| Exam Board | OCR |
|---|---|
| Module | AS Pure (AS Pure Mathematics) |
| Year | 2017 |
| Session | Specimen |
| Marks | 6 |
| Topic | Vectors Introduction & 2D |
| Type | Vector between two points |
| Difficulty | Moderate -0.8 This is a straightforward AS-level vectors question requiring only basic operations: vector subtraction to find BC, adding vectors to find D, finding a midpoint using the standard formula, and calculating magnitude using Pythagoras. All steps are routine applications of standard formulas with no problem-solving insight required, making it easier than average. |
| Spec | 1.10a Vectors in 2D: i,j notation and column vectors1.10d Vector operations: addition and scalar multiplication1.10e Position vectors: and displacement1.10f Distance between points: using position vectors |
The points $A$, $B$ and $C$ have position vectors $\begin{pmatrix} -2 \\ 1 \end{pmatrix}$, $\begin{pmatrix} 2 \\ 5 \end{pmatrix}$ and $\begin{pmatrix} 6 \\ 3 \end{pmatrix}$ respectively.
$M$ is the midpoint of $BC$.
\begin{enumerate}[label=(\alph*)]
\item Find the position vector of the point $D$ such that $\overrightarrow{BC} = \overrightarrow{AD}$. [3]
\item Find the magnitude of $\overrightarrow{AM}$. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR AS Pure 2017 Q4 [6]}}