VCE General Maths Networks and Decision Mathematics 2021 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: 12
Reading time: 3 minutes
Writing time: 18 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 - 2021 - Exam 2
Maggie's house has five rooms, A, B, C, D and E, and eight doors.
The floor plan of these rooms and doors is shown below. The outside area, F, is shown shaded on the floor plan.
The floor plan is represented by the graph below.
On this graph, vertices represent the rooms and the outside area. Edges represent direct access to the rooms through the doors.
One edge is missing from the graph.
a. On the graph above, draw the missing edge. 1 mark
(Answer on the graph above.)
b. What is the degree of vertex E? 1 mark
c. Maggie hires a cleaner to clean the house.
It is possible for the cleaner to enter the house from the outside area, F, and walk through each room only once, cleaning each room as he goes and finishing in the outside area, F.
i. Complete the following to show one possible route that the cleaner could take. 1 mark
F – – – – – F
ii. What is the mathematical term for such a journey? 1 mark
George lives in Town G and Maggie lives in Town M.
The diagram below shows the network of main roads between Town G and Town M.
The vertices G, H, I, J, K, L, M, N and O represent towns.
The edges represent the main roads. The numbers on the edges indicate the distances, in kilometres, between adjacent towns.
a. What is the shortest distance, in kilometres, between Town G and Town M? 1 mark
b. George plans to travel to Maggie's house. He will pass through all the towns shown above.
George plans to take the shortest route possible.
Which town will George pass through twice? 1 mark
The network diagram below shows the local road network of Town M.
The numbers on the edges indicate the maximum number of vehicles per hour that can travel along each road in this network.
The arrows represent the permitted direction of travel.
The vertices A, B, C, D, E and F represent the intersections of the roads.
a. Determine the maximum number of vehicles that can travel from the entrance to the exit per hour. 1 mark
b. The local council plans to increase the number of vehicles per hour that can travel from the entrance to the exit by increasing the capacity of only one road.
i. Complete the following sentence by filling in the boxes provided. 1 mark
The road that should have its capacity increased is the road from vertex to vertex .
ii. What should be the minimum capacity of this road to maximise the flow of vehicles from the entrance to the exit? 1 mark
Roadworks planned by the local council require 13 activities to be completed.
The network below shows these 13 activities and their completion times in weeks.
a. What is the earliest start time, in weeks, of activity K? 1 mark
b. How many of these activities have zero float time? 1 mark
c. It is possible to reduce the completion time for activities A, E, F, L and K.
The reduction in completion time for each of these five activities will incur an additional cost.
The table below shows the five activities that can have their completion time reduced and the associated weekly cost, in dollars.
| Activity | Weekly cost ($) |
|---|---|
| A | 140 000 |
| E | 100 000 |
| F | 100 000 |
| L | 120 000 |
| K | 80 000 |
The completion time for each of these five activities can be reduced by a maximum of two weeks.
The overall completion time for the roadworks can be reduced to 16 weeks.
What is the minimum cost, in dollars, of this change in completion time? 1 mark
End of Question and Answer Book
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