O-LevelAdditional MathematicsCircular measure4037/12 · May/June 2010 · Q97 Marks
The diagram shows a sector OXY of a circle centre O, radius 3cm and a sector OAB of a circle centre O, radius 8 cm. The point X lies on the line OA and the point Y lies on the line OB. The perimeter of the region XABYX is 15.5 cm. Find [Figure 9]
- (i)the angle AOB in radians,[3]
- (ii)the ratio of the area of the sector OXY to the area of the region XABYX in the form p : q, where p and q are integers.[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 (May/June 2010). The mark or mark type is shown in brackets.
- M1, DM1 for use of arc length
- DM1 for attempt to find perimete
- A1
- M1 for a sector area
- DM1 for attempt to find area of XABY
- DM1 for attempt to obtain ratio
- A1
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