Free ACT Math Practice Test 3

1. For all

F.
G.
H.
J.
K.

2. If the circumference of a circle is inches, how many inches long is its radius?

A.
B.
C.
D.
E.

3. If the function f satisfies the equation f(x + y) = f(x) + f(y) for every pair of real numbers x and y, what is (are) the possible value(s) of f(1)?

F. Any real number
G. Any positive real number
H. 0 and 1 only
J. 0 only
K. 1 only

4. The area of the trapezoid below is 24 square inches, the altitude is 3 inches, and the length of one base is 5 inches. What is the length, b, of the other base, in inches?

A. 3
B. 8
C. 11
D. 13
E. 16

5. If a, b, and c are consecutive positive integers and 2a × 2b × 2c = 512, then 2a + 2b + 2c =?

F. 6
G. 9
H. 14
J. 16
K. 28

6. If 30% of x equals 60% of y, which of the following expresses y in terms of x ?

A. y = 33% of x
B. y = 50% of x
C. y = 66% of x
D. y = 150% of x
E. y = 200% of x

7. For which values of x will 3(x + 4) ≥ 9(4 + x)?

F. x ≤ -4
G. x ≥ -4
H. x ≥ -16
J. x ≤ 4
K. x ≤ -16

8. If x = 6a + 3 and y = 9 + a, which of the following expresses y in terms of x?

A. y = x + 51
B. y = 7x + 12
C. y = 9 + x
D.
E.

9. ABCD is a trapezoid that is bisected by line PQ, which is parallel to lines AB and DC. If the length of line DP is 8 units, the length of line PA is 12 units, and the length of line AB is 36 units, what is the length of PQ?

F. 8
G. 9
H. 12
J. 16
K. 24

10. In real numbers, what is the solution of the equation 41-a = 82a+1?

A.
B. 0
C.
D.
E.

11. In the figure below, sin α =?

F.
G.
H. 1
J.
K.

12. For all real integers, which of the following is always an even number?

I. x3 + 4<

II. 2x + 4

III. 2x2 + 4

A. I only
B. II only
C. III only
D. I and II only
E. II and III only

13. Carol has an empty container and puts in 6 red chips. She now wants to put in enough white chips so that the probability of drawing a red chip at random from the container is . How many white chips should she put in?

F. 3
G. 6
H. 8
J. 10
K. 16

14. A wheel 27 inches in diameter rolls along a line. How many inches does the wheel roll along the line in 32 revolutions?

A. 27π
B. 32π
C. 432π
D. 864π
E. 1,728π

15. For any real number a, the equation |x - 2a| = 5. On a number line, how far apart are the 2 solutions for x?

F. 2a
G. 5 + 2a
H. 10a
J. 5
K. 10