| Exam Board | Edexcel |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Session | Specimen |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear transformations |
| Type | Matrix powers and repeated transformations |
| Difficulty | Standard +0.3 This is a straightforward Further Maths question requiring matrix multiplication and recognition of standard rotation matrices. The values 1/√2 are a clear hint for 45° rotation, and R² doubles this. While it's Further Maths content, the techniques are routine and the pattern recognition is standard, making it slightly easier than average overall. |
| Spec | 4.03b Matrix operations: addition, multiplication, scalar4.03d Linear transformations 2D: reflection, rotation, enlargement, shear |
3. The matrix $\mathbf { R }$ is given by $\mathbf { R } = \left( \begin{array} { c c } \frac { 1 } { \sqrt { 2 } } & \frac { 1 } { \sqrt { 2 } } \\ - \frac { 1 } { \sqrt { 2 } } & \frac { 1 } { \sqrt { 2 } } \end{array} \right)$
\begin{enumerate}[label=(\alph*)]
\item Find $\mathbf { R } ^ { 2 }$.
\item Describe the geometrical transformation represented by $\mathbf { R } ^ { 2 }$.
\item Describe the geometrical transformation represented by $\mathbf { R }$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP1 Q3 [5]}}