| Exam Board | OCR MEI |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2010 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Matrices |
| Type | Matrix multiplication |
| Difficulty | Moderate -0.8 This is a straightforward Further Maths question testing basic matrix operations: checking dimensions for compatibility, performing simple matrix multiplications and addition, and composing transformations. While it's FP1 content, it requires only mechanical application of standard procedures with no problem-solving or conceptual insight, making it easier than average even on an absolute scale. |
| Spec | 4.03a Matrix language: terminology and notation4.03b Matrix operations: addition, multiplication, scalar |
2 You are given that $\mathbf { A } = \left( \begin{array} { r } 4 \\ - 2 \\ 4 \end{array} \right) , \mathbf { B } = \left( \begin{array} { r r } 5 & 1 \\ 2 & - 3 \end{array} \right) , \mathbf { C } = \left( \begin{array} { l l l } 5 & 1 & 8 \end{array} \right)$ and $\mathbf { D } = \left( \begin{array} { r r } - 2 & 0 \\ 4 & 1 \end{array} \right)$.\\
(i) Calculate, where they exist, $\mathbf { A B } , \mathbf { C A } , \mathbf { B } + \mathbf { D }$ and $\mathbf { A C }$ and indicate any that do not exist.\\
(ii) Matrices $\mathbf { B }$ and $\mathbf { D }$ represent transformations B and D respectively. Find the single matrix that represents transformation B followed by transformation D.
\hfill \mbox{\textit{OCR MEI FP1 2010 Q2 [7]}}