TestMum
← 2024 HSC Extension 1 paper Question 12(e)

Variation 2 · answer guide

Absolute value inequality — Similar absolute inequality

Question

Solve .

This practice question was inspired by Question 12(e) 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.Need , . For : , so .
  2. Finish the calculation, then check that the result meets the question’s conditions.For : . Discriminant , no solutions in this case.
  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: Only the right-hand branch contributes.

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

← Back to 2024 HSC Extension 1 paper Question 12(e)