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Math · Intermediate Algebra

Hard Intermediate Algebra Drill

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

Hard Math Intermediate Algebra

All 15 questions

  1. 1 Solving a Quadratic by Factoring Solve for x: x^2 - 3 x + 2 = 0. Hard
  2. 2 Function Evaluation If f(x) = 3x^2 - 2, what is f(3)? Hard
  3. 3 System of Linear Equations Solve the system: 1x + 1y = 4 and x + y = 4. Express your answer as (x, y). Hard
  4. 4 Exponent Rules Simplify (x^2)^2 · x^2. Hard
  5. 5 Solving a Quadratic by Factoring Solve for x: x^2 - 4 x + 3 = 0. Hard
  6. 6 Function Evaluation If f(x) = 3x^2 - 1, what is f(3)? Hard
  7. 7 System of Linear Equations Solve the system: 2x + 1y = 9 and x + y = 6. Express your answer as (x, y). Hard
  8. 8 Exponent Rules Simplify (x^2)^3 · x^1. Hard
  9. 9 Solving a Quadratic by Factoring Solve for x: x^2 - 7 x + 12 = 0. Hard
  10. 10 Function Evaluation If f(x) = 3x^2 - 1, what is f(4)? Hard
  11. 11 System of Linear Equations Solve the system: 1x + 1y = 5 and x + y = 5. Express your answer as (x, y). Hard
  12. 12 Exponent Rules Simplify (x^2)^2 · x^1. Hard
  13. 13 Solving a Quadratic by Factoring Solve for x: x^2 - 3 x + 2 = 0. Hard
  14. 14 Function Evaluation If f(x) = 3x^2 - 3, what is f(2)? Hard
  15. 15 System of Linear Equations Solve the system: 3x + 1y = 7 and x + y = 5. Express your answer as (x, y). 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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