| Exam Board | Edexcel |
|---|---|
| Module | AS Paper 1 (AS Paper 1) |
| Session | Specimen |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Proof |
| Type | Algebraic inequality proof |
| Difficulty | Standard +0.3 Part (a) is a standard AM-GM inequality proof requiring algebraic manipulation (squaring both sides or rearranging to $(\sqrt{x}-\sqrt{y})^2 \geq 0$), which is a common A-level technique. Part (b) simply requires finding any negative values where the inequality fails, which is straightforward. The question tests proof skills but uses familiar methods with minimal steps for only 3 marks total. |
| Spec | 1.01a Proof: structure of mathematical proof and logical steps1.01c Disproof by counter example |
\begin{enumerate}[label=(\alph*)]
\item Prove that for all positive values of $x$ and $y$
$$\sqrt{xy} \leqslant \frac{x + y}{2}$$
[2]
\item Prove by counter example that this is not true when $x$ and $y$ are both negative.
[1]
\end{enumerate}
\hfill \mbox{\textit{Edexcel AS Paper 1 Q11 [3]}}