| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2010 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Factor & Remainder Theorem |
| Type | Verify factor then sketch or analyse curve |
| Difficulty | Moderate -0.3 This is a straightforward multi-part question testing standard C1 techniques: systematic trial of small integer roots using the factor theorem, factorization by inspection or division, basic cubic sketching, and translation. While it requires multiple steps (12 marks total), each part follows routine procedures with no novel problem-solving or insight required, making it slightly easier than average. |
| 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 $f(x) = x^3 + 6x^2 - x - 30$.
\begin{enumerate}[label=(\roman*)]
\item Use the factor theorem to find a root of $f(x) = 0$ and hence factorise $f(x)$ completely. [6]
\item Sketch the graph of $y = f(x)$. [3]
\item The graph of $y = f(x)$ is translated by $\begin{pmatrix} 1 \\ 0 \end{pmatrix}$.
Show that the equation of the translated graph may be written as
$$y = x^3 + 3x^2 - 10x - 24.$$ [3]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C1 2010 Q12 [12]}}