify where possible: (4 x − 3)(6 x − 7) a) 10x – 10 b) 10x2 – 46x – 10 c) 24x2 + 21 d) 24x2 – 46x + 21

A43

3 ⎞⎛ 3⎞ ⎛ ⎜ z + ⎟⎜ z − ⎟ 4 ⎠⎝ 4⎠ ⎝ 9 2 d) z − 16

31. Multiply and simplify where possible: 2 a) z −

3 4

b) 2z

2 c) z −

2 3

32. Multiply and simplify where possible: (5 x − z )(2 x − 7 z ) a) 10x – 37xz + 7z b) 10x2 + 7z2 c) 7x – 8y d) 10x2 – 37xz + 7z2 (6 x 2 − 3 x − 7) + (3 x 2 + 5) 33. Simplify: a) 9x2 – 3x – 2 b) 9x2 – 3x – 12 c) 3x2 – 3x – 2

d) 9x2 – 3x + 12

( z 2 − 3 z + 1) − (7 z 2 − 8 z + 5) 34. Simplify: a) -6z2 – 11z + 6 b) -6z2 + 5z – 4 c) -6z2 – 11z – 4 d) -7z2 + 5z – 4 ( z 2 + 3) + (4 z − 7) − (5 z 2 + z − 9) 35. Simplify: a) -4z2 + 5z + 5 b) -4z2 + 3z + 5 c) -4z2 + 5z – 13 d) -6z2 + 3z – 13

A44

Competency Exam Practice #2: 1. What is the perimeter of a triangle that has one side with a length of 6 cm, a second side of 9 cm, and a third side of 15 cm? a) 30 sq. cm b) 60 cm c) 30 cm d) 60 sq. cm 2. What is the area of a rectangle that has a length of 6 feet and a width of 4 feet? a) 24 sq. feet b) 20 sq. feet c) 20 feet 24 feet 3. What is the area of a triangle that has a base of 8 centimeters and a height of 7 centimeters? a) 56 sq. cm b) 28 cm c) 28 sq. cm d) 56 cm 4. What is the volume of a rectangular box that has a length of 9 feet, a width of 10 feet, and a height of 7 feet? a) 630 feet b) 630 cu. feet c) 630 sq. feet d) 26 feet 5. Use order of operations to simplify: a) 49 b) 1

14 2

d) 2

6. Use order of operations to simplify: a) 4

14 9

28 81

⎛ 12 − 4 + 6 ⎞ ⎜ ⎟ ⎝ 9 ÷ 3⋅3 ⎠

196 81

7. Use order of operations to simplify: a) -28 b) 4 c) 28 d) -8 8. Simplify: − 3 −10 + 12 a) -1 b) 5 c) -5

(16 − 8 ÷ 4) 2 4

[8 − 2(5 − 8)] − 10

d) 19

10 − −3 + 6 + 1 9. Simplify: a) 2 b) 0 c) 8 d) 14

10.

Simplify:

−5 x 2 + 3 x 3 + 7 x 2 − x 3

A45

b) −2 x − 2 x 2 1 − xy − xy Simplify: 3 4

a) 4 x 11.

a) − 12.

13.

11 2 2 x y 12

b) −

c) 2 x + 2 x

11 xy 12

Simplify: (5.3 y )(9.2 z ) a) 14.5yz b) 1.45yz

c) −

3 xy 7

c) 48.76 yz

d) 4 x

11 xy 12

d) 487.6yz

Evaluate the following expression for x = -4 and y = -2: a) 24

b) 12

c) -12

d) -24

14.

Evaluate the following expression for x = 2/3 and y = 1/2: a) 7/36 b) 4/3 c) 3/5 d) 1/9

15.

Evaluate the following expression for x = 0.8 and y = 1.6: a) 0.704 b) 0.96 c) 9.92 d) 7.04

16.

Solve for y: 8 − y = 12 a) y = 4 b) y = 20 c) y = -4

17. Solve for y: −6 + 5 y = 2 y + 9 a) y = 1 b) y = 5 c) y = 3/7 18. Solve for x: a) x = 19/2 19. Solve for x: a) x = 8/15 20. Solve for z: a) z = -11/15

( x − y )( x + y )

