Higher November 2018 Paper 1 Q5
5.
\(\mathbf{p} = \begin{pmatrix}-1\\5\end{pmatrix}, \quad \mathbf{q} = \begin{pmatrix}7\\-2\end{pmatrix}\) and \(\mathbf{r} = \begin{pmatrix}19\\4\end{pmatrix}\)
(a) Work out the column vector \(4(\mathbf{p} + \mathbf{q})\). [2]
(b) When \(2\mathbf{p} + x\mathbf{q} = \mathbf{r}\), find the value of \(x\). [2]
| Scheme | Marks | Comments |
|---|---|---|
| \(\begin{pmatrix}24\\12\end{pmatrix}\) | B2 | Mark final answer B1 for each element or for \(\mathbf{p} + \mathbf{q} = \begin{pmatrix}6\\3\end{pmatrix}\) or \(4\mathbf{p} = \begin{pmatrix}-4\\20\end{pmatrix}\) or \(4\mathbf{q} = \begin{pmatrix}28\\-8\end{pmatrix}\) seen or for \(\left(\dfrac{24}{12}\right)\) as final answer or for a correct answer seen then spoiled |
| Scheme | Marks | Comments |
|---|---|---|
| 3 | B2 | Mark final answer; allow embedded answers e.g. \(\begin{pmatrix}-2\\10\end{pmatrix} + 3\begin{pmatrix}7\\-2\end{pmatrix} = \begin{pmatrix}19\\4\end{pmatrix}\) B1 for \(-2 + 7x = 19\) or \(10 - 2x = 4\) or for \(x\begin{pmatrix}7\\-2\end{pmatrix} = \begin{pmatrix}21\\-6\end{pmatrix}\) or for \(\begin{pmatrix}-2\\10\end{pmatrix} + 3\begin{pmatrix}7\\-2\end{pmatrix} = \begin{pmatrix}19\\4\end{pmatrix}\) seen with an incorrect final answer |
| (4) |