1MA0 Higher June 2014 Paper 2 Q21
21
(a) Expand and simplify \((y - 2)(y - 5)\) (2)
*(b) Prove algebraically that \[(2n + 1)^2 - (2n + 1) \quad \text{is an even number}\] for all positive integer values of \(n\). (3)
| Working | Answer | Mark | Notes |
|---|---|---|---|
| \(y^2 - 2y - 5y + 10\) | \(y^2 - 7y + 10\) | 2 | M1 for all 4 terms correct (condone incorrect signs) or 3 out of 4 terms correct with correct signs A1 cao |
| Working | Answer | Mark | Notes |
|---|---|---|---|
| \((4n^2 + 2n + 2n + 1)\) \(\quad - (2n + 1)\) \(= 4n^2 + 4n + 1 - 2n - 1\) \(= 4n^2 + 2n\) \(= 2n(2n + 1)\) | Proof | 3 | M1 for 3 out of 4 terms correct in the expansion of \((2n + 1)^2\) or \((2n + 1)\{(2n + 1) - 1\}\) A1 for \(4n^2 + 2n\) or equivalent expression in factorised form C1 for convincing statement using \(2n(2n + 1)\) or \(2(2n^2 + n)\) or \(4n^2 + 2n\) to prove the result |