| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2014 |
| Session | January |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Single transformation sketches |
| Difficulty | Moderate -0.8 This is a straightforward C1 transformation question requiring only recall of standard rules: horizontal translation shifts x-coordinates (0,3)→(-4,3) and (4,2)→(0,2), and vertical stretch multiplies y-coordinates (0,3)→(0,6) and (4,2)→(4,4). No problem-solving or conceptual insight needed, just direct application of memorized transformation rules. |
| Spec | 1.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks | Guidance |
|---|---|---|
| (a) | Horizontal translation of \(\pm 4\) | M1 |
| Minimum point on the \(y\)-axis at \((0,2)\) | A1 | The shape remains unchanged and has a minimum at \((0,2)\). Condone U shaped curves. |
| (b) | Correct "shape" with \(P'\) adapted | M1 |
| \(y\) intercept \((0,6)\) and \(P'(4,4)\) | A1 | Correct shape, condoning U shapes with the \(y\) intercept at \((0, 6)\) and \(P' = (4,4)\). The coordinates of the points may appear in the text or besides the diagram. This is acceptable but if they contradict the diagram, the diagram takes precedence. |
(a) | Horizontal translation of $\pm 4$ | M1 | A horizontal translation of $\pm 4$. The $y$ coordinate of $P$ remains unchanged at 2. Look for $P' = (0,2)$ or $(8,2)$. Condone U shaped curves.
| Minimum point on the $y$-axis at $(0,2)$ | A1 | The shape remains unchanged and has a minimum at $(0,2)$. Condone U shaped curves.
(b) | Correct "shape" with $P'$ adapted | M1 | The curve remains in quadrant 1 and quadrant 2 with the minimum in quadrant 1. The shape must be correct. Condone U shaped curves. $P'$ must have been adapted. The mark cannot be scored for drawing the original curve with $P' = (4,2)$.
| $y$ intercept $(0,6)$ and $P'(4,4)$ | A1 | Correct shape, condoning U shapes with the $y$ intercept at $(0, 6)$ and $P' = (4,4)$. The coordinates of the points may appear in the text or besides the diagram. This is acceptable but if they contradict the diagram, the diagram takes precedence.
---4.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{6081d81b-51d2-4140-9834-71ef7fd700b0-08_835_777_118_596}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}
Figure 1 shows a sketch of a curve with equation $y = \mathrm { f } ( x )$.
The curve crosses the $y$-axis at $( 0,3 )$ and has a minimum at $P ( 4,2 )$.
On separate diagrams, sketch the curve with equation
\begin{enumerate}[label=(\alph*)]
\item $y = \mathrm { f } ( x + 4 )$,
\item $y = 2 \mathrm { f } ( x )$.
On each diagram, show clearly the coordinates of the minimum point and any point of intersection with the $y$-axis.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 2014 Q4 [4]}}