Variation 2 · answer guide

Trigonometric identity — Sine square at 4x

Question

Which integral is equivalent to ?

This practice question was inspired by Question 2 in the 2021 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: apply the named identity first and simplify before integrating or solving..
Finish the calculation, then check that the result meets the question’s conditions.Double-angle frequency is , not .
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: At , and .

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