| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2012 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Straight Lines & Coordinate Geometry |
| Type | Verify shape type from coordinates |
| Difficulty | Moderate -0.3 This is a straightforward coordinate geometry question requiring standard techniques: distance formula for equal sides, gradient multiplication for perpendicularity, and midpoint formula. All methods are routine C1 content with clear signposting across three parts totaling 11 marks. The multi-part structure and verification aspects make it slightly more substantial than a minimal exercise, but no problem-solving insight is needed—just systematic application of formulas. |
| Spec | 1.03b Straight lines: parallel and perpendicular relationships1.10f Distance between points: using position vectors1.10g Problem solving with vectors: in geometry |
\includegraphics{figure_10}
Fig. 10 is a sketch of quadrilateral ABCD with vertices A $(1, 5)$, B $(-1, 1)$, C $(3, -1)$ and D $(11, 5)$.
\begin{enumerate}[label=(\roman*)]
\item Show that $AB = BC$. [3]
\item Show that the diagonals AC and BD are perpendicular. [3]
\item Find the midpoint of AC. Show that BD bisects AC but AC does not bisect BD. [5]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C1 2012 Q10 [11]}}