YEARS 11 AND 12 ACADEMIC INFORMATION HANDBOOK

MATHEMATICS LEARNING AREA

The Senior Secondary Australian Curriculum: Mathematics consists of four subjects in mathematics, with each subject organised into four units. (Unit 1 and 2 in Year 11 and Unit 3 and 4 in Year 12).  The subjects are differentiated, each focusing on a pathway that will meet the learning needs of a particular group of senior secondary students.

 

Mathematics Essentials (General Course)

Mathematics Essentials focuses on enabling students to use mathematics effectively, efficiently and critically to make informed decisions. Mathematics Essentials provides students with the mathematical knowledge, skills and understanding to solve problems in real contexts for a range of workplace, personal, further learning and community settings. This subject provides the opportunity for students to prepare for post-school options of employment and further training.

 

Mathematics Applications (ATAR Course)

Focuses on using the techniques of discrete mathematics to solve problems in contexts that include financial modelling, network analysis, route and project planning, decision making, and discrete growth and decay. It provides an opportunity to analyse and solve a wide range of geometrical problems in areas such as measurement, scaling, triangulation and navigation. It also provides opportunities to develop systematic strategies based on the statistical investigation process for answering statistical questions that involve comparing groups, investigating associations and analysing time series.

 

Mathematics Methods (ATAR Course)

Focuses on the development of the use of calculus and statistical analysis. The study of calculus in Mathematical Methods provides a basis for an understanding of the physical world involving rates of change, and includes the use of functions, their derivatives and integrals, in modelling physical processes. The study of statistics in Mathematical Methods develops the ability to describe and analyse phenomena involving uncertainty and variation.

 

Mathematics Specialist (ATAR Course)

Provides opportunities, beyond those presented in Mathematical Methods, to develop rigorous mathematical arguments and proofs, and to use mathematical models more extensively. Specialist Mathematics contains topics in functions and calculus that build on and deepen the ideas presented in Mathematical Methods as well as demonstrate their application in many areas. Specialist Mathematics also extends understanding and knowledge of probability and statistics and introduces the topics of vectors, complex numbers and matrices. Specialist Mathematics is the only mathematics subject that cannot be taken as a stand-alone subject.

 

MATHEMATICS ESSENTIALS – GENERAL 

Mathematics Essentials focuses on enabling students to use mathematics effectively, efficiently and critically to make informed decisions in their daily lives. Mathematics Essentials provides students with the mathematical knowledge, skills and understanding to solve problems in real contexts, in a range of workplace, personal, further learning and community settings. This subject offers students the opportunity to prepare for post-school options of employment and further training.

 

Year 11 

Unit: 1 This unit develops students’ skills in solving practical problems involving calculations, measurement, formulas, and graph interpretation. It includes real-world contexts that are relevant and engaging for students. 

 

Unit: 2 Unit 2 focuses on representing and comparing data, working with percentages, rates, ratios, and understanding time and motion in real world contexts.

 

Year 12

Unit: 3 This unit covers measurement, scales, plans and models, graphing, and data collection. These skills are embedded in real-life contexts. Technology use is expected throughout, and students should develop the ability to use digital tools effectively and appropriately.

 

Unit: 4 Unit 4 explores probability, Earth geometry and time zones, and financial mathematics involving loans and compound interest. As in Unit 3, digital technologies play a key role, and students should learn to use them flexibly and wisely.

MATHEMATICS APPLICATIONS – ATAR 

Mathematics Applications is intended for students who wish to build on their Year 10 mathematics skills but do not need calculus for their future study or career paths. It suits a wide range of educational and vocational goals, including pathways to university or TAFE. The subject places a strong emphasis on real-world problem solving and the effective use of digital technologies.

  

Year 11 

Unit 1Unit 1 includes three topics: 

  • Consumer arithmetic reviews rates and percentage changes, focusing on real-life money matters like income, tax, and budgeting. It also introduces spreadsheet use.
  • Algebra and matrices builds on earlier algebra and introduces matrices, a useful tool for solving practical problems.
  • Shape and measurement extends students’ understanding of geometric shapes, using similarity and applying these skills to real-world problems, including 3D shapes.

