| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Vertical stretch y = af(x) |
| Difficulty | Moderate -0.8 This is a straightforward C1 transformation question requiring only direct application of standard rules: vertical stretch multiplies y-coordinates by 3, horizontal translation shifts x-coordinates by -2. No problem-solving or conceptual insight needed beyond recalling and applying basic transformation formulas to three given points. |
| Spec | 1.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| (a) \(-1\), accept \((-1,0)\) | B1 | The \(x\) coordinate of \(A\) is \(-1\). Accept \(-1\) or \((-1,0)\) on diagram or stated |
| (b) Correct shape (positive \(x^3\) curve with maximum and minimum) | B1 | Correct shape; position not important but must have two clear turning points |
| Touches at \((0,0)\) | B1 | Graph touches the origin (as maximum or minimum). Independent of other marks |
| Crosses at \((2,0)\) only | B1 | Graph crosses \(x\)-axis at \((2,0)\) only. If crosses at \((2,0)\) and \((0,0)\) this is B0 |
| (c) 2 solutions as curves cross twice | B1 ft | Two solutions as there are two intersections of the curves |
## Question 4:
| Answer/Working | Marks | Guidance |
|---|---|---|
| (a) $-1$, accept $(-1,0)$ | B1 | The $x$ coordinate of $A$ is $-1$. Accept $-1$ or $(-1,0)$ on diagram or stated |
| (b) Correct shape (positive $x^3$ curve with maximum and minimum) | B1 | Correct shape; position not important but must have two clear turning points |
| Touches at $(0,0)$ | B1 | Graph touches the origin (as maximum or minimum). Independent of other marks |
| Crosses at $(2,0)$ **only** | B1 | Graph crosses $x$-axis at $(2,0)$ only. If crosses at $(2,0)$ and $(0,0)$ this is B0 |
| (c) 2 solutions as **curves** cross twice | B1 ft | Two solutions as there are two intersections of the curves |
---4.
\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\includegraphics[alt={},max width=\textwidth]{307d6e38-b8ca-4473-9f1a-94c8660c0d9c-006_689_920_292_511}
\end{center}
\end{figure}
Figure 1 shows a sketch of the curve with equation $y = \mathrm { f } ( x )$. The curve passes through the origin $O$ and through the point $( 6,0 )$. The maximum point on the curve is $( 3,5 )$.
On separate diagrams, sketch the curve with equation
\begin{enumerate}[label=(\alph*)]
\item $y = 3 \mathrm { f } ( x )$,
\item $y = \mathrm { f } ( x + 2 )$.
On each diagram, show clearly the coordinates of the maximum point and of each point at which the curve crosses the $x$-axis.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q4}}