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Pre-AP Algebra II/Trigonometry Final Exam Review
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Simplify.
5
1
 2 3 (section 8.5)
4
12 x y 5 x y
y 5
y
2.
(section 8.5)
 2
2
y  3 y  10 y  y  2
1.
3.
4.
5.
6.
7.
8.
3x  6 6 x 2  12 x
(section 8.4)

x 2  9 4 x  12
25  v 2
(section 8.4)
3v 2  13v  10
2
1
y2
(section 8.4)
1
1
y2
1
log 4
(section 7.3)
256
16-1/4
log 1 27 (section 7.3)
3
 2 24  7 18 
10.  108  6 3 
9.
(section 6.2)
2
(section 6.3)
121s8 (section 6.1)
15  25 (section 6.2)
11.
12.
8
(section 6.2)
9a 3
5 3
14.
(section 6.3)
4 3
 1 0 
 3 16
15. 3 
 4

 (section 12.2)
17 11
 21 12
 2 4  3 2 7 
16. 

 (section 12.2)
 3 1 6 0 5
Solve.
17. 2 z  2  3 (section 1.6)
13.
18.
19.
20.
21.
1
4
3 x  2 y  12

(section 3.2)
2

2
x

y

14

3
2
2 x  5 x  6  0 (section 4.5-4.6)
3x 2  5 x  2 (section 4.5-4.6)
3x 2  24 x  45  0 (section 4.5-4.6)
Pre-AP Algebra II/Trigonometry Final Exam Review
22. 2x3 - 11x2 - x + 30 = 0 (section 5-5)
6
4
2


23.
(section 8.6)
x 1 x  2 x 1
24. 3 a  12 (section 6.5)
25. z  5  4  13 (section 6.5)
26. log6  2 y  8  2 (section 7.5)
3
(section 7.5)
2
28. 4log 2 x  log 2 5  log 2 405 (section 7.5)
27. log 4 x 
29. log6  2x  5  1  log6  7 x  10 (section 7.5)
30. log7 x  2log 7 x  log 7 3  log 7 72
4 n 1
(section 7.5)
2 n 1
 128
31. 16
(section 7.5)
2 x 1
2x
x4
 3  27 (section 7.5)
32. 9
1
 94 x 7 (section 7.5)
33.
27
34. 3.26x = 23 (section 7.5)
 2 3  x  12
35. 
      (section 12-4)
1 2  y   7 
36. x 4  24  2 x 2 (section 4.5)
Answer the following questions.
37. Find the inverse of f  x   3x  2 (section 6.7)
1
1  x  inverses of each other? (section 6.7)
4
39. For f  x   x  3 and g  x   2 x 2 , find  f g  x  (section 6.6)
38. Are f  x   4 x  1 and g  x  
40. Find the vertical asymptotes of y 
x2 1
. (section 8-3)
2 x2  x 1
41. Find the horizontal asymptotes of
3x 4  8 x  1
3x 2  8 x  1
3x 2  8 x  1
. (section 8-3)
y
,
y

,
&
y

5 x3  4
5 x3  4
5x2  4
1
1
1
,  ,  ,... (section 9-3)
42. Find the 8th term for the geometric sequence 
250 50 10
1
1
1
,  ,  ,... ?
43. What is the infinite sum of 
250 50 10
44. Find the geometric means in the sequence 5, ___, ___, ___, 1280. (section 9-3)
45. Find the 3rd term of (3x-2y)6. (section 5.7)
46. How many 7-digit phone numbers can be formed in the first digit cannot be 0, and
any digit can be repeated? (section 11.1)
47. How many 2 person sales teams can be formed from a group of 12 salespeople?
(section 11.1)
48. How many ways can a 4 person bobsled team be arranged in a sled from a group
of 9 athletes? (section 11.1)
2
Pre-AP Algebra II/Trigonometry Final Exam Review
49. A restaurant has 5 pieces of apple pie, 4 pieces of chocolate cream pie, and 3
pieces of blueberry pie If Janine selects a piece of pie at random for dessert, what
is the probability that she selects either apple or chocolate cream? (section 11.3)
50. A standard number cube is tossed. Find the probability of rolling an odd number
or a number greater than 2. (section 11.3)
51. What is the theoretical probability of being dealt exactly two 4’s in a 5-card hand
from a standard 52-card deck? (section 11.2)
52. For f  x   x  2 and g  x   3x 2  1 , find  g f  x  (section 6.6)
53. Identify the conic section represented by: (section 10-6)
a.
b.
c.
d.
x2 – 12x + y2 – 7y + 83 = 0
3x2 + 6x + y2 – 6y = -3
x2 – 4y2 – 2x – 8y = 7
x2 + 24y – 8x = -16
54. What are the vertices and foci of
 x  1
2
9
 y  8
 y  2

2
 1 ? (section 10-4)
16
2
 x  5

2
 1 ? (section 10-5)
144
25
56. Find the equation of a parabola with vertex at (1, 2) and focus at (4, 2). (section 10-2)
6 2
57. Evaluate
. (section 12.3)
8
5
55. What are the vertices and foci of
1 1 1
58. Evaluate 3 9 5 .
(section 12.3)
8 7 4
Solve the triangles. Round the side lengths to the nearest tenth and angle measures
to the nearest degree. (section 13.1, 13. 4, 13.5)
59. A = 80°, C = 14°, a = 40
60. A = 23°, b = 10, c = 12
13
61. Change 
to degrees. (section 13.2)
5
62. Change 56° into radians (section 13.2)
63. Find the exact value of sin 405° (section 13.3, 13.6)
11
64. Find the exact value of cos 
(section 13.3, 13.6)
4
11
65. Find the exact value of tan
(section 13.3, 13.6)
6
Find the amplitude, period, phase shift, vertical shift and graph each of the
following (section 13.4, 13.5, 13.6, 13.7)
66. y  2 cos 
67. y  sin 3
68. y  3 tan 
3
Pre-AP Algebra II/Trigonometry Final Exam Review
69. Find the exact values of the other five trig functions if  is an angle in standard
position whose terminal side is in Quadrant III and sec   10 . (section 14.1)
 3 4
70. Point P   ,  is located on the unit circle. Find sin  and cos  . (section 13.2)
 5 5
71. Use a calculator to find the value of the function cos 500 . (section 13.2)
 2
3 2 

72. Let X = 
 and Y =  5
5
4



 2
inverses. (section 12.3)
1
3  . Show whether or not the matrices are
2
3
73. Find the value of sec  , if sin   ;90    180 . (section 14.3)
4
74. Simplify: sec x – sin x tan x. (section 14-1)
75. Solve: 2cos2x + 3cosx + 1 = 0, 0 ≤ x < 2π (section 14-1)
4