1MA0 Higher November 2015 Paper 1 Q20
*20
Diagram NOT accurately drawn
\(ACEF\) is a parallelogram.
\(B\) is the midpoint of \(AC\).
\(M\) is the midpoint of \(BE\).
\(\overrightarrow{CB} = \mathbf{a}\)
\(\overrightarrow{ED} = \mathbf{b}\)
\(\overrightarrow{DC} = 2\mathbf{b}\)
Show that \(AMD\) is a straight line. (5)
| Answer | Mark | Notes |
|---|---|---|
| Proof | 5 | M1 for finding one other vector expressed as \(\mathbf{a}\) and/or \(\mathbf{b}\) M1 for method to find one of \(\overrightarrow{DM}\), \(\overrightarrow{MA}\) or \(\overrightarrow{DA}\) eg \(\overrightarrow{DM} = -\mathbf{b} + \tfrac{1}{2}(3\mathbf{b} + \mathbf{a})\) oe, \(\overrightarrow{MA} = \tfrac{1}{2}(3\mathbf{b} + \mathbf{a}) + \mathbf{a}\) oe or \(\overrightarrow{DA} = 2\mathbf{b} + 2\mathbf{a}\) oe M1 for method to find two of \(\overrightarrow{DM}\), \(\overrightarrow{MA}\) or \(\overrightarrow{DA}\) A1 for two of \(\overrightarrow{DM} = \tfrac{1}{2}(\mathbf{a} + \mathbf{b})\), \(\overrightarrow{MA} = 1.5(\mathbf{a} + \mathbf{b})\), \(\overrightarrow{DA} = 2(\mathbf{a} + \mathbf{b})\) ie simplified but oe C1 (dep on working shown) for conclusion relating to correct working |