Unit 2Unit 2 includes three topics:

  • Univariate data analysis teaches students how to collect, organise, and summarise data using the statistical investigation process.
  • Applications of trigonometry involves solving real-world problems using non-right-angled triangles, including angles of elevation, depression, and bearings.
  • Linear equations and graphs explores straight-line graphs, piecewise and step graphs, and their use in modelling everyday situations.

 

Year 12 

Unit 3

  • Bivariate data analysis explores relationships between two variables, using tools like the least-squares line, all within the statistical investigation process.
  • Growth and decay in sequences uses recursive formulas to model patterns like compound interest, population growth, and depreciation.
  • Graphs and networks introduces basic graph theory, showing how networks (points and lines) can model real-life systems like transport or communication.

Unit 4.

  • Time series analysis develops students’ ability to analyse trends and patterns in data over time, using statistical methods.
  • Loans, investments and annuities covers financial mathematics, helping students understand mortgages, savings, and investment strategies.
  • Networks and decision mathematics teaches students how to use network models to solve practical problems and make informed decisions.

MATHEMATICS METHODS – ATAR 

The major themes of Mathematics Methods are calculus and statistics. They include as necessary prerequisites studies of algebra, functions and their graphs, and probability. They are developed systematically, with increasing levels of sophistication and complexity. Calculus is essential for developing an understanding of the physical world because many of the laws of science are relationships involving rates of change. Statistics is used to describe and analyse phenomena involving uncertainty and variation. For these reasons this subject provides a foundation for further studies in disciplines in which mathematics and statistics have important roles. It is also advantageous for further studies in the health and social sciences. In summary, the subject Mathematical Methods is designed for students whose future pathways may involve mathematics and statistics and their applications in a range of disciplines at the tertiary level.

 

For all content areas of Mathematical Methods, the proficiency strands of the F-10 curriculum are still applicable and should be inherent in students’ learning of this subject. These strands are Understanding, Fluency, Problem solving and Reasoning, and they are both essential and mutually reinforcing. For all content areas, practice allows students to achieve fluency in skills, such as calculating derivatives and integrals, or solving quadratic equations, and frees up working memory for more complex aspects of problem solving. The ability to transfer skills to solve problems based on a wide range of applications is a vital part of mathematics in this subject. Because both calculus and statistics are widely applicable as models of the world around us, there is ample opportunity for problem solving throughout this subject.

 

Year 11

Unit: 1

Unit 1 begins with a review of the basic algebraic concepts and techniques required for a successful introduction to the study of functions and calculus. Simple relationships between variable quantities are reviewed, and these are used to introduce the key concepts of a function and its graph. The study of probability and statistics begins in this unit with a review of the fundamentals of probability, and the introduction of the concepts of conditional probability and independence. The study of the trigonometric functions begins with a consideration of the unit circle using degrees and the trigonometry of triangles and its application. Radian measure is introduced, and the graphs of the trigonometric functions are examined and their applications in a wide range of settings are explored.

 

Unit: 2

In Unit 2, exponential functions are introduced and their properties and graphs examined. Arithmetic and geometric sequences and their applications are introduced and their recursive definitions applied. Rates and average rates of change are introduced, and this is followed by the key concept of the derivative as an ‘instantaneous rate of change’. These concepts are reinforced numerically (by calculating difference quotients), geometrically (as slopes of chords and tangents), and algebraically. This first calculus topic concludes with derivatives of polynomial functions, using simple applications of the derivative to sketch curves, calculate slopes and equations of tangents, determine instantaneous velocities, and solve optimisation problems.

 

Year 12

Unit: 3

In this unit the study of calculus continues with the derivatives of exponential and trigonometric functions and their applications, together with some differentiation techniques and applications to optimisation problems and graph sketching. It concludes with integration, both as a process that reverses differentiation and as a way of calculating areas. The fundamental theorem of calculus as a link between differentiation and integration is emphasised. In statistics, discrete random variables are introduced, together with their uses in modelling random processes involving chance and variation. This supports the development of a framework for statistical inference.

