| Exam Board | OCR MEI |
|---|---|
| Module | Paper 3 (Paper 3) |
| Year | 2020 |
| Session | November |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors Introduction & 2D |
| Type | Linear combination of vectors |
| Difficulty | Standard +0.8 This question requires understanding of regular polygon geometry, calculating the interior angle of an octagon (135°), determining the exterior angle (45°), and applying trigonometry to find vector components. While the setup is straightforward, students must synthesize multiple concepts (polygon angles, vector addition, exact trigonometric values) rather than apply a single routine procedure, making it moderately challenging but still within standard A-level scope. |
| Spec | 1.05f Trigonometric function graphs: symmetries and periodicities1.10d Vector operations: addition and scalar multiplication |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| BC is parallel to \(\mathbf{i}+\mathbf{j}\) OR 1 unit at \(45°\) | M1 | E.g. \(k\mathbf{i}+k\mathbf{j}\) |
| \( | \mathbf{i}+\mathbf{j} | = \sqrt{2}\) |
| \(\overrightarrow{BC} = \frac{1}{\sqrt{2}}(\mathbf{i}+\mathbf{j})\) oe | A1 | Must be exact e.g. \(\cos45\mathbf{i} + \sin45\mathbf{j}\) |
## Question 4:
| Answer | Marks | Guidance |
|--------|-------|----------|
| BC is parallel to $\mathbf{i}+\mathbf{j}$ OR 1 unit at $45°$ | M1 | E.g. $k\mathbf{i}+k\mathbf{j}$ |
| $|\mathbf{i}+\mathbf{j}| = \sqrt{2}$ | M1 | Could be on diagram |
| $\overrightarrow{BC} = \frac{1}{\sqrt{2}}(\mathbf{i}+\mathbf{j})$ oe | A1 | Must be exact e.g. $\cos45\mathbf{i} + \sin45\mathbf{j}$ |
---4 Fig. 4 shows the regular octagon ABCDEFGH .
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{a13f7a05-e2d3-4354-a0c7-ef7283eff514-05_689_696_301_239}
\captionsetup{labelformat=empty}
\caption{Fig. 4}
\end{center}
\end{figure}
$\overrightarrow { \mathrm { AB } } = \mathbf { i } , \overrightarrow { \mathrm { CD } } = \mathbf { j }$, where $\mathbf { i }$ is a unit vector parallel to the $x$-axis and $\mathbf { j }$ is a unit vector parallel to the $y$-axis.
Find an exact expression for $\overrightarrow { \mathrm { BC } }$ in terms of $\mathbf { i }$ and $\mathbf { j }$.
\hfill \mbox{\textit{OCR MEI Paper 3 2020 Q4 [3]}}