| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2018 |
| Session | Specimen |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Conic sections |
| Type | Parabola area calculations |
| Difficulty | Standard +0.8 This is a Further Maths question requiring knowledge of parabola focus-directrix properties, coordinate geometry to find intersection points, and area calculation. Part (a) is routine recall, but part (b) requires multiple steps: identifying the line position, solving a quadratic to find A and B coordinates, and computing the triangle area. The conceptual demand is moderate for FM students, but the multi-step nature and need to synthesize parabola properties elevates it slightly above average A-level difficulty. |
| Spec | 1.03d Circles: equation (x-a)^2+(y-b)^2=r^21.03g Parametric equations: of curves and conversion to cartesian1.08d Evaluate definite integrals: between limits1.08e Area between curve and x-axis: using definite integrals |
\begin{enumerate}
\item A parabola $P$ has cartesian equation $y ^ { 2 } = 28 x$. The point $S$ is the focus of the parabola $P$.\\
(a) Write down the coordinates of the point $S$.
\end{enumerate}
Points $A$ and $B$ lie on the parabola $P$. The line $A B$ is parallel to the directrix of $P$ and cuts the $x$-axis at the midpoint of $O S$, where $O$ is the origin.\\
(b) Find the exact area of triangle $A B S$.\\
\hfill \mbox{\textit{Edexcel F1 2018 Q2 [5]}}