Higher November 2018 Paper 6 Q13
13 The shape below is formed from two semicircles and a straight line.
Not to scale
The radius of the large semicircle is 8 cm.
The radius of the small semicircle is \(t\) cm.
Find an expression, in terms of \(t\), for the exact perimeter of the shaded shape. [3]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(8\pi + t\pi + 16 - 2t\) oe including unsimplified expressions | 3 | B2 for two of \(\dfrac{16\pi}{2}\) oe, \(\dfrac{2t\pi}{2}\) oe, or \(16 - 2t\) oe seen or B1 for one of \(\dfrac{16\pi}{2}\) oe, \(\dfrac{2t\pi}{2}\) oe, or \(16 - 2t\) oe seen | Mark final answer Equivalent simplified expressions include: \(\pi(8 + t) + 16 - 2t\) or \(t(\pi - 2) + 8(\pi + 2)\) Penalise use of 3.14 once e.g. 25.1… and 3.14\(t\) scores B1 |