| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2006 |
| Session | January |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Sketch then solve related equations |
| Difficulty | Standard +0.3 This is a straightforward C1 curve sketching question requiring expansion of brackets, factorization, and quadratic formula. While multi-part with 13 marks total, each step is routine: sketching a cubic from factored form, algebraic expansion, factor theorem application, and solving a quadratic. No novel insight required, just systematic application of standard techniques slightly above average difficulty due to length and surd manipulation. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem1.02n Sketch curves: simple equations including polynomials |
\begin{enumerate}[label=(\roman*)]
\item Sketch the graph of $y = x(x - 3)^2$. [3]
\item Show that the equation $x(x - 3)^2 = 2$ can be expressed as $x^3 - 6x^2 + 9x - 2 = 0$. [2]
\item Show that $x = 2$ is one root of this equation and find the other two roots, expressing your answers in surd form.
Show the location of these roots on your sketch graph in part (i). [8]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C1 2006 Q12 [13]}}