Higher June 2018 Paper 5 Q15
15 \(n\) is a positive integer.
Prove that \(13n + 3 + (3n - 5)(2n + 3)\) is a multiple of 6. [4]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| [\(13n + 3 +\)] \(6n^2 + 9n - 10n - 15\) | M2 | M1 for two or three of \(6n^2 + 9n - 10n - 15\) | For M2 accept \(6n^2 + -[1]n - 15\) For M1, accept expansion on grid with negative signs shown |
| \(6n^2 + 12n - 12\) | A1 | For A1, condone \(6n^2 + 12n - 12 = 0\) | |
| \(6(n^2 + 2n - 2)\) and is a multiple of 6 oe | A1 | Dep on M2 A1 and no errors seen Accept \((6n^2 + 12n - 12) \div 6 = n^2 + 2n - 2\) and is a multiple of 6 oe | Do not accept each term is a multiple of 6 without showing the outcome \(n^2 + 2n - 2\) |