4MA0 Higher January 2012 Paper 3 Q18
18
Diagram NOT accurately drawn
\(AOD\) is a diameter of a circle, with centre \(O\) and radius 9 cm.
\(ABC\) is an arc of the circle.
\(AC\) is a chord.
Angle \(ADC = 35^\circ\)
Calculate the area of the shaded segment.
Give your answer correct to 3 significant figures.
(6)
| Scheme | Marks |
|---|---|
| AOC = 70° | B1 |
| “70”/360 × \(\pi \times 9^2\) (=49.48..) | M1ft |
| 0.5 × \(9^2\) × sin “70” = (38.057..) | M1ft |
| 49.48.. or 38.057... | A1 |
| “49.48..” − “38.057..” | M1 |
| 11.4 | A1 |
| (Total 6 marks) |
Notes
B1: Could be marked on diagram.
M1ft: Area of sector.
M1ft: Area of triangle. Follow through angles must be the same.
A1: Either area correct to 3 sf
M1: dep on both previous M1’s
A1: ( 11.42253...) awrt 11.4