ACT Math Practice Test 62

1. In the diagram b, d, and c are collinear. b = 30° and c = 45°. is perpendicular to and = 6. What is the perimeter of ΔABC to the nearest tenth?

• F. 29.9
• G. 30
• H. 32.5
• J. 34.4
• K. 36.9

2. Quadrilateral ABCD is a trapezoid with parallel to . and are perpendicular to . AB = 6, CD = 12, and AE = 4. What is the sum of the areas of ΔAED and ΔBFC?

• A. 12
• B. 24
• C. 36
• D. 48
• E. 120

3. (2 - 3i)² = ? [Note: i = ]

• F. -5
• G. 13
• H. -5 - 6i
• J. -5 - 12i
• K. -5 + 12i

4. How many prime numbers are there between 50 and 70?

• A. 4
• B. 5
• C. 6
• D. 7
• E. 8

5. If (x + 2) is a factor of 3x² - 13x + k, what is the value of k?

• F. -38
• G. -14
• H. -2
• J. 14
• K. 38

7. If f(x) = x² - 2x + 4, then f (T + 2) = ?

• F. T² - 2T + 4
• G. T² - 2T
• H. T² + 2T + 8
• J. T² + 6T + 12
• K. T² + 2T + 4

8. In the circle illustrated, the radius is 8 feet. The measure of central angle AOB is 60°. What is the length, in feet, of arc AB?

• A.
• B.
• C.
• D. 16π
• E. 24π

9. If x = 4y + 2, what is y + 6 in terms of x?

• F. x + 4
• G. x + 6
• H.
• J.
• K.

10. If sin then cos θ = ?

• A.
• B.
• C.
• D.
• E.

11. If log_bx = g and log_by = p, then log_b = ?

• F.
• G. gp³
• H. g - p
• J. g + 3p
• K. g - 3p

• A. The distance cannot be approximated without more information.
• B.
• C.
• D. 12 tan 44°
• E.

13. When -2 ≤ x ≤ 5 and -3 ≤ y ≤ 3, what is the maximum possible value for x - y?

• F. -5
• G. -2
• H. 1
• J. 2
• K. 8

14. For how many different integers b (consider positive integers, negative integers, and zero) does x² + bx + 20 factor into linear factors with integer coefficients?

• A. 1
• B. 2
• C. 3
• D. 4
• E. 6

15. m and n are prime numbers. If is a rational number, then (m)(n) = ?

• F. 8
• G. 15
• H. 21
• J. 35
• K. 735