Compass Math Practice
Questions compiled from http://www.act.org/compass/
1.
What is the average (arithmetic mean) of 8, 7, 7, 5, 3, 2, and 2?
4
7
5
4
6
6
4
7
5
4
6
5
A. 3
B.
C.
D.
E.
2.
Find the mean value for the following 91, 88, 84, 79, 73, 65
3.
What is the mean for -2, 6, -4, -3, 9, 13, -5
4.
What is the median of the numbers 11, 10, 13, 11, 12, 16, 14
5.
What is the median of the numbers 36, 25, 32, 17, 49, 28, 31, 44
6.
Find the mode of the following integers. 8, 11, 9, 14, 9, 15, 18, 6, 9, 11
7.
What is the mode of the integers 6, 3, 7, 4, 3, 8, 5, 7, 6, 2, 3, 5
8.
Adam tried to compute the average of his 7 test scores. He mistakenly divided the
correct sum of all of his test scores by 6, which yielded 84. What is Adam’s correct
average test score?
A.
B.
C.
D.
E.
9.
A total of 50 juniors and seniors were given a mathematics test. The 35 juniors
attained an average score of 80 while the 15 seniors attained an average of 70.
What was the average score for all 50 students who took the test?
A.
B.
C.
D.
E.
10.
70
72
84
96
98
73
75
76
77
78
54  6 2  4  6 = ?
A.
B.
C.
D.
E.
6
24
27
30
51
11.
2
Evaluate: 7  18  3  4
12.
2
Evaluate: 8  4 4  5  12
13.
The lowest temperature on a winter morning was –8°F. Later that same day the
temperature reached a high of 24°F. By how many degrees Fahrenheit did the
temperature increase?

A.
B.
C.
D.
E.
3°
8°
16°
24°
32°

14.
15.
Write the improper fraction,
3 2 1 2
If        is calculated and the answer reduced to simplest terms, what is
4 3 2 3
the denominator of the resulting fraction?
A.
B.
C.
D.
E.
16.
24
12
6
4
3
1 2 3 4 5
     
2 3 4 5 6
A.
B.
C.
D.
E.
1
16
17
27
13
18
7
9
5
6
2
17.
38
as a mixed number.
7
2 1 1
    =?
3 9 3
18.
How many yards of material from a 24-yard length of cloth remain after 3 pieces,
1
1
each 3 yards long, and 5 pieces, each 2 yards long, are removed?
2
4
1
4
1
B. 4
4
5
C. 4
6
A. 2
1
4
5
E. 10
6
D. 10
19.
0.537 + 15 + 7.9 = ?
20.
0.23 × 1.7 = ?
21.
3.5 ÷ .5 = ?
22.
Four students about to purchase concert tickets for $18.50 for each ticket discover
that they may purchase a block of 5 tickets for $80.00. How much would each of
the 4 save if they get a fifth person to join them, and the 5 people equally divide
the price of the 5-ticket block?
A.
B.
C.
D.
E.
$1.50
$2.50
$3.13
$10.00
$12.50
23.
Mr. Brown went grocery shopping to buy meat for his annual office picnic. He
3
1
bought 7 pounds of hamburger, 17.85 pounds of chicken, and 6 pounds of
4
2
steak. How many pounds of meat did Mr. Brown buy?
A.
B.
C.
D.
E.
32.10
31.31
26.25
22.10
21.10
24.
What is 30% of 90?
25.
24 is what percent of 30?
26.
18 is 60% of what?
27.
Philip charged $400 worth of goods on his credit card. On his first bill, he was not
charged any interest, and he made a payment of $20. He then charged another
$18 worth of goods. On his second bill a month later, he was charged 2% interest
on his entire unpaid balance. How much interest was Phillip charged on his second
bill?
A.
B.
C.
D.
E.
28.
$8.76
$7.96
$7.60
$7.24
$6.63
On a math test, 12 students earned an A. This number is exactly 25% of the total
number of students in the class. How many students are in the class?
A.
B.
C.
D.
E.
15
16
21
30
48
29.
Rico left a $5.00 tip for dinner, which cost $25.00. What percent of the total bill
did he leave as a tip?
30.
x y yz x z  = ?
31.
3xy 
32.
Simplify.
10 x 3 y 5
5x 4 y 2
33.
Simplify.
2 xy4
6x4 y5
34.
 2 xz 2 

