Higher November 2024 Paper 2 Q17
17 Here are two vectors.
\(\overrightarrow{FG} = \begin{pmatrix} -5 \\ 2 \end{pmatrix}\) \(\overrightarrow{HG} = \begin{pmatrix} 4 \\ 14 \end{pmatrix}\)
Calculate the magnitude of the vector \(\overrightarrow{HF}\)
(3)
| Scheme | Marks |
|---|---|
\((\overrightarrow{HF} =)\;\begin{pmatrix} 4 \\ 14 \end{pmatrix} + \begin{pmatrix} 5 \\ -2 \end{pmatrix}\left[= \begin{pmatrix} 9 \\ 12 \end{pmatrix}\right]\) or \(\begin{pmatrix} 4 \\ 14 \end{pmatrix} - \begin{pmatrix} -5 \\ 2 \end{pmatrix}\left[= \begin{pmatrix} 9 \\ 12 \end{pmatrix}\right]\) oe \((\overrightarrow{FH} =)\;\begin{pmatrix} -5 \\ 2 \end{pmatrix} + \begin{pmatrix} -4 \\ -14 \end{pmatrix}\left[= \begin{pmatrix} -9 \\ -12 \end{pmatrix}\right]\) or \(\begin{pmatrix} -5 \\ 2 \end{pmatrix} - \begin{pmatrix} 4 \\ 14 \end{pmatrix}\left[= \begin{pmatrix} -9 \\ -12 \end{pmatrix}\right]\) oe | M1 |
\(\sqrt{\text{``}{9}\text{''}^2 + \text{``}{12}\text{''}^2}\) or \(\sqrt{(\text{``}{-9}\text{''})^2 + (\text{``}{-12}\text{''})^2}\) Allow a complete method using their values for \(\overrightarrow{HF}\) or \(\overrightarrow{FH}\) Provided it is from \(\begin{pmatrix} \pm 4 \\ \pm 14 \end{pmatrix} - \begin{pmatrix} \pm 5 \\ \pm 2 \end{pmatrix}\) | M1indep |
| Correct answer scores full marks (unless from obvious incorrect working) Watch out for a correct answer from wrong working eg –5 + 2 + 4 + 14 = 15 Answer: 15 | A1 |
| (3) | |
| (3 marks) |
Notes
M1: a correct calculation for \(\overrightarrow{HF}\) or \(\overrightarrow{FH}\)
(for this mark allow written as coordinates)
Also allow eg 9i + 12j
M1indep: Allow their \(\overrightarrow{HF}\) or \(\overrightarrow{FH}\) provided it is from \(\begin{pmatrix} \pm 4 \\ \pm 14 \end{pmatrix} - \begin{pmatrix} \pm 5 \\ \pm 2 \end{pmatrix}\) allowing any sign error
if used (– 9)² and (– 12)² condone missing brackets if recovered
A1: from fully correct figures
eg use of \(\begin{pmatrix} 9 \\ -12 \end{pmatrix}\) would give the correct answer but would not gain this accuracy mark