At Hurlstone Agricultural High School, Mathematics is at the heart of analytical thinking, innovation, and academic excellence. Our Mathematics Faculty challenges students to engage deeply with the language of logic and pattern, developing precision, reasoning, and resilience as they tackle complex problems and abstract concepts.
High expectations underpin every aspect of mathematics learning at Hurlstone. Students are encouraged to think critically, justify their solutions, and explore multiple pathways to understanding. From foundational numeracy to advanced calculus and statistics, teaching is explicit, structured, and focused on mastery, ensuring every learner is both supported and extended to fulfil their potential.
Mathematics is studied by all students from Years 7–10, with pathways into advanced, extension, and specialist courses in the senior years. These programs prepare students for high achievement in the HSC and beyond, equipping them with the analytical confidence and intellectual curiosity essential for success in university study, professional careers, and the challenges of a data-driven future.
Teaching and Learning
Below you’ll find an overview of the Mathematics units studied from Year 7 to Year 12, showcasing how students build knowledge, skills, and hands-on experience across plant, animal, and agricultural systems.
Year 7 Mathematics
In Year 7, students begin by developing accuracy and fluency in computation with integers, indices, algebraic techniques and the essential language of mathematical reasoning. They then explore how data can be organised and represented through classification and visualisation, before strengthening their understanding of fractions, decimals, and percentages and applying these to practical problems involving length and perimeter. As the year progresses, students learn to solve equations, plot and interpret points on the number plane, and investigate the properties of angles and geometric figures. The year concludes with an introduction to area, volume, and probability, allowing students to connect numerical reasoning with spatial thinking and everyday applications of chance.
This strong foundation prepares students for the complexity and abstraction of higher levels of mathematical study at Hurlstone. By mastering these early concepts, students develop the logical reasoning, precision, and perseverance essential for success in Stage 5 and senior mathematics courses — including Advanced, Extension 1, and Extension 2 pathways. The problem-solving, data analysis, and quantitative reasoning skills fostered in Year 7 also form the basis for future success in HSC studies and a wide range of post-school fields such as science, engineering, technology, economics, and data analytics.
Year 8 Mathematics
In Year 8, students extend their mathematical understanding through increasingly complex and interconnected concepts. The year begins with the study of Pythagoras’ Theorem, indices, geometry, and algebraic equations, strengthening students’ ability to apply reasoning to spatial and numerical problems. As their confidence grows, students explore the measurement of trapeziums, kites, rhombuses, circles, and cylinders, deepening their understanding of shape, area, and volume. They apply fractions, decimals, and percentages to real-world problems, developing fluency in calculating rates and ratios. In the latter part of the year, students analyse and interpret data, explore linear relationships, and refine their use of algebraic and index laws. The introduction of trigonometry brings together measurement, geometry, and algebra, helping students make powerful mathematical connections across topics.
These experiences prepare students for the higher levels of abstraction and reasoning required in Stage 5 and senior mathematics courses. The algebraic fluency, geometric reasoning, and data interpretation skills developed in Year 8 form the basis for advanced problem-solving in Years 9–12 and underpin success in HSC Mathematics Advanced, Extension 1, and Extension 2. Beyond school, these skills are invaluable across STEM, commerce, and technology fields, where analytical thinking and quantitative literacy are essential. Year 8 Mathematics at Hurlstone continues to build the intellectual curiosity and precision that characterise high-achieving learners ready to excel in a data-driven world.
Year 9
In Year 9, students deepen their mathematical understanding through the study of increasingly abstract and applied concepts that link number, algebra, geometry, and statistics. The year begins with Financial Mathematics, where students explore interest, profit, and budgeting, applying algebraic techniques to real-world financial contexts. They extend their trigonometric skills to solve complex problems involving angles, lengths, and heights before advancing to equations, measurement, and linear relationships that connect algebra and geometry in meaningful ways. As the year progresses, students investigate the linear and non-linear properties of relationships, analyse data sets, and explore indices and numbers of any magnitude. Topics in geometry, area, surface area, volume, and probability challenge students to reason logically, interpret results, and recognise patterns across multiple mathematical strands.
This comprehensive program builds the analytical foundation necessary for success in advanced Stage 5 and senior mathematics courses. The problem-solving, modelling, and abstract reasoning developed in Year 9 are vital for excelling in HSC Mathematics Advanced, Extension 1, and Extension 2. Students also gain the capacity to apply mathematics beyond the classroom — in fields such as economics, engineering, architecture, data science, and environmental design. Year 9 Mathematics at Hurlstone nurtures intellectual rigour and mathematical maturity, preparing students to think critically, act decisively, and approach complex problems with clarity and confidence.
