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← 2022 HSC Extension 1 paper Question 5

Variation 3 · answer guide

Coordinate geometry — Open versus closed parameter interval

Question

If instead for , , the diagram should show

  1. open endpoints near and on the same arc
  2. filled endpoints at and
  3. the entire infinite parabola
  4. only the single point

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.Open parameter interval excludes the endpoint values of .
  2. Finish the calculation, then check that the result meets the question’s conditions.The geometric arc is the same but endpoints are open.
  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: Closed vs open parameter ranges control filled vs open dots.

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

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