O-LevelAdditional MathematicsCircular measure4037/12 · Oct/Nov 2022 · Q77 Marks
The diagram shows a circle, centre O, radius 10cm. The points A and B lie on the circumference of the circle. The tangent at A and the tangent at B meet at the point C. The angle AOB is θ radians. The length of the minor arc AB is 28 cm.
- (a)Find the value of θ.[1]
- (b)Find the perimeter of the shaded region.[3]
- (c)Find the area of the shaded region.[3]
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Mark scheme
Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.
- [1] (a) 2.8 or equivalent
- [1] (b) (BC = AC =) 10tan1.4 or 10sin1.4/sin0.1708
- [1] (b) Perimeter = 10(their 2.8)+2(their AC or BC)
- [1] (b) 144
- [1] (c) Area of triangle AOC or BOC = 1/2 their (AC or BC) × 10 or 1/2 their OC × 10sin1.4 seen or implied (allow premature approximation for OC)
- [1] (c) Area of minor sector AOB = 140 (follow through on 50 × their 2.8)
- [1] (c) Shaded area = 439 to 440 (must have 579 < kite area < 580)
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