| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2011 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Sketch single transformation from given curve |
| Difficulty | Moderate -0.8 This is a straightforward C1 transformation question requiring recall of standard transformations (horizontal stretch, reflection in x-axis, horizontal translation). Each part involves applying a single, well-known transformation to clearly marked points with no problem-solving or novel insight required. Easier than average A-level questions. |
| Spec | 1.02w Graph transformations: simple transformations of f(x)1.02x Combinations of transformations: multiple transformations |
| Answer | Marks | Guidance |
|---|---|---|
| (a) Shape \(\cup\) through \((0, 0)\) | B1 | |
| \((3, 0)\) | B1 | |
| \((1.5, -1)\) | B1 | |
| Notes | (a) B1: U shaped parabola through origin. B1: (3,0) stated or 3 labelled on x axis. B1: (1.5, -1) or equivalent e.g. (3/2, -1). | |
| (b) Shape \(\cap\) | B1 | |
| \((0, 0)\) and \((6, 0)\) | B1 | |
| \((3, 1)\) | B1 | |
| Notes | (b) B1: Cap shaped parabola in any position. B1: through origin (may not be labelled) and (6,0) stated or 6 labelled on x - axis. B1: (3,1) shown. | |
| (c) Shape \(\cup\), not through \((0, 0)\) | M1 | |
| Minimum in 4th quadrant | A1 | |
| \((-p, 0)\) and \((6 - p, 0)\) | B1 | |
| \((3 - p, -1)\) | B1 | |
| Notes | (c) M1: U shaped parabola not through origin. A1: Minimum in 4th quadrant (depends on M mark having been given). B1: Coordinates stated or shown on x axis. B1: Coordinates stated. Note: If values are taken for p, then it is possible to give M1A1B0B0 even if there are several attempts. (In this case all minima should be in fourth quadrant). |
(a) Shape $\cup$ through $(0, 0)$ | B1 |
$(3, 0)$ | B1 |
$(1.5, -1)$ | B1 |
Notes | | (a) B1: U shaped parabola through origin. B1: (3,0) stated or 3 labelled on x axis. B1: (1.5, -1) or equivalent e.g. (3/2, -1).
(b) Shape $\cap$ | B1 |
$(0, 0)$ and $(6, 0)$ | B1 |
$(3, 1)$ | B1 |
Notes | | (b) B1: Cap shaped parabola in any position. B1: through origin (may not be labelled) and (6,0) stated or 6 labelled on x - axis. B1: (3,1) shown.
(c) Shape $\cup$, not through $(0, 0)$ | M1 |
Minimum in 4th quadrant | A1 |
$(-p, 0)$ and $(6 - p, 0)$ | B1 |
$(3 - p, -1)$ | B1 |
Notes | | (c) M1: U shaped parabola not through origin. A1: Minimum in 4th quadrant (depends on M mark having been given). B1: Coordinates stated or shown on x axis. B1: Coordinates stated. Note: If values are taken for p, then it is possible to give M1A1B0B0 even if there are several attempts. (In this case all minima should be in fourth quadrant).
---8.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{f1bb296f-afb2-43cd-9408-2114d7b66971-09_487_743_210_603}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}
Figure 1 shows a sketch of the curve $C$ with equation $y = \mathrm { f } ( x )$.\\
The curve $C$ passes through the origin and through $( 6,0 )$.\\
The curve $C$ has a minimum at the point $( 3 , - 1 )$.
On separate diagrams, sketch the curve with equation
\begin{enumerate}[label=(\alph*)]
\item $y = \mathrm { f } ( 2 x )$,
\item $y = - \mathrm { f } ( x )$,
\item $y = \mathrm { f } ( x + p )$, where $p$ is a constant and $0 < p < 3$.
On each diagram show the coordinates of any points where the curve intersects the $x$-axis and of any minimum or maximum points.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 2011 Q8 [10]}}