Higher November 2020 Paper 2R Q19
19
Diagram NOT accurately drawn
\(A\), \(B\), \(C\) and \(D\) are points on a circle with centre \(O\) and radius 12 cm.
The area of the sector \(OADC\) of the circle is 100 cm²
Work out the size of angle \(ABC\).
Give your answer correct to 3 significant figures.
(4)
| Scheme | Marks |
|---|---|
| \(\pi \times 12^2 \times \dfrac{AOC}{360}\;(= 100)\) | M1 |
| \((AOC =)\; \dfrac{100 \times 360}{\pi \times 12^2}\;\left(= \dfrac{250}{\pi}\right)\) | M1 |
| (Angle \(ABC\) =) “79.57747” ÷ 2 (= 39.7887… or \(\dfrac{125}{\pi}\)) | M1 |
| 39.8 | A1 |
| (4) | |
| (4 marks) |
Notes
M1: oe for setting up a correct expression for the area of the sector (or equation)
M1: for correctly rearranging for \(AOC\)
M1: ft dep 1st M1 and ‘\(x\)’ less than 360 for dividing their ‘\(AOC\)’ by 2
A1: for awrt 39.8
accept \(\dfrac{125}{\pi}\)