| Exam Board | WJEC |
|---|---|
| Module | Further Unit 1 (Further Unit 1) |
| Year | 2023 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear transformations |
| Type | Augmented matrices for translations |
| Difficulty | Standard +0.3 This is a straightforward further maths question on augmented matrices for combined transformations. Part (a) requires standard technique of multiplying two 3×3 matrices (reflection and translation). Part (b) involves solving a simple system of equations to find invariant points. While it's further maths content, the execution is routine with no conceptual surprises, making it slightly easier than average A-level difficulty overall. |
| Spec | 4.03d Linear transformations 2D: reflection, rotation, enlargement, shear4.03e Successive transformations: matrix products4.03g Invariant points and lines |
4. The transformation $T$ in the plane consists of a translation in which the point $( x , y )$ is transformed to the point ( $x + 2 , y - 2$ ), followed by a reflection in the line $y = x$.
\begin{enumerate}[label=(\alph*)]
\item Determine the $3 \times 3$ matrix which represents $T$.
\item Determine how many invariant points exist under the transformation $T$.
\end{enumerate}
\hfill \mbox{\textit{WJEC Further Unit 1 2023 Q4 [7]}}