ACT Math Practice Questions: Part D

1. What fraction lies exactly halfway between and ?


2. When entering information about the budget of her charity ball, Laura records an expense of $20.00. However, Laura accidentally enters the $20.00 as income instead of an expense. The balance of the charity ball budget now shows:

A. $40 less than it should.
B. $20 less than it should.
C. the correct amount.
D. $20 more than it should.
E. $40 more than it should.

3. Rebecca is trying to schedule volunteers to help at a school carnival. There are 5 one-hour shifts to be filled by 5 different volunteers. If each shift must have one and only one volunteer, how many different arrangements can the schedule have?

F. 5
G. 20
H. 25
J. 50
K. 120

4. In the standard (x, y) coordinate plane, what is the distance between the points (4,-7) and (-1,5)?

A. 5
B. 12
C. 13
D. 20
E. 26

5. A formula for the volume, V, of a right circular cylinder is V = πr2h, where r is the radius and h is the height. If a tanker truck has a tank as shown below with a diameter of 3 meters and a length of 10 meters and is filled with water, then the weight, in pounds, of the water cargo is: (Note: 1 cubic meter of water weighs approximately 2,205 pounds.)

F. less than 75,000.
G. between 125,000 and 175,000.
H. between 175,000 and 225,000.
J. between 225,000 and 275,000.
K. more than 275,000.

6. In the figure below, line AB is parallel to the base of the triangle and creates a smaller triangle inside of the original triangle. If the lengths of segments are as shown and the smaller triangle has an area of 8 cm2, what is the area, in square centimeters, of the original triangle?

A. 16
B. 24
C. 32
D. 64
E. 128

7. The figure below is a regular hexagon. What is the measure of one of the interior angles of the hexagon?

F. 108°
G. 120°
H. 135°
J. 150°
K. 720°

8. It is estimated that, from the beginning of 1993 to the end of 1997, the average number of CDs bought by teenagers increased from 7 per year to 15 per year. During the same time period, the average number of video games purchased by teenagers increased from 6 per year to 18 per year. Assuming that in each case the rates or purchase are the same, in what year did teenagers buy the same average number of CDs and video games?

A. 1993
B. 1994
C. 1995
D. 1996
E. 1997

9. If x2 - 45b2 = 4xb, what are the 2 solutions for x in terms of b?

F. 15b or -3b
G. 5b or -9b
H. 15b or 3b
J. 45b or -4b
K. 9b or -5b

10. Which of the following is (are) equivalent to the mathematical operation a(b - c) for all real numbers a, b, and c?

I. ca - ba

II. ab - ac

III. (b - c)a

A. II only
B. I and II only
C. I and III only
D. II and III only
E. I, II and III

11. For values of x where sin x, cos x, and tan x are all defined,

G. tan2x
H. 1
J. sin2x
K. sec x

12. If a is inversely proportional to b and a = 36 when b = 12, what is the value of a when b = 48?

A. 0
D. 4
E. 9

13. For which of the following values of c will there be 2 distinct real solutions to the equation 5x2 + 16x + c = 0?

F. 3
G. 9
H. 14
J. 15
K. 20

14. If the volume of a cube is 64, what is the shortest distance from the center of the cube to the base of the cube?

A. 2
B. 4
E. 16

15. What is the slope of a line that is perpendicular to the line determined by the equation 5x + 8y = 17?

F. -3