| Exam Board | OCR MEI |
|---|---|
| Module | AS Paper 2 (AS Paper 2) |
| Year | 2021 |
| Session | November |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors Introduction & 2D |
| Type | Vector between two points |
| Difficulty | Easy -1.2 This is a straightforward AS-level vectors question requiring only basic operations: finding a vector between two points using subtraction, calculating magnitude with Pythagoras, and checking collinearity by comparing scalar multiples. All steps are routine applications of standard formulas with no problem-solving insight needed. |
| Spec | 1.10d Vector operations: addition and scalar multiplication1.10f Distance between points: using position vectors |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(\binom{6}{8} - \binom{-3}{20}\) | M1 | May see \(\binom{9}{-12}\) or \(\binom{-9}{12}\) |
| \(\ | \overrightarrow{AB}\ | = 15\) or \(\sqrt{225}\) so \(\ |
| [2] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(\overrightarrow{AC} = \binom{18}{-24} = 2 \times \binom{9}{-12}\) | M1 | FT their \(AB\); allow mark for comparison of their \(AB\) and \(AC\) |
| so \(A\), \(B\) and \(C\) are collinear | A1 | |
| [2] |
## Question 8:
### Part (a):
| Answer | Mark | Guidance |
|--------|------|----------|
| $\binom{6}{8} - \binom{-3}{20}$ | M1 | May see $\binom{9}{-12}$ or $\binom{-9}{12}$ |
| $\|\overrightarrow{AB}\| = 15$ or $\sqrt{225}$ so $\|\overrightarrow{AB}\| < 200$ or $\|AB\|$ is not greater than 200 | A1 | May see $\sqrt{9^2 + (-12)^2}$ oe. CWO |
| **[2]** | | |
### Part (b):
| Answer | Mark | Guidance |
|--------|------|----------|
| $\overrightarrow{AC} = \binom{18}{-24} = 2 \times \binom{9}{-12}$ | M1 | FT their $AB$; allow mark for comparison of their $AB$ and $AC$ |
| so $A$, $B$ and $C$ are collinear | A1 | |
| **[2]** | | |
---8 With respect to an origin O , the position vectors of the points A and B are\\
$\overrightarrow { \mathrm { OA } } = \binom { - 3 } { 20 }$ and $\overrightarrow { \mathrm { OB } } = \binom { 6 } { 8 }$.
\begin{enumerate}[label=(\alph*)]
\item Determine whether $| \overrightarrow { \mathrm { AB } } | > 200$.
The point C is such that $\overrightarrow { \mathrm { AC } } = \binom { 18 } { - 24 }$.
\item Determine whether $\mathrm { A } , \mathrm { B }$ and C are collinear.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI AS Paper 2 2021 Q8 [4]}}