ACT math practice test 57

1. image

In the quadrilateral ACGD, DF imageAC and AG imageBF. What is the value of imaged?

A. 9°
B. 12°
C. 21°
D. 26°
E. 38°

2. image

For triangle EFG, what is the value of imagea?

F. 52°
G. 58°
H. 61°
J. 71°
K. 73°

3. A boat is anchored in a small lake with a rope that is 34 feet long. A wind blows the boat until the rope is taut and the water is 16 feet deep. Measuring across the bottom of the lake, how far has the boat moved from the anchor?

A. 30
B. 50
C. 60
D. 80
E. 120

4. If a and b are real numbers and image, then what must be true of the value of b?

F. b must be positive.
G. b must be negative.
H. b must equal image.
J. b must equal 3.
K. b may have any value.

5. In the figure below, image1 is parallel to image2, and image3 is parallel to image4. What is the value of imageb?

image

A. 44
B. 46
C. 48
D. 62
E. 132

6. If 0° ≤ x ≤ 90° and cos x = image, then tan x = ?

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

7. In the figure, AD is a diameter of the circle with center O and AO = 5. What is the measure of arc BCD?

image

A. 56°
B. 116°
C. 120°
D. 124°
E. 128°

8. If sin θ = image and cos θ = image, then csc θ = ?

F. 2
G. image
H. image
J. image
K. image

9. Triangle PQR is equilateral. Find the sum of a + b + c + d.

image

A. 180°
B. 210°
C. 240°
D. 270°
E. 300°

10. If image is defined for all positive numbers a and b by image ?

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

11. The measures of the lengths of the 3 sides of a triangle are prime numbers. If 2 of the sides are 5 and 23, how many different lengths are possible for the third side?

A. 1
B. 2
C. 9
D. More than 18 but less than 29
E. An infinite number

12. If a wheel on a stationary bike is 26 inches in diameter, and Mike pedals to make the wheel revolve 50 times, what would be the total distance that the wheel would travel if it weren't stationary?

F. 169π
G. 1,300
H. 676π
J. 1,300π
K. 2,600π

13. What is the equivalent of (3i + 4)2?

A. 12i2
B. 9i2 + 16
C. 3i2 + 24i + 16
D. 7 + 24i
E. 13 + 24i

14. Maureen wants to put an exercise wheel in her hamster's cage. The height of the cage is 22 inches, but there must be a 1-inch space above and below the wheel to allow for the wheel frame. What is the radius of the largest wheel that Maureen can place in the cage?

F. 5
G. 2 image
H. 10
J. 11
K. 20

15. What is the sum of the first 15 multiples of 5?

A. 375
B. 560
C. 600
D. 750
E. 1,200