| Exam Board | OCR MEI |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2010 |
| Session | June |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Proof |
| Type | Rational and irrational number properties |
| Difficulty | Moderate -0.8 This question tests basic understanding of rational/irrational number properties through true/false statements. Parts (i) and (ii) are straightforward applications of definitions, while (iii) requires finding a simple counter-example like √2 + (-√2) = 0. Minimal calculation and problem-solving required—primarily recall and basic logical reasoning. |
| Spec | 1.01a Proof: structure of mathematical proof and logical steps |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| (A) True, (B) True, (C) False | B2,1,0 | |
| Counterexample, e.g. \(\sqrt{2} + (-\sqrt{2}) = 0\) | B1 [3] |
## Question 7:
| Answer/Working | Marks | Guidance |
|---|---|---|
| (A) True, (B) True, (C) False | B2,1,0 | |
| Counterexample, e.g. $\sqrt{2} + (-\sqrt{2}) = 0$ | B1 [3] | |
---7 State whether the following statements are true or false; if false, provide a counter-example.\\
(i) If $a$ is rational and $b$ is rational, then $a + b$ is rational.\\
(ii) If $a$ is rational and $b$ is irrational, then $a + b$ is irrational.\\
(iii) If $a$ is irrational and $b$ is irrational, then $a + b$ is irrational.
\hfill \mbox{\textit{OCR MEI C3 2010 Q7 [3]}}