Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
What is the meaning of the expression?
1)
52
A)
5·5
B)
2 ·5
C)
3
D)
7
2)
152
A)
15 ·15
B)
17
C)
2 ·15
D)
450
3)
46
A)
46
B)
4·4·4·4·4·4
C)
5
D)
6 ·4
4)
0.083
A)
0.08 ·0.08 ·0.08
B)
3 ·0.08
C)
0.000729
D)
0.00004096
5)
(-8.7)3
A)
–8.7 ·8.7 ·8.7
B)
3(–8.7)
C)
(–8.7)(–8.7)(–8.7)
D)
(8.7)(8.7)(8.7)
6)
4
5
4
A)
4
5·5·5·5
B)
4·4·4·4
5
C)
4 4
5
D)
4
5
4
5
4
5
4
5
7)
2x3
A)
2x ·2x ·2x
B)
2· x · 3
C)
2· x · x · x
D)
2·2·2· x
8)
–3q3
A)
(–3q)(–3q)(–3q)
B)
–3· q · 3
C)
–3· q · q · q
D)
(–3)(–3)(–3)(q)
Evaluate.
9)
140
A)
–1
B)
0
C)
14
D)
1
10)
–150
A)
–1
B)
0
C)
1
D)
–15
11)
(-12)0
A)
–12
B)
1
C)
0
D)
–1
12)
x0; x
0
A)
x
B)
–1
C)
1
D)
0
13)
(8x)0; x
0
A)
0
B)
8x
C)
8
D)
1
14)
a1
A)
a
B)
0
C)
1
D)
–1
15)
61
A)
1
B)
0
C)
6
D)
36
16)
–2
5
0
A)
2
5
B)
0
C)
1
D)
–1
17)
2
7
1
A)
7
2
B)
–2
7
C)
1
D)
2
7
18)
xy1
A)
y
B)
x
C)
1
D)
xy
19)
cd0
A)
d
B)
1
C)
cd
D)
c
20)
m2 when m =3
A)
5
B)
6
C)
9
D)
3
21)
m2 when m =17
A)
289
B)
578
C)
19
D)
34
22)
m5 when m =4
A)
4
B)
1024
C)
45
D)
20
23)
x1, when x =14
A)
14
B)
16
C)
392
D)
28
24)
p3, when p = 0
A)
1
B)
0
C)
9
D)
3
25)
–p3, when p =6
A)
216
B)
–216
C)
18
D)
4
26)
y18 when y = 1
A)
18
B)
0
C)
1
D)
–1
27)
x2–2 when x =-10
A)
-12
B)
x2– 10
C)
96
D)
98
28)
y1–3, when y =-4
A)
7
B)
-7
C)
–3
D)
13
29)
The volume of a cube with sides of length s is given by V =s3. Find the volume of the cube.
27 ft
27 ft
27 ft
A)
19,683 ft3
B)
729 ft3
C)
81 ft3
D)
1458 ft3
30)
The volume of a cylinder with height h and radius r is given by V =r2h. Find the volume of the cylinder. Use
3.14 for .
6.5 ft
17 ft
A)
347 ft3
B)
9021.2 ft3
C)
693.9 ft3
D)
2255.3 ft3
Express using positive exponents. Then simplify.
31)
2-3
A)
8
B)
1
8
C)
1
6
D)
–8
32)
(-5 )-2
A)
25
B)
1
25
C)
–25
D)
–1
25
33)
–2-3
A)
–8
B)
8
C)
1
6
D)
–1
8
34)
x-8
A)
x8
B)
1
x8
C)
1
x-8
D)
8x
35)
1
x-2
A)
1
x2
B)
x2
C)
x-2
D)
2x
36)
1
x–m
A)
xm
B)
mx
C)
1
xm
D)
x–m
37)
1
4
–3
A)
–64
B)
1
64
C)
64
D)
1
12
38)
2
5
–2
A)
4
25
B)
25
4
C)
–25
4
D)
–
4
25
Express the following using negative exponents.