Year 10
In Year 10, students consolidate and extend their mathematical understanding through rigorous study that bridges foundational concepts with the demands of senior-level mathematics. The year begins with an exploration of area, surface area, and volume, alongside advanced algebraic techniques and geometric reasoning. Students refine their skills in data analysis and probability, interpreting and predicting outcomes with increasing sophistication. As the year progresses, they deepen their understanding of indices, equations, trigonometry, and linear and non-linear relationships, strengthening their ability to model and solve complex, real-world problems. Later topics such as functions, polynomials, logarithms, variations, rates, circle geometry, and networks introduce students to abstract and applied thinking connecting algebraic theory with spatial and graphical reasoning across multiple contexts.
This course provides a strong foundation for success in the HSC Mathematics pathways Standard, Advanced, Extension 1, and/or Extension 2 and equips students with the analytical, problem-solving, and reasoning skills valued in tertiary study and professional fields. Whether pursuing future pathways in science, engineering, data analytics, finance, architecture, or technology, students emerge from Year 10 Mathematics at Hurlstone with a deep conceptual understanding and the intellectual confidence to apply mathematical thinking to complex challenges.
Year 11 Preliminary HSC Mathematics Standard
The Preliminary Mathematics Standard course equips students with the practical mathematical knowledge and analytical skills needed to navigate an increasingly data-driven and interconnected world. Across the year, students explore topics that link mathematics to everyday life — from managing money, measuring energy use, and interpreting data, to analysing probability, modelling linear relationships, and understanding time across global contexts. Through these studies, they learn to calculate with accuracy, interpret graphs and statistics, apply formulas and equations to real situations, and make sound, evidence-based decisions.
The course builds confidence and fluency in mathematical reasoning while reinforcing the relevance of numeracy in personal, vocational, and societal contexts. Students develop the ability to communicate their thinking clearly, evaluate information critically, and apply problem-solving skills in practical scenarios. These capabilities form a strong foundation for success in the HSC Mathematics Standard 2 course and prepare students for a wide range of post-school pathways including tertiary study, trades, business, agriculture, and technology where mathematical competence, logical reasoning, and financial literacy are essential for informed and effective participation in modern life.
Classifying and Representing Data
Exploring and Describing Data
Formula and Equations
Earning and Managing Money
Probability
Measurement Practicalities
Perimeter, Area and Volume
Budgeting and Household Expenses
Units of Energy
Linear Functions
Money Matters
Working with Time
Year 11 Preliminary HSC Mathematics Advanced
In Year 11, students extend their mathematical thinking through the study of advanced concepts that form the foundation of higher-level mathematics. The year begins with an exploration of functions, where students learn to represent, interpret, and manipulate relationships between variables. This understanding deepens through the study of trigonometry and the measurement of angles, where students apply trigonometric identities and explore inverse trigonometric functions to model and solve complex problems. As the course progresses, students are introduced to differentiation and rates of change, developing an appreciation for how calculus describes motion, growth, and optimisation in real-world and theoretical contexts.
Students also explore the power of algebraic reasoning through topics such as polynomials, logarithms, and exponentials, learning to express generalised relationships and solve problems with efficiency and precision. Probability and discrete probability distributions extend their ability to analyse uncertainty and make informed predictions, while combinatorics builds logical reasoning through counting principles and pattern recognition. Together, these studies provide a rich, interconnected understanding of mathematics as both an abstract discipline and a practical tool. The Year 11 Mathematics Advanced course prepares students for the rigour of HSC Mathematics Advanced and Extension pathways, while also laying the groundwork for future study and careers in science, engineering, finance, technology, and data-driven industries.
Year 11 Preliminary HSC Mathematics Extension 1
Year 12 HSC Mathematics Standard
The HSC Mathematics Standard 2 course equips students with the mathematical understanding, fluency, and analytical skills needed to make informed decisions in a modern, data-rich world. Throughout the course, students apply mathematics to practical, real-life contexts from managing finances and investments to analysing data, interpreting networks, and modelling relationships between variables. They learn to use mathematical reasoning to plan projects, solve complex problems, and communicate solutions with precision and clarity.
By engaging with topics such as depreciation, annuities, and critical path analysis, students gain valuable financial literacy and project management skills. Through the study of regression, normal distribution, and non-linear relationships, they develop a deep understanding of how mathematics describes trends and informs decision-making. Geometry and trigonometry further extend students’ ability to apply abstract concepts to tangible problems in design, construction, and the sciences.
This course builds confidence in using mathematics as a language for interpreting the world, preparing students for success in the HSC and beyond. The knowledge and skills gained are essential for tertiary study and careers in fields such as business, health, agriculture, engineering, and technology where analytical thinking, quantitative reasoning, and evidence-based problem-solving are vital for success.
