ACT math practice test 46

1. In the figure shown below, ΔABC is a right triangle, image is 8 inches long, and image is 10 inches long. What is the area, in square inches, of square ACDE?

image

F. 2 image
G. image
H. 36
J. 8 image
K. 164

2. In the standard coordinate plane, what is the distance between the points (5, 7) and (13, 11)?

A. 80
B. 12
C. image
D. 8
E. image

3. What value must be added to 9x2 - 30x in order to complete the square (that is, make it a perfect square trinomial)?

F. -5
G. 5
H. 9
J. 25
K. 45

4. A circle in the standard (x, y) coordinate plane is tangent to the x-axis at -a, and tangent to the y-axis at a, with a > 0. The radius of the circle is 4 units. What is the equation of the circle?

A. x2 + y2 = 4
B. x2 + y2 = 16
C. (x - 4)2 + (y - 4)2 = 4
D. (x + 4)2 + (y + 4)2 = 16
E. (x + 4)2 + (y - 4)2 = 16

5. Compared to the graph of y = sin x, the graph of y = 2 sin(4x) has:

F. 8 times the amplitude and the same period.
G. 2 times the amplitude and 4 times the period.
H. 2 times the amplitude and image the period.
J. image the amplitude and 4 times the period.
K. image the amplitude and image the period.

6. Which of the following is the solution set for x such that 3x - 9 ≥ - 3(9 - x)?

A. The empty set
B. The set containing only zero
C. The set of negative numbers
D. The set of positive numbers
E. The set of real numbers

7. In the figure below, square ABCD has a side length of 6 inches, and squares AEFG and CHIJ each have a side length of 1 inch. What is the area, in square inches, of the shaded pentagon DGFIJ?

image

F. 9
G. 12.5
H. 17
J. 18
K. 20.5

8. Let the operation # be defined for the set of real numbers by:

image

Which of the following statements are true for all real numbers x, y, and z?

I. x # y = y # x

II. (x # y) # z = x # (y # z)

III. 0 # x = 0

A. I only
B. II only
C. III only
D. I and III only
E. II and III only

9. If x2 - 36a2 = 5ax, what are the two solutions for x in terms of a?

F. -4a and -9a
G. -4a and 9a
H. -3a and 12a
J. 3a and -12a
K. 4a and -9a

10. For all values of θ over which sin θ and cos θ are nonzero, image

A. 1
B. tan θ
C. cot θ
D. sec θ
E. cscθ

11. For values of x where csc x, sec x, and tan x are all defined, (csc x) o (sec x) o (tan x) = ?

F. sec2x
G. csc2x
H. tan2x
J. 1
K. -1

12. What is the solution set for the equation |-x| = x?

A. All real numbers
B. x ≥ 0
C. x ≤ 0
D. Only x = 0
E. Only x = -1

13. For which of the following values of a will there be exactly one real solution to the equation 2x2 - ax + 8 = 0?

F. 2 image
G. 4
H. 4 image
J. 6
K. 8

14. If x = 3T + 4 and y = 5 - T, then which of the following equations expresses y in terms of x?

A. y = image
B. y = image
C. y = 9 - x
D. y = x + 9
E. y = x - 1

15. In the circle below, radius image has a length of 10 meters, and central angle ∠AOB measures 30°. What is the area, in square meters, of shaded sector AOB?

image

F. image
G. image
H. image
J. image
K. image