Variation 1 · answer guide

Differential equation — Reciprocal slope DE

Question

Which equation best represents solutions of (for )?

This practice question was inspired by Question 4 in the 2021 NSW HSC Mathematics Extension 1 examination, © NESA. It is an original TestMum variation that practises the same mathematical idea, not an official NESA question.

Set up the solution: separate or integrate the differential equation, include the constant, then use the initial condition.Separate: .
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: Straight lines through the origin (and the singular solution ).

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