| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2012 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Horizontal translation of factored polynomial |
| Difficulty | Moderate -0.3 This is a straightforward C1 question testing standard techniques: forming a cubic from roots, sketching using intercepts, and applying translations. All parts follow routine procedures with no problem-solving required, making it slightly easier than average, though the multi-part structure and translation work prevent it from being trivial. |
| 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) |
A cubic curve has equation $y = f(x)$. The curve crosses the $x$-axis where $x = -\frac{1}{2}$, $-2$ and $5$.
\begin{enumerate}[label=(\roman*)]
\item Write down three linear factors of $f(x)$. Hence find the equation of the curve in the form $y = 2x^3 + ax^2 + bx + c$. [4]
\item Sketch the graph of $y = f(x)$. [3]
\item The curve $y = f(x)$ is translated by $\begin{pmatrix} 0 \\ -8 \end{pmatrix}$. State the coordinates of the point where the translated curve intersects the $y$-axis. [1]
\item The curve $y = f(x)$ is translated by $\begin{pmatrix} 3 \\ 0 \end{pmatrix}$ to give the curve $y = g(x)$.
Find an expression in factorised form for $g(x)$ and state the coordinates of the point where the curve $y = g(x)$ intersects the $y$-axis. [4]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C1 2012 Q11 [12]}}