| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2023 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Matrices |
| Type | Area transformation under matrices |
| Difficulty | Standard +0.3 Part (i) requires knowing that area scale factor equals |det(A)| and solving |−3k + 24| = 3, which is straightforward application of a standard result. Part (ii) involves finding C = B^(-1)(BC), requiring matrix inversion with a parameter—routine Further Maths technique but slightly more involved than typical C1-C4 questions. |
| Spec | 4.03i Determinant: area scale factor and orientation4.03l Singular/non-singular matrices4.03o Inverse 3x3 matrix |
\begin{enumerate}
\item (i) $\mathbf { A } = \left( \begin{array} { c c } - 3 & 8 \\ - 3 & k \end{array} \right) \quad$ where $k$ is a constant The transformation represented by $\mathbf { A }$ transforms triangle $T$ to triangle $T ^ { \prime }$ The area of triangle $T ^ { \prime }$ is three times the area of triangle $T$
\end{enumerate}
Determine the possible values of $k$\\
(ii) $\mathbf { B } = \left( \begin{array} { r r } a & - 4 \\ 2 & 3 \end{array} \right)$ and $\mathbf { B C } = \left( \begin{array} { l l l } 2 & 5 & 1 \\ 1 & 4 & 2 \end{array} \right)$ where $a$ is a constant Determine, in terms of $a$, the matrix $\mathbf { C }$
\hfill \mbox{\textit{Edexcel F1 2023 Q4 [8]}}