| Exam Board | WJEC |
|---|---|
| Module | Unit 1 (Unit 1) |
| Year | 2023 |
| Session | June |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Proof |
| Type | Counter example to disprove statement |
| Difficulty | Easy -1.8 This is a straightforward proof by counter-example requiring only substitution of small integers (n=4 gives 17, which is prime, but n=5 gives 26=2×13, which is composite). It tests basic understanding of proof techniques and prime numbers but requires minimal calculation and no problem-solving insight. |
| Spec | 1.01c Disproof by counter example |
Show, by counter example, that the following statement is false.
"For all positive integer values of $n$, $n^2 + 1$ is a prime number." [3]
\hfill \mbox{\textit{WJEC Unit 1 2023 Q8 [3]}}