| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Solving quadratics and applications |
| Type | Algebraic identity, find constants |
| Difficulty | Moderate -0.8 This is a straightforward algebraic manipulation question requiring expansion of two squared brackets and collection of like terms. The substitution aspect (treating √x as a variable) is implicit and routine. It's easier than average as it's purely mechanical algebra with no problem-solving required, though slightly more involved than the most basic index law recall. |
| Spec | 1.02b Surds: manipulation and rationalising denominators1.02j Manipulate polynomials: expanding, factorising, division, factor theorem |
\begin{enumerate}
\item $\quad \mathrm { f } ( x ) = ( \sqrt { x } + 3 ) ^ { 2 } + ( 1 - 3 \sqrt { x } ) ^ { 2 }$.
\end{enumerate}
Show that $\mathrm { f } ( x )$ can be written in the form $a x + b$ where $a$ and $b$ are integers to be found.\\
\hfill \mbox{\textit{OCR C1 Q1 [3]}}