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← 2024 HSC Extension 1 paper Question 11(b)

Variation 3 · answer guide

Absolute value inequality — Shifted quadratic inequality

Question

Solve .

This practice question was inspired by Question 11(b) in the 2024 NSW HSC Mathematics Extension 1 examination, © NESA. It is an original TestMum variation that practises the same mathematical idea, not an official NESA question.

Step by step

  1. Set up the solution: separate the absolute-value statement into its valid algebraic cases.Factor .
  2. Finish the calculation, then check that the result meets the question’s conditions.Roots and ; closed interval between them.
  3. State the final answer clearly in the form the question requested.Answer: .

Common mistake: changing so many features that the new example no longer tests the same mathematical idea.

Verification: Endpoints make the product zero and are included.

Any mark labels are a TestMum study aid, not an official NESA marking allocation.

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