ACT math practice test 40

1. Which of the following expresses the equation 4x - 2y = 12 in slope-intercept form for the standard (x, y) coordinate plane?

F. image
G. image
H. y = 2x - 6
J. y = -2x + 6
K. y = -2x - 6

2. Which of the following values for a in the equation 3x + 3a - 5 = 5x - a causes the solution for x to be 6?

A. -8.5
B. -4.25
C. 4.25
D. 8.5
E. 13.25

3. The centers of 3 identically sized circles lie on the diameter of a larger circle, as shown in the figure below. Each of the 4 circles is tangent to 2 other circles, as shown. If the circumference of each small circle is 8π inches, what is the circumference of the largest circle, in inches?

image

F. 16π
G. 24π
H. 48π
J. 64π
K. 144π

4. A recipe calls for cooking a turkey 1 hour for every 3 pounds it weighs. How long should a 19-pound turkey cook?

A. 6 hours and 15 minutes
B. 6 hours and 20 minutes
C. 6 hours and 30 minutes
D. 6 hours and 33image minutes
E. 6 hours and 40 minutes

5. Line T intersects parallel lines m and n. Angle measures are as shown in the figure below. What is the degree measure of imagea?

image

F. 10°
G. 80°
H. 90°
J. 100°
K. 110°

6. A photocopy machine enlarges a small triangle to produce a larger, similar triangle, as shown below. If the lengths of the sides, in inches, are as marked on the figure, and the triangles are similarly oriented, what is the value of x in inches?

image

A. 7image
B. 9
C. 9image
D. 9image
E. 11

7. If the lengths of adjacent sides of a rectangular playground have measures of 4x - 3 and 2x2 + 7 units, respectively, then which of the following expressions represents the area, in square units, of the playground?

F. 2x2 + 4x + 4
G. 4x2 + 8x + 8
H. 8x3 - 21
J. 8x3 - 6x2 + 28x - 21
K. 8x3 + 6x2 + 28x + 21

8. Which of the following is a prime factorization of 2,100?

A. 2 · 3 · 5 · 7
B. 22 · 3 · 52 · 7
C. 22 · 3 · 5 · 35
D. 22 · 52 · 21
E. 22 · 550

9. After Jean spent 90% of her vacation money, $100 remained. How much vacation money did she originally have?

F. $111
G. $191
H. $900
J. $1,000
K. $1,111

10. Which of the following is a simplified version of image whenever x ≠ 0?

A. 9x + 2
B. 9x2 + 2x
C. image
D. image
E. image

11. If 2x2 - x - 15 = 0, what are the 2 possible values for x?

F. -5 and image
G. -3 and image
H. -3 and image
J. 3 and - image
K. 5 and - image

12. All angles in the figure shown below are right angles. If each side has a length of 4 centimeters, what is the area of the figure in square centimeters?

image

A. 32
B. 40
C. 44
D. 48
E. 80

13. If m, located at (-1, 2), is the midpoint of image, and the coordinates of a are (2, 9), what are the coordinates of b?

F. (-5, 16)
G. (-4, -5)
H. (0.5, 5.5)
J. (4, -5)
K. (5, 16)

14. In the figure below, lengths in units and angle measures in degrees are as marked. How many units long is image?

image

A. 3
B. 3image
C. 3image
D. 6
E. 3image

15. To increase the mean of 5 numbers by 3, by how much would the sum of the 5 numbers need to increase?

F. 3
G. 6
H. 9
J. 15
K. 18