VCE General Maths Networks and Decision Mathematics 2022 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 - 2022
The network below shows the distances, in kilometres, along a series of roads.
The vertices \(A, B, C, D, E, F, G\) and \(H\) represent the intersections of these roads.
Prim’s algorithm can be used to find the
- A. critical path.
- B. shortest path.
- C. minimum cut.
- D. minimum allocation.
- E. minimum spanning tree.
The map below shows seven countries within Central America.
A network diagram was drawn with seven vertices to represent each of the countries on the map of Central America. Edges were drawn to represent a border shared between two countries.
The number of edges that this network has is
- A. 5
- B. 6
- C. 7
- D. 8
- E. 9
An athletics club needs to select one team of four athletes.
The team is required to have one long jump, one high jump, one shot put and one javelin competitor.
The following table shows the best distances, in metres, for each athlete for each event.
| Athlete | Long jump (m) | High jump (m) | Shot put (m) | Javelin (m) |
|---|---|---|---|---|
| Eve | 4.8 | 1.7 | 13.1 | 40.9 |
| Harsha | 4.8 | 1.6 | 13.9 | 39.5 |
| Shona | 5.1 | 1.8 | 14.4 | 41.2 |
| Taylor | 4.8 | 1.7 | 12.8 | 39.8 |
The athletics club will allocate each athlete to one event in order to maximise the total distance that the team jumps and throws.
Which allocation of athlete to event must occur in order to maximise the total distance?
- A.
long jump high jump shot put javelin Shona Harsha Eve Taylor - B.
long jump high jump shot put javelin Shona Taylor Harsha Eve - C.
long jump high jump shot put javelin Eve Harsha Taylor Shona - D.
long jump high jump shot put javelin Harsha Taylor Shona Eve - E.
long jump high jump shot put javelin Harsha Taylor Eve Shona
Consider the graph below.
The number of edges that need to be removed for this graph to be planar is
- A. 0
- B. 1
- C. 2
- D. 3
- E. 4
A connected graph consists of five vertices and four edges.
Which one of the following statements is not true?
- A. The graph could be a tree.
- B. The graph could be planar.
- C. The graph could be bipartite.
- D. The graph could contain a path.
- E. The graph could contain a cycle.
A landscaping project has 12 activities. The network below gives the time, in hours, that it takes to complete each activity.
The earliest start time, in hours, for activity \(G\) is
- A. 10
- B. 11
- C. 12
- D. 13
- E. 14
Use the following information to answer Questions 7 and 8.
A project involves 11 activities, \(A\) to \(K\).
The table below shows the earliest start time and duration, in days, for each activity.
The immediate predecessor(s) of each activity is also shown.
| Activity | Earliest start time | Duration | Immediate predecessor(s) |
|---|---|---|---|
| A | 0 | 6 | – |
| B | 0 | 7 | – |
| C | 6 | 10 | A |
| D | 6 | 7 | A |
| E | 7 | 8 | B |
| F | 15 | 2 | D, E |
| G | 15 | 2 | E |
| H | 17 | 3 | G |
| I | 20 | 6 | C, F, H |
| J | 17 | 5 | G |
| K | 26 | 2 | I, J |
A directed network for this project will require a dummy activity.
The dummy activity will be drawn from the end of
- A. activity \(A\) to the start of activity \(D\).
- B. activity \(E\) to the start of activity \(F\).
- C. activity \(F\) to the start of activity \(I\).
- D. activity \(G\) to the start of activity \(H\).
- E. activity \(I\) to the start of activity \(J\).
When this project is completed in the minimum time, the sum of all the float times, in days, will be
- A. 0
- B. 16
- C. 18
- D. 20
- E. 28
End of Multiple-Choice Question Book
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