O-LevelAdditional MathematicsCircular measure4037/12 · Oct/Nov 2024 · Q37 Marks
In this question, all lengths are in centimetres and all angles are in radians. [Figure X.X] The diagram shows a circle with centre O and radius 12, and a circle with centre C and radius 5. The circles intersect at the points A and B, such that OA and OB are tangents to the circle with centre C.
- (a)Show that the obtuse angle ACB is 2.35 radians, correct to 2 decimal places.[2]
- (b)Find the perimeter of the shaded region.[2]
- (c)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 2024). The mark or mark type is shown in brackets.
- [M1] ACB = 2 tan⁻¹(12/5) oe
- [A1] ACB = (2×1.176...) = 2.35 to 2 dp
- [B1] Arc length = 5× ACB
- [B1] Perimeter = 35.8
- [M2] M1 for area of kite or area of sector M1 dep for kite area - sector area
- [A1] 30.6
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