Rates of change — A changing sector

Question

A sector has constant area cm². If rad/s, find when cm.

This practice question was inspired by Question 12(a) 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: write the geometric constraint, differentiate every changing quantity with respect to time, then substitute., so .
Simplify the previous line carefully, keeping exact values where possible..
Simplify the previous line carefully, keeping exact values where possible..
Finish the calculation, then check that the result meets the question’s conditions.At , cm/s.
State the final answer clearly in the form the question requested.Final answer: cm/s

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

Verification: The negative sign is sensible: radius must shrink while angle grows at constant area.

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