1. How is five hundred twelve and sixteen thousandths written in decimal form?
a. 512.016
b. 512.16
c. 512,160
d. 51.216
e. 512.0016
2. 4
ᎏ
1
3
ᎏ
− 1
ᎏ
3
4
ᎏ
= ?
f. 2
ᎏ
1
7
2
ᎏ
g. 3
ᎏ
1
5
2
ᎏ
h. 3
ᎏ

a. 0.119
b. 0.095
c. 0.0595
d. 0.024
e. 0.092
– ACT MATH TEST PRACTICE–
165
6. Which of the following is NOT the graph of a function?
f.
g.
h.
i.
j.
– ACT MATH TEST PRACTICE–
166
7. 4.6 × 10
5
= ?
a. 4.60000
b. 0.000046
c. 4,600,000
d. 460,000
e. 0.0000046
8. What is the value of x
5
for x = 3?
f. 15
g. 243
h. 125
i.

d. −3
e.
ᎏ
3
7
ᎏ
– ACT MATH TEST PRACTICE–
167
12. The perimeter of a rectangle is 20 cm. If the width is 4 cm, find the length of the rectangle.
f. 6 cm
g. 16 cm
h. 5 cm
i. 12 cm
j. 24 cm
13. Find the area of the figure below.
a. 79 square inches
b. 91 square inches
c. 70 square inches
d. 64 square inches
e. 58 square inches
14. Five cans of tomatoes cost $6.50. At this rate, how much will 9 cans of tomatoes cost?
f. $13.00
g. $11.70
h. $1.30
i. $11.90
j. $12.40
15. For all x ≠ 0,
ᎏ
3
2

+
5x
3x
ᎏ
d.
ᎏ
15
2
+ x
ᎏ
e.
ᎏ
5
1
x
ᎏ
10 in
7 in
7 in
3 in
– ACT MATH TEST PRACTICE–
168
16. Which inequality best represents the graph below?
f. −1.5 > x > −1
g. x ≤ 0
h. −0.5 > x > 0
i. −1.5 < x < 0
j. −1.5 ≤ x ≤ 0
17. Simplify −(6x
4

c. x < −4
d. −x ≤−4
e. −x < 4
20. Simplify ͙
3
16x
5
y
4
ෆ
.
f. 2xy͙
3
2x
2
y
ෆ
g. 8x
2
y
h. 8xy͙
3
2
ෆ
i. 2xy͙
3
xy
ෆ
j. 4x
2

23. If 5k = 9m − 18, then m = ?
a. 5k + 18
b.
ᎏ
5
9
ᎏ
k + 2
c. −9 + 5k
d. 5k + 9
e. 9k + 18
24. What is the solution set for 5x − 7 = 5(x + 2)?
f. {2}
g. {7}
h. no solution
i. all real numbers
j. all positive numbers
25. Simplify
ᎏ
4x
2
+
x +
11
3
x − 3
ᎏ
for all x ≠−3.
a. 3x
2

b. 9
c.
ᎏ
2
3
ᎏ
d. 4
e.
ᎏ
1
2
ᎏ
28. Simplify
ᎏ
x
x
2
−
−
3
9
ᎏ
.
f. x − 12
g. x − 6
h. x + 3
i. −x
2
− 6
j. x − 3

f. −12x + 4y = 16
g. 9x − 3y = −15
h. 2y = 4x + 8
i. 7y = 14x + 7
j. 3x − 9y = 14
31. At what point do the lines x = 9 and 3x + y = 4 intersect?
a. (3, 9)
b. (
ᎏ
5
3
ᎏ
,9)
c. (−20, −9)
d. (9, −23)
e. (9, 4)
32. Which of the numbers below is the best approximation of (͙37
ෆ
)(͙125
ෆ
)?
f. 52
g. 4,600
h. 150
i. 66
j. 138
33. What is the solution set of the equation x
2
− 4x − 4 = 2x + 23?
a. {−4, 4}

