Given that y = x cos 2x, find dy/dx.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.

1. [M1] (a) [1] cos2x + x(-2sin2x) oe, isw, nfww
2. [M1] (a) for d/dx(cos2x) = -2sin2x soi or M1 FT for correct structure of product rule FT their(-2 sin 2x)
3. [A1] (a) implied by 2 marks
4. [M3] (b) -1/2 x cos2x + 1/4 sin2x + c oe, isw, nfww
5. [M2] (b) for -2∫xsin 2x dx = x cos 2x - 1/2 sin 2x +c or for -1/2 xcos2x + ksin2x + c, where k > 0 oe, or for ∫xsin2x dx = -1/2 x cos2x + ∫1/2 cos 2x dx oe,
6. [M1] (b) for -2∫xsin 2x dx = x cos2x - ∫cos 2x dx or 2∫xsin 2x dx = -xcos2x + ∫cos2x dx or xcos2x = ∫cos2x dx + ∫-2xsin2xdx oe, soi
7. [A1] (b) implied by 4 marks