Higher June 2017 Paper 2 Q16
16.
The diagram shows four patterns made using square grey tiles.
There are 4 tiles in Pattern 1.
(a) How many tiles are there in Pattern 5? [1]
(b)
(i) Find an expression for the number of tiles in Pattern \(n\). [2]
(ii) Describe how the arrangement of the tiles can be used to explain your expression in (b)(i). [1]
| Scheme | Marks | Comments |
|---|---|---|
| 28 (small grey tiles) | B1 |
| Scheme | Marks | Comments |
|---|---|---|
| (i) \(n^2 + 3\) or equivalent | B2 | B1 for \(1n^2\ (\pm a)\) |
| (ii) A suitable description, e.g. ‘a square of \(n\) by \(n\), with one tile at the right side and 2 tiles added on the bottom’, ‘square in the top left, then add 3’ | E1 | Allow ‘a square with extra 3 tiles’ FT from equivalent of \(n^2 + 3\) only |
| (4) |