| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2022 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Linear transformations |
| Type | Describe rotation from matrix |
| Difficulty | Standard +0.3 This is a straightforward Further Maths question testing standard matrix transformations. Parts (a)-(c) involve recognizing a rotation matrix, recalling a reflection matrix, and performing matrix multiplication—all routine procedures. Part (d) requires finding the inverse of 3R, which is a standard technique (inverse of scalar multiple). While it's Further Maths content, it requires no problem-solving insight, just methodical application of learned procedures, making it slightly easier than average overall. |
| Spec | 4.03b Matrix operations: addition, multiplication, scalar4.03d Linear transformations 2D: reflection, rotation, enlargement, shear4.03n Inverse 2x2 matrix |
$$\mathbf{P} = \begin{pmatrix} \frac{1}{2} & -\frac{\sqrt{3}}{2} \\ \frac{\sqrt{3}}{2} & \frac{1}{2} \end{pmatrix}$$
The matrix $\mathbf{P}$ represents the transformation $U$
\begin{enumerate}[label=(\alph*)]
\item Give a full description of $U$ as a single geometrical transformation.
[2]
\end{enumerate}
The transformation $V$, represented by the $2 \times 2$ matrix $\mathbf{Q}$, is a reflection in the line $y = -x$
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Write down the matrix $\mathbf{Q}$
[1]
\end{enumerate}
The transformation $U$ followed by the transformation $V$ is represented by the matrix $\mathbf{R}$
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Determine the matrix $\mathbf{R}$
[2]
\end{enumerate}
The transformation $W$ is represented by the matrix $3\mathbf{R}$
The transformation $W$ maps a triangle $T$ to a triangle $T'$
The transformation $W'$ maps the triangle $T'$ back to the original triangle $T$
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{3}
\item Determine the matrix that represents $W'$
[3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel F1 2022 Q5 [8]}}