Variation 3 · answer guide

Differential equation — A separable quadratic

Question

Solve with and .

This practice question was inspired by Question 7 in the 2025 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..
Simplify the previous line carefully, keeping exact values where possible..
Simplify the previous line carefully, keeping exact values where possible. gives .
Finish the calculation, then check that the result meets the question’s conditions.Solving for gives .
Match the result to the choices and state the correct option.Therefore option B is correct:

Common mistake: changing so many features that the new example no longer tests the same mathematical idea.

Verification: Differentiate the result and use .

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