General Mathematics syllabus, dot point by dot point

Fit a least-squares line y = mx + c to bivariate numerical data using technology and using m = r(s_y / s_x) and c = y-bar - m x-bar, interpret the slope and y-intercept in context, distinguish between interpolation and extrapolation, use the line to make predictions, and recognise and explain the potential dangers of extrapolation

Topic 2: Bivariate data analysis 2 - how do we model a linear relationship and use it to make predictions?

Calculate residuals for a least-squares line, construct a residual plot, and use it to assess the appropriateness of fitting a linear model to the data

Topic 2: Bivariate data analysis 2 - how do we use residuals and a residual plot to judge whether a straight line is the right model?

Construct and describe time series plots (trend, seasonality and irregular fluctuations), smooth a series with a simple moving mean or median for an odd number of data, deseasonalise using seasonal indices found by the average percentage method, and fit a least-squares line to model the long-term trend

Topic 3: Time series analysis - how do we describe patterns over time and smooth out short-term fluctuation?

Use arithmetic sequences to model straight-line depreciation and geometric sequences to model diminishing-value depreciation, with recursion, tables, graphs and the nth-term rules, and solve practical problems involving the value of an asset over time

Topic 4: Growth and decay in sequences - how do we model the loss in value of an asset over time with arithmetic and geometric sequences?

Use recursion to generate arithmetic and geometric sequences, display their terms in tabular and graphical form, use the rules t(n) = t(1) + (n - 1)d and t(n) = t(1)r^(n - 1), and model and analyse practical situations involving linear and geometric growth and decay, such as simple interest, taxi fares and population growth (use of logarithms not required)

Topic 4: Growth and decay in sequences - how do we model quantities that change by a constant amount or a constant ratio?

Understand great circles and angles of latitude and longitude, locate and state positions on Earth's surface, and calculate angular distance and distance between two places on the same meridian (D = 111.2 x angular distance) or the same parallel of latitude (D = 111.2 cos θ x angular distance)

Topic 5: Earth geometry and time zones - how do we locate points on the Earth and measure distances along its surface?

Understand the meaning of Greenwich Mean Time (GMT), the International Date Line and Coordinated Universal Time (UTC), understand the link between longitude and time, determine the number of degrees of longitude for a given time difference, calculate time differences between two places on Earth, and solve practical problems involving time zones, making allowances for daylight saving where necessary

Topic 5: Earth geometry and time zones - how do we relate longitude to local time and work out time differences between places?

Recognise and explain that an observed association between two variables does not necessarily mean there is a causal relationship, identify and communicate non-causal explanations including coincidence or the influence of another variable, and solve practical problems involving associations

Why does an observed association between two variables not necessarily mean that one causes the other, and how do we identify and communicate non-causal explanations when solving practical problems?

Understand bivariate data, construct two-way frequency tables with row and column sums and percentages, and use an appropriately percentaged table to identify and describe an association between two categorical variables in context

How do we use a two-way frequency table and percentages to decide whether two categorical variables are associated?

Deseasonalise a time series by calculating seasonal indices using the average percentage method, fit a least-squares line to model the long-term trend, and solve practical problems that involve forecasting with time series data

How do we calculate seasonal indices with the average percentage method, deseasonalise a time series, fit a least-squares trend line and use it to forecast?

Apply a square, logarithmic or reciprocal transformation to one variable to linearise a non-linear association, fit a least-squares line to the transformed data, use the transformed equation to predict, and choose the transformation that best straightens the scatter

Extension (not in the 2025 syllabus) - how do we straighten a curved relationship so a least-squares line can be fitted?

Calculate the effective annual rate of interest using i(effective) = (1 + i)^k - 1, and use the results to compare interest on loans or investments when interest is paid or charged for different compounding periods, including daily, monthly, quarterly and six-monthly

Unit 4: Investing and networking

Unit overview →

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

Use the recurrence relation A(n+1) = r A(n) - d, with r = 1 + i, and the present value annuity formula A(PV) = d[(1 - (1 + i)^(-n)) / i] to model the present value of an ordinary annuity, such as a reducing balance loan or a retirement pension, and solve practical problems for the total amount, periodic payment, total payments and total interest

Topic 1: Loans, investments and annuities 1 - how do we model a reducing balance loan or an annuity that pays out, with a recurrence relation and the present value annuity formula?

