VCE General Maths Networks and Decision Mathematics 2020 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: 10
Reading time: 4 minutes
Writing time: 22 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 - 2020
A connected planar graph has seven vertices and nine edges.
The number of faces that this graph will have is
- A. 1
- B. 2
- C. 3
- D. 4
- E. 5
Consider the graph below.
Which one of the following is not a Hamiltonian cycle for this graph?
- A. ABCDFEGA
- B. BAGEFDCB
- C. CDFEGABC
- D. DCBAGFED
- E. EGABCDFE
Which one of the following is not a spanning tree for the network above?
The directed graph below represents a series of one-way streets. The vertices represent the intersections of these streets.
The number of vertices that can be reached from \(S\) is
- A. 1
- B. 2
- C. 3
- D. 4
- E. 5
The network below shows the distances, in metres, between camp sites at a camping ground that has electricity. The vertices \(A\) to \(I\) represent the camp sites.
The minimum length of cable required to connect all the camp sites is 53 m.
The value of \(x\), in metres, is at least
- A. 5
- B. 6
- C. 8
- D. 9
- E. 11
The activity network below shows the sequence of activities required to complete a project. The number next to each activity in the network is the time it takes to complete that activity, in days.
The minimum completion time for this project, in days, is
- A. 18
- B. 19
- C. 20
- D. 21
- E. 22
Four friends go to an ice-cream shop.
Akiro chooses chocolate and strawberry ice cream.
Doris chooses chocolate and vanilla ice cream.
Gohar chooses vanilla ice cream.
Imani chooses vanilla and lemon ice cream.
This information could be presented as a graph.
Consider the following four statements:
- The graph would be connected.
- The graph would be bipartite.
- The graph would be planar.
- The graph would be a tree.
How many of these four statements are true?
- A. 0
- B. 1
- C. 2
- D. 3
- E. 4
The adjacency matrix below shows the number of pathway connections between four landmarks: \(J, K, L\) and \(M\).
\[ \begin{array}{c} \begin{array}{cccc} J & K & L & M \end{array} \\ \begin{bmatrix} 1 & 3 & 0 & 2 \\ 3 & 0 & 1 & 2 \\ 0 & 1 & 0 & 2 \\ 2 & 2 & 2 & 0 \end{bmatrix} \end{array} \begin{matrix} J \\ K \\ L \\ M \end{matrix} \]
A network of pathways that could be represented by the adjacency matrix is
The flow of liquid through a series of pipelines, in litres per minute, is shown in the directed network below.
Five cuts labelled A to E are shown on the network.
The number of these cuts with a capacity equal to the maximum flow of liquid from the source to the sink, in litres per minute, is
- A. 1
- B. 2
- C. 3
- D. 4
- E. 5
The directed network below shows the sequence of activities, \(A\) to \(I\), that is required to complete an office renovation. The time taken to complete each activity, in weeks, is also shown.
The project manager would like to complete the office renovation in less time. The project manager asks all the workers assigned to activity \(H\) to also work on activity \(F\). This will reduce the completion time of activity \(F\) to three weeks. The workers assigned to activity \(H\) cannot work on both activity \(H\) and activity \(F\) at the same time. No other activity times will be changed.
This change to the network will result in a change to the completion time of the office renovation. Which one of the following is correct?
- A. The completion time will be reduced by one week if activity \(F\) is completed before activity \(H\) is started.
- B. The completion time will be reduced by three weeks if activity \(F\) is completed before activity \(H\) is started.
- C. The completion time will be reduced by one week if activity \(H\) is completed before activity \(F\) is started.
- D. The completion time will be reduced by three weeks if activity \(H\) is completed before activity \(F\) is started.
- E. The completion time will be increased by three weeks if activity \(H\) is completed before activity \(F\) is started.
End of Multiple-Choice Question Book
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