| Exam Board | Edexcel |
|---|---|
| Module | PURE |
| Year | 2024 |
| Session | October |
| Paper | Download PDF ↗ |
| Topic | Proof |
| Type | Counter example to disprove statement |
| Difficulty | Moderate -0.5 Part (i) requires finding a simple counter-example (n=3 gives 29, n=2 gives 11, but n=5 gives 245=5×49, not prime), which is straightforward trial. Part (ii) is a standard proof by exhaustion checking m≡1,2 (mod 3), showing (m-1)(m+1) is divisible by 3 - this is a textbook exercise in modular arithmetic. Both parts are routine proof techniques with no novel insight required, making this slightly easier than average. |
| Spec | 1.01a Proof: structure of mathematical proof and logical steps1.01c Disproof by counter example |
| Answer | Marks | Guidance |
|---|---|---|
| 11(i) | E.g. n=535 +2=245 | M1 |
| Answer | Marks |
|---|---|
| 245 is divisible by 5 so not true | A1 |
| Answer | Marks |
|---|---|
| n | 3 n + 2 |
| 11 | 177149 |
Question 11:
--- 11(i) ---
11(i) | E.g. n=535 +2=245 | M1
245 is not a prime number
or e.g.
245 is divisible by 5 so not true | A1
(2)
n | 3 n + 2
11 | 177149\begin{enumerate}
\item (i) Prove by counter example that the statement\\
"If $n$ is a prime number then $3 ^ { n } + 2$ is also a prime number." is false.\\
(ii) Use proof by exhaustion to prove that if $m$ is an integer that is not divisible by 3 , then
\end{enumerate}
$$m ^ { 2 } - 1$$
is divisible by 3
\hfill \mbox{\textit{Edexcel PURE 2024 Q11}}