Use the recurrence relation A(n+1) = r A(n) + d, with r = 1 + i, and the future value annuity formula A(FV) = d[((1 + i)^n - 1) / i] to model the future value of an ordinary annuity, such as a savings plan or superannuation with periodic contributions, and solve practical problems for the total amount, periodic payment, total payments and total interest

Topic 2: Loans, investments and annuities 2 - how do regular contributions build an invested balance, and how do we find the future value of an ordinary annuity?

Understand the meaning of graph, vertex, edge, loop, degree of a vertex, subgraph, simple, complete, bipartite, directed and weighted graphs and networks, construct network diagrams for practical situations, and construct an adjacency matrix from a graph or digraph and a graph or digraph from an adjacency matrix

Topic 3: Graphs and networks - how do we represent practical situations as graphs, describe them with the right terminology, and move between a graph and its adjacency matrix?

Solve practical problems to determine the shortest path between two vertices in a weighted graph by trial-and-error methods, distinguishing the shortest path from a minimum spanning tree

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

Understand the meaning of tree, spanning tree and minimum spanning tree, determine a minimum spanning tree in a weighted connected graph, and solve practical problems involving minimum spanning trees, such as minimising the length of cable needed to connect several sites

Topic 4: Networks and decision mathematics 1 - how do we connect every vertex of a network at the least total cost?

Construct a project network diagram (activity on arc, excluding dummy activities) from an activity table, use forward and backward scanning to determine the earliest starting time (EST) and latest starting time (LST) of each activity, locate the critical path, determine the minimum completion time, calculate float times for non-critical activities, and solve small-scale practical problems

Topic 4: Networks and decision mathematics 1 - how do we schedule a project and find the shortest time to complete it?

Understand source node, sink node, cut, minimum cut and maximum flow, use a flow network diagram to identify a cut, determine the capacity of a cut, and solve small-scale practical problems involving flow networks (up to 8 possible cuts), including determining the minimum cut and the maximum flow

Topic 5: Networks and decision mathematics 2 - how much can flow from a source to a sink through a capacitated network?

Use a bipartite graph and its tabular or matrix form to represent possible assignments for an allocation problem, determine the optimum (minimum and maximum) assignment/s by inspection for small-scale problems, and use the Hungarian algorithm (3 x 3 up to 5 x 5 square matrices) to determine the optimum (minimum and maximum) assignment/s for larger practical problems

Topic 5: Networks and decision mathematics 2 - how do we allocate workers to tasks at the least total cost?

Understand the meaning of planar graph and face, and apply Euler's formula v + f - e = 2 to solve problems relating to planar graphs

What is a planar graph, what are its faces, and how does Euler's formula v + f - e = 2 connect the numbers of vertices, faces and edges?

13 min read →

How do we describe routes through a graph as walks, trails, paths, circuits and cycles, and how do we decide whether a graph is Eulerian, semi-Eulerian, Hamiltonian or semi-Hamiltonian?

Understand walks, trails, paths, circuits, cycles, connected graphs and bridges, the conditions for Eulerian trails and circuits in semi-Eulerian and Eulerian graphs, and Hamiltonian paths and cycles in semi-Hamiltonian and Hamiltonian graphs, and solve practical problems involving them

Use the recurrence relation A(n+1) = r A(n), with r = 1 + i, and the compound interest formula A = P(1 + i)^n to model compound interest loans and investments, and solve practical problems for the total amount, total interest, principal, interest rate and number of compounding periods

How do we model a compound interest loan or investment with a recurrence relation and with the compound interest formula, and use them to find the amount, interest, principal, rate or time?

Use the perpetuity formula A = d/i and solve practical problems involving perpetuities, including determining the total amount of the perpetuity, the periodic payment and the interest rate per compounding period

What is a perpetuity, and how do we use the perpetuity formula A = d/i to find the amount invested, the periodic payment or the interest rate?

13 min read →

Topics 4 and 5: Networks and decision mathematics 1 and 2 - how do we optimise connection, travel, flow and scheduling on a network?

Choose and apply the right network technique for a practical problem: minimum spanning trees for connection (Topic 4), critical path analysis for project scheduling (Topic 4), maximum flow and minimum cut for flow networks (Topic 5) and the Hungarian algorithm for assignment (Topic 5), distinguishing them from shortest path problems (Topic 3)