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← 2022 HSC Extension 1 paper Question 14(a)

Variation 3 · answer guide

Differential equation — Verify by differentiation

Question

Show that satisfies and .

This practice question was inspired by Question 14(a) 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: separate or integrate the differential equation, include the constant, then use the initial condition.Logarithmic differentiation or product rule: .
  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..

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

Verification: Direct check of the particular solution.

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

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