Foundation November 2024 Paper 3 Q21
21 Here are the first three tile patterns of a sequence.
(a) Draw Pattern 4 in the space above. [1]
(b) Complete this table.
| Pattern | Calculation | Number of tiles |
|---|---|---|
| 1 | \(1 \times 2\) | 2 |
| 2 | \(2 \times 3\) | 6 |
| 3 | \(3 \times 4\) | 12 |
| 4 | ||
| 5 | ||
| \(\vdots\) | \(\vdots\) | \(\vdots\) |
| 10 | ||
| \(\vdots\) | \(\vdots\) | \(\vdots\) |
| \(n\) | \(n^2 + n\) |
[4]
(c) Each pattern in the sequence can be split into a square of tiles and a single column of tiles.
For example, Pattern 3:
The square in Pattern \(n\) contains 4096 tiles.
Work out how many tiles are in Pattern \(n\). [3]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
Rectangle 4 by 5 correctly orientated | 1 | Does not need shading nor internal lines | |
| Answer | Marks | Part marks and guidance | |||||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| |||||||||||||||||||||||||||||||||
| 4 | B2 for first four cells correct or B1 for two of the first four cells correct B1 for \(10 \times 11\) and 110 B1 for \(n \times (n + 1)\) | Allow \(5 \times 4\) Allow \(6 \times 5\) Condone \(n \times n + n\) | |||||||||||||||||||||||||||||||
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 4160 | 3 | M2 for \(4096 + \sqrt{4096}\) oe or \(\sqrt{4096} \times (\sqrt{4096} + 1)\) or M1 for \(\sqrt{4096}\) | Accept \(64 \times 65\) May be \(\sqrt{4096} = y\) then \(y \times (y + 1)\) Accept \(64 \times 64\) for 4096 and 64 for \(\sqrt{4096}\) in M2 and M1 |