Australia · ACARA Content Descriptions
Year 12 Mathematics
A comprehensive exploration of calculus, statistics, and algebraic modeling designed for senior secondary students. This course emphasizes the transition from procedural fluency to abstract reasoning and real world problem solving.
Calculus: The Study of Change
Students investigate the fundamental principles of differentiation and integration to model dynamic systems. This unit focuses on the relationship between rates of change and accumulated quantities.
Exploring the concept of the derivative as an instantaneous rate of change and its geometric representation as a tangent slope.
Developing the Fundamental Theorem of Calculus to find areas under curves and understand accumulation functions.
Applying calculus techniques to find maximum and minimum values in practical engineering and economic scenarios.
Exponential and Logarithmic Functions
An in depth look at non linear growth and decay models using transcendental functions. Students learn to manipulate logarithmic scales and solve complex growth equations.
Understanding the unique properties of the number e and its role in continuous growth models.
Using logarithms to solve exponential equations and interpreting data on logarithmic scales like pH or Richter levels.
Applying exponential functions to carbon dating, population dynamics, and Newton's Law of Cooling.
Trigonometric Functions and Periodic Motion
Extending trigonometry beyond right angled triangles to model periodic phenomena like sound waves and tides.
Defining trigonometric ratios for any angle and transitioning from degrees to radian measure for calculus applications.
Using sine and cosine functions to model cyclic behavior and interpreting transformations of these graphs.
Proving and applying algebraic identities to simplify complex trigonometric expressions and solve equations.
Discrete and Continuous Probability
Analyzing uncertainty through the study of random variables and probability distributions.
Developing probability distributions for experiments with countable outcomes and calculating expected values.
Modeling scenarios with a fixed number of independent trials and two possible outcomes.
Investigating the bell curve and its application to natural phenomena and standardized testing.
Statistical Inference
Learning how to make valid conclusions about populations based on sample data through interval estimation and hypothesis testing.
Understanding how sample statistics vary and how they relate to the true population parameter.
Calculating and interpreting intervals that likely contain the true population mean or proportion.
Advanced Algebraic Structures
Exploring complex numbers and vectors to solve problems in multi dimensional space and non real number systems.
Introducing the imaginary unit i and performing operations in the complex plane.
Using vector algebra to describe position, displacement, and force in physical space.
Developing formal techniques of proof, including induction, contradiction, and direct derivation.