| Exam Board | OCR |
|---|---|
| Module | PURE |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Vectors Introduction & 2D |
| Type | Geometric properties using vectors |
| Difficulty | Moderate -0.8 This is a straightforward vector geometry question requiring basic vector addition and the midpoint formula. Part (i) involves routine manipulation (AC = c - a, OP = ½(a + c)), while part (ii) asks for a standard proof that diagonals bisect each other—a well-known result with a direct approach. The 7-mark allocation suggests multiple small steps rather than conceptual difficulty, making this easier than average for A-level. |
| Spec | 1.10a Vectors in 2D: i,j notation and column vectors1.10d Vector operations: addition and scalar multiplication1.10e Position vectors: and displacement1.10g Problem solving with vectors: in geometry |
$OABC$ is a parallelogram with $\overrightarrow{OA} = \mathbf{a}$ and $\overrightarrow{OC} = \mathbf{c}$. $P$ is the midpoint of $AC$.
\includegraphics{figure_7}
\begin{enumerate}[label=(\roman*)]
\item Find the following in terms of $\mathbf{a}$ and $\mathbf{c}$, simplifying your answers.
\begin{enumerate}[label=(\alph*)]
\item $\overrightarrow{AC}$ [1]
\item $\overrightarrow{OP}$ [2]
\end{enumerate}
\item Hence prove that the diagonals of a parallelogram bisect one another. [4]
\end{enumerate}
\hfill \mbox{\textit{OCR PURE Q7 [7]}}