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← 2023 HSC Extension 1 paper Question 12(a)

Variation 3 · answer guide

Antidifferentiation — Upper limit 5

Question

With , evaluate .

This practice question was inspired by Question 12(a) in the 2023 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: choose a substitution or identity that simplifies the integrand, then reverse-differentiate to check., bounds to ; .
  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: Keep exact surds when the upper limit is not .

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

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