ACT Math: Five Problems for Your Weekend (2/20/15)

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.

9.  For all x, (5x – 4)² = ?

A.  10x² – 8
B.  25x² – 16
C.  25x² + 16
D.  25x² – 20x + 16
E.  25x² – 40x + 16

20.  Which number is a solution to the following equation?


F.   2
G.  3
H.  3.5
J.  4
K.  4.5

33.  Points B and C are on a circle with center at A.  The central angle ∠BAC measures 80 degrees. What is the measure, in degrees, of ∠ABC ?

Five Problems 2-20-3

A.  40
B.  45
C.  50
D.  100
E.  There is not enough information to determine the measure of ∠ABC.

46.  Two planes take off from an airport at the same time. One is headed off at a bearing of N 34 E and the other is headed off at a bearing of S 45 E. After ten minutes, the first plane has traveled 80 miles and the second plane has traveled 100 miles. What is an expression for how far apart the planes are at that time?

(Note: The law of cosines states that for any triangle with vertices A, B, and C and the sides opposite those vertices with lengths a, b, and c, respectively, c2 = a2 + b2 – 2ab·cosC.)

Five Problems 2-20-4

F.  \sqrt{80^{2}+100^{2}}
G.  \sqrt{80^{2}+100^{2}-2(80)(100)cos34}
H.  \sqrt{80^{2}+100^{2}-2(80)(100)cos45}
J.  \sqrt{80^{2}+100^{2}-2(80)(100)cos79}
K.  \sqrt{80^{2}+100^{2}-2(80)(100)cos101}

51.  The mean of 5 numbers is 24. The largest of these five numbers is 43 and the smallest of the five numbers is 10. What is the mean of the other 3 numbers?

A.  20
B.  22 1/3
C.  23
D.  24
E.  33 1/2

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


9.  E
20.  J
33.  C
46.  K
51.  B.

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