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← 2020 HSC Extension 1 paper Question 13(a)

Variation 3 · answer guide

Differentiation techniques — Cosine power companion

Question

(i) Differentiate . Hence,

(ii) With , show by transforming to .

This practice question was inspired by Question 13(a) 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: apply product, chain or quotient rules carefully, simplifying only after differentiating.(i) .
  2. Finish the calculation, then check that the result meets the question’s conditions.Using part (i), (ii) turns the integrand into .
  3. 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: Differentiate to recover .

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

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