Year 12: VCE Specialist Mathematics

Listed Mathematics areas of study at Units 3 and 4, in the words of the Victorian Curriculum and Assessment Authority (VCAA), with the practice on this site that covers it. Checked against the source on 7 September 2026.

Sourced from the VCE Mathematics Study Design accredited from 2023. Units 3 and 4 share one set of six areas of study.

6areas of study
94skills mapped
100%have practice

Coverage is the percentage of listed areas of study with at least one linked practice skill; it does not measure how fully every part of an entry is practised. A skill can practise more than one areas of study, so some appear more than once below.

Discrete mathematics

AoS 1Discrete mathematicsIn this area of study students cover the development of mathematical argument and proof. This includes conjectures, connectives, quantifiers, examples and counter-examples, and proof techniques including mathematical induction. Proofs will involve concepts from topics such as: divisibility, inequalities, graph theory, combinatorics, sequences and series including partial sums and partial products and related notations, complex numbers, matrices, vectors and calculus. The concepts, skills and processes from this area of study are to be applied in the other areas of study.

Functions, relations and graphs

AoS 2Functions, relations and graphsIn this area of study students cover rational functions and other simple quotient functions, curve sketching of these functions and relations, and the analysis of key features of their graphs including intercepts, asymptotic behaviour and the nature and location of stationary points and points of inflection and symmetry.

Algebra, number and structure

AoS 3Algebra, number and structureIn this area of study students cover the algebra of complex numbers, including polar form, factorisation of polynomial functions over the complex field and an informal treatment of the fundamental theorem of algebra.

Calculus

AoS 4CalculusIn this area of study students cover the advanced calculus techniques for analytical and numerical differentiation and integration of a broad range of functions, and combinations of functions; and their application in a variety of theoretical and practical situations, including curve sketching, evaluation of arc length, area and volume, differential equations and kinematics, and modelling with differential equations drawing from a variety of fields such as biology, economics and science.

Space and measurement

AoS 5Space and measurementIn this area of study students cover the arithmetic and algebra of vectors; linear dependence and independence of a set of vectors; proof of geometric results using vectors; vector representation of curves in the plane and their parametric and Cartesian equations; vector kinematics in one, two and three dimensions; vector, parametric and Cartesian equations of lines and planes.

Data analysis, probability and statistics

AoS 6Data analysis, probability and statisticsIn this area of study students cover the study of linear combinations of random variables and introductory statistical inference with respect to the mean of a single population, the determination of confidence intervals, and hypothesis testing for the mean using the distribution of sample means.

Other Year 12 skills

Year 12 skills not currently linked to an entry on this page. These may include revision, extension practice, or skills still awaiting a curriculum mapping.