| Exam Board | AQA |
|---|---|
| Module | Further Paper 3 Discrete (Further Paper 3 Discrete) |
| Year | 2020 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Topic | Graph Theory Fundamentals |
| Type | Eulerian classification |
| Difficulty | Moderate -0.5 This question tests basic graph theory definitions: counting faces using Euler's formula and identifying a fundamental error in Eulerian path criteria (should be odd degree, not even). While it's Further Maths content, it requires only direct application of standard definitions with no problem-solving or proof, making it easier than average A-level questions overall. |
| Spec | 7.02g Eulerian graphs: vertex degrees and traversability7.02m Euler's formula: V + R = E + 2 |
5 The planar graph $P$ is shown below.\\
\includegraphics[max width=\textwidth, alt={}, center]{c297a67f-65fd-47e0-a60c-d38fd86c6081-08_410_406_360_817}
5
\begin{enumerate}[label=(\alph*)]
\item Determine the number of faces of $P$.\\
5
\item Akwasi claims that $P$ is semi-Eulerian as it is connected and it has exactly two vertices with even degree.
Comment on the validity of Akwasi's claim.\\
\includegraphics[max width=\textwidth, alt={}, center]{c297a67f-65fd-47e0-a60c-d38fd86c6081-09_2488_1716_219_153}
\end{enumerate}
\hfill \mbox{\textit{AQA Further Paper 3 Discrete 2020 Q5 [4]}}