Edexcel F1 2016 June — Question 2 5 marks

Exam BoardEdexcel
ModuleF1 (Further Pure Mathematics 1)
Year2016
SessionJune
Marks5
PaperDownload PDF ↗
TopicConic sections
TypeParabola area calculations
DifficultyStandard +0.8 This is a multi-step Further Maths question requiring knowledge of parabola properties (focus, directrix), coordinate geometry, and area calculations. Part (a) is straightforward recall, but part (b) requires setting up coordinates from the geometric constraints, finding intersection points, and computing the triangle area—more demanding than standard A-level but routine for FM students who know parabola theory.
Spec1.03g Parametric equations: of curves and conversion to cartesian

2. A parabola \(P\) has cartesian equation \(y ^ { 2 } = 28 x\). The point \(S\) is the focus of the parabola \(P\).
  1. Write down the coordinates of the point \(S\). 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.
  2. Find the exact area of triangle \(A B S\).
    VILM SIHI NITIIIUMI ON OC
    VILV SIHI NI III HM ION OC
    VALV SIHI NI JIIIM ION OO \includegraphics[max width=\textwidth, alt={}, center]{0b7ef4a1-51bf-4f0c-908a-7caf26a144dc-05_2264_53_315_36}

2. A parabola $P$ has cartesian equation $y ^ { 2 } = 28 x$. The point $S$ is the focus of the parabola $P$.
\begin{enumerate}[label=(\alph*)]
\item Write down the coordinates of the point $S$.

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.
\item Find the exact area of triangle $A B S$.\\

VILM SIHI NITIIIUMI ON OC\\
VILV SIHI NI III HM ION OC\\
VALV SIHI NI JIIIM ION OO

\includegraphics[max width=\textwidth, alt={}, center]{0b7ef4a1-51bf-4f0c-908a-7caf26a144dc-05_2264_53_315_36}
\end{enumerate}

\hfill \mbox{\textit{Edexcel F1 2016 Q2 [5]}}