O-LevelAdditional MathematicsCircular measure4037/12 · Oct/Nov 2021 · Q99 Marks
The diagram shows a circle, centre O, radius 12cm, and a rectangle ABCD. The diagonals AC and BD intersect at O. The sides AB and AD of the rectangle have lengths 6cm and 4cm respectively. The points M and N lie on the circumference of the circle such that MAC and NDB are straight lines. [Figure 9.1]
- (a)Show that angle AOD is 1.176 radians correct to 3 decimal places.[2]
- (b)Find the perimeter of the shaded region.[4]
- (c)Find the area of the shaded region.[3]
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Mark scheme
Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.
- [M1] For correct method to find AOD
- [A1] Need to see 4 dp or more to justify 3 dp answer
- [B1] Major arc MN =(2π−1.176)12
- [B1] ND or MA = 12-√13
- [B1] For their values in a correct plan, may be implied by a correct answer
- [B1] Perimeter = 94.1
- [B1] Minor sector area = 1/2 × 1.176 × 12²
- [B1] For their values in a correct plan, may be implied by a correct answer
- [B1] Area = 350
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