| Exam Board | OCR MEI |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2007 |
| Session | June |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Matrices |
| Type | Matrix inverse calculation |
| Difficulty | Moderate -0.8 This is a straightforward FP1 matrix question requiring routine application of the 2×2 inverse formula and determinant-area relationship. Part (i) is direct recall with simple arithmetic, and part (ii) requires only calculating det(M) = 10 and multiplying by 2. No problem-solving or insight needed, making it easier than average even for Further Maths. |
| Spec | 4.03i Determinant: area scale factor and orientation4.03o Inverse 3x3 matrix |
You are given the matrix $\mathbf{M} = \begin{pmatrix} 2 & -1 \\ 4 & 3 \end{pmatrix}$.
\begin{enumerate}[label=(\roman*)]
\item Find the inverse of $\mathbf{M}$. [2]
\item A triangle of area 2 square units undergoes the transformation represented by the matrix $\mathbf{M}$. Find the area of the image of the triangle following this transformation. [1]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI FP1 2007 Q1 [3]}}