| Exam Board | OCR MEI |
|---|---|
| Module | Paper 2 (Paper 2) |
| Year | 2021 |
| Session | November |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors Introduction & 2D |
| Type | Angle between two vectors |
| Difficulty | Moderate -0.8 This is a straightforward two-part question requiring basic vector operations: (a) computing a linear combination and finding magnitude using Pythagoras, (b) using the dot product formula to find an angle. Both are standard textbook exercises with no problem-solving insight required, making it easier than average but not trivial since it involves multiple steps and the angle calculation formula. |
| Spec | 1.10c Magnitude and direction: of vectors1.10d Vector operations: addition and scalar multiplication |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\left(\frac{2 \times 5 + 3 \times (-1)}{2 \times 3 + 3 \times 6}\right)\) soi | M1 | may be implied if one component fully correct |
| \(\sqrt{7^2 + 24^2}\) | M1 | dependent on award of first M1 |
| \(25\) | A1 | |
| [3] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\tan^{-1}\left(\frac{24}{7}\right)\) oe | M1 | or \(\cos^{-1}\left(\frac{7}{25}\right)\) or \(\sin^{-1}\left(\frac{24}{25}\right)\) FT their 7, 24 or 25 |
| \(74°\) or \(73.7°\) or awrt \(73.74°\) or \(1.3\) or \(1.29\) or awrt \(1.287\) | A1 | |
| [2] |
## Question 6(a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\left(\frac{2 \times 5 + 3 \times (-1)}{2 \times 3 + 3 \times 6}\right)$ **soi** | M1 | may be implied if one component fully correct |
| $\sqrt{7^2 + 24^2}$ | M1 | dependent on award of first **M1** |
| $25$ | A1 | |
| | **[3]** | |
---
## Question 6(b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\tan^{-1}\left(\frac{24}{7}\right)$ **oe** | M1 | or $\cos^{-1}\left(\frac{7}{25}\right)$ or $\sin^{-1}\left(\frac{24}{25}\right)$ FT their 7, 24 or 25 |
| $74°$ or $73.7°$ or awrt $73.74°$ or $1.3$ or $1.29$ or awrt $1.287$ | A1 | |
| | **[2]** | |
---6 You are given that $\mathbf { v } = 2 \mathbf { a } + 3 \mathbf { b }$, where $\mathbf { a }$ and $\mathbf { b }$ are the position vectors\\
$\mathbf { a } = \binom { 5 } { 3 }$ and $\mathbf { b } = \binom { - 1 } { 6 }$.
\begin{enumerate}[label=(\alph*)]
\item Determine the magnitude of $\mathbf { v }$.
\item Determine the angle between $\mathbf { v }$ and the vector $\binom { 1 } { 0 }$.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Paper 2 2021 Q6 [5]}}