Simplify. 
3 
 3y 
35.
25  16 = ?
4
3
3 2
2 2
=?
4
36.
3 57 5 = ?
37.
48  75 = ?
38.
39
40.
41.
2 8 = ?
3 57 3
30
=?
6
In scientific notation: 20,000 + 3,400,000 = ?
A.
B.
C.
D.
E.
42.
3.42  10
6
3.60  10
7
3.42  10
7
3.60  10
12
3.60  10
6
Write 796.5 in scientific notation.
43.
Simplify. (1.8 ×10 )(3 ×10 )
44.
Simplify. (3.2 ×10 )(5.1 ×10 )
45.
(1.5 ×106 )
Simplify.
(3 ×103 )
46.
(8.4 ×108 )
Simplify.
(2 ×103 )
4
2
3
3
47.
In a bag of red and green marbles, the ratio of red marbles to green marbles is
3:4. If there are 40 green marbles, how many red marbles are there?
48.
Ron reduced the size of a rectangle to a height of 2 in. What is the new width if it
was originally 24 inches wide and 12 inches tall?
49.
If you can buy 3 bottles of sports drink for $7, how much would 12 bottles cost?
50.
If someone walked 3 miles in 2 hours, how far would they travel in 8 hours?
24 8

x 5
51.
Solve for x.
52.
What value of x solves the following proportion?
9 x

6 8
1
3
3
B. 6
4
A. 5
C. 10
1
2
D. 11
E. 12
53.
If the total cost of x apples is b cents, what is a general formula for the cost, in
cents, of y apples?
A.
B.
C.
D.
E.
54.
b
xy
x
by
xy
b
by
x
bx
y
If x = -3, what is the value of
A. -4
B. -2
C. 2
2
D. 3
3
E. 5
x2 1
x 1
55.
If x = -1 and y = 2, what is the value of the expression 2x 3 −3xy
A.
B.
C.
D.
E.
8
4
-1
-4
-8
56.
Evaluate  x  3  4 x for x = -2
57.
Evaluate
58.
Doctors use the term maximum heart rate (MHR) when referring to the quantity
found by starting with 220 beats per minute and subtracting 1 beat per minute for
each year of a person’s age. Doctors recommend exercising 3 or 4 time each week
for at least 20 minutes with your heart rate increased from its resting heart rate
(RHR) to its training heart rate (THR), where
2
3x 2 y 3
for x = 2, y = -1, z = -2
z2
THR = RHR + .65(MHR − RHR)
Which of the following is closest to the THR of a 43-year-old person whose RHR is
54 beats per minute?
A.
B.
C.
D.
E.
59.
197
169
162
134
80
An airplane flew for 8 hours at an airspeed of x miles per hour (mph), and for 7
more hours at 325 mph. If the average airspeed for the entire flight was 350 mph,
which of the following equations could be used to find x?
A.
B.
C.
D.
E.
x + 325
x + 7(325)
8x – 7(325)
8x + 7(325)
8x + 7(325)
=
=
=
=
=
2(350)
15(350)
350
2(350)
15(350)
60.
When getting into shape by exercising, the subject’s maximum recommended
number of heartbeats per minute h  can be determined by subtracting the
subject’s age a  from 220 and then taking 75% of that value. This relation is
expressed by which of the following formulas?
A. h  .75220  a 
B.
C.
D.
E.
h  .75220  a
h  220  .75a
.75h  220  a
220  .75h  a 
61.
Set up an equation for the area of a rectangle. The length is 3 less than twice the
width. Do not solve.
62.
Which of the following expressions represents the product of 3 less than twice x
and 2 more than the quantity 3 times x ?
2
A.  6 x  25 x  6
6 x2  5x  6
2
C. 6 x  5 x  6
2
D. 6 x  5 x  6
2
E. 6 x  13 x  6
B.
63.
Which of the following is equivalent to 3a + 4b – (–6a – 3b) ?
A.
B.
C.
D.
E.
64.
16ab
–3a + b
–3a + 7b
9a + b
9a + 7b
Simplify:
 4x
2
 

 6  3x 2  5x  3   x  4
65.
What is the sum of the polynomials 3a b  2a b
2
A. 3a b  ab  3a b
2
B. 3a b  ab  2a b
2
2 2
C. 2a b  3a b
2
2
2
2
2
2
2
2
2
2
2 2
and − ab  a b ?
D. 2a b  2a b
3 3
4
E.  3a b  2a b
2
3
4
66.
3a
67.
3x  4x 2  2 x  1 = ?
68.
2
Which if the following is a factor of x  5 x  6
A.
B.
C.
D.
E.
69.
 2b
2
=?
x  2
 x  6
x  3
 x  2
x 1
2
Which of the following is a factor of the polynomial x  x  20 ?
A.
B.
C.
D.
E.
70.
2

