ACT math practice test 3

1. If pq+ 12 = 3p+ pr,and qr= 7, what is the value of p?

A. –3
B. –4
C.
D.
E.

2. On his first day working out, Anthony did 30 push-ups. On each successive day, he did exactly 3 more push-ups than on the previous day. After completing his push-ups on the 30th day, how many push-ups had he completed on all 30 days?

F. fewer than 500
G. between 500 and 1,000
H. between 1,000 and 1,500
J. between 1,500 and 2,000
K. more than 2,000

3. The following figure is a quadrilateral with one right angle. The other angles are labeled. What is the value of x?

A. 54
B. 56.25
C. 60
D. 67.5
E. 72

4. If a cube has a volume of kcm3and a surface area of 10k cm2, what is its height in centimeters?

F.
G.
H.
J.
K.

5. If , then n=

A.
B.
C.
D.
E.

6. In the following graph, nis the midpoint of . Which of the following answer choices are the coordinates of n?

F. (3, k)
G.
H.
J.
K.

7. If and bc= 7, which of the following statements must be true?

A. a and bare directly proportional.
B. aand care inversely proportional.
C. aand d are inversely proportional.
D. band care directly proportional.
E. cand dare inversely proportional.

8. In the following figure, the area of the shaded region is 10% of the area of the circle. If the radius of the circle is 10, what is the arc length from Pto Q?

F. π
G. 2π
H. 4π
J. 5π
K. 10π

9. Given that i2= –1, what is the value of (4 + 2i)(4 – 2i)?

A. 12
B. 20
C. 16 – 4i
D. 4 + 16i
E. 12 – 16i

10. Which of the following could be the graph of the equation y= 175x2– 33x– 2,000?

F.
G.
H.
J.
K.

11. Sebastian bought a meal at a restaurant and left a 15% tip. With the tip, he paid exactly $35.19. How much did the meal cost without the tip?

A. $28.98
B. $29.91
C. $30.15
D. $30.60
E. $30.85

12. If , what is the value of cos a?

F.
G.
H.
J.
K.

13. In the real numbers, which of the following is the domain of the function ?

A. x3
B. x> 3
C. x< –3
D. –3 < x< 3
E. x< –3 or x> 3

14. Andrea and Zach are both waiting for an appointment with a guidance counselor. When they arrived, each received a card from the secretary, telling the hour and minute of his or her arrival. Two minutes ago, Andrea had been waiting exactly as many minutes as Zach. Three minutes from now, Andrea will have been waiting exactly as long as Zach. If the time is now 11:30, at what time did Andrea arrive?

F. 11:16
G. 11:18
H. 11:20
J. 11:23
K. 11:25

15. In the following figure, each circle is tangent to the other two circles, and the two shaded circles are identical to each other. What is the ratio of the shaded region to the nonshaded region?

A. 1:01
B. 4:05
C. 5:04
D. 4:π
E. π:4