| Exam Board | OCR |
|---|---|
| Module | H240/01 (Pure Mathematics) |
| Year | 2018 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Topic | Proof |
| Type | Parity and evenness proofs |
| Difficulty | Moderate -0.8 This is a straightforward parity proof requiring only basic algebraic manipulation and the definition of odd/even numbers. Students need to consider two cases (n odd, n even) and show the expression is odd in both, which is a standard technique taught early in proof modules with minimal steps required. |
| Spec | 1.01a Proof: structure of mathematical proof and logical steps |
4 Prove algebraically that $n ^ { 3 } + 3 n - 1$ is odd for all positive integers $n$.
\hfill \mbox{\textit{OCR H240/01 2018 Q4 [4]}}