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← 2022 HSC Extension 1 paper Question 10

Variation 1 · answer guide

Differential equation — Sign of the right-hand side

Question

For , which property must every solution graph have?

  1. Never strictly decreasing on an interval where
  2. Always oscillatory
  3. Always has a vertical asymptote
  4. Must decrease somewhere

This practice question was inspired by Question 10 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., so is non-decreasing.
  2. 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: Autonomous RHS sign controls monotonicity.

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

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