Algebra 2 CP
Name__________________
Assignment_____________
Chapter 6 Test Review
Evaluate the expression without using a calculator.
1.
 16 
3
4
4. 125
4
3
2.
 81
5.
 325
4
4
3.
36
3
2
3
Solve the equation. Round the result to the nearest hundredth when appropriate.
4
6. 2 x 5  73  53
7. 2 x  3  162
8
Geometry Find the radius of a sphere with a volume of 589 cubic centimeters. ( V 
4 3
r )
3
Simplify the expression using the properties of radicals and rational exponents. Final answers should
be in radical form. No negative exponents, no radicals in the denominator!
3
9.
1
3
7 7
1
4
12. 5  3
4
15.
4
32
2
4
3
1
4
 23  4
10.  6 
 
 
13.
16.
2 8
4
4
11
4
11
11.
4
2
3
1
43
 3
14.  3 2 
 
 
2
Simplify the expression. Assume all variables are positive. Final answers should be in radical form. No
negative exponents, no radicals in the denominator!
5
3
17. x  x
20.
3
4
3
16x 4
x
18.
21.
 1
19.  x 2 
 
 
2
5
7
1
x5
x5
x
22.
4
5
2
4
x5
Perform the indicated operation. Assume all variables are positive.
23. 63 5  53 5
24. 5 5  2 45
25. 2 x  7 x
Write the expression in simplest form. Assume all variables are positive.
26.
x 3 y 4 z  xyz 4
27.
3
81x 2 y 3
28. Swimming Pool A wooden deck and a circular swimming pool cover an area of 514.16 square feet of the
lawn. The rectangular deck is 20 feet wide and 10 feet long. What is the radius of the pool?
Let f(x) = 7x 1/2 2, g(x) = x 1/2 + 4, and h(x) = 4x 1/2 + 1. Perform the indicated operation and state the
domain.
29. f(x) + g(x)
30. f(x) - h(x)
31. h(x) + g(x)
Let f(x) = 4x2, g(x) = x1/2, and h(x) =
4
. Perform the indicated operation and state the domain.
x  16
32. f x   g x 
33.
f x 
g x 
35. h f x 
34. hx   f x 
36. f g x
Find an equation for the inverse relation.
37. y 
40.
2x  5
f x   4 x 2  1, x  0
38.
f x  
41. y 
1
x3
5
1 1
 x
2 3
39.
f x   4x 7
42.
f x   5 5 x  4
Verify that f and g are inverse functions.
43. f  x   7 x  4 ; g  x  
45
x4
7
44.
f x   3  x ; g x   3  x
f x   x 5 ; g x   5 x
46. f  x   x 2  5, x  0 ; g  x  
x5
Graph the function f, sketch it below. Then use the horizontal line test to determine whether the
inverse of f is a function.
47. f  x  
48. g  x  
1 2
x 1
2
1 3
x
4
Solve the equation. Check your solution.
1
49. x 2  4  1
50. 3 4  3x  21
51.
52. 2x  1 2  3  7
53. 23 2 x  3  7  10
54.
1
3x  4 
2
3
3
x  43  2  6
1
55. 63 x  3  2 
57.
x  2 4
59.
3
3
1
2
8
4
x 9  3 x 6
5
61. x  6  3x
3
56. 2 x 2  3  19
58. 3x  21 3  9  90
4
60. x  3 
62.
x 1
4 x  4  5x  1  1
Velocity The velocity of a free falling object is given by V  2 gh where V is velocity (in meters per second),
g is acceleration due to gravity (in meters per second squared), and h is the distance (in meters) the object has
fallen. The value of g depends on which body/planet is attracting the object. If an object hits the surface with a
velocity of 30 meters per second, from what height was it dropped in each of the following situations?
63. You are on Jupiter where g = 24.79 m/s2.
64. You are on Saturn where g = 8.96 m/s2.
ANSWERS
1.
8
2.
81
3.
216
4.
625
5.
6.
x  -1.58
7.
x = 0, -6
8.
r = 5.2 cm
9.
73 49
10.
11.
3
4
12.
4
13. 2
16.
4
113
17. x 3
21.
5
5
x
3
26. x 2 y 2 z 2 yz
22.
15
x2
x
27. 3 y 3 3x 2
18.
5
14. 27
x
19.
23. 113 5
24.  5
28. r = 10 feet
29. 6 x  2 ; [0, )
30. 11 x  3 ; D: [0, )
31.  5 x  5 ; D: [0, )
32. 4 x 2 x ; D: [0, )
33. 4 x x ; D: (0, )
34.
4
 4 x 2 ; (,16)  (16, )
x  16
36. 4x; D: [0, )
x   7
x
4
5
x 4
42. f 1 x  
5
39. f
1
1
; D: (, 2)  (2, )
x 4
x2  5
37. f 1 x  
2
x 1
40. f 1  x  
2
35.
50. x = -15
51. x =
56. x = 4
59. x = -15
62. x = 2, 10
15. 2
20. 2 x 3 2 x
25. 9 x
38. f
41. f
1
x   5x  15
1
x   3x  3
2
43 – 46. Need to guarantee f(g(x)) = x and g(f(x)) = x
48. Yes
3
16
6
2
47. No
53. x =
1
x
-8
49. x = 25
13
27
52. x = 26
191
64
54. x = -68
55. x =
57. x = 18
60. x = 5
63. h = 18.15 meters
58. x = 2 and -16
61. x =12
64. h = 50.22 m