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Edexcel A-Level Mathematics AS D1.3.1 Algorithm for Finding the Shortest Questions

Practise route inspection problems by pairing odd nodes, choosing repeated roads and adapting start or finish points to minimise total distance.

Syllabus
First assessment 2019
Course
Mathematics YMA01
Level
AS

Exam points

  • compare pairings of odd nodes to choose the roads traversed twice in an inspection route
  • determine the best start or finish node when an open route must still cover every road
  • calculate the minimum route length by adding repeated shortest paths to the network total

Edexcel A-Level Mathematics AS D1.3.1 Algorithm for Finding the Shortest Questions question 1

[Maximum number: 8]
Figure 2

Figure 2

[The total weight of the network is 458]

Figure 2 represents a network of roads between nine towns, A, B, C, D, E, F, G, H and J. The number on each edge represents the length, in kilometres, of the corresponding road.

Question (a)

(a)

By considering the pairings of all relevant nodes, find the length of Claude's route. State the arcs that will need to be traversed twice.

If Claude does not start the inspection route at A and finish at J, a shorter inspection route is possible.

[ 5 ]

Question (b)

(b)

Determine the two towns at which Claude should start and finish so that the route has minimum length. Give a reason for your answer and state the length of this route.

[ 3 ]
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