Investments
Ratios and Rates
Equations and Linear Functions
Depreciation and Loans
Annuities
Regression and Correlation
Network Concepts
Critical Path Analysis
Non-Right-Angled Trigonometry
The Normal Distribution
Non-Linear Relationships
Year 12 HSC Mathematics Advanced
In Year 12, students refine and extend their mathematical understanding through the study of advanced functions, calculus, trigonometry, and statistics. The year begins with graphing techniques and trigonometric graphs, where students learn to analyse and interpret complex functions to describe and predict real-world patterns. Building on their knowledge of differentiation, students apply calculus to model rates of change and optimisation problems before progressing to integral calculus, where they explore area, accumulation, and the interconnectedness of mathematical concepts. Exponential and logarithmic functions further develop their ability to represent growth and decay, while advanced trigonometric functions extend their capacity to model periodic behaviour across diverse contexts.
Students also strengthen their analytical and statistical reasoning through descriptive statistics, bivariate data analysis, and random variables, learning to interpret data critically and make evidence-based decisions. The course concludes with modelling financial situations, where mathematics is applied to real-world financial planning, investments, and decision-making. Together, these studies build fluency, precision, and insight, equipping students with the conceptual understanding and problem-solving ability essential for HSC success and for future study in fields such as science, engineering, data analytics, finance, and technology. Year 12 Mathematics Advanced at Hurlstone challenges students to think deeply, reason logically, and approach complex problems with creativity and confidence.
Year 12 HSC Mathematics Extension 1
In Year 12 Mathematics Extension 1, students engage with the most abstract, rigorous, and intellectually demanding aspects of senior mathematics. Building on the foundations of the Advanced course, they extend their understanding of trigonometric, algebraic, and calculus concepts to solve complex and unfamiliar problems with precision and creativity. The year begins with trigonometric equations and graphing techniques, where students manipulate and analyse intricate functions to model real-world and theoretical situations. Proof by mathematical induction introduces formal reasoning, requiring students to construct logical, step-by-step arguments to establish the validity of mathematical statements.
As the course progresses, students deepen their expertise in differential and integral calculus, applying these tools to rates of change, motion, and optimisation problems that demand higher-order reasoning. The study of vectors introduces a geometric and analytical framework for representing magnitude and direction, while further exploration of exponential, logarithmic, and trigonometric functions enhances students’ ability to connect multiple mathematical representations. Statistical topics such as random variables, the binomial distribution, and bivariate data analysis strengthen analytical interpretation and quantitative modelling.
Throughout the course, students also apply mathematics to financial and practical contexts, demonstrating how advanced theory informs decision-making in the real world. Year 12 Mathematics Extension 1 develops exceptional problem-solving ability, precision, and mathematical maturity, preparing students for success in the HSC and providing an essential foundation for tertiary study in mathematics, engineering, physics, data science, and other analytical disciplines where depth of reasoning and conceptual fluency are paramount.
Year 12 HSC Mathematics Extension 2
n Year 12 Mathematics Extension 2, students explore the highest level of secondary mathematics, developing the depth of reasoning, abstraction, and creativity characteristic of advanced mathematical thinking. The course begins with complex numbers, introducing students to a new number system that extends beyond the real numbers to model rotation, magnitude, transformation and concepts central to modern mathematics and engineering. Through the study of proof, students refine their logical reasoning and learn to construct elegant, rigorous arguments that demonstrate the universality and precision of mathematical truth.
Vectors and calculus (integration) extend students’ understanding of geometry and change, as they apply multi-dimensional and continuous models to describe motion, force, and other real-world phenomena. The study of mechanics connects algebraic, geometric, and calculus-based reasoning, equipping students to solve intricate problems involving velocity, acceleration, and equilibrium. Across all topics, students are challenged to think critically, communicate with clarity, and synthesise ideas from multiple areas of mathematics.
Year 12 Mathematics Extension 2 represents the pinnacle of mathematical study at Hurlstone, preparing students for university-level mathematics, physics, engineering, and computer science. The course cultivates precision, persistence, intellectual independence and qualities that empower students to lead in fields that demand analytical excellence and innovation.
Support for High Potential Learners
Hurlstone’s Mathematics Faculty nurtures high potential students through rigorous extension, enrichment, and acceleration opportunities designed to challenge and inspire. Learners are encouraged to think abstractly, reason logically, and apply advanced problem-solving strategies across a range of mathematical domains. Through participation in extension programs, mathematics competitions, and inquiry-based learning, students extend their understanding beyond the classroom and connect mathematics to real-world and theoretical applications. If your child shows high potential in mathematical reasoning, contact us to learn how our High potential and gifted education (HPGE) programs in Mathematics can support them to achieve at the highest levels.
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