Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find all the factors of the number.
1)
30
A)
1, 2, 3, 5, 6, 10, 20, 30
B)
1, 2, 3, 5, 6, 10, 15, 30
C)
5, 6, 10, 30
D)
1, 5, 6, 30
2)
110
A)
1, 2, 5, 10, 11, 22, 110
B)
1, 2, 4, 5, 10, 11, 22, 55, 110
C)
2, 5, 10, 11, 55, 110
D)
1, 2, 5, 10, 11, 22, 55, 110
3)
196
A)
1, 2, 3, 4, 7, 14, 49, 98, 196
B)
1, 2, 4, 7, 14, 21, 28, 49, 98, 196
C)
1, 2, 4, 7, 14, 28, 49, 98, 196
D)
1, 2, 7, 49, 196
Find the prime factorization of the number.
4)
12
A)
B)
C)
4·3
D)
5)
396
A)
B)
C)
3·3·3·3·11
D)
6)
30
A)
B)
C)
2 · 2 ·5
D)
7)
126
A)
B)
C)
2·2·3·3·7
D)
8)
185
A)
B)
C)
5·37
D)
9)
44
A)
B)
C)
2·2·2
D)
Find the LCM using prime factorization.
10)
60, 90
A)
B)
C)
360
D)
11)
45, 28, 150
A)
B)
C)
6300
D)
12)
48, 162, 27
A)
B)
C)
1296
D)
13)
56, 96
A)
B)
C)
1344
D)
14)
60, 20, 50
A)
B)
C)
100
D)
15)
20, 30, 40, 60
A)
B)
C)
90
D)
Solve the problem.
16)
At a national computer show, two software companies continuously run videos showing their products.
Company A’s video repeats every 33 minutes, while Company B‘s video repeats every 21 minutes. If both
companies begin the videos at 1:00 P.M. when the show opens, how many minutes will elapse before they are in
sync again?
A)
B)
C)
154 minutes
D)
17)
Tom and Larry are food inspectors at a cookie making company. Tom tests every 20th batch of dough for fat
percentage. Larry tests every 28th batch of dough for carbohydrate percentage. If they both start working at the
same time, which batch will be the first that they both test?
A)
B)
C)
70
D)
18)
Cory and Melissa are racing electronic cars around a circular track. They begin at the same time going in the
same direction. Cory’s car completes a revolution in 35 seconds, while Melissa’s car completes a revolution in 30
seconds. How long will it take them before both cars reach the starting point again simultaneously?
A)
B)
C)
420 seconds
D)
19)
Robert has built a mechanical model solar system with three balls representing planets at the ends of rods
attached to the center representing the sun. The planets are aligned when he turns on the motor. The innermost
planet makes a revolution in 12 seconds, the middle planet makes a revolution in 30 seconds, and the outermost
planet makes a revolution in 42 seconds. After how many seconds will the planets be aligned again?
A)
B)
C)
210 seconds
D)
20)
A cereal manufacturer uses three large overhead bins to hold the three ingredients in one of its cereal mixes. Bin
A delivers a premeasured quantity of dried fruit every 15 minutes, bin B delivers raisins every 21 minutes, and
bin C delivers flakes every 33 minutes. If they start the morning shift at the same time, how long before they
deliver their ingredients at the same time again?
A)
B)
C)
2310 minutes
D)
Write an equivalent expression using the indicated name for 1.
21)
13
15 (Use 3
3 for 1.)
A)
B)
C)
15
39
D)
22)
15
4 (Use 40
40 for 1.)
A)
B)
C)
15
160
D)
Find an equivalent expression with the given denominator.
23)
5
15 (Denominator: 75)
A)
B)
C)
5
75
D)
24)
16
4 (Denominator: 9)
A)
B)
C)
64
8
D)
Simplify.
25)
6
14
A)
B)
C)
13
5
D)
26)
17
34
A)
B)
C)
33
16
D)
27)
56
160
A)
B)
C)
7
20
D)
28)
123
180
A)
B)
C)
179
122
D)
29)
34
460
A)
B)
C)
153
11
D)
30)
420
460
A)
B)
C)
459
419
D)
31)
350
25
A)
B)
C)
14
D)
32)
8· x
16 · x
A)
B)
C)
2x
D)
33)
20 · x
6· x
A)
B)
C)
3x
10
D)
Perform the indicated operation and, if possible, simplify.
