O-LevelAdditional MathematicsCircular measure4037/12 · Oct/Nov 2020 · Q119 Marks
In this question all lengths are in centimetres and all angles are in radians. [Figure 11.1] The diagram shows the rectangle ADEF, where AF = DE = r. The points B and C lie on AD such that AB = CD = r. The curve BC is an arc of the circle, centre O, radius r and has a length of 1.5r.
- (a)Show that the perimeter of the shaded region is (7.5 + 2 sin 0.75)r.[5]
- (b)Find the area of the shaded region, giving your answer in the form kr², where k is a constant correct to 2 decimal places.[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 2020). The mark or mark type is shown in brackets.
- B1 ∠BOC=1.5 rad
- M1 For a complete attempt to find BC must be using a right-angled triangle to get required result
- A1 Given answer
- M1 Dep on first M mark for attempt at perimeter
- A1 Given answer
- M1 for a correct plan
- M1 for (2r + 2r sin 0.75)r, using their 2r sin 0.75
- B1 for segment 1/2 r²(1.5-sin1.5) = 0.251r²
- A1 3.11r²
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