Higher January 2020 Paper 2 Q17
17 Prove that the difference between two consecutive square numbers is always an odd number.
Show clear algebraic working.
(3)
| Scheme | Marks |
|---|---|
| e.g. \(n^2 - (n - 1)^2\) or \((n + 1)^2 - n^2\) | M1 |
| e.g. \(n^2 - n^2 + 2n - 1\) or \(n^2 + 2n + 1 - n^2\) | M1 |
| Working required Answer: e.g. \(2n - 1\) is always odd | A1 |
| (3) | |
| (3 marks) |
Notes
M1: for setting up a correct algebraic expression (any letter can be used)
M1: Correct expansion of brackets and correct signs or a correct result
A1: dep on M2 for eg \(2n - 1\) or \(2n + 1\) or \(-(2n + 1)\) oe and a suitable conclusion
SCB1 for eg \((2n)^2 - (2n - 1)^2\) or \((2n + 1)^2 - (2n)^2\) oe