June 2024 Paper 1 Q15
15
(a)
Matrix M represents a reflection in the line \(\quad y = -x\)
Write down matrix M [1 mark]
(b)
\(\mathbf{N} = \begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix}\)
Describe geometrically the single transformation represented by \(\mathbf{N}^2\) [2 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(\begin{pmatrix} 0 & -1 \\ -1 & 0 \end{pmatrix}\) | B1 |
| Answer | Mark | Comments |
|---|---|---|
| \((\mathbf{N}^2 =)\ \begin{pmatrix} -1 & 0 \\ 0 & -1 \end{pmatrix}\) or describes N as a rotation \(90^\circ\) clockwise about the origin (or (0, 0)) | M1 | can be implied from A1 condone rotation of \(-90^\circ\) or \(270^\circ\) about the origin (or (0, 0)) |
| Rotation \(180^\circ\) about the origin (or (0, 0)) or Enlargement sf. \(-1\) about the origin (or (0, 0)) | A1 | clockwise or anticlockwise can be stated |
Additional guidance
| (N \(=\)) Rotation \(90^\circ\) (without clockwise) about the origin recovered with a correct answer | M1A1 |
| (N \(=\)) Rotation \(90^\circ\) anticlockwise about the origin with correct answer would be from incorrect working | M0A0 |
| (N \(=\)) Rotation \(90^\circ\) (without clockwise) about the origin without the correct answer | M0A0 |
| Missing ‘about the origin’ in M mark can be recovered in A mark | |
| Condone missing brackets in matrices |