Higher June 2022 Paper 4 Q15
15 Use algebra to prove that an odd number multiplied by a different odd number always gives an answer that is an odd number. [4]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| accept any correct method e.g. \((2n + 1)(2m + 1)\) | M1 | accept any letters condone poor use of brackets throughout if the terms are correct | for M1 accept e.g. \((2n + 1)(2m + 1)\) without any explanation BUT only accept e.g. \((x + 1)(x + 3)\) if they state that \(x\) is even |
| e.g. \(4nm + 2n + 2m + 1\) or \(4nm + 2(n + m) + 1\) | M2 | correctly expanding their brackets M1 for any three terms out of the four correct (middle term of three counts as two terms) | for M1 and M2 only accept brackets that could be the product of two odd numbers e.g. M2 for \(x^2 + [1]x + 3x + 3\) or better |
| Statement showing that the expression is odd e.g. first three terms are even and add 1 to an even gives odd | A1 | e.g. \(2(2nm + n + m) + 1\) and a short statement “even + odd = odd” A1 dep. on two method marks If 0 scored award SC1 for \(2n + 1\) etc seen or for the correct expansion of any two brackets including e.g. \(x(x + 1)\) | A1 for statement showing expression is odd e.g. \(x\) is even so \(x^2\) and \(4x\) are even so +3 makes odd |