| Exam Board | OCR MEI |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2011 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Matrices |
| Type | Area transformation under matrices |
| Difficulty | Moderate -0.3 This is a straightforward Further Maths question testing standard matrix transformation properties. Part (i) requires knowing that area scales by |det M| (det = 12, so area = 36). Part (ii) is routine matrix inversion. Part (iii) asks for conceptual understanding that det(M) × det(M⁻¹) = 1, representing inverse transformations cancelling. While this is Further Maths content, the calculations are mechanical and the concepts are core syllabus material, making it slightly easier than an average A-level question overall. |
| Spec | 4.03h Determinant 2x2: calculation4.03i Determinant: area scale factor and orientation4.03n Inverse 2x2 matrix |
2 You are given that $\mathbf { M } = \left( \begin{array} { r r } 4 & 0 \\ - 1 & 3 \end{array} \right)$.\\
(i) The transformation associated with $\mathbf { M }$ is applied to a figure of area 3 square units. Find the area of the transformed figure.\\
(ii) Find $\mathbf { M } ^ { - 1 }$ and $\operatorname { det } \mathbf { M } ^ { - 1 }$.\\
(iii) Explain the significance of $\operatorname { det } \mathbf { M } \times \operatorname { det } \mathbf { M } ^ { - 1 }$ in terms of transformations.
\hfill \mbox{\textit{OCR MEI FP1 2011 Q2 [7]}}