VCE General Maths Networks and Decision Mathematics 2024 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 - 2024
Consider the following graph.
The sum of the degrees of the vertices is
- A. 10
- B. 11
- C. 12
- D. 13
Consider the following graph.
A Eulerian trail through this graph could be
- A. ABCDEF
- B. ACBDCFDEF
- C. BACBDCFDEF
- D. BDCABCDFCDEF
Consider the following graph.
The number of faces is
- A. 5
- B. 6
- C. 7
- D. 8
Eight houses in an estate are to be connected to the internet via underground cables.
The network below shows the possible connections between the houses.
The vertices represent the houses.
The numbers on the edges represent the length of cable connecting pairs of houses, in metres.
The graph that represents the minimum length of cable needed to connect all the houses is
- A.
- B.
- C.
- D.
The network below represents paths through a park from the carpark to a lookout.
The vertices represent various attractions, and the numbers on the edges represent the distances between them in metres.
The shortest path from the carpark to the lookout is 34 m.
This can be achieved when
- A. \(x = 8\) and \(y = 8\)
- B. \(x = 9\) and \(y = 7\)
- C. \(x = 10\) and \(y = 6\)
- D. \(x = 11\) and \(y = 5\)
A connected graph has six vertices and six edges.
How many of the following four statements must always be true?
- the graph has no vertices of odd degree
- the graph contains a Eulerian trail
- the graph contains a Hamiltonian path
- the sum of the degrees of the vertices is 12
- A. 1
- B. 2
- C. 3
- D. 4
Anush, Blake, Carly and Dexter are workers on a construction site. They are each allocated one task.
The time, in hours, it takes for each worker to complete each task is shown in the table below.
| Task 1 | Task 2 | Task 3 | Task 4 | |
|---|---|---|---|---|
| Anush | 12 | 8 | 16 | 9 |
| Blake | 10 | 7 | 15 | 10 |
| Carly | 11 | 10 | 18 | 12 |
| Dexter | 10 | 14 | 16 | 11 |
The tasks must be completed sequentially and in numerical order: Task 1, Task 2, Task 3 and then Task 4.
Management makes an initial allocation of tasks to minimise the amount of time required, but then decides that it takes the workers too long.
Another worker, Edgar, is brought in to complete one of the tasks.
His completion times, in hours, are listed below.
| Task 1 | Task 2 | Task 3 | Task 4 | |
|---|---|---|---|---|
| Edgar | 9 | 5 | 14 | 8 |
When a new allocation is made and Edgar takes over one of the tasks, the minimum total completion time compared to the initial allocation will be reduced by
- A. 1 hour.
- B. 2 hours.
- C. 3 hours.
- D. 4 hours.
A project has 15 activities, \(A–O\), that need to be completed.
The directed network that represents this project is shown below.
The activities are not labelled.
The activity table that could represent this project is
End of Multiple-Choice Question Book
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