A-LevelMathematicsCircular measure9709/12 · May/June 2014 · Q45 Marks
The diagram shows a sector of a circle with radius r cm and centre O. The chord AB divides the sector into a triangle AOB and a segment AXB. Angle AOB is θ radians. [Figure 4.1]
- (i)In the case where the areas of the triangle AOB and the segment AXB are equal, find the value of the constant p for which θ = p sin θ.[2]
- (ii)In the case where r = 8 and θ = 2.4, find the perimeter of the segment AXB.[3]
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Mark scheme
Marking points from the official mark scheme (May/June 2014). The mark or mark type is shown in brackets.
- [B1] ½r²θ = ½r²θ - ½r² sin θ Correct equation.
- [B1] → 2sin θ = θ → p = 2. All ok – answer given.
- [M1] Chord length = 8sin1.2 ×2 (14.9) Needs ×2. Any method ok.
- [B1] Arc length = 2.4 × 8 (19.2) co
- [A1] Perimeter = sum of these = 34.1 co
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