ACT Math: Five Problems for Your Weekend (5/1/15)

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.

NOTE: Questions 7 & 8 both refer to the table shown below

Arial surveyed the twenty students in her class about their favorite color. The results are shown in the table below.

Color Number of Students
Red 7
Blue 4
Green 3
Purple 5
Yellow 1

7. What percent of the students said their favorite color was purple?

A.  5
B.  10
C.  20
D.  25
E.  50

8. If Arial made a circle graph (pie chart) of the data, how many degrees would the sector for the students who chose red be?

F.  35
G.  45
H.  63
J.  110
K.  126

27.  Sean ran around the track shown below. The straightaway part of the track is 300 feet long and the semicircular ends have a diameter of 100 feet. What is the approximate distance, in feet, that Sean runs in each lap around the track?

Five Problems 5-1-3

A.  600
B.  850
C.  914
D.  1228
E.  8454

42.  In the diagram below, segment AB in the larger square is 4 inches long. Angle ACB has a measure of 30 degrees. What is the area, in square inches, of the smaller shaded square?

Five Problems 5-1-4

F.  16
G.  32
H.  48
J.  64
K.  128

55.  Two complex numbers are conjugates if they are in the form a + bi  and abi. What is the result when you multiple (7 + 3i) by its conjugate?  (Note: i² = -1)

A.  40
B.  58
C.  40 + 42i
D.  40 – 42i
E.  58 + 42i

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


7.  D
8.  K
27.  C
42.  J
55.  B



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