O-LevelAdditional MathematicsCircular measure4037/12 · May/June 2023 · Q47 Marks
In this question all lengths are in centimetres and all angles are in radians. The diagram shows a circle with centre O and radius r. The points A and B lie on the circumference of the circle such that the angle AOB is θ and the length of the minor arc AB is 12. The area of the minor sector AOB is 57.6 cm². The point C lies on the tangent to the circle at A such that OBC is a straight line.
- (a)Find the values of r and θ.[4]
- (b)Find the area of the shaded region. Give your answer correct to 1 decimal place.[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 (May/June 2023). The mark or mark type is shown in brackets.
- [B1] rθ = 12 soi
- [B1] 1/2 r²θ = 57.6 soi
- [B1] r = 9.6 oe nfww
- [B1] θ = 1.25 oe nfww
- [B1] AC = 28.89
- [M1] Using their AC Shaded area = (1/2 × 28.89 × 9.6) - 57.6 soi
- [A1] 81.1
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