June 2017 Paper 1 Q12
12 The transformation matrix \(\mathbf{M}\) represents a \(90^\circ\) clockwise rotation about the origin.
(a) Write down the matrix \(\mathbf{M}\). [1 mark]
(b) Describe fully the single transformation represented by \(\mathbf{M}^2\). [2 marks]
(c) Write down the matrix for the single transformation represented by \(\mathbf{M}^2\). [1 mark]
| Answer | Mark | Comments |
|---|---|---|
| \(\begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix}\) | B1 |
| Answer | Mark | Comments |
|---|---|---|
| Rotation of \(180^\circ\) about the origin Enlargement SF \(-1\) centre the origin | B2 | B1 if either the \(180^\circ\) or the origin is missing B1 if either the SF or the centre is missing |
Additional guidance
Ignore any reference to direction Accept 'Rotation of half a turn' for B1
Answers of Rotation or Enlargement with no other description attached score B0
Rotation \(90^\circ\) is B0 (incorrect angle, no centre of rotation)
Enlargement SF2 is B0 (incorrect SF and no centre of enlargement)
| Answer | Mark | Comments |
|---|---|---|
| \(\begin{pmatrix} -1 & 0 \\ 0 & -1 \end{pmatrix}\) | B1 |
Additional guidance
If no working or answer seen in (c), look at (b) ... the matrix for \(\mathbf{M}^2\) might be written there, and, if correct, will score B1 in (c)