SPS SPS FM 2022 February — Question 4 4 marks

Exam BoardSPS
ModuleSPS FM (SPS FM)
Year2022
SessionFebruary
Marks4
TopicLinear transformations
TypeWrite down transformation matrix
DifficultyModerate -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.
Spec4.03d 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 \((0, 1)\).
  1. Draw a diagram showing the image of the unit square under \(S\). [2]
  2. Write down the matrix that represents \(S\). [2]

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]}}