ACT Math: Five Problems for Your Weekend (3/27/15)

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.

7.  The expression (3x – 4)(x + 5) is equivalent to which of the following?

A.  3x² – 20
B.  3x² + 1
C.  3x² + x – 20
D.  3x² + 11x – 20
E.  3x² + 19x – 20

22.  The solutions to the equation x² + 10x = 24 are:

F.  -12 and 2
G.  -4 and -6
H.  -2 and 12
J.   4 and -6
K.  4 and 6

35.  What is the length, in inches, of the arc AB in the circle (with center O) below if ∠AOB has a measure of 30 degrees and segment OA has a length of 6 inches?

Five Problems 2-27-3


A.  6
B.  12
C.  π
D.  2π
E.  6π

44.  What is the value of (6 – i)² given that i² = -1?

F.  35
G.  37
H.  35 – 6i
J.  35 – 12i
K.  37 – 12i

51.  The graph of the function 3sin(½ x) is shown below.

Five Problems 3-27-5

The function is:
A.  even (that is f(-x) = f(x) for all values of x)
B.  odd (that is f(-x) = –f(x) for all values of x)
C.  neither even nor odd
D.  undefined when x = 0
E.  undefined when x = 2π

If you have questions about these problems or anything else to do with the ACT, leave a comment below or send me an email at


7.  D
22.  F
35.  C
44.  J
51.  B


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