| Exam Board | OCR |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2012 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Matrices |
| Type | Matrix multiplication |
| Difficulty | Moderate -0.5 This is a straightforward Further Maths question requiring routine matrix multiplication and finding inverses of 2×2 matrices using the standard formula. While matrices are an FP1 topic (making it harder than basic C1-C3), the question involves only direct application of learned procedures with no problem-solving or insight required, placing it slightly below average difficulty overall. |
| Spec | 4.03b Matrix operations: addition, multiplication, scalar4.03p Inverse properties: (AB)^(-1) = B^(-1)*A^(-1) |
| Answer | Marks | Guidance |
|---|---|---|
| \(\begin{pmatrix} 5 & 2 \\ 13 & 6 \end{pmatrix}\) | M1 | Multiplication attempt, 2 elements correct |
| A1 | All elements correct |
| Answer | Marks | Guidance |
|---|---|---|
| \(\mathbf{B}^{-1}\mathbf{A}^{-1} = (\mathbf{AB})^{-1}\) | B1 | Stated or used |
| B1ft | Divide by correct determinant | |
| \(\frac{1}{4}\begin{pmatrix} 6 & -2 \\ -13 & 5 \end{pmatrix}\) | B1ft | Both diagonals correct |
| Answer | Marks |
|---|---|
| B1 | Either inverse correct |
| B1 | Two elements correct in final answer, both inverses must be correct |
| B1 | All elements correct |
## Question 2:
### Part (i)
$\begin{pmatrix} 5 & 2 \\ 13 & 6 \end{pmatrix}$ | M1 | Multiplication attempt, 2 elements correct
| A1 | All elements correct
**[2]**
### Part (ii)
**EITHER**
$\mathbf{B}^{-1}\mathbf{A}^{-1} = (\mathbf{AB})^{-1}$ | B1 | Stated or used
| B1ft | Divide by correct determinant
$\frac{1}{4}\begin{pmatrix} 6 & -2 \\ -13 & 5 \end{pmatrix}$ | B1ft | Both diagonals correct
**[3]**
**OR**
| B1 | Either inverse correct
| B1 | Two elements correct in final answer, both inverses must be correct
| B1 | All elements correct
---2 The matrices $\mathbf { A }$ and $\mathbf { B }$ are given by $\mathbf { A } = \left( \begin{array} { l l } 2 & 1 \\ 4 & 3 \end{array} \right)$ and $\mathbf { B } = \left( \begin{array} { l l } 1 & 0 \\ 3 & 2 \end{array} \right)$. Find\\
(i) $\mathbf { A B }$,\\
(ii) $\mathbf { B } ^ { - 1 } \mathbf { A } ^ { - 1 }$.
\hfill \mbox{\textit{OCR FP1 2012 Q2 [5]}}