Higher June 2018 Paper 1 Q12
12 Prove that the square of an odd number is always 1 more than a multiple of 4 (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| Statement supported by algebra | B1 | writing a general expression for an odd number eg \(2n + 1\) |
| M1 | (dep) for expanding (“odd number”)\(^2\) with at least 3 out of 4 correct terms | |
| A1 | for correct simplified expansion, eg \(4n^2 + 4n + 1\) | |
| C1 | (dep A1) for a concluding statement eg \(4(n^2 + n) + 1\) (is one more than a multiple of 4) |
Additional guidance
Could be \(2n - 1\), \(2n + 3\), etc
Note that \(4n^2 + 4n + 2\) or \(2n^2 + 4n + 1\) in expansion of \((2n + 1)^2\) is to be regarded as 3 correct terms