Advanced Algebra Topics COMPASS Review You will be allowed to use a calculator on the COMPASS test. Acceptable calculators are: basic calculators, scientific calculators, and graphing calculators up through the level of the TI-86. 1. If 4 2 3 ) ( 2 x x x f , find ) 2 (f . a. 20 b. 2 c. -8 d. 12 2. If 2 3 ) ( x x f and 1 4 ) ( 2 x x x g , find: ) )( ( x g f a. 3 2 3 14 11 2 x x x b. 3 4 6 1 x x c. 2 1 x x d. 2 7 3 x x 3. If 2 3 ) ( x x f and 1 4 ) ( 2 x x x g , find: ) )( ( x g f a. 2 7 3 x x b. 2 7 3 x x c. 2 1 x x d. 2 1 x x 4. If 2 3 ) ( x x f and 1 4 ) ( 2 x x x g , find: ) )( ( x fg a. 2 3 8 1 x x b. 3 2 3 14 11 2 x x x c. 2 9 24 13 x x d. 2 1 x x 5. If 2 3 ) ( x x f and 1 4 ) ( 2 x x x g , find: ) ( x g f a. 2 4 1 3 2 x x x b. 2 1 3 x c. 1 2 d. 2 3 2 4 1 x x x 6. If 2 3 ) ( x x f and 1 4 ) ( 2 x x x g , find: ) )( ( x g f a. 3 2 x b. 3 2 3 14 11 2 x x x c. 2 3 12 1 x x d. 2 9 24 13 x x 7. If 2 3 ) ( x x f and 1 4 ) ( 2 x x x g , find: ) )( ( x f g a. 2 7 3 x x b. 2 4 1 x x c. 2 9 24 13 x x d. 2 3 12 1 x x 8. If 2 3 ) ( x x f and 1 4 ) ( 2 x x x g , find: )) 2 ( ( g f 1 a. -12 b. -1 c. 1 d. -11 9. If 3 2 ) ( x x f , find ) ( 1 x f . a. 1 3 () 2 x f x b. 1 () 2 3 f x x c. 1 1 () 2 3 f x x d. 1 1 1 () 2 3 f x x 10. If 3 1 4 ) ( x x f , find ) ( 1 x f . a. 3 1 1 () 4 x f x b. 3 1 () 4 1 f x x c. 1 3 1 () 1 4 f x x d. 1 3 1 () 4 1 f x x 11. If ) ( x f contains the point (4,1), then ) ( 1 x f must contain what point? a. (-4,1) b. (1,4) c. (4,-1) d. (1, 1 4 ) 12. Find the domain of 2 () 6 5 fx x x a. ( , ) b. [1,5] c. [3, ) d. [-4, )
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Advanced Algebra Topics COMPASS Review You will be allowed to use a calculator on the COMPASS test. Acceptable calculators are:
basic calculators, scientific calculators, and graphing calculators up through the level of the TI-86.
1. If 423)( 2 xxxf , find )2(f .
a. 20 b. 2 c. -8 d. 12
2. If 23)( xxf and 14)( 2 xxxg , find: ))(( xgf
a. 3 23 14 11 2 x x x b. 34 6 1 x x c. 2 1 x x d. 2 7 3 x x
3. If 23)( xxf and 14)( 2 xxxg , find: ))(( xgf
a. 2 7 3 x x b. 2 7 3 x x c. 2 1 x x d. 2 1 x x
4. If 23)( xxf and 14)( 2 xxxg , find: ))(( xfg
a. 23 8 1 x x b. 3 23 14 11 2 x x x c. 29 24 13 x x d. 2 1 x x
5. If 23)( xxf and 14)( 2 xxxg , find: )(xg
f
a. 2 4 1
3 2
x x
x b.
2
1
3x c.
1
2 d.
