VCE General Maths Networks and Decision Mathematics 2020 Exam 2 Mini Test
VCAA General Maths Exam 2
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: 15
Reading time: 4 minutes
Writing time: 22 minutes
Instructions
• Answer all questions in the spaces provided.
• Write your responses in English.
• In all questions where a numerical answer is required, you should only round your answer when instructed to do so.
• Unless otherwise indicated, the diagrams in this book are not drawn to scale.
Networks and decision mathematics - 2020 - Exam 2
The Sunny Coast Cricket Club has five new players join its team: Alex, Bo, Cameron, Dale and Emerson.
The graph below shows the players who have played cricket together before joining the team.
For example, the edge between Alex and Bo shows that they have previously played cricket together.
a. How many of these players had Emerson played cricket with before joining the team? 1 mark
b. Who had played cricket with both Alex and Bo before joining the team? 1 mark
c. During the season, another new player, Finn, joined the team.
Finn had not played cricket with any of these players before.
Represent this information on the graph above. 1 mark
A cricket team has 11 players who are each assigned to a batting position.
Three of the new players, Alex, Bo and Cameron, can bat in position 1, 2 or 3.
The table below shows the average scores, in runs, for each player for the batting positions 1, 2 and 3.
| Batting position | ||||
|---|---|---|---|---|
| 1 | 2 | 3 | ||
| Player | Alex | 22 | 24 | 24 |
| Bo | 25 | 25 | 21 | |
| Cameron | 24 | 25 | 19 | |
Each player will be assigned to one batting position.
To which position should each player be assigned to maximise the team’s score? Write your answer in the table below.
| Player | Batting position |
| Alex | |
| Bo | |
| Cameron |
A local fitness park has 10 exercise stations: \(M\) to \(V\).
The edges on the graph below represent the tracks between the exercise stations.
The number on each edge represents the length, in kilometres, of each track.
The Sunny Coast cricket coach designs three different training programs, all starting at exercise station S.
| Training program number |
Training details |
|---|---|
| 1 | The team must run to exercise station O. |
| 2 | The team must run along all tracks just once. |
| 3 | The team must visit each exercise station and return to exercise station S. |
a. What is the shortest distance, in kilometres, covered in training program 1? 1 mark
b. i. What mathematical term is used to describe training program 2? 1 mark
ii. At which exercise station would training program 2 finish? 1 mark
c. To complete training program 3 in the minimum distance, one track will need to be repeated.
Complete the following sentence by filling in the boxes provided. 1 mark
This track is between exercise station and exercise station .
Training program 1 has the cricket team starting from exercise station S and running to exercise station O.
For safety reasons, the cricket coach has placed a restriction on the maximum number of people who can use the tracks in the fitness park.
The directed graph below shows the capacity of the tracks, in number of people per minute.
a. How many different routes from S to O are possible? 1 mark
When considering the possible flow of people through this network, many different cuts can be made.
b. Determine the capacity of Cut 1, shown above. 1 mark
c. What is the maximum flow from S to O, in number of people per minute? 1 mark
The Sunny Coast cricket clubroom is undergoing a major works project.
This project involves nine activities: A to I.
The table below shows the earliest start time (EST) and duration, in months, for each activity.
The immediate predecessor(s) is also shown.
The duration for activity C is missing.
| Activity | EST | Duration | Immediate predecessor(s) |
|---|---|---|---|
| A | 0 | 2 | – |
| B | 0 | 5 | – |
| C | 5 | A, B | |
| D | 7 | 7 | C |
| E | 7 | 9 | C |
| F | 5 | 3 | B |
| G | 14 | 4 | D |
| H | 8 | 9 | F |
| I | 18 | 2 | E, G, H |
The information in the table above can be used to complete a directed network.
This network will require a dummy activity.
a. Complete the following sentence by filling in the boxes provided. 1 mark
This dummy activity could be drawn as a directed edge from the end of activity to the start of activity
b. What is the duration, in months, of activity C? 1 mark
c. Name the four activities that have a float time. 1 mark
d. The project is to be crashed by reducing the completion time of one activity only.
What is the minimum time, in months, that the project can be completed in? 1 mark
End of Question and Answer Book
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