Variation 1 · answer guide
Differential equation — IVP domain and range
Question
Solve through , then find the domain and range of the solution function.
This practice question was inspired by Question 14(a) in the 2024 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.Separate: . With : , so .
- Simplify the previous line carefully, keeping exact values where possible.Domain: , i.e. .
- Finish the calculation, then check that the result meets the question’s conditions.Range: .
- State the final answer clearly in the form the question requested.Answer: ; domain ; range .
Common mistake: changing so many features that the new example no longer tests the same mathematical idea.
Verification: Check .
Any mark labels are a TestMum study aid, not an official NESA marking allocation.
← Back to 2024 HSC Extension 1 paper Question 14(a)