VCE General Maths Networks and Decision Mathematics 2019 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 - 2019 - Exam 2
Fencedale High School has six buildings. The network below shows these buildings represented by vertices. The edges of the network represent the paths between the buildings.
a. Which building in the school can be reached directly from all other buildings? 1 mark
b. A school tour is to start and finish at the office, visiting each building only once.
i. What is the mathematical term for this route? 1 mark
ii. Draw in a possible route for this school tour on the diagram below. 1 mark
Fencedale High School offers students a choice of four sports, football, tennis, athletics and basketball.
The bipartite graph below illustrates the sports that each student can play.
Each student will be allocated to only one sport.
a. Complete the table below by allocating the appropriate sport to each student. 1 mark
| Student | Sport |
|---|---|
| Blake | |
| Charli | |
| Huan | |
| Marco |
b. The school medley relay team consists of four students, Anita, Imani, Jordan and Lola.
The medley relay race is a combination of four different sprinting distances: 100 m, 200 m, 300 m and 400 m, run in that order.
The following table shows the best time, in seconds, for each student for each sprinting distance.
| Student | Best time for each sprinting distance (seconds) | |||
|---|---|---|---|---|
| 100 m | 200 m | 300 m | 400 m | |
| Anita | 13.3 | 29.6 | 61.8 | 87.1 |
| Imani | 14.5 | 29.6 | 63.5 | 88.9 |
| Jordan | 13.3 | 29.3 | 63.6 | 89.1 |
| Lola | 15.2 | 29.2 | 61.6 | 87.9 |
The school will allocate each student to one sprinting distance in order to minimise the total time taken to complete the race.
To which distance should each student be allocated?
Write your answers in the table below. 2 marks
| Student | Sprinting distance (m) |
|---|---|
| Anita | |
| Imani | |
| Jordan | |
| Lola |
Fencedale High School is planning to renovate its gymnasium.
This project involves 12 activities, \(A\) to \(L\).
The directed network below shows these activities and their completion times, in weeks.
The minimum completion time for the project is 35 weeks.
a. How many activities are on the critical path? 1 mark
b. Determine the latest start time of activity \(E\). 1 mark
c. Which activity has the longest float time? 1 mark
It is possible to reduce the completion time for activities \(C\), \(D\), \(G\), \(H\) and \(K\) by employing more workers.
d. The completion time for each of these five activities can be reduced by a maximum of two weeks.
What is the minimum time, in weeks, that the renovation project could take? 1 mark
e. The reduction in completion time for each of these five activities will incur an additional cost to the school.
The table below shows the five activities that can have their completion times reduced and the associated weekly cost, in dollars.
| Activity | Weekly cost ($) |
|---|---|
| \(C\) | 3000 |
| \(D\) | 2000 |
| \(G\) | 2500 |
| \(H\) | 1000 |
| \(K\) | 4000 |
The completion time for each of these five activities can be reduced by a maximum of two weeks.
Fencedale High School requires the overall completion time for the renovation project to be reduced by four weeks at minimum cost.
Complete the table below, showing the reductions in individual activity completion times that would achieve this. 2 marks
| Activity | Reduction in completion time (0, 1 or 2 weeks) |
|---|---|
| \(C\) | |
| \(D\) | |
| \(G\) | |
| \(H\) | |
| \(K\) |
End of Question and Answer Book
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