Higher January 2021 Paper 2R Q15
15 Prove algebraically that the product of any two odd numbers is always an odd number.
(4)
| Scheme | Marks |
|---|---|
| eg \((2m + 1)(2n + 1)\) or eg \((2m - 1)(2n + 3)\) | M2 |
| eg \(4mn + 2m + 2n + 1\) or eg \(4n^2 + 4n + 1\) or eg \(4n^2 - 1\) or eg \(4n^2 + 8n + 3\) | M1 |
| eg \(2(2mn + m + n) + 1\) therefore odd Working required Answer: Proved | A1 |
| (4) | |
| (4 marks) |
Notes
M2: Product of 2 different odd numbers (in the form \(2n + k\) where \(k\) is odd).
Must have different letters/variables.
(M1 for the product of same or different odd numbers where the variable is the same eg \((2n + 1)(2n - 1)\) or \((2n + 1)(2n + 3)\))
M1: dep M1 Multiplying out the two brackets with odd numbers correctly.
A1: dep M3 Factorising and a conclusion
or stating that the 3 leading terms are all even, hence result is odd.