| 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 | Standard +0.3 This question tests basic proof techniques and number properties at C3 level. Part (i) requires a simple counterexample (e.g., 9 and 11, where 9 is composite), while part (ii) needs a short algebraic proof showing consecutive even numbers are 2k and 2k+2, giving product 4k(k+1) which is divisible by 8. Both parts are straightforward applications of proof methods with minimal steps, making this slightly easier than a typical C3 question. |
| Spec | 1.01a Proof: structure of mathematical proof and logical steps1.01c Disproof by counter example |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | (i) | False e.g. neither 25 and 27 are prime |
| as 25 is div by 5 and 27 by 3 | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| [2] | correct counter-example identified | |
| justified correctly | Need not explicitly say ‘false’ | |
| 1 | (ii) | True: one has factor of 2, the other 4, so |
| product must have factor of 8. | B2 | |
| [2] | or algebraic proofs: e.g. 2n(2n+2) = | |
| 4n(n+1) = 4×even×odd no so div by 8 | B1 for stating with justification div by 4 |
| Answer | Marks | Guidance |
|---|---|---|
| Quueessttion | Answer | Marks |
Question 1:
1 | (i) | False e.g. neither 25 and 27 are prime
as 25 is div by 5 and 27 by 3 | B1
B1
[2] | correct counter-example identified
justified correctly | Need not explicitly say ‘false’
1 | (ii) | True: one has factor of 2, the other 4, so
product must have factor of 8. | B2
[2] | or algebraic proofs: e.g. 2n(2n+2) =
4n(n+1) = 4×even×odd no so div by 8 | B1 for stating with justification div by 4
e.g. both even, or from 4(n2 + n) or 4pq
Quueessttion | Answer | Marks | GuidanceEither prove or disprove each of the following statements.
\begin{enumerate}[label=(\roman*)]
\item 'If $m$ and $n$ are consecutive odd numbers, then at least one of $m$ and $n$ is a prime number.' [2]
\item 'If $m$ and $n$ are consecutive even numbers, then $mn$ is divisible by 8.' [2]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C3 Q1 [4]}}