ACT math practice test 62

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

image

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

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

image

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

3. (2 - 3i)2 = ? [Note: i = image]

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

6. If the radius of a sphere is tripled, the volume of the resulting sphere is how many times the volume of the original sphere?

[The volume of a sphere = image]

A. 1
B. 3
C. 9
D. 27
E. 81

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?

image

A. image
B. image
C. image
D. 16π
E. 24π

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

F. x + 4
G. x + 6
H. image
J. image
K. image

10. If sin image then cos θ = ?

A. image
B. image
C. image
D. image
E. image

11. If logbx = g and logby = p, then logbimage = ?

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

12. The measures of imagea and imageb are 35° and 44°, respectively. The length of image is 12 miles. Which of the following expressions, if any, gives the approximate distance, in miles, of side image?

[Note: The law of sines states that the ratio between the length of the side opposite an angle and the sine of that angle is the same for all interior angles in the same triangle.]

image

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

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 image is a rational number, then (m)(n) = ?

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