| Exam Board | OCR |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2013 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Matrices |
| Type | Matrix arithmetic operations |
| Difficulty | Moderate -0.8 This is a straightforward matrix arithmetic question testing basic operations (scalar multiplication, subtraction, and multiplication) with simple numbers. Part (i) is routine calculation, and part (ii) requires recognizing that a 2×2 matrix formed from CB needs determinant checking—standard FP1 content but below average difficulty even for Further Maths due to minimal conceptual demand. |
| Spec | 4.03b Matrix operations: addition, multiplication, scalar4.03l Singular/non-singular matrices |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \((7 \quad 23)\) | B1B1 | Each element correct, missing brackets B1 only |
| [2] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\begin{pmatrix} 6 & -15 \\ 4 & -10 \end{pmatrix}\) | M1 | Obtain \(2 \times 2\) matrix |
| A1 | Obtain 2 correct elements | |
| A1 | Obtain other 2 correct elements | |
| \(\det \mathbf{CB} = 0\) | A1FT | Obtain their det CB, must be a \(2 \times 2\) matrix |
| singular | A1FT | Correct conclusion from their det CB |
| [5] |
## Question 2(i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $(7 \quad 23)$ | B1B1 | Each element correct, missing brackets B1 only |
| **[2]** | | |
---
## Question 2(ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\begin{pmatrix} 6 & -15 \\ 4 & -10 \end{pmatrix}$ | M1 | Obtain $2 \times 2$ matrix |
| | A1 | Obtain 2 correct elements |
| | A1 | Obtain other 2 correct elements |
| $\det \mathbf{CB} = 0$ | A1FT | Obtain their det **CB**, must be a $2 \times 2$ matrix |
| singular | A1FT | Correct conclusion from their det **CB** |
| **[5]** | | |
---2 The matrices $\mathbf { A } , \mathbf { B }$ and $\mathbf { C }$ are given by $\mathbf { A } = \left( \begin{array} { l l } 5 & 1 \end{array} \right) , \mathbf { B } = \left( \begin{array} { l l } 2 & - 5 \end{array} \right)$ and $\mathbf { C } = \binom { 3 } { 2 }$.\\
(i) Find $3 \mathbf { A } - 4 \mathbf { B }$.\\
(ii) Find CB. Determine whether $\mathbf { C B }$ is singular or non-singular, giving a reason for your answer.
\hfill \mbox{\textit{OCR FP1 2013 Q2 [7]}}