Mathematics Standard • Year 12 • Module 6 • Lesson 2
Activity Networks and Precedence Tables — Past-Paper Style
Practise HSC Mathematics Standard 2-style writing on precedence tables: building tables, identifying parallel work, and one structured response on table verification and project structure.
1. Short-answer questions
1.1 A project has activities P(3), Q(5), R(4), S(2). P first. Q and R both need P. S needs Q and R. Write the precedence table in (activity, duration, immediate predecessors) format and state the start and finish activities. 3 marks Band 3
1.2 A student writes the precedence table A(4, —), B(3, A), C(2, A and B). State which entry is incorrect and rewrite the table so it lists only immediate predecessors. Explain in one sentence why listing all ancestors creates problems when drawing the activity network. 3 marks Band 3-4
1.3 A project has table A(4, —), B(3, A), C(2, A), D(5, B), E(1, C), F(3, D and E), G(2, B and E).
(a) Identify all start activities and all finish activities.
(b) Identify one pair of activities that can run strictly in parallel (same predecessors, independent of each other).
(c) Explain in one or two sentences whether F and G can ever start at exactly the same time. 4 marks Band 4
2. Extended response
2.1 A construction firm describes a small commercial fit-out (days):
Site clear SC(3, —)
Permit lodge PL(2, —)
Foundation FN(5, SC and PL)
Frame FR(7, FN)
Mechanical ME(4, FR)
Electrical EL(3, FR)
Plumbing PB(4, FR)
Inspection IN(1, ME and EL and PB)
(a) Identify all start and finish activities, and identify which activities can run strictly in parallel after Frame (FR) finishes.
(b) A student writes "EL(3, FN and FR)" instead of "EL(3, FR)". Identify the rule that has been broken and give the cleaned-up entry.
(c) The firm proposes adding a new activity Safety audit SA(2, —) that has no predecessor and is not a predecessor of anything. State whether this is allowed in a valid project network, and explain in one sentence what this implies about start and finish activities. 7 marks Band 5-6
Explicit marking criteria
Part (a) — 3 marks
• 1 mark — all start activities correctly identified (SC and PL).
• 1 mark — finish activity correctly identified (IN).
• 1 mark — the strict parallel set after FR named (ME, EL, PB).
Part (b) — 2 marks
• 1 mark — names the rule (only immediate predecessors / no redundant ancestors).
• 1 mark — cleaned entry EL(3, FR).
Part (c) — 2 marks
• 1 mark — states that SA is allowed (it is both a start activity and a finish activity).
• 1 mark — clear sentence explaining that a project network can have any number of start and finish activities (here, SA is both at once and is structurally disconnected from the rest of the project).
Your response:
Stuck on (c)? Ask: does the table forbid an activity from being both a start activity (no predecessor) AND a finish activity (no successor)?How did this worksheet feel?
What I'll revisit before next class:
1.1 — Build a PQRS table (3 marks)
Sample response. Table: P(3, —), Q(5, P), R(4, P), S(2, Q and R). Start activity: P. Finish activity: S.
Marking notes. 1 mark — Q and R rows correct. 1 mark — S row correct (both Q and R listed). 1 mark — start and finish named. A response with only the table and no start/finish loses 1 mark.
1.2 — Redundant ancestor (3 marks)
Sample response. The incorrect entry is C(2, A and B). B already has A as its predecessor, so listing A again under C is redundant. Cleaned table: A(4, —), B(3, A), C(2, B). Listing all ancestors creates a problem when drawing the network because it would add an unnecessary direct arrow A → C, falsely suggesting C only needs A to finish (not A then B).
Marking notes. 1 mark — identifies the C row as incorrect. 1 mark — cleaned entry. 1 mark — one-sentence reason about extra arrows / wrong dependency. Answers that "fix" by removing B (incorrect) score 1/3.
1.3 — Read the table and analyse parallelism (4 marks)
(a) Sample response. Start activity: A. Finish activities: F and G (neither appears as a predecessor of any other activity).
(b) Sample response. Strict parallel pair: B and C — both have A as their only predecessor and are independent of each other.
(c) Sample response. F waits on D and E; G waits on B and E. They are not strict parallel activities (different predecessor sets), but they could start at the same time if D finishes at the same moment as B (so both F and G are ready to start together as soon as E also finishes). In general it depends on durations.
Marking notes. (a) 1 mark — both start and finish named. (b) 1 mark — B and C as the parallel pair. (c) 1 mark — recognises they share predecessor E but differ on the other; 1 mark — clear sentence about when they could/could not start together. A bare "no" or "yes" without reasoning scores 0 on (c).
2.1 — Commercial fit-out (7 marks): sample Band-6 response with annotations
Sample Band-6 response.
(a) Start, finish and parallelism.
Start activities: SC and PL (both have — in the predecessor column). [1 mark.]
Finish activity: IN (no activity has IN as a predecessor). [1 mark.]
Strictly parallel after FR: ME, EL and PB — all three share the single predecessor FR and none depends on the others. [1 mark.]
(b) Redundant predecessor fix.
The rule broken is "list only the immediate predecessors". FN is already in EL's chain (FN → FR → EL), so listing FN under EL is a redundant ancestor. [1 mark — rule named.]
Cleaned entry: EL(3, FR). [1 mark — entry corrected.]
(c) Standalone activity SA.
SA is a valid activity. With no predecessor it is a start activity, and with no successor it is also a finish activity. [1 mark — SA is allowed.]
This shows that a project network can have any number of start activities and any number of finish activities; an activity can even be both at once if it is disconnected from the rest of the work. The minimum project time is then taken as the maximum of every path-sum across the whole network, including SA's standalone "path" of duration 2. [1 mark — clear sentence on the structural implication.]
Total: 7/7.
Band descriptors for marker.
Band 3: Identifies one start activity and the finish activity; lists 1-2 of the parallel three; no useful answer on (b) or (c). ≈ 3 marks.
Band 4: All of (a) correct; (b) entry corrected but the rule not named (or vice versa); no clear answer on (c). ≈ 5 marks.
Band 5: (a) and (b) complete with the rule named; (c) says SA is allowed but only gives "it has no predecessor" without the broader structural point about start/finish multiplicity. ≈ 6 marks.
Band 6: All three parts complete with explicit naming of rules in (b) and a clear sentence in (c) that a network can have multiple start/finish activities (and SA is both). 7/7.