| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2022 |
| Session | February |
| Marks | 4 |
| Topic | Linear transformations |
| Type | Write down transformation matrix |
| Difficulty | Moderate -0.8 This is a straightforward question on shear transformations requiring basic recall and application. Part (i) is a simple sketch, and part (ii) requires knowing the standard form of a shear matrix and using one point to determine the shear factor—both routine exercises with minimal problem-solving demand. |
| Spec | 4.03d Linear transformations 2D: reflection, rotation, enlargement, shear |
The transformation $S$ is a shear parallel to the $x$-axis in which the image of the point $(1, 1)$ is the point $(0, 1)$.
\begin{enumerate}[label=(\roman*)]
\item Draw a diagram showing the image of the unit square under $S$. [2]
\item Write down the matrix that represents $S$. [2]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM 2022 Q4 [4]}}