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← 2021 HSC Extension 1 paper Question 13(b)

Variation 1 · answer guide

Vector motion — Max height only

Question

With , , (same displacement model with -term ), find the maximum height.

This practice question was inspired by Question 13(b) 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: differentiate position to get velocity and acceleration, then translate the angle condition into a dot product.Apex when : .
  2. Finish the calculation, then check that the result meets the question’s conditions..
  3. State the final answer clearly in the form the question requested.Maximum height is .

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

Verification: Maximum height equals .

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

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