2
3 2
4 1
x
x x
6. If 23)( xxf and 14)( 2 xxxg , find: ))(( xgf
a. 3 2x b. 3 23 14 11 2 x x x c. 23 12 1 x x d. 29 24 13 x x
7. If 23)( xxf and 14)( 2 xxxg , find: ))(( xfg
a. 2 7 3 x x b. 2 4 1 x x c. 29 24 13 x x d. 23 12 1 x x
8. If 23)( xxf and 14)( 2 xxxg , find: ))2((gf 1
a. -12 b. -1 c. 1 d. -11
9. If 32)( xxf , find )(1 xf .
a. 1 3( )
2
xf x
b. 1( ) 2 3f x x c. 1 1( )
2 3f x
x
d. 1 1 1( )
2 3f x x
10. If 3 14)( xxf , find )(1 xf .
a.3
1 1( )
4
xf x
b. 31( ) 4 1f x x c. 1 3
1( ) 1
4f x x d. 1
3
1( )
4 1f x
x
11. If )(xf contains the point (4,1), then )(1 xf must contain what point?
a. (-4,1) b. (1,4) c. (4,-1) d. (1,1
4)
12. Find the domain of 2( ) 6 5f x x x
a. ( , ) b. [1,5] c. [3, ) d. [-4, )
13. Find the domain of 7
( )4 8
f xx
a. | 2x x b. | 0x x c. ( ,2) (2, ) d. ( ,0) (0, )
14. Find the domain of 82
1)(
2
xx
xxf
a. ( ,0) (0, ) b. ( ,1) (1, ) c. ( , 2) ( 2,1) (1,4) (4, ) d. ( , 2) ( 2,4) (4, )
15. Find the domain of ( ) 3 9 1f x x
a. [ 3, ) b. ( 3, ) c. (0, ) d. [0,3]
16. If 12)3(
)32( 2
x
x
kxx, find the value of k .
a. k = –7 b. k = – 5 c. k = 5 d. k = 7
17. If 14 yx and 53 xz , find an expression for z in terms of y .
a. z = 4y + 1 b. z = 12y – 2 c. z = 12y – 19 d. z = 3y – 5
18. Find the vertex of the function, 563)( 2 xxxf .
a. (-3,-5) b. (1,-8) c. (-1,-2) d. (-1,-8)
19. What are the zeros of the function, 382)( 2 xxxf ?
a. 2 2 10 b. 10
82
c. 8 2 10 d. 10
22
20. What are the zeros of the function, 1892)( 23 xxxxf ?
a. x = 3, x = –3, x = 2 c. x = 3, x = –3, x = – 2
b. x = 0, x = –3, x = 3, x = –2, x = 2 d. x = 0, x = 9, x = 2, x = – 2
21. Find the sum of the solutions of 452 2 xx .
a. 5
2 b. 5 c.
5
4 d. 4
22. Write a cubic function that has ,2,0 xx and 5x as zeros.
a. 3 2( ) 7 10f x x x x b. 3 2( ) 7 10f x x x x c. 3 2( ) 3 10f x x x x d. 3 2( ) 3 10f x x x x
23. Write a quadratic function that has a vertex at (2,-3) and contains the point (-2,5).
a. 2( ) ( 2) 3f x x b. 21( ) 2 1
2f x x x c. 2( ) ( 2) 3f x x d. 2( ) 4 1f x x x
24. Simplify 3
2
2 )(a
a. 8
3a b. 4
3a c. 2
3a d. 1
3a
25. Simplify 8
62
6
3
ab
ba
a. 22ab b. 2
2
ab c.
22
a
b d.
2
2
ab
26. Simplify
2
1
5
3
a
a
a. 1
10a b. 3
10a c. 1
5a d. 2
5a
27. Simplify 7
32 )4(x
x
a. 212x b. 1312x c.
64
x
d. 1364x
28. Simplify 2
5
2
3
2
3
2
1
23 baba
a. 3 15
4 46a b b. 2 45a b c. 3 86a b d. 2 46a b
29. Simplify
3
63
52
3
2
yx
yx
a. 3
3
2
3
y
x b.
3
3
8
27
y
x c.
33
15
27
8
y
x d.
