Higher November 2017 Paper 5 Q18
18 Prove that the difference between two consecutive square numbers is always odd. [4]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \((x + 1)^2 - x^2\) oe | M2 | M1 for \(x\) and \(x + 1\) shown oe | For M2 or M1 Condone any two consecutive expressions written algebraically and condone reversal |
| Expands all brackets correctly for their expression eg \(x^2 + 2x + 1 - x^2\) | M1 | If reversed then brackets needed or all signs need to be correct | |
| \(2x + 1\) is always odd oe | A1 | With no errors seen and brackets expanded for their expressions If 0 scored, SC1 for 2 correct numeric examples or correct reasoning with consecutive odds and evens | Condone \(-2x - 1\) for reversal FT from their correct consecutive square expressions eg square numbers 1, 4, 9, 16, go odd, even, odd etc, odd – even = odd, even – odd = odd |