QCE General Mathematics: complete 2026 guide to Units 3 and 4 (General subject)
A complete 2026 guide to QCE General Mathematics Units 3 and 4. The Problem-solving and Modelling Task (IA1), the two internal examinations (IA2 and IA3), the External Assessment (50 percent), the Unit 3 and Unit 4 subject matter (bivariate data, time series, sequences, loans and annuities, networks), and links to every dot-point answer we have written for QCE General Mathematics.
QCE General Mathematics Units 3 and 4 is the Year 12 sequence that applies mathematics to data, finance and networks. It sits below Mathematical Methods in the QCAA mathematics suite and is the standard mathematics choice for students heading into health, business, education, humanities and design pathways that do not require calculus.
This page is the index. Below you will find the structure of the course, what each instrument assesses, the Unit 3 and Unit 4 subject matter, and links to every dot-point answer we have written for QCE General Mathematics.
The four instruments in 2026
QCE General Mathematics is assessed across three internal assessments (IAs) and one External Assessment (EA), in line with the QCAA General Mathematics General Senior Syllabus.
- IA1: Problem-solving and Modelling Task (PSMT)
- A take-home modelling report completed over several weeks. You are given a real-world problem (often with a stimulus), develop a mathematical model, solve it with technology, evaluate the model against assumptions and limitations, and report your findings against the QCAA problem-solving and modelling approach. Worth 20 percent of the subject result and the single highest-weighted internal assessment.
- IA2: Internal Examination (Unit 3)
- A school-based written examination on Unit 3 subject matter. Worth 15 percent of the subject result, sat near the end of Term 3. It tests bivariate data, time series and sequences.
- IA3: Internal Examination (Unit 4)
- A school-based written examination on Unit 4 subject matter, the same format as IA2. Worth 15 percent, sat early in Term 4. It tests loans and annuities, graphs and networks, and decision mathematics.
- EA: External Assessment
- A centrally-set QCAA examination sat in the November assessment block, technology-active, worth 50 percent of the subject result. It is cumulative across Units 3 and 4, so Unit 3 content remains examinable months after IA2.
Unit 3: Bivariate data, sequences and change, and Earth geometry
Unit 3 of the QCAA General Mathematics syllabus applies statistics and sequence modelling. It contains the following subject matter, each examinable in IA1, IA2 and the EA.
- Topic 1: Bivariate data and time series analysis
- Scatterplots and describing association by direction, form and strength. Pearson's correlation coefficient and the coefficient of determination. Least-squares regression, interpretation of slope and intercept, interpolation and extrapolation, and residual analysis. Time series plots, trend and seasonality, moving-average smoothing, seasonal indices, deseasonalising and forecasting.
- Topic 2: Growth and decay in sequences
- Arithmetic and geometric sequences and first-order recurrence relations. Linear growth and decay (simple interest) and geometric growth and decay (compound interest, reducing-balance depreciation), with nth-term and sum formulas.
- Topic 3: Earth geometry and time zones
- Latitude and longitude, distances along great circles using nautical miles, and time differences between locations from the 15-degrees-per-hour rotation rule.
Our 2026 QCE General Mathematics Unit 3 dot-point answers
Every link below is a focused answer to one QCAA Unit 3 subject-matter dot point. Each page identifies the dot point, gives the worked answer, and shows arithmetic-verified examples.
Topic 1: Bivariate data and time series analysis
- Bivariate data analysis and correlation
- Least-squares regression and prediction
- Residual analysis
- Data transformation and linearisation
- Time series analysis and smoothing
Topic 2: Growth and decay in sequences
Topic 3: Earth geometry and time zones
Unit 4: Investing and networking
Unit 4 applies recurrence relations to finance and graph theory to connection and scheduling problems. It is examined in IA3 and contributes around half the External Assessment.
- Topic 1: Loans, investments and annuities
- Compound interest investments, reducing-balance loans and annuities modelled with first-order recurrence relations, amortisation tables, and the effect of changing the rate, repayment or compounding period.
- Topic 2: Graphs and networks
- Vertices, edges and degree, the handshaking result, types of graphs, Euler's formula for planar graphs, and Eulerian and Hamiltonian trails and circuits.
- Topic 3: Networks and decision mathematics
- Minimum spanning trees (Prim's algorithm), shortest paths, maximum flow and minimum cut, and critical path analysis with earliest and latest times and float.
Our 2026 QCE General Mathematics Unit 4 dot-point answers
Topic 1: Loans, investments and annuities
- Loans, investments and annuities
- Annuities and superannuation
- Comparing investments and effective interest rates
Topic 2: Graphs and networks
Topic 3: Networks and decision mathematics
- Networks and decision mathematics
- Minimum spanning trees and connector problems
- Shortest path problems
- Flow networks, maximum flow and minimum cut
- Critical path analysis and scheduling
- Assignment problems
How the units map to the assessments
- IA1 PSMT (20 percent)
- QCAA Problem-solving and Modelling Tasks for General Mathematics commonly use a Unit 3 context: a regression and prediction problem, a time series forecasting problem, or a sequence and finance model. Strong reports formulate the problem cleanly, justify the model, solve it with technology, evaluate against stated assumptions and limitations, and refine in a second pass. Tie every step to the problem-solving and modelling approach in the syllabus.
- IA2 Internal Examination (15 percent)
- An exam on Unit 3 only: bivariate data (correlation, regression, residuals), time series (moving averages, seasonal indices, forecasting) and sequences (arithmetic and geometric models). Most marks come from methodical, technology-supported calculation rather than abstract proof.
- IA3 Internal Examination (15 percent)
- An exam on Unit 4: loans and annuities (recurrence and amortisation), graphs and networks (degree, Euler's formula, trails), and decision mathematics (spanning trees, shortest path, flow, critical path).
- EA (50 percent)
- Cumulative across Units 3 and 4. Expect bivariate and time series questions alongside finance and network questions, often in multi-step extended-response items.
How to use this hub
If you are starting Unit 3 this term, read the bivariate data and regression dot points first; they anchor Topic 1 and feed straight into the PSMT. If you are two weeks from IA3, drill the loans and annuities recurrence and the critical path method under timed conditions. If you are six weeks from the EA, revise the full Unit 3 and Unit 4 sets above, then work past QCAA papers.
The system around QCE General Mathematics
QCE General Mathematics sits inside the wider QCE system. Related explainers:
- How the QCE ATAR is calculated covers QTAC's top-5-General aggregate and scaling.
- Internal vs External Assessments breaks down the 50/50 IA/EA weighting and the PSMT criteria.
- AARA special arrangements covers QCAA's Access Arrangements and Reasonable Adjustments.
- QCE exam day: what to actually expect covers EA logistics.
Every guide on this hub was written by ExamExplained (an initiative of Better Tuition Academy and XLev). For the official QCAA General Mathematics General Senior Syllabus, IA specifications, sample papers and past EA papers, refer to qcaa.qld.edu.au.
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