4
(x – 5)
(x – 4)
(x + 2)
(x + 5)
(x + 10)
2 2
2
2
Factor: 2 x y  6 xy  14 x y
71.
Factor: x  10 xy  25 y
72.
2
Factor: x  1
73.
If 2x  5  11 , then x = ?
2
A.
B.
C.
D.
E.
74.
If
A.
B.
C.
D.
E.
75.
76.
2
 21
2
–8
 11
2
–3
1
2
4  3
1
     x  1 , then x = ?
5  10 
2
2
1
-1
-2
-10
Solve for x. 4x  1  3x  2  0
The sum of 4 more than 3 times a number is 13? What is the number?
77.
A student has earned scores of 87, 81, and 88 on the first 3 of 4 tests. If the
student wants an average (arithmetic mean) of exactly 87, what score must she
earn on the fourth test?
A.
B.
C.
D.
E.
78.
85
86
87
92
93
This year, 75% of the graduating class of Harriet Tubman High School had taken
at least 8 math courses. Of the remaining class members, 60% had taken 6 or 7
math courses. What percent of the graduating class had taken fewer than 6 math
courses?
A.
B.
C.
D.
E.
0%
10%
15%
30%
45%
79.
If a computer went on sale with a 20% discount, and the sale price is $600, what
was the original price of the computer?
80.
For all x  4 , which of the following is equivalent to the expression below.
x 2  12 x  32
x4
A.
B.
C.
D.
E.
x+3
x+8
x+11
x+16
x+28
81.
r 2  5r  6
For all r  2 ,
r2  4
A.
B.
C.
D.
E.
82.
r 3
r2
r 2
r2
r 2
r 3
r 3
r 2
r 3
r2
16r 3tz 5
For all nonzero r, t, and z values, simplify
 4rt 3 z 2
4z 3
r 2t 2
4r 2 z 3
 2
t
4rz

t
 4r 4 t 4 z 7
 4r 2 t 2 z 3
A. 
B.
C.
D.
E.
83.
6
4
Simplify. x  x
84.
z2
Simplify. 3
z
85.
Saying that 4  x  9 is equivalent to saying what about x?
A.
B.
C.
D.
E.
0 x5
0  x  65
2 x3
4 x9
16  x  81
86.
What is the equation of the line that contains the points with x, y  coordinates
 3,7 and 5,1 ?
A. y  3 x  2
B. y  x  10
1
C. y   x  8
3
2
11
D. y   x 
3
4
E. y   x  4
87.
What is the slope of the line with the equation 2 x  3 y  6  0 ?
A. -6
B. -3
C. -2
2
D. 3
2
E.
3
88.
Isolate the y variable. 4 x  3 y  12
89.
Express the solution as an ordered pair.
90.
Express the solution as an ordered pair.
2x  y  3
3 x  y  8
3x  y  8
x  2y  5
91.
John gave piano lessons for $18 and banjo lessons for $25. If he made $265 from
12 clients in one day, how many of each lesson did he give?
92.
A basketball team made a total of 39 two- and three-point shots. The team had a
final score of 83. How many of each shot was made?
93.
3
x2

=?
2x  4 x  2
94.
4x3
3x 2

=?
x 2 1 x 2  2x 1
95.
2
x3
 2
=?
x  4 x  9 x  20
96.
4
3

=?
2 x  1 5x
97.
Solve for x.
3 6

1
x 3x
98.
Solve for x.
3 x 2  75
99.
Solve for x.
x2  x  6  0
100. Solve for x.
x
1

x2 x
Answer Key
1.
2.
3.
4.
C
80
2
12
43.
44.
45.
46.
5.
31.5
47. 30
6.
7.
8.
9.
10.
11.
12.
13.
14.
9
3
B
D
E
-3
-9
E
5 73
48.
49.
50.
51.
52.
53.
54.
55.
56.
5.4 10 7
1.632 10 6
510 2
4.2 105
4 inches
$28
12 miles
15
E
D
A
B
17
15. B
16. C
17. 79
57. -3
58. D
59. E
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
60.
61.
62.
63.
64.
65.
66.
67.
68.
69.
70.
A
23.437
0.391
7
B
A
27
80%
30
B
48
29. 20%
30. x 6 y 2 z 5
31. 9 x 2 y 6
2 y3
x
1
33.
3x 3 y
16 x 4 z 8
34.
81y12
32.
35.
36.
37.
38.
39.
40.
1
10 5
9 3
4
21 15
5
41. A
42. 7.965 10 2
A
Area  2w 2  3w
D
E
 7x2  6x 1
A
9a 4  12a 2 b  4b 2
3 x 2  10 x 2  11x  4
B
A
2 xyxy  3 y  7 x 
71.  x  5 y 
72. x  1x  1
73. E
2
74. C
75. -2
76. 3
77.
78.
79.
80.
81.
82.
D
B
$750
B
A
B
1
83. 2
x
85.
86.
87.
88.
E
E
D
y  43 x  4
89.  1,5
90. 3,1
91. 5 piano, 7 banjo
92. 5 three-pointers,
34 two-pointers
3
2x  4
4x2  4x
94.
3x  3
x7
95. 2
x  9 x  20
26 x  3
96.
10 x 2  5 x
93.
97. 5
98.  5
99. 3, -2
100. -1, 2