Download Algebra 2A Semester Review 2010-2011 DO NOT

Algebra 2A Semester Review 2010-2011
DO NOT WRITE ON THIS REVIEW!! You must SHOW ALL WORK ON YOUR OWN PAPER to
receive credit.
Vocabulary—You should be able to match the vocabulary term with the definition.
Domain
Rational number
Standard Form of a Quadratic
Dependent variable
Irrational number
Function
Range
Natural number
Vertex Form of a Quadratic
Function
Y- Intercept
Function
Independent variable
Axes of Symmetry
Maximum/Minimum Value
Real number
Vertex of a Parabola
Parent function graphs (square root, cubic, linear, reciprocal, absolute value, and quadratic)
Simplify or Evaluate
1. 3x + 4y -2(x +5y -3)
2. 4(x + 2) +x (3y – 9)
3. 7y + 2 when y = 4
4. m + 2(m – 3) when m = 10
5. (3a)2 + 4 when a = 2
6. 20 ÷ 5 + 5 • 4
7. 23 – 3 • 6 ÷ 9
8. 1 + 7 • 4 – 5
9. (5 + 3i) ( 4 – 2i)
10. ( - 6 + 5i)2
11.( 5 – 2i) ( 5 + 2i)
12. 3 80
13.
−8
14.
16.
5 − 4i
6 + 2i
−6
17.
Find the domain and range.
19. {(1, 5), (4, 8), (-3, -8), (-12, 4), (0, 6)}
21. y = x2 + 6x – 16
23.
5 56
15.
−7
(3i 5 )
2
20. y = 3x – 1
22. y =
3x + 12
24.
26. Use the graph at the right to determine:
Domain ____________________Range _____________________
Which of the following is an element of the range?
a. 6
b. 4 c. 8 d. 7
25.
2 + 3i
6i
Tell whether the relation is a function or not. (yes / no)
27. y = x2 + 8
28. y = 4x – 8
30. y = |x – 4|
31. y =
33.
34.
x
32. {(2, 3), (3, 4), (2,5)}
Solve
1
x − 12 = 4
2
35. 2x + 3 = x – 7
36.
38. 6t + 7 ≥ 25
39. -7 ≤ 5y – 2 ≤ 3
40. –x + 5 < 3x + 1
41. yb + c = d solve for b
42. |4 – 6x| = 2
43. |7 + 2h| ≥ 9
44. |8 – x| > 25
45. |11 + 2y| < 3
46. 12x2 – 10 = 122
48. 25 + b2 = 169
49. -x2 + 72 = 2x2 + 6x
47.
3 2
x + 5 = 32
4
37. 3(x – 2) = 6(5 + x)
50. Which point(s) are solutions of 21x – 10y > 4? a. (2, 3)
Use the following matrices for questions 58-64.
 −3 4 
 −2 0 
A =  5 0 
B= 

 4 8
 1 −2
58. The dimensions of A.
61. A • B
b. (-1, 0)
 −3 4 7 
C= 

 −1 0 5 
59. Det (B)
62. A + B
Factor completely.
65. 4x3 – 20x2
66. 4x2 – 81
69. x2 – x – 20
70. x2 + 10x + 25
 −1 5
D = 2 6
0 1
8
3 
1 
60. Find the inverse of D
63. B • A
64. C • A
67. x2 – 121
71. 3x2 + 10x – 8
68. x2 – 20x + 36
72. 6x2 + 3x – 9
Graph.
73. y = -2.
74. 4y – 3x = 24
75. –x > 2
76. -3x + 6y < 12
77. 4x – 3y > 15
78.  y ≤ − x + 4

x > − 1
y > − 2

Describe the transformations of y = x2 when it is changed to:
79. y = 4x2 – 2
80. y = - x2 + 1
81. y = - (x – 3)2 + 2
82. y =
1
(x + 5)2 – 3
5
Write the equation given by the description or the graph.
83. The absolute value function, f(x), that has been translated so that the vertex is (-3, 1).
84. The quadratic function, f(x), that has been translated so that the vertex is (5, 6).
85.
86.
87. The line containing the point (4, 3) and perpendicular to 5x + 8y = 12.
88. The line containing the point (-6,5) and parallel to the line 4x – 3y = 15.
89. The line having an x-intercept of -3 and parallel to the y-axis.
90 The line having a y-intercept of 9 and perpendicular to the y-axis.
91. The line with slope = -4 and through (3, 2). Put the final answer in slope intercept form.
92. The line that contains (3, 9) and (0, -6). Put the final answer in slope intercept form.
Find the x-and y-intercepts.
93. y = -x2 + x + 6
94. y = x2 + 5x + 4
96. y = -2(x + 3)(x – 1)
97. -8x + 10y = 20
Write the function, f(x) with the given roots.
98. -4 and 7
99. -2 and
2
3
95. y = -x2 + 8x + 15
Systems of Equations.
100. How many solutions does the following linear system have?
101. How many solutions does the following linear system have?
102. Solve the linear system by any convenient method:
103. Solve the system of linear equations:
-x + 3y = 3
2x – 6y = 30
x – 4y = 2
x + 4y = 2
3x + 5y = 12
x + 4y = 11
5x + 5y = -3
y = -x
104. Tickets to a local movie were sold at $5.00 for adults and $3.50 for students. If 235 tickets were
sold for a total of $1,152.50, then how many adult tickets were sold?
105. Sam is charged $75 for 600 minutes on his cell phone plan. The next month he is charged $83.50
for 700 minutes. Find the amount he will pay for 650 minutes.
106. John has several movies and cd’s. The total number of items in his collection is 98. The number
of cd’s is 40 less than twice the number of movies. How many of each item does he have?
107. Solve the system of equations:
x+y+z=2
-2x – y + z = -5
x – 2y – z = -2
108. Solve the system of equations:
x + 2y – 4z = -12
-x
+z =1
x+ y+ z =1
109. Line 1 contains (3,3) and (0,-3). Line 2 contains (6, 9) and (-8, 2). Are the lines parallel,
perpendicular, or neither?
110. Line 1 contains (30,3) and (0, -7). Line 2 contains (6, -4) and (15, -1). Are the lines parallel,
perpendicular, or neither?
111. Find the rate of change in the equation 9x – 10y = 20.
Graph and state the following.
a. axis of symmetry:__________
b. vertex ___________________
c. y-intercept_______ & symmetric point _________
d. roots ____________________
112. y = x2 + 1
113. y = -x2 + 4x+ 12
114. y = -x2 – 3
115. y = ( x – 2)2 + 3
116. y = |x – 5| + 1
117. y = − 2 | x + 4 |