Foundation November 2019 Paper 2 Q30
30 Here are two column vectors.
\(\mathbf{a} = \begin{pmatrix} 5 \\ 2 \end{pmatrix}\qquad \mathbf{b} = \begin{pmatrix} 3 \\ -1 \end{pmatrix}\)
On the grid below, draw and label the vector \(\mathbf{a} - 2\mathbf{b}\) (3)
| Answer | Mark | Mark scheme |
|---|---|---|
| Vector drawn | M1 | for \(5 - 2 \times 3\ (= -1)\) or \(2 - 2 \times -1\ (= 4)\) seen as a calculation OR for \(\begin{pmatrix} 5 \\ 2 \end{pmatrix} - \begin{pmatrix} 2 \times 3 \\ 2 \times -1 \end{pmatrix}\) OR for \(\begin{pmatrix} -1 \\ b \end{pmatrix}\) or \(\begin{pmatrix} a \\ 4 \end{pmatrix}\) OR for \(\begin{pmatrix} 5 \\ 2 \end{pmatrix}\) or \(\begin{pmatrix} -3 \\ 1 \end{pmatrix}\) or \(\begin{pmatrix} -6 \\ 2 \end{pmatrix}\) drawn |
| M1 | for \(\begin{pmatrix} -1 \\ 4 \end{pmatrix}\) OR for \(\begin{pmatrix} -1 \\ 4 \end{pmatrix}\) drawn with no arrow or incorrect arrow OR for \(\begin{pmatrix} -1 \\ b \end{pmatrix}\) or \(\begin{pmatrix} a \\ 4 \end{pmatrix}\) drawn with arrow, where \(b \neq 4\) and \(a \neq -1\) | |
| A1 | cao |
Additional guidance
May be in a column vector
Condone missing arrows
For this mark (A1) the drawn vector must include an arrow showing direction.