ACT math practice test 36

1. As shown in the figure below, a skateboard ramp leading from the top of a boulder is 10 feet long and forms a 32° angle with the level ground. Which of the following expressions represents the height, in feet, of the boulder?

F. 10 tan 32°
G.
H.
J. 10 sin 32°
K. 10 cos 32°

2. The 4 integers j, j, k, and n have an average of 0. Which of the following equations must be true?

A. k = n
B. k = -j
C. k + n = -2j
D. k + n = 0
E. k + n = j

3. If f(x) = and the composite function f(g(x)) = , which of the following could be g(x)?

F.
G.
H. 2x2 - 25
J. 4x2 - 5
K. 16x4 - 5

4. In the qualifying rounds for a race, Rusty and Dale drive their cars around a 6,000-foot oval track. Rusty and Dale each drive 8 laps in the qualifying rounds in lanes of identical length.

On day one of the qualifying rounds, Rusty and Dale start from the same point, but their cars are reversed and each drives opposite ways. Rusty drives at a constant speed that is 8 feet per second faster than Dale's constant speed. Rusty passes Dale for the first time in 150 seconds. Rusty drives at a constant rate of how many feet per second?

A. 16
B. 20
C. 24
D. 32
E. 40

5. In the qualifying rounds for a race, Rusty and Dale drive their cars around a 6,000-foot oval track. Rusty and Dale each drive 8 laps in the qualifying rounds in lanes of identical length.

In the qualifying rounds, Rusty averages 180 seconds per lap until he begins the last lap. He then goes into a lower gear. He averages 190 seconds per lap for this qualifying round. How many seconds does Rusty take to drive the final lap?

F. 155
G. 160
H. 185
J. 200
K. 260

6. In the qualifying rounds for a race, Rusty and Dale drive their cars around a 6,000-foot oval track. Rusty and Dale each drive 8 laps in the qualifying rounds in lanes of identical length.

Dale drives 6 laps in 90 minutes. At what average rate, in feet per hour, does Dale drive these 6 laps?

A. 400
B. 5,400
C. 10,000
D. 24,000
E. 48,000

7. Circle A has its center at point (-5,2) with a radius of 2, and circle B is represented by the equation (x + 4)2 + (y-- 2)2 = 9. Where is point (-2,2) located?

F. Inside circle A only
G. Inside circle B only
H. Inside both circle A and circle B
J. Outside both circle A and circle B
K. Cannot be determined from given information

8. A heart-shaped ornament is made from a square and two semicircles, each of whose diameter is a side of the square. The ornament is shown in the standard (x,y) coordinate plane below, where 1 coordinate unit represents 1 inch. The coordinates of six points on the border of the ornament are given. What is the perimeter, in inches, of the ornament?

A. 4 + 2π
B. 8 + 4π
C. 8 + 8π
D. 16 + 4π
E. 16 + 8π

9. A function f(x) is defined as even if and only if f(x) = f(-x) for all real values of x. Which one of the following graphs represents an even function f(x)?

F.
G.
H.
J.
K.

10. In the standard (x,y) coordinate plane, point A is located at (w,w + 5) and point B is located at (4w,w-- 5). In coordinate units, what is the distance between A and B?

A.
B.
C. 9w2 + 100
D.
E. |w|

11. RST is a right triangle with side lengths of r, s, and t, as shown below. What is the value of cos2 S + cos2 R?

F. 1
G.
H.
J.
K.

12. In isosceles triangle ABC below, the measures of BAC and BCA are equal and . The diagonals of trapezoid DECA intersect at F. The lengths of and are 6 centimeters, the length of is 9 centimeters, and the length of is 27 centimeters. What is the length, in centimeters, of ?

A. 12
B. 15
C. 18
D. 33
E. 36

13. Which of the following represents the product of the matrices below?

F.
G.
H. [-6]
J. [6 -12]
K. [-4 -12]

14. If , then n! =?

A. 6
B. 10
C. 12
D. 24
E. 120

15. What is the ratio of a circle's radius to its circumference?

F. 2π:1
G. 2:01
H. π:1
J. 1:π
K. 1:2π