| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2006 |
| Session | January |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Sketch translations and stretches/reflections on separate diagrams |
| Difficulty | Moderate -0.8 This is a straightforward C1 transformations question requiring only recall of standard transformation rules (horizontal/vertical translations and stretches). Each part is routine application of a single transformation with no problem-solving or synthesis required, making it easier than average but not trivial since students must apply three different transformations accurately. |
| Spec | 1.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks | Guidance |
|---|---|---|
| (a) | M1 | Clearly through origin (or \((0,0)\) seen) |
| A1 | 3 labelled (or \((3,0)\) seen) | |
| (b) | M1 | Stretch parallel to y-axis |
| A1 | 1 and 4 labelled (or \((1,0)\) and \((4,0)\) seen) | |
| A1 | 6 labelled (or \((0,6)\) seen) | |
| (c) | M1 | Stretch parallel to x-axis |
| A1 | 2 and 8 labelled (or \((2,0)\) and \((8,0)\) seen) | |
| A1 | 3 labelled (or \((0,3)\) seen) |
| Answer | Marks |
|---|---|
| Guidance: (a) M1: [sketch shown]; (b) M1: [sketch shown] with at least two of: \((1,0)\) unchanged, \((4,0)\) unchanged, \((0,3)\) changed; (c) M1: [sketch shown] with at least two of: \((1,0)\) changed, \((4,0)\) changed, \((0,3)\) unchanged. Beware: Candidates may sometimes re-label the parts of their solution. |
**(a)** | M1 | Clearly through origin (or $(0,0)$ seen)
| A1 | 3 labelled (or $(3,0)$ seen)
**(b)** | M1 | Stretch parallel to y-axis
| A1 | 1 and 4 labelled (or $(1,0)$ and $(4,0)$ seen)
| A1 | 6 labelled (or $(0,6)$ seen)
**(c)** | M1 | Stretch parallel to x-axis
| A1 | 2 and 8 labelled (or $(2,0)$ and $(8,0)$ seen)
| A1 | 3 labelled (or $(0,3)$ seen)
**Total: 9 marks**
| Guidance: (a) M1: [sketch shown]; (b) M1: [sketch shown] with at least two of: $(1,0)$ unchanged, $(4,0)$ unchanged, $(0,3)$ changed; (c) M1: [sketch shown] with at least two of: $(1,0)$ changed, $(4,0)$ changed, $(0,3)$ unchanged. Beware: Candidates may sometimes re-label the parts of their solution.
---\begin{enumerate}[label=(\alph*)]
\item $y = \mathrm { f } ( x + 1 )$,
\item $y = 2 \mathrm { f } ( x )$,
\item $y = \mathrm { f } \left( \frac { 1 } { 2 } x \right)$.
On each diagram show clearly the coordinates of all the points where the curve meets the axes.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 2006 Q6 [9]}}