| Exam Board | OCR |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2009 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Inequalities |
| Type | Curve above or below axis |
| Difficulty | Standard +0.8 This is a Further Pure 2 inequality requiring algebraic manipulation to rearrange into a form revealing the minimum value, likely involving completing the square or calculus. It's more challenging than standard A-level inequalities due to the rational function structure and the need for rigorous proof, but follows established FP2 techniques. |
| Spec | 1.01a Proof: structure of mathematical proof and logical steps1.07n Stationary points: find maxima, minima using derivatives |
2 Given that $y = \frac { x ^ { 2 } + x + 1 } { ( x - 1 ) ^ { 2 } }$, prove that $y \geqslant \frac { 1 } { 4 }$ for all $x \neq 1$.
\hfill \mbox{\textit{OCR FP2 2009 Q2 [4]}}