/Comp

West Campus State Math Competency Test Info and Practice Question 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Answers

Page Skill A3 Simplify using order of operations (No grouping/No exponents) A4 Simplify using order of operations (With grouping and exponents) A5 Absolute value with addition and subtraction A6 Simplify algebraic expression using distributive property A7 Evaluate an algebraic expression A8 Solve a linear equation A9-10 Solve a linear equation with fraction coefficient(s) A11 Solve a literal equation A12-13 Translate a word problem to an algebraic equation A14-15 Solve a word problem A16-17 Translate word problems to a proportion A18-21 Simplify exponential expression (positive integer exponents) A22-25 Simplify exponential expression (also negative integer exponents) A26 Simplify exponential expression (also zero exponents) A27 Scientific notation (Change To or Change From) A28 (Polynomial) – (Polynomial) A29 (Monomial) (Binomial) A30-31 (Binomial) (Binomial) A32 Factor a polynomial - Greatest Common Factor(s) A33 Factor a polynomial – Difference of Squares A34 Factor a polynomial – By Grouping A35 Factor a trinomial – Identify a factor A36 Simplify a rational expression – Reduce by factoring A37 Solve a quadratic equation by factoring (a = 1) A38 Solve a quadratic equation by factoring (a ≠ 1) A39 Simplify square root of a monomial A40 Simplify square roots in a polynomial using distributive property A41 Solve a linear inequality A42 Identify intercepts of a linear equation (ax + by = c) A43-47 Match linear equation to its graph (ax + by = c) or (y = mx + b) A48-49 Answers to all the practice problems above.

Practice #1 Practice #2 Answers

A50-53 Sample test with 1 question from each of the 30 topics above.

A54-57 Sample test with 1 question from each of the 30 topics above.

A58 Answers to Practice Test #1 and Practice Test #2.

Test taking tips: Before beginning the test, write down any information that you feel might cause you to make an error on the test. (Data Dump) Then during the test 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 scratch paper.

State Math Competency Test Information: To pass this course, you MUST pass the State Test AND your class.

Questions: Time limit: Calculator: Formulas:

30 multiple-choice 90 minutes May NOT be used Will NOT be provided

Test will be taken during the last two (2) weeks of the term. • If you fail the exam on your first try, you may be given a second opportunity if you are passing the class with C average or better. • Failure to pass the State Comp. Test will result in earning a maximum grade of a D for the class, and you will be required to retake the class.

The following practice problems are the type of questions you will see on the state test.

Question #1 Order of Operations (no grouping or exponents) 1. Simplify: a. 55

2. Simplify: a. 19

a. 8

a. −80

c. −4

d. 12

d. −18

−2 + 3 − 5 (−2) − 8 ⋅ 4

b. −21

c. 21

d. −43

7. Simplify:

−8 − 6 ( 3) ÷ ( −2 ) − ( −4 )( −3)( −1) − 1

a. 30

b. 12

c. −61

d. 6

−12 − 8 + 7 ( −2 )( 4 ) + 10 b. −11

a. 88

c. 114

b. 66

a. 571

a. 2

a. −8

d. −66

c. 9

d. 10

2 ( 6 − 4 + 23 )

2

c. 128

(12 ÷ 6 ÷ 2 )

b. −5

d. 200 4

− 32

c. 10

d. −2

(8 − 5 + 3 )( 2 ) 2

b. 72

7. Simplify:

d. 19

6 − ( 32 − 23 ) − 4

b. 72

6. Simplify:

a. 560

c. 16

b. 1

5. Simplify:

d. 53

2

4. Simplify: a. 32

c. 41

b. 31

3. Simplify:

3

4 (9 − 3 ⋅ 2) − 5

2. Simplify:

a. 54

8. Simplify: a. 46

d. −14

5 + 6 (8 ÷ 4 )

d. 5

6 − 4⋅ 2 − 7⋅3+ 5

b. −28

6. Simplify: a. 0

c. 16

c. −2

1. Simplify:

8 ÷ 4⋅2 + 2⋅6 ÷3

b. 5

5. Simplify:

c. −1

b. 1

d. 29

2−7 −3+ 5+ 4− 2

b. −3

4. Simplify:

c. 27

a. −12

d. 68

8 + 3⋅ 2 + 5

b. 77

3. Simplify: a. −19

c. 100

12 ÷ 6 ÷ ( −2 )( −1) − 8 + ( −6 ) − ( −1)

Question #2 Order of Operations (with grouping and/or exponents)

4 ⋅ 2 + 3⋅5

b. 23

10. Simplify:

c. 96

3

d. 288

( 8 + 3 ⋅ 2 ) 2 + 3 ( 24 )

b. 1120

c. 76

d. 92

9. Simplify:

( −4) ÷ 2 ( −1) − ( −3) + ( −5)

a. 6

b. 10

c. 0

d. −6

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A1

8. Simplify: a. 529

( −1) ⎡⎣( −4 ) 2 − 5 ( −3) ⎤⎦

b. −529

c. 49

2

d. −49

9. Simplify:

−2 + 3 ⎡⎣( −12 ) ÷ ( −6 )( −2 ) ⎤⎦ a. −194

b. −38

10. Simplify: a. −57

b. −71

Question #3 Absolute Value 1. Simplify: a. 0

a. −8

a. −2

a. −6

a. 95

d. −16

d. 12

d. 18

2 − 7 − 1 − −3 + 5 c. 2

d. 8

− −3 + 7 − ( −2 ) c. −12

d. 12

2 + 3 −7 − 4 ( 3 )

b. 165

a. −5

a. −10

c. 59

d. 17

c. 10

d. 16

−4 32 − 5 + −4 + 7

b. −1

c. 19

d. −13

4 ÷ 2 ( −1) ( − −5 )

9. Simplify:

a. −1

c. 0

b. 6

6. Simplify:

d. −7

6−3 − 3− 6

b. 4

b. −16

b. −7

10. Simplify:

c. 40

b. −6

5. Simplify:

5

3 −8 + 5 + 1

b. 10

4. Simplify:

c. −121

c. −8

3. Simplify: a. 6

3

−5 + 9 − 4

b. 10

2. Simplify:

d. −64

−5 − 4 + ( −2 ) 2

a. 28

8. Simplify:

3

c. −36

2 + ( −5 )( 2 ) 3 − 4 −2

7. Simplify:

c. −3

d. 7

− ( −3)( 4 ) ÷ ( −2 )( 6 )

b. −36

c. 1

d. 0

Question #4 Simplify algebraic expression using distributive property 1. Simplify: a. 19 −3x + 18

b. 3x + 6

2. Simplify:

3. Simplify:

c. 13x − 4

c. 23x − 3

c. 10

d.

d. 9 x + 1

2 + 3x ( 2 x + 7 ) − 2 x 2

a. −2 x 2 + 27 x + 2 b. 4 x 2 + 9 c. 4 x 2 + 21x + 2 d. 4 x 4 + 21x 2 + 2 © Valencia Community College – All Rights Reserved

d.

( 3x − 4 ) 5 − 3 ( 2 x − 7 )

a. 9 x 2 + 1 b. 10 x − 22 5. Simplify:

d.

2 ⎡⎣3 ( 4 x − 5 ) + 2 ⎤⎦ − x

b. 23x − 26

4. Simplify:

c. 3x + 16

2 ( 5 x − 7 ) + 4 ( 2 x + 1) b. 18 x − 10

a. 18 x − 6 18 x 2 − 10

a. −2 22 x − 18

3 ( 2 x + 5) − 3x + 1

A2

2. Evaluate the given expression when x

6. Simplify:

6 − x ( 4 x − 3) − 3 ( 2 x + 5 ) + x

= -3 and y = -5:

a. −4 x 2 − 2 x − 9 c. −4 x 2 − 5 x + 8

a. 165

b. −4 x 2 − 11 d. −9 x 2 + 8

2 x + 3 y ( 2 x + 3 y ) − xy b. 2 x + 3 y + 5 xy d. 9 y 2 + 5 xy + 2 x

b. −211

a. −66

c. 211

d. 219

5. Evaluate the given expression when x a. −759

−2 ⎡⎣( 3 x − y ) 5 − ( −2 x + 3 y ) ⎤⎦

(x

b. 351

2

− y 3 )( x 3 − y ) y

c. −351

d. 759

c. −34 x + 16 y 6. Evaluate the given expression when x = -1, y = -2, and z = -3:

d. −34 x 2 + 16 y 2 10. Simplify:

−3 x 2 ( −2 x 2 y + 5 xy − 7 xy 2 + x − y ) a. 6 x y − 15 x y + 21x y − 3 x + 3 x y 2

d. −24

x ( −3 x 2 + 2 y 2 ) − y

= -2 and y = 3:

b. −4 x + 7 y

c. 144

2

4. Evaluate the given expression when x = -5 and y = -4:

9. Simplify:

a. −10 x + 4 y

b. −576

a. 576

a. −6 x 4 + 10 x 2 b. −5 x 2 + 8 x − 5 c. −6 x 4 + 24 x 3 − 14 x 2 d. 4x11

c. 2 x 2 + 9 y 2 − xy

d. 135

( −3x + xy − y )

= -2 and y = 6:

3x 2 ( −2 x 2 + 8 x − 5 ) + x 2

a. 9 y 2 + 5 x 2 y 2 + 2 x

c. 195

3. Evaluate the given expression when x

7. Simplify:

8. Simplify:

b. −165

xy − 4 x 2 y

3

2

2

2

2

b. 6 x 4 y − 15 x 3 y + 21x 3 y 2 − 3 x 3 + 3 x 2 y c. −5 x 4 y + 2 x 3 y − 10 x 3 y 2 − 2 x3 − 4 x 2 y d. 6 x 4 y − 15 x 2 y + 21x 2 y 2 − 3 x 2 + 3 x 2 y

xy − 2 xz − yz

a. 14

b. −10

c. 2

d. −2

7. Evaluate the given expression when x = 3, y = -4, and z = -3:

z ( 2 x 2 − yz )

2

a. −2700 b. 324

c. −108

d. 0

Question #5 Evaluate an expression

8. Evaluate the given expression when x = -5, y = -1, and z = 2:

1. Evaluate the given expression when x

a. −32

= 3 and y = -4: a. −42

b. −293

2x − 3y c. −14

( x − y) − ( x − z) + ( y + z) 2

2

b. 66

2

c. 8

d. −31

d. 54

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2

A3

9. Evaluate the given expression when x = -3, y = 3, and z = -3:

xy 2 2 ( x y − 6z ) z b. −189

a. 297

c. −54

12 a. x = 23 x=0

d. 189

10. Evaluate the given expression when x = -1, y = 4, and z = -3:

( z − 2x )

2 2

a. −11

− x yz 3

b. 13

c. 37

d. −35

Question #6 Solve a linear equation using integers 1. Solve: a. x = 12 x=9 2. Solve: a. x = 5 x =1 3. Solve:

3x − 5 = 2 ( x + 7 ) 9 b. x = 5

12 a. x = − 19 x=−

d.

