| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2009 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Route Inspection |
| Type | Optimal starting/finishing vertices |
| Difficulty | Standard +0.3 This is a standard route inspection algorithm question with a straightforward extension. Part (a) requires identifying odd vertices, pairing them optimally, and adding repeated arcs—a routine D1 procedure. Part (b) asks about optimal finishing vertex when starting point is fixed, requiring recognition that removing one edge from the odd-degree pairing minimizes the route. Both parts follow textbook methods with no novel insight required, making this slightly easier than average. |
| Spec | 7.04e Route inspection: Chinese postman, pairing odd nodes |
| Answer | Marks | Guidance |
|---|---|---|
| Answer: \(CD + EG = 45 + 38 = 83\); \(CE + DG = 39 + 43 = 82\) ←; \(CG + DE = 65 + 35 = 100\); Repeat CE and DG; Length \(625 + 82 = 707\) (m) | M1 1A1; 2A1; 3A1; 4A1ft | (6) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer: DE (or 35) is the smallest. So finish at C. New route \(625 + 35 = 660\) (m) | M1; A1ft; A1ft=1B1 | (3) |
**Part (a)**
Answer: $CD + EG = 45 + 38 = 83$; $CE + DG = 39 + 43 = 82$ ←; $CG + DE = 65 + 35 = 100$; Repeat CE and DG; Length $625 + 82 = 707$ (m) | M1 1A1; 2A1; 3A1; 4A1ft | (6) | 1M1: Three pairings of their four odd nodes. 1A1: one row correct. 2A1: two rows correct. 3A1: three rows correct. 4A1ft: ft their least, but must be the correct shortest route arcs on network. (condone DG). 5A1ft: $625$ + their least = a number. Condone lack of m.
**Part (b)**
Answer: DE (or 35) is the **smallest**. So finish at C. New route $625 + 35 = 660$ (m) | M1; A1ft; A1ft=1B1 | (3) | 1M1: Identifies their shortest from a choice of at least 2 rows. 1A1ft: ft from their least or indicates C. 2A1ft = 1Bft: correct for their least. (Indept of M mark).
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\begin{figure}[h]
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\includegraphics[alt={},max width=\textwidth]{c1482d20-7bce-46cb-9ac8-c659ecad30de-5_940_1419_262_322}
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\caption{Figure 3}
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[The total weight of the network is 625 m ]\\
Figure 3 models a network of paths in a park. The number on each arc represents the length, in m , of that path.\\
Rob needs to travel along each path to inspect the surface. He wants to minimise the length of his route.
\begin{enumerate}[label=(\alph*)]
\item Use the route inspection algorithm to find the length of his route. State the arcs that should be repeated. You should make your method and working clear.\\
(6)
The surface on each path is to be renewed. A machine will be hired to do this task and driven along each path.\\
The machine will be delivered to point G and will start from there, but it may be collected from any point once the task is complete.
\item Given that each path must be traversed at least once, determine the finishing point so that the length of the route is minimised. Give a reason for your answer and state the length of your route.\\
(3)
\end{enumerate}
\hfill \mbox{\textit{Edexcel D1 2009 Q5 [9]}}