| Exam Board | OCR |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2006 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Matrices |
| Type | Matrix arithmetic operations |
| Difficulty | Easy -1.3 This is a straightforward matrix arithmetic question requiring only basic operations (scalar multiplication, addition, subtraction) with 2×2 matrices. Part (i) is pure computation, and part (ii) involves simple verification that the result is a scalar multiple of the identity matrix. No problem-solving or conceptual depth required—purely mechanical application of definitions. |
| Spec | 4.03b Matrix operations: addition, multiplication, scalar |
| Answer | Marks | Guidance |
|---|---|---|
| Part (i) Matrix: \(\begin{pmatrix} 7 & 4 \\ 0 & -1 \end{pmatrix}\) | B1 | Two elements correct |
| B1, 2 | All four elements correct | |
| Part (ii) Matrix: \(\begin{pmatrix} 3 & 0 \\ 0 & 3 \end{pmatrix}\) | B1 | \(A - B\) correctly found |
| Part (iii) \(k = 3\) | B1, 2 | Find \(k\) |
**Part (i)** Matrix: $\begin{pmatrix} 7 & 4 \\ 0 & -1 \end{pmatrix}$ | B1 | Two elements correct
| B1, 2 | All four elements correct
**Part (ii)** Matrix: $\begin{pmatrix} 3 & 0 \\ 0 & 3 \end{pmatrix}$ | B1 | $A - B$ correctly found
**Part (iii)** $k = 3$ | B1, 2 | Find $k$$\mathbf { 1 }$ The matrices $\mathbf { A }$ and $\mathbf { B }$ are given by $\mathbf { A } = \left( \begin{array} { l l } 4 & 1 \\ 0 & 2 \end{array} \right)$ and $\mathbf { B } = \left( \begin{array} { r r } 1 & 1 \\ 0 & - 1 \end{array} \right)$.\\
(i) Find $\mathbf { A } + 3 \mathbf { B }$.\\
(ii) Show that $\mathbf { A } - \mathbf { B } = k \mathbf { I }$, where $\mathbf { I }$ is the identity matrix and $k$ is a constant whose value should be stated.
\hfill \mbox{\textit{OCR FP1 2006 Q1 [4]}}