| Exam Board | Edexcel |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2010 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Conic sections |
| Type | Parabola focus and directrix properties |
| Difficulty | Standard +0.3 This is a straightforward application of standard parabola properties (focus, directrix) from FP1. Part (a) requires recalling that y²=4ax has focus at (a,0), giving a=3. Part (b) involves finding coordinates using the focus-directrix definition and calculating distances. While it requires multiple steps and understanding of parabola geometry, it's a standard textbook exercise with no novel insight required, making it slightly easier than average overall. |
| Spec | 1.03g Parametric equations: of curves and conversion to cartesian |
| Answer | Marks | Guidance |
|---|---|---|
| \((3, 0)\) | B1 (1) | cao |
| Answer | Marks | Guidance |
|---|---|---|
| \(P\): \(x = \dfrac{1}{3}\) \(\Rightarrow\) \(y = 2\) | B1 | Both B marks can be implied by correct diagram with lengths labelled or coordinates of vertices stated |
| \(A\) and \(B\) lie on \(x = -3\) | B1 | |
| \(PB = PS\) or a correct method to find both \(PB\) and \(PS\) | M1 | Second M1 for their four values added together |
| Perimeter \(= 6 + 2 + 3\dfrac{1}{3} + 3\dfrac{1}{3} = 14\dfrac{2}{3}\) | M1 A1 (5) | \(14\dfrac{2}{3}\) or awrt 14.7 for final A1 |
## Question 4:
**(a)**
$(3, 0)$ | B1 (1) | cao
**(b)**
$P$: $x = \dfrac{1}{3}$ $\Rightarrow$ $y = 2$ | B1 | Both B marks can be implied by correct diagram with lengths labelled or coordinates of vertices stated
$A$ and $B$ lie on $x = -3$ | B1 |
$PB = PS$ or a correct method to find both $PB$ and $PS$ | M1 | Second M1 for their four values added together
Perimeter $= 6 + 2 + 3\dfrac{1}{3} + 3\dfrac{1}{3} = 14\dfrac{2}{3}$ | M1 A1 (5) | $14\dfrac{2}{3}$ or awrt 14.7 for final A1
---4.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{cfad960a-f56a-4471-b4ad-92ab670d8121-05_791_874_265_518}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}
Figure 1 shows a sketch of part of the parabola with equation $y ^ { 2 } = 12 x$.\\
The point $P$ on the parabola has $x$-coordinate $\frac { 1 } { 3 }$.\\
The point $S$ is the focus of the parabola.
\begin{enumerate}[label=(\alph*)]
\item Write down the coordinates of $S$.
The points $A$ and $B$ lie on the directrix of the parabola.\\
The point $A$ is on the $x$-axis and the $y$-coordinate of $B$ is positive.
Given that $A B P S$ is a trapezium,
\item calculate the perimeter of $A B P S$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP1 2010 Q4 [6]}}