| Exam Board | CAIE |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2021 |
| Session | March |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Function Transformations |
| Type | Graph to graph transformation description |
| Difficulty | Moderate -0.5 This is a straightforward graph transformation question requiring students to identify two basic transformations (likely a translation and/or reflection/stretch) from visual inspection and write the combined transformation equation. While it requires understanding of transformation notation, it's a standard P1 exercise with no complex problem-solving or novel insight needed—slightly easier than average due to its routine nature. |
| Spec | 1.02w Graph transformations: simple transformations of f(x)1.02x Combinations of transformations: multiple transformations |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| (a) Stretch, factor 3 in \(y\) direction or parallel to the \(y\)-axis | B1 B1 | |
| (a) Translation \(\begin{pmatrix} 4 \\ 0 \end{pmatrix}\) | B1 B1 | Allow Translation 4 (units) in \(x\) direction. Transformations can be given in either order |
| (b) \([y =]\ 3f(x-4)\) | B1 B1 | B1 for 3, B1 for \((x-4)\) with no extra terms |
## Question 5:
| Answer | Marks | Guidance |
|--------|-------|----------|
| (a) Stretch, factor 3 in $y$ direction **or** parallel to the $y$-axis | B1 B1 | |
| (a) Translation $\begin{pmatrix} 4 \\ 0 \end{pmatrix}$ | B1 B1 | Allow Translation 4 (units) in $x$ direction. Transformations can be given in either order |
| (b) $[y =]\ 3f(x-4)$ | B1 B1 | B1 for 3, B1 for $(x-4)$ with no extra terms |
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\includegraphics[max width=\textwidth, alt={}, center]{54f3f051-e124-470d-87b5-8e25c35248a9-07_775_768_260_685}
In the diagram, the graph of $y = \mathrm { f } ( x )$ is shown with solid lines. The graph shown with broken lines is a transformation of $y = \mathrm { f } ( x )$.
\begin{enumerate}[label=(\alph*)]
\item Describe fully the two single transformations of $y = \mathrm { f } ( x )$ that have been combined to give the resulting transformation.
\item State in terms of $y$, f and $x$, the equation of the graph shown with broken lines.
\end{enumerate}
\hfill \mbox{\textit{CAIE P1 2021 Q5 [6]}}