| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | Simultaneous equations |
| Type | Line intersecting general conic |
| Difficulty | Standard +0.3 This is a straightforward C1 question requiring basic coordinate geometry skills: finding axis intercepts, solving simultaneous equations by substitution, and verifying perpendicularity using gradients. While part (c) requires calculating two gradients and showing their product is -1, all techniques are standard and the algebra is manageable with 6 marks allocated for the main solving step. |
| Spec | 1.02c Simultaneous equations: two variables by elimination and substitution1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.03d Circles: equation (x-a)^2+(y-b)^2=r^21.10g Problem solving with vectors: in geometry |
\includegraphics{figure_2}
Figure 2 shows the curve with equation $y^2 = 4(x - 2)$ and the line with equation $2x - 3y = 12$.
The curve crosses the $x$-axis at the point $A$, and the line intersects the curve at the points $P$ and $Q$.
\begin{enumerate}[label=(\alph*)]
\item Write down the coordinates of $A$. [1]
\item Find, using algebra, the coordinates of $P$ and $Q$. [6]
\item Show that $\angle PAQ$ is a right angle. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q37 [11]}}