Year 10 Advanced Mathematics is designed for students who are ready to move beyond the core curriculum and deepen their mathematical thinking in preparation for senior study. Alongside the full Australian Curriculum Version 9 content, students engage with additional extension topics that strengthen algebraic fluency, analytical reasoning and abstract thinking.
Students extend their understanding of algebra through working with surds and fractional indices, completing the square, deriving and applying the quadratic formula, and analysing the features of quadratic graphs. They explore exponential and logarithmic relationships, investigate the sine and cosine functions using the unit circle, and solve related equations. In geometry, students examine circle theorems and develop deductive reasoning
skills. Statistical thinking is broadened through deeper analysis of measures of spread, while probability is strengthened through counting principles, factorial notation and combinatorial reasoning.
This course develops precision, persistence and higher-order reasoning. Students are challenged not only to calculate accurately, but to explain, justify and connect mathematical ideas across topics.
Year 10 Advanced Mathematics provides a strong and intentional pathway into Mathematical Methods and/or Specialist Mathematics in Years 11 and 12. It builds the conceptual depth and algebraic agility required for these subjects, positioning students for success in senior mathematics and future study in fields such as engineering, science, economics, technology and medicine.
Unit 1: Modelling Change, Chance
and Connections
Students explore how mathematics models real-world situations involving growth, uncertainty and networks. They examine how small rounding errors an build up in repeated calculations. They investigate exponential and logarithmic relationships, including how they are related, and use them to interpret logarithmic scales for very arge or small quantities. Students also learn counting techniques, including factorials, to determine possible outcomes. They apply this to conditional probability to analyse and solve problems involving combined events.
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Unit 2: Modelling Relationships and Solving Systems Students explore how mathematical relationships can be represented and used to solve real-world problems. They test ideas about functions using digital tools to identify patterns and justify conclusions. They apply modelling to problems involving growth and decay, using linear, quadratic and exponential functions. Students solve equations using graphs and numerical methods and interpret their solutions in context. The unit builds algebra skills by simplifying expressions and working with quadratic functions, including different forms. Students also solve simultaneous equations and inequalities graphically, explaining their reasoning. They use logical reasoning and known rules to solve spatial (geometric) problems.
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Assignment & Exam
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Unit 3 In this unit, students use trigonometry and Pythagoras’ theorem to solve practical problems involving right-angled triangles. They calculate surface area and volume of composite objects and examine how measurement errors affect accuracy. Students apply proportion and scaling to realworld situations through mathematical modelling, evaluating their methods and results. They also explore the graphs of sine function and cosine function, using them to solve related problems and model repeating patterns.
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Unit 4: Statistics, Data Analysis and Change In this unit, students investigate relationships between variables and analyse how data is used to make conclusions. They plan and conduct statistical investigations using bivariate data, representing results with tables and scatter plots to identify and describe possible associations. Students critically evaluate statistical claims in the media, identifying potential bias and assessing the validity of conclusions. They also compare distributions of continuous data using a range of displays, describing key features such as centre, spread, shape and outliers.Additionally, students explore how small changes in variables affect the average rate of change, developing an understanding of how values approach a limiting value.
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CADI Clusters for Maths
Informers – Analyse data and explain mathematical thinking clearly.
Coordinators – Follow logical steps and organise solutions carefully.
Innovators – Solve problems creatively and design new approaches.
Makers – Apply formulas and build accurate mathematical models.