| Exam Board | OCR MEI |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2014 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Proof |
| Type | Counter example to disprove statement |
| Difficulty | Standard +0.3 This question tests basic proof techniques and number properties at a straightforward level. Part (i) requires only a simple counterexample (e.g., 9 and 11, where 9 is composite), while part (ii) needs a short algebraic proof showing consecutive even numbers are 2k and 2k+2, giving product 4k(k+1) which is divisible by 8 since k(k+1) is always even. Both parts are accessible with standard C3 proof skills and minimal problem-solving insight. |
| Spec | 1.01c Disproof by counter example |
Either prove or disprove each of the following statements.
\begin{enumerate}[label=(\roman*)]
\item 'If $m$ and $n$ are consecutive odd numbers, then at least one of $m$ and $n$ is a prime number.' [2]
\item 'If $m$ and $n$ are consecutive even numbers, then $mn$ is divisible by 8.' [2]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C3 2014 Q7 [4]}}