CleverPath

Networks, Paths and Trees

We estimate MS1-11-NP is worth about 2 marks out of 100 under the new Mathematics Standard 1 syllabus. Practise 4 exam-style questions (multiple choice, numerical answer) with instant marking and a worked solution for every question.

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Topic notes

Network terminology (vertices, edges, degree, weighted and directed networks, paths, cycles, trees), drawing networks from tables and maps, minimum spanning trees with Kruskal's and Prim's methods, and shortest paths, with worked examples.

  1. 1What you need to know
  2. 2Network concepts
  3. 3Paths, cycles and trees
  4. 4Minimum spanning trees
  5. 5Shortest paths
  6. 6Common mistakes
  7. 7Exam tips
  8. 8Links to other topics
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Example questions

Example 1 · 1 mark · multiple choice

A connected network has five vertices with degrees 3, 3, 2, 2 and 4. How many edges does the network have?

  1. A7
  2. B14
  3. C5
  4. D9

Example 2 · 1 mark · multiple choice

A network has vertices A, B, C, D and E. The weighted edges are:

EdgeWeight
A–B4
A–C7
B–C3
B–D6
C–D5
C–E8
D–E4

What is the total weight of a minimum spanning tree?

  1. A16
  2. B11
  3. C17
  4. D37

Answers and worked solutions appear when you practise these questions.

Other Mathematics Standard 1 topics