| Exam Board | Edexcel |
|---|
| Module | P2 (Pure Mathematics 2) |
|---|
| Year | 2022 |
|---|
| Session | January |
|---|
| Topic | Proof |
|---|
10. (i) Prove by counter example that the statement
"if \(p\) is a prime number then \(2 p + 1\) is also a prime number" is not true.
(ii) Use proof by exhaustion to prove that if \(n\) is an integer then
$$5 n ^ { 2 } + n + 12$$
is always even.