Edexcel D1 2003 November — Question 1 4 marks

Exam BoardEdexcel
ModuleD1 (Decision Mathematics 1)
Year2003
SessionNovember
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicRoute Inspection
TypeDouble traversal (both sides of street)
DifficultyModerate -0.8 This is easier than a standard route inspection problem because requiring double traversal of every edge eliminates the need to identify odd vertices and find pairings. Students simply need to recognize that doubling all edges makes every vertex even (thus Eulerian), then sum twice the total edge weights. It's primarily conceptual understanding with straightforward arithmetic.
Spec7.04e Route inspection: Chinese postman, pairing odd nodes

1. \begin{figure}[h]
\captionsetup{labelformat=empty} \caption{Figure 1} \includegraphics[alt={},max width=\textwidth]{75ea31c7-11e7-4dd9-9312-4cf32bba622b-02_992_1292_477_342}
\end{figure} A local council is responsible for maintaining pavements in a district. The roads for which it is responsible are represented by arcs in Fig. 1.The junctions are labelled \(A , B , C , \ldots , G\). The number on each arc represents the length of that road in km. The council has received a number of complaints about the condition of the pavements. In order to inspect the pavements, a council employee needs to walk along each road twice (once on each side of the road) starting and ending at the council offices at \(C\). The length of the route is to be minimal. Ignore the widths of the roads.
  1. Explain how this situation differs from the standard Route Inspection problem.
  2. Find a route of minimum length and state its length.

1.

\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Figure 1}
  \includegraphics[alt={},max width=\textwidth]{75ea31c7-11e7-4dd9-9312-4cf32bba622b-02_992_1292_477_342}
\end{center}
\end{figure}

A local council is responsible for maintaining pavements in a district. The roads for which it is responsible are represented by arcs in Fig. 1.The junctions are labelled $A , B , C , \ldots , G$. The number on each arc represents the length of that road in km.

The council has received a number of complaints about the condition of the pavements. In order to inspect the pavements, a council employee needs to walk along each road twice (once on each side of the road) starting and ending at the council offices at $C$. The length of the route is to be minimal. Ignore the widths of the roads.
\begin{enumerate}[label=(\alph*)]
\item Explain how this situation differs from the standard Route Inspection problem.
\item Find a route of minimum length and state its length.
\end{enumerate}

\hfill \mbox{\textit{Edexcel D1 2003 Q1 [4]}}