2024 HSC Mathematics Extension 1
Question 11(b):
Absolute value inequality
Solve .
How to recognise this question
Question type: absolute value inequalities
- The command and notation point to absolute value inequalities.
- The requested response is a worked solution.
How to handle it: separate the absolute-value statement into its valid algebraic cases.
Watch out: Do not select a formula until its domain, interval, sign and units match the question.
Step-by-step answer
- Factor: .
- Critical points and . The parabola opens upwards, so between the roots (inclusive).
- Solution: .
- NESA 11(b): 2 marks for the correct closed interval; 1 mark for attempting to factor the LHS (or equivalent merit).
Common mistake: choosing a familiar formula before checking that its conditions, signs, interval and units match this question.
The paper records 2 total marks for this group. Where the official marking guide provides useful partial-credit criteria, those criteria are stated in the steps above.
Try your hand at it again by answering these questions
Question 1
Solve .
Question 2
Solve .
Question 3
Solve .