39)
1
63
A)
6-3
B)
3-6
C)
63
D)
6-4
40)
1
38
A)
38
B)
3-9
C)
3-8
D)
8-3
41)
1
x9
A)
x-9
B)
9–x
C)
9–x+1
D)
x9
42)
1
b2
A)
b-2
B)
2–b
C)
2–b–1
D)
b2
43)
1
t12
A)
t12
B)
12t
C)
12–t
D)
t-12
Multiply and simplify.
44)
35·33
A)
1
B)
38
C)
311
D)
8
5
45)
3-3 ·36
A)
1
B)
36
C)
39
D)
33
46)
59·5-2
A)
52
B)
55
C)
59
D)
57
47)
t6·t4
A)
1
t2
B)
1
t10
C)
t10
D)
t2
48)
y8·y0
A)
y8
B)
1
C)
y80
D)
0
49)
x ·x-5
A)
1
x4
B)
1
x6
C)
x4
D)
x6
50)
y-9 ·y-2
A)
1
y11
B)
1
y7
C)
1
y–11
D)
y11
51)
a-9 ·a9
A)
0
B)
1
a9
C)
1
D)
–1
52)
x–9·x3·x–8
A)
x20
B)
x14
C)
1
x20
D)
1
x14
53)
(8x)12(8x)8
A)
(8x)96
B)
8x96
C)
(8x)20
D)
8x20
54)
(x2y5)(x7y)
A)
x14y5
B)
x9y5
C)
x9y6
D)
2x92y6
55)
(mn6)(m3n6)
A)
2m42n12
B)
m4n12
C)
m3n12
D)
m3n36
Divide and simplify.
56)
t4
t8
A)
t4
t4
B)
1
t4
C)
t4
D)
t–8
57)
(3p)10
(3p)6
A)
81p4
B)
1
81p4
C)
81
p4
D)
p4
81
58)
(12x)13
(12x)13
A)
x
B)
1
x13
C)
1
D)
x13
59)
(29x)5
(29x)6
A)
1
29x5
B)
29x
C)
1
x5
D)
1
29x
60)
p2
p-7
A)
p9
B)
p-9
C)
1
p9
D)
p-5
61)
t-3
t-8
A)
t11
B)
t-11
C)
t5
D)
t-5
62)
z-9
z-5
A)
z14
B)
1
z-4
C)
1
z4
D)
z4
63)
y-15
y4
A)
1
y-11
B)
1
y19
C)
y19
D)
y11
64)
t7
t
A)
t7
B)
t6
C)
1
t6
D)
t
65)
x
x12
A)
1
x12
B)
x12
C)
1
x11
D)
x11
Simplify.
66)
(85)-6
A)
-6 ·85
B)
1
830
C)
830
D)
8-1
67)
(x–2)-5
A)
-5x–2
B)
x-3
C)
1
x10
D)
x10
68)
(-2a6)4
A)
(-2)24a24
B)
(-2)24a6
C)
-8a6
D)
(-2)4a24
69)
(-4x3y)2
A)
(-4)2x6y2
B)
-8x3y2
C)
-8x3y
D)
(-4)2x5y2
70)
-3(x3y)–5
A)
-15x3y5
B)
1
(-3)5x15y5
C)
-3
x15y5
D)
-3x15y5
71)
-3(x–3y–1)–4
A)
x12y4
(-3)4
B)
-3
x12y4
C)
-3x12y4
D)
(-3)4x12y4
72)
(-3p6q6r6)3
A)
-9p9q9r9
B)
(-3)3p9q9r9
C)
(-3)3p18q18r18
D)
(-3)18p18q18r18
73)
(-2p–3q3r–3)5
A)
(-2)5p15
q15r15
B)
(-2)5q15
p15r15
C)
(-2)5
p15q15r15
D)
(-2)5p15q15r15
74)
4
x
4
A)
256
x
B)
256x4
C)
4
x4
D)
256
x4
75)
5
2y
2
A)
25
4y2
B)
25y2
4
C)
25
2y2
D)
25
4y
76)
5a
2
4
A)
625a4
2
B)
625a
16
C)
5a4
16
D)
625a4
16
77)
a3
b4
2
A)
a4
b8
B)
a6
b8
C)
a8
b6
D)
a6
b4
78)
x7
5
5
A)
x2
3125
B)
x35
3125
C)
a35
5
D)
x12
3125
79)
2
b–4
5
A)
32
b20
B)
b20
32
C)
1
32b20
D)
32b20
80)
x3y
z5
3
A)
x9y3
z5
B)
x9y3
z15
