| Exam Board | OCR MEI |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Proof |
| Type | Algebraic inequality proof |
| Difficulty | Standard +0.3 This is a structured algebraic proof question requiring expansion of brackets and manipulation of expressions (part i), followed by a guided inequality proof (part ii). While it involves multiple steps, the algebraic manipulations are straightforward, and the proof structure is heavily scaffolded by the given identities. It's slightly above average difficulty due to the proof element, but the guidance makes it accessible to competent C3 students. |
| Spec | 1.01a Proof: structure of mathematical proof and logical steps1.02j Manipulate polynomials: expanding, factorising, division, factor theorem |
\begin{enumerate}[label=(\roman*)]
\item Show that
\begin{enumerate}[label=(\Alph*)]
\item $(x - y)(x^2 + xy + y^2) = x^3 - y^3$,
\item $(x + \frac{1}{2}y)^2 + \frac{3}{4}y^2 = x^2 + xy + y^2$. [4]
\end{enumerate}
\item Hence prove that, for all real numbers $x$ and $y$, if $x > y$ then $x^3 > y^3$. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C3 Q9 [7]}}