| Exam Board | OCR |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2013 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear transformations |
| Type | Combined transformation matrix product |
| Difficulty | Moderate -0.8 This is a straightforward Further Maths question testing standard 2D transformation matrices with routine recall (parts i-ii), simple matrix multiplication (part iii), and recognition of a combined transformation (part iv). While it's Further Maths content, it requires no problem-solving or novel insight—just application of memorized matrices and basic matrix operations, making it easier than average overall. |
| Spec | 4.03d Linear transformations 2D: reflection, rotation, enlargement, shear4.03e Successive transformations: matrix products |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix}\) | B1B1 | Each column correct |
| [2] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}\) | B1B1 | Each column correct |
| [2] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}\) | M1 | Attempt at matrix multiplication in correct order |
| A1FT | Obtain correct answer from their (i) and (ii) | |
| [2] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Reflection, in \(y = x\) | B1B1 | Correct description of their (iii) only |
| [2] |
## Question 7(i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix}$ | B1B1 | Each column correct |
| **[2]** | | |
---
## Question 7(ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}$ | B1B1 | Each column correct |
| **[2]** | | |
---
## Question 7(iii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}$ | M1 | Attempt at matrix multiplication in correct order |
| | A1FT | Obtain correct answer from their (i) and (ii) |
| **[2]** | | |
---
## Question 7(iv):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Reflection, in $y = x$ | B1B1 | Correct description of their **(iii) only** |
| **[2]** | | |
---7 (i) Find the matrix that represents a rotation through $90 ^ { \circ }$ clockwise about the origin.\\
(ii) Find the matrix that represents a reflection in the $x$-axis.\\
(iii) Hence find the matrix that represents a rotation through $90 ^ { \circ }$ clockwise about the origin, followed by a reflection in the $x$-axis.\\
(iv) Describe a single transformation that is represented by your answer to part (iii).
\hfill \mbox{\textit{OCR FP1 2013 Q7 [8]}}