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← 2020 HSC Extension 1 paper Question 4

Variation 2 · answer guide

Vectors — 3-4-5 resultant

Question

Starting at the origin, a particle travels along , then , then . Find the distance from the origin.

This practice question was inspired by Question 4 in the 2020 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.Sum: .
  2. Finish the calculation, then check that the result meets the question’s conditions.Distance .
  3. Match the result to the choices and state the correct option.Therefore option C is correct.

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

Verification: The resultant is the -- vector .

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

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