 

Unit: 4

The calculus in this unit deals with derivatives of logarithmic functions. In probability and statistics, continuous random variables and their applications are introduced and the normal distribution is used in a variety of contexts. The study of statistical inference in this unit is the culmination of earlier work on probability and random variables. Statistical inference is one of the most important parts of statistics, in which the goal is to estimate an unknown parameter associated with a population using a sample of data drawn from that population. In Mathematical Methods statistical inference is restricted to estimating proportions in two-outcome populations.

MATHEMATICS SPECIALIST – ATAR 

Specialist Mathematics develops high-level mathematical reasoning, offering a deeper exploration of mathematical and statistical models than Mathematical Methods. It equips students with a powerful, logical, and precise way of thinking and communicating, while fostering problem-solving and proof-based reasoning.

The course expands on core concepts in functions, calculus, probability, and statistics, and introduces new topics such as vectors, complex numbers, and matrices. It systematically builds the foundation for university studies in mathematics, science, engineering, economics, and related fields.

Designed to be taken alongside Mathematical Methods, Specialist Mathematics reinforces and extends its content, encouraging a coherent progression from two-dimensional to three-dimensional thinking, particularly in vectors and geometry. Calculus applications extend into areas such as motion, biology, and statistical modelling.

The course emphasizes the four proficiency strands from the F–10 curriculum:

  • Understanding, 
  • Fluency, 
  • Problem Solving, and 
  • Reasoning

with a particular focus on formal mathematical proof. Skills are built through practice and applied to complex, real-world contexts.

Structured across four units, the course steadily increases in complexity and abstraction. 

  

Year 11 

Unit: 1 Unit 1 includes three topics that build on Mathematical Methods and extend students' mathematical thinking: Geometry, Combinatorics, and Vectors in the plane.

  • In Geometry, students develop formal reasoning skills and mathematical argumentation, continuing the F–10 proficiency strand of Reasoning. This topic consolidates and extends knowledge of Euclidean geometry, forming a strong foundation for future topics like vectors and complex numbers.
  • Combinatorics introduces essential techniques for counting and arrangement, useful in probability, algebra, and beyond.
  • Vectors in the plane presents new ways to represent and work in two-dimensional space and sets the stage for the extension to three dimensions in Unit 3.

Together, these topics broaden students' understanding of mathematics, enhance their versatility, and deepen their appreciation of its scope and practical applications.

 

Unit: 2  Unit 2 covers three interconnected topics: Trigonometry, Matrices, and Real and complex numbers.

  • Matrices introduce powerful tools for modelling and manipulating data in two-dimensional space.
  • Real and complex numbers continue the exploration of number systems, extending earlier work into more abstract concepts.
  • Trigonometry provides techniques fundamental to further study in this and later units, particularly in calculus, vectors, and geometry.

This unit also introduces proof by mathematical induction, equipping students with a formal method for constructing rigorous mathematical arguments across multiple topics.

  

Year 12 

Unit: 3  Unit 3 covers three main topics: Vectors in three dimensions, Complex numbers, and Functions and sketching graphs.

  • Building on Unit 1, which focused on two-dimensional vectors, this unit introduces three-dimensional vectors, vector equations, and vector calculus—extending concepts from Mathematical Methods. Students learn to use Cartesian and vector equations, as well as equations of planes, to solve geometric and motion problems in 3D space.
  • The Cartesian form of complex numbers introduced in Unit 2 is expanded to include the polar form.
  • The study of functions and graph sketching, begun in Mathematical Methods, is deepened with a focus on applying these techniques to integration and problem-solving.

Use of technology is assumed to support computational aspects throughout this unit.

Unit: 4 Unit 4 explores three key topics: Integration and its applications, Rates of change and differential equations, and Statistical inference.

  • The unit continues the study of differentiation and integration, applying these techniques to simple differential equations, with a focus on real-world contexts like biology and kinematics.
  • Students consolidate their prior learning in probability and statistics through the study of statistical inference, particularly the distribution of sample means and confidence intervals.

As in Unit 3, technology is assumed for computational support.