CP Algebra II Midterm Review Packet 2017-2018 · CP Algebra II Midterm Review Packet 2017-2018 1.3...
Transcript of CP Algebra II Midterm Review Packet 2017-2018 · CP Algebra II Midterm Review Packet 2017-2018 1.3...
CP Algebra II Midterm Review Packet 2017-2018
1.3 Solving Equations 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
1.5 Solving Inequalities
Solve each inequality. Graph the solution set.
6. 2 5 7z 7. 3 6x 8. 2 3 4 28f
10. Which of the following is a solution to the inequality 2 5 9x ?
a. 5 b. 6 c. 7 d. 8
11. 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.
12. 13.
Function? ___________ Function? ___________
Domain: ____________ Domain: ____________
Range: _____________ Range: _____________
1
3
-5
8
2
-3
4
5
14. (7, 2), (4, 5), (6, 8), (9, -2), (7, 5) 15.
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.
16. 1
3 42
y x x-intercept_______ y – intercept________
17. 3
2 44
y x x-intercept_______ y – intercept________
18. 5 10 25y x x-intercept_______ y – intercept________
3 -4 5 6
-2 8
9 -4
0 1
Name the x and y-intercepts.
19. 2 5 10x y 20. 3 4 12 0x y
2.3 Slope
Find the slope of the line that passes through each pair of points.
21. 6, 5 ,(4,1) 22. 4,1.5 ,(4,6.5)
23. 6,8 ,( 4,8) 24. 3, 10 ,( 2, 4)
25. Find the slope of the line parallel to the given line.
a. 1
273
y x b. 6 3 18x y
26. Find the slope of the line perpendicular to the given line.
a. 2 18y x b. 4 16x y
2.4 Writing Linear Equations
State the slope and y-intercept of the graph of each equation.
27. 3 5 20x y 28. 2 4 10x y 29. 12y 30. 1x
Write the equation in slope-intercept form for the line that satisfies each set of conditions.
31. slope is 3, passes through (0,-6). 32. slope 3
4, passes through (-5,1).
33. passes through (-2,5) and (3,1). 34. passes through (7,1) and (6,2).
35. Determine if the lines are parallel, perpendicular or neither.
a. b. c.
29
5
511
2
y x
y x
27
3
2 3 36
y x
x y
168
492
x
y
3.1 Solving Systems of Equations by Graphing
Solve the system by graphing:
36. 2 0
6
x y
x y
37.
2
4
y x
x y
3.2 Solving Systems of Equations Algebraically
Solve the system of equations by substitution or elimination:
38. 3 2 8
2 12 5
x y
y x
39.
3 5 6
4 2 5
x y
x y
40. 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?
41. 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.
42. 25 nn 43. 4 2 3x x x
44. 34 )2( y 45. 2 5 4 3 1(4 )( 5 )d t v dt v
46. 2
8
m
m 47.
4
65
3
12
xy
yx
48.
2
32
32
ba
ab 49. 3)2(8 zu
50.
2
52
232
yx
yx 51. 6523464 )()( pnmnm
5.2 Polynomials
Simplify completely.
52. )272()33( 22 xxxx 53. )53()264( 22 yyyy
54. )43(2 4aaba 55. )432(3 3242 cddcdc
56. )4)(7( gg 57. )23)(23( yy
58. 2(3 1)x 59. 2( 1)(2 3 1)x x x
60. 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?
61. 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?
61a. 3 2
3 2
3 7 5
2 8 13
x x
x x
Find the sum of the two polynomials shown above?
5.4 Factoring Polynomials
Factor the following by using GCF.
62. 3 57 3y y 63. 3 4 2 3 29 6 15x y x p y p
Factor the following by using Grouping.
64. 2 5 5y y xy x 65. 21 7 3y x xy
Factor.
66. 2 10 24y y 67. 2 6 16z z
68. 28 10 3y y 69. 29 18 8x x
Factor the following Difference of Squares.
70. 29 25x 71. 2 216a c Factor the following Sum/Difference of Cubes.
72. 38 27x 73. 3 364x y
Factor. Look for GCF first.
74. 22 22 60y y 75. 33 12x x
76. 2 2 1n n 77. 3 2 4 5 33 5x y x y x y
78. 22 13 7x x 79. 25 30 40x x
1.4 Solving Absolute Value Equations
Solve each equation.
80. 2 1 7x 81. 4 2x
82. 2 3 2 18x 83. 5 3 1 20x
2.6 Special Functions
Graph each of the following. State the domain, range and any transformations.
84. ( ) 3f x x 85. ( ) 2 2 1f x x
Domain: ___________________ Domain: _____________________
Range: ____________________ Range: ______________________
Transformations: ____________ Transformations: ______________
__________________________ _____________________________
7.7 Operations on Functions
Use the following functions for #86-#96 2( ) 6 ( ) 2 9 18f x x g x x x ( ) 4 2 3h x x k x x
86. f g x 87. g h x 88. ( )h k x
89. ( )g
xf
90. ( )( )f k x 91. ( )h k x
92. ( )( )f h x 93. ( )h
xf
94. ( ( ))f h x
95. 3h k 96. 2h g
7.8 Inverse Functions and Relations
For #97-98, use the following functions.
2,5 , 1, 4 , 3, 2 , 5,0
4,2 , 3,5 , 6,0 , 1,3
f
g
97. Find the inverse of f 98. Find the inverse of g For #99-#103, find the inverse of each function.
99. 3 2
( )4
xh x
100. ( ) 5h x x
101. 1
32
f x x 102. 2 5f x x
103. 1y x
7. 9 Square Root Functions:
Graph the following. Find the domain and range.
104. 2 1y x 105. ( ) 4 6f x x
Domain: ___________________ Domain: ____________________
Range: ____________________ Range: ______________________
Transformations: ____________ Transformations: ______________
__________________________ _____________________________
5.3 Dividing Polynomials:
106. Simplify: 2 3 4 636 9 45
9
x y xy x y
xy