| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2013 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Vertical translation of cubic with factorisation |
| Difficulty | Moderate -0.8 This is a straightforward C1 curve sketching question requiring routine skills: plotting a cubic from factored form, applying a horizontal translation to find roots, expanding brackets, and factorising using the factor theorem. All parts follow standard procedures with no problem-solving insight needed, making it easier than average but not trivial due to the multi-step algebraic manipulation required. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem1.02n Sketch curves: simple equations including polynomials1.02w Graph transformations: simple transformations of f(x) |
You are given that $\text{f}(x) = (2x - 3)(x + 2)(x + 4)$.
\begin{enumerate}[label=(\roman*)]
\item Sketch the graph of $y = \text{f}(x)$. [3]
\item State the roots of $\text{f}(x - 2) = 0$. [2]
\item You are also given that $\text{g}(x) = \text{f}(x) + 15$.
\begin{enumerate}[label=(\Alph*)]
\item Show that $\text{g}(x) = 2x^3 + 9x^2 - 2x - 9$. [2]
\item Show that $\text{g}(1) = 0$ and hence factorise $\text{g}(x)$ completely. [5]
\end{enumerate}
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C1 2013 Q11 [12]}}