Higher June 2017 Paper 1 Q4
4.
\[\mathbf{p} = \begin{pmatrix}6\\-1\end{pmatrix} \text{ and } \mathbf{q} = \begin{pmatrix}-4\\7\end{pmatrix}\](a) Work out the column vector \(\mathbf{p} + 3\mathbf{q}\). [2]
(b) When \(\mathbf{p} + m\mathbf{q} = \begin{pmatrix}10\\n\end{pmatrix}\), find the value of \(m\) and the value of \(n\). [3]
| Scheme | Marks | Comments |
|---|---|---|
| \(\begin{pmatrix}-6\\20\end{pmatrix}\) | B2 | B1 for each element or for \((3\mathbf{q} =) \begin{pmatrix}-12\\21\end{pmatrix}\) or equivalent seen or for \(\left(\dfrac{-6}{20}\right)\) or for \(\begin{matrix}-6\\20\end{matrix}\) or for \(\dfrac{-6}{20}\) |
| Scheme | Marks | Comments |
|---|---|---|
| \(6 - 4m = 10\) or for \(\begin{pmatrix}6\\-1\end{pmatrix} + \begin{pmatrix}4\\-7\end{pmatrix} = \begin{pmatrix}10\\-8\end{pmatrix}\) or \(\begin{pmatrix}6\\-1\end{pmatrix} - \begin{pmatrix}-4\\7\end{pmatrix} = \begin{pmatrix}10\\-8\end{pmatrix}\) | M1 | |
| \(m = -1\) | A1 | |
| \(n = -8\) | B1 | FT \(-1 + 7m\) for ‘their derived \(m\)’ |
| (5) |