O-LevelAdditional MathematicsCircular measure4037/11 · May/June 2020 · Q78 Marks
The diagram shows an isosceles triangle OAB such that OA = OB and angle AOB = θ radians. The points C and D lie on OA and OB respectively. CD is an arc of length 9.6 cm of the circle, centre O, radius 12 cm. The arc CD touches the line AB at the point M. [Figure X.X]
- (a)Find the value of θ.[1]
- (b)Find the total area of the shaded regions.[4]
- (c)Find the total perimeter of the shaded regions.[3]
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Mark scheme
Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.
- [B1] 0.8
- [B1] Sector area = 1/2 12^2 (0.8) Allow unsimplified (57.6)
- [M1] Attempt at AM using their θ/2 Allow unsimplified
- [M1] Area of triangle using their AM, allow unsimplified
- [A1] Shaded area 3.28
- [M1] Attempt to find OA using their θ/2 and their AM
- [M1] Allow if using their θ/2 and their CM
- [A1] Perimeter = 21.8
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