| Exam Board | OCR |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2012 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear transformations |
| Type | Write down transformation matrix |
| Difficulty | Moderate -0.8 This is a straightforward Further Maths question testing basic knowledge of transformation matrices. Part (a) requires recall of a standard reflection matrix, part (b)(i) asks students to identify a simple stretch from a diagonal matrix, and part (b)(ii) connects the determinant to area scale factor—all routine applications with no problem-solving or novel insight required. |
| Spec | 4.03d Linear transformations 2D: reflection, rotation, enlargement, shear4.03h Determinant 2x2: calculation |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\begin{pmatrix}0&-1\\-1&0\end{pmatrix}\) | B1, B1 | Each column correct |
| [2] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Stretch, scale factor 4 in the \(y\) direction | B1, DB1 | Not "in the \(y\)-axis" |
| [2] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(4\) | B1, B1 | Correct value of determinant; Scale factor for area (allow scale factor of stretch or equiv.) |
| [2] |
## Question 5(a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\begin{pmatrix}0&-1\\-1&0\end{pmatrix}$ | B1, B1 | Each column correct |
| **[2]** | | |
---
## Question 5(b)(i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Stretch, scale factor 4 in the $y$ direction | B1, DB1 | Not "in the $y$-axis" |
| **[2]** | | |
---
## Question 5(b)(ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $4$ | B1, B1 | Correct value of determinant; Scale factor for area (allow scale factor of stretch or equiv.) |
| **[2]** | | |
---5
\begin{enumerate}[label=(\alph*)]
\item Find the matrix that represents a reflection in the line $y = - x$.
\item The matrix $\mathbf { C }$ is given by $\mathbf { C } = \left( \begin{array} { l l } 1 & 0 \\ 0 & 4 \end{array} \right)$.
\begin{enumerate}[label=(\roman*)]
\item Describe fully the geometrical transformation represented by $\mathbf { C }$.
\item State the value of the determinant of $\mathbf { C }$ and describe briefly how this value relates to the transformation represented by $\mathbf { C }$.
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{OCR FP1 2012 Q5 [6]}}