Elementary Algebra Practice Questions on the ACT

By Lisa Zimmer Hatch, Scott A. Hatch

The ACT Math Test gives you all sorts of opportunities to tackle elementary algebra questions, where you “solve the equation for x.” You learn this type of material in your first semester or two of algebra.

About one-eighth of the questions cover elementary algebra. Here are two questions for you to try.

Sample questions

  1. Solve for x in the equation:

    image0.png

    (A) 7

    (B)

    image1.png

    (C) 5

    (D)

    image2.png

    (E) 2

  2. Which of the following is a possible sum of the two solutions for this equation:

    image3.png

    (F) –17

    (G) –11

    (H) –1

    (J) 11

    (K) 1

Answers and explanations

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

    Don’t ask for trouble. Keep life simple by starting with the simple answers first, and begin in the middle with Choice (C). That is, try plugging in 5. When it doesn’t work, don’t bother plugging in

    image4.png

    That’s too much work. Go right down to 2.

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

    You find the solutions for a quadratic equation by finding its binomial factors and setting both equal to 0. The two values whose product is 30 and whose sum is –11 are –6 and –5:

    image5.png

    So the binomial factors are

    image6.png

    Set both equal to 0 and solve for x:

    image7.png

    So the two solutions are 5 and 6. Their sum is 11, which is Choice (J). If you pick Choice (G), you are missing a step. You’ve forgotten to set the factors equal to zero and solve for x. The signs for the solutions to a quadratic are the opposite of those of the values within the binomial factor.