Foundation November 2022 Paper 1 Q21
21 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 |