Higher November 2019 Paper 1 Q26
26 Here are a circle and a sector of the circle.
They each have radius \(r\).
Not drawn accurately
circumference of circle = perimeter of sector
Work out the size of angle \(x\).
Give your answer in terms of \(\pi\) [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1: using the radius | ||
| \(2\pi r\) | M1 | |
| \(2\pi r \times \dfrac{x}{360}\) | M1dep | oe length of arc |
| \(2\pi r = 2\pi r \times \dfrac{x}{360} + 2r\) or \(\pi = \dfrac{\pi x}{360} + 1\) or \(2\pi = \dfrac{2\pi x}{360} + 2\) | M1dep | oe equation |
| \(\dfrac{360(\pi - 1)}{\pi}\) or \(\dfrac{360\pi - 360}{\pi}\) or \(360 - \dfrac{360}{\pi}\) | A1 | oe expression in \(\pi\) with \(r\) cancelled throughout |
| Alternative method 2: using the diameter | ||
| \(\pi d\) | M1 | oe |
| \(\pi d \times \dfrac{x}{360}\) | M1dep | oe length of arc |
| \(\pi d = \pi d \times \dfrac{x}{360} + d\) or \(\pi = \dfrac{\pi x}{360} + 1\) | M1dep | oe equation |
| \(\dfrac{360(\pi - 1)}{\pi}\) or \(\dfrac{360\pi - 360}{\pi}\) or \(360 - \dfrac{360}{\pi}\) | A1 | oe expression in \(\pi\) with \(d\) cancelled throughout |
Additional guidance
| Ignore attempts to simplify, cancel or expand a correct expression | M1M1M1A1 |