4400 Higher June 2009 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.
The radius of the circle is 6 cm.
Angle \(AOB = 78^\circ\).
Calculate the perimeter of the shaded segment \(APB\).
Give your answer correct to 3 significant figures.
(6)
| Scheme | Marks |
|---|---|
\(2 \times 6 \sin 39^\circ\) or \(2 \times 6 \cos 51^\circ\) or \(6^2 + 6^2 - 2 \times 6 \times 6 \cos 78^\circ\) or \(\dfrac{6 \sin 78^\circ}{\sin 51^\circ}\) | M1 |
| 7.551... | A1 |
| eg \(\dfrac{78}{360} \times \pi \times 12\) | M1 |
| M1 | |
| 8.16 − 8.17 inc oe inc \(\dfrac{13\pi}{5}\), \(2.6\pi\) oe | A1 |
| 15.7 | A1 |
| (6) | |
| (6 marks) |
Notes
A1: for answer rounding to 7.55
M1: for \(\dfrac{78}{360}\) oe inc 0.2166... rounded or truncated to at least 3 decimal places
or for \(\dfrac{360}{78}\) oe inc 4.6153... rounded or truncated to at least 3 decimal places
M1: for \(\pi \times 12\) or for \(2\pi \times 6\)
(\(\pi \to\) 37.699... 3.14 \(\to\) 37.68 3.142 \(\to\) 37.704)
A1: for 8.17 or better (\(\pi \to\) 8.168... 3.14 \(\to\) 8.164 3.142 \(\to\) 8.1692)
A1: for ans rounding to 15.7 (\(\pi \to\) 15.7199... 3.14 \(\to\) 15.7158... 3.142 \(\to\) 15.7202...)