| Exam Board | OCR MEI |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2013 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear transformations |
| Type | Describe enlargement or stretch from matrix |
| Difficulty | Moderate -0.8 This is a straightforward Further Maths question requiring recognition of standard transformations (reflection in y=x and a stretch) and basic matrix multiplication. While it's Further Maths content, these are elementary operations with no problem-solving required—pure recall and routine calculation. |
| Spec | 4.03d Linear transformations 2D: reflection, rotation, enlargement, shear |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| A is a reflection in the line \(y = x\) | B1 | |
| B is a two way stretch, (scale) factor 2 in the \(x\)-direction and (scale) factor 3 in the \(y\)-direction | B1, B1 | Stretch, with attempt at details. Details correct. |
| [3] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\mathbf{BA} = \begin{pmatrix} 2 & 0 \\ 0 & 3 \end{pmatrix}\begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix} = \begin{pmatrix} 0 & 2 \\ 3 & 0 \end{pmatrix}\) | M1, A1 | Attempt to multiply in correct order |
| [2] |
## Question 1:
### Part (i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| A is a reflection in the line $y = x$ | B1 | |
| B is a two way stretch, (scale) factor 2 in the $x$-direction and (scale) factor 3 in the $y$-direction | B1, B1 | Stretch, with attempt at details. Details correct. |
| | **[3]** | |
### Part (ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\mathbf{BA} = \begin{pmatrix} 2 & 0 \\ 0 & 3 \end{pmatrix}\begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix} = \begin{pmatrix} 0 & 2 \\ 3 & 0 \end{pmatrix}$ | M1, A1 | Attempt to multiply in correct order |
| | **[2]** | |
---1 Transformation A is represented by matrix $\mathbf { A } = \left( \begin{array} { l l } 0 & 1 \\ 1 & 0 \end{array} \right)$ and transformation B is represented by matrix $\mathbf { B } = \left( \begin{array} { l l } 2 & 0 \\ 0 & 3 \end{array} \right)$.\\
(i) Describe transformations A and B .\\
(ii) Find the matrix for the composite transformation A followed by B .
\hfill \mbox{\textit{OCR MEI FP1 2013 Q1 [5]}}