15
33
3
2
x
y
30. Evaluate 2
1
6
1
88
a. 4 b. 1
1264 c. 1
128 d. 16
31. Evaluate 3
2
3
1
33
a. 1 b. 3 c. 2
99 d. Not possible
32. Simplify, assuming that the variables represent positive numbers:3 2aa
a. a a b. a c. 6a a d. Not possible
33. Simplify, assuming that the variables represent positive numbers: 53 ba
a. 15 ab b. 15 5 3a b c. 8 ab d. Not possible
34. Simplify, assuming that the variables represent positive numbers: baba 42 82
a. 34a b b. 34a b c. 44a b d. 6 216a b
35. Simplify, assuming that the variables represent positive numbers:4 354 52 44 baba
a. 7 816a b b. 42 3 2 32a b a b c. 3 44a b a d. 42 32ab a
36. Rewrite using logarithmic notation: 1642
a. 16log 4 2 b.
4log 2 16 c. 4log 16 2 d.
2log 16 4
37. Rewrite using logarithmic notation: yM x
a. logx y M b. log y M x c. logM x y d. logM y x
38. Rewrite using exponential notation: 2100log10
a. 210 100 b. 102 100 c. 2100 10 d. 1002 10
39. Rewrite using exponential notation: 13
1log3
a. 3 1( 1)
3 b. 1 1
33
c. 1
33 1 d. 3
11
3
40. Evaluate without a calculator:
4
1log2
a. 1
2
b. 2 c. -2 d.
1
16
41. Expand:3
2
logz
yxa
a. 2 3loga x y z b. 2log 3loga ax y z c. 2log log 3loga a ax y z d. 1
2log log log3
a a ax y z
42. Express as a single logarithm: tzy 10101010 log8log6log43log2
a. 106log (3 )yzt b.
10log (6 4 6 8 )y z t c. 4
10 6 8
9log
y
z t
d. 108log (3 )y z t
43. Simplify i2
to i, -i, 1, or -1.
a. i b. -i c. 1 d. -1
44. Simplify 8i to i, -i, 1, or -1.
a. i b. -i c. 1 d. -1
45. Simplify 11i to i, -i, 1, or -1.
a. i b. -i c. 1 d. -1
46. Add and write your answer in a+bi form: (1 + i) + (3 + 5i)
a. 4 + 6i b. -2 c. 4 – 6i d. 4 + 5i2
47. Subtract and write your answer in a+bi form:(3 – 4i) – (7 – i)
a. -4 – 5i b. 0 – 9i c. -4 – 3i d. 0 – 16i
48. Multiply and write your answer in a+bi form: 43 i
a. 0 + 12i b. 0 + 7i c. -12 d. 7
49. Multiply and write your answer in a+bi form: ii 52
a. 10i2 b. -10i c. -10 + 0i c. -10 + 0i
50. Multiply and write your answer in a+bi form: )52(7 ii
a. 35 + 14i b. 14 – 2i c. 2 – 35i d. -2 + 35i
51. Multiply and write your answer in a+bi form: )43)(21( ii
a. 3 + 8i b. 3 + 6i c. 5 – 10i d. -5 + 10i
52. Multiply and write your answer in a+bi form: 3)2( i
a. 8 – i3 b. 6 – i c. 2 – 11i d. 8 – 3i
53. Divide and write your answer in a+bi form: i3
2
a. 2
3 b. 6 + i c.
20
3i d. 6i
54. Divide and write your answer in a+bi form: i32
6
a. -1i b.
