| Exam Board | OCR MEI |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 2 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Proof |
| Type | Counter example to disprove statement |
| Difficulty | Moderate -0.8 This is a straightforward disproof by counterexample question requiring minimal calculation. Students only need to test small values of n (n=1 gives 5, n=2 gives 11, n=3 gives 19, n=4 gives 29, n=5 gives 41, n=6 gives 55=5×11) to find a counterexample. The conceptual demand is low—understanding what constitutes a valid disproof—and the arithmetic is trivial, making this easier than average. |
| Spec | 1.01c Disproof by counter example |
Prove that the following statement is false.
For all integers $n$ greater than or equal to 1, $n^2 + 3n + 1$ is a prime number. [2]
\hfill \mbox{\textit{OCR MEI C3 Q12 [2]}}