Higher June 2024 Paper 3 Q8
8
\[\mathbf{a} = \begin{pmatrix} 3 \\ 2 \end{pmatrix} \qquad \mathbf{b} = \begin{pmatrix} -1 \\ 4 \end{pmatrix}\]On the grid below, draw and label the vector \(2\mathbf{a} + \mathbf{b}\) (3)
| Answer | Mark | Mark scheme |
|---|---|---|
| Vector \(\begin{pmatrix} 5 \\ 8 \end{pmatrix}\) drawn | M1 | for \(2 \times 3 + {-1}\ (= 5)\) or \(2 \times 2 + 4\ (= 8)\) seen as a calculation or for \(\begin{pmatrix} 2 \times 3 \\ 2 \times 2 \end{pmatrix}\) + \(\begin{pmatrix} -1 \\ 4 \end{pmatrix}\) or for \(\begin{pmatrix} 5 \\ b \end{pmatrix}\) or \(\begin{pmatrix} a \\ 8 \end{pmatrix}\) or for \(\begin{pmatrix} 3 \\ 2 \end{pmatrix}\) drawn or \(\begin{pmatrix} 6 \\ 4 \end{pmatrix}\) drawn or \(\begin{pmatrix} -1 \\ 4 \end{pmatrix}\) drawn |
| M1 | for \(\begin{pmatrix} 5 \\ 8 \end{pmatrix}\) or for \(\begin{pmatrix} 5 \\ 8 \end{pmatrix}\) drawn with no arrow or incorrect arrow or for \(\begin{pmatrix} 5 \\ b \end{pmatrix}\) drawn with arrow or \(\begin{pmatrix} a \\ 8 \end{pmatrix}\) drawn with arrow, where \(b \neq 8\) and \(a \neq 5\) | |
| A1 | cao |
Additional guidance
May be in the correct position in a column vector or coordinate.
Condone missing arrows
For this mark the drawn vector must include an arrow showing direction.
Need not be labelled but do not award if there is any ambiguity