General Mathematics Level 3 (MTG315123) course and External Assessment Specifications v1.2
The external assessment is one 180-minute written examination with an additional 15 minutes of preparation time for notes on the supplied note paper and highlighting only. Sections A, B, C and D are compulsory; Section E offers two whole alternatives and students answer either Part 1 Networks and decision mathematics or Part 2 Trigonometry and Earth geometry. Each attempted section carries 36 marks and assesses one criterion: Section A Criterion 3, B Criterion 5, C Criterion 6, D Criterion 7 and E Criterion 8. A complete original practice paper contains 216 offered marks because both 36-mark Section E alternatives are supplied, while a candidate attempts 180 marks by choosing one. TASC converts each section mark to a criterion rating, so the final award is not reported as a percentage out of 180. Multiple-choice drills on this site are a learning format rather than a reproduction of the written examination.
Past papers on this subject span more than one course document. Papers written under an older one still work as practice, but the modules they test have changed — the index labels every paper with the course document it was set under.
Current EAS v1.2 five-section structure · 2024–2025Current MTG315123 course before EAS v1.2 structure · 2023–2023Predecessor General Mathematics courses — check structure and criterion numbering · 2018–2021
The modules, one by one
Each area below lists the concepts named in the course document, what the TASC exam asks of them, and the mistake that most often costs marks.
- Module 1: Mathematical modelling, problem solving and statistical investigation
- Module 2 Topic 1: Statistical analysis
- Module 2 Topic 2: Growth and decay in sequences
- Module 3 Topic 1: Investment, loans and annuities
- Module 3 Topic 2a: Trigonometry and Earth geometry
- Module 3 Topic 2b: Graphs, networks and decision mathematics
Area 1 of 6
Module 1: Mathematical modelling, problem solving and statistical investigation
Select mathematical or statistical models, use technology appropriately, interpret results in context and test the reasonableness of conclusions across statistics, sequences, finance and two-dimensional problems.
What the exam asks
Formulate and solve unfamiliar problems, relate findings to the real situation, discuss assumptions and limitations, and draw evidence-based conclusions under Criterion 3.
Where marks go missing
A numerical result is not a complete conclusion. Name the variables and units, check reasonableness and keep association separate from causation.
Area 2 of 6
Module 2 Topic 1: Statistical analysis
Analyse categorical association with percentaged two-way tables and numerical association with scatterplots, least-squares lines, correlation, coefficients of determination and residuals. Smooth and model time series with moving averages, seasonal indices and trend lines.
What the exam asks
Construct and interpret statistical displays, fit and assess linear models, distinguish interpolation from extrapolation, calculate seasonal indices, deseasonalise data and reseasonalise trend predictions.
Where marks go missing
Residual means actual minus predicted. Interpret r and r² using the named variables, and multiply a deseasonalised forecast by its seasonal index to return to actual units.
Area 3 of 6
Module 2 Topic 2: Growth and decay in sequences
Use arithmetic and geometric sequences and series, together with first-order linear recurrence relations, to model discrete linear, exponential and steady-state behaviour.
What the exam asks
Generate and graph discrete terms, determine explicit and recursive rules, calculate finite and infinite sums, find thresholds numerically or graphically and analyse long-term recurrence behaviour.
Where marks go missing
Do not join discrete sequence points as though the domain were continuous. S∞ is an accumulated series total, while d/(1−r) is an equilibrium of a first-order recurrence.
Area 4 of 6
Module 3 Topic 1: Investment, loans and annuities
Model compound interest, inflation, reducing-balance loans, straight-line and reducing-balance depreciation, annuities, sinking funds and perpetuities with formulas, recurrences and calculator finance functions.
What the exam asks
Convert rates and periods consistently, compare effective rates, calculate present and future values, repayments and contributions, and justify a financial recommendation from stated assumptions.
Where marks go missing
Begin versus End changes annuity timing. An accounting book value is not a resale price, and an immediate deposit must be separated from the amount financed.
Area 5 of 6
Module 3 Topic 2a: Trigonometry and Earth geometry
Solve right and non-right triangle problems using trigonometric ratios, sine and cosine rules, area rules and Heron’s rule. Apply bearings, latitude, longitude, great and small circles, spherical cosine, time zones and travel calculations.
What the exam asks
Create labelled sketches, select formulas, retain precision, use Earth radius 6371 km, apply signed latitudes and calculate routes, times and distances in multi-stage contexts.
Where marks go missing
The ambiguous sine-rule case is outside the course. Use a method that determines a unique angle, distinguish small-circle travel from a shortest great-circle route, and separate longitude models from civil time zones.
Area 6 of 6
Module 3 Topic 2b: Graphs, networks and decision mathematics
Represent graphs and digraphs, analyse paths and cycles, find minimum connectors and shortest routes, schedule projects, maximise flows and optimise assignments.
What the exam asks
Use adjacency matrices, Euler’s formula, degree conditions, trial-and-error routes, Prim’s algorithm, EST/LST and float, maximum-flow minimum-cut and the Hungarian algorithm.
Where marks go missing
Shortest paths and travelling-salesman problems use trial and error in this course; minimum spanning trees use inspection or Prim’s algorithm. A feasible flow needs a matching cut to prove maximality.
Common questions
Are these official TASC examination questions?
No. ATARMAxxing practice questions and worked guides are original. Official papers, exemplars and assessment reports are linked separately.
How long is the examination?
The written examination has 180 minutes of working time plus 15 minutes of preparation time. During preparation, notes may be made on the supplied note paper and key words may be highlighted, but answers may not be started.
How does the Section E choice work?
Answer one complete alternative only: Part 1 Networks and decision mathematics or Part 2 Trigonometry and Earth geometry. Each alternative is a full 36-mark pathway for Criterion 8.
Why can a complete practice-paper file contain 216 marks?
Sections A–D offer 144 marks and both Section E alternatives together offer another 72. The candidate chooses one 36-mark alternative, so the attempted total is 180 marks.
What equipment and information are supplied?
TASC-approved calculators and the current MTG315123 General Mathematics Information Sheet are approved. The sheet includes regression, sequence, finance, trigonometry, Earth-geometry and network formulas or procedures.
How should older papers be used?
The 2023 paper predates the current EAS v1.2 five-section structure. The 2018–2021 papers belong to predecessor course codes and use older criterion numbering, and the 2020 paper was reduced to 150 marks. Use each with its era note and current course documents.