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Math · Pre-Algebra

Hard Pre-Algebra Drill

15 hard-difficulty ACT Math questions on Pre-Algebra. Each question is on its own page with a worked answer explanation, the underlying rule, and a quick study tip.

Hard Math Pre-Algebra

All 15 questions

  1. 1 Percent of a Number What is 20% of 200? Hard
  2. 2 Splitting a Total in a Ratio A total of 220 dollars is divided between two people in the ratio 3:8. How much does the f Hard
  3. 3 Mean of a Data Set Find the mean of the data set: 11, 8, 7, 9, 7. Hard
  4. 4 Evaluating an Exponent What is the value of 5^4? Hard
  5. 5 Adding Fractions with Different Denominators Compute 3/3 + 2/5. Express the answer in lowest terms. Hard
  6. 6 Percent of a Number What is 35% of 150? Hard
  7. 7 Splitting a Total in a Ratio A total of 90 dollars is divided between two people in the ratio 3:6. How much does the fi Hard
  8. 8 Mean of a Data Set Find the mean of the data set: 12, 9, 12, 6, 6. Hard
  9. 9 Evaluating an Exponent What is the value of 2^2? Hard
  10. 10 Adding Fractions with Different Denominators Compute 2/4 + 3/6. Express the answer in lowest terms. Hard
  11. 11 Percent of a Number What is 35% of 120? Hard
  12. 12 Splitting a Total in a Ratio A total of 280 dollars is divided between two people in the ratio 2:12. How much does the Hard
  13. 13 Mean of a Data Set Find the mean of the data set: 9, 8, 11, 8, 10. Hard
  14. 14 Evaluating an Exponent What is the value of 5^2? Hard
  15. 15 Adding Fractions with Different Denominators Compute 1/5 + 2/5. Express the answer in lowest terms. Hard

How to use this drill

Open the questions one at a time. Read the prompt, decide on an answer before scrolling, then check the explanation. The point of a drill is not to "get the question right" — it's to internalize the rule so you can apply it cold under timed conditions on test day.

If you're missing more than a third of the questions in this set, drop down a difficulty tier and rebuild from there. If you're getting all of them quickly, jump up a tier and try a mixed drill across subtopics.

What "Hard" means here

Hard questions are designed to separate strong test-takers. They typically require multiple rules applied in sequence, or careful elimination among answers that all look plausible. Expect to see these appear later in real ACT sections; even strong test-takers miss a couple per test.

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