ACT Sample Math Questions, Part 1

1. Steven wants to put trim around the edge of a quilt that is 7 feet long by 6 feet wide. How much trim, in feet, does Steven need?

A. 13
B. 14
C. 26
D. 28
E. 30

2. A teacher graded the first 5 tests in a stack. She gave a 76, 80, 69 and 71 for the first four tests. If she gave an average grade of 74 for the five tests, what grade did she give the fifth test?

F. 74
G. 75
H. 76
J. 77
K. 79

3. Mary ate 1 2/3 cups of rice last week and 2 and 3/7 cups of rice this week. How much rice total did she eat in those two weeks?

A. 3 5/10
B. 4 5/10
C. 3 2/21
D. 4 2/21
E. 5 2/21

4. If 3x – 2 = 5x -14, then x equals:

F. 3
G. 6
H. 9
J. 12
K. 14

5. Mathilda’s new job comes with a salary increase of 8%. If she currently makes $64,000 per year, which of the following is closest to what she will earn per year at her new job?

A. $69,000
B. $70,000
C. $71,000
D. $72,000
E. $76,000

6. If David biked 10 miles in 4 hours and Mary biked three times as much in half the time, what was Mary’s average rate of speed?

F. 5 mph
G. 10 mph
H. 15 mph
J. 20 mph
K. 25 mph

7. The expression (4x – 3)(x + 2) is equivalent to

A. 4x2 – x + 2
B. x – 6
C. 4x2 + 8x – 6
D. 4x2 + 5x – 6
E. 4x – 6

8. |-4 | 2 + | -7 | – 2 =

F. 21
G. 13
H. 7
J. 25
K. 17

Answer Key

1. The best answer is C. For the trim to cover the entire perimeter of the quilt it would need to be 7 + 6 + 7 + 6 = 26 feet long.

2. The best answer is F. 74 x 5 = 370. 76 + 80 + 69 + 71 = 296. 370 – 296 = 74.

3. The best answer is D. 1 2/3 + 2 3/7 = 5/3 + 17/7 = 35/21 + 51/21 = 86/21 = 4 2/21

4. The best answer is G. If 3x – 2 = 5x – 14, then 2x = 12 so x = 6

5. The best answer is A. 8% of $64,000 = 8/100 x 64,000 = 5,120. Mathilda will be making $64,000 + $5120, or $69,120. This is closest to $69,000.

6. The best answer is H. If Mary biked three times as much as David, she biked 30 miles. She biked it in ½ of the time David biked in, or 2 hours. 30 miles in 2 hours is a rate of 15 mph.

7. The best answer is D. Remember to multiply out these equations using the order FOIL (first, outside, inside, last). Using this approach, we get 4x2+ 8x – 3x – 6 or 4x2 + 5x – 6

8. The best answer is F. The absolute value of -4 squared is 16. The absolute value of -7 is 7. Therefore solve for the equation 16 + 7 – 2. The answer is 21.