4MA0 Higher January 2015 Paper 4 Q19

EdexcelHigherOld spec5 marksVectors

19 \(\mathbf{a} = \begin{pmatrix} 5 \\ -2 \end{pmatrix}\quad \mathbf{b} = \begin{pmatrix} 1 \\ 7 \end{pmatrix}\quad \mathbf{c} = \begin{pmatrix} -7 \\ 0 \end{pmatrix}\)

(a) Write, as a column vector, \(2\mathbf{a}\) (1)

(b) Write, as a column vector, \(3\mathbf{b} - \mathbf{c}\) (2)

Scheme	Marks
\(\begin{pmatrix} 10 \\ -4 \end{pmatrix}\)	B1
	(1)

Mark scheme (b)

Scheme	Marks
\(3\begin{pmatrix} 1 \\ 7 \end{pmatrix} - \begin{pmatrix} -7 \\ 0 \end{pmatrix}\) or \(\begin{pmatrix} 3 \\ 21 \end{pmatrix}\)	M1
\(\begin{pmatrix} 10 \\ 21 \end{pmatrix}\)	A1
	(2)

Notes

M1: or \(\begin{pmatrix} x \\ 21 \end{pmatrix}\) or \(\begin{pmatrix} 10 \\ y \end{pmatrix}\)

Scheme	Marks
\(5^2 + (-2)^2\) or \(5^2 + 2^2\) or 29	M1
\(\sqrt{29}\)	A1
	(2)
	(5 marks)