Foundation June 2017 Paper 1 Q24
24.
\(\mathbf{p} = \begin{pmatrix} 6 \\ -1 \end{pmatrix}\) 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) |