ACT math practice test 20

1. Which trigonometric function (where defined) is equivalent to ?

H. sin x

2. When ab, the expression . Which of the following describes the complete set of x values that make this inequality true?

A. x = -4 only
B. x = 4 only
C. x = - only
D. x < 0
E. x > 0

3. The volume of a cone, which is derived by treating it as a pyramid with infinitely many lateral faces, is given by the formula V = πr2h, where r is the radius of the base and h is the height. If the radius is halved and the height is doubled, what will be the ratio of the new volume to the old volume?

F. 4:01
G. 2:01
H. 1:01
J. 1:02
K. 1:04

4. Al bikes a trail to the top of a hill and back down. He bikes up the hill in m minutes, then returns twice as quickly downhill on the same trail. What is the total time, in hours, that Al spends biking up the hill and back down?

E. 2m

5. Pippin the guinea pig is running on her wheel when, due to a manufacturing error, the wheel breaks free of its axis. Pippin remains in her wheel, running in a straight line until the wheel has rotated exactly 15 times. If the diameter of the wheel is 10 inches, how many inches has the wheel rolled?

F. 75
G. 150
H. 75π
J. 150π
K. 1,500π

6. A circle is inscribed in a square, as shown below. If x is the distance from the center of the circle to a vertex of the square, then what is the length of the radius of the circle, in terms of x?

A. 2x
B. x
C. x
E. Cannot be determined from the information given

7. A function is defined for x and y such that f(x, y) = -2xy + y + x - 4. So, for x = 2 and y = 3, f(2, 3) = -2 × 2 × 3 + 3 + 2 - 4 = -12 + 1 = -11. If x and y are to be chosen such that f(x,y) = f(y,x), then which of the following restrictions must be placed on x and y?

F. x > 0 and y > 0
G. x < 0 and y < 0
H. x = y
J. xy < 0
K. No restrictions are needed.

8. A pipe of radius 4 feet sends water to two smaller pipes of equal size. If each of the smaller pipes allows exactly half as much water to flow as the larger pipe, what is the radius of one of the smaller pipes?

A. 2
B. 2π
C. 2
D. 4
E. 2π

9. The cross-sectional view of a tent is shown below. If the tent is 6 feet wide at its base, then which of the following expressions could be used to calculate the height of the tent, in feet?

G. 3 tan 40°
J. 6 tan 40°
K. 3 tan 80°

10. Two girls walk home from school. Starting from school, Susan walks north 2 blocks and then west 8 blocks, while Cindy walks east 3 blocks and then south 1 block. Approximately how many blocks apart are the girls' homes?

A. 7.1
B. 10.4
C. 11.4
D. 12.7
E. 16

11. For all integer values of a and b such that a > 0 and b<0, which of the following must also be an integer?

F. 3a+b
G. 3a-b
H. 3ab
J. 3-a

12. If x and y are real numbers and 0 < x < y < , which of the following gives the set of all values which could have?


13. A circular running track is being built in a fenced-in athletic field 100 feet wide and 150 feet long. If a border of 10 feet is needed between the outside edge of the track and the fence, what is the radius of the largest track that can be built?

F. 40
G. 45
H. 65
J. 90
K. 110

14. If a sphere is cut by two different planes, dividing it into sections, how many sections is it possible to end up with?

A. 2 only
B. 2 or 4 only
C. 3 only
D. 3 or 4 only
E. 2, 3, or 4 only

15. For all real values of a and b, the equation |a - b| = 5 can be interpreted as "the positive difference of a and b is 5." What is the positive difference between the 2 solutions for a?

F. b
G. b + 5
H. 2b
K. 10