
About ACT Exam
Math Sample Questions
Click
on the letter choices to determine if you have the correct answer
and for question explanations.
(An actual ACT Mathematics Test contains 60 questions to be answered in 60
minutes.) 
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. 
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. 
1. 
Which of the following is equivalent to (x)(x)(x)(x),
for all x ?
A. 4x
B. x^{4}
C. x + 4
D. 4 ^{x}
E. 2x^{2} 

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
The correct answer is K. The
rectangle is 3 inches by 6 inches, so the area is 3(6) = 18 square inches.
F. If the
area were 6, then l = = 2, but this length isn't twice
the width.
G. If the
area were 9, then l = = 3, but this length isn't twice
the width.
H. If the
area were 12, then l = = 4, but this length isn't twice
the width.
J. If the
area were 15, then l = = 5, but this length isn't twice
the width. 

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.
The
correct answer is A. There are 14 balloons, of which 9 are yellow. If a yellow
balloon is sold, there are 13 balloons left, of which 8 are yellow. The
probability of selecting a yellow balloon is .B. cannot be the probability of
selecting a yellow balloon; because 9(13) 8(13).
C. cannot
be the probability of selecting a yellow balloon; because 5(13) = 65,
14(8) = 112, and 65 112.
D. cannot
be the probability of selecting a yellow balloon; because 8(13) 8(14).
E. cannot
be the probability of selecting a yellow balloon; because 9(13) = 117,
14(8) = 112, and 117 112. 

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
The
correct answer is F. By the Pythagorean theorem, the length of the hypotenuse is .
G. is
the hypotenuse of a right triangle with legs 12 and 4, since ; so can't
be the hypotenuse of a right triangle with legs 12 and 8.
H. can't
be the hypotenuse because is would be the shortest side of the triangle.
J. can't
be the hypotenuse because it would be shorter than one of the legs.
K. 4 <
8, so 4 can't be the hypotenuse because it would be the shortest side of the
triangle. 

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 x^{2}  15 = 0 ?
F. 0
G. 1
H. 2
J. 4
K. 15 

9. 
A circle with center (3,4) is tangent to
the xaxis 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. The correct
answer is F. Since sin^{2}A + cos^{2}A = 1, ()^{2} + cos^{2}A = 1, cos^{2}A = 1  , cos^{2}A = ,
so cosA = � = � . But
since A is acute, cosA = .
G. ()^{2} + ()^{2} = + = 1, so
cosA .
H. ()^{2} + ()^{2} = + = 1, so
cosA .
J. ()^{2} + ()^{2} = + = 1, so
cosA .
K. ()^{2} + ()^{2} = + = = 1, so cosA . 

11. 
What are the values of a and b,
if any, where ab  2 < 0 ?
A. a < 0 and b 2
B. a < 0 and b = 2
C. a 0 and b > 2
D. a > 0 and b < 2
E. There are no such values of a and b.
The correct answer is A. If ab  2 < 0, one of a or b  2 must be negative and one must
be positive.
Since b  2 can't be negative, a must be
negative. Then b 2 must be positive, so b 2. 

12. 
In a shipment of 1,000 light bulbs, of
the bulbs were defective.
What is the ratio of defective bulbs to nondefective bulbs?
F.
G.
H.
J.
K. 
