Year 10 Mathematics - Core

ACARA Subject

Unlock the Power of Numbers:
Build Confidence, Solve Problems, Shape Your Future.

Year 10 Mathematics provides students with a strong foundation in key mathematical concepts and skills, preparing them for senior studies and real-world applications. The course is designed to build confidence, develop procedural skills, encourage logical thinking and develop problem-solving abilities across a range of topics.

Throughout the year, students will explore algebra, geometry, trigonometry, statistics, financial mathematics, and probability. They will learn to interpret and analyse data, solve equations, apply formulas, and use digital tools to model and investigate mathematical relationships.

Students completing the full year of Mathematics Core will be well-prepared for General Mathematics.

Assessment includes exams and a problem solving and modelling task aimed at developing mathematical fluency and critical thinking. This subject equips students with essential skills for future academic ATAR pathways and everyday life.

Prerequisites

Students should have achieved:

a mid C standard (B preferable) or equivalent in 9 Maths

Pathways

Students who select this subject will be equipped to study the following subjects in Senior:

General Mathematics
Chemistry
Psychology
Biology

This subject will also support understanding in:

and applications for:

Defence Force
Police Force
Apprenticeships in Trades
Traineeships in Finance, IT, and Engineering

Course Information

Course Overview

Mathematics in Year 10 is more than just numbers—it's about developing logical thinking, solving real-world problems, and building a strong foundation for future learning. Whether students are preparing for advanced mathematical studies or aiming to strengthen their everyday numeracy, this course offers a rich and supportive environment to grow their skills and confidence. With opportunities to explore data, algebra, geometry, financial maths, and more, students will discover how mathematics connects to the world around them and their future pathways.

What Will Students Learn?

What Will Students Learn?

Students in the Mathematics Core course will:

Explore data representation and interpretation, including box plots, scatter plots, and statistical analysis.
Study algebra, including operations with algebraic fractions, substitution, factorising, and expanding.
Apply Pythagoras’ Theorem and trigonometry to solve real-world problems, including 3D applications.
Work with surface area and volume of prisms, cylinders, pyramids, cones, and spheres.
Make connections between equations and their graphs, solving linear and simultaneous equations.
Compare simple and compound interest in financial contexts.
Investigate probability and chance, including conditional probability and multi-step experiments.
Explore geometric reasoning, Earth geometry, and networking concepts.

Students who demonstrate strong performance may be invited to join the Advanced Mathematics stream in Semester Two, which introduces topics aligned with Year 11 Mathematical Methods. Those completing the full year of Mathematics Core will be well-prepared for Year 11 General Mathematics.

Skills Students Will Develop:

Problem Solving: Apply mathematical reasoning to real-life and abstract problems.
Analytical Thinking: Interpret data, identify patterns, and make informed decisions.
Algebraic Fluency: Manipulate expressions, solve equations, and understand functions.
Geometric Reasoning: Visualise and solve spatial problems using logic and measurement.
Financial Literacy: Understand interest, budgeting, and real-world financial scenarios.
Digital Proficiency: Use technology to model, graph, and analyse mathematical relationships.

These skills are essential for academic success and are highly valued in careers across science, business, technology, and trades.

Assessment Activities Include:

Problem-Solving and Modelling Task (PSMT): STudents apply the QCAA problem solving and modelling approach to a real-world scenario. Students complete a PSMT in Term 3.
Exams: Students complete exams in Terms 1 and 2, and a semester exam in Term 4.

Structure

Unit 1	Unit 2	Unit 3	Unit 4
Data Representation and Interpretation In this unit, students determine quartiles and interquartile range, construct and interpret box plots and use them to compare data sets. They compare shapes of box plots to corresponding histograms and dot plots and use scatter plots to investigate and comment on relationships between two numerical variables. Students investigate and describe bivariate numerical data where the independent variable is time and evaluate statistical reports in the media and other places by linking claims to displays, statistics and representative data. Students calculate and interpret the mean and standard deviation of data and use these to compare data sets. They use information technologies to investigate bivariate numerical data sets. Where appropriate, students use a straight line to describe the relationship allowing for variation	Pythagoras and Trigonometry In this unit, students solve right-angled triangle problems including those involving direction and angles of Location and transformation elevation and depression. They apply Pythagoras’ Theorem and trigonometry to solving three-dimensional problems in right-angled triangles. Patterns and Algebra Students expand binomial products and factorise monic quadratic expressions using a variety of strategies. Students factorise algebraic expressions by taking out a common algebraic factor and simplify algebraic products and quotients using index laws. They apply the four operations to simple algebraic fractions with numerical denominators and substitute values into formulas to determine an unknown. Students define rational and irrational numbers and perform operations with fractional indices. Units of Measurements Students solve problems involving surface area and volume for a range of prisms, cylinders and composite solids and solve problems involving surface area and volume of right pyramids, right cones, spheres and related composite solids	Money and Financial Mathematics Students connect the compound interest formula to repeated applications of simple interest using appropriate digital technologies. Linear and Non-Linear Relationships In this unit, students solve problems involving linear equations, including those derived from formulas. They solve linear inequalities and graph their solutions on a number line. Students solve linear simultaneous equations, using algebraic and graphical techniques, including using digital technology. They solve problems involving parallel and perpendicular lines and linear equations involving simple algebraic fractions. Chance Students describe the results of two- and three- step chance experiments, both with and without replacements, and assign probabilities to outcomes and determine probabilities of events. They investigate the concept of independence and use the language of ‘if ....then, ‘given’, ‘of’, ‘knowing that’ to investigate conditional statements and identify common mistakes in interpreting such language.	Geometric Reasoning Students formulate proofs involving congruent triangles and angle properties and apply logical reasoning, including the use of congruence and similarity, to proofs and numerical exercises involving plane shapes. Earth Geometry and Time Zones Students investigate Latitude and Longitude, Distance on the Earth’s Surface and Time Zones. Geometry Networks They investigate Vertices(nodes), edges/arcs, region, and Eulers’ formula.

