A-LevelMathematicsCircular measure9709/12 · Feb/Mar 2020 · Q76 Marks
The diagram shows a sector AOB which is part of a circle with centre O and radius 6cm and with angle AOB = 0.8 radians. The point C on OB is such that AC is perpendicular to OB. The arc CD is part of a circle with centre O, where D lies on OA. [Figure X.X]
- Find the area of the shaded region.[6]
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Mark scheme
Marking points from the official mark scheme (Feb/Mar 2020). The mark or mark type is shown in brackets.
- [M1] OC = 6cos0.8 SOI
- [A1] OC = 4.18(0)
- [M1] Area sector OCD = 1/2 (their 4.18)² × 0.8 OE
- [M1] ∆OCA = 1/2 × 6 × their 4.18 × sin 0.8 OE
- [DM1] Required area = their ∆OCA – their sectorOCD SOI. If not seen their areas of sector and triangle must be seen
- [A1] 2.01 CWO. Allow or better e.g. 2.0064
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