Your ACT Math score can only get better with practice. Getting the score you want takes time and effort on your part, but hard work is usually rewarded on test day. Here are five problems similar to what you’ll encounter on the ACT. I hope you have a few minutes this weekend to find a quiet place and give them a try.

The numbering of the problems is meant to give you an idea of where in a section a problem might appear.

Answers appear at the end of the post. Full solutions can be found here.

15. What is the sixth term in the geometric sequence 243, 162, 108, …… ?

A. 27

B. 32

C. 48

D. 54

E. 72

22. Tom places a 20 feet ladder 6 feet from the base of a wall that is perpendicular to the ground. To the nearest tenth of a foot, how many feet is the top of the ladder above the ground?

F. 14.0

G. 17.3

H. 18.5

J. 19.1

K. 20.9

35. A circle is inscribed inside a square that has its vertices in the standard (*x*, *y*) coordinate plane at the points (2, 0), (2, 8), (10, 0) and (10, 8) as shown in the diagram below. What is the equation of the circle?

A. (*x* – 5)² + (*y* – 4)² = 4

B. (*x* – 5)² + (*y* – 4)² = 5

C. (*x* – 5)² + (*y* – 4)² = 16

D. (*x* – 6)² + (*y* – 4)² = 16

E. (*x* + 6)² + (*y* + 4)² = 16

40. Michelle has a circular flower bed in her back yard. This summer, she plans to double the diameter of the garden. She is trying to figure out how much garden soil, mulch and edging she will need for the garden. Which of the following statement is true about the effect that doubling the diameter will have on the garden’s area and its circumference?

F. The area will double; the circumference will double

G. The area will be four times as large; the circumference will double

H. The area will be four times as large; the circumference will be four times as large

J. The area will be eight times as large; the circumference will be four times as large

K. The area will be eight times as large; the circumference will be eight times as large

53. The 20 juniors in the Key Club at Roswell High School sold an average of 18 boxes of oranges during a recent fundraiser. The 30 seniors in the club sold an average of 24 boxes of oranges during the same event. If the club consists of only these juniors and seniors, what is the average number of boxes sold by the members of the club?

A. 20.0

B. 21.0

C. 21.4

D. 21.6

E. 22.4

If you have questions about these problems or anything else to do with the ACT, send us an email at info@cardinalec.com.

Solutions:

15. B

22. J

35. D

40. G

53. D

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