Mathematics Standard • Year 12 • Module 6 • Lesson 3
Drawing Activity Networks — Past-Paper Style
Practise HSC Mathematics Standard 2-style writing on AOA networks: drawing, dummy placement, event numbering and one structured response.
1. Short-answer questions
1.1 Draw the AOA network for A(3, —), B(4, A), C(2, A), D(5, B and C). Number every event and state whether a dummy is needed. 3 marks Band 3
1.2 A network has activities P, Q, R, S. P has no predecessor. Q and R both need P. S needs only Q. Draw the AOA network, number events and state how many dummies are needed (if any). In one sentence, explain your choice. 3 marks Band 3-4
1.3 The precedence table is A(2, —), B(3, —), C(4, A), D(2, A and B), E(3, C and D).
(a) Draw the AOA network with events numbered.
(b) State how many dummies appear in your network and explain in one sentence why each is needed. 4 marks Band 4
2. Extended response
2.1 A small construction project is described by the precedence table below (days):
Site clear SC(2, —)
Plumbing rough PR(3, SC)
Electrical rough ER(2, SC)
Wall frame WF(4, PR and ER)
Roof RF(3, ER)
Drywall DW(5, WF)
Painting PT(3, DW and RF)
(a) Draw the AOA network with every event numbered.
(b) State how many events and how many dummies your network uses, and explain in one or two sentences where each dummy goes.
(c) A student claims "ER could be drawn from SC's end event with no dummy because WF needs both PR and ER." Explain in one or two sentences why a dummy is still needed and where it must go in the canonical AOA drawing. 7 marks Band 5-6
Explicit marking criteria
Part (a) — 3 marks
• 1 mark — start activity SC drawn from event 1; PR and ER both leaving SC's end event.
• 1 mark — WF correctly fed by both PR and ER (via a dummy if needed); RF leaving ER's end event separately.
• 1 mark — DW, PT placed correctly so PT merges DW and RF at one event; events numbered so all arrows go from lower to higher.
Part (b) — 2 marks
• 1 mark — correct count of events.
• 1 mark — correct count of dummies AND placement described (or shown).
Part (c) — 2 marks
• 1 mark — clear statement that ER has TWO successors (WF and RF), so it must end at a unique event before being routed.
• 1 mark — explanation of where the dummy goes (from PR's end event to ER's end event so WF can start from a single merge event while RF continues from ER alone, OR vice versa).
Your response:
Stuck on (c)? ER feeds two different successors (WF and RF). RF needs ONLY ER, while WF needs both ER AND PR. The dummy separates these partial dependencies.How did this worksheet feel?
What I'll revisit before next class:
1.1 — Simple 4-activity AOA (3 marks)
Sample response. 1 → A → 2; 2 → B → 3; 2 → C → 4; dummy 3 → 4; 4 → D → 5. Dummy needed: yes, because B and C both leave event 2 and D needs both to converge; without the dummy, B and C would share both start (2) and end events, breaking the unique-event rule.
Marking notes. 1 mark — events numbered 1-5 (or equivalent) and all arrows forward. 1 mark — dummy correctly placed between B's end event and C's end event. 1 mark — one-line reason naming the unique-event rule. A "no dummy" answer that has B and C share both end events scores 0/3.
1.2 — Partial dependency (3 marks)
Sample response. 1 → P → 2; 2 → Q → 3; 2 → R → 4; 3 → S → 5. Zero dummies needed. S only depends on Q, so it leaves Q's end event (3) directly. R has nowhere else to go in this network — its end event (4) is a finish event. Q and R do not share both start and end events.
Marking notes. 1 mark — Q and R correctly drawn from event 2 to different end events. 1 mark — S drawn from Q's end event only. 1 mark — "no dummies" with a one-sentence reason. Common error: adding a redundant dummy from R to Q's end event because the student thinks Q and R must converge — they don't, because nothing in the table requires them to.
1.3 — Two start activities and a partial dependency (4 marks)
(a) Sample response. 1 → A → 3; 2 → B → 4; 3 → C → 5; dummy 3 → 4; 4 → D → 5; 5 → E → 6.
(b) Sample response. One dummy, from event 3 to event 4. It is needed because D depends on both A and B, but C only depends on A; the dummy lets D wait for A and B at event 4 while C leaves event 3 independently.
Marking notes. (a) 1 mark — start activities A and B drawn from separate events; 1 mark — partial-dependency dummy placed correctly; 1 mark — events numbered so arrows go forward. (b) 1 mark — dummy count and reason. A response that merges A and B at one event before C/D scores 0 on the partial-dependency mark because C would then incorrectly depend on B too.
2.1 — Construction project (7 marks): sample Band-6 response with annotations
Sample Band-6 response.
(a) AOA drawing.
1 → SC → 2
2 → PR → 3
2 → ER → 4
dummy 3 → 4 (so WF starts where both PR and ER have arrived)
4 → WF → 5
4 → RF → 6 (RF needs ER only; ER's end event is 4)
5 → DW → 7
dummy 6 → 7 (so PT can wait for both DW and RF at one event)
7 → PT → 8
[1 mark — start + PR/ER from SC; 1 mark — WF correctly fed by both with dummy; 1 mark — DW, PT placed and events numbered forward.]
(b) Counts.
Events = 8. Dummies = 2. [1 mark — event count.]
Dummy 1: event 3 → event 4 (merges PR with ER so WF can leave one event). Dummy 2: event 6 → event 7 (merges RF with DW so PT can leave one event). [1 mark — dummy count and placement described.]
(c) Why a dummy is still needed.
ER has two different successors: WF (which also needs PR) and RF (which needs ER only). If WF were drawn directly from event 2 (where ER and PR both start), it would also need a way to wait for PR; if PR and ER both ended at the same event, the unique-event rule would be broken. [1 mark — recognises ER's two successors create the conflict.]
The dummy from PR's end event (3) to ER's end event (4) lets WF start from event 4 having waited for both, while RF also leaves event 4 needing only ER. Without the dummy, you cannot distinguish "needs both PR and ER" (WF) from "needs ER only" (RF). [1 mark — explains placement and the partial-dependency reason.]
Total: 7/7.
Band descriptors for marker.
Band 3: Draws a network that is structurally close but misses the partial-dependency dummy for ER/RF; events numbered. ≈ 3 marks.
Band 4: Correct AOA with both dummies but no explanation of why the second one is needed for PT. ≈ 5 marks.
Band 5: Correct AOA, counts correct, but (c) only restates the unique-event rule without explicitly explaining the WF vs RF partial dependency. ≈ 6 marks.
Band 6: Complete — correct AOA with both dummies, accurate counts, AND (c) explicitly distinguishes ER's two successors and explains the dummy's placement in those terms. 7/7.