O-LevelAdditional MathematicsCircular measure4037/12 · May/June 2011 · Q97 Marks
The figure shows a circle, centre O, radius r cm. The length of the arc AB of the circle is 9π cm. Angle AOB is θ radians and is 3 times angle OBA. [Figure 9.1]
- (i)Show that θ = 3π/5.[2]
- (ii)Find the value of r.[2]
- (iii)Find the area of the shaded region.[3]
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Mark scheme
Marking points from the official mark scheme (May/June 2011). The mark or mark type is shown in brackets.
- (i) ΔOBA : θ + 2(θ/3) = π; M1 for using angles in an isosceles triangle; A1
- (ii) 9π = r × (3π/5); M1 for use of s = rθ; A1
- r = 15
- (iii) Area = ½ × 15² × (3π/5) – ½ × 15² × sin (3π/5); M1 for use of ½r²θ or ½rs; M1 for use of ½r² sin θ or other correct method; A1
- = 105
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