4MA0 Higher January 2015 Paper 4R Q15

EdexcelHigherOld spec8 marksVectors

15 Here is the parallelogram ABCD.

Diagram NOT accurately drawn

\(\overrightarrow{AD} = \begin{pmatrix} 1 \\ 2 \end{pmatrix},\ \overrightarrow{AB} = \begin{pmatrix} 5 \\ 3 \end{pmatrix}\)

(a) Find the magnitude of \(\overrightarrow{AD}\).
Give your answer correct to 3 significant figures. (2)

The point A has coordinates (4, 2)

(b) Work out the coordinates of the point C. (3)

The diagonals of the parallelogram ABCD cross at the point E.

Mark scheme (b)

Scheme	Marks
\(\overrightarrow{AC} = \begin{pmatrix} 1 \\ 2 \end{pmatrix} + \begin{pmatrix} 5 \\ 3 \end{pmatrix}\left(= \begin{pmatrix} 6 \\ 5 \end{pmatrix}\right)\) or B (4+5, 3+2) or (9, 5)	M1
\(\overrightarrow{OC} = \text{“}\begin{pmatrix} 6 \\ 5 \end{pmatrix}\text{”} + \begin{pmatrix} 4 \\ 2 \end{pmatrix}\left(= \begin{pmatrix} 10 \\ 7 \end{pmatrix}\right)\) or C (4+5+1, 3+2+2)	M1
(10, 7)	A1
	(3)

M1: dep

A1: cao

SC: B1 for (10, y) or (x, 7)

Mark scheme (c)

Scheme	Marks
\(\overrightarrow{AE} = \dfrac{1}{2}\text{“}\begin{pmatrix} 6 \\ 5 \end{pmatrix}\text{”}\left(= \begin{pmatrix} 3 \\ 2.5 \end{pmatrix}\right)\) or \(\overrightarrow{AE} = \dfrac{1}{2}\overrightarrow{AC}\) or \(E\left(\dfrac{4 + \text{“}10\text{”}}{2}, \dfrac{2 + \text{“}7\text{”}}{2}\right)\)	M1
\(\overrightarrow{OE} = \begin{pmatrix} 4 \\ 2 \end{pmatrix} + \dfrac{1}{2}\text{“}\begin{pmatrix} 6 \\ 5 \end{pmatrix}\text{”}\) or \(\overrightarrow{OE} = \overrightarrow{OA} + \overrightarrow{AE}\) or E (“7”, “4.5”)	M1
\(\begin{pmatrix} 7 \\ 4.5 \end{pmatrix}\)	A1
	(3)
	(8 marks)

A1: cao