ACT Math: Five Problems for Your Weekend (5/8/15)

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.

9.  The expression (4x + 9)(4x – 9) is equivalent to which of the following?

A.  8x² – 81
B.  8x² – 72x – 81
C.  16x² – 81
D.  16x² – 72x – 81
E.  16x² + 72x – 81

24.  The dimensions of a right triangle are shown in the diagram below. What is the value of cos θ?

Five Problems 5-8-2

F.  a/b
G.  a/c
H.  b/a
J.  b/c
K.  c/a

35.  In the standard (x, y) coordinate plane, a line contains the points (-5, 2) and (1, k). If the slope of the line is ½, what is the value of k?

A.  3
B.  4
C.  5
D.  8
E.  14

42.  A sweater is on sale for 30% off the regular price. Sarah receives an employee discount of an additional 20% off the sale price. The final price that Sarah pays is what percent of the original price of the sweater?

F.  50
G. 56
H.  60
J.  70
K.  90

55.  The graph below shows the function f(x) = 3sin(πx). If a represents the amplitude of the function and p represents the period of the function, what is the value of a + p?

Five Problems 5-8-5

A.  4
B.  5
C.  8
D.  3 + 2π
E.  6 + 2π

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


9.  C
24.  G
35.  C
42.  G
55.  B

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