A2 June 2025 Paper 1 Q1
1
(a) A matrix \(\mathbf{M}\) is given by \(\mathbf{M} = \begin{pmatrix} 5 & 0 \\ 0 & 5 \end{pmatrix}\).
Describe the transformation represented by \(\mathbf{M}\). [2]
Describe the transformation represented by \(\mathbf{M}\). [2]
(b) Write down the \(2 \times 2\) matrix that represents a rotation of \(90^\circ\) anticlockwise about the origin. [1]
(c) Write down the \(3 \times 3\) matrix that represents a reflection in the \(x\)–\(z\) plane. [1]
| Scheme | Marks | AO |
|---|---|---|
| Enlargement, scale factor 5, centre at the origin | B2 | 1.2 1.1 |
| [2] |
Notes
B2: for all three correct components, B1 for any two
Accept “enlarge” and accept “stretch” but only if specified in both \(x\) and \(y\) directions
For ‘scale factor’ accept just ‘factor’ or ‘SF’ but not just ‘5’
For ‘origin’ accept \(O\) or \((0, 0)\) allow omission of ‘centre’ provided intention is clear (e.g. ‘about \(O\)’)
If more than two transformations given, then B0 (unless this is two stretches in both \(x\) and \(y\) directions)
| Scheme | Marks | AO |
|---|---|---|
| \(\begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix}\) | B1 | 1.1 |
| [1] |
Notes
B1: cao
| Scheme | Marks | AO |
|---|---|---|
| \(\begin{pmatrix} 1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 1 \end{pmatrix}\) | B1 | 1.1 |
| [1] |
Notes
B1: cao – only penalise the lack of a bracket around the entries once in parts (b) and (c)