| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2011 |
| Session | January |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Vertical translation of cubic with factorisation |
| Difficulty | Moderate -0.8 This is a structured, multi-part question with clear signposting through each step. Part (i) involves routine sketching and algebraic expansion; part (ii) guides students through factor theorem, polynomial division, and discriminant analysis; part (iii) requires recognizing a simple vertical translation. All techniques are standard C1 content with no novel problem-solving required—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) |
12
\begin{enumerate}[label=(\roman*)]
\item You are given that $\mathrm { f } ( x ) = ( 2 x - 5 ) ( x - 1 ) ( x - 4 )$.\\
(A) Sketch the graph of $y = \mathrm { f } ( x )$.\\
(B) Show that $\mathrm { f } ( x ) = 2 x ^ { 3 } - 15 x ^ { 2 } + 33 x - 20$.
\item You are given that $\mathrm { g } ( x ) = 2 x ^ { 3 } - 15 x ^ { 2 } + 33 x - 40$.\\
(A) Show that $\mathrm { g } ( 5 ) = 0$.\\
(B) Express $\mathrm { g } ( x )$ as the product of a linear and quadratic factor.\\
(C) Hence show that the equation $\mathrm { g } ( x ) = 0$ has only one real root.
\item Describe fully the transformation that maps $y = \mathrm { f } ( x )$ onto $y = \mathrm { g } ( x )$.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C1 2011 Q12 [13]}}