| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2016 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Vertical stretch y = af(x) |
| Difficulty | Easy -1.2 This is a straightforward C1 transformation question requiring only direct application of standard rules: multiply y-coordinates by 3 for part (a) and subtract 4 from all y-coordinates for part (b). No problem-solving or conceptual insight needed—purely mechanical application of basic transformation formulas taught early in the course. |
| Spec | 1.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Similar cubic shape passing through origin, max in 2nd quadrant, min in 4th quadrant, with evidence of change in at least one \(y\)-coordinate (not \(x\)-coordinates) | B1 | Inconsistent changes in \(y\)-coordinates acceptable but not \(x\)-coordinates |
| Maximum at \((-2, 12)\) and minimum at \((3, -24)\), coordinates written correctly | B1 | Coordinates may appear on sketch or separately in text. Condone missing brackets |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Positive cubic not through origin, max to left of \(y\)-axis, min to right of \(y\)-axis | M1 | |
| Maximum at \((-2, 0)\), minimum at \((3, -12)\) | A1 | Curve must touch \(x\)-axis at \((-2, 0)\). Allow just \(-2\) or \((0,-2)\) if marked in correct place. Condone missing brackets |
| Crosses \(y\)-axis at \((0, -4)\) | A1 | Allow just \(-4\) (not \(+4\)). Allow \((-4, 0)\) if marked in correct place |
# Question 4(a):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Similar cubic shape passing through origin, max in 2nd quadrant, min in 4th quadrant, with evidence of change in at least one $y$-coordinate (not $x$-coordinates) | B1 | Inconsistent changes in $y$-coordinates acceptable but **not** $x$-coordinates |
| Maximum at $(-2, 12)$ and minimum at $(3, -24)$, coordinates written correctly | B1 | Coordinates may appear on sketch or separately in text. Condone missing brackets |
**Total: [2]**
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# Question 4(b):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Positive cubic not through origin, max to left of $y$-axis, min to right of $y$-axis | M1 | |
| Maximum at $(-2, 0)$, minimum at $(3, -12)$ | A1 | Curve must **touch** $x$-axis at $(-2, 0)$. Allow just $-2$ or $(0,-2)$ if marked in correct place. Condone missing brackets |
| Crosses $y$-axis at $(0, -4)$ | A1 | Allow just $-4$ (not $+4$). Allow $(-4, 0)$ if marked in correct place |
**Total: [3] — 5 marks**4.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{b0413ecc-b780-4f77-b76a-da7c699c12cb-05_709_744_269_607}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}
Figure 1 shows a sketch of part of the curve with equation $y = \mathrm { f } ( x )$. The curve has a maximum point $A$ at $( - 2,4 )$ and a minimum point $B$ at $( 3 , - 8 )$ and passes through the origin $O$.
On separate diagrams, sketch the curve with equation
\begin{enumerate}[label=(\alph*)]
\item $y = 3 \mathrm { f } ( x )$,
\item $y = \mathrm { f } ( x ) - 4$\\
(3)
On each diagram, show clearly the coordinates of the maximum and the minimum points and the coordinates of the point where the curve crosses the $y$-axis.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 2016 Q4 [5]}}