| Exam Board | OCR MEI |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2011 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Proof |
| Type | Divisibility proof for all integers |
| Difficulty | Standard +0.3 Part (i) is a straightforward difference of two squares requiring simple algebraic manipulation. Part (ii) requires recognizing that 3^(2n) - 1 = (3^n + 1)(3^n - 1) and showing both factors contribute factors of 2, which is a standard divisibility proof technique but requires some insight about odd powers of 3. The total of 4 marks and the 'hence' structure make this slightly easier than average, as the path is clearly signposted. |
| Spec | 1.01a Proof: structure of mathematical proof and logical steps |
\begin{enumerate}[label=(\roman*)]
\item Multiply out $(3^n + 1)(3^n - 1)$. [1]
\item Hence prove that if $n$ is a positive integer then $3^{2n} - 1$ is divisible by 8. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C3 2011 Q7 [4]}}