Australia · ACARA Content Descriptions
Year 9 Mathematics
This course bridges the gap between arithmetic and abstract reasoning through algebraic modelling and geometric proof. Students investigate proportional reasoning and data analysis to make sense of the world while developing fluency in non linear relationships.
The Language of Algebra
Students expand their algebraic repertoire by simplifying expressions, expanding binomials, and solving complex linear equations.
Mastering the distributive law to expand binomial products and reversing the process through factorisation.
Solving multi step equations and representing solutions to inequalities on a number line.
Applying index laws to simplify expressions and using scientific notation for very large or small numbers.
Linear and Non Linear Relationships
Exploring the geometry of the Cartesian plane through gradients, intercepts, and an introduction to parabolas.
Calculating the slope of a line and sketching linear functions using intercepts.
Using coordinates to find the distance between two points and the location of the midpoint.
Investigating the basic properties and shapes of non linear quadratic relationships.
Geometric Reasoning and Trigonometry
Applying Pythagoras Theorem and basic trigonometric ratios to solve problems involving right angled triangles.
Utilising the relationship between the sides of right angled triangles to find missing lengths.
Defining sine, cosine, and tangent as ratios of sides in right angled triangles.
Using conditions for similarity and congruence to solve geometric problems and proofs.
Measurement and Surface Area
Calculating the surface area and volume of composite shapes, prisms, and cylinders.
Breaking down complex 2D shapes into simpler components to calculate total area.
Developing and applying formulas to find the exterior area of three dimensional objects.
Investigating the relationship between base area and height to determine the capacity of prisms.
Financial Mathematics and Proportion
Applying percentage increases and decreases to financial contexts including simple interest and profit/loss.
Calculating percentage profit and loss and determining original values after a percentage change.
Calculating interest earned or paid over time using the simple interest formula.
Solving problems involving direct proportion and comparing rates in different units.
Statistics and Probability
Analysing data sets using measures of center and spread, and exploring multi step probability events.
Investigating relationships between two numerical variables and identifying correlations.
Using tree diagrams and tables to calculate the probability of independent and dependent events.
Comparing data sets using five point summaries and box and whisker plots.