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CHAPTER 6 TEST B
Directions: Show all work.
Name: __________________________
Section: _________________________
4
 5
1. Which one of the following expressions is equivalent to    ?
 2
625
625
16
16
b.
c. 
d.
e. 
a. 10
16
16
625
625
2. Which one of the following power functions is consistent with the table below?
x
1
2
5
4
5
2
f  x
2
5
25
4
25
32
1
20
2
a. f  x   x3
5
4
b. f  x   x3
5
4
c. f  x   x 3
5
2
f  x   x 3
5
d.
5
e. f  x   x 2
2
3. Which one of the following expressions is an equivalent form of 162/3 ?
3
3
4
32
2
4
b. 3
c. 
a.
e.
d. 3 4
3
2
8
4
4. Which one of the following expressions is an equivalent form of
4 5
a. 13
4
b. 13
4
c. 13
5
5
5
d. 13
134 ?
5
5
4
e. 13
4
5. Which equation represents a circle in the x-y plane with radius 7 and center at (5,1)?
2
2
2
2
a. x 2  10 x  y 2  2 y  49 b.  x  5    y  1  7
c.  x  5    y  1  23
d. x 2  5 x  y 2  y  23
x 2  10 x  y 2  2 y  23
e.
f.
x 2  5 x  y 2  y  23
6. Which one of the following is a solution to the equation
1/3
1/ 2
 2 x  9    3x  4   3 ?
a.
x  1
b. x  5
c.
x 9
d. x  4
e.
x  18
4
7. The volume of a sphere of radius r is given by V   r 3 . Write in scientific
3
notation the volume of a sphere of radius 10 feet. Use three significant digits.
8. The surface area of the Great Lakes is 95,000 square miles, or about 2.65 1012
square feet and the total volume of the Great Lakes is about 8.12 1014 cubic feet.
Use these facts to approximate the average depth of the Great Lakes (in feet) to two
significant digits and write this value in scientific notation.
Chapter 6 Test/Form B
6
3
 m 2   6h 
9. Simplify:   5   2  .
 2h   m 
10. Write the expression without negative exponents and simplify:
14w

4
4w6 7 w3

3
.
11. Write the expression in radical form: 7 y1.25 .
12. A computer file contains 1,784,565 bytes after being compressed by 17%.
Approximate the size of the file before compression to two significant figures.
Write this number in scientific notation.
13. Solve the equation: 3n 2 / 3  45  2n2 / 3 .
 4  3t 
14. If G  t   

 2 
3/ 2
, find t so that G  t   8 .
15. Use the distributive law to expand the product, then simplify:

3
xy 2  3 x 2 y

3
x 2 y  3 xy 2

16. Write the equation in standard form. State the center and radius of the circle.
1
x2  8x  y 2  y  
4
17. Find an equation for the circle whose diameter has endpoints at 8,0 and  0,10 .
2
.
x 2
18. Write an equivalent expression without a radical in the denominator:
19. Write an equivalent expression without a radical in the denominator:
Chapter 6 Test/Form B
6
1
.
27x
20. Find both solutions to the equation:
3x  1  x  1  2 .
21. Use a calculator to approximate E 100 for E  r  
22. Use a calculator to approximate E  2.001 for E  r  
1
2
1
r
.
1
2
1
r
.
23. The speed of light in a vacuum is c  2.99792458 108 meters/second . The
Gravitational constant is G  6.6726 1011 meters3 /  kilogram-second 2  . Thus the
c2
c2
has units of kilogram/meter. Use a calculator to simplify
. Write
G
G
the value in scientific notation.
expression
24. Use a calculator to solve the equation
4  3x  3  x  2 .
25. There are four real solutions to the equation 15 x 2/5  25 x 2/3  1 . Use a calculator to
find 4-digit approximations for all four.
Chapter 6 Test/Form B
Solutions For Chapter 6 Test Form B.
1. d
2. d
3. a
4. c
5. e
6. d
3
7. The volume of the sphere is approximately 4.19 10 cubic feet.
8. The Great Lakes have an average depth  8.12 1014  2.65 1012  3.1 102 feet.
6
3
 m 2   6h 
m12 2333 h3 27m6



9. 
.
5  
2 
6 30 6
2
h
m
2
h
m
8h 27




10.
14w
4

4w6 7 w3

3
247 4 w4
w11
.
  2 3 15  
448
27 w
11. 7 y1.25  7 y 5/ 4  7 4 y 5 .
12. Let x represent the size of the computer file before compression. Then
1.784565 106
0.83x  1,784,565  x 
 2.2 106 bytes—or 2.2 Megabytes.
0.83
13. 3n 2 / 3  45  2n 2 / 3  n 2 / 3  9  n  93/ 2  27 .
 4  3t 
14. If 8  

 2 
15.

3
xy 2  3 x 2 y
3/ 2


3
4  3t
4  3t 1
7
 82 / 3 
 t .
2
2
4
6
 
x 2 y  3 xy 2  
3
xy 2  3 x 2 y

3

xy 2  3 x 2 y   3 x 2 y 4  3 x 4 y 2
 x 3 xy 2  y 3 x 2 y . Equivalently, x 4/3 y 2/3  x 2/3 y 4/3 .
2
16. x 2  8 x  y 2  y  
2
1
8
1
 x 2  8 x     y 2  y     16
4
2
2
2
1

 1
  x  4    y    16 is a circle centered at  4,  with radius 4 .
2

 2
17. The midpoint of the diameter,  4,5 gives the center coordinates. The radius is
2
42  52  41 and so the standard form for the equation of the circle is
 x  4    y  5
2
18.
19.
2
x 2
1
6
27 x
2
 41 .
x 2
2x  2
.

x2
x 2
6
27 x5
6
27 x5

6
27 x5
.
3x
Chapter 6 Test/Form B
20.

 4 x 1
3x  1  x  1  2 
  2x  4
2
2
3x  1
  2 
2
x 1

2
 3x  1  4  4 x  1  x  1
 4 x 2  16 x  16  16  x  1  x 2  8 x  0 . So x  8 .
Note that x = 0 is not a solution to the original equation.
21. E 100  
1
1
2
100

1
22. E  2.001 
1
2
2.001
1
5 2

 1.01015
7
49
50

1
 2001  44.7325
1
2001
8
c 2  2.9979 10 
23.

 1.3469 1027 kilogram/meter.
11
G
6.6726 10
2
24. Using the
graphing utility,
you can graph
both the
function on the
left side of the equation and the function on the right side of the equation and zoom
in and trace to the solution at the point of intersection. For a more precise value, the
TI-85 has an “ISECT” feature that will find the coordinates. It appears the solution
is about x = -1.977081728
25. 15x2/5  25x2/3  1  y  x   15x2/5  25x2/3 1  0 . Graphing this function on the
interval 1  x  1 and then using the “ROOT” feature on the TI-85 and observing
the symmetry through the y-axis, we find solutions near x  0.003712 and
x  0.06355
Chapter 6 Test/Form B