| Exam Board | OCR |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2011 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Matrices |
| Type | Matrix arithmetic operations |
| Difficulty | Easy -1.8 This is a straightforward matrix arithmetic question testing basic operations: scalar multiplication, matrix addition, and matrix multiplication with compatible dimensions. All three parts are direct applications of definitions with no problem-solving required, making it significantly easier than average A-level questions. |
| Spec | 4.03b Matrix operations: addition, multiplication, scalar |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \((7 \quad 9)\) | B1B1 2 | Each element correct; SC (7,9) scores B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \((18)\) | B1* depB1 2 | Obtain correct value; Clearly given as a matrix |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\begin{pmatrix} 12 & -4 \\ 6 & -2 \end{pmatrix}\) | M1 | Obtain \(2 \times 2\) matrix |
| A1 | Obtain 2 correct elements | |
| A1 3 | Obtain other 2 correct elements |
## Question 1:
**Part (i)**
| Answer | Marks | Guidance |
|--------|-------|----------|
| $(7 \quad 9)$ | B1B1 **2** | Each element correct; SC (7,9) scores B1 |
**Part (ii)**
| Answer | Marks | Guidance |
|--------|-------|----------|
| $(18)$ | B1* depB1 **2** | Obtain correct value; Clearly given as a matrix |
**Part (iii)**
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\begin{pmatrix} 12 & -4 \\ 6 & -2 \end{pmatrix}$ | M1 | Obtain $2 \times 2$ matrix |
| | A1 | Obtain 2 correct elements |
| | A1 **3** | Obtain other 2 correct elements |
---$\mathbf { 1 }$ The matrices $\mathbf { A } , \mathbf { B }$ and $\mathbf { C }$ are given by $\mathbf { A } = \left( \begin{array} { l l } 2 & 5 \end{array} \right) , \mathbf { B } = \left( \begin{array} { l l } 3 & - 1 \end{array} \right)$ and $\mathbf { C } = \binom { 4 } { 2 }$. Find\\
(i) $2 \mathbf { A } + \mathbf { B }$,\\
(ii) $\mathbf { A C }$,\\
(iii) CB.
\hfill \mbox{\textit{OCR FP1 2011 Q1 [7]}}