| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2009 |
| Session | June |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Topic | Proof |
| Type | Divisibility proof for all integers |
| Difficulty | Moderate -0.8 This is a straightforward algebraic proof requiring factorization of n³-n = n(n-1)(n+1) and recognizing that consecutive integers guarantee an even product. It's easier than average as it's a standard C1 proof with a clear path and minimal steps, though not trivial since students must structure a formal argument. |
| Spec | 1.01a Proof: structure of mathematical proof and logical steps |
Prove that, when $n$ is an integer, $n^3 - n$ is always even. [3]
\hfill \mbox{\textit{OCR MEI C1 2009 Q6 [3]}}