O-LevelAdditional MathematicsCircular measure4037/12 · Oct/Nov 2019 · Q1011 Marks
The diagram shows a circle centre O, radius 10cm. The points A, B and C lie on the circumference of the circle such that AB = BC = 18 cm. [Figure 10.1]
- (i)Show that angle AOB = 2.24 radians correct to 2 decimal places.[3]
- (ii)Find the perimeter of the shaded region.[5]
- (iii)Find the area of the shaded region.[3]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.
- [1] M1 Attempt to use cosine rule
- [1] A1 Allow unsimplified
- [1] A1 Must justify 2 dp
- [1] M1 For attempt to find angle AOC or ABC
- [1] A1 Condone 1.8 or 1.80
- [1] M1 For attempt at arc length using 10×their AOC
- [1] M1 For attempt at AC using their AOC, or ABC but AOC ≠ 2.24 or 2π/3
- [1] A1 Allow awrt 33.7
- [1] M1 For attempt at sector area
- [1] M1 For attempt at area of triangle
- [1] A1 Lack of accuracy is penalised here
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