| Exam Board | Edexcel |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Session | Specimen |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear transformations |
| Type | Find image coordinates under transformation |
| Difficulty | Moderate -0.5 This is a straightforward application of matrix transformations requiring multiplication of a 2×2 matrix by coordinate vectors, calculation of a determinant, and using the area scaling property (area scales by |det A|). All steps are routine FP1 techniques with no novel insight required, making it slightly easier than average. |
| Spec | 4.03d Linear transformations 2D: reflection, rotation, enlargement, shear4.03h Determinant 2x2: calculation |
2. The rectangle $R$ has vertices at the points $( 0,0 ) , ( 1,0 ) , ( 1,2 )$ and $( 0,2 )$.
\begin{enumerate}[label=(\alph*)]
\item Find the coordinates of the vertices of the image of $R$ under the transformation given by the matrix $\mathbf { A } = \left( \begin{array} { c c } a & 4 \\ - 1 & 1 \end{array} \right)$, where $a$ is a constant.
\item Find det $\mathbf { A }$, giving your answer in terms of $a$.
Given that the area of the image of $R$ is 18 ,
\item find the value of $a$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP1 Q2 [7]}}