O-LevelAdditional MathematicsCircular measure4037/11 · Oct/Nov 2010 · Q1010 Marks
The diagram shows a circle, centre O, radius 4 cm, enclosed within a sector PBCDP of a circle, centre P. The circle centre O touches the sector at points A, C and E. Angle BPD is `π/3` radians. [Figure 10.1]
- (i)Show that `PA = 4√3 cm` and `PB = 12cm`.[2]
- (ii)the area of the shaded region,[4]
- (iii)the perimeter of the shaded region.[4]
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 (Oct/Nov 2010). The mark or mark type is shown in brackets.
- B1 B1 for PA (answer given)
- B1 B1 for PB (answer given)
- √ B1 √ B1 sector area, ft on their PB
- M1, A1 M1 for attempt to find area of kite or appropriate triangle
- A1
- B1, B1, B1 B1 for each of the 3 terms
- B1 B1 for final answer
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