ACT Assessment : Sample Questions : Math Set 1

Set 1

SAMPLE MATHEMATICS TEST QUESTIONS

Click on the letter choices to determine if you have the correct answer and for question explanations.
(An actual ACT Assessment 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. 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. What are the values of a and b, if any, where a|b - 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.

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.

Back to Sample Tests
Subject 3 – Set 1
Math – Set 2

1.	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.	What are the values of a and b, if any, where a\|b - 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.

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.



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