Higher January 2021 Paper 2 Q8
8 \(A\), \(B\) and \(C\) are points on a circle with centre \(O\).
Diagram NOT accurately drawn
\(AOC\) is a diameter of the circle.
\(AB\) = 8 cm \(BC\) = 15 cm
Angle \(ABC = 90^\circ\)
Work out the total area of the regions shown shaded in the diagram.
Give your answer correct to 3 significant figures.
(5)
| Scheme | Marks |
|---|---|
| \(8^2 + 15^2\) (= 289) | M1 |
| \(\sqrt{8^2 + 15^2}\) (= 17) | M1 |
| \(\pi \times \left(\text{“}\dfrac{17}{2}\text{”}\right)^2\) (= 226.98...) or 0.5 × 15 × 8 (= 60) | M1 |
\(\pi \times \left(\text{“}\dfrac{17}{2}\text{”}\right)^2 - 0.5 \times 15 \times 8\) (“226.98” – “60”) | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: 167 | A1 |
| (5) | |
| (5 marks) |
Notes
A1: Accept answers which round to 167