ACT Math: Five Problems for Your Weekend (4/24/15)

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.

5.  What would the next number in the sequence 7, 9, 12, 16, 21, _____ be?

A.  23
B.  24
C.  25
D.  26
E.  27

20.  An isosceles triangle has one side that is 3 inches long and another side that is 5 inches long. Which of the following could be the length of the third side of the triangle?

I.  3 inches
II.  4 inches
III.  5 inches

F.  I only
G.  II only
H.  III only
J.   I and III
K.  I, II and III

35.  Each edge of a cube is k inches long. What is the ratio of the surface area of the cube to the volume of the cube?

Five Problems 4-27-3

A.  1:2
B.  1:3
C.  1:6
D.  6:k
E.  6:

46.  What is the area, in square units, of the isosceles trapezoid shown in the diagram below?

Five Problems 4-27-4

F.  16
G.  16√2
H.  16√3
J.  32
K.  32√3

57.  If cos θ, rounded to the nearest thousandth, is -0.674, which of the following could be true?

A.  0 < θ < π/4
B.  π/4 < θ < π/2
C.  π/2 < θ < 2π/3
D.  2π/3 < θ < π
E.  3π/2 < θ < 2π

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


5.  E
20.  J
35.  D
46.  H
57.  D

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