O-LevelMathematicsGeometry4024/22 · May/June 2015 · Q49 Marks
(a) A, B, C, D and E are five points on the circumference of a circle. EB is parallel to DC, EÂC = 72° and AÊB = 25° . X is the intersection of AC and EB. Find [Figure 4.1]
- (a)(i)EBC,[1]
- (a)(ii)CÂB,[1]
- (a)(iii)EDC,[1]
- (a)(iv)ACD.[1]
- (b)The angle of a sector of a circle, radius 6 cm, is 40°. [Figure 4.2]
- (b)(i)The area of the sector is kπ cm². Find the value of k.[2]
- (b)(ii)Find an expression, in terms of π, for the perimeter of the sector. Give your answer in the form (a + bπ) centimetres.[2]
- (b)(iii)A geometrically similar sector has perimeter (72 + nπ) centimetres. Find the value of n.[1]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (May/June 2015). The mark or mark type is shown in brackets.
- [1] 72
- [1] 83
- [1] 108
- [1FT] 83 Their (ii)
- [2] B1 for π × 6² × 40/360 or for 40/360; 4 (π) cao
- [2] B1 for (a =) 12, or for (b =) 4/3; 12 + 4/3 π final answer
- [1ft] 8
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