3 b. x = 2

7 c. x = 10

4 c. x = 11

12 b. x = 11

12 c. x = 17

1 b. x = − 7

c. x = 0

17 a. x = 8 7 x= 5

−6 − ( 8 x − 3) = −4 ( x − 4 ) − 5 x + 1 14 b. x = − 17

c. x = 6

10. Solve:

( 6 x + 5) − 2 x + 3 = − ( −3x + 7 ) − 1

d.

a. x = 0 1 x= 7

b. x = −16

16 c. x = 7

d.

3 + 2 ( 2 x + 5 ) = 4 ( 3x − 1) 9 b. x = 16

7 c. x = 2

d.

9. Solve:

20 11

5. Solve:

d.

2 ( x + 1) − 3 ( 3x − 1) = 0

8. Solve:

d.

4 ( x − 4 ) = 5 ( 3x + 2 ) − 6 b. x = 0

d.

3 ( 4 x − 5 + x ) = 7 − 2 x − 10

2 a. x = 15 2 x= 11

5 a. x = 7 5 x=− 7

8 c. x = − 7

1 d. x = − 57

2 ( 5 x + 3) = 3 ( 2 x − 1) 9 c. x = − 4

3 b. x = − 7

7. Solve:

a. x = 20

3 ( 2 x − 4) = x + 3 − 5x

3 a. x = −1 b. x = 16 4 x=− 9

4. Solve:

c. x = 19

−2 ( 4 x + 1) = 5 ( −3x − 2 )

6. Solve:

d.

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A4

d.

Question #7 Solve a linear equation using fractions 1. Solve:

3 x+2=8 4

9 a. x = 8 b. x = 2 15 40 x= x= d.

2 3

2. Solve:

a. x = 3 21 c. x = − 4

3 Solve:

25 a. x = − 64

c. x = −1

2 5 − x+ =2 3 6

6. Solve:

7 a. x = − 9

c. x=

17 9

x=−

7 d. x = − 3

x=−

c.

2 2 x−2= 5 5

a. x = 3 b. x = −4 24 x= d. x = 6 25

5. Solve:

5 3 1 x+ = 8 4 8

40 9

5 b. x = − 2

9 3 1 x− = 4 2 3 c.

4 3 5 − x− =− 3 2 4

10. Solve:

1 a. x = − 3 x=−

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c.

20 d. x = − 9

22 33 a. x = 27 b. x = 8 14 21 x=− x=− d.

27 8

c.

c.

1 d. x = 3

8 a. x = − 9

9. Solve: 4. Solve:

1 15

25 b. x = − 12

3 1 − x +1 = 2 4 3

8. Solve:

1 2 x+ =4 5 3

c.

17 d. x = − 9

5 a. x = − 12

27 b. x = 4

2 70 a. x = 3 b. x = 3 50 14 x= x= d.

3 15

7 b. x = − 4

5 1 1 x− =− 2 3 2

7. Solve:

2 1 x−4= 3 2

25 b. x = 64 7 d. x = 5

11 3

3 b. x = − 16

33 d. x = − 16

A5

c.

2 a. y = 7 x + 5

3 2 1 x+ x = 5 5 5

11. Solve:

a. x =

1 x=− 3

1 5

b. x =

c. y =

2 5

c.

2x + 5 7

4. Solve for y:

2 1 x + x =1 3 2 a. x = 2

x=

7 6

d. x =

13. Solve:

5 36

c.

d. x =

b. x =

11 20

c.

7. Solve for x:

4x + 3y = 8

3 7 c. y = − 5 x + 5

3. Solve for y:

8. Solve for x:

3 b. x = 4 y + 2 3 1 d. x = − 4 y + 2

−5 y + 2 x = 7

c. x = 2 y + 5 9. Solve for x:

5 5 b. y = 3 x − 7 3 d. y = 5 x − 7

b. x = −2 y + 5

d. x = 2 y − 5

−4 x + 4 y = 10

5 2 a. x = y − 2 b. x = y + 5 5 2 d. x = y − 5 c. x = − y − 2

−2 x + 7 y = 5

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d.

2 y − x = −5

a. x = −2 y − 5

3x − 5 y = 7

3 7 a. y = 5 x − 5

4x + 3y = 8

2 7 b. a. x = 5 y + 2 5 2 5 7 x=− y+ x= y+ c.

2 7 2 2 2 2 x= y+ 5 7

55 36

3 3 8 a. y = − 4 x + 8 b. y = 3 − 4 x 4 4 8 c. y = − 3 x + 8 d. y = − 3 x + 3

2. Solve for y:

d. y = 2 x + 3

4 1 c. x = 3 y + 2

Question #8 Solve a literal equation 1. Solve for y:

b. y = 2 x − 3

3 a. x = − 4 y + 2

3 2 1 x− = 5 3 4 5 7

5x − 9 3

− 2 x − y = −3

c. y = −2 x − 3 6. Solve for x:

3 b. y = 5 x − 3

d. y =

a. y = −2 x + 3

6 7

a. x =

x=−

5. Solve for y:

−2 x + 5 7

−5 x + 3 y = − 9

c. y = 5 x − 3

5 b. x = 3

d. y =

5 a. y = − 3 x − 3

d. x = 5

12. Solve:

2 5 b. y = − 7 x − 7

A6

10. Solve for x:

−3 x − 5 y = − 6

5 a. x = − 3 y − 2 5 x=− y+2 3 3 x=− y+2 5

a. x + ( x + 2) + ( x + 4) = 264 b. x + 2 x + 3x = 264 c. x + ( x + 1) + ( x + 2) = 264

b.

3 1 c. x = 5 y + 2

d. x + 1 + 2 + 3 = 264

d.

Question #9 Translate a word problem into an algebraic equation 1. If 5 times a number is increased by 15, the result is 17 less than the square of the number. Choose the equation that could be used to find this number, x. a. 5( x + 15) = x 2 − 17 b. 5 x + 15 = x 2 − 17 c. 20 x = x 2 − 17

4. The sum of a number and 4 is 6 more than twice the number. Choose the equation that could be used to find this number, x. a. x + 4 = 2( x + 6) x + 4 = x2 + 6 c. 4 x = 2 x + 6

5. The sum of 3 consecutive odd integers is equal to 386. Choose the equation that could be used to find the first number, x. a. x + ( x + 1) + ( x + 3) = 386

2. If we double the sum of 5 and some number, x, the result will be equal to the square of the number. Choose the equation that could be used to find this number, x.

c. 2(5 + x) = 2 x

d.

x + 4 = 2x + 6

d. 5 x + 15 = 17 − x 2

a. 2 ⋅ 5 + x = x 2 2(5 + x) = x 2

b.

b.

b. x + 3x + 5 x = 386 c. x + 2 x + 4 x = 386 d. x + ( x + 2) + ( x + 4) = 386 6. The opposite of the quotient of 24 and some number, x is equal to 12 less than the number, x. Choose the equation that could be used to find this number, x.

d.

a. −(24 ÷ x ) = x − 12

5 + 2x = x 2

3. If the sum of 3 consecutive natural numbers is equal to 264. Choose the equation that could be used to find the first number, x.

b. −24 ÷ x = x − 12 c. −(24 ÷ x ) = 12 − x d. −( x ÷ 24) = x − 12 7. If two times a number is decreased by 4, the result is 7 more than the number. Choose the equation that could be used to find this number, x.

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A7

a. 2 x − 4 = x + 7 2( x − 4) = x + 7

b.

c. 2 x − 4 + 7 = x 4 − 2x = x + 7

d.

8. The square of the difference between negative 7 and some number, x is equal to 5 more the number, x. Choose the equation that could be used to find this number, x. a. ( x − 7)2 = 5 + x (−7 − x) 2 = x + 5

b.

c. (7 − x) 2 = x + 5 2( −7 − x ) = 5 + x

d.

a. −8 − x − 5 = − x + 9 b. (−8 − x) − 5 = −( x + 9) c. ( x − 8) − 5 = −( x + 9) d. 5 − (−8 − x) = −( x + 9) 10. Twice the sum of a number and 8 is the same as the difference of 3 and the number. Find the equation that could be used to find the number, x.

c. 2( x + 8) = 3 − x

2 a. 3 x + 9 = x

3(9 + x) = x d. 3 ⋅ 9 + x = x 2 2

b. c. 3(9 + x ) = 2 x

12. 5 less than x is equal to twice the difference of x and 12. Choose the equation that could be used to find this number, x. a. 5 − x = 12 − 2 x

b.

c. 5 − x = 2 x − 12

d.

5 − x = 2( x − 12)

9. 5 less than the difference of negative 8 and some number is equal to the opposite of the sum of the number and 9. Choose the equation that could be used to find this number, x.

a. 2 x + 8 = x − 3 2( x + 8) = x − 3

11. If we triple the sum of 9 and some number, x, the result will be equal to the square of the number. Choose the equation that could be used to find this number, x.

b. d.

x − 5 = 2( x − 12)

Question #10 Solve a word problem 1. The perimeter of a rectangle is 34 feet. Find the width of the rectangle if the length is 5 feet more than twice the width. a. 4 feet b. 2 feet c. 3 feet d. 5 feet 2. The perimeter of a triangle is 36 inches. The short side is 4 inches less than the medium length side.

The long side is 7 inches longer that the medium length side. Find the length of the medium length side. a. 9 inches b. 14 inches c. 11 inches d. 21 inches

2x + 8 = 3 − x © Valencia Community College – All Rights Reserved

A8

3. Two cars leave Orlando heading towards Atlanta. The first car is going at 50 mph and the second car is going 70 mph. The first car leaves at 9AM and the second car leaves at 11AM. How long will it take for the second car to pass the first car? a. 7 hours b. 6 hours c.

4 hours d. 5 hours 4. A store is having a 35% off sale on musical instruments. A customer was able to purchase a flute for $312.

