Higher November 2022 Paper 2 Q20
20.
Diagram not drawn to scale
The diagram shows a sector of a circle, centre \(O\), radius 12 cm.
\(A\hat{O}B\) is 55°.
(a) Find the area of the shaded region. [4]
(b) Find the perimeter of the shaded region. [6]
| Scheme | Marks | Comments |
|---|---|---|
| \(\dfrac{55}{360} \times \pi \times 12^2\) oe | B1 | |
| \(\dfrac{1}{2} \times 12^2 \times \sin 55\) oe | B1 | |
| \(\dfrac{55}{360} \times \pi \times 12^2 - \dfrac{1}{2} \times 12^2 \times \sin 55\) or better | M1 | (= \(22\pi - 72\sin 55\)); FT their difference of areas providing at least B1 previously awarded |
| 10.1(36....) | A1 | CAO Accept answers in the range 10.1 to 10.15; accept 10 following correct working |
| Scheme | Marks | Comments |
|---|---|---|
| \(\sqrt{12^2 + 12^2 - 2(12)(12)\cos 55}\) oe OR \(\dfrac{12\sin(55)}{\sin(62.5)}\) OR \(2(12\sin(27.5))\) | M2 | M1 for sight of \(12^2 + 12^2 - 2(12)(12)\cos 55\) oe OR \(\dfrac{[\ldots]}{\sin(55)} = \dfrac{12}{\sin(62.5)}\) oe OR \(\sin(27.5) = \dfrac{\frac{1}{2}[\ldots]}{12}\) oe |
| 11(.0819…) | A1 | |
| \(\dfrac{11}{3}\pi\) oe | B2 | B1 for \(\dfrac{55}{360} \times 2 \times \pi \times 12\) oe |
| 22.6(01...) | B1 | FT providing at least M1 B1 previously awarded |
| (10) |