| Exam Board | Edexcel |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2019 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Function Transformations |
| Type | Stationary points after transformation |
| Difficulty | Moderate -0.3 This is a standard P1 transformations question testing understanding of reflections, stretches, and translations applied to key features (asymptotes, turning points, intercepts). All parts require direct application of transformation rules with no problem-solving or novel insight—slightly easier than average due to its routine nature, though the multiple parts and need for careful tracking of coordinates prevent it from being trivial. |
| Spec | 1.02w Graph transformations: simple transformations of f(x)1.02x Combinations of transformations: multiple transformations |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(y = 4\) | B1 | May be written on a new graph |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \((16, 9)\) only | B1 | Condone lack of brackets; must be only answer. May be written on graph |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(k \leqslant 4\) | B1 | Sight of either \(k \leqslant 4\) or \(k=9\). Must be in terms of \(k\) |
| \(k = 9\) | B1 | Both required. Where several inequalities given, mark only final answers for each. Ignore inequalities within \(k \leqslant 4\). Note: \(y \leqslant 4,\ y=9\) scores B1B0 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(a = 6\) | B1 | 6 on its own sufficient. Also allow \((y=)f(x)-6\); isw if they then state \(a=-6\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(y = f(x-3)\) | B1 | Also accept \(y=-f(x)+6\), \(y=f(x+4)-9\) or rearrangements such as \(f(x)=6-y\). Do not accept combinations of different transformations |
## Question 8:
### Part (a):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $y = 4$ | B1 | May be written on a new graph |
### Part (b):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $(16, 9)$ only | B1 | Condone lack of brackets; must be only answer. May be written on graph |
### Part (c):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $k \leqslant 4$ | B1 | Sight of either $k \leqslant 4$ or $k=9$. Must be in terms of $k$ |
| $k = 9$ | B1 | Both required. Where several inequalities given, mark only final answers for each. Ignore inequalities within $k \leqslant 4$. Note: $y \leqslant 4,\ y=9$ scores B1B0 |
### Part (d)(i):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $a = 6$ | B1 | 6 on its own sufficient. Also allow $(y=)f(x)-6$; isw if they then state $a=-6$ |
### Part (d)(ii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $y = f(x-3)$ | B1 | Also accept $y=-f(x)+6$, $y=f(x+4)-9$ or rearrangements such as $f(x)=6-y$. Do not accept combinations of different transformations |8.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{c8f8d35d-c2dd-4a1f-a4bb-a4fa06413d12-16_647_970_306_488}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{center}
\end{figure}
The curve $C$ with equation $y = \mathrm { f } ( x )$ is shown in Figure 4.
The curve $C$
\begin{itemize}
\item has a single turning point, a maximum at ( 4,9 )
\item crosses the coordinate axes at only two places, $( - 3,0 )$ and $( 0,6 )$
\item has a single asymptote with equation $y = 4$\\
as shown in Figure 4.
\begin{enumerate}[label=(\alph*)]
\item State the equation of the asymptote to the curve with equation $y = \mathrm { f } ( - x )$.
\item State the coordinates of the turning point on the curve with equation $y = \mathrm { f } \left( \frac { 1 } { 4 } x \right)$.
\end{itemize}
Given that the line with equation $y = k$, where $k$ is a constant, intersects $C$ at exactly one point,
\item state the possible values for $k$.
The curve $C$ is transformed to a new curve that passes through the origin.
\item \begin{enumerate}[label=(\roman*)]
\item Given that the new curve has equation $y = \mathrm { f } ( x ) - a$, state the value of the constant $a$.
\item Write down an equation for another single transformation of $C$ that also passes through the origin.
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{Edexcel P1 2019 Q8 [6]}}