ACT math practice test 61

1. In the figure all angles are right angles and each dimension given is in inches. What is the perimeter of the figure in inches?

image

A. 21
B. 35
C. 36
D. 54
E. 72

2. Which of the following graphs represents the solution set of the inequality |x| > 2 on the real number line?

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

3. In a game, 100 marbles numbered 0-99 are placed into a box. A player draws 1 marble at random from the box. Without replacing the first marble, the player draws a second marble at random. If both marbles drawn have the same tens digit (that is, both are numbered 0-9 or 10-19 or 20-29, etc.), the player is a winner. If the first marble drawn is numbered 56, what is the probability that Terry will be a winner on the next draw?

A. image
B. image
C. image
D. image
E. image

4. In the diagram image intersects image at c and image is parallel to image Which of the following statements must be true?

image

F. imagea is congruent to imaged.
G. Δ ACB is congruent to ΔECD.
H. image is congruent to image
J. Δ ACB is similar to ΔECD.
K. imageACB is congruent to imageCED.

5. At the same time that a 6-foot man has a 4-foot shadow, a flag pole has a 14-foot shadow. What is the height of the flag pole, in feet?

A. image
B. 12
C. 16
D. 21
E. 28

6. The formula for surface area of a right circular cylinder is a = 2πR(R + h) where a is surface area, R = radius of the cylinder, and h is the height of the cylinder. Then h = ?

image

F. a - 2πR - R
G. image
H. image
J. image
K. image

7.

Employees of We-Bug-U sell merchandise by telephone. Employees are offered 2 different pay options. Option A offers employees $8.00 per hour plus a commission equal to 10% of their sales. Option B offers $11.00 per hour with no commission. Each employee must choose one of these options at the beginning of each pay period.

Juanita, an employee of We-Bug-U, worked for 6 hours and earned $68.00 for the 6-hour period. What was the amount of her sales for the 6-hour period?

A. $20.00
B. $80.00
C. $100.00
D. $200.00
E. $400.00

8. Romeo and Juliet (both employees of We-Bug-U) each worked 15 hours and had sales of $400.00. Romeo chose Option A while Juliet chose Option B. Which employee made more money and how much more?

F. Romeo: $5.00 more
G. Juliet: $5.00 more
H. They earned the same amount.
J. Juliet: $25.00 more
K. Romeo: $355.00 more

9. The width of a rectangle is 27 feet and the length is 36 feet. What is the length of a diagonal of the rectangle in feet?

A. 63
B. 54
C. 45
D. 42
E. 36

10. The vertices of a parallelogram in the coordinate plane are (3, 3), (7, 3), (8, 8), and (4, 8). What is the area of this parallelogram?

F. 10
G. image
H. 16
J. 20
K. image

11. The point (-1, 1) is the midpoint of the line segment in the standard (x, y) coordinate plane joining the point (1, 6) and the point (a, b). Which of the following is (a, b)?

A. (-2, 3)
B. (-3, -4)
C. (0, 3.5)
D. (3, 11)
E. (2, 5)

12. The first term of the geometric sequence below is 27. What is the twelfth term? 27, 9, 3….

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

13. In ΔABC, AB = AC = 14. Which of these values could NOT be the length of the third side, image?

image

A. 5
B. 7
C. 14
D. 16
E. 28

14. If 43x+1 = 8x+2, then x = ?

F. image
G. image
H. image
J. 3
K. None of these

15. If f(x) = x2 and g(x) = 2x - 1, then f(g(x)) = ?

A. 4x2 - 4x + 1
B. 4x2 + 1
C. 2x2 - 1
D. x2 - 1
E. 4x2 + 4x + 1