General Mathematics General Senior Syllabus 2025 v1.3 (for completion in 2026 or later)
The external assessment covers Units 3 and 4 and contributes 50% of the subject result. Paper 1 contributes 30% and assesses simple familiar questions; Paper 2 contributes 20% and assesses complex familiar and complex unfamiliar questions. Each paper allows 5 minutes perusal and 90 minutes working time. Students may use a handheld QCAA-approved scientific calculator, and QCAA supplies the current formula book. Classroom CAS or spreadsheet demonstrations do not establish permission to use those tools in the external examination.
Past papers on this subject span more than one syllabus. Papers written under an older one still work as practice, but the units and topics they test have changed — the index labels every paper with the syllabus it was set under.
General Mathematics 2019 syllabus · 2020–2025General Mathematics 2025 syllabus (v1.3) · 2026–present
The units and topics, one by one
Each area below lists the concepts named in the syllabus, what the QCAA exam asks of them, and the mistake that most often costs marks.
- Unit 1: Money, measurement, algebra and linear equations (school-based, not EA-examinable)
- Unit 2: Applications of linear equations and trigonometry, matrices and univariate data analysis (school-based, not EA-examinable)
- Unit 3: Bivariate data and time series analysis, sequences and Earth geometry (EA-examinable)
- Unit 4: Investing and networking (EA-examinable)
Area 1 of 4
Unit 1: Money, measurement, algebra and linear equations (school-based, not EA-examinable)
Unit 1 sets the arithmetic and algebra that later units assume you own. Consumer arithmetic covers percentages, rates, mark-ups and discounts, wages, taxation and currency conversion — the everyday finance that returns in Unit 4 as loans and annuities. Shape and measurement covers perimeter, area, surface area and volume, including composite solids and unit conversion, with attention to rounding and significant figures. Similarity and scale extend this into scale factors and scale drawings, and the different ways length, area and volume scale. The algebra topic covers substitution, rearranging formulas and solving equations, and the unit finishes with linear equations and their graphs: gradient, intercepts and reading a straight-line model in context. None of it is externally examined, yet almost every Unit 3 and 4 question depends on fluency in it.
What the syllabus lists under this area · 5 points
- Consumer arithmetic
- Shape and measurement
- Similarity and scale
- Algebra
- Linear equations and their graphs
What the exam asks
This unit is assessed at school only. Its content still decides marks in the external assessment indirectly, because errors in rounding, unit conversion, percentage change and formula rearrangement are the most common reason a correct method in Units 3 and 4 produces an incorrect final answer.
Where marks go missing
Rounding too early. Carrying a rounded intermediate value through a multi-step calculation pushes the final answer outside the accepted range, and the mark goes even though the method displayed on the page is completely correct.
Area 2 of 4
Unit 2: Applications of linear equations and trigonometry, matrices and univariate data analysis (school-based, not EA-examinable)
Unit 2 applies the tools of Unit 1 and adds two new ones. Applications of linear equations cover simultaneous equations, piecewise models and break-even analysis, read from algebra and from graphs. Applications of trigonometry cover right-angled triangles, the sine and cosine rules, angles of elevation and depression, and bearings — the same techniques that return in Unit 3 as Earth geometry. Matrices are introduced as a way of organising and operating on data: order, addition, scalar multiplication, matrix multiplication and their use in contexts such as inventories and route counting, which underpins the network work of Unit 4. Univariate data analysis covers displaying and describing a single variable, including distribution shape, centre, spread, outliers and comparison between grouped data sets.
What the syllabus lists under this area · 5 points
- Applications of linear equations and their graphs
- Applications of trigonometry
- Matrices
- Univariate data analysis 1
- Univariate data analysis 2
What the exam asks
Not externally examined. The trigonometry and matrix skills are the ones that resurface most visibly, in Earth geometry calculations and in network questions where a matrix representation of connections is expected, so this unit is worth revising before the external assessment rather than filing away.
Where marks go missing
Mixing up bearings and ordinary angles. A true bearing is measured clockwise from north and written as three digits, so an answer measured from the wrong reference direction follows an otherwise correct method to a wrong result.
Area 3 of 4
Unit 3: Bivariate data and time series analysis, sequences and Earth geometry (EA-examinable)
Unit 3 is the first externally assessed unit and it leans heavily statistical. Bivariate data analysis covers scatterplots, the correlation coefficient, the least-squares regression line, interpretation of gradient and intercept in context, residual plots, and the difference between association and causation, including the role of a confounding variable. Time series analysis adds trend, seasonality and smoothing, using moving averages and seasonal indices to deseasonalise data and forecast, together with an honest account of how far a forecast can be trusted. Growth and decay in sequences covers arithmetic and geometric sequences and recurrence relations used to model population change, depreciation and repeated percentage change. Earth geometry closes the unit with latitude and longitude, great circle distances, and time zone calculations across the international date line. For the 2026 course, students calculate both r and r squared using technology and interpret the coefficient of determination.
What the syllabus lists under this area · 6 points
- Bivariate data analysis 1
- Bivariate data analysis 2
- Time series analysis
- Growth and decay in sequences
- Earth geometry and time zones
- 2026 scope: calculate r and r squared using technology
What the exam asks
External assessment items in this unit mix computation with written interpretation. You are asked to fit and apply a regression line, comment on the strength and direction of an association, deseasonalise or forecast from a time series, generate terms from a recurrence relation, and calculate distance or local time between two named locations.
Where marks go missing
Interpreting the gradient of a regression line without units or context. Stating that the gradient is 2.4 earns nothing; the mark requires the change in the response variable per unit increase in the explanatory variable, named in the units of the question.
Area 4 of 4
Unit 4: Investing and networking (EA-examinable)
Unit 4 has two distinct halves. The finance half covers loans, investments and annuities: simple and compound interest, effective annual rates, reducing balance loans, repayment schedules built from recurrence relations, annuities and perpetuities, and the effect of altering the repayment amount or the compounding frequency. Amortisation tables are read and completed rather than merely described. The networks half moves into graph theory: vertices, edges, degree, adjacency matrices, connected and planar graphs, and Euler and Hamiltonian paths and circuits. Decision mathematics then applies these, with minimum spanning trees for cheapest connection problems, shortest path for routing, and project networks with critical path analysis and float for scheduling. Both halves reward setting the problem up correctly, because the calculation that follows is usually short. Current scope specifies activity-on-arc critical path analysis and Hungarian algorithm minimisation and maximisation with square matrices up to 5 by 5.
What the syllabus lists under this area · 6 points
- Loans, investments and annuities 1
- Loans, investments and annuities 2
- Graphs and networks
- Networks and decision mathematics 1
- Networks and decision mathematics 2
- 2026 scope: activity-on-arc critical path analysis; Hungarian minimisation and maximisation up to5 by5 square matrices
What the exam asks
Finance questions require appropriate formulas or recurrence relations, correct period conversions and contextual conclusions. The external examination permits a QCAA-approved scientific calculator. Network tasks include paths, spanning trees, activity-on-arc scheduling and assignment problems, including Hungarian algorithm minimisation and maximisation up to 5 by 5.
Where marks go missing
Mismatching the interest rate to the payment period. A quoted annual rate used with monthly repayments, or a monthly rate left annual, produces a plausible-looking figure that then fails every subsequent part of the question.