VCE General Maths Networks and Decision Mathematics 2018 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 - 2018
Consider the graph with five isolated vertices shown below.
To form a tree, the minimum number of edges that must be added to the graph is
- A. 1
- B. 4
- C. 5
- D. 6
- E. 10
Niko drives from his home to university.
The network below shows the distances, in kilometres, along a series of streets connecting Niko’s home to the university.
The vertices \(A, B, C, D\) and \(E\) represent the intersection of these streets.
The shortest path for Niko from his home to the university could be found using
- A. a minimum cut.
- B. Prim’s algorithm.
- C. Dijkstra’s algorithm.
- D. critical path analysis.
- E. the Hungarian algorithm.
A planar graph has five faces.
This graph could have
- A. eight vertices and eight edges.
- B. six vertices and eight edges.
- C. eight vertices and five edges.
- D. eight vertices and six edges.
- E. five vertices and eight edges.
Consider the graph below.
Which one of the following is not a path for this graph?
- A. PRQTS
- B. PQRTS
- C. PRTSQ
- D. PTQSR
- E. PTRQS
The directed network below shows the sequence of 11 activities that are needed to complete a project.
The time, in weeks, that it takes to complete each activity is also shown.
How many of these activities could be delayed without affecting the minimum completion time of the project?
- A. 3
- B. 4
- C. 5
- D. 6
- E. 7
Which one of the following graphs is not a planar graph?
A project requires nine activities (A–I) to be completed. The duration, in hours, and the immediate predecessor(s) of each activity are shown in the table below.
| Activity | Duration (hours) | Immediate predecessor(s) |
|---|---|---|
| A | 4 | – |
| B | 3 | A |
| C | 7 | A |
| D | 2 | A |
| E | 5 | B |
| F | 2 | C |
| G | 4 | E, F |
| H | 5 | D |
| I | 3 | G, H |
The minimum completion time for this project, in hours, is
- A. 14
- B. 19
- C. 20
- D. 24
- E. 35
Annie, Buddhi, Chuck and Dorothy work in a factory.
Today each worker will complete one of four tasks, 1, 2, 3 and 4.
The usual completion times for Annie, Chuck and Dorothy are shown in the table below.
| Task 1 | Task 2 | Task 3 | Task 4 | |
|---|---|---|---|---|
| Annie | 7 | 3 | 8 | 2 |
| Buddhi | \(k\) | \(k\) | 3 | \(k\) |
| Chuck | 5 | 6 | 9 | 2 |
| Dorothy | 4 | 8 | 5 | 3 |
Buddhi takes 3 minutes for Task 3.
He takes \(k\) minutes for each other task.
Today the factory supervisor allocates the tasks as follows:
- Task 1 to Dorothy
- Task 2 to Annie
- Task 3 to Buddhi
- Task 4 to Chuck
This allocation will achieve the minimum total completion time if the value of \(k\) is at least
- A. 0
- B. 1
- C. 2
- D. 3
- E. 4
End of Multiple-Choice Question Book
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