| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2008 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Sketch two translations on separate diagrams |
| Difficulty | Moderate -0.8 This is a straightforward C1 transformations question requiring only direct application of standard rules: vertical translation shifts the y-coordinates by +3, and horizontal stretch by factor 1/2 halves the x-coordinates. Both transformations are routine textbook exercises with no problem-solving or insight required beyond recalling the transformation rules. |
| Spec | 1.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| (a) U-shaped curve, minimum in first quadrant, not touching \(x\)-axis, cutting positive \(y\)-axis | B1 | 1st B1: moving given curve up; must be U shaped, minimum in first quadrant, not touching \(x\)-axis but cutting positive \(y\)-axis |
| Curve cutting \(y\)-axis at \((0, 10)\) | B1 | 2nd B1: curve cutting \(y\)-axis at \((0,10)\); point 10 (or even \((10,0)\)) marked on positive \(y\)-axis is OK |
| Minimum indicated at \((7, 3)\) | B1 (3) | 3rd B1: minimum at \((7,3)\); must have both coordinates in right order |
| (b) U-shaped curve, touching positive \(x\)-axis, crossing \(y\)-axis at \((0,7)\) | B1 | 1st B1: U shaped curve touching positive \(x\)-axis and crossing \(y\)-axis at \((0,7)\); condone \((7,0)\) if marked on positive \(y\)-axis, or 7 marked on \(y\)-axis |
| Minimum at \((3.5, 0)\) | B1 (2) | 2nd B1: minimum at \((3.5,0)\) or \(3.5\) or \(\frac{7}{2}\) marked on \(x\)-axis; do not condone \((0, 3.5)\) here |
| Redrawing \(f(x)\) scores B1B0 in part (b); points on sketch override points given in text/table |
# Question 3:
| Answer/Working | Marks | Guidance |
|---|---|---|
| **(a)** U-shaped curve, minimum in first quadrant, not touching $x$-axis, cutting positive $y$-axis | B1 | 1st B1: moving given curve up; must be U shaped, minimum in first quadrant, not touching $x$-axis but cutting positive $y$-axis |
| Curve cutting $y$-axis at $(0, 10)$ | B1 | 2nd B1: curve cutting $y$-axis at $(0,10)$; point 10 (or even $(10,0)$) marked on positive $y$-axis is OK |
| Minimum indicated at $(7, 3)$ | B1 (3) | 3rd B1: minimum at $(7,3)$; must have both coordinates in right order |
| **(b)** U-shaped curve, touching positive $x$-axis, crossing $y$-axis at $(0,7)$ | B1 | 1st B1: U shaped curve touching positive $x$-axis and crossing $y$-axis at $(0,7)$; condone $(7,0)$ if marked on positive $y$-axis, or 7 marked on $y$-axis |
| Minimum at $(3.5, 0)$ | B1 (2) | 2nd B1: minimum at $(3.5,0)$ or $3.5$ or $\frac{7}{2}$ marked on $x$-axis; do not condone $(0, 3.5)$ here |
| | | Redrawing $f(x)$ scores B1B0 in part (b); points on sketch override points given in text/table |
---3.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{9451ec48-d955-44a8-9988-68f7c0fb9821-04_463_703_276_589}
\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 point ( 0,7 ) and has a minimum point at ( 7,0 ).
On separate diagrams, sketch the curve with equation
\begin{enumerate}[label=(\alph*)]
\item $y = \mathrm { f } ( x ) + 3$,
\item $y = \mathrm { f } ( 2 x )$.
On each diagram, show clearly the coordinates of the minimum point and the coordinates of the point at which the curve crosses the $y$-axis.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 2008 Q3 [5]}}