C)
x3y9
z15
D)
x6y3
z8
81)
x5
y5z6
3
A)
x15
y5z18
B)
x15
y15z18
C)
x8
y9z9
D)
x9
y15z18
82)
b6
5
-2
A)
b-12
5
B)
25
b12
C)
b12
52
D)
b-8
5-2
83)
xy4
w6z
-6
A)
xy-24
w-36z
B)
x-6y-2
w0z-6
C)
x6y-24
w-36z6
D)
w36z6
x6y24
Write the number in scientific notation.
84)
558,406
A)
5.58406 × 105
B)
5.58406 × 101
C)
5.58406 × 10-5
D)
5.58406 × 106
85)
377.9
A)
3.779 × 10-3
B)
3.779 × 102
C)
3.779 × 10-2
D)
3.779 × 103
86)
453.29
A)
4.5329 × 10-2
B)
4.5329 × 10-3
C)
4.5329 × 102
D)
4.5329 × 103
87)
770,000
A)
7.7 × 105
B)
7.7 × 104
C)
7.7 × 10-4
D)
7.7 × 10-5
88)
89,000,000
A)
8.9 × 107
B)
8.9 × 10-7
C)
8.9 × 108
D)
8.9 × 10-8
89)
0.000281
A)
2.81 × 104
B)
2.81 × 10–5
C)
2.81 × 10–4
D)
2.81 × 10–3
90)
0.000030116
A)
3.0116 × 104
B)
3.0116 × 10–4
C)
3.0116 × 10–5
D)
3.0116 × 105
91)
0.000007064
A)
7.064× 10–5
B)
7.064× 10–7
C)
7.064× 10–6
D)
7.064× 106
92)
0.00000070109
A)
7.0109 × 10–7
B)
7.0109 × 10–6
C)
7.0109 × 106
D)
7.0109 × 107
93)
0.0000000862016
A)
8.62016 × 10–8
B)
8.62016 × 10–7
C)
8.62016 × 108
D)
8.62016 × 10–9
If the number in the statement is written in scientific notation, write it without exponents. If it is written without
exponents, write it in scientific notation.
94)
The population of a small country is 6,344,000 .
A)
6.344 × 105
B)
6.344 × 10–5
C)
6.344 × 104
D)
6.344 × 106
95)
A company produces 916,000 small appliances in one year.
A)
9.16 × 105
B)
9.16 × 10–5
C)
9.16 × 106
D)
91.6 × 104
96)
The earth is approximately 92,900,000 miles from the sun.
A)
9.29 × 108
B)
9.29 × 106
C)
9.29 × 10–7
D)
9.29 × 107
97)
The speed of light is 1.86 × 105 miles per hour.
A)
1,860,000
B)
0.0000186
C)
18,600,000
D)
186,000
98)
A computer can do one calculation in 1.4 × 10–7 seconds.
A)
14,000,000
B)
0.00000014
C)
0.000000014
D)
0.000014
99)
It has been estimated that the average American watches 58,240 hours of television in a lifetime.
A)
5.824 ×104 hours
B)
5.824 ×103 hours
C)
58.24 ×103 hours
D)
5.824 ×105 hours
100)
The life span of the average male human being is approximately 37,843,200 minutes.
