4MA0 Higher January 2018 Paper 4 Q18
18 \(A\), \(C\) and \(D\) are points such that
\(\overrightarrow{AC} = \begin{pmatrix} 3 \\ -8 \end{pmatrix}\) \(\overrightarrow{DC} = \begin{pmatrix} 5 \\ 6 \end{pmatrix}\)
(a) Find \(\overrightarrow{DA}\) as a column vector. (2)
Given that the position vector of \(D\) is \(\begin{pmatrix} 2 \\ 5 \end{pmatrix}\) and \(E\) is the point such that \(\overrightarrow{DE} = 2\overrightarrow{AC}\)
(b) find the coordinates of \(E\). (2)
| Scheme | Marks |
|---|---|
| \(\begin{pmatrix} 5 \\ 6 \end{pmatrix} + \begin{pmatrix} -3 \\ 8 \end{pmatrix}\) or \(\begin{pmatrix} 5 \\ 6 \end{pmatrix} - \begin{pmatrix} 3 \\ -8 \end{pmatrix}\) | M1 |
| \(\begin{pmatrix} 2 \\ 14 \end{pmatrix}\) | A1 |
| (2) |
Notes
M1: or \(\overrightarrow{DA} = \overrightarrow{DC} + \overrightarrow{CA}\) oe or (2, 14)
or for \(\begin{pmatrix} a \\ 14 \end{pmatrix}\) or \(\begin{pmatrix} 2 \\ b \end{pmatrix}\) or correct vector values written without brackets
| Scheme | Marks |
|---|---|
| \(\begin{pmatrix} 2 \\ 5 \end{pmatrix} + 2\begin{pmatrix} 3 \\ -8 \end{pmatrix}\) or \(\begin{pmatrix} 8 \\ -11 \end{pmatrix}\) | M1 |
| (8, −11) | A1 |
| (2) |
Notes
M1: for a correct sum of vectors or the correct values in a column vector or for (8, \(y\)) or (\(x\), −11)