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← 2020 HSC Extension 1 paper Question 7

Variation 1 · answer guide

Differential equation — Sign chart for a related DE

Question

For , which statement is true in the first quadrant ()?

  1. Slopes are positive
  2. Slopes are negative
  3. Slopes are zero
  4. Slopes are undefined everywhere in Q1

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.In Q1 both and are positive, so .
  2. Finish the calculation, then check that the result meets the question’s conditions.Therefore slopes are positive.
  3. Match the result to the choices and state the correct option.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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