| Exam Board | OCR |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2011 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Matrices |
| Type | Matrix arithmetic operations |
| Difficulty | Easy -1.2 This is a straightforward matrix arithmetic question requiring only direct application of basic operations (addition, scalar multiplication, matrix multiplication). No problem-solving or conceptual insight needed—purely mechanical calculation with 2×2 matrices, making it easier than average even for Further Maths. |
| Spec | 4.03b Matrix operations: addition, multiplication, scalar |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\begin{pmatrix} 4 & 4a \\ 12 & 0 \end{pmatrix}\) | B1 | \(3\mathbf{B}\) seen or implied |
| B1 | 2 elements correct | |
| B1 [3] | Other 2 elements correct, a.e.f., including brackets |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\begin{pmatrix} 4+4a & 3a \\ 4 & 1 \end{pmatrix}\) | M1 | Sensible attempt at matrix multiplication for \(\mathbf{AB}\) or \(\mathbf{BA}\) |
| A1 [2] | Obtain correct answer |
## Question 1:
### Part (i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\begin{pmatrix} 4 & 4a \\ 12 & 0 \end{pmatrix}$ | B1 | $3\mathbf{B}$ seen or implied |
| | B1 | 2 elements correct |
| | B1 **[3]** | Other 2 elements correct, a.e.f., including brackets |
### Part (ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\begin{pmatrix} 4+4a & 3a \\ 4 & 1 \end{pmatrix}$ | M1 | Sensible attempt at matrix multiplication for $\mathbf{AB}$ or $\mathbf{BA}$ |
| | A1 **[2]** | Obtain correct answer |
---1 The matrices $\mathbf { A }$ and $\mathbf { B }$ are given by $\mathbf { A } = \left( \begin{array} { l l } 2 & a \\ 0 & 1 \end{array} \right)$ and $\mathbf { B } = \left( \begin{array} { l l } 2 & a \\ 4 & 1 \end{array} \right)$. I denotes the $2 \times 2$ identity matrix. Find\\
(i) $\mathbf { A } + 3 \mathbf { B } - 4 \mathbf { I }$,\\
(ii) AB.
\hfill \mbox{\textit{OCR FP1 2011 Q1 [5]}}