ACT Math Practice Test 64

1. Four actors (Jessica, Kevin, Lisa, and Michael) stand around a circular stage of circumference 19 feet. Kevin stands 5 feet counterclockwise from Jessica. Lisa stands 9 feet clockwise from Jessica. Michael stands 6 feet clockwise from Jessica and 13 feet counterclockwise from Jessica. In what order do the actors stand, starting with Jessica and going clockwise around the stage?

F. Jessica, Kevin, Lisa, Michael
G. Jessica, Kevin, Michael, Lisa
H. Jessica, Lisa, Kevin, Michael
J. Jessica, Michael, Kevin, Lisa
K. Jessica, Michael, Lisa, Kevin

2. In 1905, the distance between the edge of a lake and Marker X was 75 meters. In 2005, the distance between the edge of this lake and Marker X was 825 meters. If the edge of this lake withdrew from Marker X at a linear rate, then what was the distance, in meters, between the edge of the lake and Marker X in 1985 ?

A. 675
B. 682.5
C. 690
D. 705
E. 750

3. For a decorating project, Beatrice found the area and perimeter of a drawing she made of a beach scene. She found that the area of her rectangular drawing was 144 square inches and that the perimeter was 80 inches. When she arrived at the craft store to purchase a frame for her drawing, she discovered that she had forgotten to write down the dimensions of her drawing. What are the dimensions of Beatrice's drawing, in inches?

F. 4 by 36
G. 6 by 24
H. 8 by 18
J. 9 by 16
K. 12 by 12

4. Which of the following is equivalent to 5.046 × 10-3 ?

A. 5,046
B. 504.6
C. 5.046
D. 0.05046
E. 0.005046

5. If the values of s and t are directly proportional and s = 8 when t = 10, then what is the value of s when t = 15 ?

F.
G.
H. 12
J. 13
K. 18

6. The cost to rent headphones at the listening library is $3.50 for the first hour (or any fraction thereof), $2.50 for the second hour (or any fraction thereof), and $1.25 for each additional hour (or any fraction thereof) beyond the first two. If you rent headphones at 2:12 P.M. and are charged $9.75 when you return them, then which of the following could be the time you return the headphones? (Note: Assume that this listening library does not charge additional taxes or fees.)

A. 5:30 P.M.
B. 6:30 P.M.
C. 7:30 P.M.
D. 8:00 P.M.
E. 8:30 P.M.

7. The degree measures of the 4 angles of quadrilateral LMNO, shown below, form a geometric sequence with a common ratio of 2. What is the last term of the sequence?

F. 24°
G. 96°
H. 160°
J. 192°
K. 216°

8. Points E, F, and G are collinear. Point H is a point not on EG. If the measure of ∠GFH is 64°, then what is the measure of ∠EFH ?

A. 26°
B. 58°
C. 64°
D. 116°
E. 296°

9. If 6x + 10y = 14 and 3x + 4y = 2, then what is the value of 5x + 7y ?

F. 5
G. 2
H. -5
J. -7
K. -12

10. Which of the following correctly solves the equation = 6 for any b ?

A. b = 12a
B. b = 12 - a
C. b = 3 - a
D. b = a - 3
E. b = a - 12

11. The product of which of the following results in a negative odd number?

F. A positive even number and a negative even number
G. Two negative odd numbers
H. A positive even number and a negative odd number
J. A negative even number and a negative odd number
K. A positive odd number and a negative odd number

12. A bag contains 11 purple marbles, 11 yellow marbles, 11 red marbles, and 11 black marbles. John begins removing marbles at random from the bag, and the first 4 marbles removed are all purple. What is the probability that the fifth marble removed will also be purple?

A.
B.
C.
D.
E.

13. A student in Miss Ruane's class must repeat a test if that student earns less than 70% of the points available on that test. There were 30 points available on the first test of this semester. If Oliver scored p points on this test and therefore must repeat it, then which of the following is true?

F. p < 20
G. p > 20
H. p < 21
J. p = 21
K. p > 21

14. A work crew paints a broken yellow line down the middle of a straight road 16 miles long over the course of 3 days. On Day 1, the crew records 5 miles of road painted. On Day 2, the crew forgets to measure how much road was painted, but on Day 3, the crew records 3 miles painted to finish the job. According to the measurements available, how many miles of road did the crew paint on Day 2 ?

A. 7
B. 7
C. 7
D. 6
E. 6

15. The owners of the Movie Palace use the Illuminator 100 light bulb in their projectors, but are now considering switching to the Illuminator 100 Plus, a more powerful light bulb that projects movies onto larger screens farther away. The Illuminator 100 Plus projects movies onto screens 108 feet wide and 180 feet from the projector, while the Illuminator 100 projects movies onto screens only 81 feet wide, as shown in the figure below. How much farther from the projector, in feet, is the screen for the Illuminator 100 Plus than the screen for the Illuminator 100 ?

F. 27
G. 40
H. 45
J. 50
K. 55