| Exam Board | OCR MEI |
|---|---|
| Module | Further Pure Core AS (Further Pure Core AS) |
| Year | 2023 |
| Session | June |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear transformations |
| Type | Matrix powers and repeated transformations |
| Difficulty | Easy -1.2 This is a straightforward Further Maths question requiring recall of a standard reflection matrix, simple matrix multiplication, and interpretation of the identity matrix. While it's Further Maths content, the question involves minimal problem-solving—just direct application of known results about reflections and the geometric meaning of M² = I. |
| Spec | 4.03a Matrix language: terminology and notation4.03d Linear transformations 2D: reflection, rotation, enlargement, shear |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | (a) | − 1 0 |
| Answer | Marks | Guidance |
|---|---|---|
| 0 1 | B1 | |
| [1] | 1.1 | must be 2 by 2 |
| 1 | (b) | 1 0 |
| Answer | Marks | Guidance |
|---|---|---|
| 0 1 | B1 | |
| [1] | 1.1 | 1 0 |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | (c) | [M2 is the identity matrix] |
| Answer | Marks | Guidance |
|---|---|---|
| the identity transformation. | B1 | |
| [1] | 2.4 | M2 must be an identity matrix (condone 33) |
Question 1:
1 | (a) | − 1 0
M =
0 1 | B1
[1] | 1.1 | must be 2 by 2
1 | (b) | 1 0
M 2 =
0 1 | B1
[1] | 1.1 | 1 0
Condone from M =
0 −1
1 | (c) | [M2 is the identity matrix]
It represents the combination of two reflections, which is
the identity transformation. | B1
[1] | 2.4 | M2 must be an identity matrix (condone 33)
oe, e.g. R is self-inverse1 The transformation R of the plane is reflection in the line $x = 0$.
\begin{enumerate}[label=(\alph*)]
\item Write down the matrix $\mathbf { M }$ associated with R .
\item Find $\mathbf { M } ^ { 2 }$.
\item Interpret the result of part (b) in terms of the transformation $R$.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Pure Core AS 2023 Q1 [3]}}