| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2024 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Linear transformations |
| Type | Combined transformation matrix product |
| Difficulty | Moderate -0.3 This is a straightforward multi-part question testing standard Further Maths matrix transformation knowledge: identifying a stretch, writing a rotation matrix (with exact trig values for a standard angle), computing a matrix product, and applying the determinant-area relationship. All parts are routine recall and calculation with no problem-solving insight required, making it slightly easier than average. |
| Spec | 4.03d Linear transformations 2D: reflection, rotation, enlargement, shear4.03e Successive transformations: matrix products4.03i Determinant: area scale factor and orientation |
4.
$$\mathbf { A } = \left( \begin{array} { l l }
1 & 0 \\
0 & 3
\end{array} \right)$$
\begin{enumerate}[label=(\alph*)]
\item Describe the single geometrical transformation represented by the matrix $\mathbf { A }$.
The matrix $\mathbf { B }$ represents a rotation of $210 ^ { \circ }$ anticlockwise about centre $( 0,0 )$.
\item Write down the matrix $\mathbf { B }$, giving each element in exact form.
The transformation represented by matrix $\mathbf { A }$ followed by the transformation represented by matrix $\mathbf { B }$ is represented by the matrix $\mathbf { C }$.
\item Find $\mathbf { C }$.
The hexagon $H$ is transformed onto the hexagon $H ^ { \prime }$ by the matrix $\mathbf { C }$.
\item Given that the area of hexagon $H$ is 5 square units, determine the area of hexagon $H ^ { \prime }$
\end{enumerate}
\hfill \mbox{\textit{Edexcel F1 2024 Q4 [7]}}