Variation 3 · answer guide
Differential equation — A separable quadratic
Question
Solve with and .
This practice question was inspired by Question 12(d) 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.
Step by step
- 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 .
- State the final answer clearly in the form the question requested.Final answer:
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.
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