Higher November 2023 Paper 3 Q15
15 \(\mathbf{a} = \begin{pmatrix} m \\ 3 \end{pmatrix} \qquad \mathbf{b} = \begin{pmatrix} -4 \\ p \end{pmatrix}\)
The diagram shows the vector \(\quad 2\mathbf{a} + \mathbf{b}\)
Work out the values of \(m\) and \(p\). [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(\begin{pmatrix} 8 \\ 5 \end{pmatrix}\) or \(\begin{pmatrix} 2m \\ 6 \end{pmatrix} + \begin{pmatrix} -4 \\ p \end{pmatrix}\) or \(2m - 4\) or \(6 + p\) | M1 | oe may be seen in a single vector |
| \(2m - 4 =\) their 8 or \(6 + p =\) their 5 | M1dep | oe their 8 and their 5 must come from a vector or be shown on the diagram |
| \(m = 6\) or \(p = -1\) | A1 | |
| \(m = 6\) and \(p = -1\) | A1 | SC3 \(m = 4.5\) and \(p = 2\) SC2 \(m = 4.5\) or \(p = 2\) |
Additional guidance
SC are for using \(\begin{pmatrix} 5 \\ 8 \end{pmatrix}\)
\(2m - 4 = 8\) or \(6 + p = 5\) implies M2