Foundation June 2018 Paper 3 Q12
12
(a) \(\overrightarrow{\text{PQ}} = \begin{pmatrix}3\\4\end{pmatrix}\)
Work out \(5\overrightarrow{\text{PQ}}\). [1]
(b) Find the values of \(h\) and \(k\).\[\begin{pmatrix}h\\5\end{pmatrix} + \begin{pmatrix}2\\k\end{pmatrix} - \begin{pmatrix}3\\3\end{pmatrix} = \begin{pmatrix}0\\0\end{pmatrix}\]
[2]
(c) Triangle ABC is drawn on a coordinate grid.
\(\overrightarrow{\text{AB}} = \begin{pmatrix}0\\-8\end{pmatrix}\)
(i) Use the diagram to complete this vector sum.\[\overrightarrow{\text{AB}} + \overrightarrow{\text{BC}} + \overrightarrow{\text{CA}} = \begin{pmatrix}0\\-8\end{pmatrix} + \begin{pmatrix}\quad\\\quad\end{pmatrix} + \begin{pmatrix}\quad\\\quad\end{pmatrix} = \begin{pmatrix}\quad\\\quad\end{pmatrix}\]
[2]
(ii) Give a reason why the answer to the sum could be written down without doing any working. [1]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(\begin{pmatrix}15\\20\end{pmatrix}\) | 1 | Do not allow fraction line in vector | |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| [\(h\) =] 1 [\(k\) =] \(-2\) | 2 | B1 for each or both correct but reversed | |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| (i) \(\begin{pmatrix}6\\0\end{pmatrix}\) [+] \(\begin{pmatrix}-6\\8\end{pmatrix}\) [=] \(\begin{pmatrix}0\\0\end{pmatrix}\) | 2 | B1 for \(\begin{pmatrix}6\\0\end{pmatrix}\) or \(\begin{pmatrix}-6\\8\end{pmatrix}\) or \(\begin{pmatrix}0\\k\end{pmatrix}\) or \(\begin{pmatrix}k\\0\end{pmatrix}\) as final vector | Do not allow fraction line in vector |
| (ii) [Return to] the starting point oe | 1 | Do not accept “No movement” or a calculation | |
Appendix
Exemplars: 12c
| Comment | Mark |
|---|---|
| Start and finish at the same point | 1 |
| Come back to A | 1 |
| It’s a closed shape | 1 |
| The numbers are easy to add up | 0 |
| You can see it on the shape | 0 |