A-LevelMathematicsCircular measure9709/12 · May/June 2022 · Q76 Marks
The diagram shows a sector OBAC of a circle with centre O and radius 10cm. The point P lies on OC and BP is perpendicular to OC. Angle AOC = π/6 and the length of the arc AB is 2cm. [Figure 7.1]
- (a)Find the angle BOC.[2]
- (b)Hence find the area of the shaded region BPC giving your answer correct to 3 significant figures.[4]
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Mark scheme
Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.
- [B1] [AOB=] 2/10
- [B1] [BOC =] π/6 + 0.2 or 5π/30 + 6/30
- [M1] [BP] = 10sin('their BOC') and [OP] = 10cos('their BOC')
- [A1] Area of ΔOBP = (1/2) × 10sin('their BOC') × 10cos('their BOC') or (1/2)BP × OP.
- [M1] [Sector BOC] = (1/2) × 10² × 'their BOC'
- [A1] Area of region BPC = 11.4
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