CP Algebra II Midterm Review Packet 2016-2017

1.3 Solving Equations Solve each equation.

1. 5 8 88t 2. 27 4x 3. 8 3 5(2 1)x x

4. 3( 2) 4k k 5. 1

8 463

q q 6. 2 1

73 2

x x

7. 2 5

3 4m 8.

4

3 6

x x

1.5 Solving Inequalities

Solve each inequality. Graph the solution set.

9. 2 5 7z 10. 3 6x 11. 2 3 5 28f

12. 3 2 9y 13. 7 5 4 7a a 14. 6 14

x

15. Which of the following is a solution to the inequality 2 5 9x ?

a. 5 b. 6 c. 7 d. 8

16. Which of the following is NOT a solution to the inequality 2 12 3 5x x ?

a. 16 b. 17 c. 18 d. 19

2.1 Relations and Functions

Determine if the relation is a function. State the domain and range.

17. 18.

Function? ___________ Function? ___________

Domain: ____________ Domain: ____________

Range: _____________ Range: _____________

19. (7, 2), (4, 5), (6, 8), (9, -2), (7, 5) 20.

Function? ___________ Function? ___________

Domain: ____________ Domain: ____________

Range: _____________ Range: _____________

2.2 Linear Equations

Write each equation in Standard Form and find the x-intercept and y-intercept . Remember, Standard Form is Ax By C , where A, B, and C are whole numbers.

21. 1

3 42

y x x-intercept_______ y – intercept________

3 -4 5 6

-2 8

9 -4

0 1

1

3

-5

8

2

-3

4

5

22. 3

2 44

y x x-intercept_______ y – intercept________

23. 5 10 25y x x-intercept_______ y – intercept________

Find the x-intercept and the y-intercept of the graph of each equation. Then graph the equation.

24. 2 5 10x y 25. 3 4 12 0x y 26. 6y

2.3 Slope

Find the slope of the line that passes through each pair of points.

27. 6, 5 ,(4,1) 28. 4,1.5 ,(4,6.5)

29. 6,8 ,( 4,8) 30. 3, 10 ,( 2, 4)

Graph the line passing through the given point with the given slope.

31. 2

(2, 2),3

m 32. (3,1), 0m 33. 1

( 3,8),5

m

Graph the line that satisfies each set of conditions.

34. passes through (-2,2), parallel to a line whose slope is -1.

35. passes through (-4,1), perpendicular to a line whose slope is 3

2

36. passes through (-2,1), parallel to graph of 2 3 6x y .

37. passes through (3,3), perpendicular to 3 7x y

2.4 Writing Linear Equations

State the slope and y-intercept of the graph of each equation.

38. 3 5 20x y 39. 2 4 10x y 40. 12y 41. 1x

Write the equation in slope-intercept form for the line that satisfies each set of conditions.

42. slope is 3, passes through (0,-6). 43. slope 3

4, passes through (-5,1).

44. passes through (-2,5) and (3,1). 45. passes through (7,1) and (6,2).

46. passes through (4,6), parallel to the graph of 2

53

y x .

47. passes through (6,-5), perpendicular to the graph 1

74

y x .

3.1 Solving Systems of Equations by Graphing

Solve the system by graphing:

48. 2 0

6

x y

x y

49.

2

4

y x

x y

3.2 Solving Systems of Equations Algebraically

Solve the system of equations by substitution or elimination:

50. 3 2 8

2 12 5

x y

y x

51.

3 5 6

4 2 5

x y

x y

52. Three lift tickets and two ski rentals cost Al Gebra’s family $335. The next week they went skiing

again and brought some friends. Seven lift tickets and three ski rentals cost $690. What is the cost of

one lift ticket? One rental?

53. There are 42 more boys than girls in the sophomore class. The total number of students in the

sophomore class is 506. How many girls are in the sophomore class?

5.1 Monomials

Simplify completely. Assume that no variable equals zero. DO NOT LEAVE ANY NEGATIVE EXPONENTS IN YOUR ANSWER.