What was the original price of the flute? a. $480 b. $202.80 c. $421.20 d. $347 5. Find the amount of money now necessary to be invested at 11% simple interest to yield $570.90 interest in 6 years? a. $3767.94 b. $579.55 c. $865.00 d. $376.79 6. Two cars leave the same point at the same time traveling in opposite directions. One car travels west at 70 miles per hour and the other travels east at 20 miles per hour. In how many hours will they be 250 miles apart? a. 50/9 hours b. 225 hours c. 25/9 hours

d. 5 hours

a. $5500 b. $2200 $2800 d. $300

c.

8. If a pair of shoes originally marked $90 is discounted 40%, what is the cost of the shoes after the discount? a. $30 b. $36 c. $50 d. $54 9. The area of a triangle is 25 square inches. If the height is half the length of the base, what is the measurement of the base of the triangle? a. 10 inches b. 5 inches c. 12.5 inches d. 25 inches 10. The total price of a new television, including a 15% delivery charge, is $1725. What is the price of the television excluding the delivery charge? a. $2029.41 b. $1275 c. $1500 d. $ 225 11. Two cars leave the same point going in the same direction at the same time. The first car leaves and traveling at 40 mph while the second car goes at 70 mph. How long before the 2 cars are 90 miles apart? a. 1 hour b. 2 hours c. 3 hours d. 4 hours

12. A $20,000 car has a 20% discount 7. You are planning on putting $2500 sticker on it. How much will you into your saving account at the bank. have to pay for the car after the The bank is giving you an interest discount? rate of 3%. What would the total a. $24,000 b. $16,000 c. amount be in your account after 4 $19,600 d. $16,666.67 years? Š Valencia Community College – All Rights Reserved A9

13. Your bill for dinner is $35.40. If you are going to leave an 18% tip, how much should you add (rounded to the nearest penny) to the price of dinner? a. $6.37 b. $6.40 c. $41.77 d. $29.03

Question #11 Translate a word problem into an algebraic expression 1. Identify the proportion listed below that solves this problem.

A car can travel 145 miles on 16 gallons of gasoline. How far can the car travel on 36 gallons?

14. The width of a rectangle is 7 inches less than the length. If the perimeter of the rectangle is 86 inches, what is the width? a. 18 square inches b. 25 inches c. 11 inches d. 18 inches 15. Your bank is giving you 4.5% interest on your savings account. If you leave your money in there for 3 years, they will give you $162 in interest. How much would you have to put in the bank to get this amount of interest? a. $3600 b. $218.70 c. $1200 d. $2187 16. Two weeks ago I paid $2.80 for a gallon of gas. Today when I went to fill up my gas tank, the cost of a gallon of gas was $3.01. What was the percentage of increase in the cost of gasoline? a. 93.02% b. 7.5% c.

1.075% d. 9.3%

145 36 145 16 = = b. x x 16 36 16 x 145 x c. 145 = 36 d. 16 = 36

a.

2. Identify the proportion listed below that solves this problem.

If 7 monkeys can eat 20 bananas each day, how many monkeys will it take to eat 120 bananas each day? a.

7 20 = x 120

x 20 x 20 = b. = 120 7 7 120 7 120 d. = 20 x

c.

3. Identify the proportion listed below that solves this problem.

17. A car dealer has a sticker on a car that says the original price was $18,500 and the price today is $11,100. What was the percentage of decrease in the cost of the car? a. 40% b. 16.66% c. 60% d. 6%

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It will take 13 people to pick 112 watermelons in a day. How many people will it take to pick 200 watermelons in a day?

112 200 13 200 a. 13 = x b. 112 = x 112 x 13 200 c. 13 = 200 d. x = 112

A10

4. Identify the proportion listed below that solves this problem.

If 23 pounds of jelly beans cost 59 cents, how many pounds of jelly beans can be purchased for 187 cents?

a.

12 x c. 7 = 375

375 7 b. 12 = x 12 7 d. 375 = x

8. Identify the proportion listed below that solves this problem.

59 x 23 187 b. x = 59 a. 23 = 187 59 187 23 59 c. 23 = x d. 187 = x

A farmer produces 84 bushels of soy beans on a 5 acre farm. How many bushels could be produced on a 78 acre farm?

5. Identify the proportion listed below that solves this problem.

5 x 84 5 a. 78 = 84 b. x = 78 5 x 84 78 = = d. x 84 78 5

It takes 7 painters a week to paint 3 homes. How many homes could 10 painters paint in a week?

3 10 7 10 b. 3 = x c. a. 7 = x x 7 10 3 = = d.

3 10 7 x 6. Identify the proportion listed below that solves this problem.

375 7 = x 12

c.

9. Identify the proportion listed below that solves this problem.

It takes 34 workers to pack 230 tomato boxes in a day. How many workers will it take to pack 400 boxes in a day?

230 x 34 400 b. 230 = x a. 400 = 34 x 400 x 230 c. 34 = 230 d. 400 = 34

The scale on a road map uses 3 inches to represent 110 miles. If two cities are 11 inches apart on the map, how many miles apart are the two cities?

110 11 3 x b. 110 = 11 a. 3 = x x 11 3 x d. 11 = 110 c. 110 = 3

7. Identify the proportion listed below that solves this problem.

Your car can go 375 miles on 12 gallons of gas. How far can you go on just 7 gallons of gas?

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A11

10. Identify the proportion listed below that solves this problem.

You can write a 2000 word essay in 9 hours. At this rate how many word essay could you write in 10 hours?

10 9 2000 10 b. 9 = x a. x = 2000 x 10 2000 9 c. 9 = 2000 d. 10 = x

Question #12A Exponents: Multiplying and dividing with positive exponents 1. Simplify:

a. x18 b. x 9 3. Simplify: x 9 a. x 4

a. x12 y 6

b.

c. x 4

x3 ⋅ y 2 ⋅ x 4 ⋅ y 3 12 c. ( xy ) xy

11. Simplify: a. x12

a. x14

a. x 36

d. x 7 y 5

a. x 7 y 4

b. x6 y 3

8. Simplify: a. 864x15

c. x8 y 5

b. x 9

16. Simplify:

x7 ⋅ y 4 ⋅ y ⋅ x

x8 x2

x b. y

d. x 2

1 c. x 4

d. x 2

c. x 4

d. x10

c. x 4

1 d. x 4

c. x 4

d. x15

x5 x9

b. x 45

15. Simplify:

a. x5 y 9 7. Simplify:

b. x16

c. x 4

x4 x8

b. x 4

d. x

d. x 6

c. 12 x3 ⋅ 2 y 4

x8 x4

b. x 32

14. Simplify:

x 2 ⋅ x12 c. x10

b. 24x3 y 4

d. x 2 d. x −4

d. 400 x 4

d. 24x 2 y 4

a. x 6

x3 ⋅ x

b. x 24

6. Simplify:

c. x 45

a. 24x 4 y 4

c. 20

4 x3 ⋅ 2 y 4 ⋅ 3x

13. Simplify:

d. x 4

⋅ x5

b. x 2

5. Simplify: a. x14

c. x3

b. 20 x 2

10. Simplify:

a. x12

⋅ x3

b. x14

4. Simplify: a. x3

c. x 2

a. 20 x 4

5x2 ⋅ 4 x2

12. Simplify:

x8 ⋅ x 4

b. x 32 a. x12 2. Simplify: x 6

9. Simplify:

x12 x3

x3 ⋅ y 4 x2 ⋅ y5 c. xy

y d. x

d. ( xy )

13

2 x5 ⋅ 3x3

b. 864x8

c. 6x 2

d. 6x8

© Valencia Community College – All Rights Reserved

A12

a. x14

x8 ⋅ y 2 y6 ⋅ x2

17. Simplify:

( xy ) 8 ( yx )

10

a. x y 4

3

b. x y 10

d.

x3 d. 4

c. 4 x 7

b. 48 x12

x6 d. 3

c. 3 x3

4 a. x y 2 c. 100x10 y 9

a. x8

(x )

2. Simplify: a. x10

b. x

3. Simplify: a. 27 x 5

2

( 4x ) 4

b. 8 x8

5. Simplify:

(x

c. x 5

d. x

c. x 25

d. x 0

3

c. 9 x 6

3

12. Simplify: a. x 6

⋅ x4

a. x8

3

2

3

⋅ x4 ⋅ y ⋅ y3

(x

14. Simplify: a. x 6

⋅ y 3 ⋅ x3 ⋅ y 5 c. x12 y16

d. 16 x 6

1 a. x 9

b. x 9

)

2

d. x 2 y 4

2

d. 144 x 9

⋅ 3 y3 ⋅ 2 x2 ⋅ 2 y 4

⎛ x6 ⎞ ⎜ 4⎟ ⎝x ⎠

3

d. 3375x12 y 36

3

⎛ x3 ⎞ ⎜ 7⎟ ⎝x ⎠

2

c. x 5

⎛ x9 ⎞ ⎜ 3⎟ ⎝x ⎠

d. x 30

1 d. x 6

2

c. x12

⎛ x5 ⎞ ⎜ 10 ⎟ ⎝x ⎠

d. x8

4

c. x 20

1 d. x 20

2

© Valencia Community College – All Rights Reserved

)

b. 1728x12 y 21

c. x13

b. x 24

3

d. x9 y 7

c. 24 x16 2

)

d. x

c. x9 y 6

3

1 b. x 8

15. Simplify:

)

)

(3x ⋅ 4 x )

b. x 5

d. 27 x 6

2

c. 8 x 6

⋅ y3

d. x3

c. xy15

b. 24 x 6

5

( 3x )

b. 9 x 5

4. Simplify: a. 16 x8

(x ) 5

2

b. x11 y17

13. Simplify:

3

b. x 6

3

c. 1000x12 y 21

6

d. x 49

c. x 24

b. x18 y12

(x

)

⋅ x4

a. 3375x6 y 21

Question #12B Exponents: Powers on powers with positive exponents 1. Simplify:

