Variation 1 · answer guide

Rates of change — Different ambient and excess

Question

If , what is the initial temperature of the object?

This practice question was inspired by Question 1 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: write the geometric constraint, differentiate every changing quantity with respect to time, then substitute..
Finish the calculation, then check that the result meets the question’s conditions.Ambient is ; excess is ; initial is their sum.
Match the result to the choices and state the correct option.Therefore option C is correct.

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

Verification: As , , so the constant term is ambient, not initial.

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