Higher January 2023 Paper 2R Q14
14 \(A\), \(B\) and \(C\) are points on a circle, centre \(O\)
Diagram NOT accurately drawn
The radius of the circle is 8.5 cm
Angle \(ABC = 132°\)
Work out the perimeter of the shaded sector \(AOC\)
Give your answer correct to 3 significant figures.
(3)
| Scheme | Marks |
|---|---|
| \((\angle AOC =)\;132 \times 2\;(= 264)\) | M1 |
eg \(\dfrac{\text{``}{264}\text{''}}{360} \times 2 \times \pi \times 8.5\;\left(= 39.1\ldots \text{ or } \dfrac{187}{15}\pi\right)\) or \(2 \times \pi \times 8.5 - \dfrac{360 - \text{``}{264}\text{''}}{360} \times 2 \times \pi \times 8.5\;\left(= 39.1\ldots \text{ or } \dfrac{187}{15}\pi\right)\) or \(\dfrac{\text{``}{264}\text{''}}{360} \times 2 \times \pi \times 8.5 + 2 \times 8.5\) or \(2 \times \pi \times 8.5 - \dfrac{360 - \text{``}{264}\text{''}}{360} \times 2 \times \pi \times 8.5 + 2 \times 8.5\) | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: 56.2 | A1 |
| (3) | |
| (3 marks) |
Notes
M1: for method to find angle at the centre. Do not award this mark if contradicted on the diagram eg if obtuse \(AOC\) is labelled as 264
M1: for a method to find the length of arc \(AC\) or perimeter of the sector – allow use of their \(AOC\) as long as clearly labelled
A1: accept 56.1 – 56.2