ACT math practice test 52

1. In imgABC below, what is tan imagea?

img

F. img
G. img
H. img
J. img
K. img

2. Jenna wants to serve a large pot of soup to 25 people by 1:15 P.M. If it takes her 7 minutes to assemble the ingredients, 20 minutes to cut up the vegetables, and img hours to cook the soup on the stove, what is the latest time that Jenna could begin her meal preparation?

A. 9:53 A.M.
B. 9:58 A.M.
C. 10:18 A.M.
D. 10:21 A.M.
E. 10:28 A.M.

3. Hiram's garden contains 45 tomato plants, 15 watermelon plants, and 120 lettuce plants. Approximately what percent of the garden is occupied by watermelon plants?

F. 0.12%
G. 8.30%
H. 12%
J. 15%
K. 83%

4. What is the additive inverse of the polynomial 5x3 - 4x2 + 6x - 9?

A. -5x3 + 4x2 - 6x - 9
B. -5x3 + 4x2 - 6x + 9
C. 5x3 - 4x2 + 6x - 9
D. -9 + 6x - 4x2 + 5x3
E. 9 - 6x - 4x2 + 5x3

5. In the standard (x, y) coordinate plane, if image has endpoint a at (-2, 4) and midpoint m at (3, 9), where is endpoint b located?

F. (0.5, 6.5)
G. (6.5, 0.5)
H. (7, 1)
J. (8, 14)
K. (14, 8)

6. Which of the following, if any, is equivalent to the inequality |x| - 4 < -7?

A. x < -3 and x > 3
B. x > -3 and x < 3
C. -3 < x < 3
D. -3 > x and 3 < x
E. None of these.

7. What is the sum of the interior angles of pentagon imgLMNPR?

img

F. 180°
G. 540°
H. 600°
J. 720°
K. 900°

8. Which of the following values of n makes the statement n? = 4 true?

A. 16
B. 8
C. 4
D. 2
E. img

9. If a and b can be any two real numbers such that b < -6 and 3a - b = 21, which of the following is a solution set for a?

F. a ≤ 9
G. a ≤ 5
H. a < 5
J. a ≥ 9
K. a ≥ -5

10. Darcy used a 12-m piece of rope to tie her dog to a tree while she mowed her front yard. The dog could only walk in a semicircle because the tree was located directly next to the house (see diagram below). Assuming 3.14 for π, how much area, in square meters, could the dog cover?

img

A. 57
B. 75
C. 113
D. 226
E. 452

11. For 3x ≠ 2y, the polynomial expression img is equivalent to which of the following?

F. 2x - 3y
G. 2x - 12y
H. 3x - 2y
J. 8x - 3y
K. 8x + 3y

12. Jose recently opened a new business. He projects that his profit will be $25,000 for the first year, and will increase by 7% over the next 8 years. Which of the following best describes the sequence formed by his annual profits?

A. Geometric with a common ratio of 0.07
B. Geometric with a common ratio of 1.07
C. Geometric with a common ratio of 1.7
D. Arithmetic with a common difference of 25.07
E. Arithmetic with a common difference of 25,000

13. The trapezoid shown below in the standard (x, y) coordinate plane has vertices as marked. What is the area of the trapezoid in square units?

img

F. 49.5
G. 59.5
H. 66
J. 99
K. 119

14. What is the greatest common factor of the terms 12x4y2 and 6xy3?

A. 6xy2
B. 6x4y2
C. 6x4y3
D. 12xy2
E. 12x4y3

15. In the figure below, m is the midpoint of image and imgLMP is equilateral. If image = 8, what is the length of image?

img

F. 4
G. img
H. img
J. 8
K. img