TestMum
← 2025 HSC Extension 1 questions

2025 HSC Mathematics Extension 1

Question 1:
Absolute value inequality

1 markabsolute value inequalities

What is the solution to ?

  2. or
  4. or

How to recognise this question

Question type: absolute value inequalities

  • The command and notation point to absolute value inequalities.
  • The requested response is a multiple choice.

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

  1. means .
  2. Subtract : .
  3. Divide by : , so option A is correct.

Common mistake: choosing a familiar formula before checking that its conditions, signs, interval and units match this question.

The paper records 1 total mark 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 .

  2. or
  4. or
See the step-by-step answer guide →

Question 2

Solve .

  2. or
  3. or
  4. or
See the step-by-step answer guide →

Question 3

Solve .

  1. or
  2. or
  3. or
  4. only
See the step-by-step answer guide →