| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2013 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Proof |
| Type | Divisibility proof for all integers |
| Difficulty | Moderate -0.8 This is a straightforward proof question requiring basic algebraic manipulation. Part (i) is trivial algebra showing (n-1)+n+(n+1)=3n. Part (ii) requires expanding three squares and collecting terms to get 3n²+2, then observing the remainder when divided by 3. While it involves multiple steps, the techniques are elementary and the question explicitly guides students through what to show, making it easier than average for A-level. |
| Spec | 1.01a Proof: structure of mathematical proof and logical steps |
$n - 1$, $n$ and $n + 1$ are any three consecutive integers.
\begin{enumerate}[label=(\roman*)]
\item Show that the sum of these integers is always divisible by 3. [1]
\item Find the sum of the squares of these three consecutive integers and explain how this shows that the sum of the squares of any three consecutive integers is never divisible by 3. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C1 2013 Q9 [4]}}