VCE General Maths Networks and Decision Mathematics 2016 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 - 2016 - Exam 2
A map of the roads connecting five suburbs of a city, Alooma (A), Beachton (B), Campville (C), Dovenest (D) and Easyside (E), is shown below.
a. Starting at Beachton, which two suburbs can be driven to using only one road? 1 mark
A graph that represents the map of the roads is shown below.
One of the edges that connects to vertex E is missing from the graph.
b. i. Add the missing edge to the graph above. 1 mark
ii. Explain what the loop at D represents in terms of a driver who is departing from Dovenest. 1 mark
The suburb of Alooma has a skateboard park with seven ramps. The ramps are shown as vertices T, U, V, W, X, Y and Z on the graph below.
The tracks between ramps U and V and between ramps W and X are rough, as shown on the graph above.
a. Nathan begins skating at ramp W and follows an Eulerian trail. At which ramp does Nathan finish? 1 mark
b. Zoe begins skating at ramp X and follows a Hamiltonian path. The path she chooses does not include the two rough tracks. Write down a path that Zoe could take from start to finish. 1 mark
c. Birra can skate over any of the tracks, including the rough tracks. He begins skating at ramp X and will complete a Hamiltonian cycle. In how many ways could he do this? 1 mark
A new skateboard park is to be built in Beachton. This project involves 13 activities, A to M. The directed network below shows these activities and their completion times in days.
a. Determine the earliest start time for activity M. 1 mark
b. The minimum completion time for the skateboard park is 15 days. Write down the critical path for this project. 1 mark
c. Which activity has a float time of two days? 1 mark
d. The completion times for activities E, F, G, I and J can each be reduced by one day. The cost of reducing the completion time by one day for these activities is shown in the table below.
| Activity | Cost ($) |
|---|---|
| E | 3000 |
| F | 1000 |
| G | 5000 |
| I | 2000 |
| J | 4000 |
What is the minimum cost to complete the project in the shortest time possible? 1 mark
e. The skateboard park project on page 22 will be repeated at Campville, but with the addition of one extra activity. The new activity, N, will take six days to complete and has a float time of one day. Activity N will finish at the same time as the project.
i. Add activity N to the network below. 1 mark
ii. What is the latest start time for activity N? 1 mark
End of Question and Answer Book
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