34)
3
7+2
7
A)
B)
C)
5
14
D)
35)
6
16 +1
16
A)
B)
C)
5
16
D)
36)
6
7+3
4
A)
B)
C)
9
28
D)
37)
10
13 +5
8
A)
B)
C)
5
7
D)
38)
5
48 +6
18
A)
B)
C)
7
16
D)
39)
3
5–1
5
A)
B)
C)
3
5
D)
40)
7
22 –6
22
A)
B)
C)
1
22
D)
41)
4
7–
1
2
A)
B)
C)
14
D)
42)
7
9–
3
7
A)
B)
C)
63
22
D)
43)
4
5–
2
3
A)
B)
C)
4
225
D)
44)
5
8·
1
6
A)
B)
C)
3
7
D)
45)
3
7·
2
9
A)
B)
C)
2
21
D)
46)
5
9·
7
10
A)
B)
C)
19
29
D)
47)
13
17 ·
6
13
A)
B)
C)
102
169
D)
48)
7
8·
7
8
A)
B)
C)
49
64
D)
49)
8
5·
5
4
A)
B)
C)
13
9
D)
50)
13
3·3
13
A)
B)
C)
13
3
D)
51)
2
3÷
1
5
A)
B)
C)
2
3
D)
52)
14
19 ÷
8
17
A)
B)
C)
7
76
D)
53)
45
8÷5
A)
B)
C)
8
9
D)
54)
3÷9
4
A)
B)
C)
4
3
D)
55)
2
17
2
11
A)
B)
C)
9
17
D)
56)
63
16 ÷28
A)
B)
C)
9
64
D)
Write exponential notation.
57)
4·4·4·4·4·4
A)
B)
C)
45
D)
58)
7×7×7×7
A)
B)
C)
28
D)
59)
6×6×6×6×6
A)
B)
C)
30
D)
60)
6·6·6
A)
B)
C)
36
D)
Evaluate.
61)
44
A)
B)
C)
16
D)
62)
112
A)
B)
C)
22
D)
63)
19.62
A)
B)
C)
3841.6
D)
64)
(0.05)3
A)
B)
C)
0.000216
D)
65)
5
8
2
A)
B)
C)
25
8
D)
66)
3000 ×(1.06)3
A)
B)
C)
10,112,400
D)
A
Calculate.
67)
3+ 29 ×8+29
A)
B)
C)
264
D)
C
68)
13 + (4)(15) –23
A)
B)
C)
232
D)
A
69)
30(19) + 23(10)
A)
B)
C)
82
D)
A
70)
16 + 42 ×3+20
A)
B)
C)
84
D)
C
71)
(6 + 4)[8+ (8+ 4)]
A)
B)
C)
26
D)
D
72)
4(2 + 6) + 4 ×5
4(5 – 1)
A)
B)
C)
90
19
D)
D
73)
5(7 – 6) + 5 ×7
5(2 – 1)
A)
B)
C)
8
D)
C
74)
5[4 + 8(5 + 4)]
A)
B)
C)
536
D)
B
9
D
75)
24 ÷6+15 ÷5
A)
B)
C)
3.8
D)
76)
9·3– (8–3) ÷5– (2–7)
A)
B)
C)
31
D)
Find the mean.
77)
81, 91, 67, 87, 64
A)
B)
C)
65
D)
78)
75, 84, 62, 80, 59, 84, 60
A)
B)
C)
63
D)
79)
4.8, 5.6, 2.6, 5.6, 2.4
A)
B)
C)
3.5
D)
80)
$81.74, $95.02, $93.15, $98.35, $81.74
A)
B)
C)
$75.00
D)
Find the median.
81)
2, 7, 20, 22, 39, 41, 47
A)
B)
C)
39
D)
82)
10, 28, 37, 48, 68, 75, 84
A)
B)
C)
48
D)
83)
66, 57, 219, 148, 294, 241, 236
A)
B)
C)
219
D)
84)
14, 33, 243, 245, 421, 438
A)
B)
C)
245
D)
85)
10, 6, 23, 15, 25, 45, 36, 30
A)
B)
C)
23.5
D)
86)
8.1, 5.1, 2.5, 6.5
A)
B)
C)
2.5
D)
87)
$33.15, $14.96, $48.58, $38.35, $14.96
A)
B)
C)
$48.58
D)
Find any modes that exist.
88)
5, 9, 27, 3, 2, 8, 39, 1, 4, 16
A)
B)
C)
8
D)
89)
20, 42, 46, 42, 49, 42, 49
A)
B)
C)
46
D)
90)
70, 25, 70, 13, 25, 29, 56, 70
A)
B)
C)
70, 25
D)
91)
108, 150, 156, 108, 188, 199, 162
A)
B)
C)
86
D)
92)
4.8, 5.1, 3.1, 5.1, 2.9
A)
B)
C)
4.2
D)
93)
$95, $35, $32, $35, $29, $95
A)
B)
C)
$35
D)
Solve the problem.
94)
The five sales people at Southwest Appliances earned commissions last year of $13,000, $23,000, $39,000,
$18,000, and $35,000. Find the mean commission.
A)
B)
C)
$25,600
D)
95)
The Wellspring Company has a fleet of seven trucks which get gas mileages of 16, 9, 17, 12, 19, 11, and 22 miles
per gallon, respectively. What is the mean gas mileage for the fleet? Round your answer to the nearest mpg.
