ACT Math Practice Test 65

1. What is the distance, in coordinate units, between points J(-5, 4) and K(6,-2) in the standard (x,y) coordinate plane?

A.
B.
C.
D. 10
E. 17

2. Cynthia decorates the ceiling of her bedroom with stars that glow in the dark. She puts 1 star on the ceiling on the 1st day of decorating, 2 stars on the ceiling on the 2nd day of decorating, 3 stars on the 3rd day, and so on. If she puts stars on the ceiling in this pattern for 30 days (so she puts 30 stars on the ceiling on the 30th day), then what will be the total number of stars on the ceiling at the end of the 30 days?

F. 155
G. 435
H. 450
J. 465
K. 480

3. In ΔPQR, side PQ is 12 inches long and side QR is 41 inches long. Which of the following CANNOT be the length, in inches, of side PR ?

A. 17
B. 30
C. 38
D. 44
E. 52

4. Which of the following is equivalent to the expression ?

F.
G.
H. d
J.
K.

5. Merav's school has an Olympic-size pool that is 50 meters long, 25 meters wide, and 2 meters deep. The pool is surrounded by special non-slip tiles, as shown in the figure below.

Merav's school laid non-slip tiles on the floor around its pool to reduce injuries among its athletes. These non-slip tiles extend 5 meters beyond the pool on all sides. What is the area, in square meters, of the floor space that has the non-slip tiles?

A. 800
B. 850
C. 900
D. 950
E. 1,000

6. Merav's school has an Olympic-size pool that is 50 meters long, 25 meters wide, and 2 meters deep. The pool is surrounded by special non-slip tiles, as shown in the figure below.

For the synchronized swimming team, each swimmer needs an area within the pool to perform her routine without colliding with a teammate. Each area is 5 meters wide and 5 meters long. What is the maximum number of synchronized swimmers in the pool who can perform the routine without any collisions?

F. 75
G. 50
H. 25
J. 15
K. 10

7. Merav's school has an Olympic-size pool that is 50 meters long, 25 meters wide, and 2 meters deep. The pool is surrounded by special non-slip tiles, as shown in the figure below.

Merav pays $4.00 for a ticket to her school's first swim meet to watch her classmates compete. While there, Merav buys a slice of pizza and a soda. She pays $3.75 for the pizza and $1.75 for the soda, plus 10% sales tax for both of these items. What is the total amount Merav pays for her ticket, pizza, and soda?

A. $ 3.75
B. $ 9.50
C. $10.05
D. $10.45
E. $10.75

8. Points G and H lie on circle F as shown below. If the measure of ∠FGH is 40°, then what is the measure of central angle ∠GFH?

F. 60°
G. 80°
H. 100°
J. 120°
K. Cannot be determined from the information given

9. The pie chart below shows the operating expenses of Stephanie's office for the month of July, during which time the expenses totaled $10,000.

Stephanie tries to reduce her operating expenses for August by making her office more energy efficient and asking her landlord to lower her rent. She hopes to reduce her electricity expenses by $700 and her rent by $1,300. If she is successful in both of these goals and the rest of her expenses are unchanged, then what percent of her August expenses will be for office supplies?

 

A. 5.0%
B. 7.5%
C. 10.0%
D. 12.5%
E. 15.0%

10. Assuming q is a positive integer, then the difference between 14q and 5q is always divisible by:

F. 5
G. 9
H. 14
J. 19
K. 70

11. Ron earns $1,800 for a 6-week assignment. While working a 6-week assignment, Ron works a minimum of 20 hours each week. Ron's hourly rate of pay, therefore, depends upon how many hours he works. If r is Ron's average hourly pay, in dollars, for a 6-week assignment, then which of the following best describes r ?

A. r ≤ $15.00
B. r ≥ $15.00
C. r ≤ $90.00
D. r ≥ $90.00
E. r ≥ $180.00

12. In the standard (x, y) coordinate plane, the endpoints of EF lie at (-5,9) and (3,-3). What is the y-coordinate of the midpoint of EF ?

F. -6
G. -3
H. -1
J. 3
K. 6

13. Two wires connect the top of a flagpole to the ground, as shown below. Each wire makes a 75° angle with the ground at a point 8 feet from the flagpole. Which of the following expressions gives the height, in feet, of the flagpole?

A. 8cos75°
B. 8sin75°
C. 8tan75°
D.
E.

14. As shown in the figure below, ΔXYZ is a right triangle with legs of length x units and y units and hypotenuse of z units, such that 0 < x < y. Quadrilaterals ABYX, CDZY, and EFXZ are squares.

What is the perimeter, in units, of polygon CDZXY ?

F. 3x + y + z
G. 3x + 2y + z
H. 3x + 3y + 3z
J. 4x + y + z
K. 4x + 4y + 4z

15. As shown in the figure below, ΔXYZ is a right triangle with legs of length x units and y units and hypotenuse of z units, such that 0 < x < y. Quadrilaterals ABYX, CDZY, and EFXZ are squares.

Given that 0 < x < y, which of the following correctly lists the angles ∠BYC, ∠AXF, and ∠EZD in order of their measures from least to greatest?

A. ∠AXF, ∠EZD, ∠BYC
B. ∠BYC, ∠EZD, ∠AXF
C. ∠BYC, ∠AXF, ∠EZD
D. ∠EZD, ∠AXF, ∠BYC
E. ∠EZD, ∠BYC, ∠AXF