ACT math practice test 23

1. Two hoses attached to separate water sources are available to fill a cylindrical swimming pool. If both hoses are used, the time it will take to fill the pool can be represented by the following equation: , where T1 and T2 represent the time needed for hoses 1 and 2, respectively, to fill the pool on their own, and Tc represents the time needed for hoses 1 and 2 to fill the pool working together. If hose 1 alone can fill the pool in exactly 20 minutes and hose 2 alone can fill the pool in exactly 60 minutes, how many minutes will it take to fill the pool if both hoses work simultaneously?

A. 3
B. 10
C. 15
D. 18
E. 40

2. A 5-sided die, which has sides 2, 3, 4, 5, and 6, is thrown. What is the probability that the die will NOT land on a prime-numbered face?

F.
G.
H.
J.
K. 0

3. For f(x,y) = 7x + 9y, what is the value of f(x,y) when and x = 3?

A.
B.
C. 36
D. 46
E. 96

4. What is the length, in coordinate units, of a diagonal of a square in the standard (x,y) coordinate plane with vertices at points (0,0), (4,0) and (4,4)?

F. 3
G. 4
H. 4
J.
K. 8

5. What is the value of a if log4a = 3?

A. 120
B. 64
C. 12
D.
E. 4

6. A certain 18-quart stockpot is filled completely with water and exposed to a heat source so that the water boils away at a constant rate. The water remaining in the stockpot can be approximated by the following equation: y = 18 - 0.2x, where x is the number of minutes that the pot has been heated for 0 ≤ x ≤ 90, and y is the number of quarts remaining in the pot. According to this equation, which of the following statements is true about this stockpot?

F. After 0.2 minutes, 1 quart of water has boiled away.
G. After 1 minute, 0.2 quarts of water have boiled away.
H. After 18 minutes, 0.2 quarts of water have boiled away.
J. After 18 minutes, 1 quart of water has boiled away.
K. After 36 minutes, 18 quarts of water have boiled away.

7. The volume of a right circular cone with the bottom removed to create a flat base can be calculated from the following equation: V = πh(R2 + r2 + Rr), where h represents the height of the shape and R and r represent its radii as shown in the figure below:

This formula can be used to determine the capacity of a large coffee mug. Approximately how many cubic inches of liquid can the cup shown below hold if it is filled to the brim and its handle holds no liquid?

A. 19
B. 50
C. 105
D. 109
E. 438

8. Which of the following is the set of real solutions for the equation 9x + 12 = 3(3x + 4)?

F. The set of all real numbers
G. {0,1}
H. {0}
J.
K. The empty set

9. The expression equals:

A.
B.
C.
D.
E.

10. A thin slice is cut from a bagel, creating the cross-section represented below. The diameter of the bagel is 144 mm and the width from the inner edge of the bagel to the outer edge is uniformly 56 mm. Which of the following is closest to the area, in square millimeters, of the shaded empty space inside the cross-section of the bagel?

F. 100
G. 450
H. 800
J. 3,200
K. 16,000

11. For all nonzero real numbers a, b, and c, what is the value of a0 + b0 + c0?

A. Undefined
B. a + b + c
C. 0
D. 1
E. 3

12. In the figure below, ABCD is a rectangle, AB = AE, and E, F, G, and H lie on AD. Of the angles BEA, BFA, BGA, BHA, and BDA, which one has the greatest tangent?

F. BEA
G. BFA
H. BGA
J. BHA
K. BDA

The graph of y = f(x) is shown in the standard (x,y) coordinate plane below with points V, W, X, Y, and Z labeled.

13.

The y-intercept of the graph of y = f(x) is located at which of the following points?

A. V
B. W
C. X
D. Y
E. Z

The graph of y = f(x) is shown in the standard (x,y) coordinate plane below with points V, W, X, Y, and Z labeled.

14.

The function y = f(x) can be classified as one of which of the following types of functions?

F. Trigonometric
G. Quadratic
H. Absolute value
J. Cubic
K. Linear

The graph of y = f(x) is shown in the standard (x,y) coordinate plane below with points V, W, X, Y, and Z labeled.

15.

If y = f(x) is to be reflected across the line y = x, which of the following graphs represents the result?

A.
B.
C.
D.
E.