(x

11. Simplify:

4 b. x y 3 d. 4x 4 y 2

4

(x

10. Simplify: a. 144 x8

4

b. x6 y 9

8. Simplify: a. x 24 y9

(x

c. x 2

b. x 0

7. Simplify:

a. x18 y 30

20 x 2 ⋅ y 3 5 x8 ⋅ y 6

2

a. x 5

9. Simplify:

12 x3 4 x9

20. Simplify:

6. Simplify:

a. x5 y 6

b. 16 x 3

19. Simplify: 3 a. x 6

8

2 x5 8x2

18. Simplify: 1 a. 4 x 3

x6 c. y 4

b. x 24

A13

⎛ x12 ⎞ ⎜ 2⎟ ⎝x ⎠

16. Simplify: a. x 60

b. x 36

x4 b. y 5

18. Simplify: a. x 40 ⋅ y 60

25 x 28 a. 9

⎛ 8 x3 ⎞ ⎜ 6 ⎟ ⎝ 10 x ⎠

x5 d. y 20

3

64 d. 125 x 9

2

10 x16 c. 9

⎛ 5x2 ⋅ y5 ⎞ ⎜ 8 6 ⎟ ⎝ 25 x ⋅ y ⎠

5 x6 d. 3

3

1 b. 125x18 y 3

1 c. x 7

1 a. x12 b. x 2 c. x 4 4. Simplify: x 5 ⋅ x −10

1 d. x 32

1 1 1 a. x 50 b. x 2 c. x15 5. Simplify: x −6 ⋅ x −6

1 d. x 5

a. x

6. Simplify:

x −3 ⋅ x 6

1 d. x12

c. x 36

x −3 ⋅ y 2 ⋅ x5 ⋅ y −4

x2 b. y 2

7. Simplify:

c. x y 2

1 d. x y 6

2

8

x −2 ⋅ y −5 ⋅ y −3 ⋅ x 7

1 x5 y15 a. x3 y 3 b. x14 c. y 8 8. Simplify: 2 x −4 ⋅ 6 x −7

x8 d. y 9

336 a. 336 x 28 b. 12 x 28 c. x11 9. Simplify: −3 x 7 ⋅ 4 x −3 x4 12 a. −12 x 4 b. 12 c. − x10

12 d. x11

d. x 4

4 x −5 ⋅ −2 y 6 ⋅ 5 x −1 ⋅ 3 y −3

3 y3 120 y 3 − − a. 10 x 6 b. x6 x5 y3 18 c. 120 y d. 120 x 6

y3 d. 15 x12

1 1 a. x 3 b. x18 c. x3 2. Simplify: x −4 ⋅ x −3

b. x 0

10. Simplify:

Question #13A Exponents: Multiplying and dividing with negative exponents 1. Simplify:

1 a. x12 b. x12 1 d. x 3. Simplify: x 8 ⋅ x −4

a. xy

64 x 27 c. 125

⎛ 15 x9 ⎞ ⎜ 5 ⎟ ⎝ 9x ⎠

1 a. 15x18 y 3 125 c. x30 y

x3 d. y 6

5

1 c. y 20

25 x8 b. 9

21. Simplify:

3

⎛ y4 ⋅ x4 ⎞ ⎜ 4 8⎟ ⎝ x ⋅y ⎠

1 b. 8 x 27

20. Simplify:

d. x12

c. x3 y 6

x5 b. y10

19. Simplify:

12 x 27 a. 15

c. x16

⎛ x5 ⋅ y 2 ⎞ ⎜ 4 4⎟ ⎝x ⋅y ⎠

17. Simplify: a. x 27 y18

6

11. Simplify: 1 a. x 9

1 b. x 3

x −3 x6 c. x3

d. x 9

1 d. x 2

© Valencia Community College – All Rights Reserved

A14

x4 x −8

12. Simplify: 1 a. x12

1 a. x 8

b. x

c. x

2

d. x

4

x −2 x −6

d. x 4

c. x8

d. x12

1 c. x10

d. x 21

x −7 x −3

14. Simplify: a. x10

20. Simplify:

12

13. Simplify:

1 b. x 4

1 a. x18

x x9

c. x 0 −5

y3 a. x 2

1 6 a. x y 4

5

x12 d. y 7

y −4 ⋅ y x −2 ⋅ x −3 5

x c. y 3

4

y d. x5

3x −4 9 x −2

x6 b. 3

b. −2

1 a. x16

a. x 33

1 a. x 40

x a. y 6 3 c. x 6

1 d. 3x 2

−8 x 4 x5

1 c. 2

2 d. − x10

(x

−4

5

⋅ x −6

1 b. x14

(x

−5

3

)

⋅ x −2

d. x10

−3

)

d. x3

−4

c. x11 6

d. x 28

⋅ y 3 ⋅ x −3 ⋅ y − 7

)

−2

x5 d. y 6

1 18 c. x y10

y8 b. x 6

(x

)

1 c. x 3

1 b. x 28

−4

( 3x

x6 c. y12 5

a. −144 x 6 c. 24 x 6

)

⋅ y −1 ⋅ y − 3 ⋅ x 6

x5 b. y

7. Simplify:

© Valencia Community College – All Rights Reserved

⋅ x9

1 d. x 20

c. x8

(x

(x

)

2

1 c. x14

b. x15

6. Simplify:

x a. y 2

(

x 2 ⋅ x −5

1 b. x 5

5. Simplify:

−5

1 a. 2 x10

1. Simplify:

4. Simplify: 5

x b. y 4

19. Simplify:

Question #13B Exponents: Powers on powers with negative exponents

3. Simplify:

xy c. x5 y 5

y7 b. x12

18. Simplify:

x8 a. 3

d. x18

x ⋅y x 7 ⋅ y −2

17. Simplify:

3x15 y 4 b.

2 3 y10 − d. 2 x15

2. Simplify:

b. x

16. Simplify:

2 y4 a. 3x 2x c. 3 y10

1 a. x 6

−9

15. Simplify:

−12 x 7 ⋅ y −3 − 8 x −8 ⋅ y −7

⋅ −4 x −8

)

3

y12 d. x30 −2

b. 144 x80 x6 d. 144

A15

( −5 x

8. Simplify:

−4

⋅ − 2 x −2

)

−3

18

x a. 1000 30 c. − x18 9. Simplify:

( −5 y

4

b. −1000 x3 30 d. − x 24

⋅ 4 x −3 ⋅ − 6 x ⋅ − 2 y − 1

240 x 2 a. y 3

b.

−

)

a. x 7 c. −240x3 y 4

9 y3 − d. x2 10. Simplify: 1 b. x 6

a. x18

11. Simplify:

1 b. x18

a. x15

12. Simplify:

13. Simplify: x6 a. y 6

32

−3

1 d. x 8

3

x9 c. y15

⎛ 4 x −5 ⎞ ⎜ 3 ⎟ ⎝ −2 x ⎠

1 d. x6 y 6

4

−2

1 d. x18

c. x 2

⎛ x −2 ⋅ y 3 ⋅ x −4 ⋅ y 5 ⎞ ⎜ ⎟ x 3 ⋅ y −2 ⎝ ⎠

y 30 b. x 27

x15 c. y 51

y13 d. x12

⎛ −5 x 2 ⎞ ⎜ −3 −3 ⎟ ⎝ −3 x ⋅ 2 x ⎠

5x7 − b.

6

3

−1

6 x4 − c.

5

6 d. 5 x 4

⎛ 3x −4 ⋅ −2 y −1 ⋅ − x 6 ⎞ 19. Simplify: ⎜⎝ 5 y −3 ⋅ 2 x −2 ⋅ −6 y −4 ⎟⎠ 100 a. 100 y16 b. x8 y12 x8 x8 − c. 4356 y16 d. 36 y12

Question #14 Exponents: Positive, negative, and zero 1. Simplify: 1 a. x 3

16 c. − x12

⎛ −12 x ⋅ y ⎞ ⎜ −4 −1 ⎟ ⎝ 4x ⋅ y ⎠ 4

15. Simplify:

d. x 6

−2

⎛ x 4 ⋅ y −7 ⎞ ⎜ −2 5 ⎟ ⎝ x ⋅y ⎠

8 b. x 8

6 a. 5 x8

d.

−2

c. x 24

x18 b. y 36

14. Simplify:

d. x 6

c. x 45

⎛ x −4 ⎞ ⎜ −8 ⎟ ⎝x ⎠

b. x 2

a. x 6

a. −8 x

⎛ x −10 ⎞ ⎜ 5 ⎟ ⎝ x ⎠

1 b. x11

18. Simplify:

1 c. x 4

c. 9 y 6

⎛ x −3 ⋅ x 7 ⎞ ⎜ 4 −9 ⎟ ⎝ x ⋅x ⎠

17. Simplify: a. x9 y18

2

1 b. − 27 x 24

16. Simplify:

−1

x2 240 y 3

⎛ x3 ⎞ ⎜ −6 ⎟ ⎝x ⎠

9 y6 a. x 24 27 x 24 y6

−1

16 d. x 32 −3

1 b. x 7

2. Simplify: 1 a. x12

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x4 ⋅ x0 x7 c. x11

d. 0

x 0 ⋅ x −3 x4

1 b. x 7

c. x

d. 0

A16

3. Simplify:

⎛ x6 ⋅ x0 ⎞ ⎜ −3 0 ⎟ ⎝ x ⋅x ⎠

1 b. x 2

a. 0

4. Simplify:

1 a. x y 2 6

5. Simplify: a. x12 y12

⎛ x −2 ⋅ y −3 ⎞ ⎜ 4 −1 ⎟ ⎝ x ⋅y ⎠

⎛ x 0 ⋅ y −3 ⎞ ⎜ −3 0 ⎟ ⎝x ⋅y ⎠

2 b. x 2

( −5x )

7. Simplify: 1 a. 100 1 − 100x 2

1 b. − 20

8. Simplify:

4. Convert to Standard form:

5.34 x 10−6 a. 534,000,000 b.

5,340,000 c. 0.000000534 d. 0.00000534

d. −2 x 2

2

⎛ ⎞ 3 0 ⎜ −4 x ⋅ 2 y ⎟ ⎜ −5 x −2 0 ⋅ y −1 ⎟ ) ⎠ ⎝(

a. −1 8 c. x 3 y

a. 650,000,000 b.

0.0000000065 c.

6,500,000,000 d. 0.000000065

x d. y

−1

x c. 4

c.

3. Convert to Standard form:

0

( −10 x ) 0

1.27 x 103

6.5 x 108

2

c. x 2

2. Convert to Standard form: a. 127,000 b. 1,270 0.000127 d. 0.00127

d. xy

x6 c. y 6

⎛ −3 x −2 ⎞ ⎜ 0 ⎟ ⎝ 6x ⎠

1 d. x18

0

c. 0

x5 b. y 5

6. Simplify:

x2 − a. 3

1 c. x 6

b. 1

a. 342,000 b. 34,200,000 c. 0.000342 d. 0.00000342

−2

5. Convert to Standard form: d.

−1

7.1 x 10−4 a. 0.00071 b. 0.000071 c. 71,000 d. 710,000 6. Convert to Standard form:

2.123 x 10−7 a. 21,230,000 b.

0.0000002123 c.

0.000000002123 d.

