| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2014 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | Linear transformations |
| Type | Describe rotation from matrix |
| Difficulty | Moderate -0.3 This is a standard Further Maths transformation question requiring recognition of a rotation matrix (cos 30°, sin 30° pattern), writing down a reflection matrix, matrix multiplication, and finding an invariant point. All parts are routine applications of learned techniques with no novel problem-solving required, making it slightly easier than average. |
| Spec | 4.03b Matrix operations: addition, multiplication, scalar4.03d Linear transformations 2D: reflection, rotation, enlargement, shear4.03e Successive transformations: matrix products |
7.
$$\mathbf { P } = \left( \begin{array} { c c }
\frac { \sqrt { 3 } } { 2 } & - \frac { 1 } { 2 } \\
\frac { 1 } { 2 } & \frac { \sqrt { 3 } } { 2 }
\end{array} \right)$$
\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 $x$-axis.
\item Write down the matrix $\mathbf { Q }$.
Given that $V$ followed by $U$ is the transformation $T$, which is represented by the matrix $\mathbf { R }$,
\item find the matrix $\mathbf { R }$.
\item Show that there is a real number $k$ for which the transformation $T$ maps the point $( 1 , k )$ onto itself. Give the exact value of $k$ in its simplest form.
\end{enumerate}
\hfill \mbox{\textit{Edexcel F1 2014 Q7 [11]}}