Unit 1

Unit 2

Unit 3

Unit 4

Data Representation and Interpretation

In this unit, students determine quartiles and interquartile range, construct and interpret box plots and use them to compare data sets.

They compare shapes of box plots to corresponding histograms and dot plots and use scatter plots to investigate and comment on relationships between two numerical variables.

Students investigate and describe bivariate numerical data where the independent variable is time and evaluate statistical reports in the media and other places by linking claims to displays, statistics and representative data.

Students calculate and interpret the mean and standard deviation of data and use these to compare data sets. They use information technologies to investigate bivariate numerical data sets. Where appropriate, students use a straight line to describe the relationship allowing for variation

Pythagoras and Trigonometry

In this unit, students solve right-angled triangle problems including those involving direction and angles of Location and transformation elevation and depression. They apply Pythagoras’ Theorem and trigonometry to solving three-dimensional problems in right-angled triangles.

Patterns and Algebra

Students expand binomial products and factorise monic quadratic expressions using a variety of strategies.

Students factorise algebraic expressions by taking out a common algebraic factor and simplify algebraic products and quotients using index laws.

They apply the four operations to simple algebraic fractions with numerical denominators and substitute values into formulas to determine an unknown.

Students define rational and irrational numbers and perform operations with fractional indices.

Units of Measurements

Students solve problems involving surface area and volume for a range of prisms, cylinders and composite solids and solve problems involving surface area and volume of right pyramids, right cones, spheres and related composite solids

Money and Financial Mathematics

Students connect the compound interest formula to repeated applications of simple interest using appropriate digital technologies.

Linear and Non-Linear Relationships

In this unit, students solve problems involving linear equations, including those derived from formulas. They solve linear inequalities and graph their solutions on a number line.

Students solve linear simultaneous equations, using algebraic and graphical techniques, including using digital technology. They solve problems involving parallel and perpendicular lines and linear equations involving simple algebraic fractions.

Chance

Students describe the results of two- and three- step chance experiments, both with and without replacements, and assign probabilities to outcomes and determine probabilities of events.

They investigate the concept of independence and use the language of ‘if ....then, ‘given’, ‘of’, ‘knowing that’ to investigate conditional statements and identify common mistakes in interpreting such language.

Geometric Reasoning

Students formulate proofs involving congruent triangles and angle properties and apply logical reasoning, including the use of congruence and similarity, to proofs and numerical exercises involving plane shapes.

Earth Geometry and Time Zones

Students investigate Latitude and Longitude, Distance on the Earth’s Surface and Time Zones.

Geometry Networks

They investigate Vertices(nodes), edges/arcs, region, and Eulers’ formula.

Essential Equipment

Assessment

Formative assessment

Formative Assessment provides critical feedback to both students and teachers about student progress in the course of study. It does not count towards student grades. Regular formative assessment will occur in the form of online quizzes through JacPlus. The quizzes with be automatically marked and immediate feedback will be available.

Summative assessment

Summative Assessment counts towards student grades and is averaged across two terms for each semester report. Assessment Adjustments for identified students are administered by Home Educators. These include 5 mins per 30 mins working time for Extra Time in Exams AND 5 mins per 30 minutes for Rest breaks. Extra time on assignments in available in consultation with Learning Enrichment.

Exam Conditions:

Exam is available for 48 hours
Working Time: 90 minutes + 5 minutes perusal
Type: Individual, supervised
Part A: Simple Familiar 60%
Part B: Complex Familiar 20%
Part B: Complex Unfamiliar 20%
Technology: Scientific calculator use is expected
Exams need to be downloaded, completed and uploaded as per the task instructions, under home educator supervision.

Problem Solving and Modelling Task (PSMT) conditions:

Type: Individual assignment
Format: Mathematical report (typed)
Page Count: Up to 6 pages
Word Count: Maximum 600-800 words
Technology: Scientific calculator, Google Sheets and or Excel use may be required.

Unit 1	Unit 2	Unit 3	Unit 4
Summative Internal Assessment 1 - Exam	Summative Internal Assessment 2 - Exam	Summative Internal Assessment 3 - PSMT	Summative Internal Assessment 4 - Exam

Intensives

Teacher

Odette Watson

Senior Secondary Mathematics

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