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.
01Algebraic Foundations and Quadratics
Explores the manipulation of algebraic expressions and the properties of quadratic functions to solve non linear problems.
Revisiting fundamental algebraic operations including addition, subtraction, multiplication, and division of polynomials.
Mastering the distribution of terms and the factorization of complex expressions to simplify mathematical models.
Exploring various methods for factoring polynomials, including grouping, difference of squares, and sum/difference of cubes.
Simplifying, multiplying, dividing, adding, and subtracting rational expressions, and solving rational equations.
Defining quadratic functions and exploring their basic properties, including vertex, axis of symmetry, and intercepts.
Analyzing the geometric properties of parabolas and their relationship to quadratic equations.
Applying factoring techniques to find the roots or zeros of quadratic equations.
Mastering the method of completing the square to solve quadratic equations and convert to vertex form.
Using the quadratic formula to solve any quadratic equation and interpreting the discriminant.
Solving real-world problems involving quadratic models, such as projectile motion and optimization.
Solving systems of two linear equations using graphical, substitution, and elimination methods.
Representing solutions to linear and quadratic inequalities graphically on a coordinate plane.
Solving systems of linear and non-linear inequalities to identify feasible regions for optimization.
02Trigonometry and Periodic Phenomena
Extending right angled trigonometry to circular functions to model repetitive motions like sound waves and tides.
Revisiting SOH CAH TOA and applying it to solve problems involving right-angled triangles.
Moving beyond degrees to use radians as a more natural measure of rotation and arc length.
Extending sine, cosine, and tangent definitions to angles in all four quadrants using the unit circle.
Applying the Sine Rule to solve for unknown sides and angles in non-right-angled triangles.
Applying the Cosine Rule to solve for unknown sides and angles in non-right-angled triangles.
Applying Sine and Cosine rules to solve for unknowns in any triangular configuration.
Calculating the area of any triangle using the formula involving two sides and the included angle.
Sketching and analyzing the basic graphs of y = sin(x) and y = cos(x), identifying amplitude and period.
Investigating the effects of amplitude, period, phase shift, and vertical shift on trigonometric graphs.
Proving and applying fundamental trigonometric identities, including Pythagorean identities.
Finding general and specific solutions to trigonometric equations within a given domain.
Understanding the domain and range restrictions of inverse trigonometric functions and their graphs.
Modeling real-world periodic phenomena such as tides, sound waves, and seasonal variations.
03Introduction to Differential Calculus
Developing the concept of the derivative to measure instantaneous rates of change in dynamic systems.
Understanding average rate of change and introducing the concept of instantaneous rate of change.
Investigating the behavior of functions as they approach specific values or infinity.
Deriving the formula for the derivative using the limit definition (first principles).
Learning and applying the power rule for differentiating polynomial functions.
Applying rules for differentiating sums, differences, and functions multiplied by a constant.
Learning and applying rules for differentiating exponential functions, especially those with base 'e'.
Learning and applying rules for differentiating logarithmic functions, especially natural logarithms.
Learning and applying rules for differentiating sine, cosine, and tangent functions.
Finding the equations of tangent and normal lines to a curve at a given point.
Identifying stationary points (local maxima, minima, and points of inflection) using the first derivative.
Using the second derivative to determine concavity and identify points of inflection.
Solving real-world problems that require finding maximum or minimum values using differentiation.
Solving problems where two or more quantities are changing with respect to time and are related.
04Probability and Discrete Random Variables
Analyzing uncertainty and the distribution of outcomes in random processes.
Revisiting fundamental concepts of probability, including sample space, events, and calculating probabilities.
Calculating the likelihood of events occurring based on prior knowledge or conditions.
Applying Bayes' Theorem to update probabilities based on new evidence.
Defining variables that take on distinct values and calculating their probability distributions.
Calculating and interpreting the expected value and variance for discrete probability distributions.
Modeling scenarios with only two possible outcomes, such as success or failure.
Solving real-world problems using the binomial distribution, including cumulative probabilities.
Introducing the concept of continuous random variables and probability density functions.
Exploring the properties of the normal distribution, including its shape, mean, and standard deviation.
Standardizing normal distributions using z-scores to compare different data sets.
Solving real-world problems involving normal distributions, including finding probabilities and values.