Higher November 2021 Paper 3 Q22
22 A sequence of patterns is made using horizontal sticks and vertical sticks.
The table shows the number of horizontal sticks and vertical sticks in each pattern.
| Pattern | Number of horizontal sticks | Number of vertical sticks |
|---|---|---|
| 1 | 2 | 2 |
| 2 | 4 | 3 |
| 3 | 6 | 4 |
What fraction of the total number of sticks in Pattern \(n\) are horizontal?
Give your answer in terms of \(n\). [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(\dfrac{2n}{3n + 1}\) | B3 | oe eg \(\dfrac{2n}{2n + (n + 1)}\) B2 any two correct \(n\)th terms from \(2n\) or \(n + 1\) or \(3n + 1\) B1 any one correct \(n\)th term from \(2n\) or \(n + 1\) or \(3n + 1\) |
Additional guidance
| May be seen in a fraction or added eg \(2n + (n + 1)\) | B2 |
| Do not accept \(2n\) embedded in an incorrect expression eg \(2n - 2\) | B0 |