| Exam Board | WJEC |
|---|---|
| Module | Further Unit 1 (Further Unit 1) |
| Session | Specimen |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear transformations |
| Type | Augmented matrices for translations |
| Difficulty | Standard +0.8 This is a Further Maths question requiring composition of three transformations using 3×3 matrices (including homogeneous coordinates for translation), then solving a system to find fixed points. While systematic, it demands careful matrix multiplication, understanding of augmented matrices for affine transformations, and algebraic manipulation—significantly above average A-level difficulty but standard for Further Maths. |
| Spec | 4.03d Linear transformations 2D: reflection, rotation, enlargement, shear4.03e Successive transformations: matrix products4.03f Linear transformations 3D: reflections and rotations about axes4.03g Invariant points and lines |
The transformation $T$ in the plane consists of a reflection in the line $y = x$, followed by a translation in which the point $(x, y)$ is transformed to the point $(x + 1, y - 2)$, followed by an anticlockwise rotation through $90°$ about the origin.
\begin{enumerate}[label=(\alph*)]
\item Find the $3 \times 3$ matrix representing $T$. [6]
\item Show that $T$ has no fixed points. [3]
\end{enumerate}
\hfill \mbox{\textit{WJEC Further Unit 1 Q6 [9]}}