ACT math practice test 35

1. If a, b, and c are positive prime numbers, in the equation ab = c, either b or c must represent which number?

A. 13
B. 11
C. 7
D. 5
E. 2

2. Pierre competes in a triathlon, along a course as shown in the figure below. He begins swimming at starting point S and swims straight across the lake, gets on his bicycle at station A, bikes to station B, and then runs to finishing line F. The judges use a stopwatch to record his elapsed times of tA, tB, and tF hours from point S to points A, B, and F, respectively. If the distance, in miles, between points S and A along the racecourse is denoted by SA, then what is Pierre's average speed for this race, in miles per hour?

F.
G.
H.
J.
K.

3. The triangle shown below has a hypotenuse with a length of 13 feet. The measure of A is 20° and the measure of B is 70°. Which of the following is closest to the length, in feet, of ?

(Note: sin 70° ≈ 0.9397
cos 70° ≈ 0.3420
tan 70° ≈ 2.747)

A. 4.4
B. 5
C. 12
D. 12.2
E. 35.7

4. What is the value of when x = -3 and y = -4?

F. -
G. -
H.
J.
K.

5. As shown in the figure below, with angles as marked, a ramp is being designed that will have a vertical height of 4 feet. Which of the following is closest to the horizontal length of the ramp, in feet?

A. 5
B. 6
C. 7
D. 8
E. 9

6. In the diagram below, ABC is isosceles and BCD is equilateral. = and the measure of ABC is half the measure of BAC. What is the measure of ABD?

F. 36°
G. 60°
H. 72°
J. 96°
K. 150°

7. The coordinates of the vertices of MON are shown in the standard (x,y) coordinate plane below. Rectangle MPQR is shown shaded. Point P lies on , point Q lies on , and point R lies on .

What is the slope of MON?

A. -2
B. -
C. 0
D.
E. 2

8. The coordinates of the vertices of MON are shown in the standard (x,y) coordinate plane below. Rectangle MPQR is shown shaded. Point P lies on , point Q lies on , and point R lies on .

Which of the following is closest to the perimeter, in coordinate units, of MON?

F. 12
G. 16.9
H. 18
J. 20.9
K. 92

9. The coordinates of the vertices of MON are shown in the standard (x,y) coordinate plane below. Rectangle MPQR is shown shaded. Point P lies on , point Q lies on , and point R lies on .

What is the value of cos (MON)?

A.
B.
C. 2
D.
E.

10. In a Spanish class there are m students, of which n did NOT pass the last exam. Which of the following is a general expression for the fraction of the class that did receive a passing grade?

F.
G.
H.
J.
K.

11. The solution set of 5x + 9 ≥ 2(3x + 4) + 7 is shown by which of the following number line graphs?

A.
B.
C.
D.
E.

12. An artist wants to cover the entire outside of a rectangular box with mosaic tiles. The dimensions of the box shown below are given in centimeters. If each tile is exactly one square centimeter, and the artist lays the tiles with no space between them, how many tiles will he need?

F. 75
G. 96
H. 108
J. 126
K. 150

13. In the figure shown below, and are parallel and = . If ABC is 130° and BAF is 22°, what is the measure of AEF?

A. 50°
B. 118°
C. 152°
D. 158°
E. 164°

14. Given the figure below, what is the area of the trapezoid, in square inches?

F. 18
G. 30
H. 42
J. 50
K. 52

15. What is the solution set of

A. {4}
B. {8}
C. {-4, 8}
D. {-8, 4}
E. {-2, ±2}