21,230,000,000

1 − 3 b. 8x y 5 − 3 d. 4x y

Question #15 Exponents: Multiplying and dividing with negative exponents

7. Convert to Scientific Notation: 34,500,000 a. 3.45 x 107 b. 3.45 x 105 c. 3.45 x 10−7

d. 345 x 105

1. Convert to Standard form:

3.42 x 105 © Valencia Community College – All Rights Reserved

A17

8. Convert to Scientific Notation: 27,000 a. 2.7 x 103 b. 2.7 x 104 c. 27 x 10

3

d. 2.7 x 10

d. 3.564 x 108

10. Convert to Scientific Notation: 0.000023 a. 2.3 x 105 b. 23 x 10−6 c. 2.3 x 10−4

d. 2.3 x 10−5

11. Convert to Scientific Notation: 0.00572 b. 5.72 x 103 a. 5.72 x 10−3 c. 5.72 x 10−2

d. 572 x 10−5

12. Convert to Scientific Notation: 0.0000008 a. 8 x 10−7 b. 8 x 10−6 c. 8 x 10

7

d. 8 x 10

a. −3x − 6 c. 7 x − 8

−4

9. Convert to Scientific Notation: 356,400,000 a. 3.564 x 105 b. 3.564 x 10−8 c. 3564 x 105

c. − x + 7 d. −13x − 7 4. Simplify: (2 x − 7) − (5 x − 1)

6

Question #16 Subtracting polynomials

5. Simplify:

a. 8 x 2 + 2 x + 5 c. −2 x 2 − 2 x − 5 2. Simplify:

(7 x + 3) − (4 x + 9)

a. 3x + 12 c. −3x 3. Simplify:

b. 2 x 2 + 14 x + 9 d. 2 x 2 + 2 x + 5 b. 3x − 6 d. 11x − 12

b. 5x + 3 d. 5 x + 11

6. Simplify:

( x 2 + 2 x − 1) − (5 x 2 − 3x + 4) a. −4 x 2 − x + 3 c. −6 x 2 + 5 x − 5

b. −4 x 2 + 5 x − 5 d. 4 x 2 + 6 x − 4

7. Simplify:

(3x 2 − 5 x − 6) − (7 x 2 + 2 x − 5) a. −4 x 2 − 3 x − 11 c. −4 x 2 − 7 x − 1 8. Simplify:

b. 10 x 2 − 7 x − 1 d. 4 x 2 − 3 x − 11

(5 x 2 − x + 2) − ( x 2 − 6 x − 8)

a. 4 x 2 + 7 x + 6 c. 4 x 2 − 7 x − 6

b. 6 x 2 + 5 x + 10 d. 4 x 2 + 5 x + 10

9. Simplify:

(9 x 2 − 2 x − 5) − (−2 x 2 + x − 1) a. 11x 2 − 3 x − 4 c. 11x 2 + 3 x + 4 10. Simplify:

b. 7 x 2 − x − 6 d. 7 x 2 − 3 x − 4

(−8 x 2 − 3) − (7 x 2 − 3x + 4) a. − x 2 − 6 x − 7 c. − x 2 − 3 x + 1

b. −15 x 2 + 3 x − 7 d. −15 x 2 − 6 x − 7

11. Simplify:

(8 x + 7) + (2 x 2 + 3) − (4 x 2 + 2 x + 1) a. −2 x 2 + 6 x + 9 c. 6 x 2 + 10 x + 11

b. −2 x 2 + 10 x + 11 d. −2 x 5 + 8 x 2 − 1

12. Simplify:

(−3x 2 + 2 x − 4) − (−6 x + 5) + (4 x 2 − 3)

(6 x + 5) − (7 x − 2)

a. − x + 3

(3 x − 4) − ( −2 x − 7)

a. 5 x − 11 c. x + 11

1. Simplify:

(5 x 2 + 8 x + 7) − (3x 2 + 6 x + 2)

b. 3x + 6 d. −3x − 8

b. −13x + 3

© Valencia Community College – All Rights Reserved

b. 7 x 2 − 4 x − 2 a. −7 x 2 + 8 x − 12 c. x 2 − 8 x − 2 d. x 2 + 8 x − 12

A18

13. Simplify:

a. 2x 2 + y

(3 x 2 + 2 x) + (6 x 2 − 5) − ( x 2 + 5 x + 4) a. 8 x 2 + 7 x − 1 b. 8 x 2 − 3 x − 9 d. 8 x 6 + 2 x 2 − 4 c. 10 x 2 − 3 x − 9 14. Simplify:

5. Multiply and simplify where possible:

(2 x3 + 3 y 3 ) x 2 a. 2 x5 + 3x 2 y 3

b. x 2 + 5 x

c. − x 2 + 5 x + 2 15. Simplify:

c. 2 x3 + 3x 2 y 3

d. − x 2 + 5 x

b. 5 x 2 + 4 x − 4 d. 6 x 2 − 3 x − 4

Question #17 Multiplying polynomials: Monomial x Binomial

a. 5 x + 7 xy

b. 6 x + 4 xy

c. 6 x3 + 12 xy 2

2

−2 y ( x 2 + 6 y 2 ) b. −12x 2 y 3 d. −2 x 2 y − 6 y 2

3. Multiply and simplify where possible:

(−3x3 + y ) x a. −3x3 + xy c. −3x 4 + xy

b. 3x 4 + xy d. −3x 4 y

4. Multiply and simplify where possible:

a. 3x3 y 4 z

b. 4x 2 y 3 + xyz

c. 3x3 y 4 + xyz

d. 3x 2 y 3 + xyz

8. Multiply and simplify where possible:

−6 x 3 (4 x 2 − 2 xy 2 ) a. −12x6 y 2

b. −2 x5 − 8 x 4 y 2

c. −24 x5 + 12 x 4 y 2

d.

−24 x 6 + 12 x3 y 2

2. Multiply and simplify where possible:

c. −2 x 2 y − 12 y 3

d. 5xy8

c. 5 xy 3 + 5 y10

d. 18x3 y 2

a. −2 x 2 y − 8 y 3

b. 5 xy 3 + 5 y 7

(3 x 2 y 3 + z ) ( xy )

3x(2 x 2 + 4 y 2 ) 2

a. 5 xy 2 + 5 y 7

7. Multiply and simplify where possible:

1. Multiply and simplify where possible: 3

d. 5x5 y 3

5 y 2 ( xy + y 5 )

2

a. 7 x 2 − 2 x − 10 c. 5 x 2 − 2 x − 10

b. 2 x 6 + 3x 2 y 3

6. Multiply and simplify where possible:

(6 x − 7) − (− x − 5) − ( x − 3 x + 2) 2

d. x 4 + x 2 y

c. 2x 2 + x 2 y

(2 x + 3) − (5 x 2 − 1) + (4 x 2 + 3 x − 2) a. 9 x 2 + 5 x + 2

b. 2 x 4 + 2 x 2 y

9. Multiply and simplify where possible:

−4 x 2 y 3 (−3xy 2 + xy ) a. 12 x 2 y 6 − 4 x 2 y 3

b. 12 x3 y 5 − 4 x3 y 4

c. −7 x3 y 5 − 3x 2 y 3

d. 8x 4 y 6

10. Multiply and simplify where possible:

(5 x 7 − 8 x3 y 5 ) (− x 4 y ) a. −5 x 28 y + 8 x12 y 5 c. 4 x3 y + 9 xy 4

b. −5 x11 y + 8 x 7 y 6 d. −5 x11 + 8 x 7 y 5

x 2 ( x 2 + y) © Valencia Community College – All Rights Reserved

A19

Question #18 Multiplying polynomials: Binomial x Binomial

7. Multiply and simplify where possible:

1. Multiply and simplify where possible:

8. Multiply and simplify where possible:

(2 x + 3) (3 x + 5)

(7 x − 1) (2 x + 3)

a. 14 x 2 − 19 x + 3 c. 14 x 2 + 19 x − 3

( x + 1) 2 b. x 2 + 1 a. x 2 + x + 2 c. x 2 + 2 d. x 2 + 2 x + 1

b. 5 x 2 + 13 x + 8 a. 6 x 2 + 19 x + 15 c. 5x + 8 d. 25 x + 15 2. Multiply and simplify where possible:

(5 x + 4) ( x + 7)

9. Multiply and simplify where possible:

( x − 4) 2

a. 6 x 2 + 39 x + 11 b. 5 x 2 + 39 x + 28 c. 44 x + 28 d. 5 x 2 + 28 3. Multiply and simplify where possible:

(3 x − 2) ( x − 4)

a. 3 x 2 + 14 x − 8 c. 3 x 2 − 14 x − 8

b. 3 x 2 − 14 x + 8 d. 3 x 2 + 8

4. Multiply and simplify where possible:

(4 x − 7) (2 x + 5)

a. 8 x 2 − 34 x + 35 c. 8 x 2 − 6 x − 35

b. 8 x 2 + 6 x + 35 d. 8 x 2 + 6 x − 35

a. x 2 − 8 x + 16 b. 2 x 2 − 8 x − 16 c. x 2 + 16 d. x 2 − 16 10. Multiply and simplify where possible:

(2 x − 3) 2 a. 4 x 2 − 12 x + 9 b. 4 x 2 + 9 c. x 2 − 9 d. 4 x 2 − 6 x + 9 11. Multiply and simplify where possible:

3 ⎞⎛ 3⎞ ⎛ ⎜ x − ⎟⎜ x + ⎟ 4 ⎠⎝ 4⎠ ⎝ 9 a. 2 x − 16

(6 x + 1) (3 x − 2)

b. 18 x 2 − 2 d. 18 x 2 − 15 x − 2

6. Multiply and simplify where possible:

( x − 2) ( x − 7)

a. x 2 − 14 x − 14 c. x 2 − 9 x + 14

b. 2 x 2 − 9 x + 14 d. x 2 + 14

9 2 b. x − 16

3 9 2 c. x − 2 x − 16

5. Multiply and simplify where possible: a. 18 x 2 − 9 x − 2 c. 9 x 2 − 9 x − 2

b. 9 x 2 + 19 x − 3 d. 14 x 2 − 3

9 2 d. x + 16

12. Multiply and simplify where possible: 5 ⎞⎛ 5⎞ ⎛ ⎜ x + ⎟⎜ x − ⎟ 6 ⎠⎝ 6⎠ ⎝ 25 5 25 2 2 b. x − 3 x − 36 a. x + 36 25 5 2 2 c. x − 36 d. x − 3

© Valencia Community College – All Rights Reserved

A20

13. Multiply and simplify where possible: 1 ⎞⎛ 1⎞ ⎛ ⎜ x − ⎟⎜ x + ⎟ 3 ⎠⎝ 3⎠ ⎝ 1 1 2 2 a. x − 9 b. x + 9 c.

2 1 2 x2 + x − x2 − d.

