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ACT Practice
Sample ACT Math Test
Taken from www.actstudent.org
Name ___________________________
SAMPLE MATHEMATICS TEST QUESTIONS
(An actual ACT Mathematics Test contains 60 questions to be answered in 60
minutes.) You will do 40 questions in 40 minutes! Put all answers on scantron
provided.
DIRECTIONS: Solve each problem, choose
the correct answer, and then fill in the
corresponding oval on your answer
document.
Do not linger over problems that take too
much time. Solve as many as you can; then
return to the others in the time you have left
for this test.
You are permitted to use a calculator on
this test. You may use your calculator for
any problems you choose, but some of the
problems may best be done without using a
calculator.
1.
Note: Unless otherwise stated, all of the
following should be assumed.
1. Illustrative figures are NOT
necessarily drawn to scale.
2. Geometric figures lie in a plane.
3. The word line indicates a straight
line.
4. The word average indicates
arithmetic mean.
Which of the following is equivalent to (x)(x)(x)(x), for all x ?
A. 4x
B. x4
C. x + 4
D. 4 x
E. 2x2
2.
A rectangle is twice as long as it is wide. If the width of the rectangle is 3 inches, what is
the rectangle's area, in square inches?
F. 6
G. 9
H. 12
J. 15
K. 18
3.
A vendor has 14 helium balloons for sale: 9 are yellow, 3 are red, and 2 are green. A
balloon is selected at random and sold. If the balloon sold is yellow, what is the
probability that the next balloon, selected at random, is also yellow?
A.
B.
C.
D.
E.
4.
3 10 – 4 = ?
F. –30,000
G. –120
H. 0.00003
J. 0.0003
K. 0.12
5.
For all x > 0,
simplifies to:
A. x + 3
B. x + 4
C. 2(x + 3)
D. 2(x + 4)
E. 2(x + 3)(x + 4)
6.
If one leg of a right triangle is 8 inches long, and the other leg is 12 inches long, how
many inches long is the triangle's hypotenuse?
F.
G.
H.
J.
K. 4
7.
In the standard (x, y) coordinate plane, the graph of (x – 2)2 + (y + 4)2 = 9 is a circle.
What is the area enclosed by this circle, expressed in square coordinate units?
A. 3
B. 4
C. 6
D. 9
E. 16
8.
How many solutions are there to the equation x2 – 15 = 0 ?
F. 0
G. 1
H. 2
J. 4
K. 15
9.
A circle with center (–3,4) is tangent to the x-axis in the standard (x,y) coordinate plane.
What is the radius of this circle?
A. 3
B. 4
C. 5
D. 9
E. 16
10. In ABC, if A and B are acute angles, and sin A =
what is the value of cos A ?
,
F.
G.
H.
J.
K.
11. Which of the following is divisible by 3 (with no remainder)?
A. 2,725
B. 4,210
C. 4,482
D. 6,203
E. 8,105
12. A particle travels 1 10 8 centimeters per second in a straight line for 4 10 –6 seconds.
How many centimeters has it traveled?
F. 2.5 10 2
G. 2.5 10 13
H. 4 10 2
J. 4 10 –14
K. 4 10 –48
13. The triangle below is isosceles and is drawn to scale. What is the measure of N ?
A. 22°
B. 68°
C. 78°
D. 79°
E. 89°
14. In the figure below,
ABC ?
and
is 10 units long. What is the area, in square inches, of
F. 12.5
G. 25
H.
J. 50
K. Cannot be determined from the given information
15. If 7y = 2 x – 5, then x = ?
A. 5y + 5
B. y – 5
C. y + 5
D.
E.
16. Which of the following statements completely describes the solution set for 3(x – 4) = 3 x
– 12 ?
F. x = 3 only
G. x = 0 only
H. x = –12 only
J. There are no solutions for x.
K. All real numbers are solutions for x.
17. When graphed in the (x,y) coordinate plane, at what point do the lines x + y = 5 and
y = 7 intersect?
