1MA0 Higher November 2012 Paper 1 Q28
28
Diagram NOT accurately drawn
\(APB\) is a triangle.
\(N\) is a point on \(AP\).
\(\overrightarrow{AB} = \mathbf{a}\) \(\overrightarrow{AN} = 2\mathbf{b}\) \(\overrightarrow{NP} = \mathbf{b}\)
(a) Find the vector \(\overrightarrow{PB}\), in terms of a and b. (1)
\(B\) is the midpoint of \(AC\).
\(M\) is the midpoint of \(PB\).
*(b) Show that \(NMC\) is a straight line. (4)
| Answer | Mark | Notes |
|---|---|---|
| \(\mathbf{a} - 3\mathbf{b}\) | 1 | B1 for \(\mathbf{a} - 3\mathbf{b}\) oe |
| Answer | Mark | Notes |
|---|---|---|
| 4 | M1 for (NC =) \(2\mathbf{a} - 2\mathbf{b}\) oe M1 for (NM =) \(\mathbf{b} + \frac{1}{2}\)“\(\mathbf{a} - 3\mathbf{b}\)” A1 for \(\frac{1}{2}(\mathbf{a} - \mathbf{b})\) oe and \(2\mathbf{a} - 2\mathbf{b}\) oe C1 for NC is a multiple of NM (+ common point) OR M1 for (NC =) \(2\mathbf{a} - 2\mathbf{b}\) oe M1 for (MC =) \(\frac{1}{2}\)“\(\mathbf{a} - 3\mathbf{b}\)”\(+\, \mathbf{a}\) A1 for \(\frac{3}{2}(\mathbf{a} - \mathbf{b})\) oe and \(2\mathbf{a} - 2\mathbf{b}\) oe C1 for NC is a multiple of MC (+ common point) OR M1 for (NM =) \(\mathbf{b} + \frac{1}{2}\)“\(\mathbf{a} - 3\mathbf{b}\)” M1 for (MC =) \(\frac{1}{2}\)“\(\mathbf{a} - 3\mathbf{b}\)”\(+\, \mathbf{a}\) A1 for \(\frac{1}{2}(\mathbf{a} - \mathbf{b})\) oe and \(\frac{3}{2}(\mathbf{a} - \mathbf{b})\) oe C1 for NM is a multiple to MC (+ common point) |