Implementing Mathematics Extension 1 Syllabus – 2017

Mathematics Extension 1 is a revised calculus-based mathematics course that was implemented for the first time in 2019.

About the syllabus

The course has been designed to offer opportunities for students to develop an awareness of the interconnected nature of mathematics.

The Mathematics Extension 1 course:

  • is focused on enabling students to develop thorough knowledge, understanding and skills in working mathematically by constructing rigorous mathematical arguments and proofs
  • has been developed with the assumption that students have achieved the outcomes of all substrands of Stages 5.1, 5.2 and 5.3, including the optional substrands of polynomials, logarithms, functions and other graphs, and circle geometry.
  • includes the Mathematics Advanced course.

Key content

Mathematics Extension 1 is comprised of four topics in Years 11 and five in Year 12.

Year 11

  • Functions
  • Trigonometric Functions
  • Calculus
  • Combinatorics

Year 12

  • Proof
  • Vectors
  • Trigonometric Functions
  • Calculus
  • Statistical analysis


Assessment in Mathematics Extension 1 consists of school-based assessment, as well as the HSC examination.

School-based assessment requirements

Year 11:

  • Three formal assessment tasks with a minimum weighting of 20% and a maximum weighting of 40%
  • One task will be an assignment or investigative-style task with a weighting of 20-30%

Year 12:

  • A maximum of four assessment tasks with a minimum weighting of 10% and a maximum weighting of 40%
  • One task will be an assignment or investigative-style task with a weighting of 15-30%
  • Only one task may be a formal written examination with a maximum weighting of 30%.

Additional information

Additional information for teachers

The assignment or investigative-style task

The assignment or investigative-style task will provide opportunities for students to demonstrate knowledge and skills in different ways to the HSC examinations. It must include application and modelling opportunities, an authentic use of technology to investigate, organise, model or interpret information and the chance for students to communicate, evaluate and justify their conclusions.

New language and notations

Across the course are several new concepts, language and notations that have not been previously used or explored in Mathematics Extension 1. The topics of combinatorics, proof and statistical analysis, though they appear to be new inclusions to the Mathematics Extension 1 courses, the content explored within these topics is similar to the previous course with a very small number of new concepts.


Proof is the study of proof by mathematical induction but with the added component exploring when mathematical induction is not appropriate.

Combinatorics and statistical analysis

The Year 11 topic of combinatorics is the study of permutations and combinations, the binomial expansion and Pascal’s triangle. The pigeonhole principle is explored within this subtopic, which is a new concept to the course. Statistical analysis builds upon this study in Year 12 to explore the binomial distribution.

New topics


The Functions topic in Mathematics Extension 1 is moved content, as it previously existed in the Mathematics Extension 2 course.


The introduction of vectors into Mathematics Extension 1 aligns with the Australian Curriculum unit from Specialist Mathematics. In this course, the study is limited to vectors in two-dimensional space.


  • Mathematics Extension 1
  • Stage 6

Business Unit:

  • Educational Standards
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