| Exam Board | OCR MEI |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Proof |
| Type | Counter example to disprove statement |
| Difficulty | Easy -1.2 This question requires only basic arithmetic and checking small cases. Part (i) involves computing 2^2-1=3, 2^3-1=7, 2^5-1=31, 2^7-1=127 and verifying primality of small numbers. Part (ii) gives the factorization hint (23×89=2047=2^11-1) to show the statement fails for p=11. No conceptual depth or problem-solving is needed—just routine calculation and verification. |
| Spec | 1.01a Proof: structure of mathematical proof and logical steps1.01c Disproof by counter example |
\begin{enumerate}[label=(\roman*)]
\item Verify the following statement:
$$\text{'} 2^p - 1 \text{ is a prime number for all prime numbers } p \text{ less than 11'.} [2]
\item Calculate $23 \times 89$, and hence disprove this statement:
$$\text{'} 2^p - 1 \text{ is a prime number for all prime numbers } p \text{'.} [2]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C3 Q10 [4]}}