| Exam Board | WJEC |
|---|---|
| Module | Unit 3 (Unit 3) |
| Year | 2024 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Proof |
| Type | Contradiction proof of inequality |
| Difficulty | Standard +0.3 This is a straightforward proof by contradiction of a standard AM-GM inequality result. Students need to assume x + 81/x < 18, rearrange to get a quadratic inequality, and show this leads to a contradiction (no real positive solutions). The technique is routine and the algebra is simple, making this easier than average. |
| Spec | 1.01d Proof by contradiction |
Prove by contradiction the following proposition:
When $x$ is real and positive, $x + \frac{81}{x} \geq 18$. [4]
\hfill \mbox{\textit{WJEC Unit 3 2024 Q5 [4]}}