| Exam Board | Edexcel |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Session | Specimen |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Network Flows |
| Type | Find missing flow values |
| Difficulty | Easy -1.2 This is a straightforward application of flow conservation at nodes to find missing values, followed by basic max-flow verification. Part (a) requires only arithmetic using the conservation principle (flow in = flow out), and part (b) asks for inspection rather than applying an algorithm like Ford-Fulkerson. This is simpler than average A-level questions as it tests basic understanding rather than problem-solving. |
| Spec | 7.04a Shortest path: Dijkstra's algorithm7.04b Minimum spanning tree: Prim's and Kruskal's algorithms |
1.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{899a26d1-7599-4051-b1cf-596542624997-2_730_1534_285_264}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}
Figure 1 shows a directed, capacitated network where the number on each arc is its capacity. A possible flow is shown from $S$ to $T$ and the value in brackets on each arc is the flow in that arc.
\begin{enumerate}[label=(\alph*)]
\item Find the values of $x , y$, and $z$.\\
(3)
\item Find, by inspection, the maximal flow from $S$ to $T$ and verify that it is maximal.\\
(2)
\end{enumerate}
\hfill \mbox{\textit{Edexcel D2 Q1 [5]}}