| Exam Board | OCR MEI |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Proof |
| Type | Rational and irrational number properties |
| Difficulty | Moderate -0.8 This question tests understanding of rational and irrational numbers through simple true/false statements. Parts (i) and (ii) are standard results requiring minimal reasoning, while part (iii) requires finding a basic counter-example like √2 + (-√2) = 0. The question involves recall and elementary logic rather than multi-step problem-solving, making it easier than average for A-level. |
| Spec | 1.01c Disproof by counter example |
State whether the following statements are true or false; if false, provide a counter-example.
\begin{enumerate}[label=(\roman*)]
\item If $a$ is rational and $b$ is rational, then $a + b$ is rational.
\item If $a$ is rational and $b$ is irrational, then $a + b$ is irrational.
\item If $a$ is irrational and $b$ is irrational, then $a + b$ is irrational. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C3 Q7 [3]}}