| Exam Board | OCR |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2010 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Matrices |
| Type | Matrix multiplication |
| Difficulty | Moderate -0.8 This is a straightforward matrix multiplication and arithmetic question testing basic definitions. Part (i) is a simple 1×2 times 2×1 multiplication giving a scalar. Part (ii) requires computing a 2×1 times 1×2 product (giving a 2×2 matrix) and subtracting a scalar multiple of another 2×2 matrix. While this is FP1, it's purely mechanical computation with no problem-solving or conceptual challenge—easier than the average A-level question. |
| Spec | 4.03b Matrix operations: addition, multiplication, scalar |
The matrices $\mathbf{A}$, $\mathbf{B}$ and $\mathbf{C}$ are given by $\mathbf{A} = \begin{pmatrix} 1 & -4 \end{pmatrix}$, $\mathbf{B} = \begin{pmatrix} 5 \\ 3 \end{pmatrix}$ and $\mathbf{C} = \begin{pmatrix} 3 & 0 \\ -2 & 2 \end{pmatrix}$. Find
\begin{enumerate}[label=(\roman*)]
\item $\mathbf{AB}$, [2]
\item $\mathbf{BA} - 4\mathbf{C}$. [4]
\end{enumerate}
\hfill \mbox{\textit{OCR FP1 2010 Q2 [6]}}