Higher November 2019 Paper 2 Q11
11. The diagram shows quadrilateral \(OABC\).
\(\mathbf{OA} = 5\mathbf{x}\), \(\mathbf{OB} = 12\mathbf{x} + 6\mathbf{y}\) and \(\mathbf{OC} = 8\mathbf{y}\).
Diagram not drawn to scale
(a) Express \(\mathbf{CA}\) in terms of \(\mathbf{x}\) and \(\mathbf{y}\). [1]
(b) \(P\) is the midpoint of \(OB\).
Express each of the following in terms of \(\mathbf{x}\) and \(\mathbf{y}\).
Give each of your answers in the simplest form.
Express each of the following in terms of \(\mathbf{x}\) and \(\mathbf{y}\).
Give each of your answers in the simplest form.
(i) \(\mathbf{OP}\) [1]
(ii) \(\mathbf{PA}\) [1]
(c) Does \(P\) lie on \(CA\)?
Yes ☐ No ☐
You must give a reason for your answer. [1]
| Scheme | Marks | Comments |
|---|---|---|
| \(5\mathbf{x} - 8\mathbf{y}\) | B1 |
| Scheme | Marks | Comments |
|---|---|---|
| (i) \(6\mathbf{x} + 3\mathbf{y}\) | B1 | |
| (ii) \(-\mathbf{x} - 3\mathbf{y}\) | B1 | FT ‘\(-\)(b)(i) \(+\ 5\mathbf{x}\)’ simplified correctly |
| Scheme | Marks | Comments |
|---|---|---|
| States or implies ‘No’ with a reason, e.g. ‘\(5\mathbf{x} - 8\mathbf{y}\) is not a multiple of \(-\mathbf{x} - 3\mathbf{y}\)’ | E1 | |
| (4) |