(0.4)( y 2 − x)

d) y = -20

d) y = -11

4(5 x − 1) = 3(6 x + 5) b) x = 11/2

c) x = 1/2

4 2 = 3 5 b) x = 3/10 c) x = -14/15

d) x = 11/38

x−

d) x = 26/15

3 3 z= 4 5

b) z = 29/15

c) z = 4/5

d) z = 9/20

21. Solve for x: 0.3x − x = 14.07 a) x = -20.1 b) x = 45.9 c) x = -9.849 A46

3x 2 y

d) x = -46.9

22. Solve for x: a) x = 2.484

x = 2.07 1.2 b) x = 1.725

c) x = 0.87

d) x = 3.27

23. The formula for the area of a triangle is: Solve for ‘b’ when A = 17 and h = 8. a) b = 26 b) b = 2.375 c) b = 4.25

bh 2

d) b = 68

24. The Rug King is selling silk rugs for $2350. Sales tax in Seminole County is 7%. Using ‘P’ as the amount you will have to pay for the rug (including sales tax), write an algebraic equation that describes this transaction. a) P = 2350 ÷ 0.07 b) P = (0.07)(2350) c) P = 2350(0.93) d) P = 2350 + (0.07)(2350) 25. Juan took Brooke out for dinner at the Outback. The bill was $40.00. Juan left a 15% tip. Using ‘T’ as the total of the bill and the tip, write an algebraic equation that describes this transaction. a) T = 40(0.15) b) T = 40 ÷ 0.15 c) T = 40 + 40(0.15) d) T = 40 – 40(0.15) 26. Alfred decided to rent an apartment with two other friends, Alfred agreed to pay the security deposit of $125 in addition to his share of the first month’s rent. All three of them agreed to contribute equally toward the monthly rent. Using ‘R’ as the total rent due each month, translate this problem into an algebraic expression that will show how much Alfred will pay for the first month. R R + 125 + 125 c) 3 R + 125 a) d) R + 125 b) 3 3 27. Multiply and simplify where possible: a) 45xy b) 14xy c) 25x + 20xy

5 x(5 + 4 y ) d) 10x + 9xy

4 x ( y 2 − 8 x + 3) 28. Multiply and simplify where possible: a) 4xy2 – 32x2 + 12x b) 5xy2 – 4x2 + 7x c) 4xy – 20x d) 4xy2 – 32x + 12

A47

xy 29. Multiply and simplify where possible: b) 9 xy 2 z 3 + 2 x 2 y 3 a) 10 xy 2 z 3 + 3 x 2 y 3 c) 11x 2 y 3 z 3 d) 9 xy 2 z 3 + 2 xy 2

(9 z 3 + 2 xy )

30. Multiply and simplify where possible: (5 z + 7)(7 z − 1) a) 12z2 + 44z + 4 b) 35z2 – 7 c) 35z2 + 44z – 7 d) 12z2 + 18z + 6

31. Multiply and simplify where possible: 2 a) x −

2 5

2 b) x −

4 25

2 c) x −

4 5

2 ⎞⎛ 2⎞ ⎛ ⎜ x + ⎟⎜ x − ⎟ 5 ⎠⎝ 5⎠ ⎝ d) 2x

32. Multiply and simplify where possible: (5 x + 2 z )( x − 3z ) a) 5x2 – 6z2 b) 5x2 – 13xz – 6z2 c) 5x – 13xz – 6z d) 6x – z (2 z − 5) + (8 z 2 − z + 7) 33. Simplify: a) 8z2 – z – 12 b) 8z2 + 2z + 2

c) 8z2 – 2z + 12

d) 8z2 + z + 2

(7 z 2 − z − 5) − (6 z 2 + 8 z − 2) 34. Simplify: a) 13z2 + 7z – 7 b) z2 – 9z – 3 c) z2 – 9z + 7 d) z2 + 7z – 7 (4 x 2 − 5) − (8 x 2 + 2 x − 5) + (6 x − 1) 35. Simplify: a) -4x2 + 8x – 6 b) 12x2 + 4x – 1 c) -4x2 + 4x – 1 d) -4x2 + 8x – 1

A48

Competency Exam Practice Answers: Practice #1 1. B 2. C 3. C 4. C 5. A 6. D 7. B 8. D 9. A 10. D 11. A 12. B 13. B 14. C 15. B 16. D 17. D 18. B 19. C 20. D 21. D 22. D 23. B 24. C 25. A 26. D 27. D 28. D 29. A 30. D 31. D 32. D 33. A 34. B 35. B

Practice #2 1. C 2. A 3. C 4. B 5. A 6. D 7. B 8. B 9. C 10. C 11. B 12. C 13. D 14. A 15. A 16. C 17. B 18. A 19. D 20. C 21. A 22. A 23. C 24. D 25. C 26. B 27. C 28. A 29. B 30. C 31. B 32. B 33. D 34. B 35. C

A49