A-LevelMathematicsCircular measure9709/12 · May/June 2019 · Q55 Marks
The diagram shows a semicircle with diameter AB, centre O and radius r. The point C lies on the circumference and angle AOC = θ radians. The perimeter of sector BOC is twice the perimeter of sector AOC. Find the value of θ correct to 2 significant figures.
- The diagram shows a semicircle with diameter AB, centre O and radius r. The point C lies on the circumference and angle AOC = θ radians. The perimeter of sector BOC is twice the perimeter of sector AOC. Find the value of θ correct to 2 significant figures.[5]
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Mark scheme
Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.
- [B1] Perimeter of AOC = 2r + rθ
- [B1] Angle COB = π- θ
- [B1] Perimeter of BOC = 2r + r(π – θ)
- [M1] (2r +) πr – rθ = 2((2r) + rθ) or (2 + π - θ = 4 + 2θ → θ = (π-2)/3)
- [A1] θ = 0.38
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