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← 2022 HSC Extension 1 paper Question 12(a)

Variation 1 · answer guide

Differential equation — Same field, new points

Question

For , find the slopes at and .

This practice question was inspired by Question 12(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.: .
  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: Substitute coordinates carefully into numerator and denominator.

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

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