ᎏ
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172
35. What is
ᎏ
1
2
ᎏ
% of 90?
a. 45
b. 0.045
c. 4.5
d. 0.45
e. 450
36. Between which two integers does ͙41
ෆ
lie?
f. 5 and 6
g. 8 and 9
h. 4 and 5
i. 7 and 8
j. 6 and 7
37. Mike has 12 bags of shredded cheese to use to make pizzas. If he uses
ᎏ
3
4
ᎏ
of a bag of cheese for each
pizza, how many pizzas can he make?
a. 12

ᎏ
d.
ᎏ
3
7
ᎏ
e.
ᎏ
1
6
ᎏ
– ACT MATH TEST PRACTICE–
173
40. What is the product of 5 × 10
−4
and 6 × 10
8
?
f. 11 × 10
4
g. 3 × 10
4
h. 1.1 × 10
5
i. 3 × 10
5
j. 5.6 × 10
−4
41. What is the sine of angle B in the triangle below?
a.

g.
ᎏ
3
4
ᎏ
h.
ᎏ
4
3
ᎏ
i.
ᎏ
6
3
ᎏ
j.
ᎏ
5
3
ᎏ
4
5
3
x°
A
B
8
6
C
– ACT MATH TEST PRACTICE–

f. ͙13
ෆ
g. ͙5
ෆ
h. ͙65
ෆ
i. ͙97
ෆ
j. 13
4
9
3
4
3
– ACT MATH TEST PRACTICE–
175
47. A circular lid to a jar has a radius of 3
ᎏ
1
2
ᎏ
inches. Find the area of the lid.
a.
ᎏ
1
4
2
9
ᎏ
π sq in

− 1?
f. 2
g. 16
h. 64
i. ͙5
ෆ
j. 0
49. The senior class at Roosevelt High has 540 students. Kristen won the election for class president with
60% of the vote. Of that 60%, 75% were female. Assuming that the entire senior class voted, how many
females voted for Kristen?
a. 195
b. 405
c. 324
d. 227
e. 243
50. If cosθ =
ᎏ
1
6
7
ᎏ
and tanθ =
ᎏ
5
6
ᎏ
, then sinθ = ?
f.
ᎏ
1

1
3
ᎏ
d. 27
e. 81
– ACT MATH TEST PRACTICE–
176
52. In a right triangle, the two non-right angles measure 7x and 8x. What is the measure of the smaller
angle?
f. 15°
g. 60°
h. 30°
i. 48°
j. 42°
53. What is the length of the missing leg in the right triangle below?
a. ͙181
ෆ
b. 1
c. ͙19
ෆ
d. 4
e. ͙21
ෆ
54. The length of a rectangle is twice the width. If the perimeter of the rectangle is 72 feet, what is the
length of the rectangle?
f. 12 feet
g. 6 feet
h. 36 feet
i. 48 feet
j. 24 feet

9
– ACT MATH TEST PRACTICE–
177
56. Three of the vertices of a square are (−2, 3), (5, 3), and (−2, −4). What is the length of a side of the
square?
f. 5
g. 4
h. 3
i. 7
j. 8
57. Which of the following lines is perpendicular to y = 3x + 1?
a. 6x + 5 = 2y
b. 4 + y = 3x
c. −9y = −3 + 2x
d. 2x + y = 4
e. 3y + x = 5
58. Which statement best describes the lines −2x + 3y = 12 and −60 + 15y = 10x?
f. the same line
g. parallel
h. skew
i. perpendicular
j. intersect at one point
59. What is the midpoint of X
ෆ
Y
ෆ
if X(−4, −2) and Y(3, 8)?
a. (−7, 6)
b. (−0.5, 3)
c. (−1, 6)

