| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2009 |
| Session | June |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Horizontal translation of factored polynomial |
| Difficulty | Moderate -0.8 This is a straightforward C1 question testing routine algebraic expansion, basic curve sketching from factored form, simple transformations, and factor theorem with quadratic formula. All parts follow standard textbook procedures with no problem-solving insight required, making it easier than average. |
| Spec | 1.02f Solve quadratic equations: including in a function of unknown1.02j Manipulate polynomials: expanding, factorising, division, factor theorem1.02n Sketch curves: simple equations including polynomials1.02w Graph transformations: simple transformations of f(x) |
\begin{enumerate}[label=(\roman*)]
\item You are given that $\text{f}(x) = (x + 1)(x - 2)(x - 4)$.
\begin{enumerate}[label=(\alph*)]
\item Show that $\text{f}(x) = x^3 - 5x^2 + 2x + 8$. [2]
\item Sketch the graph of $y = \text{f}(x)$. [3]
\item The graph of $y = \text{f}(x)$ is translated by $\begin{pmatrix} 3 \\ 0 \end{pmatrix}$.
State an equation for the resulting graph. You need not simplify your answer.
Find the coordinates of the point at which the resulting graph crosses the $y$-axis. [3]
\end{enumerate}
\item Show that 3 is a root of $x^3 - 5x^2 + 2x + 8 = -4$. Hence solve this equation completely, giving the other roots in surd form. [5]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C1 2009 Q12 [13]}}