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← 2025 HSC Extension 1 paper Question 1

Variation 1 · answer guide

Absolute value inequality — A bounded interval

Question

Solve .

  2. or
  4. or

This practice question was inspired by Question 1 in the 2025 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.
  2. Simplify the previous line carefully, keeping exact values where possible.
  3. Finish the calculation, then check that the result meets the question’s conditions.
  4. Match the result to the choices and state the correct option.Therefore option A is correct:

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

Verification: Test (inside) and (outside) in the original inequality.

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

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