| Exam Board | Edexcel |
|---|---|
| Module | FP3 (Further Pure Mathematics 3) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Conic sections |
| Type | Ellipse focus-directrix properties |
| Difficulty | Moderate -0.8 This is a straightforward recall question on standard ellipse properties. Students need only identify a=4, b=3, apply the formula e=√(1-b²/a²)=√7/4, and state foci at (±√7, 0). While it's Further Maths content, it requires no problem-solving or insight—just direct application of memorized formulas, making it easier than average A-level questions. |
| Spec | 4.09a Polar coordinates: convert to/from cartesian4.09b Sketch polar curves: r = f(theta) |
An ellipse has equation $\frac{x^2}{16} + \frac{y^2}{9} = 1$.
\begin{enumerate}[label=(\alph*)]
\item Sketch the ellipse. [1]
\item Find the value of the eccentricity $e$. [2]
\item State the coordinates of the foci of the ellipse. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP3 Q1 [5]}}