A. (–2,0)
B. (–2,7)
C. (0,7)
D. (2,5)
E. (5,7)
18.
The area of a trapezoid is h(b1 + b2), where h is the altitude, and b1 and b2 are the
lengths of the parallel bases. If a trapezoid has an altitude of 5 inches, an area of 55
square inches, and one base 13 inches long, what is the length, in inches, of its other
base?
F. 9.0
G. 16.8
H. 19.4
J. 45.0
K. 97.0
19. If you have gone 4.8 miles in 24 minutes, what was your average speed, in miles per
hour?
A. 5.0
B. 10.0
C. 12.0
D. 19.2
E. 50.0
20. If a and b are any real numbers such that 0 < a < 1 < b, which of the following must be
true of the value of ab ?
F. 0 < ab < a
G. 0 < ab < 1
H. a < ab < 1
J. a < ab < b
K. b < ab
21. In right triangle ABC below, what is the sine of A ?
A.
B.
C.
D.
E.
22. Which of the following is equal to
A. 2
B. 2
C. 4
D. 10
E. 10
?
23. In the figure below, X is on
the measure of XZY ?
, XYZ measures 45°, and AXZ measures 130°. What is
F. 45°
G. 60°
H. 85°
J. 95°
K. 105°
24. What is the slope of the line 5y = –3x + 10 ?
A. –3
B. –
C.
D. 2
E. 10
25. What is the least value of x that satisfies the equation x2 – 7x + 6 = 6 ?
F. –7
G. –6
H. –4
J. 0
K. 1
26.
A box of cereal contains 18 cups of cereal. At most, how many persons can you serve
from this box of cereal if each serving must be at least cup?
A. 14
B. 18
C. 19
D. 24
E. 25
27. What is the largest possible product for 2 even integers whose sum is 34 ?
F. 64
G. 68
H. 120
J. 240
K. 288
28. In the graphs below, all axes have the same scale. One of the graphs shows y = 3x + 1.
Which is that graph?
A.
D.
B.
E.
C.
29. The measures of the angles of a triangle are in the ratio of 2x:3x:5x as illustrated below.
What is the measure of the smallest angle in the triangle?
F. 18°
G. 20°
H. 30°
J. 36°
K. 40°
30. If x + 2y = 1, and 2x + y = 5, then x + y = ?
F. 1
G. 2
H. 3
J. 4
K. 5
31.
What integer most nearly approximates
A.
20
B.
40
C.
63
D. 200
E. 2,000
32. If 5a = 25, then a2 = ?
A. 5
B. 20
C. 25
D. 125
E. 625
?
33. A rock group gets 30% of the money from sales of their newest compact disc. That 30%
is split equally among the 5 group members. If the disc generates $1,000,000 in sales,
how much does one group member receive?
F. $ 30,000
G. $ 50,000
H. $ 60,000
J. $200,000
K. $300,000
34. If the expression x2 – kx – 12 is equal to zero when x = 4, what is the value of k ?
A. 7
B. 1
C. –1
D. –3
E. –7
35.
If
=
, then u = ?
A. –3
B. –1
C. 3
D. 4
E. 5
36. What positive value of k would make the lines below parallel in the standard ( x, y)
coordinate plane?
kx + 2y = 8
18x + ky = 12
F. 0
G. 2
H. 6
J. 8
K. 12
37. Lengths for the triangle below are given in feet. What is the value of x ?
A. 2
B.
C. 4
D. 5
E.
38. Which of the following is the graph of the solution set of –2x > 4 ?
F.
G.
H.
J.
K.
39. Which of the following is an equation of a line that passes through the origin and is
parallel to the line 2x – y = 5 ?
A. –2x + y = 5
B. 2x + y = 5
C. x – y = 0
D. 2x – y = 0
E. 2x + y = 0
40. If 60% of the weight of a 2,200-pound car should be supported by the rear tires, how
many pounds should be supported by the rear tires?
A. 120
B. 600
C. 1,200
D. 1,320
E. 1,600