ᎏ
h.
ᎏ
3
x
x
+
+
3
5
ᎏ
i.
ᎏ
3x
2
−
1
3
5
x
x
+20
ᎏ
j.
ᎏ
x
2
+
1
4

8
3
x
5
ᎏ
e.
ᎏ
8
1
x
5
ᎏ
62. If 4x = 3y + 15 and 2y − x = 0, find x.
f. 6
g. 3
h. 2
i. −1
j. 5
63. Simplify 36
ᎏ
−
2
3
ᎏ
.
a. −6
b. −216
c. −12
d.
ᎏ

f. 99°
g. 39°
h. 21°
i. 121°
j. 106°
67. Find the radius of the circle with center (4, −2) that is tangent to the y-axis.
a. 2
b. 6
c. 1
d. 4
e. 10
68. Find the area, in square units, of the circle represented by the equation (x − 5)
2
+ (y − 2)
2
= 36.
f. 6π
g. 36π
h. 25π
i. −2π
j. 4π
69. m∠ABC = 120° and m∠CDE = 110°. Find the measure of ∠BCD.
a. 70°
b. 50°
c. 60°
d. 150°
e. 40°
AB
C
D

a. 9
b. 0
c. −90
d. −2
e. −9
72. A triangle with angles measuring 30°, 60°, and 90° has a smallest side length of 7. Find the length of
the hypotenuse.
f. 14
g. 7͙3
ෆ
h. 2
i. 12
j. 18
73. The Abrams’ put a cement walkway around their rectangular pool. The pool’s dimensions are 12 feet
by 24 feet and the width of the walkway is 5 feet in all places. Find the area of the walkway.
a. 748 square feet
b. 288 square feet
c. 460 square feet
d. 205 square feet
e. 493 square feet
74. Triangle XYZ is an equilateral triangle. Y
ෆ
W
ෆ
is an altitude of the triangle. If Y
ෆ
X
ෆ
is 14 inches, what is the
length of the altitude?

͙
10
11
ෆ
ᎏ
g.
ᎏ
5
4
ᎏ
h.
ᎏ
1
9
0
ᎏ
i.
ᎏ
1
1
0
9
0
ᎏ
j.
ᎏ
͙
10
19
ෆ

ᎏ
= 1
g. 25x
2
+ 9y
2
= 1
h.
ᎏ
2
x
5
2
ᎏ
−
ᎏ
y
9
2
ᎏ
= 1
i.
ᎏ
2
y
5
2
ᎏ
+
ᎏ

f. {x | x ≠ 0}
g. Ø
h. All real numbers
i. {x | x ≠ 3}
j. {x | x ≠−4 and x ≠ 1}
(0,3)
(5,0)
(0,−3)
(−5,0)
– ACT MATH TEST PRACTICE–
183

Practice Questions Answers and Explanations
1. Choice a is correct. The word and indicates a decimal point. Therefore, the decimal point should go
after five hundred twelve and before sixteen thousandths. The number 16 must end in the thousandths
place, which is three digits to the right of the decimal. The correct answer is 512.016.
Choice b is “five hundred twelve and sixteen hundredths.”
Choice c is “five hundred twelve thousand, one hundred sixty.”
Choice d is “fifty one and two hundred sixteen thousandths.”
Choice e is “five hundred twelve and sixteen ten thousandths.”
2. Choice f is correct. First, change the fractional parts of the problem to have the common denominator
of 12.
4
ᎏ
1
4
2
ᎏ
− 1
ᎏ

7
2
ᎏ
.
3. Choice b is correct. The correct order of operations must be used to simplify the expression. You may
remember this as PEMDAS or “Please Excuse My Dear Aunt Sally.” The P stands for parentheses or any
grouping symbol. Absolute value is a grouping symbol, so it will be done first.
|−8| + 4 × 2
3
=
8 + 4 × 2
3
Next, perform the exponent part.
8 + 4 × 8
Then, the multiplication.
8 + 32
Last, the addition.
The final answer is 40.
4. Choice g is correct. This problem can be approached a couple of different ways. The simplest way
might be to look at multiples of 4 and 5 until the multiples add to 18. If both 4 and 5 are multiplied by
2, they become 8 and 10. 8 plus 10 is 18. Therefore, there are 8 boys and 10 girls in the class.
The problem can also be done with an equation.
4x + 5x = 18
When solved, x = 2. Multiply 4 by 2 to find that there are 8 boys.
– ACT MATH TEST PRACTICE–
184
5. Choice c is correct. To find the median, place the numbers in order from least to greatest and find the
middle number. In order, the numbers are:
0.008, 0.024, 0.024, 0.095, 0.1, 0.3
Since there are an even number of numbers, there are two middle numbers (0.024 and 0.095). Take the

