ACT math practice test 45

1. What is the solution set for the inequality 6 - 4(x - 2) > 4x + 5?

A. x < - image
B. x < - image
C. x < image
D. x > - image
E. x > image

2. For the circle whose standard equation is (x - 1)2 + (y + 2)2 = 8, the center and radius are:

F. center = (-1, 2); radius = 2image.
G. center = (-1, 2); radius = 4.
H. center = (0, 0); radius = 4.
J. center = (1, -2); radius = 2image.
K. center = (1, -2); radius = 4.

3. Parallelogram RSTU is shown below, with image = 4 inches, image = 7 inches, and image = 5 inches. What is the area of RSTU in square inches?

image

A. 16
B. 20
C. 28
D. 35
E. 40

4. If the lengths of the sides of the triangle below are shown in inches, how many inches long is side image?

image

F. 2 image
G. 10
H. 4image
J. 26
K. 42

5. Which of the following is the equation for a circle with diameter image, given that a = (4, 2) and b = (8, -4)?

A. x2 + y2 = 13
B. x2 + y2 = 26
C. (x - 6)2 + (y + 1)2 = 13
D. (x + 6)2 + (y - 1)2 = 13
E. (x - 6)2 + (y + 1)2 = 26

6. Which of the following comprises all of the values of x for which image?

F. x < 1
G. x < image
H. x < 7
J. x > image
K. x > 7

7. A guide wire for a telephone tower makes an angle of 50° with the level ground and is 14 meters from the base of the tower. How many meters long is the guide wire?

image

A. 3.8
B. 13.5
C. 16.68
D. 21.78
E. 22.58

8. For all image is equivalent to:

F. -1
G. image
H. 1
J. image
K. image

9. In the standard (x, y) coordinate plane, the midpoint of image is (5, 7) and a is located at (2, 3). If the coordinates of b are (x, y), what is the value of (x + y)?

A. 19
B. 17
C. 11
D. 8.5
E. 8

10. If the solutions to the equation (x + a)(x + b) = 0 are x = 8 and x = -image, then a + b = ?

F. -13
G. -12
H. -6.5
J. 6.5
K. 12

11. In the figure below, all line segments intersect at right angles, and all measurements are given in inches. What is the perimeter of the figure in inches?

image

A. 23
B. 28
C. 46
D. 130
E. Cannot be determined

12. If cot θ = P, which of the following expressions must also equal P?

F. tan θ
G. csc θ - 1
H. sin θ - cos θ
J. image
K. image

13. A line in the standard (x, y) coordinate plane contains the points (5, 9) and (8, 3). What is the x-intercept of this line?

A. 19
B. image
C. 0
D. -2
E. - image

14. Each side of a given cube is a square with an area of 729 square inches. What is the volume of the cube in cubic inches?

F. 33
G. 39
H. 312
J. 318
K. 364

15. If p and q are positive integers, and 6pq4 and 12p2q2 have a greatest common factor of 1,050, then which of the following is a possible value for the sum of p and q?

A. 6
B. 8
C. 12
D. 35
E. 42