A)
37.8432 ×106 minutes
B)
3.78432 ×106 minutes
C)
3.78432 ×107 minutes
D)
3.78432 ×105 minutes
Convert to decimal notation.
101)
6.06 × 103
A)
606
B)
6060
C)
60,600
D)
181.8
102)
7.687 × 105
A)
76,870
B)
768,700
C)
7,687,000
D)
384.35
103)
4.3872 × 107
A)
43,872,000
B)
438,720,000
C)
307.104
D)
4,387,200
104)
6.35 × 10–4
A)
0.00635
B)
0.0000635
C)
0.000635
D)
–635,000
105)
7.942 × 10–5
A)
0.0007942
B)
–794,200
C)
0.000007942
D)
0.00007942
106)
9.907 × 10–6
A)
0.000009907
B)
0.00009907
C)
–9,907,000
D)
0.0000009907
107)
1.0892 × 10–7
A)
0.000000010892
B)
0.00000010892
C)
-108,920,000
D)
0.0000010892
108)
108
A)
10,000,000,000
B)
100,000,000
C)
1,000,000,000
D)
10,000,000
109)
10-6
A)
0.000001
B)
0.00001
C)
0.0001
D)
0.0000001
Multiply or divide and write scientific notation for the result.
110)
(5 ×107)(8×107)
A)
4×1014
B)
4×1015
C)
40 ×1015
D)
40 ×1049
111)
(7.08 × 10-5)(8.45 × 10-3)
A)
6.0 × 1015
B)
5.98 × 10-7
C)
5.98 × 1015
D)
6.0 × 10-7
112)
20 × 106
4× 107
A)
10 × 1013
B)
10 × 10-1
C)
5× 10-1
D)
5× 1013
113)
21.62 × 103
4.6 × 10-1
A)
9.4 × 104
B)
4.7 × 102
C)
4.7 × 104
D)
9.4 × 102
114)
(8.25 ×10–1) ÷(3 ×10-4)
A)
5.5 × 103
B)
2.75 × 10-5
C)
5.5 × 10-5
D)
2.75 × 103
115)
(2 × 109) ÷ 104
A)
2× 106
B)
2× 1013
C)
2× 105
D)
2× 106
Solve the problem. Express the answer in scientific notation to two decimals unless requested otherwise.
116)
The national debt of a small country is $7,870,000,000 and the population is 2,747,000. What is the amount of
debt per person?
A)
$2.86 × 106
B)
$2.86 × 103
C)
$28.60
D)
$2.86
117)
A company produced 2,580,000 small appliances in one year and made a profit of $7,530,000. What was the
profit on each appliance?
A)
$29.20
B)
$2.92 × 103
C)
$2.92
D)
$2.92 × 106
118)
The earth is approximately 92,900,000 miles from the sun. If 1 mile = 1.61 × 103 m, what is the distance to the
sun in meters?
A)
5.7 × 10–10 m
B)
1.50 × 1010 m
C)
5.7 × 1010 m
D)
1.50 × 1011 m
119)
If the distance from the earth to the sun were 82,000,000 miles. How long would it take a rocket, traveling at 3.8
× 103 miles per hour, to reach the sun? (Round to three places)
A)
2.158 hr
B)
2.158 × 104 hr
C)
2.158 × 103 hr
D)
2.158 × 102 hr
120)
If the speed of light is 3.00 × 108 m/sec, how long does it take light to travel 2.29 × 1011 m, the distance from the
sun to Mars?
A)
7.6 × 103 sec
B)
7.6 × 102 sec
C)
7.6 × 102 min
D)
76 sec
121)
A light–year is the distance that light travels in one year. Find the number of miles in a light–year if light travels
1.86 × 105 miles/second.
A)
5.87 × 1012 miles
B)
5.87 × 107 miles
C)
5.87 × 1014 miles
D)
5.87 × 105 miles
122)
A computer can do one calculation in 1.4 × 10–7 seconds. How long would it take the computer to do a trillion
(1012) calculations?
