Higher November 2019 Paper 6 Q9
9 Vector \(\mathbf{a} = \begin{pmatrix} 3 \\ -1 \end{pmatrix}\) and vector \(\mathbf{b} = \begin{pmatrix} 1 \\ 3 \end{pmatrix}\).
(a) Find the values of \(k\) and \(n\) so that
\(k(\mathbf{a} + \mathbf{b}) = \begin{pmatrix} 10 \\ n \end{pmatrix}\). [3]
(b) Gavin starts to draw a diagram to show that \(\mathbf{a} + 2\mathbf{b} = \begin{pmatrix} 5 \\ 5 \end{pmatrix}\).
Complete Gavin’s diagram. [3]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 2.5 5 | 3 | B2 for [\(k\) =] 2.5 or B1 for \(\begin{pmatrix} 4 \\ 2 \end{pmatrix}\) B1 for [\(n\) =] 5 | |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
 | 1 | Correct arrow and label \(\begin{pmatrix} 5 \\ 5 \end{pmatrix}\) or \(\mathbf{a} + 2\mathbf{b}\) | Accept single arrowhead |
| 1 | Correct arrows on a and 2b | ||
| 1 | Correct labels on a and 2b | ||