| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Simultaneous equations |
| Type | Line intersecting general conic |
| Difficulty | Standard +0.3 This is a standard C1 simultaneous equations question combining a parabola and line. Part (a) is trivial substitution, part (b) is routine algebraic manipulation to solve the system, and part (c) requires showing perpendicular gradients using coordinate geometry—all textbook techniques with no novel insight required. Slightly above average only due to the multi-step nature and the geometric verification in part (c). |
| Spec | 1.02c Simultaneous equations: two variables by elimination and substitution1.02q Use intersection points: of graphs to solve equations |
\includegraphics{figure_1}
Figure 1 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 Q5 [11]}}