Higher November 2022 Paper 1 Q7
7 The diagram shows the vectors \(\mathbf{a}\) and \(\mathbf{b}\).
As a column vector \(\quad \mathbf{a} = \) \(\begin{pmatrix} 3 \\ 2 \end{pmatrix}\)
(a) What is \(\mathbf{b}\) as a column vector? [2 marks]
(b) Work out \(4\mathbf{a}\) as a column vector. [1 mark]
(c) \(\mathbf{a} + \mathbf{c} = \) \(\begin{pmatrix} 3 \\ 0 \end{pmatrix}\)
Work out \(\mathbf{c}\) as a column vector.
Circle your answer. [1 mark]
- \(\begin{pmatrix} 2 \\ 0 \end{pmatrix}\)
- \(\begin{pmatrix} 0 \\ 2 \end{pmatrix}\)
- \(\begin{pmatrix} -2 \\ 0 \end{pmatrix}\)
- \(\begin{pmatrix} 0 \\ -2 \end{pmatrix}\)
| Answer | Mark | Comments |
|---|---|---|
| \(\begin{pmatrix} 4 \\ -1 \end{pmatrix}\) | B2 | B1 \(\begin{pmatrix} 4 \\ \ldots \end{pmatrix}\) or \(\begin{pmatrix} \ldots \\ -1 \end{pmatrix}\) or \((4, -1)\) SC1 \(\begin{pmatrix} -4 \\ 1 \end{pmatrix}\) or \(\begin{pmatrix} -1 \\ 4 \end{pmatrix}\) |
Additional guidance
Ignore fraction lines
| Answer | Mark | Comments |
|---|---|---|
| \(\begin{pmatrix} 12 \\ 8 \end{pmatrix}\) | B1 |
Additional guidance
| \(4\)\(\begin{pmatrix} 3 \\ 2 \end{pmatrix}\) or \(\begin{pmatrix} 12 \\ 8 \end{pmatrix}\) in working with answer \(\begin{pmatrix} 3 \\ 2 \end{pmatrix}\) | B0 |
| Ignore fraction lines |
| Answer | Mark | Comments |
|---|---|---|
| \(\begin{pmatrix} 0 \\ -2 \end{pmatrix}\) | B1 |