Free Online ACT Math Practice Test 10

1. Let x = 3y -4z + 7. What happens to the value of x if the value of y decreases by 2 and the value of z is increased by 1?

F. It increases by 3.
G. It increases by 5.
H. It decreases by 1.
J. It decreases by 10.
K. It is unchanged.

2. Which of the following represents the values of x that are solutions for the inequality (x - 1)(4 - x) < 0?

A.
B. x < 1 or x > 4
C.
D. -4 < x < 1
E.

3. In the figure below, triangle PQR is an isosceles right triangle. What is the ratio of the hypotenuse to the length of PQ?

F.
G.
H.
J.
K.

4. If and 0° ≤ x° ≤ 90°, then cos x = ?

A.
B.
C.
D.
E.

5. For all a ≠ 0 and b ≠ 0,

F.
G.
H.
J.
K.

6. In the figure below, PQRS is a rectangle with sides of lengths shown. X is the midpoint of . What is the perimeter of triangle PXQ?

A. 10
B.
C.
D.
E.

7. A line in the standard (x, y) coordinate plane has a slope of and passes through points (3,4) and (t,-2). What is the value of t?

F. 3
G. 2
H. 0
J. -2
K. -6

8. Sean is building a scale model of a sailboat, complete with a main sail. The actual sailboat's main sail measures 56 feet high with a base of 32 feet. If the model sailboat's main sail has a base of 8 inches, how tall will the model's main sail be, in inches?

A. 14
B. 28
C. 32
D. 56
E. 112

9. What values of x make the inequality -5x - 7 > 3x + 1 true?

F. x > 1
G. x < 8
H. x < -1
J. x > -4
K. x < 2

10. In the figure below, the lengths of the sides of right triangle BAC are as shown. bisects side . What is the length of DC?

A.
B. 2
C. 3
D.
E. 4

11. Which of the following intervals contains the solution to the equation

F. -6 < x < 11
G. 11 ≤ x < 15
H. 6 < x ≤ 10
J. -5 < x ≤ -3
K. -11 ≤ x ≤ -2

12. In the figure below, P and Q lie on the circle R, which has a radius of 9. If the angle PRQ is 120°, what is the area of sector PRQ?

A. 3π
B. 9π
C. 27π
D. 81π
E. 243π

13. Given the graph below in the standard (x, y) coordinate plane, the slope of line a is ma and the slope of line b is mb. Which of the following statements about the slope of lines a and b is true?

F.
G. ma + mb = 0
H.
J. ma - 1 = mb
K. ma - mb = 0

14. If and , what is sin x?

A.
B.
C.
D.
E. Cannot be determined from the given information.

15. A total of f men went on a fishing trip. Each of the r boats that were used to carry the fishermen could accommodate a maximum number of m passengers. If one boat had 5 open spots and the remaining boats were filled to capacity, which of the following expresses the relationship among f, r, and m?

F. rm + 5 = f
G. rm - 5 = f
H. r + m + 5 = f
J. rf = m + 5
K. rf = m - 5