4MA0 Higher June 2012 Paper 3 Q19
19
Diagram NOT accurately drawn
The diagram shows a sector \(OAPB\) of a circle, centre \(O\).
\(AB\) is a chord of the circle.
\(OA = OB\) = 5.4 cm.
Angle \(AOB = 72^\circ\)
Calculate the area of the shaded segment \(APB\).
Give your answer correct to 3 significant figures.
(5)
| Scheme | Marks |
|---|---|
| eg \(\dfrac{72}{360} \times \pi \times 5.4^2 - \dfrac{1}{2} \times 5.4^2 \times \sin 72^\circ\) | M1 |
| M1 | |
| M1 | |
| 18.321… (or 18.312…) − 13.866… | A1 |
| 4.46 or 4.45 | A1 |
| (Total 5 marks) |
Notes
M1: for \(\dfrac{72}{360}\) oe inc 5
M1: for \(\pi \times 5.4^2\)
or value which rounds to 91.6 seen
M1: for completely correct method of finding the area of triangle \(OAB\) eg \(\frac{1}{2} \times 5.4^2 \times \sin 72^\circ\)
or 5.4 × sin 36° × 5.4 × cos 36°
A1: for either area correctly evaluated – may be rounded or truncated to 1 dp
A1: for answer rounding to 4.46
(\(\pi \to\) 4.45536…)
or for answer rounding to 4.45
(3.14 → 4.44607…)
If all M1s scored, award 5 marks for an answer which rounds to 4.46 or 4.45