| Exam Board | OCR |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2016 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Matrices |
| Type | Matrix arithmetic operations |
| Difficulty | Easy -1.2 This is a straightforward matrix arithmetic question testing basic operations (scalar multiplication, subtraction, and matrix multiplication) with simple numbers. All three parts are routine calculations requiring only recall of definitions with no problem-solving or conceptual insight needed. Even for Further Maths FP1, this represents below-average difficulty. |
| Spec | 4.03a Matrix language: terminology and notation4.03b Matrix operations: addition, multiplication, scalar |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \((5a-3b \quad 10 \quad 0)\) | B1 | 2 elements correct, must be a \(1\times3\) matrix (not coordinates) |
| B1 | 3rd element correct | |
| [2] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \((6b-5)\) | M1 | Single value |
| A1 | Correct answer, must be a matrix | |
| [2] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\begin{pmatrix}6a & 12 & 18\\ 4a & 8 & 12\\ -a & -2 & -3\end{pmatrix}\) | M1 | Obtain a \(3\times3\) matrix |
| A1 | All elements correct | |
| [2] |
## Question 4:
### Part (i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $(5a-3b \quad 10 \quad 0)$ | B1 | 2 elements correct, must be a $1\times3$ matrix (not coordinates) |
| | B1 | 3rd element correct |
| **[2]** | | |
### Part (ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $(6b-5)$ | M1 | Single value |
| | A1 | Correct answer, must be a matrix |
| **[2]** | | |
### Part (iii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\begin{pmatrix}6a & 12 & 18\\ 4a & 8 & 12\\ -a & -2 & -3\end{pmatrix}$ | M1 | Obtain a $3\times3$ matrix |
| | A1 | All elements correct |
| **[2]** | | |
---4 The matrices $\mathbf { A } , \mathbf { B }$ and $\mathbf { C }$ are given by $\mathbf { A } = \left( \begin{array} { l l l } a & 2 & 3 \end{array} \right) , \mathbf { B } = \left( \begin{array} { l l l } b & 0 & 5 \end{array} \right)$ and $\mathbf { C } = \left( \begin{array} { r } 6 \\ 4 \\ - 1 \end{array} \right)$. Find\\
(i) $5 \mathbf { A } - 3 \mathbf { B }$,\\
(ii) BC,\\
(iii) CA .
\hfill \mbox{\textit{OCR FP1 2016 Q4 [6]}}