ACT math practice test 58

1. If image, then (n - 2)! = ?

F. 6
G. 20
H. 30
J. 60
K. 120

2. At a local restaurant a customer can order a lunch special with the following choices: a salad or 2 kinds of soup and a sandwich with 4 types of meat, 2 types of bread, and 3 types of cheese. How many different combinations could be made for the lunch special?

A. 11
B. 12
C. 48
D. 72
E. 96

3. What is the distance, in coordinate units, between the points S (-image, 7) and T(-3image, 9) in the standard (x, y) coordinate plane?

F. 2
G. 3
H. 2image
J. 4image
K. 6

4. Which of the following expressions is equivalent to image if all integers a, b, and c are positive?

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

5. The sum of twice a smaller number and three times a larger number is 49. The larger of the two numbers exceeds four times the smaller number by 7. If x is the smaller number, which equation below determines the correct value of x?

F. 2(4x + 7) + 3x = 49
G. 2(4x - 7) + 3x = 49
H. (12x + 7) + 2x = 49
J. 3(4x + 7) + 2x = 49
K. 3(4x - 7) + 2x = 49

6. If x = 3T - 7 and y = 4 - T, which of the following expresses y in terms of x?

A. y = 5 - x
B. image
C. y = 4 - x
D. y = 11 - 3x
E. image

7. Which of the following is an equation of the line that passes through the points (2, 4) and (-2, -12) in the standard (x, y) coordinate plane?

F. y = 8
G. 4x - y = 4
H. 4x + y = -4
J. 7x - 3y = 2
K. 8x - 2y = 7

8. If f(x) = 7x2 - 4x - 10, then f(-3) = ?

A. 85
B. 65
C. 41
D. -1
E. -61

9. How much larger, in degrees, is the measure of one angle in a regular 8-sided polygon than the measure of one angle in a regular 6-sided polygon? (The measure of each interior angle of a regular n-sided polygon is image.)

F. 15°
G. 27°
H. 108°
J. 120°
K. 135°

10. Which of the following expressions is equivalent to image when x, y, and z are positive real numbers?

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

11. For all x > 10, image ?

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

12. If the amplitude of a trigonometric function is image the nonnegative difference between the maximum and minimum values of the function, which of the following trigonometric functions has an amplitude of 3?

A. imagecos x
B. cos 3x
C. sin imagex
D. 3 tan x
E. 3 sin x

13. If 90° < x < 180°, which of the following equals sin x, if image?

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

14. Which of the following is the factored form of the expression 12x2 - x - 6?

A. (3x + 2) (4x - 3)
B. (3x - 2) (4x + 3)
C. (4x + 2) (3x - 3)
D. (6x + 1) (2x - 6)
E. (x - 2) (12x + 3)

15. Harry has a bag containing jelly beans: 7 pink, 8 blue, and 9 orange. How many additional pink beans must be added to the 24 jelly beans already in the bag so that the probability of randomly drawing a pink jelly bean is image?

F. 1
G. 5
H. 7
J. 9
K. 10