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← 2020 HSC Extension 1 paper Question 7

Variation 2 · answer guide

Differential equation — Where slopes vanish

Question

For , where are the slope marks horizontal (away from )?

  1. On the -axis ()
  2. On the -axis ()
  3. On the line
  4. Nowhere

This practice question was inspired by Question 7 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.Horizontal means , so (with ).
  2. Finish the calculation, then check that the result meets the question’s conditions.On the DE is undefined, not horizontal.
  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: Substitute into the slope formula.

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

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