A)
1.4 × 1012 sec
B)
1.4 × 106 sec
C)
1.4 × 105 sec
D)
1.4 × 10–7 sec
123)
Assume that the volume of the earth is 5 × 1014 cubic meters and the volume of a bacterium is 2.5 ×10–16 cubic
meters. If the earth could be filled with bacteria, how many would it contain?
A)
5.0 × 1031 bacteria
B)
2.0 × 10–30 bacteria
C)
2.0 × 1030 bacteria
D)
5.0 × 10–31 bacteria
124)
The national debt of a country is $28,400,000,000 and the population is 3,550,000. What is the debt per person?
Write answer without exponents.
A)
$100,820,000
B)
$8000
C)
$80,000
D)
$800
125)
The national debt of a country is $68,760,000,000 and the population is 7,640,000. What is the debt per person?
Write answer without exponents.
A)
$525,326,400
B)
$90,000
C)
$9000
D)
$900
Evaluate the polynomial.
126)
4x + 3, when x =8
A)
64
B)
29
C)
35
D)
7
127)
-5x +6, when x =5
A)
-19
B)
-31
C)
-50
D)
1
128)
4x2+ 6x – 10, when x =3
A)
40
B)
34
C)
44
D)
20
129)
2x2– 5x – 5, when x =-2
A)
1
B)
13
C)
9
D)
3
130)
9x2+ 6x – 7, when x = 0
A)
-7
B)
0
C)
6
D)
9
131)
6–1
9x, when x = 0
A)
6
B)
–1
9
C)
0
D)
–6
132)
2x3– 6x2+ 18, when x =4
A)
40
B)
50
C)
38
D)
122
133)
4x3+ 5x2– 15, when x =-2
A)
-37
B)
-39
C)
-57
D)
-27
134)
24 – 3x2 + 4x3, when x =-2
A)
–32
B)
–20
C)
-2
D)
–30
135)
5x3– 3x2– x + 10, when x =-2
A)
-22
B)
-52
C)
-50
D)
-40
15
136)
3x3+ 3x2– x + 32, when x = 0
A)
-29
B)
-19
C)
32
D)
0
Solve the problem.
137)
The distance D, in feet, it takes a car travelling at x mph to come to a full stop after hitting the brakes is given by
D =1.24x2+0.067x. What is the stopping distance for a car travelling at 50 mph?
A)
186 ft
B)
3100 ft
C)
124 ft
D)
3103.35 ft
138)
The distance D in feet it takes a car travelling at x mph to come to a full stop after hitting the brakes is given by
D =1.27x2+0.056x. Use the graph below to find the approximate value of 1.27x2+0.056x for x =35.
A)
1000 feet
B)
1700 feet
C)
1400 feet
D)
1600 feet
139)
During the first seconds, the height h in feet of a baseball after t seconds is given by h = – 16t2+119t +3.1. Use
the graph below to estimate the height of the ball after 4 seconds.
A)
323 feet
B)
223 feet
C)
479 feet
D)
179 feet
17
140)
During the first seconds, the height h in feet of a baseball after t seconds is given by h = – 16t2+99t +4.4. Use the
graph below to estimate the height of the ball after 3 seconds.
A)
157 feet
B)
139 feet
C)
193 feet
D)
-144 feet
18
141)
The average weight W (in ounces) of a fish caught in a certain lake is given by W =0.001x3+0.03x2+1.1, where
x is the length in inches. Use the graph below to estimate the weight of a fish from the lake that is 14 inches long.
A)
13 ounces
B)
11 ounces
C)
9 ounces
D)
7 ounces
19
142)
The weight W (in ounces) of a fish caught in a certain lake is given by W =0.001x3+0.03x2+1.2, where x is the
length in inches. Use the graph below to find the approximate value of 0.001x3+0.03x2+1.2 for x =14.
A)
13 ounces
B)
11 ounces
C)
9 ounces
D)
7 ounces
20