| Exam Board | OCR |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2007 |
| Session | January |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Matrices |
| Type | Matrix arithmetic operations |
| Difficulty | Moderate -0.8 This is a straightforward matrix arithmetic question testing basic operations (scalar multiplication, addition, and multiplication). Part (i) requires simple arithmetic to find one unknown, while part (ii) involves matrix multiplication followed by solving a linear equation. Both parts are routine calculations with no conceptual challenges beyond knowing the definitions of matrix operations. |
| Spec | 4.03b Matrix operations: addition, multiplication, scalar |
| Answer | Marks | Guidance |
|---|---|---|
| (i) \(a = -3\) | B1 | State correct value |
| (ii) \(2a - 3 = 7\) or \(3a - 6 = 9\) giving \(a = 5\) | M1 | Sensible attempt at multiplication |
| A1 | Obtain correct answer |
(i) $a = -3$ | B1 | State correct value
(ii) $2a - 3 = 7$ or $3a - 6 = 9$ giving $a = 5$ | M1 | Sensible attempt at multiplication
| A1 | Obtain correct answer$\mathbf { 1 }$ The matrices $\mathbf { A }$ and $\mathbf { B }$ are given by $\mathbf { A } = \left( \begin{array} { l l } 2 & 1 \\ 3 & 2 \end{array} \right)$ and $\mathbf { B } = \left( \begin{array} { c c } a & - 1 \\ - 3 & - 2 \end{array} \right)$.\\
(i) Given that $2 \mathbf { A } + \mathbf { B } = \left( \begin{array} { l l } 1 & 1 \\ 3 & 2 \end{array} \right)$, write down the value of $a$.\\
(ii) Given instead that $\mathbf { A B } = \left( \begin{array} { l l } 7 & - 4 \\ 9 & - 7 \end{array} \right)$, find the value of $a$.
\hfill \mbox{\textit{OCR FP1 2007 Q1 [3]}}