Unit 4: Investing and networking

10 dot points across 10 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

Topic 1: Loans, investments and annuities - how do regular contributions build, and regular withdrawals draw down, an invested balance?

Model an annuity investment (regular deposits earning compound interest) and an annuity that pays a regular income (drawing down a lump sum) using first-order recurrence relations, compute the future value of contributions and the duration a payout annuity lasts, and apply this to superannuation

A focused answer to the QCE General Mathematics Unit 4 dot point on annuities and superannuation. Covers annuity investments with regular deposits, payout annuities that draw down a balance, the future-value recurrence, working out how long a payout lasts, and superannuation applications, with arithmetic-verified worked examples for IA3 and the external assessment.

6 min answer →

Topic 3: Networks and decision mathematics - how do we allocate workers to tasks at the least total cost?

Represent an allocation as a bipartite graph or a cost matrix, solve a small assignment problem to minimise total cost or time using the Hungarian algorithm, handle maximisation by converting it to a minimisation, and interpret the optimal allocation

A focused answer to the QCE General Mathematics Unit 4 dot point on assignment problems. Covers modelling an allocation as a bipartite graph or cost matrix, the Hungarian algorithm steps for minimising total cost or time, converting maximisation problems, and interpreting the optimal one-to-one allocation, with arithmetic-verified worked examples for IA3 and the external assessment.

6 min answer →

Topic 1: Loans, investments and annuities - how do we fairly compare two financial products with different compounding periods?

Distinguish nominal and effective annual interest rates, calculate the effective annual rate for a given nominal rate and compounding frequency, and use the effective rate to compare investments or loans that compound at different frequencies

A focused answer to the QCE General Mathematics Unit 4 dot point on comparing financial products. Covers nominal versus effective annual interest rates, the effective rate formula, why compounding frequency changes the true return, and using the effective rate to compare loans and investments fairly, with arithmetic-verified worked examples for IA3 and the external assessment.

6 min answer →

Topic 3: Networks and decision mathematics - how do we schedule a project and find the shortest time to complete it?

Represent a project as an activity network with durations and dependencies, perform forward and backward scanning to find earliest and latest start times, identify the critical path and minimum completion time, and calculate float for non-critical activities

A focused answer to the QCE General Mathematics Unit 4 dot point on critical path analysis. Covers building an activity network, forward and backward scanning for earliest and latest start times, finding the critical path and minimum completion time, and calculating float for non-critical activities, with arithmetic-verified worked examples for IA3 and the external assessment.

6 min answer →

Topic 3: Networks and decision mathematics - how much can flow from a source to a sink through a capacitated network?

Model a flow problem on a directed network with edge capacities, find the maximum flow from source to sink by inspection, identify cuts and their capacities, and use the maximum-flow minimum-cut theorem to confirm the maximum flow

A focused answer to the QCE General Mathematics Unit 4 dot point on flow networks. Covers modelling flow on a directed capacitated network, finding maximum flow by inspection, defining a cut and its capacity, and the maximum-flow minimum-cut theorem to confirm the answer, with arithmetic-verified worked examples for IA3 and the external assessment.

6 min answer →

Topic 2: Graphs and networks - how do we represent and analyse connections using vertices and edges?

Represent a situation as a graph or network using vertices and edges, determine the degree of vertices and verify the handshaking result, classify graphs as connected, simple, complete, bipartite or planar, apply Euler's formula, and identify Eulerian and Hamiltonian trails and circuits

A focused answer to the QCE General Mathematics Unit 4 dot point on graphs and networks. Covers vertices, edges and degree, the handshaking lemma, types of graphs, Euler's formula for planar graphs, and Eulerian versus Hamiltonian trails and circuits, with arithmetic-verified worked examples for IA3 and the external assessment.

6 min answer →

Topic 1: Loans, investments and annuities - how do we model financial situations with recurrence relations and amortisation?

Model compound interest investments, reducing-balance loans and annuities using first-order recurrence relations, compute future value, repayment and balance using technology, build and interpret an amortisation table, and analyse the effect of changing the rate, repayment or compounding period

A focused answer to the QCE General Mathematics Unit 4 dot point on loans, investments and annuities. Covers compound interest, reducing-balance loans, annuities and recurrence modelling, amortisation tables, and the effect of changing rate or repayment, with arithmetic-verified worked examples for IA3 and the external assessment.

6 min answer →

Topic 3: Networks and decision mathematics - how do we connect every vertex of a network at the least total cost?

Define a tree and a spanning tree, identify the minimum spanning tree of a weighted connected graph using Prim's algorithm, calculate its total weight, and apply minimum spanning trees to minimum connector problems such as cabling or pipelines

A focused answer to the QCE General Mathematics Unit 4 dot point on minimum spanning trees. Covers trees and spanning trees, Prim's algorithm for finding the minimum spanning tree of a weighted graph, calculating total weight, and applying minimum connector problems to real cabling and pipeline contexts, with arithmetic-verified worked examples for IA3 and the external assessment.

6 min answer →

Topic 3: Networks and decision mathematics - how do we optimise connection, travel, flow and scheduling on a network?

Find minimum spanning trees using Prim's algorithm, determine shortest paths through a weighted network, calculate maximum flow using the maximum-flow minimum-cut idea, and schedule a project using critical path analysis to find the earliest completion time and float

A focused answer to the QCE General Mathematics Unit 4 dot point on networks and decision mathematics. Covers minimum spanning trees with Prim's algorithm, shortest paths, maximum flow and minimum cut, and critical path analysis with earliest and latest times and float, with arithmetic-verified worked examples for IA3 and the external assessment.

6 min answer →

Topic 3: Networks and decision mathematics - how do we find the cheapest or quickest route between two points in a network?

Find the shortest path between two vertices in a weighted network by inspection and by systematic labelling, distinguish the shortest path from the minimum spanning tree, and apply shortest-path methods to travel-time and cost problems

A focused answer to the QCE General Mathematics Unit 4 dot point on shortest paths. Covers finding the shortest route between two vertices in a weighted network by inspection and systematic labelling, how the shortest path differs from a minimum spanning tree, and travel-time and cost applications, with arithmetic-verified worked examples for IA3 and the external assessment.

6 min answer →