OCR FP1 2010 June — Question 2 6 marks

Exam BoardOCR
ModuleFP1 (Further Pure Mathematics 1)
Year2010
SessionJune
Marks6
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicMatrices
TypeMatrix multiplication
DifficultyModerate -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.
Spec4.03b 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
  1. \(\mathbf{AB}\), [2]
  2. \(\mathbf{BA} - 4\mathbf{C}\). [4]

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]}}