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← 2022 HSC Extension 1 paper Question 11(d)

Variation 2 · answer guide

Vectors — Integer roots

Question

Find so is perpendicular to .

This practice question was inspired by Question 11(d) 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: write the vector relationship component by component, then use a dot product, magnitude or scalar multiple as required..
  2. State the final answer clearly in the form the question requested..

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

Verification: Solve the resulting quadratic exactly.

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

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