ACT math practice test 32

1. During their daily training race, Carl has to stop to tie his shoes. Melissa, whose shoes are velcro, continues to run and gets 20 feet ahead of Carl. Melissa is running at a constant rate of 8 feet per second, and Carl starts running at a constant rate of 9.2 feet per second to catch up to Melissa. Which of the following equations, when solved for s, gives the number of seconds Carl will take to catch up to Melissa?

F. 8s + 20 = 9.2s
G. 8s - 20 = 9.2s
J. 8s = 20
K. 9.2s = 20

2. Which of the following defines the solution set for the system of inequalities given below?

0 > 3x - 6
-4 < x

A. x > - 4
B. x < 2
C. -4 < x < 18
D. -4 < x < -2
E. -4 < x < 2

3. At the company YouGroove, 35 employees work in the sales department and 50 employees work in the operations department. Of these employees, 15 work in both the sales and the operations departments. How many of the 110 employees at YouGroove do NOT work in either the sales or the operations departments?

F. 10
G. 15
H. 20
J. 35
K. 40

4. The slope of a line in the standard (x,y) coordinate plane is 4. What is the slope of a line perpendicular to that line?

A. 4
C. -
D. -1
E. -4

5. The point (24,3) on a standard (x,y) coordinate plane is halfway between points (z,2z + 1) and (15z,z - 4). What is the value of z?

F. 1
G. 1.5
H. 3
J. 7
K. 24

6. How many 4-letter orderings, where no letters are repeated, can be made using the letters of the word BADGERS?

A. 4
B. 7
C. 256
D. 840
E. 2,401

7. As shown in the (x,y,z) coordinate space below, the cube with vertices L through S has edges that are 2 coordinate units long. The coordinates of Q are (0,0,0), and S is on the positive x-axis. What are the coordinates of O?

F. (2,0,2)
G. (2,2,2)

8. Whenever a, b, and c are positive real numbers, which of the following expressions is equivalent to

D. log4(a - c) - log8 2b
E. log4(a - c) - log8b2

9. If -6≤a≤-4 and 3≤b≤7, what is the maximum value of |a - 2b|?

F. 10
G. 11
H. 18
J. 20
K. 42

10. The measure of the sum of the interior angles of a regular n-sided polygon is (n - 2)180°. A regular octagon is shown below. What is the measure of the designated angle?

A. 135°
B. 144°
C. 200°
D. 225°
E. 315°

11. Which of the following trigonometric functions has an amplitude of 3?

(Note: the amplitude of a trigonometric function is the nonnegative difference between the maximum and minimum values of the function.)

F. f(x) = sin x
G. f(x) = cos 3x
H. f(x) = sin(x)
J. f(x) = 3 tan x
K. f(x) = 3 cos x

12. If A, x, and y are all distinct numbers, and A = , which of the following represents x in terms of A and y?


13. In the figure below, lines p and q are parallel and angle measures are as marked. If it can be determined, what is the value of a?

F. 35°
G. 45°
H. 55°
J. 100°
K. Cannot be determined from the information given

14. In the triangle below, the lengths of the two given sides are measured in centimeters. What is the value, in centimeters, of x?

A. 9 sin 40°
B. 9 sin 50°
C. 9 cos 50°
D. 9 tan 40°
E. 9 tan 50°

15. An angle in the standard (x,y) coordinate plane has its vertex at the origin and its initial side on the positive x-axis. If the measure of an angle in standard position is (1,314°), it has the same terminal side as an angle of each of the following measures EXCEPT:

F. 594°
G. 314°
H. 234°
J. -126°
K. -486°