Higher January 2021 Paper 1 Q8
8 The region, shown shaded in the diagram, is a path.
Diagram NOT accurately drawn
The boundary of the path is formed by two semicircles, with the same centre \(O\), and two straight lines.
The inner semicircle has a radius of 7 metres.
The path has a width of 2 metres.
Work out the perimeter of the path.
Give your answer correct to one decimal place.
(3)
| Scheme | Marks |
|---|---|
| 2 × \(\pi\) × 7 (= 43.982… or \(14\pi\)) or (2 × \(\pi\) × 7) ÷ 2 (= 21.991… or \(7\pi\)) or 2 × \(\pi\) × 9 (= 56.548… or \(18\pi\)) or (2 × \(\pi\) × 9) ÷ 2 (= 28.274… or \(9\pi\)) | M1 |
| e.g. “21.991” + “28.274” (= 50.26…) or “\(7\pi\)” + “\(9\pi\)” (= \(16\pi\)) or “21.991” + “28.274” + 2 (= 52.26…) or “\(7\pi\)” + “\(9\pi\)” + 2 (= 52.26…) or “21.991” + “28.274” + 2 + 2 or “\(7\pi\)” + “\(9\pi\)” + 2 + 2 | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: 54.3 | A1 |
| (3) | |
| (3 marks) |
Notes
M1: for finding the circumference of either the full circle or the length of the arc for either semicircle
M1: for a method to find the length of the two arcs with intention to add
A1: accept 54.2 – 54.3