Higher November 2024 Paper 5 Q15
15
(a) The diagram shows a rectangle, OPQR, and a circle, centre O, which passes through Q.
OR = 6 cm and RQ = 8 cm.
OR = 6 cm and RQ = 8 cm.
Not to scale
Find the circumference of the circle.
Give your answer in terms of \(\pi\). [4]
(b) AOB is a sector of a circle, centre O and radius 8 cm.
Angle AOB = \(x^\circ\).
The arc, AB, has length \(2\pi\) cm.
Angle AOB = \(x^\circ\).
The arc, AB, has length \(2\pi\) cm.
Not to scale
Find the area of the sector.
Give your answer in terms of \(\pi\). [4]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(20\pi\) final answer | 4 | M2 for \(\sqrt{8^2 + 6^2}\) oe or M1 for 62 and 82 oe M1dep for \(2 \times \pi \times\) their r | Accept e.g. \(C = 20\pi\) M2 implied by 10 M1 dep on at least M1 |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(8\pi\) final answer | 4 | B2 for \(x = 45\) or \(\frac{45}{360}\) oe or \(\frac{2[\pi]}{2[\pi]8}\) oe or M1 for \(\frac{x}{360} \times 2 \times \pi \times 8 = 2\pi\) oe M1 for \(\frac{\textit{their } 45}{360} \times \pi \times 8^2\) oe or \(\frac{x}{360} \times \pi \times 8^2\) | 0 < their 45 < 90 M1 for e.g. \(\frac{2[\pi]}{2[\pi]8} \times \pi \times 8^2\) |