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← 2022 HSC Extension 1 paper Question 5

Variation 1 · answer guide

Coordinate geometry — Right half of the same parabola

Question

For , with , which description is correct?

  1. From to , filled endpoints, concave down
  2. From to , concave down
  3. From to , open endpoints
  4. Full parabola through both sides of

This practice question was inspired by Question 5 in the 2022 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: convert between parametric and Cartesian forms carefully, noting the direction of the parameter.; ; closed interval filled ends.
  2. Finish the calculation, then check that the result meets the question’s conditions.Still on .
  3. Match the result to the choices and state the correct option.Therefore option A is correct.

Common mistake: changing so many features that the new example no longer tests the same mathematical idea.

Verification: Check endpoints and the eliminated Cartesian equation.

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

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