| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2023 |
| Session | September |
| Marks | 9 |
| Topic | Curve Sketching |
| Type | Single transformation sketches |
| Difficulty | Moderate -0.3 This question tests graph sketching of a cubic with a repeated root and understanding of transformations. Part (a) is straightforward - finding intercepts and sketching a standard cubic. Parts (b)(i-iii) require recognizing horizontal stretches/reflections and translations, which are routine A-level transformations. The question involves multiple parts but each is a standard technique with no novel problem-solving 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)1.02x Combinations of transformations: multiple transformations |
A cubic curve $C$ has equation
$$y = (3-x)(4+x)^2.$$
\begin{enumerate}[label=(\alph*)]
\item Sketch the graph of $C$. [3]
The sketch must include any points where the graph meets the coordinate axes.
\item Sketch in separate diagrams the graph of $\ldots$
\begin{enumerate}[label=(\roman*)]
\item $\ldots y = (3-2x)(4+2x)^2$. [2]
\item $\ldots y = (3+x)(4-x)^2$. [2]
\item $\ldots y = (2-x)(5+x)^2$. [2]
\end{enumerate}
Each of the sketches must include any points where the graph meets the coordinate axes.
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Pure 2023 Q8 [9]}}