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Edexcel A-Level Mathematics AS D1.2.1 Minimum Spanning Tree Questions

Practise finding minimum spanning trees from networks or matrices, stating selected arcs, total weight and conditions for changed arc weights.

Syllabus
First assessment 2019
Course
Mathematics YMA01
Level
AS

Exam points

  • use Prim’s algorithm from the stated vertex and record the order of chosen arcs
  • state the MST weight from selected arcs, a matrix, or a shortest path through all vertices
  • find conditions on x so a changed arc keeps the same unique minimum spanning tree

Edexcel A-Level Mathematics AS D1.2.1 Minimum Spanning Tree Questions question 1

[Maximum number: 2]
Figure 2

Figure 2

Figure 2 models a network of tracks between nine ranger stations, A, B, C, D, E, F, G, H and J, in a forest. The number on each edge gives the time, in minutes, to travel along the corresponding track. The forest ranger wishes to travel from A to J as quickly as possible.

Figure for Question Edexcel A-Level Mathematics AS D1.2.1 Minimum Spanning Tree Questions question 1 — Edexcel A-Level Mathematics AS

Shortest time to travel from A to J:
Quickest route from A to J:

Hence determine the weight of the minimum spanning tree for the network given in Figure 2. Give a reason for your answer.

You do not need to find the minimum spanning tree.

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