ACT Math Practice Test 90

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 m_a and the slope of line b is m_b. Which of the following statements about the slope of lines a and b is true?

• F.
• G. m_a + m_b = 0
• H.
• J. m_a - 1 = m_b
• K. m_a - m_b = 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