Higher January 2022 Paper 1 Q16
16 The diagram shows a circle with centre \(O\)
Diagram NOT accurately drawn
\(A\), \(B\) and \(C\) are points on the circle so that the length of the arc \(ABC\) is 5 cm.
Given that angle \(AOC = 55^\circ\)
work out the area of the circle.
Give your answer correct to one decimal place.
(4)
| Scheme | Marks |
|---|---|
eg \(\dfrac{55}{360} \times \pi \times d = 5\) or \(\dfrac{55}{360} \times \pi \times 2 \times r = 5\) oe OR \(\dfrac{360}{55} \times 5\) (= 32.7…) oe | M1 |
eg \(d = \dfrac{5 \times 360}{55\pi}\) (= 10.4…) or \(r = \dfrac{5 \times 360}{55 \times 2 \times \pi}\) (= 5.2…) OR \(d = \dfrac{32.7\ldots}{\pi}\) (= 10.4…) or \(r = \dfrac{32.7\ldots}{2 \times \pi}\) (= 5.2…) | M1 |
| (area =) eg \(\pi \times \left(\dfrac{\text{``}{10.4\ldots}\text{''}}{2}\right)^2\) or \(\pi \times \text{``}{5.2\ldots}\text{''}^2\) | M1 |
| 85.2 | A1 |
| (4) | |
| (4 marks) |
Notes
M1: for a correct equation for the diameter or radius OR for a method to find the circumference of the circle
M1: for a method to work out the diameter or radius
A1: allow 84.9 – 85.4