Foundation November 2022 Paper 3 Q30
30
\[\mathbf{a} = \begin{pmatrix} 2 \\ 3 \end{pmatrix} \qquad \mathbf{b} = \begin{pmatrix} -1 \\ 2 \end{pmatrix} \qquad \mathbf{c} = \begin{pmatrix} 4 \\ 1 \end{pmatrix}\](a) Work out as a column vector
(i) \(\mathbf{a} + \mathbf{b}\) (1)
(ii) \(2\mathbf{a} - \mathbf{c}\) (2)
The vector \(\mathbf{d}\) is drawn on the grid.
(b) From the point \(P\), draw the vector \(2\mathbf{d}\) (1)
| Answer | Mark | Mark scheme |
|---|---|---|
| (i) \(\begin{pmatrix} 1 \\ 5 \end{pmatrix}\) | B1 | for \(\begin{pmatrix} 1 \\ 5 \end{pmatrix}\) |
| (ii) \(\begin{pmatrix} 0 \\ 5 \end{pmatrix}\) | M1 | for substitution of values eg \(\begin{pmatrix} 2 \times 2 - 4 \\ 3 \times 2 - 1 \end{pmatrix}\) oe OR for \(\begin{pmatrix} 0 \\ b \end{pmatrix}\) or \(\begin{pmatrix} a \\ 5 \end{pmatrix}\) where \(a\), \(b\) are integer values. |
| A1 | for \(\begin{pmatrix} 0 \\ 5 \end{pmatrix}\) |
Additional guidance
(ii) M1: Need not be shown in brackets at this stage
| Answer | Mark | Mark scheme |
|---|---|---|
| correct vector drawn | C1 | for a correct vector drawn from point \(P\) |
Additional guidance
Need not be labelled but do not award if there is any ambiguity.