The idea, step by step
Events are not activities
In an activity-on-arrow network, each arrow is a task and its label gives a duration. A numbered vertex is an event: it marks completion of all arrows entering it and the point from which outgoing work may start. The arrow's length on the page has no timing meaning.
Arrows must point from earlier to later events, and a valid project network has no directed cycle. A single start and finish makes the overall project easy to scan. Where a network has several incoming arrows, every one of those activities must be complete before the event is reached.
Read dependencies carefully
In the displayed network, D starts after A. E starts after both D and B; the dashed zero-duration connection records B's requirement. F starts only after C and E. C can run while D and E run, so a path is one possible chain through the project rather than a list of every activity.
To check a drawing, compare it with the original table activity by activity. Look for missing requirements and accidental extra ones. A drawing that forces independent work into a single chain gives a valid-looking picture but a different and usually slower model.
| Activity | Duration | Immediate predecessors |
|---|---|---|
| A | 4 | None |
| B | 3 | None |
| C | 5 | A |
| D | 4 | A |
| E | 2 | B and D |
| F | 3 | C and E |
A common trap
Adding every activity duration because every arrow must be completed.
Instead: Some activities run at the same time. The network records dependencies so the completion time is determined by the controlling chain, not automatically by the sum of all durations.
See the thinking
Read a start event
An event has incoming activities P and Q, lasting 4 and 7 days from the project start. Activity R leaves that event. When can R first begin?
- The event cannot be reached until both incoming activities finish.
- P finishes at day 4 and Q at day 7.
- Use the later finish, not their sum.
Check a proposed chain
A and B may start together. C follows A only. A student draws A → B → C as one chain. What dependency errors have been introduced?
- Putting B after A adds a requirement that was not stated.
- Putting C after B adds another requirement.
- The correct drawing must allow A and B to start independently and C to follow A.
Check your understanding
At event 5 of the displayed network, C and E enter and F leaves. Must both C and E finish before F starts?
Show answer
Yes.
An event is reached only after all incoming activities are complete.
Your turn
6 questions · 12 marks · Work at your own pace.
Read the questions online
- In the displayed network, give the start and finish event numbers for D.1 mark
- In the displayed network, which labelled real activities may start directly at event 1?2 marks
- A network has A: 1→2, B: 1→3 and C: 2→4. Does C require B to finish? Explain.2 marks
- A project diagram uses arrow lengths 3 cm and 8 cm for tasks of 9 days and 2 days. Is the drawing necessarily wrong?2 marks
- List the real activity sequences along the displayed start-to-finish paths, ignoring the dummy as a real task.3 marks
- Describe one check that detects an accidental extra dependency in a project network.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- In the displayed network, give the start and finish event numbers for D.1 mark
Read the tail and head of the arrow labelled D: 4.
D runs from event 2 to event 4. - In the displayed network, which labelled real activities may start directly at event 1?2 marks
Their arrows leave the project start.
A dummy is not needed for either starting task.
A and B. - A network has A: 1→2, B: 1→3 and C: 2→4. Does C require B to finish? Explain.2 marks
There is no dependency path from event 3 to event 2.
C requires the incoming work at event 2, which is A.
No. - A project diagram uses arrow lengths 3 cm and 8 cm for tasks of 9 days and 2 days. Is the drawing necessarily wrong?2 marks
Activity durations are read from their numerical labels.
Project networks are dependency diagrams, not scaled time lines.
No; arrow length does not encode duration unless a scale is explicitly stated. - List the real activity sequences along the displayed start-to-finish paths, ignoring the dummy as a real task.3 marks
Trace each directed route from event 1 to event 6.
The B route reaches event 4 through the zero-duration dummy.
A–C–F; A–D–E–F; B–E–F through the dummy connection. - Describe one check that detects an accidental extra dependency in a project network.2 marks
A valid drawing must include every stated requirement.
It must not force an activity to wait for an unrelated branch.
Compare the incoming requirements at each activity's start with its immediate predecessors in the table.
Curriculum reference & lesson scope
SACE Board of South Australia
Stage 2 General Mathematics: discrete models, project scheduling and assignment. Activity-on-arrow conventions are used for project networks; technology may verify calculations but does not replace interpreting the model.
Official curriculum source ↗