Networks | HSC Standard 2

Assessment evidence

What these examples cover

These examples show assessable skills, not an official HSC topic weighting or prediction. The 2024 NSW syllabuses have their first HSC examination in 2027; students sitting the 2026 HSC continue under the applicable 2017 syllabus.

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Teacher verification note: check the mathematics, notation, permitted technology and syllabus fit for your cohort before classroom or assessment use.

3 deterministic examples

Networks questions with worked solutions

Each question is generated from an existing curriq QDSL archetype at a fixed seed. Marks and catalog content mappings travel with the generated question.

Worked example 1

2 marksstd2-n2-2

Unique shortest route Four candidate routes connect

A

H

. Route ABEFH contains an edge of weight

x

and has a further 27 minutes of travel.

Candidate route times
Route	Time excluding x (minutes)	Complete fixed time (minutes)
ACEGH	not applicable	37
ABEGH	not applicable	35
ABDFH	not applicable	36
ABEFH	27	x plus the fixed time

Part a · 2 marks

If ABEFH must be the unique shortest route, find the largest whole-number value of $x$ .

Worked solution

Answer: 7

Shortest Path: 35
Integer Inequality: 7

Catalog reference: std2_bar25_unique_shortest_path_weight · seed 41001

Worked example 2

4 marksstd2-n3-1

Project scheduling The activity table gives predecessors and completion times. A proposed activity

J

must follow

F

and finish before

I

begins.

Activity schedule
Activity	Predecessor	Duration (days)
A	Start	27
B	Start	9
F	B	3
C	B	15
G	A	18
I	C F G	24

Part a · 1 mark

Find the minimum project completion time.

Worked solution

Answer: 69

Critical Path Forward Pass: 69

Part b · 1 mark

Find the latest start time of activity $C$ .

Worked solution

Answer: 30

Latest Start Time: 30

Part c · 2 marks

Find the maximum duration of $J$ without delaying the project.

Worked solution

Answer: 33

Precedence Window: [12,45]
Activity Duration: 33

Catalog reference: std2_kil25_project_schedule_new_activity · seed 41001

Worked example 3

1 markstd2-n3-2

Capacity of a cut The table lists the directed edges that cross Cut 1 from the source side to the sink side.

Edges crossing Cut 1
Edge	Capacity
A to D	4
B to E	5
C to F	7

Part a · 1 mark

Find the capacity of Cut 1.

Worked solution

Answer: 16

Cut Capacity: 16

Catalog reference: std2_sgs25_flow_cut_capacity · seed 41001

Content mapping and common errors

Networks content identifiers

MS-N2

Network Concepts

Identify and use network terminology; apply networks to solve problems involving shortest paths and minimum spanning trees.

Common student mistakes

·Confusing weighted and unweighted shortest-path algorithms
·Not checking that a minimum spanning tree includes all vertices

MS-N3

Critical Path Analysis

Use critical path analysis to schedule tasks and determine the minimum time to complete a project.

Common student mistakes

·Forgetting to compute the float time for non-critical activities
·Misidentifying the critical path when two paths have equal length

Source and methodology

Examples are deterministic curriq catalog generations from existing QDSL archetypes at the published fixed seed. The generator copies only student-facing prompts, mark allocations, topic mappings, display tables or options, checked answers and marking-path results into this resource.

Review the official NSW Curriculum source ↗

From the blog

Practice

HSC Maths Past Papers by Topic

Outcomes

NESA Outcome Codes Explained

Assessment

How to Write an HSC Maths Assessment Task

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What these examples cover

Networks questions with worked solutions

Worked example 1

Worked example 2

Worked example 3

Networks content identifiers

Network Concepts

Critical Path Analysis

Source and methodology

Other Standard 2 topics

From the blog

Generate a Networks worksheet in 30 seconds