| Exam Board | Edexcel |
|---|---|
| Module | AEA (Advanced Extension Award) |
| Year | 2017 |
| Session | June |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Sketch rational with linear numerator |
| Difficulty | Challenging +1.2 This question requires understanding of rational function transformations and asymptotes. Part (a) is straightforward identification from the given function. Part (b)(i) involves a standard horizontal shift and vertical translation. Part (b)(ii) is more challenging as it requires understanding the effect of |x| on the graph, creating reflection symmetry, but this is still a well-practiced transformation technique at A-level. The question is above average difficulty due to the multiple transformations and the AEA context, but doesn't require novel insight beyond applying standard transformation rules. |
| Spec | 1.02n Sketch curves: simple equations including polynomials1.02s Modulus graphs: sketch graph of |ax+b|1.02w Graph transformations: simple transformations of f(x) |
5.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{15e3f7f2-a77c-4ee4-8f0a-ac739e9fede5-5_946_1498_210_287}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{center}
\end{figure}
Figure 2 shows a sketch of the curve with equation $y = \mathrm { f } ( x )$ where
$$f ( x ) = \frac { 4 ( x - 1 ) } { x ( x - 3 ) }$$
The curve cuts the $x$-axis at $( a , 0 )$. The lines $y = 0 , x = 0$ and $x = b$ are asymptotes to the curve.
\begin{enumerate}[label=(\alph*)]
\item Write down the value of $a$ and the value of $b$.\\
(2)
\item On separate axes, sketch the curves with the following equations. On your sketches, you should mark the coordinates of any intersections with the coordinate axes and state the equations of any asymptotes.
\begin{enumerate}[label=(\roman*)]
\item $y = \mathrm { f } ( x + 2 ) - 4$
\item $y = \mathrm { f } ( | x | ) - 3$
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{Edexcel AEA 2017 Q5 [14]}}