ACT math practice test 16

1. In the standard (x,y) coordinate plane, what is the area of the circle (x - 3)2 + (y + 2)2 = 25?

F. 5π
G. 10π
H. 25π
J. 125π
K. 225π

2. In the standard (x,y) coordinate plane below, the base of a right triangle lies along the x-axis and is bisected by the y-axis. The vertex of the angle opposite the base is on the graph of the parabolic function f(x) = 2x2 - 4. Let b represent any value of x such that - < x < 0. Which of the following is an expression in terms of b for the area, in square coordinate units, of any such right triangle?

A. 4b4 - 16b2 + 16
B. 4b3 - 8b
C. 2b3 - 4b
D. 2b2 + b - 4
E. b2 - 4b + 4

3. Which of the following expressions must be an even integer if x is an integer?

F. x + 5
G.
H. x4
J. 4x
K. 5x

4. Which of the following ranges of consecutive integers contains the value of the expression ?

A. 0 and 1
B. 1 and 2
C. 2 and 3
D. 5 and 6
E. 7 and 8

5. The employees at Belinda's Paint Store are having a competition to see who can create the most new accounts over a period from January to June in a certain year. Data is missing because one of the employees began to erase it from the white board, thinking that the competition was over. The numbers in the chart below have been confirmed with the assistant manager's personal records.

Which of the following is closest to the percent decrease in Cameron's new accounts from January to February?

F. 4.00%
G. 17.40%
H. 19.40%
J. 20.00%
K. 21.10%

6. The employees at Belinda's Paint Store are having a competition to see who can create the most new accounts over a period from January to June in a certain year. Data is missing because one of the employees began to erase it from the white board, thinking that the competition was over. The numbers in the chart below have been confirmed with the assistant manager's personal records.

At the beginning of the year, Maura wanted to average 30 new accounts per month for the first four months of the year. How many new accounts did she need to create in March in order to reach this goal?

A. 25
B. 27
C. 29
D. 31
E. 37

7. The employees at Belinda's Paint Store are having a competition to see who can create the most new accounts over a period from January to June in a certain year. Data is missing because one of the employees began to erase it from the white board, thinking that the competition was over. The numbers in the chart below have been confirmed with the assistant manager's personal records.

Additional records are uncovered that show that Don's sales decreased 5% each month from January to May because his responsibilities in the store mounted and he could not seek out new accounts as frequently. Which of the following is closest to the number of new accounts Don created in May?

F. 44
G. 52
H. 56
J. 72
K. 84

8. The amplitude of the trigonometric function shown below is defined as the average of the absolute values of the maximum value of f(x) and the minimum value of f(x). The trigonometric function graphed below can be described by the equation f(x) = a sin(bx + c), where a, b, and c are real numbers. Which of the following values describes the amplitude of this function?

A. 1
B. 2
C. 3
D. π
E. 2π

9. A group of die-hard baseball fans has purchased a house that gives them a direct view of home plate, although their view of the rest of the field is largely impeded by the outfield wall. The house is 30 meters tall, and their angle of vision from the top of the building to home plate has a tangent of . What is the horizontal distance, in meters, from home plate to the closest wall of the fans' house?

F. 35
G. 32
H. 25.7
J. 5
K. 4.3

10. Given the equation |y2 - 11| - 2 = 0, which of the following is a solution but NOT a rational number?

A.
B. 4
C. 2
D.
E. 3

11. Below is the graph that a specialty automobile manufacturer uses to plot the speed tests done on his new cars. The speed is recorded in units of and is conducted for a period of 9 seconds. A certain order of 3 of the following 6 actions describes the results of the speed test depicted in the graph below. Which order is it?

I. Constant speed for 1 second

II. Constant speed for 3 seconds

III. Speed increase for 4 seconds

IV. Speed increase for 9 seconds

V. Speed decrease for 2 seconds

VI. Speed decrease for 7 seconds

F. IV, II, VI
G. III, II, V
H. I, III, V
J. III, I, VI
K. V, I, II

12. As shown in the figure below, a compass has marks for every 10° and "North" and "South" are the endpoints of a line segment. If the point of the needle of this compass travels 42 mm as it moves in a clockwise direction from "East" to "North," how long is the needle to the nearest tenth of a millimeter?

A. 6.7
B. 8.9
C. 13.4
D. 14
E. 17.8

13. For θ, an angle whose measure is between 270° and 360°, cos θ = . Which of the following equals tan θ?

F. -
G. -
H.
J.
K.

14. Consider all positive integer values a and b such that the product ab = 8. For how many values does there exist a positive integer c that satisfies both 2a = c and cb = 256?

A. Infinitely many
B. 6
C. 4
D. 2
E. 0

15. A sphere is inscribed in a cube with a diagonal of 3 ft. In feet, what is the diameter of the sphere?

F. 3
G. 2
H. 2
J. 3
K. 3