Foundation November 2018 Paper 1 Q23
23 Two consecutive whole numbers are \(n\) and \(n + 1\)
(a) Simplify \(\quad n - (n + 1)\) [1 mark]
(b) Multiply out \(\quad n(n + 1)\) [1 mark]
(c) The two numbers are added.
Show that the answer must be an odd number. [2 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(-1\) | B1 |
| Answer | Mark | Comments |
|---|---|---|
| \(n^2 + n\) or \(n + n^2\) | B1 |
Additional guidance
| Accept \(1n^2 + 1n\) or \(1n^2 + n\) or \(n^2 + 1n\) etc… | B1 |
| Do not accept \(n \times n + n\) or \(n^2 + n1\) | B0 |
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \((n + n + 1 =)\ 2n + 1\) and states that \(2n\) is even and states that even + 1 = odd or even + odd = odd | B2 | B1 \((n + n + 1 =)\ 2n + 1\) |
| Alternative method 2 | ||
| States that one of the numbers is even and the other is odd and states that even + odd = odd | B2 | B1 states that one of the numbers is even and the other is odd or states that even + odd = odd |
Additional guidance
| Numerical examples with no other explanation | B0 |
| \(n + n + 1 = 2n + 1 = 3n\) | B0 |