× 3 × 7.
84
2
42
76
3
2
0, 3, 8, 15, 24, . . .
+3 +5 +7 +9 +11
4.60000. = 460,000
– ACT MATH TEST PRACTICE–
185
11. Choice c is correct. To easily see the slope, change the equation into the form y = mx + b. The equation
is then y =
ᎏ
7
3
ᎏ
x + 3. The coefficient of x is the slope.
ᎏ
7
3
ᎏ
is the answer.
12. Choice f is correct. The perimeter is twice the width plus twice the length: P = 2w + 2l. Insert 20 for P
and 4 for w, then solve for l.
20 = 2(4) + 2l
20 = 8 + 2l
20 − 8 = 2l
12 = 2l

9
.50
ᎏ
x = $11.70
15. Choice c is correct. Find a common denominator (15x). Multiply the first fraction by
ᎏ
5
5
ᎏ
and the second
fraction by
ᎏ
3
3
x
x
ᎏ
. The result is
ᎏ
1
1
5
0
x
ᎏ
+
ᎏ
1
3
5

3
)
2
).
When you have a power to a power you multiply the exponents. Thus, −(36x
8
y
6
). Apply the negative
for the final answer of − 36x
8
y
6
.
10 in
7 in
4 in
3 in
30
28
– ACT MATH TEST PRACTICE–
186
18. Choice h is correct. Use substitution to solve for x and y. First, solve the second equation for y.
y = 4x − 47
Next, substitute the above value for y into the first equation and solve for x.
2x + 3(4x − 47) = 55
2x + 12x − 141 = 55
14x − 141 = 55
14x = 196
x = 14

y
3
y
ෆ
Any exponent divisible by 3 is a cube root. Take out the perfect cubes and leave everything else under
the radical.
2xy͙
3
2x
2
y
ෆ
is the answer.
21. Choice c is correct. Substitute the value 63° for C.
F =
ᎏ
5
9
ᎏ
(63) + 32
F = 35 + 32
F = 67
The answer is 67°F.
– ACT MATH TEST PRACTICE–
187
22. Choice h is correct. The equation is quadratic, so there are two ways to solve it. First, try to factor the
left-hand side of the equation. Since it is factorable, solve the equation using factoring.
x
2
+ 8x + 15 = 0

2
6
ᎏ
= −3 x =
ᎏ
−
2
10
ᎏ
= −5
The solution set is {−5, −3}.
23. Choice b is correct. Solve the equation for m using inverse operations.
5k = 9m − 18
5k + 18 = 9m
ᎏ
5k +
9
18
ᎏ
= m
Since this answer does not appear as one of the choices, you must determine if any of the choices are
equivalent to it. If you divide each of the numerator terms by 9 you get
ᎏ
5
9
ᎏ
k + 2 = m, which is choice b.
24. Choice h is correct. Solve the equation by moving all x terms to one side.
5x − 5x − 7 = 5x − 5x + 10
− 7 = 10

−b ± ͙b
2
− 4a
ෆ
c
ෆ
ᎏᎏ
2a
– ACT MATH TEST PRACTICE–
188
26. Choice f is correct. Subtract the numbers in y from the corresponding numbers in x.
[]
=
[]
27. Choice b is correct. log
3
x = 2 is equivalent to 3
2
= x. Therefore, x = 9.
28. Choice h is correct. Factor the numerator. Use the denominator as a clue. Most likely, one of the fac-
tors in the numerator will be the same as the denominator. Also, notice that the numerator is the dif-
ference of two squares.
ᎏ
(x −
x
3)
−
(x
3
+3)

ෆ
d = ͙(−1)
2
+
ෆ
(−4)
2
ෆ
d = ͙1 + 16
ෆ
d = ͙17
ෆ
To use the Pythagorean theorem (which is what the distance formula is derived from), draw the seg-
ment on a coordinate plane and create a right triangle where A
ෆ
C
ෆ
is the hypotenuse.
The legs of the right triangle are 1 and 4. Use the Pythagorean theorem to find the length of the
hypotenuse.
a
2
+ b
2
= c
2
1
2
+ 4
2