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← 2021 HSC Extension 1 paper Question 8

Variation 2 · answer guide

Coordinate geometry — Shifted centre lower half

Question

Which pair parametrises the lower semicircle centre , radius , diameter on the -axis from to ?

  1. for
  2. for
  3. for
  4. for

This practice question was inspired by Question 8 in the 2021 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.At : ; : ; : — lower semicircle.
  2. Finish the calculation, then check that the result meets the question’s conditions.Option B is the upper semicircle.
  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: Lowest point confirms the lower half.

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

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