O-LevelAdditional MathematicsCircular measure4037/21 · May/June 2012 · Q1110 Marks
The diagram shows a right-angled triangle ABC and a sector CBDC of a circle with centre C and radius 12 cm. Angle ACB = 1 radian and ACD is a straight line.
- (i)Show that the length of AB is approximately 10.1 cm.[1]
- (ii)Find the perimeter of the shaded region.[5]
- (iii)Find the area of the shaded region.[4]
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Mark scheme
Marking points from the official mark scheme (May/June 2012). The mark or mark type is shown in brackets.
- [1] (i) AB = 12 sin 1 = 10.1 AG B1
- [1] (ii) AC = 12 cos 1 = 6.48 or 6.5 oe B1
- [1] ∠BCD = 2.14 or (π−1) B1
- [1] Use s = rθ (25.7) M1
- [1] Use complete plan M1
- [1] 54.3 A1
- [1] (iii) Area ACB = (1/2) × base × height M1
- [1] Area BCD = (1/2)r²θ M1
- [2] 154 or 32.7 (or 33) A1; 187 A1
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