3 9 3 14. Multiply and simplify where possible:

( x − y) ( x + y) a. x − y 2

c. x − 2 xy − y 2

d. 2 x − 2 y

2

2

( x − y)2 c. 2 x − 2 y

b. x 2 − 2 xy + y 2 d. x 2 + y 2

21. Multiply and simplify where possible:

(6 x − 5 y ) (5 x − 6 y )

b. 8 x 2 + 15 y 2

c. 8 x 2 + 26 xy + 15 y 2

d. 8 x 2 + 14 xy + 15 y 2

17. Multiply and simplify where possible:

( x + 3 y ) (2 x + y )

a. 2 x + 7 xy + 3 y

b. 2 x + 3 y

2

2

c. 3 x + 7 xy + 4 y

1. Factor completely: a. 2 x (3 x + 4)

(2 x − y ) (5 x − 4 y )

10 x − 13xy + 4 y

2

b. 10 x 2 + 4 y 2

c.

d. 7 x 2 − 13xy − 5 y 2

19. Multiply and simplify where possible:

6x2 + 8x b. 8 x 2 (2 + x ) d. 8 x (2 x + 1)

a. xy (12 y + 16 x ) c. 4(3 x + 4 y )

12 x + 16 y b. 12( x + 4 y ) d. 4 xy (3 y + 4 x )

3. Factor completely:

12 x 2 + 18 x 3

a. 12 x 2 (1 + 6 x )

b. 6(2 x 2 + 3 x 3 )

c. x 2 (12 + 18 x )

d. 6 x 2 (2 + 3 x )

4. Factor completely:

18. Multiply and simplify where possible:

2

c. 2(3 x 2 + 4 x )

2

d. 2 x 2 + 5 xy + 3 y 2

a. 10 x 2 − 40 xy + 4 y 2

d. 30 x 2 + 30 y 2

2. Factor completely:

a. 6 x 2 + 26 xy + 8 y 2

2

b. 30 x 2 − 30 y 2

Question #19 Factoring out the GCF of a polynomial

16. Multiply and simplify where possible:

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

b. 16 x 2 + 9 y 2

d. c. 8 x + 7 xy + 6 y 16 x 2 + 24 xy + 9 y 2

c. 11x − 61xy − 11 y

2

15. Multiply and simplify where possible: a. x 2 − y 2

a. 8 x 2 + 24 xy + 6 y 2

a. 30 x 2 − 61xy + 30 y 2

b. 2 x − 2 y

2

20. Multiply and simplify where possible: (4 x + 3 y ) 2

20 x 5 − 30 x10

a. 10 x 2 (2 x 3 − 3 x 8 )

b. 10 x 5 (2 − 3 x 5 )

c. 10 x 2 (2 x 3 − 3 x 5 )

d. 5 x 5 (4 − 6 x 5 )

5. Factor completely:

24 x3 y + 36 xy 3

a. 6 xy (4 x 2 + 6 y 2 ) b. 12 x 3 y 3 (2 y + 3 x ) c.

12 xy (2 x 2 + 3 y 2 ) d. xy (12 x 2 + 36 y 2 )

(2 x − 3 y ) ( x + y )

a. 2 x 2 − 6 xy − 3 y 2 c. 3 x − xy − 2 y

b. 2 x 2 − 3 y 2 d. 2 x 2 − xy − 3 y 2

© Valencia Community College – All Rights Reserved

A21

6. Factor completely:

8x + 6x − 4x 5

3

2

a. 2 x 2 (4 x 3 + 3 x − 2) b. 8 x 2 ( x 3 + 2 x − 4) c.

x 2 (8 x 3 + 6 x − 4) d. 2 x 5 (4 + 3 x 2 − 2 x 3 )

Question #20 Factoring a polynomial – Difference of squares

7. Factor completely:

10 x 3 − 25 x 5 + 15 x 4

1. Factor completely:

a. 5 x 5 (2 x 2 − 5 + 3 x )

a. ( x − 3) ( x − 3)

b. 5 x (2 x 2 − 5 x 4 + 3 x 3 ) c. 5 x 3 (2 − 5 x 2 + 3 x ) d. 5(2 x − 5 x + 3 x ) 3

5

d. ( x − 3) ( x + 3)

2. Factor completely:

a. 12 x 3 y 4 (2 xy − 3) c. 6 x 3 y 3 (4 − 7 y )

b. ( x − 16) ( x + 1) d. ( x − 4) (9 x + 4) c. (3 x − 4) (3 x + 4)

b. 4 x 2 y 3 (6 − 8 xy ) d. 8 x 2 y 3 (3 − 4 xy )

3. Factor completely:

9. Factor completely:

30 x y − 45 x y 6

c. (4 x − 5 y ) 2 d. (8 x − 5 y ) (2 x + 5 y )

b. 90 x 6 y 7 (3 x 2 − 2 y 4 ) c. 15 xy (2 x 3 y 6 − 3 x 5 y 2 )

4. Factor completely: a. 5(2 x + 2 y ) (2 x − 2 y )

d. 5 x 4 y 3 (6 y 4 − 9 x 2 )

d. (5 x − 2 y ) (2 x + 5 y )

36 x 3 y 5 − 54 x 4 y 4 a. 3 x 2 y 4 (12 xy − 18 x 2 ) b. x y (36 y − 54 x ) c. 9 xy (4 x y − 6 x y ) 4

2

4

3

d. 18 x y (2 y − 3 x )

3

5. Factor completely:

4

11. Factor completely: a. 8 x( x + 2) c. x(8 x + 16)

a. 3x(4 x 2 + 3x) c. x (12 x + 9) 2

8 x 2 + 16 x b. 8( x 2 + 2 x)

d. 4 x(2 x + 4)

12. Factor completely:

10 x 2 − 10 y 2

b. 10( x + y ) ( x − y ) c. 10( x − y ) 2

10. Factor completely:

3

16 x 2 − 25 y 2

a. (4 x + 5 y ) (4 x − 5 y ) b. (5 x + 4 y ) (4 x − 5 y )

3

a. 15 x 4 y 3 (2 y 4 − 3 x 2 )

3

9 x 2 − 16

a. ( x − 4) 2

24 x 2 y 3 − 32 x 3 y 4

7

b. ( x 2 − 3) ( x 2 + 3)

4

8. Factor completely:

4

c. ( x − 3)2

x2 − 9

12 x 3 + 9 x 2 b. 3x 2 (4 x + 3) d. 12 x ( x − 3) 2

x2 −

4 9 2

4 ⎞⎛ 4⎞ ⎛ a. ⎜ x − ⎟ ⎜ x + ⎟ 9 ⎠⎝ 9⎠ ⎝ 2 ⎞⎛ 2⎞ ⎛ d. c. ⎜ x − ⎟ ⎜ x + ⎟ 3 ⎠⎝ 3⎠ ⎝

2⎞ ⎛ b. ⎜ x − ⎟ 3⎠ ⎝ 4⎞ ⎛ ⎜ x − ⎟ ( x + 1) 9⎠ ⎝

6. Factor completely:

9 x2 −

16 25

4 ⎞⎛ 4⎞ 4⎞ ⎛ ⎛ a. ⎜ 3 x − ⎟ ⎜ 3 x + ⎟ b. ⎜ 3 x − ⎟ 5 ⎠⎝ 5⎠ 5⎠ ⎝ ⎝ 4 ⎞⎛ 4⎞ 16 ⎞ ⎛ ⎛ c. ⎜ 9 x − ⎟ ⎜ x + ⎟ d. ⎜ x − ⎟ ( 9 x + 1) 5 ⎠⎝ 5⎠ 25 ⎠ ⎝ ⎝

© Valencia Community College – All Rights Reserved

A22

2

4. Factor completely:

4 2 k − 36 81

7. Factor completely:

⎛2 ⎞ a. ⎜ k − 6 ⎟ 2 b. ⎝9 ⎠ ⎛2 ⎞⎛ 2 ⎞ c. ⎜ k − 9 ⎟ ⎜ k + 4 ⎟ ⎝9 ⎠⎝ 9 ⎠ ⎛2 ⎞⎛ 2 ⎞ ⎜ k + 6⎟⎜ k − 6⎟ ⎝9 ⎠⎝ 9 ⎠

xy − wx − my + mw

a. ( x − m) ( w − y )

b. ( m − x) ( y − w)

⎛ 4 ⎞ ⎜ k − 6 ⎟ ( k + 6) ⎝ 81 ⎠

c. ( x − w) ( y − m)

d. ( x − m) ( y − w)

d.

5. Factor completely:

8. Factor completely:

100m 2 − 144 p 2 a. (10m + 12 p )(10m − 12 p )

6 gp + 4 gb − 21ap − 14ab a. (2 g − 7 a ) (3 p + 2b) b. (2 g + 7 a ) (3 p − 2b)

c. (2 g − 2b) (3 p + 7 a ) d. (2 g − 7 a ) (3 p − 2b) 6. Factor completely:

2 xy − 10 x + 3 y − 15

b. 2(5m − 6 p ) (5m + 6 p ) c. 4(5m + 6 p ) (5m − 6 p )

a. (2 x + 3) ( y − 5)

b. (2 x − 3) ( y + 5)

c. (3 x + 2) ( y − 5)

d. (3 x − 2) ( y + 5)

d. (10m − 12 p ) 2

7. Factor completely:

Question #21 Factoring a polynomial – By grouping 1. Factor completely:

am + 5a + 3m + 15

a. ( a + 3) ( m + 5)

b. ( am + 3) ( ma + 5)

c. ( a + 5) (m + 3)

d. ( a + 1) ( m + 15)

2. Factor completely:

2 xy − 6 x + 5 y − 15

a. (2 x − 5) ( y + 3)

b. (2 x + 5) ( y − 3)

c. (2 x − 3) ( y + 5)

d. (2 x − 5) ( y − 3)

3. Factor completely:

15 pz − 21 p − 20 z + 28

a. (3 p + 4) (5 z − 7)

b. (3 p − 7) (5 z − 4)

c. (3 p − 4) (5 z − 7)

d. (3 p − 4) (5 z + 7)

4 x − xz − 12m + 3mz

a. ( x − 4m) (3 − z )

b. (4 − z ) ( z + 3m)

c. ( x + 3m) ( z − 4) d. ( x − 3m) (4 − z ) 8. Factor completely:

am + ag − mr − gr

a. ( a + r ) ( m − g ) c. ( r − a ) ( m + g )

b. ( a − r ) ( m + g ) d. ( a + g ) ( m − r )

