The diagram shows a triangle OAB where OA = OB = 10cm and angle AOB = 0.8 radians. Points C and D on OA and OB respectively are such that the arc CD is part of a circle with centre O and radius 6 cm. The shaded region is bounded by the arc CD and the line segments CA, AB and BD. [Figure X.X]

Mark scheme

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

1. [B1] 6 × 0.8
2. [M1] AB² =10² +10² −2×10×10cos0.8 or AB = 2(10sin 0.4) or AB = 10 sin 0.8 / sin ((π - 0.8)/2) Allow angles correctly converted to degrees for this mark. 0.8rad = 45.8°, OAB = OBA=67.1°. (π-0.8)/2 = 1.17. This mark can be implied by AWRT 7.8.
3. [A1] 20.6 AWRT
4. [B1] [Area of sector =] ½×6²×0.8
5. [M1] [Area of triangle =] ½×10²×sin0.8 or 10sin0.4×10cos0.4 or other complete method. OE Allow use of their value of θ or ½θ in degrees.
6. [A1] 21.5 AWRT