Name ____________________________

CP Algebra II Midterm Review Packet 2019-2020

Unit 1: Linear Equations and Inequalities

Solve each equation.

1. 2 3

3 5x 2. 3 4( 5) 6 22x x x 3. 8 3 5(2 1)x x

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

3 6

x x

6. V lhw for h 7. x y

bz

for x

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

8. 6, 5 ,(4,1) 9. 4,1.5 ,(4,6.5)

10. 6,8 ,( 4,8) 11. 3, 10 ,( 2, 4)

Find the slope of the line.

12. 13. 14.

Write the equation in slope-intercept form for each graph.

15. 16. 17.

Graph each line.

18. 𝑦 = −1

3𝑥 + 4 19. 𝑥 = 3 20. 2𝑦 − 4𝑥 = −4

Find the x- and y-intercepts. Write as points!

21. 2 5 10x y 22. 3 4 12 0x y

Find the slope of the line parallel to the given line.

23. a. 1

273

y x b. 6 3 18x y

Find the slope of the line perpendicular to the given line.

24. a. 2 18y x b. 4 16x y

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

25. 3 5 20x y 26. 2 4 10x y 27. 12y 28. 1x

Determine if the lines are parallel, perpendicular or neither.

29. a. b. c.

29

5

511

2

y x

y x

27

3

2 3 36

y x

x y

168

492

x

y

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

30. slope is 3, passes through (0,-6). 31. slope 3

4, passes through (-5,1).

32. passes through (-2,5) and (3,1). 33. passes through (7,1) and (6,2).

Solve each inequality. Graph the solution set.

34. 2 5 7z 35. 3 6x 36. 2 3 4 28f

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

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

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

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

Graph each inequality.

39. 1

52

y x 40. 4 5 10 5x y

Unit 2: Systems of Linear Equations and Inequalities

Graph the following systems of equations on the coordinate plane. Find the solution to the system.

41. 2 0

6

x y

x y

42.

2

4

y x

x y

solution ___________________ solution ___________________

Solve the system of equations by substitution or elimination:

43. 3 2 8

2 12 5

x y

y x

44.

3 5 6

4 2 5

x y

x y

Graph the following systems of inequalities on the coordinate plane. Shade the solution region.

45. 2 4

2

y x

y x

46.

3 2 6

4 2

x y

x y

Unit 3: Relations and Functions

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

47. 48.

Function? ___________ Function? ___________

One-to-one? __________ One-to-one? __________

Domain: ____________ Domain: ____________

Range: _____________ Range: _____________

Continuous or Discrete? _____________ Continuous or Discrete? _____________

49. (7, 2), (4, 5), (6, 8), (9, -2), (7, 5) 50.

Function? ___________ Function? ___________

One-to-one ?__________ One-to-one? __________

Domain: ____________ Domain: ____________

Range: _____________ Range: _____________

Continuous or Discrete? _____________ Continuous or Discrete? _____________

Name the quadrant in which the point is located.

51. 8, 6 52. 7, 1

3 -4

5 6

-2 8

9 -4

0 1

1

3

-5

8

2

-3

4

5

Evaluate the function.

53. ( 3) if ( ) 4 8f f x x 54. (5)g if 2( ) 2 4 1g x x x

State whether each function is a linear function. Write yes or no then explain.

55. 7

( )x

g xx

56. 12 4 8y x

Describe the end behavior for each linear function.

57. 58.

As , ( ) _________

As , ( ) ________

x f x

x f x

As , ( ) _________

As , ( ) ________

x f x

x f x

59.

As , ( ) _________

As , ( ) ________

x f x

x f x

Unit 4: Graphing Absolute Value and Quadratic Functions

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

60. ( ) 3f x x 61. ( ) 2 1f x x

Domain: ___________________ Domain: _____________________

Range: ____________________ Range: ______________________

Transformations: ____________ Transformations: ____________

__________________________ ___________________________

62. 2( 2) 1y x 63.

2( ) 4 6f x x

Domain: ___________________ Domain: ____________________

Range: ____________________ Range: ______________________

Transformations: ____________ Transformations: ____________

__________________________ ___________________________

Find the vertex, the y- intercept, the axis of symmetry and graph the quadratic equation. State whether

the function has a maximum or minimum value and find that value.

64. 23 6 1y x x 65.

2 6 3y x x

Axis of symmetry _________ Axis of symmetry _________

Vertex ____________ Vertex ____________

y- intercept _______________ y- intercept ____________

symmetric point ____________ symmetric point ___________

Minimum/maximum __________ Minimum/maximum __________

Unit 5: Radicals, Complex Numbers, and Factoring

Foil each.

66. )4)(7( gg 67. )23)(23( yy 68. 2(3 1)x

Simplify.

69. 3 20 15 45 6 80 10 500 70. 2

6 5

Simplify.

71. 2(3 5) 72.

3 83 24b a b c

73. 10 10x x 74. 3 6 2 3

Rationalize the denominator.

75. 5

3 76.

10

5 77.

6

3

Simplify.

78. ii 72 79. 100 80. 120

81. 212i 82. ii 5243 83. 272 i

Simplify.

84. ii 8243 85. ii 10236

86. 16i 87.

23i

88. 1510 89. (6 )(2 )i i

Solve.

90. 0483 2 x 91. 324 2 x

Factor the following by taking out the GCF.

92. 3 57 3y y 93.

3 4 2 3 29 6 15x y x p y p

Factor the following by grouping.

94. 2 5 5y y xy x 95. 21 7 3y x xy

Factor each trinomial.

96. 2 10 24y y 97.

2 6 16z z

98. 28 10 3y y 99.

29 18 8x x

Factor the following Difference of Squares.

100. 29 25x 101.

2 216a c

Factor the following Sum/Difference of Cubes.

102. 38 27x 103.

3 364x y

Factor completely. Look for GCF first.

104. 22 22 60y y 105.

33 12x x

Factor completely. Look for GCF first.

106. 2 2 1n n 107.

3 2 4 5 33 5x y x y x y

108. 22 13 7x x 109.

25 30 40x x

Solve by factoring:

110. 22 7 15x x 111.

2 6x x

112. 2 3 18x x 113.

2 16 64x x

Some formulas you may need:

Slope: 2 1

2 1

y ym

x x

Slope intercept form: y mx b

Point- slope form: 1 1y y m x x

Standard form: Ax By C

Difference of squares: 2 2a b a b a b

Sum of cubes: 3 3 2 2a b a b a ab b

Difference of cubes: 3 3 2 2a b a b a ab b

*When factoring, don’t forget about the GCF!