9. Factor completely:

10 f − 2 fx + 15 g − 3 gx a. (5 − x ) (2 f + 3 g ) b. ( x − 5) (2 f + 3 g )

c. (2 f − 3 g ) (5 + x ) d. (3 g − 2 f ) ( x − 5) 10. Factor completely:

14 − 7 z − 2 y + yz

a. (2 − y ) (7 − z )

b. ( y − 7) ( z − 2)

c. (7 + y ) (2 − z )

d. (7 − y ) (2 − z )

© Valencia Community College – All Rights Reserved

A23

11. Factor completely:

12mr + 9my − 20ry − 15 y

6. Identify a factor of this trinomial: 2

a. (3m + 5 y ) (4r − 3 y )

a. (5 x − 2)

b. (2 x + 7)

b. (3m − 5 y ) (4r + 3 y ) c. (5 y − 3m) (4r + 3 y )

c. (5 x + 2)

d. (5 x − 7)

d. (3m − 4r ) (3 y − 5 y )

7. Identify a factor of this trinomial:

Question #22 Factoring a trinomial – Identifying a factor 1. Identify a factor of this trinomial:

2 x2 + 7 x + 6 a. ( x − 2)

b. (2 x + 3)

c. (2 x + 2)

d. ( x + 3)

2. Identify a factor of this trinomial:

3 x 2 + 11x − 4 a. (3 x − 4) c. ( x − 4)

10 x 2 − 31x − 14

b. (3x − 1) d. (3 x + 4)

3. Identify a factor of this trinomial:

6 x − 19 x + 10 2

a. (2 x + 5)

b. (3 x + 2)

c. (3 x − 2)

d. (3 x − 10)

4. Identify a factor of this trinomial:

4x2 + 9x − 9 a. ( x − 3)

b. (4 x + 3)

c. (4 x − 9)

d. ( x + 3)

x 2 − 14 x + 24 a. ( x − 4)

b. ( x − 6)

c. ( x − 8)

d. ( x − 2)

8. Identify a factor of this trinomial:

36 x 2 − 5 xy − 24 y 2 a. (6 x − 3 y ) c. (4 x − 3 y )

b. (9 x − 8 y ) d. (8 x − 9 y )

9. Identify a factor of this trinomial:

10v 2 + 5vz − 30 z 2 a. (2v + 3 z ) c. (10v − 15 z )

b. (2v − 3 z ) d. (5v + 10 z )

10. Identify a factor of this trinomial:

21m 2 − 44m + 15 a. (3m − 5)

b. (7m − 15)

c. (7m + 3)

d. (m − 15)

11. Identify a factor of this trinomial:

8 p 2 − 14 p − 15 a. (2 p − 3) c. (4 p + 3)

b. (4 p − 5) d. (2 p + 5)

5. Identify a factor of this trinomial:

9 x 2 + 3 x − 20 a. (3 x + 4)

b. (3 x − 4)

c. (3 x − 5)

d. (9 x + 5)

© Valencia Community College – All Rights Reserved

A24

Question #23 Simplify a rational expression by factoring x 2 + 7 x + 12 x2 − 9

1. Simplify: x+4 a. x − 3 x+4 c. x + 3

x−4 b. x + 3 x −3 d. x + 4

2. Simplify: x+2 a. x − 2 2x + 5 c. x + 2

x+3 a. x − 2 x−2 c. 2 x

2 x 2 + 9 x + 10 x2 − 4

7. Simplify:

x2 + x − 6 2x2 − 4x

2

11x + 5 a. −5 x − 3 x+5 c. x + 3

x+5 b. x − 3 2x +1 d. x − 3

5. Simplify:

3x 2 − 4 x + 1 x2 − 2x + 1

3x − 1 a. x − 1 3x + 1 c. x + 1

6. Simplify:

3x − 4 b. x − 2 x −1 d. x + 1

8 x 2 − 14 x + 5 12 x 2 + x − 20

2x −1 b. 4 x − 5 2x +1 d. 3 x − 4

Question #24 Solving a quadratic equation by factoring (a = 1) 1. Solve:

2 x + 11x + 5 2 x2 − 5x − 3

6 x 2 − 13 x + 6 4 x 2 − 12 x + 9

2x + 3 b. 2 x − 3 3x + 2 d. 2 x + 3

8. Simplify: 2x −1 a. 3 x + 4 4x − 5 c. 3 x + 4

x+3 b. 2 x x+3 d. x + 2

4. Simplify:

x+3 b. 2 x + 3 x −3 d. 2 x + 3

3x − 2 a. x − 3 3x − 2 c. 2 x − 3

2x + 5 b. x − 2 2x − 5 d. x + 2

3. Simplify:

x+3 a. x − 3 x c. 2 x − 3

x 2 − x − 12 = 0

a. x = −3, 4

b. x = 3, − 4

c. x = −2, 6

d. x = 3, 4

2. Solve:

x 2 − 13 x + 30 = 0

a. x = 3, − 10

b. x = −3,10

c. x = −3, − 10

d. x = 3,10

3. Solve:

x 2 + 10 x − 24 = 0

a. x = −2,12 c. x = −2, − 12 4. Solve:

x2 − 9 2 x 2 − 3x − 9

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b. x = 2, − 12 d. x = 2,12

x 2 − 7 x − 60 = 0

a. x = 5,12 c. x = −5,12

b. x = −5, − 12 d. x = 5, − 12

A25

5. Solve: x − 5 x + 6 = 0 a. x = 2,3 b. x = −2, − 3 2

d. x = −1, 6

c. x = 1, − 6

x 2 + 8 x + 15 = 0

6. Solve:

a. x = −3, − 5 c. x = −3,5

b. x = 3,5 d. x = 3, − 5

7. Solve: x − 10 x + 24 = 0 a. x = 4, 6 b. x = −4, − 6 2

c. x = −4, 6 8. Solve: a. x = −4,10

d. x = −2,12

x + 6 x − 40 = 0 2

b. x = 4, − 10

c. x = −4, − 10

d. x = 4,10

x 2 − 36 = 0

c. x = 6, 6

d. x = 6, − 6

10. Solve: a. x = 7, − 8

x 2 + x − 56 = 0

c. x = 7,8

d. x = −7, − 8

b. x = −6, − 6

b. x = −7,8

c. x = −10,12

2

b. x = 10. − 12 d. x = 10,12

2 x 2 − 5 x − 12 = 0

2 c. x = − , − 4 3

1 1 b. x = , 3 2

14 x 2 + 27 x − 20 = 0

2 4 5 7 a. x = − , b. x = , − 5 7 2 4 2 7 5 4 c. x = − , − d. x = − , 5 4 2 7 4. Solve:

12 x 2 − 25 x + 12 = 0

4 3 3 4 a. x = − , b. x = − , 3 4 4 3 4 3 3 4 c. x = − , − d. x = , 3 4 4 3

10 x 2 + 9 x − 9 = 0

3 3 3 3 a. x = , − b. x = − , 5 2 5 2 5 2 5 2 c. x = , − d. x = − , 3 3 3 3

24 x 2 + 43 x + 18 = 0 2 9 a. x = , 3 8

− 2 x − 120 = 0

3 a. x = , − 4 2

3. Solve:

6. Solve:

Question #25 Solving a quadratic equation by factoring (a > 1) 1. Solve:

6x2 − 5x + 1 = 0

1 1 a. x = − , − 3 2 d. x = 2,3 c. x = −2, − 3

5. Solve:

9. Solve: a. x = 1,36

11. Solve: x a. x = −10, − 12

2. Solve:

2 b. x = , 4 3

3 d. x = − , 4 2

2 8 c. x = , 3 9 7. Solve:

2 9 b. x = − , − 3 8 3 8 d. x = − , − 2 9

20 x 2 − 9 x − 18 = 0

3 6 3 6 a. x = − , b. x = , − 4 5 4 5 4 5 3 6 d. x = − , − c. x = − , 3 6 4 5 8. Solve:

6 x 2 − 13 x − 28 = 0

3 2 4 7 a. x = , − b. x = , − 4 7 3 2 4 7 3 2 c. x = − , d. x = − , − 3 2 4 7

© Valencia Community College – All Rights Reserved

A26

9. Solve:

a. 147 x 2 y 3 2 y

56 x 2 − 95 x + 36 = 0

c. 21x 2 y 3 2 y

4 9 4 9 a. x = − , − b. x = , 7 8 7 8 8 7 8 4 c. x = , d. x = − , 9 4 9 7

a. 3y x

b. 3 xy

c. 3 xy

d. y 3 x

9. Simplify completely: a. x 6 y 5

9xy 2

c. 36 x3 2

xy 4 x10 y

b. x6 y 2 y d. x 4 y 2 xy

10. Simplify completely: 9 xy 2 400 x 4 y16

a. 3x 3 y

a. 29x 3 y 6

27x 2 y

a. 25y 2 y

d. 1800x3 y16

Question #27 Simplify a square root using distributive property

d. 3x 2 3 y

3. Simplify completely:

b. 180x3 y10

c. 209x5 y10

b. 9 x 3 y

c. 13.5x y

50 y 3 b. 25 y 2 y

c. 5 y 2 y

1. Simplify completely:

d. 5 y 10 y

a.

4. Simplify completely:

c. 4

3 32x3

b. 48 x 2 2 x a. 12 2x3 d. 7 x 2 x 12 x 2 x 5. Simplify completely:

a. 12x 2 y 3 x

75x 7 y

(

(

8

(

d. 12x 3 y 3 x

c. 6 15 + 9 2

b. 5 15 + 9 2 d. 6 15 + 27 2

4. Simplify completely:

2 5

3 y 98 x y

3+ 8

)

a. 9 33

2 x 100 x 3 y 6

5

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(

7 +3 2

)

5+ 7

3. Simplify completely:

3 3 2 5+ 6

4

3+ 5

b. 4 6 + 8 d. 2 22

a. 2 6 + 4 c. 2 6 + 8

b. 20x 2 y 3 x

7. Simplify completely:

b.

