QCE General Mathematics: complete 2026 guide to Units 3 and 4 (General subject)

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 assessment instrument covers, the Unit 3 and Unit 4 subject matter, and links to every dot-point answer we have written for QCE General Mathematics.

The four assessment instruments in 2026

IA1: Problem-solving and modelling task (20 percent)

A written response to a specific investigative scenario or context, using subject matter from at least one of the topics in Unit 3 or Unit 4. You must address every stage of the problem-solving and mathematical modelling approach, using technology in a way that goes beyond simple computation. Conditions: 3 hours of class time plus your own time, individual task, up to 10 A4 pages or 2000 words (appendixes are not marked).

IA2: Examination, short response (15 percent)

A school-set examination of unseen short response questions that samples subject matter from any three of the five topics in Unit 3. 5 minutes perusal, 90 minutes working time, with the QCAA formula book provided and technology required.

IA3: Examination, short response (15 percent)

The same format as IA2, sampling any three of the five topics in Unit 4.

External Assessment: Examination, combination response (50 percent)

A QCAA-set examination on Units 3 and 4, sat by all schools at the same time. Paper 1 (30 percent) contains simple familiar multiple-choice and short response questions; Paper 2 (20 percent) contains complex familiar and complex unfamiliar short response questions. Each paper has 5 minutes perusal and 90 minutes working time. The QCAA formula book is provided and you may use a handheld QCAA-approved scientific calculator, not a graphics calculator.

Unit 3: Bivariate data and time series analysis, sequences and Earth geometry

Topic 1: Bivariate data analysis 1

Two-way frequency tables, row and column percentages, and describing an association between two categorical variables. Explanatory and response variables, scatterplots, and describing an association by direction, form and strength. Pearson's correlation coefficient $r$ and the coefficient of determination $R^2$ from technology, and converting between them.

Topic 2: Bivariate data analysis 2

Fitting the least-squares line $y = mx + c$ with technology or from $m = r\frac{s_y}{s_x}$ and $c = \bar{y} - m\bar{x}$. Residual plots to judge whether a linear model is appropriate, interpreting slope and intercept, interpolation against extrapolation, and prediction. Association and causation, including non-causal explanations such as coincidence or the influence of another variable.

Topic 3: Time series analysis

Time series plots and their features (trend, seasonality, irregular fluctuations). Smoothing with a simple moving average (mean or median) over an odd number of data, deseasonalising with seasonal indices calculated by the average percentage method, and fitting a least-squares trend line.

Topic 4: Growth and decay in sequences

Arithmetic sequences $t_n = t_1 + (n - 1)d$ for linear growth and decay (simple interest, flag fall and per-kilometre fares, straight-line depreciation) and geometric sequences $t_n = t_1r^{n-1}$ for geometric growth and decay (population growth, diminishing-value depreciation), generated by recursion and displayed in tables and graphs.

Topic 5: Earth geometry and time zones

Great circles, latitude and longitude, angular distance, and distance in kilometres using $D = 111.2 \times$ angular distance (same meridian) and $D = 111.2\cos\theta \times$ angular distance (same parallel). GMT, UTC, the International Date Line, the link between longitude and time, and time-difference problems including daylight saving.

Our 2026 QCE General Mathematics Unit 3 dot-point answers

Every link below is a focused answer to QCAA Unit 3 subject matter. Each page states the syllabus point, gives the worked answer, and shows arithmetic-checked examples.

Topics 1 and 2: Bivariate data analysis

• Associations between two categorical variables
• Bivariate data analysis and correlation
• Least-squares regression and prediction
• Residual analysis
• Association and causation
• Data transformation and linearisation (extension, not in the 2025 syllabus)

Topic 3: Time series analysis

• Time series analysis and smoothing
• Seasonal indices and deseasonalising

Topic 4: Growth and decay in sequences

• Sequences, growth and decay
• Depreciation models

Topic 5: Earth geometry and time zones

• Latitude, longitude and great-circle distances
• Time zones and time differences

Unit 4: Investing and networking

Topic 1: Loans, investments and annuities 1

Compound interest loans and investments with the recurrence $A_{n+1} = rA_n$ (where $r = 1 + i$) and $A = P(1 + i)^n$; the effective annual rate $i_{\text{effective}} = (1 + i)^k - 1$ to compare compounding periods; and the present value of an ordinary annuity with $A_{n+1} = rA_n - d$ and the present value annuity formula (reducing balance loans, retirement pensions).

Topic 2: Loans, investments and annuities 2

The future value of an ordinary annuity (regular contributions to an investment) by recurrence and formula, and perpetuities.

Topic 3: Graphs and networks

Graph terminology, network diagrams and adjacency matrices; planar graphs, faces and Euler's formula; walks, trails, paths, circuits and cycles; shortest paths between two vertices in a weighted graph; Eulerian and semi-Eulerian graphs; Hamiltonian and semi-Hamiltonian graphs.

Topic 4: Networks and decision mathematics 1

Trees, spanning trees and minimum spanning trees; project networks (activity on arc), forward and backward scanning for earliest and latest starting times, the critical path, minimum completion time and float.

Topic 5: Networks and decision mathematics 2

Flow networks: source, sink, cuts, the capacity of a cut, minimum cut and maximum flow. Assignment problems with bipartite graphs and the Hungarian algorithm (3 by 3 up to 5 by 5).

Our 2026 QCE General Mathematics Unit 4 dot-point answers

Topics 1 and 2: Loans, investments and annuities

• Compound interest loans and investments
• Comparing investments and effective interest rates
• Loans, investments and annuities
• Annuities and superannuation
• Perpetuities

Topic 3: Graphs and networks

• Graphs and networks
• Planar graphs and Euler's formula
• Eulerian and Hamiltonian graphs
• Shortest path problems

Topics 4 and 5: Networks and decision mathematics

• Networks and decision mathematics overview
• Minimum spanning trees and connector problems
• Critical path analysis and scheduling
• Flow networks, maximum flow and minimum cut
• Assignment problems

How the units map to the assessments

IA1 (20 percent)

The scenario can draw on any Unit 3 or Unit 4 topic, so a bivariate data, time series, sequence, finance or network context are all possible. Strong responses formulate the problem with clearly stated assumptions and observations, solve it with technology, evaluate and verify the model against its limitations, and communicate the result in context.

IA2 (15 percent)

Unseen short response questions sampling any three of the five Unit 3 topics. Because you do not know in advance which three, revise all five.

IA3 (15 percent)

The same format sampling any three of the five Unit 4 topics.

External Assessment (50 percent)

Covers Units 3 and 4. Paper 1 rewards fast, accurate routine work on simple familiar questions; Paper 2 rewards choosing and justifying a method on complex familiar and complex unfamiliar questions. Both papers allow a handheld QCAA-approved scientific calculator (see QCAA's scientific calculator list and the external assessment equipment list, and check them each year). Practise using the formula book and working regression, finance and network problems with the scientific calculator you will actually be allowed to bring.

How to use this hub

If you are starting Unit 3, read the two-way table, correlation and regression pages first; they anchor Topics 1 and 2 and feed straight into many IA1 scenarios. Before IA3, drill the annuity recurrence and formulas, Euler's formula and critical path analysis under timed conditions. In the weeks before the External Assessment, revise the full Unit 3 and Unit 4 sets above with your scientific calculator and the formula book, 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. For the official QCAA General Mathematics syllabus, assessment specifications, sample papers and past External Assessment papers, refer to qcaa.qld.edu.au.