O-LevelAdditional MathematicsCircular measure4037/22 · Oct/Nov 2011 · Q78 Marks
In the diagram AD and BE are arcs of concentric circles centre O, where OA = 6cm and AB = 8 cm. The area of the region ABED is 32 cm². The triangle OCF is isosceles with OC = OF = 20 cm. [Figure 7.1]
- (i)Find the angle θ in radians.[3]
- (ii)Find the perimeter of the region BCFE.[5]
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Mark scheme
Marking points from the official mark scheme (Oct/Nov 2011). The mark or mark type is shown in brackets.
- [M1A1] (i) 1/2 (14² - 6²)θ = 32
- [A1] (i) 0.4
- [M1] (ii) CF = 20 sin 0.2 or CF² = 20² + 20² - 2 × 20 × 20 cos 0.4
- [A1] (ii) (CF=)7.95
- [M1] (ii) Uses s = rθ
- [M1] (ii) Complete plan including s = rθ
- [A1] (ii) 25.5 or 25.6
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