← Maths Standard 2 syllabus

NSWMaths Standard 2

Year 12: Networks

5 dot points across 5 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

What is the critical path in a project network, and how does it determine the minimum project duration?

Construct an activity network from a precedence table, identify the critical path and find the minimum project duration
A focused answer to the HSC Maths Standard 2 dot point on critical path analysis. Building an activity network from a precedence table, identifying paths through the network, and determining the minimum project duration via the critical (longest) path with worked Australian construction examples.
8 min answer →

How do forward and backward scanning give the earliest and latest start times of each activity, and how is float calculated?

Perform forward and backward scanning to find earliest start, latest start, earliest finish, latest finish times and float for each activity
A focused answer to the HSC Maths Standard 2 dot point on forward and backward scanning. Computing earliest start, latest start, earliest finish, latest finish and float for each activity in a project network, with worked Australian construction and renovation examples.
9 min answer →

What is a minimum spanning tree, and how is it found using Prim's or Kruskal's algorithm?

Find a minimum spanning tree for a weighted graph using Prim's or Kruskal's algorithm
A focused answer to the HSC Maths Standard 2 dot point on minimum spanning trees. Definition of a spanning tree and minimum spanning tree, step-by-step Prim's and Kruskal's algorithms, and worked examples for utility networks and rural Australian infrastructure planning.
8 min answer →

What are the basic terms and components of a network, and how are real-world systems represented as graphs?

Use network terminology including vertex, edge, weight, degree, path, cycle and directed graph to describe and analyse networks
A focused answer to the HSC Maths Standard 2 dot point on network terminology. Vertices, edges, weights, directed and undirected graphs, paths and cycles, connected and disconnected components, and worked Australian examples for transport networks and project schedules.
7 min answer →

How is the shortest path between two vertices in a weighted network found?

Find the shortest path between two vertices in a weighted network by inspection or by systematic labelling
A focused answer to the HSC Maths Standard 2 dot point on shortest paths. Inspection method for small networks, systematic labelling for larger ones, and worked examples for road network distances and Sydney transport routes.
7 min answer →