| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2017 |
| Session | January |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | Linear transformations |
| Type | Extract enlargement and rotation parameters |
| Difficulty | Standard +0.3 This is a straightforward Further Maths question testing standard matrix transformations. Part (i) requires recognizing a reflection and writing down a stretch matrix (basic recall). Part (ii) involves finding the scale factor from det(M) or matrix magnitude, extracting the rotation angle from matrix entries using arctan, and computing a 2×2 matrix inverse using the standard formula. All techniques are routine for F1 students with no novel problem-solving required, making it slightly easier than average. |
| Spec | 4.03d Linear transformations 2D: reflection, rotation, enlargement, shear4.03o Inverse 3x3 matrix |
7. (i)
$$\mathbf { A } = \left( \begin{array} { r r }
- 1 & 0 \\
0 & 1
\end{array} \right)$$
\begin{enumerate}[label=(\alph*)]
\item Describe fully the single transformation represented by the matrix $\mathbf { A }$.
The matrix $\mathbf { B }$ represents a stretch, scale factor 3 , parallel to the $x$-axis.
\item Find the matrix $\mathbf { B }$.\\
(ii)
$$\mathbf { M } = \left( \begin{array} { r r }
- 4 & 3 \\
- 3 & - 4
\end{array} \right)$$
The matrix $\mathbf { M }$ represents an enlargement with scale factor $k$ and centre ( 0,0 ), where $k > 0$, followed by a rotation anticlockwise through an angle $\theta$ about ( 0,0 ).\\
(a) Find the value of $k$.\\
(b) Find the value of $\theta$, giving your answer in radians to 2 decimal places.
\item Find $\mathbf { M } ^ { - 1 }$
\end{enumerate}
\hfill \mbox{\textit{Edexcel F1 2017 Q7 [10]}}