| Exam Board | Edexcel |
|---|---|
| Module | AEA (Advanced Extension Award) |
| Year | 2020 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Sketch rational with reciprocal terms |
| Difficulty | Challenging +1.8 This AEA question requires finding asymptotes and turning points of a rational function (standard A-level), but part (c) demands sophisticated understanding of combined transformations (horizontal shift) with absolute value and vertical shift. Students must track how asymptotes, turning points, and intercepts transform through multiple operations, then sketch accurately—this requires strong visualization and systematic analysis beyond typical A-level curve sketching. |
| Spec | 1.02n Sketch curves: simple equations including polynomials1.02o Sketch reciprocal curves: y=a/x and y=a/x^21.02w Graph transformations: simple transformations of f(x)1.07n Stationary points: find maxima, minima using derivatives |
1.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{4d5b914c-28b2-4485-a42e-627c95fa16e2-02_723_1002_248_584}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}
Figure 1 shows a sketch of the curve with equation $y = \mathrm { f } ( x )$ where
$$\mathrm { f } ( x ) = 1 + \frac { 4 } { x ( x - 3 ) }$$
The curve has a turning point at the point $P$, and the lines with equations $y = 1 , x = 0$ and $x = a$ are asymptotes to the curve.
\begin{enumerate}[label=(\alph*)]
\item Write down the value of $a$.
\item Find the coordinates of $P$, justifying your answer.
\item Sketch the curve with equation $y = \left| \mathrm { f } \left( x + \frac { 3 } { 2 } \right) \right| - 1$
On your sketch, you should show the coordinates of any points of intersection with the coordinate axes, the coordinates of any turning points and the equations of any asymptotes.\\
\includegraphics[max width=\textwidth, alt={}, center]{4d5b914c-28b2-4485-a42e-627c95fa16e2-02_2255_50_311_1980}
\end{enumerate}
\hfill \mbox{\textit{Edexcel AEA 2020 Q1 [12]}}