The diagram shows the curve y = sin x cos 2x for 0 ≤ x ≤ ½π, and its maximum point M. [Figure 11.1]

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2022). The mark or mark type is shown in brackets.

1. [1] Use correct product rule or chain rule
2. [1] Obtain correct derivative in any form cos x.cos 2x – sin x.2sin 2x
3. [1] Equate derivative to zero and use a correct double angle formula
4. [1] Obtain an equation in one trigonometric variable
5. [1] Obtain 6sin²x = 1, 6cos²x = 5 or 5tan²x = 1
6. [1] Obtain final answer x = 0.421
7. [1] State or imply du = –sin x dx
8. [1] Using double angle formula, express integral in terms of u and du
9. [1] Integrate and obtain ±(u – ⅔u³)
10. [1] Use limits u = 1, u = 1/√2 in an integral of the form au + bu³, where ab ≠ 0
11. [1] Obtain ⅓(√2 – 1) or ⅓√2 – ⅓ or ⅓(√2 – 1) or simplified equivalent