| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2010 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Straight Lines & Coordinate Geometry |
| Type | Equation of line through two points |
| Difficulty | Moderate -0.3 This is a multi-part coordinate geometry question covering standard C1 techniques: finding line equations, calculating areas, perpendicular bisectors, and circle equations. While it has 12 marks total and requires multiple steps, each part uses routine methods (gradient formula, perpendicular gradient = -1/m, midpoint, distance formula) with no novel problem-solving required. The 'show that' parts provide target answers, reducing difficulty. Slightly easier than average due to straightforward application of standard techniques. |
| Spec | 1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.03b Straight lines: parallel and perpendicular relationships1.03d Circles: equation (x-a)^2+(y-b)^2=r^21.03e Complete the square: find centre and radius of circle |
\includegraphics{figure_11}
Fig. 11 shows the line through the points A $(-1, 3)$ and B $(5, 1)$.
\begin{enumerate}[label=(\roman*)]
\item Find the equation of the line through A and B. [3]
\item Show that the area of the triangle bounded by the axes and the line through A and B is $\frac{32}{3}$ square units. [2]
\item Show that the equation of the perpendicular bisector of AB is $y = 3x - 4$. [3]
\item A circle passing through A and B has its centre on the line $x = 3$. Find the centre of the circle and hence find the radius and equation of the circle. [4]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C1 2010 Q11 [12]}}