Intermediate Algebra Practice Questions on the ACT

By Lisa Zimmer Hatch, Scott A. Hatch

The ACT Math Test includes questions on intermediate algebra, which range from radicals to probabilities to percent increase. Here are three practice questions for you to try.

Sample questions

  1. 1. Find the value of

    image0.png

    (A)

    image1.png

    (B)

    image2.png

    (C)

    image3.png

    (D)

    image4.png

    (E) 1,221

  2. Ross has 2 black socks and 2 white socks lying in his drawer. If he blindly selects two socks from the drawer, what is the chance that he will select the black pair?

    (F)

    image5.png

    (G)

    image6.png

    (H)

    image7.png

    (J)

    image8.png

    (K)

    image9.png

  3. 3. In 2010, Coach Denges won 20 prizes at the county fair by tossing a basketball into a bushel basket. In 2011, he won 25 prizes. What was his percent increase?

    (A) 100

    (B) 30

    (C) 25

    (D) 20

    (E)

    image10.png

Answers and explanations

  1. 1. The correct answer is Choice (D).

    This problem calls for straightforward multiplication:

    image11.png

  2. 2. The correct answer is Choice (F).

    Before you find the chance Ross will pick two black socks, you first have to find the chance that the first sock he picks will be black. That chance is

    image12.png

    because 2 out of 4 socks are black. Then, you have to multiply that fraction by the probability that the second sock will be black. Be careful, because the second probability isn’t also

    image13.png

    because Ross has already picked a black sock from the drawer. After the first sock, only 3 socks remain in the drawer and only 1 is black. So the chance that the second sock he picks will be black is actually

    image14.png

    The chance that both socks Ross picks will be black can then be found by multiplying

    image15.png

  3. 3. The correct answer is Choice (C).

    The number by which his prizes increased, from 20 to 25, is 5. That’s the numerator. The original whole, or what he began with, is 20. That’s the denominator. So your fraction looks like this:

    image16.png