Higher November 2017 Paper 6 Q8
8 The design below is made from two sectors of circles, centre O.
Calculate the perimeter of the shaded part.
Give your answer correct to 3 significant figures.
........................................ cm [5]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 13.7 | 5 | M4 for \(\dfrac{45}{360} \times 2 \times \pi \times 6 + \dfrac{45}{360} \times 2 \times \pi \times 2.5 + 2 \times 3.5\) oe soi | by 13.67… to 13.68 |
| OR M3 for \(\dfrac{45}{360} \times 2 \times \pi \times 6\) oe and \(\dfrac{45}{360} \times 2 \times \pi \times 2.5\) oe soi | by 4.71… and 1.96… or by 6.67… to 6.68 | ||
| OR M2 for \(\dfrac{45}{360} \times 2 \times \pi \times 6\) oe or \(\dfrac{45}{360} \times 2 \times \pi \times 2.5\) oe soi or \(2 \times \pi \times 6 + 2 \times \pi \times 2.5\) oe soi | by 4.71… or 1.96…or 53.4.. | ||
| OR M1 for \(2 \times \pi \times 6\) oe or \(2 \times \pi \times 2.5\) oe soi | by 37.699… to 37.7 or 15.7… | ||
| If 0 scored SC2 for \(\dfrac{45}{360} \times \pi \times 6^2\) oe and \(\dfrac{45}{360} \times \pi \times 2.5^2\) oe soi by 14.1… and 2.45… or by 11.6 to 11.7 OR SC1 for \(\dfrac{45}{360} \times \pi \times 6^2\) oe or \(\dfrac{45}{360} \times \pi \times 2.5^2\) oe soi by 14.1… or 2.45… | Method marks may be awarded for multiples of \(\pi\) seen in correct working. Eg. \(\dfrac{45}{360} \times 2 \times \pi \times 6 = \dfrac{3}{2}\pi\) \(\dfrac{45}{360} \times 2 \times \pi \times 2.5 = \dfrac{5}{8}\pi\) | ||