Higher June 2017 Paper 1 Q16
16 \(n\) is an integer greater than 1
Prove algebraically that \(n^2 - 2 - (n - 2)^2\) is always an even number. (4)
| Answer | Mark | Notes |
|---|---|---|
| \(2(2n - 3)\) even | C1 | correct expansion of brackets to give at least 3 terms from \(n^2 - 2n - 2n + 4\) |
| C1 | arrives at \(n^2 - 2 - n^2 + 4n - 4\) oe | |
| C1 | reduces to \(2(2n - 3)\) or \(4n - 6\) | |
| C1 | for conclusion e.g. \(2(2n - 3)\) always even, \(4n - 6\) is always even since both are even numbers, they are multiples of 2. |