ACT math practice test 18

1. trapezoid is found by multiplying the height byIf a square has an area of 64 square units, what is the area of the largest circle that can be inscribed inside the square?

F. 4π
G. 8π
H. 16π
J. 64
K. 64π

2. What is the product of the solutions of the expression x2 - 5x - 14 = 0?

A. -14
B. -2
C. 0
D. 5
E. 7

3. Factoring the polynomial x12 -9 reveals a number of factors for the expression. Which of these is NOT one of the possible factors?

F. x6 + 3
G. x12 - 3
H. x3 +
J. x3 -
K. x3 -

4. What is the value of when x= ?

A. 4
B. 2
C.
D. 12
E. 24

5. If you drive 60 miles at 90 miles an hour, how many minutes will the trip take you?

F. 15
G. 30
H. 40
J. 60
K. 90

6. The area of a trapezoid is found by multiplying the height by the average of the bases: A= h(b1+b2). Given the side measurements below, what is the area, in square inches, of the trapezoid?

A. 15
B. 22
C. 24
D. 24
E. 30

7. If x = - and x = are the roots of the quadratic equation ax2 + bx + c = 0, then which of the following could represent the two factors of ax2 + bx + c?

F. (3x + 2) and (4x - 1)
G. (3x + 1) and (4x - 2)
H. (3x - 1) and (4x + 2)
J. (3x - 2) and (4x + 1)
K. (3x - 2) and (4x - 1)

8. In the rhombus below, diagonal AC = 6 and diagonal BD = 8. What is the length of each of the four sides?

A.
B.
C. 5
D. 7
E. 10

9. A rectangular rug has an area of 80 square feet, and its width is exactly 2 feet shorter than its length. What is the length, in feet, of the rug?

F. 8
G. 10
H. 16
J. 18
K. 36

10. In the Cartesian plane, a line runs through points (1,-5) and (5,10). Which of the following represents the slope of that line?

A.
B.
C. 1
D.
E.

11. The equation of a circle in the standard (x,y) coordinate plane is given by the equation (x + 5)2 + (y - 5)2 = 5. What is the center of the circle?

F. (-, )
G. (-5, 5)
H. (, -)
J. (5, -5)
K. (5, 5)

12. The graph below shows the function f(x) in the coordinate plane. Which of the following choices best describes the domain of this function?

(Note: The domain is defined as the set of all values of x for which a function is defined.)

A. {0, 1, 2, 3, 4}
B. {0, 1, 2}
C. {x: 0 < x < 2}
D. {x: 0 < x < 4}
E. All real values of x

13. Amber decides to graph her office and the nearest coffee shop in the standard (x,y) plane. If her office is at point (-1,-5) and the coffee shop is at point (3,3), what are the coordinates of the point exactly halfway between those of her office and the shop? (You may assume Amber is able to walk a straight line between them.)

F. (1,-1)
G. (1, 4)
H. (2,-1)
J. (2, 4)
K. (2, 0)

14. For a chemistry class, Sanjay is doing an experiment that involves periodically heating a container of liquid. The graph below shows the temperature of the liquid at different times during the experiment. What is the average rate of change of temperature (in degrees Celsius per minute) during the times in which Sanjay is applying heat to this container?

A. 4
B. 5
C. 8
D. 10
E. 20

15. If a5 for a ≠ 0, which of the following statements must be true?

F. x ≠ 0 and y ≠ 0
G. x + y = 5
H. x - y = 5
J. xy = 5
K. = 5