| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2021 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | Linear transformations |
| Type | Find image coordinates under transformation |
| Difficulty | Moderate -0.8 This is a straightforward Further Maths question testing basic matrix transformations with routine calculations. Part (a) requires simple matrix-vector multiplication, parts (b-c) test standard transformation recall, part (d) is matrix multiplication, and part (e) requires recognizing the combined transformation. All steps are mechanical with no problem-solving or novel insight required, making it easier than average even for Further Maths. |
| Spec | 4.03d Linear transformations 2D: reflection, rotation, enlargement, shear4.03e Successive transformations: matrix products |
\begin{enumerate}
\item The triangle $T$ has vertices $A ( 2,1 ) , B ( 2,3 )$ and $C ( 0,1 )$.
\end{enumerate}
The triangle $T ^ { \prime }$ is the image of $T$ under the transformation represented by the matrix
$$\mathbf { P } = \left( \begin{array} { r r }
0 & 1 \\
- 1 & 0
\end{array} \right)$$
(a) Find the coordinates of the vertices of $T ^ { \prime }$\\
(b) Describe fully the transformation represented by $\mathbf { P }$
The $2 \times 2$ matrix $\mathbf { Q }$ represents a reflection in the $x$-axis and the $2 \times 2$ matrix $\mathbf { R }$ represents a rotation through $90 ^ { \circ }$ anticlockwise about the origin.\\
(c) Write down the matrix $\mathbf { Q }$ and the matrix $\mathbf { R }$\\
(d) Find the matrix $\mathbf { R Q }$\\
(e) Give a full geometrical description of the single transformation represented by the answer to part (d).\\
\hfill \mbox{\textit{Edexcel F1 2021 Q3 [10]}}