O-LevelAdditional MathematicsCircular measure4037/21 · May/June 2014 · Q86 Marks
A sector of a circle of radius r cm has an angle of θ radians, where θ < π. The perimeter of the sector is 30 cm.
- (i)Show that the area, A cm², of the sector is given by A = 15r - r².[3]
- (ii)Given that r can vary, find the maximum area of the sector.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2014). The mark or mark type is shown in brackets.
- [M1] 2r + rθ = 30 giving θ = (30-2r)/r correct arc formula + (2)r rearranged
- [M1] Substitute their expression for θ into A = 1/2 r²θ
- [A1] Correct simplification to A=15r – r² AG
- [M1] their dA/dr = 0
- [A1] r = 7.5
- [A1] 56.25 56.3 is A0 unless 56.25 seen; if M0, then SC2 for A = 56.25 with no working; or SC1 for r = 7.5 with no working
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