| Exam Board | OCR MEI |
|---|---|
| Module | AS Paper 1 (AS Paper 1) |
| Year | 2023 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors Introduction & 2D |
| Type | Vector between two points |
| Difficulty | Easy -1.3 This is a straightforward vector question requiring only basic operations: adding vectors to find a position vector, then calculating and comparing two distances using Pythagoras. Both parts are routine applications of fundamental vector concepts with no problem-solving insight needed, making it easier than average for A-level. |
| Spec | 1.10e Position vectors: and displacement1.10f Distance between points: using position vectors |
| Answer | Marks | Guidance |
|---|---|---|
| Position vector of C is \(\begin{pmatrix}2\\-1\end{pmatrix} + \begin{pmatrix}-2\\2\end{pmatrix} = \begin{pmatrix}0\\1\end{pmatrix}\) | B1 | Correct column vector notation. ISW if the modulus of the vector is given as well. |
| Answer | Marks | Guidance |
|---|---|---|
| \(\overrightarrow{AB} = \begin{pmatrix}5-2\\4-(-1)\end{pmatrix}\), \(\overrightarrow{BC} = \begin{pmatrix}0-5\\1-4\end{pmatrix}\) | M1 | Attempt to calculate one of vectors \(\overrightarrow{AB}\), \(\overrightarrow{BA}\), \(\overrightarrow{CB}\) or \(\overrightarrow{BC}\) |
| \(AB = \sqrt{3^2 + 5^2} = \sqrt{34}\), \(BC = \sqrt{5^2 + 3^2} = \sqrt{34}\) | M1 | Attempts to find both lengths. Also allow argument without distances based on matching components. |
| Distances equal, so B is equidistant from A and C. | E1 | Complete argument www |
## Question 3:
**(a)**
Position vector of C is $\begin{pmatrix}2\\-1\end{pmatrix} + \begin{pmatrix}-2\\2\end{pmatrix} = \begin{pmatrix}0\\1\end{pmatrix}$ | B1 | Correct column vector notation. ISW if the modulus of the vector is given as well.
**(b)**
$\overrightarrow{AB} = \begin{pmatrix}5-2\\4-(-1)\end{pmatrix}$, $\overrightarrow{BC} = \begin{pmatrix}0-5\\1-4\end{pmatrix}$ | M1 | Attempt to calculate one of vectors $\overrightarrow{AB}$, $\overrightarrow{BA}$, $\overrightarrow{CB}$ or $\overrightarrow{BC}$
$AB = \sqrt{3^2 + 5^2} = \sqrt{34}$, $BC = \sqrt{5^2 + 3^2} = \sqrt{34}$ | M1 | Attempts to find both lengths. Also allow argument without distances based on matching components.
Distances equal, so B is equidistant from A and C. | E1 | Complete argument www
---3 The points $A$ and $B$ have position vectors $\binom { 2 } { - 1 }$ and $\binom { 5 } { 4 }$ respectively. The vector $\overrightarrow { \mathrm { AC } }$ is $\binom { - 2 } { 2 }$.
\begin{enumerate}[label=(\alph*)]
\item Write down the position vector of C as a column vector.
\item Show that B is equidistant from A and C .
\end{enumerate}
\hfill \mbox{\textit{OCR MEI AS Paper 1 2023 Q3 [4]}}