O-LevelMathematicsMensuration4024/13 · May/June 2025 · Q206 Marks
OAB and OCD are sectors of circles, each with centre O and angle 60°. Sector OAB has radius 6 cm. Sector OCD has radius 9 cm. [Figure 20.1]
- (a)The perimeter of the shaded region is (aπ + b) cm. Find the value of a and the value of b.[3]
- (b)Calculate the area of the shaded region. Give your answer in its simplest form in terms of π.[3]
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Mark scheme
Marking points from the official mark scheme (May/June 2025). The mark or mark type is shown in brackets.
- [3] (a) [a=] 5, [b=] 6
- B2 for a = 5
- or M2 for (60/360) × 2π×9 - (60/360) × 2π×6[ + 2 × 3] oe
- or M1 for (60/360) × 2π×9 or (60/360) × 2π×6 oe
- [3] (b) (15π/2) or 7.5π oe
- M2 for (60/360) ×π×9² - (60/360) ×π×6² oe
- or M1 for (60/360) ×π×9² oe or (60/360) ×π×6² oe
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