2020 HSC Mathematics Extension 1
Question 1:
Quadratic inequality
Which diagram best represents the solution set of ?
How to recognise this question
Question type: quadratic inequalities
- The command and notation point to quadratic inequalities.
- The requested response is a multiple choice.
How to handle it: factor the quadratic, identify its roots, then use the sign of the quadratic on each interval.
Watch out: Do not select a formula until its domain, interval, sign and units match the question.
Step-by-step answer
- Factor the quadratic: .
- The critical points are and . Because the inequality is non-strict (), both roots are included.
- The parabola opens upwards, so the product is non-negative outside the roots: or .
- Only option A shows filled endpoints at the correct roots with outward rays. Option B shades outward from the wrong roots, while options C and D shade between their endpoints.
- Answer: A. (NESA multiple-choice key: A.)
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
Which diagram best represents the solution set of ?
Question 2
Which diagram best represents the solution set of ?
Question 3
Which diagram best represents the solution set of ?
