OCR MEI FP1 2007 June — Question 1 3 marks

Exam BoardOCR MEI
ModuleFP1 (Further Pure Mathematics 1)
Year2007
SessionJune
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicMatrices
TypeMatrix inverse calculation
DifficultyModerate -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.
Spec4.03i Determinant: area scale factor and orientation4.03o Inverse 3x3 matrix

You are given the matrix \(\mathbf{M} = \begin{pmatrix} 2 & -1 \\ 4 & 3 \end{pmatrix}\).
  1. Find the inverse of \(\mathbf{M}\). [2]
  2. 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]

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]}}