O-LevelAdditional MathematicsCircular measure4037/22 · May/June 2021 · Q76 Marks
DAB is a sector of a circle, centre A, radius 18 cm. The lines CB and CD are tangents to the circle. Angle DAB is (7π/9) radians. [Figure 7.1]
- (a)Find the perimeter of the shaded region.[3]
- (b)Find the area of the shaded region.[3]
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Mark scheme
Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.
- (a) M2 [Arc length + 2 × tangent length] M1 for [Arc length] 18 × 7π/9 oe or [Tangent length] 18 × tan (7π/18) oe or [Tangent length] 18 / tan (π/9) oe or [Tangent length] 18 × sin(7π/18) / sin(π/18) oe
- (a) A1 143 or 142.9 or awrt 142.9 (cm)
- (b) M2 FT their BC or CD from (a) providing it is not 18 [Area of kite – area of sector] M1 for [area of sector] (1/2) × 18² × (7π/9) oe or [area of kite] 18 × their(18 × tan(7π/18)) oe or [area of kite] 18 × their(18×tan70) oe
- (b) A1 494 or 494.3 or awrt 494.3 (cm²)
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