| Exam Board | Edexcel |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear transformations |
| Type | Matrix powers and repeated transformations |
| Difficulty | Moderate -0.8 This is a straightforward FP1 matrix question requiring basic matrix multiplication and recognition of standard transformations. Part (a) is trivial calculation, part (b) is routine 2×2 multiplication, and part (c) requires identifying a reflection (likely in y=-x), which is standard knowledge. No problem-solving or novel insight needed. |
| Spec | 4.03b Matrix operations: addition, multiplication, scalar4.03d Linear transformations 2D: reflection, rotation, enlargement, shear |
1.
$$\mathbf { R } = \left( \begin{array} { l l }
0 & 1 \\
1 & 0
\end{array} \right) \text { and } \mathbf { S } = \left( \begin{array} { r r }
0 & - 1 \\
- 1 & 0
\end{array} \right)$$
\begin{enumerate}[label=(\alph*)]
\item Find $\mathbf { R } ^ { 2 }$.
\item Find $\mathbf { R S }$.
\item Describe the geometrical transformation represented by $\mathbf { R S }$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP1 Q1 [5]}}