4MA0 Higher January 2015 Paper 4 Q24
24 The diagram shows a sector OAPB of a circle, centre O.
Diagram NOT accurately drawn
AB is a chord of the circle.
\(OA = OB = 6\) cm.
The area of sector OAPB is \(5\pi\) cm2
Calculate the perimeter of the shaded segment.
Give your answer correct to 3 significant figures.
(6)
| Scheme | Marks |
|---|---|
| \(\dfrac{x}{360} \times \pi \times r^2 = 5\pi\) | M1 |
| \(x = 50\) | A1 |
| \((AB^2 =)\ 6^2 + 6^2 - 2 \times 6 \times 6 \times \cos(\text{“}50\text{”})\) | M1 |
| \((AB =)\ \sqrt{25.7\ldots}\) or 5.07.... | M1 |
\(\dfrac{\text{“}50\text{”}}{360} \times 2 \times \pi \times 6\) or \(\dfrac{5\pi \times 2\pi \times 6}{\pi \times 6^2}\) or \(\dfrac{5}{3}\pi\) or 5.23... | M1 |
| 10.3 | A1 |
| (6 marks) |
Notes
M1: for this mark only condone an incorrect value for \(r\)
A1: cao for angle \(AOB = 50\)
M1: dep on first M1
or 6×sin(“50”/2)
M1: dep or
2× 6×sin(“50”/2)
M1: dep on first M1 if “50” used but
indep if angle not used
A1: for answer in range 10.2 – 10.31
M2 for \((AB =)\ \sqrt{25.7\ldots}\) or 5.07....or 2× 6×sin“50”/2