| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2003 |
| Session | January |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Route Inspection |
| Type | Route inspection with parameter |
| Difficulty | Standard +0.3 This is a standard route inspection (Chinese Postman) problem with straightforward application of the algorithm. Part (a) requires identifying odd vertices, parts (b)-(c) involve comparing path lengths with a parameter, and part (d) applies the standard formula. While it requires understanding of the algorithm and some algebraic manipulation with the parameter x, it follows a well-defined procedure with no novel insights needed, making it slightly easier than average. |
| Spec | 7.04e Route inspection: Chinese postman, pairing odd nodes |
\includegraphics{figure_2}
The arcs in Fig. 2 represent roads in a town. The weight on each arc gives the time, in minutes, taken to drive along that road. The times taken to drive along $AB$ and $DE$ vary depending upon the time of day.
A police officer wishes to drive along each road at least once, starting and finishing at $A$. The journey is to be completed in the least time.
\begin{enumerate}[label=(\alph*)]
\item Briefly explain how you know that a route between $B$ and $E$ will have to be repeated.
[1]
\item List the possible routes between $B$ and $E$. State how long each would take, in terms of $x$ where appropriate.
[2]
\item Find the range of values that $x$ must satisfy so that $DE$ would be one of the repeated arcs.
[3]
Given that $x = 7$,
\item find the total time needed for the police officer to carry out this journey.
[3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel D1 2003 Q4 [9]}}