Edexcel D1 2003 June — Question 2 6 marks

Exam BoardEdexcel
ModuleD1 (Decision Mathematics 1)
Year2003
SessionJune
Marks6
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicRoute Inspection
TypeFind parameter values from route length
DifficultyModerate -0.3 Part (a) is a standard proof recall question about the handshaking lemma (sum of degrees is even, so odd vertices come in pairs). Part (b) requires understanding that the route inspection solution adds the shortest pairing of odd vertices to the total edge weight, but the calculation is straightforward once the concept is grasped. This is a typical D1 textbook exercise with minimal problem-solving demand.
Spec7.02a Graphs: vertices (nodes) and arcs (edges)7.04e Route inspection: Chinese postman, pairing odd nodes

  1. Explain why it is impossible to draw a network with exactly three odd vertices. [2]
\includegraphics{figure_1} The Route Inspection problem is solved for the network in Fig. 1 and the length of the route is found to be 100.
  1. Determine the value of \(x\), showing your working clearly. [4]

\begin{enumerate}[label=(\alph*)]
\item Explain why it is impossible to draw a network with exactly three odd vertices.
[2]
\end{enumerate}

\includegraphics{figure_1}

The Route Inspection problem is solved for the network in Fig. 1 and the length of the route is found to be 100.

\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Determine the value of $x$, showing your working clearly.
[4]
\end{enumerate}

\hfill \mbox{\textit{Edexcel D1 2003 Q2 [6]}}