OCR C4 2011 June — Question 2 3 marks

Exam BoardOCR
ModuleC4 (Core Mathematics 4)
Year2011
SessionJune
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicVectors Introduction & 2D
TypeUnit vector in given direction
DifficultyEasy -1.2 This is a straightforward application of the unit vector formula requiring only calculation of magnitude and division. It's a routine procedural question with no problem-solving element, though the √12 requires minor simplification care. Easier than average A-level content.
Spec1.10c Magnitude and direction: of vectors

2 Find the unit vector in the direction of \(\left( \begin{array} { c } 2 \\ - 3 \\ \sqrt { 12 } \end{array} \right)\).

Question 2:
AnswerMarks Guidance
Answer/WorkingMarks Guidance
\(2^2+(-3)^2+(\sqrt{12})^2\) soi e.g. 25 or 5M1 Allow \(2^2-3^2+\sqrt{12}^2\)
\(5\)A1 May be implied by 5 or 1/5 in final answer
\(\frac{1}{5}\begin{pmatrix}2\\-3\\\sqrt{12}\end{pmatrix}\) or \(\begin{pmatrix}\frac{2}{5}\\-\frac{3}{5}\\\frac{\sqrt{12}}{5}\end{pmatrix}\) AEF\(\sqrt{}\)A1 3 FT their '5'. Accept \(-\frac{1}{5}\begin{pmatrix\ \end{pmatrix}\) or \(\frac{1}{\pm 5}\begin{pmatrix\ \end{pmatrix}\)
# Question 2:

| Answer/Working | Marks | Guidance |
|---|---|---|
| $2^2+(-3)^2+(\sqrt{12})^2$ soi e.g. 25 or 5 | M1 | Allow $2^2-3^2+\sqrt{12}^2$ |
| $5$ | A1 | May be implied by 5 or 1/5 in final answer |
| $\frac{1}{5}\begin{pmatrix}2\\-3\\\sqrt{12}\end{pmatrix}$ or $\begin{pmatrix}\frac{2}{5}\\-\frac{3}{5}\\\frac{\sqrt{12}}{5}\end{pmatrix}$ AEF | $\sqrt{}$A1 **3** | FT their '5'. Accept $-\frac{1}{5}\begin{pmatrix\ \end{pmatrix}$ or $\frac{1}{\pm 5}\begin{pmatrix\ \end{pmatrix}$ |

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2 Find the unit vector in the direction of $\left( \begin{array} { c } 2 \\ - 3 \\ \sqrt { 12 } \end{array} \right)$.

\hfill \mbox{\textit{OCR C4 2011 Q2 [3]}}