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ACT Math Practice Questions with Answers

Try each question before opening the solution. Time yourself at about one minute per question, which is the ACT's average pace.

These questions are written by NextPoint in the style of the ACT. They are not taken from any official test. The ACT Math section has 5 answer choices per question, as here.

  1. If 4(x − 3) = 2x + 10, what is the value of x?

    • A. 7
    • B. 9
    • C. 11
    • D. 13
    • E. 22
    Show answer and solution

    Answer: C. Distribute: 4x − 12 = 2x + 10. Subtract 2x from both sides: 2x − 12 = 10. Add 12: 2x = 22. So x = 11. Plug it back to check: 4(8) = 32 and 2(11) + 10 = 32.

  2. A jacket is on sale for $60 after a 20% discount. What was the original price?

    • A. $72
    • B. $75
    • C. $78
    • D. $80
    • E. $48
    Show answer and solution

    Answer: B. After a 20% discount you pay 80% of the original, so 0.8 × original = 60. Original = 60 ÷ 0.8 = 75. The $72 choice comes from adding 20% to $60, which is the common trap.

  3. A right triangle has legs of length 9 and 12. What is its perimeter?

    • A. 21
    • B. 30
    • C. 34
    • D. 36
    • E. 108
    Show answer and solution

    Answer: D. This is a 3-4-5 triangle scaled by 3, so the hypotenuse is 15. Check: 81 + 144 = 225 and the square root of 225 is 15. The perimeter is 9 + 12 + 15 = 36.

  4. If f(x) = 2x² − 3x + 1, what is f(−2)?

    • A. 15
    • B. 3
    • C. 11
    • D. −13
    • E. 19
    Show answer and solution

    Answer: A. Substitute −2: 2(−2)² − 3(−2) + 1 = 2(4) + 6 + 1 = 8 + 6 + 1 = 15. The choice 3 comes from dropping the sign on −3(−2).

  5. The mean of 5 numbers is 12. When a sixth number is added, the mean of all 6 numbers is 14. What is the sixth number?

    • A. 14
    • B. 18
    • C. 20
    • D. 26
    • E. 24
    Show answer and solution

    Answer: E. The first five sum to 5 × 12 = 60. All six sum to 6 × 14 = 84. The sixth number is 84 − 60 = 24.

How to review a missed question

  • Name the skill (percent change, Pythagorean triples, function notation, mean).
  • Write down the one step where you went wrong, not just the answer.
  • Redo the question a few days later without looking. If you get it right, the fix has stuck.

Want more? Read how to raise your ACT score from 28 to 34, or see what a good ACT score is.

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