| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2018 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Linear transformations |
| Type | Write down transformation matrix |
| Difficulty | Moderate -0.8 This is a straightforward Further Maths question testing standard recall of rotation matrices and basic properties of transformations. Part (a) requires writing down a standard 45° rotation matrix (textbook knowledge), part (b) identifies a scaling transformation (immediate from the matrix form), and part (c) applies the determinant-area relationship with simple arithmetic. No problem-solving insight or multi-step reasoning required beyond direct application of learned formulas. |
| Spec | 4.03d Linear transformations 2D: reflection, rotation, enlargement, shear4.03e Successive transformations: matrix products4.03h Determinant 2x2: calculation4.03i Determinant: area scale factor and orientation |
\begin{enumerate}
\item The transformation represented by the $2 \times 2$ matrix $\mathbf { P }$ is an anticlockwise rotation about the origin through 45 degrees.\\
(a) Write down the matrix $\mathbf { P }$, giving the exact numerical value of each element.
\end{enumerate}
$$\mathbf { Q } = \left( \begin{array} { c c }
k \sqrt { 2 } & 0 \\
0 & k \sqrt { 2 }
\end{array} \right) \text {, where } k \text { is a constant and } k > 0$$
(b) Describe fully the single geometrical transformation represented by the matrix $\mathbf { Q }$.
The combined transformation represented by the matrix $\mathbf { P Q }$ transforms the rhombus $R _ { 1 }$ onto the rhombus $R _ { 2 }$.
The area of the rhombus $R _ { 1 }$ is 6 and the area of the rhombus $R _ { 2 }$ is 147\\
(c) Find the value of the constant $k$.\\
\hfill \mbox{\textit{Edexcel F1 2018 Q2 [7]}}