| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Session | Specimen |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Conic sections |
| Type | Parabola focus and directrix properties |
| Difficulty | Standard +0.3 This is a straightforward Further Maths parabola question requiring knowledge of the standard form y²=4ax and basic coordinate geometry. Part (a) uses symmetry (trivial), part (b) substitutes into the equation (routine), and part (c) finds a line through two points (standard). While it's Further Maths content, the question involves only direct application of definitions with no problem-solving insight required, making it slightly easier than an average A-level question overall. |
| Spec | 1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.03g Parametric equations: of curves and conversion to cartesian |
3.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{fa5a23b5-d52c-4bae-97c7-2eb7220a3dc4-04_736_659_299_660}
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\caption{Figure 1}
\end{center}
\end{figure}
Figure 1 shows a sketch of the parabola $C$ with equation $y ^ { 2 } = 8 x$.\\
The point $P$ lies on $C$, where $y > 0$, and the point $Q$ lies on $C$, where $y < 0$ The line segment $P Q$ is parallel to the $y$-axis.
Given that the distance $P Q$ is 12 ,
\begin{enumerate}[label=(\alph*)]
\item write down the $y$ coordinate of $P$,
\item find the $x$ coordinate of $P$.
Figure 1 shows the point $S$ which is the focus of $C$.
The line $l$ passes through the point $P$ and the point $S$.
\item Find an equation for $l$ in the form $a x + b y + c = 0$, where $a$, $b$ and $c$ are integers.
\end{enumerate}
\hfill \mbox{\textit{Edexcel F1 Q3 [7]}}