Higher June 2018 Paper 1 Q15
15. The diagram shows a trapezium, ABCD, with AD parallel to BC.
Diagram not drawn to scale
The vectors \(\mathbf{AB}\) and \(\mathbf{BC}\) are shown in the diagram.
The side AD is 3 times the length of the side BC.
Find \(\mathbf{DC}\) in terms of \(\mathbf{p}\) and \(\mathbf{q}\).
Give your answer in its simplest form. [3]
| Scheme | Marks | Comments |
|---|---|---|
| \((\mathbf{AD} =)\ 3\mathbf{q}\) | B1 | may be on diagram |
| \((\mathbf{DC} =)\ -3\mathbf{q} + 3\mathbf{p} + \mathbf{q}\) | M1 | − ‘their \(3\mathbf{q}\)’ \(+\ 3\mathbf{p} + \mathbf{q}\) |
| \(3\mathbf{p} - 2\mathbf{q}\) | A1 | CAO |
| (3) |