O-LevelAdditional MathematicsCircular measure4037/21 · May/June 2016 · Q45 Marks
The diagram shows 3 circles with centres A, B and C, each of radius 5 cm. Each circle touches the other two circles. Angle BAC is θ radians. [Figure 4]
- (i)Write down the value of θ.[1]
- (ii)Find the area of the shaded region between the circles.[4]
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Mark scheme
Marking points from the official mark scheme (May/June 2016). The mark or mark type is shown in brackets.
- [B1] π/3 isw
- [M1] [Area triangle ABC =] ½ × 10² × sin (their π/3) oe seen or implied by 25√3 or 43.3(0...)
- [M1] [Area 1 sector = ] ½ × 5² × their π/3 oe or π×5²×their 60°/360 seen or implied by 25π/6 or 13.0(8...) or 13.09
- [M1] Complete correct plan e.g. their triangle – 3(their sector)
- [A1] 4.03(1...) or 25√3 - 25π/2 isw Units not required
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