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Math · Intermediate Algebra

Medium Intermediate Algebra Drill

15 medium-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.

Medium Math Intermediate Algebra

All 15 questions

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

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 "Medium" means here

Medium questions add a layer — multi-step calculation, two competing rules, or a mildly tempting wrong answer that requires careful reading. A student scoring around 26 composite should be solid here; this is also the sweet spot for most score-improvement work.

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