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← 2021 HSC Extension 1 paper Question 14(b)

Variation 3 · answer guide

Differential equation — Numerical check

Question

Evaluate to the nearest thousand.

This practice question was inspired by Question 14(b) in the 2021 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..
  2. Simplify the previous line carefully, keeping exact values where possible.Numerator .
  3. Finish the calculation, then check that the result meets the question’s conditions.Denominator .
  4. State the final answer clearly in the form the question requested. (nearest thousand ; paper says approximately ).

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

Verification: Matches the exam approximation.

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

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