Free ACT Math Practice Test 1

1. In the figure below, S and T are points on RU. What is the ratio of the area of square STVX to the area of parallelogram RUVY?

F. 3:8
G. 1:11
H. 3:11
J. 9:11
K. 3:24

2. If f(x) = 2x2 - 6x + 7, then f(-3) =?

A. 7
B. 18
C. 25
D. 36
E. 43

3. A map is drawn so that 1.2 inches represents 50 miles. About how many miles do 1.4 inches represent?

F. 54
G. 58
H. 65
J. 70
K. 100

4. (5x3 + 3xz2 - 17z) - (4xz2 + 5z - 2x3) = ?

A. 7x3 - xz2 - 22z
B. 7x3 - xz2 - 12z
C. 3x3 - xz2 - 12z
D. 3x3 + 7xz2 - 22z
E. 3x3 + 7xz2 - 12z

5. In the standard (x,y) coordinate plane shown below, what is the distance on the y-axis, in units, from point A to point B?

F. -3
G. -5
H. 3
J. 5
K. 11

6. Which of the following is NOT a solution of (x - 5)(x - 3)(x + 3)(x + 9) = 0?

A. 5
B. 3
C. -3
D. -5
E. -9

7. If 0 < pr < 1, then which of the following CANNOT be true?

F. p < 0 and r < 0
G. p < -1 and r < 0
H. p < -1 and r < -1
J. p < 1 and r < 1
K. p < 1 and r > 0

8. If n = 10, then which of the following represents 552?

A. 5n + 2
B. 5n2 + 2
C. 5n2 + 5n + 2
D. 5n3 + 5n + 2
E. 5n4 + 5n + 2

9. What is the value of b in the solution to the system of equations below?

3a - b = 18

a + 3b = -4

F. -10
G. -3
H. 3
J. 6
K. cannot be determined with the given information

10. Which of the following is an equivalent form of x + x(x + x + x)?

A. 5x
B. x2 + 3x
C. 3x2 + x
D. 5x2
E. x3 + x

11. Due to inflation, a refrigerator that formerly sold for $450 now sells for 7% more. Which of the following calculations gives the current cost, in dollars, of the refrigerator (excluding sales tax)?

F. 450 + 7
G. 450 + 450(0.07)
H. 450 + 450(0.7)
J. 450 + 450(7)
K. 450(0.07)

12. In a 3-dimensional (x, y, z) space, the set of all points 5 units from the x-axis is:

A. a line.
B. 2 parallel lines.
C. a circle.
D. a sphere.
E. a cylinder.

13. An overlay of an accessibility ramp of a building is placed on the standard (x, y) coordinate plane so that the x-axis aligns with the horizontal. The line segment representing the side view of the ramp goes through the points (-2,-1) and (16,2). What is the slope of the accessibility ramp?

F. -3
G.
H.
J.
K.

14. The number 0.002 is 100 times as large as which of the following numbers?

A. 0.000002
B. 0.00002
C. 0.0002
D. 0.02
E. 0.2

15. The volume, V, of a sphere is determined by the formula , where r is the radius of the sphere. What is the volume, in cubic inches, of a sphere with a diameter 12 inches long?

F. 48π
G. 72π
H. 288π
J. 864π
K. 2304π