Higher November 2018 Paper 6 Q20
20
(a) b is a vector.
Given that b + \(\begin{pmatrix} 5 \\ 2 \end{pmatrix}\) is parallel to \(\begin{pmatrix} 2 \\ 1 \end{pmatrix}\), find two possible answers for b. [3]
(b) Given that\[m\begin{pmatrix} 4 \\ 1 \end{pmatrix} + n\begin{pmatrix} 5 \\ 2 \end{pmatrix} = \begin{pmatrix} 12 \\ 6 \end{pmatrix}\]
find the value of \(m\) and the value of \(n\). [5]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| eg. \(\begin{pmatrix} 1 \\ 1 \end{pmatrix}\) and \(\begin{pmatrix} 3 \\ 2 \end{pmatrix}\) | 3 | B2 for one correct answer or M1 for any multiple of \(\begin{pmatrix} 2 \\ 1 \end{pmatrix}\) seen | Other correct answers include: \(\begin{pmatrix} 5 \\ 3 \end{pmatrix}\), \(\begin{pmatrix} -1 \\ 0 \end{pmatrix}\), \(\begin{pmatrix} -3 \\ -1 \end{pmatrix}\), \(\begin{pmatrix} -7 \\ -3 \end{pmatrix}\), \(\begin{pmatrix} -9 \\ -4 \end{pmatrix}\), \(\begin{pmatrix} -11 \\ -5 \end{pmatrix}\), \(\begin{pmatrix} -13 \\ -6 \end{pmatrix}\) and \(\begin{pmatrix} -15 \\ -7 \end{pmatrix}\) For others, check that top + 5 is double bottom + 2 |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(m = -2\), \(n = 4\) | 5 | B1 for \(\begin{pmatrix} 4m \\ m \end{pmatrix}\) or \(\begin{pmatrix} 5n \\ 2n \end{pmatrix}\) soi and M1 for \(4m + 5n = 12\) or \(m + 2n = 6\) and M1 for multiplication by scalar(s) to equate coefficients in m or n or reduction to one variable by substitution e.g. \(4(6 - 2n) + 5n = 12\) and M1 for elimination or simplification to \(3m = -6\) or \(3n = 12\) oe | |