A-LevelMathematicsCircular measure9709/12 · Oct/Nov 2018 · Q87 Marks
The diagram shows an isosceles triangle ACB in which AB = BC = 8 cm and AC = 12 cm. The arc XC is part of a circle with centre A and radius 12 cm, and the arc YC is part of a circle with centre B and radius 8 cm. The points A, B, X and Y lie on a straight line.
- (i)Show that angle CBY = 1.445 radians, correct to 4 significant figures.[3]
- (ii)Find the perimeter of the shaded region.[4]
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Mark scheme
Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.
- [M1] Correct method for ABC, expect 1.696°awrt
- [M1] For attempt at CBY = π – ABC
- [A1] CBY = 1.445°AG
- [B1] Arc YC = 8 × 1.445
- [*M1] For a valid attempt at BAC, may be from (i). Expect 0.7227°
- [DM1] Arc XC = 12 × (their BAC)
- [A1] Perimeter = 11.56 + 8.673 + 4 = 24.2 cm awrt www
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