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 are posted here.

9. If *f*(*x*) = 5*x**² +* 3*x* – 7, then *f*(-3) = ?

A. -61

B. -31

C. -1

D. 29

E. 209

20. If *x* + *y* = 37 and *x* – *y = *13, then * y * = ?

F. 6

G. 12

H. 18

J. 25

K. 50

35. One side of a triangle is 22 cm long and another side is 8 cm long. Which of the following could be the length, in centimeters, for the third side?

A. 7

B. 10

C. 16

D. 31

E. 35

48. The graph of *f*(*x*) = *x*² is shown below in the standard (*x*, *y*) coordinate plane. Which of the following could be the graph of *g*(*x*), also shown below. (Note: the coordinates of the vertex are given for each of the parabolas.)

F. *g*(*x*) = (*x* + 4)² – 5

G. *g*(*x*) = (*x* + 4)² + 5

H. *g*(*x*) = (*x* – 4)² + 5

J. *g*(*x*) = (*x* – 5)² + 4

K. *g*(*x*) = (*x* + 5)² + 4

51. What is the set of all values of *k* that satisfy the equation below for all nonzero values of *x*?

A. {0}

B. {1)

C. {-3, -4}

D. {3, 4}

E. {7, 12}

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 info@cardinalec.com.

Solutions:

9. D

20. G

35. C

48. H

51. C

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