| Exam Board | Edexcel |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2024 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Function Transformations |
| Type | Multiple separate transformations (sketch-based, standard transformations) |
| Difficulty | Moderate -0.3 This is a standard P1 function transformation question requiring application of horizontal translation and combined reflection/stretch. While it involves two separate transformations and careful tracking of key points, these are routine textbook exercises with no novel problem-solving required. The transformations are straightforward applications of standard rules, making it slightly easier than average. |
| Spec | 1.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Correct shape: translation of original curve parallel to \(x\)-axis | B1 | Same shape translated parallel to \(x\)-axis with no evidence from \(x\)-intercepts that transformation is anything other than a translation. \(x\)-intercepts (if labelled) must be 4 units apart. |
| Minimum at the origin \((0,0)\) | B1 | Origin does not have to be labelled |
| Passes through \((-4, 0)\) | B1 | Allow just \(-4\) marked in correct place. Condone \((0,-4)\) as long as marked in correct place on sketch |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Reflection in \(y\)-axis with minimum on negative \(x\)-axis and maximum in quadrant 2 | B1 | Maximum must NOT be on \(y\)-axis; curve must continue upwards left of \(y\)-axis; curve must extend into quadrant 4 |
| Minimum at \((-1, 0)\) | B1 | Allow just \(-1\) marked in correct place; condone \((0,-1)\) if marked correctly; must correspond to sketch |
| Passes through \((0, 2)\) and passes through or touches \(\left(\frac{1}{3}, 0\right)\) | B1 | Condone \((2,0)\) and/or \(\left(0, \frac{1}{3}\right)\) if marked in correct place; must correspond to sketch |
## Question 3(a):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Correct shape: translation of original curve parallel to $x$-axis | B1 | Same shape translated parallel to $x$-axis with no evidence from $x$-intercepts that transformation is anything other than a translation. $x$-intercepts (if labelled) must be 4 units apart. |
| Minimum at the origin $(0,0)$ | B1 | Origin does not have to be labelled |
| Passes through $(-4, 0)$ | B1 | Allow just $-4$ marked in correct place. Condone $(0,-4)$ as long as marked in correct place on sketch |
## Question 3(b):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Reflection in $y$-axis with minimum on negative $x$-axis and maximum in quadrant 2 | B1 | Maximum must NOT be on $y$-axis; curve must continue upwards left of $y$-axis; curve must extend into quadrant 4 |
| Minimum at $(-1, 0)$ | B1 | Allow just $-1$ marked in correct place; condone $(0,-1)$ if marked correctly; must correspond to sketch |
| Passes through $(0, 2)$ and passes through or touches $\left(\frac{1}{3}, 0\right)$ | B1 | Condone $(2,0)$ and/or $\left(0, \frac{1}{3}\right)$ if marked in correct place; must correspond to sketch |
---3.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{7e2b7c81-e678-4078-964b-8b78e3b63f43-06_688_771_251_648}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}
Figure 1 shows a sketch of the curve with equation $y = \mathrm { f } ( x )$.\\
The curve passes through the points $( - 1,0 )$ and $( 0,2 )$ and touches the $x$-axis at the point $( 3,0 )$.
On separate diagrams, sketch the curve with equation
\begin{enumerate}[label=(\alph*)]
\item $y = \mathrm { f } ( \mathrm { x } + 3 )$
\item $y = \mathrm { f } ( - 3 x )$
On each diagram, show clearly the coordinates of all the points where the curve cuts or touches the coordinate axes.
\end{enumerate}
\hfill \mbox{\textit{Edexcel P1 2024 Q3 [6]}}