| Exam Board | OCR MEI |
|---|---|
| Module | Paper 3 (Paper 3) |
| Year | 2018 |
| Session | June |
| Marks | 2 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Proof |
| Type | Contradiction proof of inequality |
| Difficulty | Moderate -0.8 This question tests understanding of domain restrictions for the AM-GM inequality rather than proof technique. Students need only explain why √(ab) is undefined or not real when signs differ or both are negative—a conceptual check requiring minimal calculation or formal reasoning, making it easier than average A-level questions. |
| Spec | 1.01b Logical connectives: congruence, if-then, if and only if |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| The geometric mean cannot be calculated | E1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| The arithmetic mean will be less than the geometric mean | E1 | E.g. The arithmetic mean will be negative |
## Question 11(i):
| Answer | Mark | Guidance |
|--------|------|----------|
| The geometric mean cannot be calculated | E1 | |
---
## Question 11(ii):
| Answer | Mark | Guidance |
|--------|------|----------|
| The arithmetic mean will be less than the geometric mean | E1 | E.g. The arithmetic mean will be negative |
---11 Line 8 states that $\frac { a + b } { 2 } \geqslant \sqrt { a b }$ for $a$, $b \geqslant 0$. Explain why the result cannot be extended to apply in each of the following cases.\\
(i) One of the numbers $a$ and $b$ is positive and the other is negative.\\
(ii) Both numbers $a$ and $b$ are negative.
\hfill \mbox{\textit{OCR MEI Paper 3 2018 Q11 [2]}}