54. 25 nn 55. 4 2 3x x x

56. 34 )2( y 57. 2 5 4 3 1(4 )( 5 )d t v dt v

58. 2

8

m

m 59.

4

65

3

12

xy

yx

60.

2

32

32

ba

ab 61. 3)2(8 zu

62.

2

52

232

yx

yx 63. 6523464 )()( pnmnm

5.2 Polynomials

Simplify completely.

64. )272()33( 22 xxxx 65. )53()264( 22 yyyy

66. )43(2 4aaba 67. )432(3 3242 cddcdc

68. )4)(7( gg 69. )23)(23( yy

70. )52)(13( 22 xxx 71. 2( 1)(2 3 1)x x x

72. 22 (3 5) 3(3 5)x x x ax bx c

In the equation above, a, b and c are constants. If the equation is true for all values of x, what is the

value of b?

73. 2 22( 3 5) (4 4 10)x x x x

If the expression above is rewritten in the form 2ax bx c , where a, b, and c are constants, what is

the value of a?

5.4 Factoring Polynomials

Factor the following by using GCF.

74. 3 57 3y y 75. 3 4 2 3 29 6 15x y x p y p

Factor the following by using Grouping.

76. 2 5 5y y xy x 77. 21 7 3y x xy

Factor the following Trinomials ( 1a ).

78. 2 10 24y y 79. 2 6 16z z

Factor the following.

80. 28 10 3y y 81. 29 18 8x x

Factor the following Difference of Squares.

82. 4 25x 83. 2 2 416a b c Factor the following Sum/Difference of Cubes.

84. 38 27x 85. 6 364x y

Factor COMPLETELY.

86. 22 22 60y y 87. 33 12x x

88. 2 2 1n n 89. 3250 2x

90. 3 2 4 5 33 5x y x y x y 91. 5 44 4 8 8x x x

92. 616 121y 93. 25 30 40x x

94. 354 128x 95. 8 680 45y y

1.4 Solving Absolute Value Equations

Solve each equation.

96. 2 1 7x 97. 4 2x

98. 2 3 2 18x 99. 5 3 1 20x

2.6 Special Functions

Graph each of the following. State the domain, range and any transformations.

100. 3y x 101. 2 2 1y x

Domain: ___________________ Domain: _____________________

Range: ____________________ Range: ______________________

Transformations: ____________ Transformations: ______________

__________________________ _____________________________

7.7 Operations on Functions

Use the following functions for #102-#110 2( ) 6 ( ) 2 9 18f x x g x x x ( ) 4 2 3h x x k x x

102. f g x 103. g h x 104. ( )h k x

105. ( )g

xf

106. ( )( )f k x 107. ( )h k x

108. ( )( )f h x 109. ( )h

xf

108. ( ( ))f h x

109. 3h k 110. 2h g

7.8 Inverse Functions and Relations

For #111-117, use the following functions.

2,5 , 1, 4 , 3, 2 , 5,0

4,2 , 3,5 , 6,0 , 1,3

f

g

111. Find the inverse of f 112. Find the inverse of g For #118-#122, find the inverse of each function.

113. 3 2

( )4

xh x

114. ( ) 5h x x

115. 1

32

f x x 116. 2 5f x x

117. 1y x

7. 9 Square Root Functions:

Graph the following. Find the domain and range.

118. 2 1y x 119. ( ) 2 6f x x

Domain: ___________________ Domain: ____________________

Range: ____________________ Range: ______________________

Transformations: ____________ Transformations: ______________

__________________________ _____________________________

5.3 Dividing Polynomials:

120. Simplify: 2 3 4 636 9 45

9

x y xy x y

xy

Use synthetic division to simplify:

121. 4 3 29 80 100 10x x x x x 122. 4 36 6 32 6b b b b

5.6 Radical Expressions:

Simplify:

123. 3 20 15 45 6 80 10 500 124. ( 6 6)(5 3)( 2)

125. (3 5)( 2 8) 126. 3 824a b c

127. 26 17 92 64xy x y z