OCR MEI C3 — Question 7 3 marks

Exam BoardOCR MEI
ModuleC3 (Core Mathematics 3)
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicProof
TypeRational and irrational number properties
DifficultyModerate -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.
Spec1.01c Disproof by counter example

State whether the following statements are true or false; if false, provide a counter-example.
  1. If \(a\) is rational and \(b\) is rational, then \(a + b\) is rational.
  2. If \(a\) is rational and \(b\) is irrational, then \(a + b\) is irrational.
  3. If \(a\) is irrational and \(b\) is irrational, then \(a + b\) is irrational. [3]

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]}}