Foundation November 2017 Paper 2 Q23
23
(a) \(n\) is an integer.
(i) Explain why \(2n + 1\) is an odd number. [1]
(ii) Write down an algebraic expression for the next odd number after \(2n + 1\). [1]
(b) Use algebra to show that the sum of two consecutive odd numbers will always be a multiple of 4. [2]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| (i) Valid explanation | 1 | Such as ‘because \(2n\) is always even so \(2n + 1\) will be odd’ | Must mention even and odd See Appendix |
| (ii) \(2n + 3\) oe | 1 | ||
Appendix
Exemplar responses for Q23ai
| Response | Mark |
|---|---|
| Any number x 2 will be even, so add 1 makes it odd | 1 |
| If I put a even or odd number, after x2 give me a even number but add 1, is a odd | 1 |
| 2 x 1 = 2 2 + 1 = 3. (substitution of values isn’t enough to score) | 0 |
| Any number you x by 2 then +1 will always be an odd number because 2 is an even number | 0 |
| Because if you x something by 2 and add one, it will be odd. (must identify even) | 0 |
| +1 to an even number and you get an odd one | 0 |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(2n + 1 + 2n + 3\) | M1 | ||
| \(= 4n + 4\) [\(= 4(n + 1)\)] which is a multiple of 4 | A1 | If 0 scored SC1 for \(2n + 1\) + their \((2n + 3)\) | their \((2n + 3)\) must be an algebraic expression in \(n\) |