| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2012 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Route Inspection |
| Type | Effect of adding/removing edge |
| Difficulty | Standard +0.3 This is a straightforward application of the route inspection algorithm with a standard follow-up about adding an edge. Part (a) requires identifying odd vertices, pairing them optimally, and stating repeated arcs—routine D1 procedure. Part (b) asks students to recognize that adding BF creates new odd vertices and compare the new pairing cost, requiring only basic algorithmic understanding without novel insight. |
| Spec | 7.04e Route inspection: Chinese postman, pairing odd nodes |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(BD + EF = 10 + 17 = 27\) | M1 A1 | Three pairings of their four odd nodes; one row correct including pairing and total |
| \(BE + DF = 15 + 10 = 25\) ← | A1 | Two rows correct including pairing and total |
| \(BF + DE = 20 + 14 = 34\) | A1 | Three rows correct including pairing and total |
| Repeat arcs BC, CE and DF | A1ft | Their smallest repeated arcs (accept BCE) |
| Length of route \(= 129 + 25 = 154\) | B1ft | \(129 +\) their least out of a choice of at least two possible, distinct, pairings |
| 6 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| We add BF(12) to the network so only have to repeat DE (14) | M1 | DE identified, using/repeating \(12 +\) their DE [ft from (a)] |
| Length of route is therefore \(129 + 12 + 14 = 155\) | A1 | CAO, conclusion, numerical argument e.g. ref to 155 or 26 etc. |
| \(155 > 154\) so his route would be increased | ||
| 2 |
# Question 2:
## Part (a):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $BD + EF = 10 + 17 = 27$ | M1 A1 | Three pairings of their four odd nodes; one row correct including pairing and total |
| $BE + DF = 15 + 10 = 25$ ← | A1 | Two rows correct including pairing and total |
| $BF + DE = 20 + 14 = 34$ | A1 | Three rows correct including pairing and total |
| Repeat arcs BC, CE and DF | A1ft | Their smallest repeated arcs (accept BCE) |
| Length of route $= 129 + 25 = 154$ | B1ft | $129 +$ their least out of a choice of at least two possible, distinct, pairings |
| | **6** | |
## Part (b):
| Answer/Working | Marks | Guidance |
|---|---|---|
| We add BF(12) to the network so only have to repeat DE (14) | M1 | DE identified, using/repeating $12 +$ their DE [ft from (a)] |
| Length of route is therefore $129 + 12 + 14 = 155$ | A1 | CAO, conclusion, numerical argument e.g. ref to 155 or 26 etc. |
| $155 > 154$ so his route would be increased | | |
| | **2** | |
---2.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{e02c4a9a-d2ab-489f-b838-9b4d902c4457-3_650_1357_260_354}
\captionsetup{labelformat=empty}
\caption{Figure 2\\[0pt]
[The weight of the network is 129 miles]}
\end{center}
\end{figure}
Figure 2 models a network of canals. The number on each arc gives the length, in miles, of that canal.
Brett needs to travel along each canal to check that it is in good repair. He wishes 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.
A canal between B and F , of length 12 miles, is to be opened and needs to be included in Brett's inspection route.
\item Determine if the addition of this canal will increase or decrease the length of Brett's minimum route. You must make your reasoning clear.
\end{enumerate}
\hfill \mbox{\textit{Edexcel D1 2012 Q2 [8]}}