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← 2023 HSC Extension 1 paper Question 3

Variation 3 · answer guide

Differential equation — Sign of slope in Q2

Question

For with and , the solution curves are

  1. increasing
  2. decreasing
  3. horizontal
  4. vertical

This practice question was inspired by Question 3 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: separate or integrate the differential equation, include the constant, then use the initial condition.In Q2, because is negative and positive.
  2. Finish the calculation, then check that the result meets the question’s conditions.Positive slope means increasing curves.
  3. Match the result to the choices and state the correct option.Therefore option A is correct.

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

Verification: At the slope is .

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

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