Edexcel D1 2017 January — Question 5 9 marks

Exam BoardEdexcel
ModuleD1 (Decision Mathematics 1)
Year2017
SessionJanuary
Marks9
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicRoute Inspection
TypeEffect of adding/removing edge
DifficultyStandard +0.3 This is a standard route inspection (Chinese Postman) problem requiring identification of odd-degree vertices and pairing them optimally, followed by a straightforward analysis of adding an edge. Part (c) requires recognizing that adding AC creates more odd vertices, increasing the route length by a predictable amount. While multi-step, it follows a well-defined algorithm with no novel insight required—slightly easier than average A-level.
Spec7.04e Route inspection: Chinese postman, pairing odd nodes

5. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{8c9bce2c-4156-4bf6-8d02-9e01d6f11948-06_897_1499_239_283} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} [The total weight of the network is 106.7]
Figure 3 models a network of cycle tracks that have to be inspected. The number on each arc represents the length, in km , of the corresponding track. Angela needs to travel along each cycle track at least once and wishes to minimise the length of her inspection route. She must start and finish at A.
  1. Use an appropriate algorithm to find the tracks that will need to be traversed twice. You should make your method and working clear.
  2. Find a route of minimum length, starting and finishing at A . State the length of your route. A new cycle track, AC, is under construction. It will be 15 km long. Angela will have to include this new track in her inspection route.
  3. State the effect this new track will have on the total length of her route. Justify your answer.

5.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{8c9bce2c-4156-4bf6-8d02-9e01d6f11948-06_897_1499_239_283}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{center}
\end{figure}

[The total weight of the network is 106.7]\\
Figure 3 models a network of cycle tracks that have to be inspected. The number on each arc represents the length, in km , of the corresponding track. Angela needs to travel along each cycle track at least once and wishes to minimise the length of her inspection route. She must start and finish at A.
\begin{enumerate}[label=(\alph*)]
\item Use an appropriate algorithm to find the tracks that will need to be traversed twice. You should make your method and working clear.
\item Find a route of minimum length, starting and finishing at A . State the length of your route.

A new cycle track, AC, is under construction. It will be 15 km long. Angela will have to include this new track in her inspection route.
\item State the effect this new track will have on the total length of her route. Justify your answer.
\end{enumerate}

\hfill \mbox{\textit{Edexcel D1 2017 Q5 [9]}}