| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Factorise then sketch |
| Difficulty | Moderate -0.8 This is a straightforward C1 question requiring basic factorisation (taking out x, then factorising a quadratic) and sketching a cubic with clearly identified intercepts. Both parts are routine textbook exercises with no problem-solving insight needed, making it easier than average but not trivial since it requires correct execution of multiple steps. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem1.02n Sketch curves: simple equations including polynomials |
$$\text{f}(x) = 4x - 3x^2 - x^3.$$
\begin{enumerate}[label=(\roman*)]
\item Fully factorise $4x - 3x^2 - x^3$. [3]
\item Sketch the curve $y = \text{f}(x)$, showing the coordinates of any points of intersection with the coordinate axes. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR C1 Q4 [6]}}