6 + 10 d. 10

2. Simplify completely:

d. 5x6 3xy

6. Simplify completely:

2

c.

b. 5x3 3xy

a. 25 x6 3xy

c. 20 x x3 y 6

72x9

a. 12x 3 b. 6 x3 2 d. 6 x 4 2 x

c. x6 y 4 y

2. Simplify completely:

c. 5 3x 7 y

d. 10 x 2 y 4 2 y

8. Simplify completely:

Question #26 Simplify square root of a monomial 1. Simplify completely:

b. 21x 2 y 2 y 5

)

A27

)

a. 2 35 + 6 10 c. 3 35 + 6 7 5. Simplify completely:

9

(

4+ 2

a. 6 + 3 2 b. 9 2 d. 2 6 c. 13 + 11

6. Simplify completely:

4 2

(

6 −2 3

)

b. 8 3 − 8 6

a. 8 2 − 8 5 c. 5 8 − 6 6

d. 16 3 − 8 6

7. Simplify completely:

(

12 2 − 3 5

)

a. 4 3 − 6 15 b. c. 2 12 + 3 60 2 6 − 3 60 d. −2 15

(

)

1. Solve: a. x < 1

)

a. 220 b. 8 8 + 36 7 c. 6 15 + 13 10 d.

8 15 + 36 10

(

2 −7 2

b. x ≤ −3 d. x ≥ 3

3. Solve:

2 x − 3 > 3x − 4

a. x > 1 c. x > −1 4. Solve:

17. Solve:

(

a. 1000

b. 30 30 + 70 70 d. c. 13 13 + 17 17 30 13 + 70 17

8. Solve:

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b. x ≥ −2 d. x ≤ −2

2 ( 3x − 1) ≤ 4 x + 6 b. x ≤ 4 d. x ≥ −4

− ( 2 x − 3) > x − 3 a. x < −2 c. x < 2

)

b. x > 1 d. x < −1

4x − 3 ≥ x − 9 a. x ≤ 2 c. x ≥ 2

10. Simplify completely:

10 10 3 3 + 7 7

2 x + 5 < 5x + 8 a. x < 1 c. x > −1

6. Solve:

d. x < 6

b. x < 1 d. x < −1

a. x ≥ 4 c. x ≤ −4 b. −28 2

c. x < 4

a. x ≤ 3 c. x ≥ −3

)

a. 2 16 − 14 16 c. −8 d. −48

b. x > 1

−3x ≥ 9

9. Simplify completely:

2 8

2x + 3 < 5

2. Solve:

5. Solve:

8. Simplify completely:

4 5 2 3 +9 2

Question #28 Solving a linear inequality

b. 2 35 + 5 10 d. 3 3 + 5 7

b. x > −2 d. x > 2

2 ( 3x − 1) < −3 ( 2 x + 1) a. x > −12 1 c. x > − 12

b. x < −12 1 d. x < − 12 A28

9. Solve:

5. Find the x-intercept for:

y = −x − 2

5 x − 6 x + 4 > 2 − 10 + x a. x > 6 1 c. x > 6

1 b. x < 6

d. x < 6

10. Solve:

4 − ( −2 x + 5) ≥ −2 ( 3x + 1) + 4 x 1 a. x ≤ − 4

c. x ≥ −4

Question #29

b. x ≤ −4 1 d. x ≥ − 4

1. Find the x-intercept for:

2x − 3y = 6 a. ( 3,0 ) c. ( −2, 0 )

b. ( 0,3) d. ( 0, −2 )

3. Find the x-intercept for:

4x = 2 y − 3

a. ( −7, 0 ) ⎛ 4 ⎞ − ,0 c. ⎜⎝ 3 ⎟⎠

⎛ 3 ⎞ − ,0 b. ⎜⎝ 4 ⎟⎠

d. ( 2,0 )

− y + x = −1 a. ( 0,1) c. (1, 0 )

c. ( 0, 2 )

b. ( 0, −6 ) d. ( 0, −3)

b. ( 0, −1) d. ( −1, 0 )

8. Find the y-intercept for:

3x + 4 y = 5

⎛ 5⎞ 0, a. ⎜⎝ 4 ⎟⎠ ⎛ 5⎞ 0, c. ⎜⎝ 3 ⎟⎠

⎛ 3⎞ 0, b. ⎜⎝ 5 ⎟⎠ 5⎞ ⎛ 0, − ⎟ ⎜ d. ⎝ 4⎠

9. Find the x-intercept for:

−2 y − x = − 7 a. ( −7, 0 ) c. ( 0, −7 )

b. ( 7,0 ) d. ( 0,7 )

10. Find the y-intercept for:

2 y = 3x + 7

⎛ 2⎞ 0, a. ⎜⎝ 3 ⎟⎠ ⎛ 2⎞ 0, c. ⎜⎝ 7 ⎟⎠

4x = 2 y − 3

a. ( 0, −2 )

d. ( 0, 2 )

7. Find the x-intercept for:

4. Find the y-intercept for: ⎛ 3⎞ 0, b. ⎜⎝ 2 ⎟⎠ 3⎞ ⎛ 0, − ⎟ d. ⎜⎝ 2⎠

c. ( 0, −2 )

2 y − 4 x = 12 a. ( 6,0 ) c. ( 0,6 )

b. ( 0, 2 ) d. ( 3,0 )

b. ( 2,0 )

6. Find the y-intercept for:

2. Find the y-intercept for:

2x − 3y = 6 a. ( 0, −2 ) c. ( 0,3)

a. ( −2, 0 )

⎛ 3⎞ 0, b. ⎜⎝ 2 ⎟⎠ ⎛ 7⎞ 0, d. ⎜⎝ 2 ⎟⎠

Question #30 Matching a linear equation with its graph

© Valencia Community College – All Rights Reserved

A29

1. Find the graph that best matches the given linear equation: y = 2x − 2

a.

2. Find the graph that best matches the given linear equation:

y = 3x − 6

b. a.

b.

c.

d.

c.

d.

© Valencia Community College – All Rights Reserved

A30

3. Find the graph that best matches the given linear equation: y = 2x +1

a.

b.

c.

d.

4. Find the graph that best matches the given linear equation:

© Valencia Community College – All Rights Reserved

y = −5 x + 6

a.

b.

c.

d.

A31

5. Find the graph that best matches the given linear equation:

a.

c.

y = x−4

6. Find the graph that best matches the given linear equation:

y = −x + 5

b. a.

b.

c.

d.

d.

© Valencia Community College – All Rights Reserved

A32

7. Find the graph that best matches the given linear equation:

8. Find the graph that best matches the given linear equation:

y = −2 x − 3

a.

y = 3x + 5

b.

a.

b.

c.

d. c.

© Valencia Community College – All Rights Reserved

d.

A33

9. Find the graph that best matches the given linear equation:

10. Find the graph that best matches the given linear equation:

y = −3 x − 1

a.

c.

y = −4 x

a.

b.

c.

d.

b.

d.

© Valencia Community College – All Rights Reserved

A34

State Comp. Test Answer Key Q1

Q2

Q3

Q4

Q5

Q6

Q7

Q8

Q9

Q10

Q11

1. b

1. d

1. a

1. c

1. a

1. c

1. a

1. d

1. b

1. a

1. d

2. a

2. b

2. b

2. b

2. c

2. b

2. b

2. a

2. b

2. c

2. c

3. c

3. b

3. c

3. b

3. c

3. c

3. c

3. c

3. c

3. d

3. a

4. a

4. d

4. b

4. d

4. d

4. d

4. d

4. d

4. d

4. a

4. c

5. d

5. a

5. a

5. c

5. d

5. a

5. c

5. a

5. d

5. c

5. b

6. b

6. c

6. c

6. a

6. b

6. c

6. b

6. a

6. a

6. c

6. c

7. b

7. c

7. d

7. c

7. c

7. c

7. c

7. c

7. a

7. c

7. d

8. d

8. d

8. d

8. d

8. a

8. a

8. a

8. c

8. b

8. d

8. b

9. c

9. a

9. a

9. c

9. a

9. a

9. a

9. a

9. b

9. a

9. c

10. a

10. c

10. b

10. b

10. b

10. b

10. b

10. b

10. c

10.c

11. a

11. b

11. c

12. d

12. d

12. b

13. d

13. a 14. d 15. c 16. b 17. a

10. a

Q12A

Q12B

Q13A

Q13B

Q14

Q15

Q16

Q17

Q18

Q19

Q20

1. a

1. b

1. c

1. a

1. a

1. a

1. d

1. c

1. a

1. a

1. d

2. b

2. c

2. c

2. b

2. b

2. b

2. b

2. c

2. b

2. c

2. c

3. b

3. d

3. c

3. d

3. d

3. a

3. c

3. c

3. b

3. d

3. a

4. c

4. a

4. d

4. d

4. b

4. d

4. a

4. d

4. d

4. b

4. b

5. a

5. a

5. d

5. b

5. c

5. a

5. b

5. a

5. a

5. c

5. c

6. d

6. c

6. b

6. c

6. d

6. b

6. b

6. b

6. c

6. a

6. a

7. c

7. b

7. c

7. d

7. a

7. a

7. c

7. c

7. c

7. c

7. d

8. d

8. b

8. d

8. a

8. b

8. b

8. d

8. c

8. d

8. d

8. a

9. a

9. c

9. a

9. b

9. d

9. a

9. b

9. a

9. a

10. a

10. a

10. b

10. a

10. d

10. b

10. b

10. a

10. d

11. c

11. b

11. a

11. c

11. a

11. a

11. b

11. a

12. c

12. a

12. b

12. d

12. a

12. d

12. c

12. b

13. a

13. b

13. b

13. b

13. b

13. a

14. d

14. c

14. b

14. d

14. c

14. a

15. b

15. d

15. a

15. b

15. b

15. b

16. b

16. a

16. b

16. d

16. c

17. c

17. d

17. c

17. b

17. a

18. d

18. c

18. d

18. a

18. c

19. a

19. d

19. d

19. b

19. d

20. b

20. b

20. b

20. d

21. b

21. a

Q21

Q22

Q23

Q24

Q25

Q26

Q27

Q28

Q29

Q30

1. a

1. b

1. a

1. a

1. d

1. a

1. a

1. a

1. a

1. a

2. b

2. b

2. b

2. d

2. b

2. a

2. c

2. b

2. a

2. b

3. c

3. c

3. b

3. b

3. d

3. c

3. c

3. b

3. b

3. c

4. d

4. d

4. b

4. c

4. d

4. c

4. a

4. c

4. b

4. c

5. a

5. b

5. a

5. a

5. a

5. b

5. a

5. b

5. a

5. a

6. a

6. c

6. b

6. a

6. b

6. b

6. b

6. b

6. c

6. b

7. d

7. d

7. c

7. a

7. a

7. c

7. a

7. c

7. d

7. c

8. b

8. b

8. a

8. b

8. c

8. d

8. d

8. d

8. a

8. c

9. a

9. b

9. d

9. b

9. c

9. d

9. d

9. b

9. b

10. d

10. a

10. a

10. b

10. b

10. d

10. d

10. d

11. b

11. c

11. c