| Exam Board | OCR MEI |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2008 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear transformations |
| Type | Area scale factor from determinant |
| Difficulty | Moderate -0.8 This is a straightforward Further Maths question requiring basic matrix multiplication and direct application of the determinant-area relationship. Part (i) is routine computation, and part (ii) simply requires finding |BA| and multiplying by 3, with no conceptual challenges beyond recall of the standard result. |
| Spec | 4.03b Matrix operations: addition, multiplication, scalar4.03i Determinant: area scale factor and orientation |
1 You are given that matrix $\mathbf { A } = \left( \begin{array} { r r } 2 & - 1 \\ 0 & 3 \end{array} \right)$ and matrix $\mathbf { B } = \left( \begin{array} { r r } 3 & 1 \\ - 2 & 4 \end{array} \right)$.\\
(i) Find BA.\\
(ii) A plane shape of area 3 square units is transformed using matrix $\mathbf { A }$. The image is transformed using matrix B. What is the area of the resulting shape?
\hfill \mbox{\textit{OCR MEI FP1 2008 Q1 [5]}}