| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2018 |
| Session | Specimen |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | Linear transformations |
| Type | Describe rotation from matrix |
| Difficulty | Moderate -0.3 This is a standard Further Maths question on linear transformations requiring recognition of rotation matrix form, knowledge of standard reflection matrices, matrix multiplication, and finding invariant lines. While it involves multiple parts and some calculation, all techniques are routine for F1 students with no novel problem-solving required—slightly easier than average A-level difficulty. |
| Spec | 4.03c Matrix multiplication: properties (associative, not commutative)4.03d Linear transformations 2D: reflection, rotation, enlargement, shear |
| VIAV SIHI NI BIIIM ION OC | VGHV SIHI NI GHIYM ION OC | VJ4V SIHI NI JIIYM ION OC |
7.
$$\mathbf { P } = \left( \begin{array} { c c }
\frac { 5 } { 13 } & - \frac { 12 } { 13 } \\
\frac { 12 } { 13 } & \frac { 5 } { 13 }
\end{array} \right)$$
\begin{enumerate}[label=(\alph*)]
\item Describe fully the single geometrical transformation $U$ represented by the matrix $\mathbf { P }$.
The transformation $V$, represented by the $2 \times 2$ matrix $\mathbf { Q }$, is a reflection in the line with equation $y = x$
\item Write down the matrix $\mathbf { Q }$.
Given that the transformation $V$ followed by the transformation $U$ is the transformation $T$, which is represented by the matrix $\mathbf { R }$,
\item find the matrix $\mathbf { R }$.
\item Show that there is a value of $k$ for which the transformation $T$ maps each point on the straight line $y = k x$ onto itself, and state the value of $k$.\\
\begin{center}
\end{center}
\includegraphics[max width=\textwidth, alt={}, center]{38217fcb-8f26-49ac-9bb1-61c2f304006e-17_2261_54_312_34}
\begin{center}
\begin{tabular}{|l|l|l|}
\hline
VIAV SIHI NI BIIIM ION OC & VGHV SIHI NI GHIYM ION OC & VJ4V SIHI NI JIIYM ION OC \\
\hline
\end{tabular}
\end{center}
\begin{center}
\end{center}
\end{enumerate}
\hfill \mbox{\textit{Edexcel F1 2018 Q7 [10]}}