A-LevelMathematicsCircular measure9709/12 · Oct/Nov 2022 · Q108 Marks

The diagram shows a cross-section RASB of the body of an aircraft. The cross-section consists of a sector OARB of a circle of radius 2.5m, with centre O, a sector PASB of another circle of radius 2.24m with centre P and a quadrilateral OAPB. Angle AOB = 4π/3 and angle APB = 5π/6. [Figure X.X]

(a)Find the perimeter of the cross-section RASB, giving your answer correct to 2 decimal places.[3]
(b)Find the difference in area of the two triangles AOB and APB, giving your answer correct to 2 decimal places.[2]
(c)Find the area of the cross-section RASB, giving your answer correct to 1 decimal place.[3]

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 2022). The mark or mark type is shown in brackets.

B1 For either arc correct. Arc ARB could be AR+RB. 2.5 × 4π/3
M1 For adding two (or three) arc lengths using different radii and angles and nothing else. SOI. 2.5 × 4π/3 + 2.24 × 5π/6
A1 AWRT. Condone 16.33 only. 16.34 or 26π/5
M1 For either ΔAOB or ΔAPB (AB = 4.33, h= 1.25, 0.58) or any other valid method. 1/2 × 2.5² sin(4π/3) [= 2.706] or 1/2 × 2.24² sin(5π/6) [= 1.254]
A1 AWRT Condone 1.46 only. [Difference =] 1.45
B1 For either sector area correct. 1/2 × 2.5² × 4π/3 [= 13.09] or 1/2 × 2.24² × 5π/6 [= 6.57]
M1 Adding two sector areas from different sectors and 'their 10(b)' and nothing else. SOI. 1/2 × 2.5² × 4π/3 + 1/2 × 2.24² × 5π/6 + "their 10(b)"
A1 CAO Condone slight inaccuracies in intermediate working if the correct answer is arrived at. 21.1

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