Download Final Exam Review WS

Final Exam Review WS
Algebra 2 Trig
Name________________
10
on a number line.
7
Evaluate the expression for the given value of the variable.
2. 5a + 5b; a = -6, b = -5
3. 4b  4  3  b 2  2b3 ; b  2
1. Graph
4. Combine like terms: -3(-4y + 3) + 7y
Solve the absolute value equation or inequality. Graph the solution.
5. 2 x  1  3
6. 4 4 x  3  8  4
7. 2 x  7  23
8. Find the domain and range of the relation.
9. Determine whether y varies directly with x.
If so, find the constant of variation k and write
the equation.
x
y
5
20
15
60
45
180
135 540
10. The function f(x) = x2. The graph of g(x) is f(x) translated to the left 6 units and down 5
units. What is the function rule for g(x)?
What is the graph of the absolute value equation?
11. y  3x  5
12. y  x  3  4
14. y   3x  7  6
15. y  x  1  3
Solve the system of equations.
2 x  y  14
16. 
3x  y  11
2.5 x  y  13.5
17. 
2.25 x  y  12.25
13. y  2 x
7 x  2 y  11
18. 
4 x  7 y  10
Graph each function. How is each graph a translation of f(x) = x2?
19. y = x2 - 5
20. y = (x + 3)2 + 4
Identify the vertex, axis of symmetry, and the maximum or minimum value.
21. y = 2(x + 2)2 - 3
22. y = -2(x - 3)2 - 4
Factor the expression.
23. x2 - 6x + 8
24. 16x2 + 8x
25. 2x2 + 16x + 30
26. -4x2 + 8x + 32
27. 3x2 + 26x + 35
28. 5x2 - 22x - 15
Final Exam Review WS Cont.
Solve.
29. x2 + 11x = -28
Algebra 2 Trig
Pg 2
30. 3x2 + 25x + 42 = 0
31. 2x2 + x - 4 = 0
Find the zeros of the function.
34. y = (x + 3)(x - 3)(x - 4)
35. x3 - 216 = y
36. x4 - 6x2 + 8 = y
37. 21x2 - 100 = -x4
38. y = 2x3 + x2 + 1
39. y = x4 + 3x3 + x2 - 12x - 20
32. 16x2 + 4 = 0
33. Simplify
360
40. Divide 4x3 + 2x2 + 3x + 4 by x + 4
41. Use the rational root theorem to list all possible rational roots of the polynomial equation
x3 - 4x2 + 7x - 8 = 0. Do not find the actual roots.
42. How many roots does -12x2 - 25x + 5 + x3 = 0 have.
Use Pascal's Triangle to expand the binomial.
43. (d + 6)7
44. (d - 3b)3
45. What is the fourth term of (d + 4b)5?
Simplify if possible.
46.
36g 6
47.
4
81x 20 y 8
48.
49.
6
50.
3
128a13b6
51.
52.
2
90 x 18
2x
1
1
53.
7  2 8  2 
55. 122 27 2
56. 2 72  3 32
Solve each equation.
58. x  10  7  5
59.
2x  8  6  4
3
27x15 y 24
4
400
4
1
5
1
54. 3 3 9 3
57. 8 3 5  3 40  2 3 135
60.
3 x  28  8  x
Let f(x) = -5x – 4 and g(x) = 6x – 7. Find the following.
61. f(x) + g(x)
62. f(x) – g(x)
65. Let f(x) = -2x – 7 and g(x) = -4x + 3. Find (f ◦ g)(-5).
63. f(x) ∙ g(x)
64.
f (x)
g( x )
Final Exam Review WS Cont.
Algebra 2 Trig
Pg 3
Graph each equation.
x
66. y  x  1
67. y  x  3
 1
68. y  5    2
4
69. Suppose you invest $1600 at an annual interest rate of 4.6% compounded continuously.
How much will you have in the account after 4 years?
70. Write 25  32 in logarithmic form.
Evaluate the logatithm.
1
71. log5
625
72. log 0.01
73. log7 25
74. Write 3 logb q + 6 logb v as a single logarithm.
57
.
74
Solve each equation.
76. 44x – 8
77. 54x = 2115
78. log(x + 9) – log x = 3
79. log 5x + log 14 = 1
80. ln 2 + ln x = 5
81. 8e 4 x 8  15
75. Expand log5
82. Is the relationship between the variables in the table a direct variation, an inverse variation,
or neither? If it is direct or inverse variation, write a function to model it.
x -9 -7 -2 -1
y 36 28 8 4
8
81. Suppose that x and y vary inversely and that y  when x = 8. Write a function that
3
models the inverse variation and find y when x = 4.
Graph the following function.
5
1
82. y 
x 1
83. y 
2x  4
x 1
84. What are the points of discontinuity? Are they all removable? y 
Simplify.
x 2  7 x  10
10
85. 2

x  2x  15 x  3
87.
z 2  11z  30 z 2  2z  24
 2
z 2  z  20
z  9z  18
 x  7  x  3 
x 2  10 x  21
n 2  10n  24
9

2
n  13n  42 n  7
y 1
2
y y 6
88.
y 6
y 3
86.
Final Exam Review WS Cont.
Algebra 2 Trig
Solve the equation.
4
1

89.
x 1 x  5
90.
Pg 4
7
2
3
 
x  5 x x 2 x  10
2
91. Find the amplitude, period and equation of the midline of the periodic function.
Find the 6 exact trigonometric values for the following angles.
7
92. 180
93. 120
94. 
95. -240
4
96.
5
6
97. In ABC,  C is a right angle, what is the measure of x?
C
8
A
x
21
Graph each equation.
98. y = 3 sin 4x


101. y  cos      
4

B
99. y = -2 cos 2x
100. y = tan ½ 
102. y = csc 2 + 1
1
103. y  sec 
4
Verify each identity.
sin
 sin2 
csc 
104. sin  sec  cot  = 1
105.
Simplify.
107. sec  cos2 
108. cos  tan 
Solve each equation for  with 0 ≤  ≤ 2.
110. 2 tan + 2 = 0
111. 2cos  3  0
106. sintan + cos = sec
109. cot2  - csc2 
112. 2 cos2  + cos = 0