ACT Math: Five Problems for Your Weekend (3/20/15)

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.

15.  Which of the following is the equation of a line perpendicular to the line with equation 4x – 8y = 24?

A.  y = -4x + 7
B.  y = -2x + 3
C.  y = -1/2x – 5
D.  y = 1/2x + 1
E.  y = 2x + 6

32.  If ab = 5, then a²b² + a³b³ = ?

F.  5a + 5b
G.  5a + 10b
H.  10a + 10b
J.  125
K.  150

41.  What is the area, in square units, of ΔABC in the figure below?
(Note: the length of segment AD is 24 units and ∠ ADB is a right angle)

Five Problems 3-20-3

A.  155
B.  180
C.  240
D.  270
E.  310

44.  A ramp is 20 feet long and makes an angle with the ground of 3.8 degrees as shown in the diagram below. To the nearest tenth of a foot, how high is the ramp off the ground at its highest point?

Five Problems 3-20-4

F.  1.3
G.  1.6
H.  2.4
J.   3.8
K.  20.0

53.  In the triangle below tanA = 2/3.  What is the length of segment CB?

Five Problems 3-20-5

A.  3
B.  4
C.  6
D.  7
E.  8

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


15.  B
32.  K
41.  A
44.  F
53.  C

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