A)
B)
C)
16 mpg
D)
96)
Some players are thinking about quitting the company softball team. Their batting averages are 0.204, 0.302,
0.220, 0.292, 0.207, 0.286, and 0.293, respectively. What is the mean batting average of these players? Round
your answer to the nearest thousandth.
A)
B)
C)
0.235
D)
97)
Jeremy’s car gets 275 miles of highway driving on 11 gallons of gasoline. What is the mean number of miles
expected per gallon – – that is, what is its gas mileage?
A)
B)
C)
26 mpg
D)
98)
Anthony wanted to buy a particular kind of cheese. He checked in five different stores and found the following
prices per pound:
$6.25, $5.45, $6.60, $5.95, and $4.95.
What was the mean price per pound?
A)
B)
C)
$5.84
D)
99)
The following prices per pound of ocean perch were found at seven supermarkets:
$7.69, $8.59, $8.49, $8.69, $7.69,$8.39, $7.49
What is the median price per pound?
A)
B)
C)
$8.69
D)
100)
The following is a list of heights, in inches, of six people:
Susan 64
Umar 72
Mark 73
Dorota 64
Mike 74
Gina 63
What is the median height?
A)
B)
C)
64 inches
D)
101)
The following prices per pound of ocean perch were found at seven supermarkets:
$8.99, $9.89, $9.79, $9.99, $8.99,$9.69, $8.79
What is the mode?
A)
B)
C)
$9.99
D)
102)
The following is a list of heights, in inches, of six people:
Susan 64
Umar 75
Mark 74
Dorota 64
Mike 76
Gina 63
What is the mode?
A)
B)
C)
69.5 inches
D)
Use synthetic division to divide.
103)
(x3–4x2+2x – 7) ÷ (x + 4)
A)
x3–4x2+34x –143
B)
x2–8x +18 +
-79
x + 4
C)
x2–8x +34 +
-143
x + 4
D)
x2–8x +34 +
-143
(x3–4x2+2x – 7)
12
104)
(5x2– 26x – 63) ÷(x – 7)
A)
B)
C)
x + 9
D)
105)
(5m3+ 22m2– 6m + 45) ÷ (m + 5)
A)
B)
C)
m2+ 4m + 5
D)
106)
(6r3– 50r2– 32r – 36) ÷ (r – 9)
A)
B)
C)
r2+ 4r + 4
D)
107)
(x4– 16) ÷ (x + 2)
A)
B)
C)
x3+ 2x2+ 4x + 8
D)
108)
(x4+81) ÷ (x –3)
A)
x3+3x2+9x +27 +81
x –3
B)
x3–3x2+9x –27 +162
x –3
C)
x3+3x2+9x +27
D)
x3+3x2+9x +27 +162
x –3
109)
(x5– 243) ÷ (x – 3)
A)
x4– 3x3+ 9x2– 27x + 81
B)
x4+ 3x3+ 3x2+ 3x + 3
C)
x4+ 3x3+ 9x2+ 27x + 81
D)
x4+ 3x3+ 9x2+ 27x + 81 +
–243
x – 3
110)
(y6+3) ÷ (y – 1)
A)
y5–y4+y3–y2+ y – 1 +4
y – 1
B)
y5+y4+y3+y2+ y + 1
C)
y5–y4+y3–y2+ y – 1
D)
y5+y4+y3+y2+ y + 1 +4
y – 1
111)
(y9+ 1) ÷ (y + 1)
A)
y8+y7+y6+y5+y4+y3+y2+ y + 1
B)
y8+y7+y6+y5+y4+y3+y2+ y + 1 +2
y + 1
C)
y8–y7+y6–y5+y4–y3+y2– y + 1 +
–2
y + 1
D)
y8–y7+y6–y5+y4–y3+y2– y + 1
13
Evaluate.
112)
7 5
5 7
A)
B)
C)
-24
D)
113)
6 6
9 4
A)
B)
C)
30
D)
114)
12
23
A)
B)
C)
–1
D)
115)
9 7 5
4 7 8
5 9 9
A)
B)
C)
-608
D)
116)
-5 4 5
4-2 -3
-5 -3 5
A)
B)
C)
–155
D)
117)
3 2 3
5 5 3
5 4 3
A)
B)
C)
6
D)
118)
5 2 5
1 5 4
4 1 4
A)
B)
C)
9
D)
119)
4-1 9
0 2 6
0 0 -9
A)
B)
C)
66
D)
120)
1 0 0
8-6 0
-6 9 3
A)
B)
C)
–18
D)
121)
0 0 5
9-9 5
0 1 1
A)
B)
C)
–45
D)
Solve using Cramer‘s rule.
122)
6x + 4y =-18
2x + y =-7
A)
B)
C)
(5, -3)
D)
123)
3x + 4y =23
4x + 2y =24
A)
B)
C)
(5, 2)
D)
124)
2x + 2y =18
3x – 2y =17
A)
B)
C)
(7, 2)
D)
15