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← 2022 HSC Extension 1 paper Question 5

Variation 2 · answer guide

Coordinate geometry — Direction of travel

Question

On , for , the particle moves

  1. from to , left half of an upward parabola, endpoints included
  2. from to
  3. along the full parabola
  4. vertically only

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.; ; for .
  2. Finish the calculation, then check that the result meets the question’s conditions.Motion is toward the vertex as increases.
  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: Always evaluate endpoints and eliminate the parameter.

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

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