| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2014 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Matrices |
| Type | Area transformation under matrices |
| Difficulty | Standard +0.3 This is a straightforward Further Maths question testing standard knowledge that area scales by |det(A)|. Part (a) is trivial calculation of a 2×2 determinant, part (b) applies the area scaling formula directly, and part (c) uses det(A^n) = (det A)^n. All parts are routine applications of well-known results with no problem-solving required. |
| Spec | 4.03h Determinant 2x2: calculation4.03i Determinant: area scale factor and orientation |
3.
$$\mathbf { A } = \left( \begin{array} { l l }
6 & 4 \\
1 & 1
\end{array} \right)$$
\begin{enumerate}[label=(\alph*)]
\item Show that $\mathbf { A }$ is non-singular.
The triangle $R$ is transformed to the triangle $S$ by the matrix $\mathbf { A }$.\\
Given that the area of triangle $R$ is 10 square units,
\item find the area of triangle $S$.
Given that
$$\mathbf { B } = \mathbf { A } ^ { 4 }$$
and that the triangle $R$ is transformed to the triangle $T$ by the matrix $\mathbf { B }$,
\item find, without evaluating $\mathbf { B }$, the area of triangle $T$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel F1 2014 Q3 [6]}}