ACT Mathematics Practice Questions

Note: Unless otherwise stated, all of the following should be assumed.
Illustrative figures are NOT necessarily drawn to scale.
Geometric figures lie in a plane.
The word line indicates a straight line.
The word average indicates arithmetic mean.

1. If x2 – mx – 27 = 0 when x = 6, what is the value of m?

A. 1.5
B. 2
C. 3.5
D. 5

2. For all x, what is the simplest equivalent of (2x)(x)(2x)(x)(x)?

A. 2x6
B. 4x6
C. 4x5
D. 6x3


3. Given that the above triangle is isosceles, if angle WXY is 44°, what measurement must angle XWY have?

A. 64°
B. 68°
C. 72°
D. 76°

4. If segment WY is 16 units long and segment XZ is 15 units long, how long is segment WX?

A. 17
B. 18
C. 19
D. 20

5. Given the equations 2x + 2y = 16 and 4x – 3y = -3, what are the values of x and y?

A. x = 4, y = 6
B. x = 2, y = 4
C. x = 3, y = 5
D. x = 5, y = 3

6. Two friends take a drive around the city. When they get home, they look at the odometer and their watches, and determine they traveled 54 miles in 72 minutes. What was their average speed in miles per hour?

A. 40 miles/hr
B. 45 miles/hr
C. 50 miles/hr
D. 55 miles/hr

7. Provide the simplest equivalent expression to √72.

A. 8√3
B. 4√18
C. 8√12
D. 6√2


8. Given the curve as sketched out on this graph, what is the domain of the function seen here?

A. -5 < x < 6
B. -6 ≤ x ≤ 2
C. -5 ≤ x ≤ 6
D. -6 < x < 2

9. Given the curve as sketched on this graph, what is the range of the function seen here?

A. -5 < y < 6
B. -6 ≤ y ≤ 2
C. -5 ≤ y ≤ 6
D. -6 < y < 2

10. A student cuts out a cardboard circle that has a radius of 8 inches. What is the total circumference of the circle?

A. 8Π inches
B. 12Π inches
C. 16Π inches
D. 20Π inches

11. As part of a wood shop project, two students build a cabinet that is 6 feet tall, 2 feet wide and 3 feet deep. Half of the cabinet’s interior volume will be used for storing tools, leaving the other half free for personal items. How much volume will be available for students to use?

A. 18 cubic feet
B. 24 cubic feet
C. 36 cubic feet
D. 48 cubic feet

12. Given two variables x and y that are directly proportional such that x = 3 when y = 8, what value will y have when x = 6?

A. 12
B. 16
C. 20
D. 24

13. A student enrolls in a course where the final grade is an average of four exams. Before the final exam, the student reviews the previous three exam scores, which were 89, 97 and 88. What score would the student have to receive on the last exam to achieve at least a 90 average for the course?

A. 78
B. 82
C. 86
D. 90

14. A teacher goes to the local big box store to purchase supplies for a class activity. The teacher buys two bags of apples for a class snack, and four bottles of glue. The total comes to $5.00 for the apples and $6.50 for the glue. Sales tax for food items is 6%, and for non-food items is 4%. How much total tax does the teacher pay for the purchases?

A. $0.36
B. $0.42
C. $0.49
D. $0.56

15. Given the points on the line with the labeled coordinates, what is the slope?

A. 1/3
B. 1/4
C. 1/5
D. 1/6

16. Having determined the slope of the line, what is the slope-intercept equation of the line shown passing through (6,5)?

A. y = 2/3 x + 2
B. y = 1/3 x + 1
C. y = 2/3 x + 4
D. y = 1/3 x + 3

17. A rectangle is three times as long as it is wide. If the total area of the rectangle is 48 square inches, what is the length of the rectangle?

A. 3 inches
B. 9 inches
C. 12 inches
D. 18 inches

18. As a prize for winning a game at school, a student gets to pick a colored egg from a box. Each egg has a slip of paper inside it describing the prize. Red eggs are for candy, blue eggs are for toys, and green eggs are for books. There were 12 red eggs in the box, 8 blue eggs and 15 green eggs. Students must draw blind, and the previous student to draw pulled out an egg for a book. What are the chances that the next student to draw will get an egg for a toy?

A. 15/34
B. 8/34
C. 12/35
D. 20/35

19. A physicist is studying a radioactive element in a lab that has a half-life of 21 days, meaning after 21 days, half of the sample would be inert. If the initial sample of the element was 500 grams, and the study was scheduled to continue for a total of 12 weeks, how much of the element would still be radioactive at the end of the study?

A. 125 grams
B. 93.75 grams
C. 62.5 grams
D. 31.25 grams

20. A student has to finish up work on a project for metal shop. The last piece that needs to be finished is the painting of a metal sphere for the top of a large diorama. The sphere has a radius of 8 inches, and must be painted with two coats of paint in order to be presentable. A quart of the paint the student has in shop class will cover 450 square inches of metal. How many quarts will be sufficient to paint the sphere with two coats?

A. 3
B. 4
C. 5
D. 6

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