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

Variation 3 · answer guide

Absolute value inequality — Find critical equality points

Question

For with , , find all solutions of the equality.

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.: (take the root ).
  2. Finish the calculation, then check that the result meets the question’s conditions.: or .
  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: These are the boundary points of the exam solution set.

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

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