12 18
13 13i
c. 3 – 2i d. 12 – 18i
55. Divide and write your answer in a+bi form: 10 10
1 3
i
i
a. 2 + 4i b. -10 +
10
3i
c. 2 – 4i d. -40 – 2i
56. Solve for x over the complex number system: 0252 x
a. 5x i b. 5x c. 5x d. 5x
57. Solve for x over the complex number system: 422 xx
a. 1 3x i b. 2x c. 0,2x d. 2x i
58. Solve for x over the complex number system: 122 x
a. 3, 4x b. 2 3x i c. 3,4x d. 2 3x
59. Write the first five terms of the sequence having the general term 2
1 1)1(
n
na n
n
a. 3 4 5 6
2, , , ,4 9 16 25
b. 3 4 5 6
1, , , ,9 16 25 36
c. 2 3 4
0,1, , ,9 16 25
d. 1 3 4 5 6
, , , ,2 4 5 16 25
60. A certain arithmetic sequence has 561 a and 2611 a . Find 17a .
a. 21 b. 18 c. 3 d. 8
61. A certain geometric sequence has 641 a and 3245 a . Find 7a .
a. 2059 b. 454 c. 1358 d. 1358
62. Find the sum of the first ten terms of an arithmetic sequence having 271 a and 9d .
a. 117 b. 1.8x1010 c. 675 d. 108
63. Find the sum of the first ten terms of a geometric sequence having 30721 a and 2
3r .
a. 41,472 b. 6157.5 c. 348,150 d. 118,098
64. Evaluate
23
1
)36(n
n .
a. 1587 b. 60 c. 1518 d. 135
65. Evaluate
14
1 2
18
n
n
a. 15 b. 4 c. 1 d. 64
66. Evaluate 9!
3! 6!
a. 1 b. 84 c. 1
2 d.
45
126
67. Give the entry in the first row and the first column for
62
30
43
5
05
73
28
a. 11 b. 5 c. -7 d. 47
68. Give the entry in the second row and the first column for
30
52
43
65
32
a. 21 b. 33 c. 24 d. 26
69. Evaluate 53
912
a. 87 b. -33 c. -87 d. 33
70. Evaluate
132
065
213
a. 1 b. 0 c. 66 d. 7
71. Give the z-value of the solution to the following system:
12
72
1154
zy
zx
yx
a. 2 b. -1 c. 1 d. 4
72. If r
aS
1, then r = ?
a. S a
S
b. S a c. 1
S
a
d. 1S a
73. If 2 3 1 6 8
5 6 0 2 15 17
k
, then k =?
a. 3 b. 4 c. 8 d. 3
2
74. If is defined to be: 1 yxyx and 315x , then x = ?
a. 26 b. 6.2 c. 2 d. 36
75. If 1
4 2
k=10, then k = ?
a. 5
4 b. 3 c. 10 d. 7
76. In the list 12,5
3,2.16,
8
0,,25,7,
2
1 , the sum of all the rational numbers is:
a. 28.2 b. 33.3 c. 28.3 d. 5.5
77. How many integers are in the list: 12,5
3,2.16,
8
0,,25,7,
2
1 ?
a. 4 b. 3 c. 1 d. 6
78. Find the fourth term in the expansion of 7)3( zy .
a. 4 335y z b. 4 32835y z c. 4 31701y z d. 4 32835y z
79. How many terms are in the expansion of 7)3( zy ?
a. 2 b. 6 c. 7 d. 8
80. A set containing five elements has how many subsets?
a. 15 b. 31 c. 32 d. 10
Answers to Advanced Algebra Topics COMPASS Review
1. a
2. c
3. b
4. b
5. d
6. c
7. c
8. d
9. a
10. a
11. b
12. a
13. c
14. d
15. a
16. a
17. b
18. d
19. d
20. c
21. a
22. d
23. b
24. b
25. c
26. a
27. d
28. d
29. c
30. a
31. b
32. c
33. b
34. a
35. d
36. c
37. d
38. a
39. b
40. c
41. d
42. c
43. d
44. c
45. b
46. a
47. c
48. a
49. c
50. a
51. d
52. c
53. c
54. b
55. a
56. a
57. a
58. b
59. a
60. d
61. d
62. c
63. c
64. a
65. a
66. b
67. c
68. a
69. d
70. d
71. b
72. a
73. a
74. c
75. d
76. b
77. b
78. d
79. d
80. c
2/2012
Solutions to Advanced Algebra Topics COMPASS Review