Australia · ACARA Content Descriptions
Year 11 Mathematics
This course bridges abstract mathematical theory with practical application, preparing students for tertiary study and real world problem solving. It focuses on developing rigorous logical arguments, interpreting complex data patterns, and mastering the functions that govern physical phenomena.
Algebraic Foundations and Quadratics
Explores the manipulation of algebraic expressions and the properties of quadratic functions to solve non linear problems.
Mastering the distribution of terms and the factorization of complex expressions to simplify mathematical models.
Analyzing the geometric properties of parabolas and their relationship to quadratic equations.
Solving systems where linear and non linear relationships intersect to find equilibrium points.
Trigonometry and Periodic Phenomena
Extending right angled trigonometry to circular functions to model repetitive motions like sound waves and tides.
Moving beyond degrees to use radians as a more natural measure of rotation and arc length.
Applying Sine and Cosine rules to solve for unknowns in any triangular configuration.
Graphing sine and cosine waves and using identities to simplify complex trigonometric expressions.
Introduction to Differential Calculus
Developing the concept of the derivative to measure instantaneous rates of change in dynamic systems.
Investigating the behavior of functions as they approach specific values or infinity.
Learning the formal definition of the derivative and the shortcuts used to differentiate polynomials.
Using derivatives to find stationary points and solve optimization problems in business and science.
Probability and Discrete Random Variables
Analyzing uncertainty and the distribution of outcomes in random processes.
Calculating the likelihood of events occurring based on prior knowledge or conditions.
Defining variables that take on distinct values and calculating their probability distributions.
Modeling scenarios with only two possible outcomes, such as success or failure.
Exponential and Logarithmic Functions
Studying growth and decay models and the inverse relationship between exponents and logarithms.
Modeling populations, radioactive decay, and compound interest using base e and other constants.
Using logarithms to solve equations where the unknown is an exponent.
Applying logarithms to measure intensity in pH, decibels, and the Richter scale.
Statistical Analysis and Bivariate Data
Investigating relationships between two variables and using regression to make predictions.
Visualizing and quantifying the strength and direction of linear relationships.
Fitting a line of best fit and evaluating its accuracy using residual analysis.
Critically analyzing how data is presented and identifying potential biases in reporting.