Variation 1 · answer guide

Differential equation — Isocline reading

Question

On a direction field for , the slope mark at is

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.

Set up the solution: separate or integrate the differential equation, include the constant, then use the initial condition.At : , so the mark is horizontal.
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 the point into the DE.

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