Australia · ACARA Content Descriptions
Year 10 Mathematics
This course bridges foundational arithmetic with advanced algebraic reasoning and statistical analysis. Students explore complex relationships through functions, spatial geometry, and probabilistic modeling to prepare for senior secondary mathematics pathways.
Patterns of Change and Algebraic Reasoning
Students extend their understanding of algebraic expansion and factorization to solve complex equations and describe non linear relationships.
Exploring the structural relationship between expanded algebraic expressions and their factored forms using area models.
Solving equations using a variety of algebraic techniques and understanding the conditions for multiple solutions.
Representing ranges of possibilities on number lines and coordinate planes through inequality notation.
Geometric Reasoning and Trigonometry
Applying deductive logic to geometric proofs and using trigonometry to solve problems in three dimensional space.
Using formal logic and known geometric properties to prove congruency and similarity in triangles.
Mastering the ratios of sine, cosine, and tangent to find unknown sides and angles in right angled triangles.
Applying 2D trigonometric skills to solve problems involving heights and distances in three dimensional models.
Linear and Non Linear Relationships
Graphing and interpreting various functions including parabolas and circles to model physical phenomena.
Using coordinates to calculate distance, midpoint, and gradient to describe line segments.
Exploring the features of parabolas including intercepts, turning points, and axes of symmetry.
Investigating the equations of circles and the nature of non linear growth and decay.
Probability and Multi Step Events
Evaluating the likelihood of complex outcomes using tree diagrams, Venn diagrams, and two way tables.
Organizing data to calculate probabilities of events occurring simultaneously or exclusively.
Using tree diagrams to list sample spaces and calculate probabilities for events with and without replacement.
Exploring how the occurrence of one event affects the probability of another event.
Statistical Investigations and Data Analysis
Analyzing bivariate data and comparing data sets using measures of center and spread.
Examining the relationship between two numerical variables and identifying trends.
Using box plots and histograms to compare the distribution of different data groups.
Real World Measurement and Finance
Applying mathematical modeling to solve problems involving surface area, volume, and financial growth.
Calculating the capacity and external area of composite shapes including pyramids and spheres.
Modeling the growth of investments and the cost of loans over time using interest formulas.
Using scientific notation and index laws to handle very large and very small numbers accurately.