Variation 2 · answer guide

Rates of change — Limiting temperature

Question

For , the temperature the object approaches as is

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., so .
Finish the calculation, then check that the result meets the question’s conditions.The limiting value is the ambient temperature in Newton's law of cooling.
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: Initial temperature would be .

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