ACT Math Practice Test 69

1. Esther is making 2 gallons of punch for a large party. While mixing the punch, she uses gallon of pineapple juice. What fraction of the punch consists of pineapple juice?

A.
B.
C.
D.
E.

2. Point O is the center of the circle shown below, and XZ is the diameter of the circle. If XZ = 8 ft, Y lies on the circle, and OX = XY, then what is the area, in square feet, of ΔXYZ?

F. 4
G. 8
H. 16
J. 32
K. 64

3. Which of the following values provides one of the roots for the equation y2 - 4y - 5 = 7?

A. -12
B. -6
C. -2
D. -1
E. 5

4. The plastic model house shown below consists of a right pyramid atop a right rectangular prism. The length and width of the prism and of the pyramid are 20 millimeters. The height of the prism is 16 millimeters, and the height of the pyramid is 12 millimeters. Which of the following is closest to the volume of the plastic model house, in cubic millimeters? (Note: The volume of a right pyramid is given by lwh, where l is the length, w is the width, and h is the height. The volume of a right rectangular prism is given by lwh, where l is the length, w is the width, and h is the height.)

F. 6,900
G. 8,000
H. 9,100
J. 12,300
K. 25,600

5. An isosceles trapezoid has bases of length 5 inches and 11 inches. The area of the trapezoid is 40 square inches. What is the height of the trapezoid, in inches?

A. 4
B. 5
C. 7.5
D. 17.5
E. 35

6. What is the slope of the line that passes through the points (-2,6) and (3,-9) in the standard (x,y) coordinate plane?

F.
G. -
H. -
J. -3
K. -5

7. Right triangle ΔWXY is isosceles and has its right angle at Point X. Point Z is collinear with points X and Y, with Y between X and Z. What is the measure of ∠WYZ ?

A. 45°
B. 90°
C. 120°
D. 135°
E. 145°

8. The decimal construction of repeats and can be written as 0.384615384615???. What is the 99th digit to the right of the decimal point in this decimal construction?

F. 1
G. 3
H. 4
J. 5
K. 6

9. Points W(-2,2), X(2,2), and Y(2,-2) lie in the standard (x,y)coordinate plane and are 3 of the vertices of square WXYZ. What is the length, in coordinate units, of XZ ?

A. 2
B. 4
C. 16
D. 2
E. 4

10. The equation y = x2 is graphed in the standard (x,y) coordinate plane, then reflected across the x-axis. Which of the following is the equation of this reflection?

F. y = x2
G. y = -x2
H. y = (-x)2
J. y = |x|
K. |y| = |x|

11. In the figure below, JK||MN, and JM and KN intersect at L. Which of the following statements must be true?

A. JK ? MN
B. JL ? LM
C. ΔJKL ? ΔMNL
D. ΔJKL is similar to ΔMNL
E. JM bisects KN

12. The Wildcat athletic department at Wilson High School needs to raise $3,000.00 to fill a gap in its annual budget. The athletic department can choose 1 of the 2 options below to raise the needed funds.

Sell "Wildcat baseball caps" option: After paying a one-time fee of $23.00 to rent the necessary equipment, the athletic department can sell baseball caps featuring the school's logo. The athletic department will buy plain caps and print the school logo on each, at a cost of $3.50 per cap. The athletic department will sell each cap for $5.00.

Sell "Wildcat T-shirts" option: After paying a one-time fee of $19.00 to rent the necessary equipment, the athletic department can sell T-shirts featuring the school's logo. The athletic department will buy plain T-shirts and print the school logo on each, at a cost of $2.25 per T-shirt. The athletic department will sell each T-shirt for $4.00.

For the "Wildcat baseball caps" option, at least how many baseball caps must be sold in order to cover the one-time fee of renting the necessary equipment?

F. 14
G. 15
H. 16
J. 17
K. 23

13. The Wildcat athletic department at Wilson High School needs to raise $3,000.00 to fill a gap in its annual budget. The athletic department can choose 1 of the 2 options below to raise the needed funds.

Sell "Wildcat baseball caps" option: After paying a one-time fee of $23.00 to rent the necessary equipment, the athletic department can sell baseball caps featuring the school's logo. The athletic department will buy plain caps and print the school logo on each, at a cost of $3.50 per cap. The athletic department will sell each cap for $5.00.

Sell "Wildcat T-shirts" option: After paying a one-time fee of $19.00 to rent the necessary equipment, the athletic department can sell T-shirts featuring the school's logo. The athletic department will buy plain T-shirts and print the school logo on each, at a cost of $2.25 per T-shirt. The athletic department will sell each T-shirt for $4.00.

The Wildcat athletic department sold 540 tickets to Friday's football game. Of those tickets, 60% were adult tickets and the remainder were student tickets. The revenue from these ticket sales had already been factored into the annual budget. Jordan suggested raising the price of the adult tickets $2.00 to help fill the budget gap. If the athletic department had raised the price of each adult ticket $2.00, then by approximately what percent would the budget gap have been filled?

A. 22%
B. 23%
C. 24%
D. 25%
E. 26%

14. The Wildcat athletic department at Wilson High School needs to raise $3,000.00 to fill a gap in its annual budget. The athletic department can choose 1 of the 2 options below to raise the needed funds.

Sell "Wildcat baseball caps" option: After paying a one-time fee of $23.00 to rent the necessary equipment, the athletic department can sell baseball caps featuring the school's logo. The athletic department will buy plain caps and print the school logo on each, at a cost of $3.50 per cap. The athletic department will sell each cap for $5.00.

Sell "Wildcat T-shirts" option: After paying a one-time fee of $19.00 to rent the necessary equipment, the athletic department can sell T-shirts featuring the school's logo. The athletic department will buy plain T-shirts and print the school logo on each, at a cost of $2.25 per T-shirt. The athletic department will sell each T-shirt for $4.00.

The Wildcat athletic department chose the "Wildcat T-shirt" option and successfully filled the budget gap. What is the minimum number of T-shirts the athletic department must have sold?

F. 1,480
G. 1,664
H. 1,709
J. 1,726
K. 1,812

15. The graph of y2 = x is shown in the standard (x,y) coordinate plane below for values of x such that 0 ≤ x ≤ 4. The x-coordinates of points D and E are both 4. What is the area of ΔDEO, in square coordinate units?

A.
B. 4
C. 8
D. 12
E. 16