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← 2020 HSC Extension 1 paper Question 11(e)

Variation 3 · answer guide

Differential equation — With initial condition

Question

Solve with , giving in terms of .

This practice question was inspired by Question 11(e) 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: separate or integrate the differential equation, include the constant, then use the initial condition.General: .
  2. Finish the calculation, then check that the result meets the question’s conditions.At , : .
  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: When , ; derivative check holds.

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

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