Higher November 2021 Paper 5 Q21
21 AOB is a sector of a circle, centre O and radius 10 cm.
Not to scale
The area of the sector is \(40\pi\) cm².
Work out the perimeter of the sector.
Give your answer in the form \(a + b\pi\), where \(a\) and \(b\) are integers.
You must show your working. [6]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(20 + 8\pi\) final answer with correct working | 6 | For full marks “correct working” requires evidence of at least M1 AND M1 ie use of formulas for sector area and arc length or alternate convincing approach | |
| B3 for [angle at centre ]= 144 with correct working or \(\frac{4}{10}\) [of circle] oe or M2 for \(\dfrac{[360 \times]\,40\pi}{\pi \times 10^2}\) oe or M1 for \(\dfrac{\theta}{360} \times \pi \times 10^2\) oe | For B3 “correct working” requires at least M1 for use of formula for sector area M2 method for finding fraction of circle | ||
| AND M2 for answer \(20 + k\pi\) where \(k = \dfrac{\textit{their } \theta}{18}\) or M1 for \(\dfrac{\textit{their } \theta}{360} \times 2 \times \pi \times 10\) oe or answer \(20 + k\pi\) | M1 Implied by \(8\pi\) For M1 \(k \ne 0\) | ||
| If 0 scored SC2 for answer \(20 + 8\pi\) | May be on diagram | ||