VCE General Maths Networks and Decision Mathematics 2021 Exam 1 Mini Test
VCAA General Maths Exam 1
This is the full VCE General Maths Exam with worked solutions. You can also try Mini-Tests, which are official VCAA exams split into short tests you can do anytime.
Number of marks: 8
Reading time: 3 minutes
Writing time: 18 minutes
Instructions
• Answer all questions in pencil on your Multiple-Choice Answer Sheet.
• Choose the response that is correct for the question.
• A correct answer scores 1; an incorrect answer scores 0.
• Marks will not be deducted for incorrect answers.
• No marks will be given if more than one answer is completed for any question.
• Unless otherwise indicated, the diagrams in this book are not drawn to scale.
Networks and decision mathematics - 2021
Module 2 – Networks and decision mathematics
Question 1Consider the graph below.
The number of vertices with a degree of 3 is
- A. 1
- B. 2
- C. 3
- D. 4
- E. 5
Five friends ate fruit for morning tea. The bipartite graph below shows which types of fruit each friend ate.
Which one of the following statements is not true?
- A. Only Lee ate pear.
- B. Eric and Kai each ate apple.
- C. Van ate only strawberry.
- D. Quinn and Kai each ate banana.
- E. Orange was the most eaten type of fruit.
Consider the graph below.
The number of faces is
- A. 2
- B. 3
- C. 4
- D. 5
- E. 6
Consider the directed network below.
The number of vertices that cannot be reached from \(X\) is
- A. 1
- B. 2
- C. 3
- D. 4
- E. 5
Consider the following five statements about the graph above:
- The graph is planar.
- The graph contains a cycle.
- The graph contains a bridge.
- The graph contains an Eulerian trail.
- The graph contains a Hamiltonian path.
How many of these statements are true?
- A. 1
- B. 2
- C. 3
- D. 4
- E. 5
The directed graph below shows the sequence of activities required to complete a project. The time taken to complete each activity, in hours, is also shown.
The minimum completion time for this project is 18 hours. The time taken to complete activity \(E\) is labelled \(x\). The maximum value of \(x\) is
- A. 2
- B. 3
- C. 4
- D. 5
- E. 6
The network below shows the pathways between five buildings: \(J, K, L, M\) and \(N\).
An adjacency matrix for this network is formed. The number of zeros in this matrix is
- A. 8
- B. 9
- C. 10
- D. 11
- E. 12
A network of roads connecting towns in an alpine region is shown below. The distances between neighbouring towns, represented by the vertices, are given in kilometres.
The region receives a large snowfall, leaving all roads between the towns closed to traffic. To ensure each town is accessible by car from every other town, some roads will be cleared. The minimum total length of road, in kilometres, that needs to be cleared is
- A. 361 if \(x = 50\) and \(y = 55\)
- B. 361 if \(x = 50\) and \(y = 60\)
- C. 366 if \(x = 55\) and \(y = 55\)
- D. 366 if \(x = 55\) and \(y = 60\)
- E. 371 if \(x = 55\) and \(y = 65\)
End of Multiple-Choice Question Book
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