Higher June 2017 Paper 2 Q17
17
\(ONQ\) is a sector of a circle with centre \(O\) and radius 11 cm.
\(A\) is the point on \(ON\) and \(B\) is the point on \(OQ\) such that \(AOB\) is an equilateral triangle of side 7 cm.
Calculate the area of the shaded region as a percentage of the area of the sector \(ONQ\).
Give your answer correct to 1 decimal place. (5)
| Answer | Mark | Notes |
|---|---|---|
| 66.5 | B1 | for recognising an angle of 60 at \(AOB\) |
| P1 | for a process to find the area of the sector, e.g. \(\dfrac{\text{``}60\text{''}}{360} \times \pi \times 11^2\) \(\left(= 63.3\ldots \text{ or } \dfrac{121\pi}{6}\right)\) | |
| P1 | for a process to find the area of the triangle, e.g. \(\dfrac{1}{2} \times 7^2 \times \sin \text{``}60\text{''}\) \(\left(= 21.2\ldots \text{ or } \dfrac{49\sqrt{3}}{4}\right)\) | |
| P1 | for a process to find the required percentage, eg. \(\dfrac{\text{``}63.3\ldots\text{''} - \text{``}21.2\ldots\text{''}}{\text{``}63.3\ldots\text{''}} \times 100\) | |
| A1 | for answer in the range 66.5 to 66.6 |