A-LevelMathematicsCircular measure9709/12 · Oct/Nov 2023 · Q46 Marks
The diagram shows the shape of a coin. The three arcs AB, BC and CA are parts of circles with centres C, A and B respectively. ABC is an equilateral triangle with sides of length 2cm. [Diagram provided]
- (a)Find the perimeter of the coin.[2]
- (b)Find the area of the face ABC of the coin, giving the answer in terms of π and √3.[4]
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 2023). The mark or mark type is shown in brackets.
- [B1] Finding one correct arc length – may be implied by correct final answer.
- [B1] AWRT
- [B1] SOI AWRT
- [B1] AWRT Allow use of 60°
- [M1] OE Or 3 sectors - 2 triangles (3 × (2π/3) - 2 × √3) or Sector + 2 segments ( (2π/3) + 2( (2π/3) - √3 ) )
- [A1] Must be one of these simplified versions but equivalent decimal answers can score B1B1M1
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