VCE General Maths Networks and Decision Mathematics 2017 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 - 2017
Module 2 – Networks and decision mathematics
Question 1Which one of the following graphs contains a loop?
Two graphs, labelled Graph 1 and Graph 2, are shown below.
The sum of the degrees of the vertices of Graph 1 is
- A. two less than the sum of the degrees of the vertices of Graph 2.
- B. one less than the sum of the degrees of the vertices of Graph 2.
- C. equal to the sum of the degrees of the vertices of Graph 2.
- D. one more than the sum of the degrees of the vertices of Graph 2.
- E. two more than the sum of the degrees of the vertices of Graph 2.
Consider the following graph.
The adjacency matrix for this graph, with some elements missing, is shown below.
\( \begin{array}{c@{}c} & \begin{array}{@{}cccc@{}} W & X & Y & Z \end{array} \\ \begin{matrix} W \\ X \\ Y \\ Z \end{matrix} & \left[ \begin{array}{@{}cccc@{}} 1 & - & - & - \\ - & 0 & - & - \\ - & - & 0 & - \\ - & - & - & 1 \end{array} \right] \end{array} \)
This adjacency matrix contains 16 elements when complete.
Of the 12 missing elements
- A. eight are '1' and four are '2'.
- B. four are '1' and eight are '2'.
- C. six are '1' and six are '2'.
- D. two are '0', six are '1' and four are '2'.
- E. four are '0', four are '1' and four are '2'.
Use the following information to answer Questions 4 and 5.
The directed graph below shows the sequence of activities required to complete a project.
The time to complete each activity, in hours, is also shown.
The earliest starting time, in hours, for activity \(N\) is
- A. 3
- B. 10
- C. 11
- D. 12
- E. 13
To complete the project in minimum time, some activities cannot be delayed.
The number of activities that cannot be delayed is
- A. 2
- B. 3
- C. 4
- D. 5
- E. 6
An Eulerian trail for the graph above will be possible if only one edge is removed.
In how many different ways could this be done?
- A. 1
- B. 2
- C. 3
- D. 4
- E. 5
A graph with six vertices has no loops or multiple edges.
Which one of the following statements about this graph is not true?
- A. If the graph is a tree it has five edges.
- B. If the graph is complete it has 15 edges.
- C. If the graph has eight edges it may have an isolated vertex.
- D. If the graph is bipartite it will have a minimum of nine edges.
- E. If the graph has a cycle it will have a minimum of three edges.
The flow of oil through a series of pipelines, in litres per minute, is shown in the network below.
The weightings of three of the edges are labelled \(x\).
Five cuts labelled A–E are shown on the network.
The maximum flow of oil from the source to the sink, in litres per minute, is given by the capacity of
- A. Cut A if \(x = 1\)
- B. Cut B if \(x = 2\)
- C. Cut C if \(x = 2\)
- D. Cut D if \(x = 3\)
- E. Cut E if \(x = 3\)
End of Multiple-Choice Question Book
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