NSW Year 10 Maths - Advanced Coursebook
Year 10 Advanced is the bridge to senior maths, where procedural methods stop being enough. Every concept is built from the ground up, with a fully worked solution for every question.
Both formats: a fully worked solution for every question · QR-code video tutorials · aligned to the NSW Year 7 syllabus
The Challenge
Year 10 Advanced Maths is a critical transition year. Students are expected to move beyond procedural methods and develop a deep understanding of key concepts, particularly algebra. Without strong foundations, students can struggle when entering Year 11 Advanced or Extension 1 courses.
Our Solution
The Class Mathematics NSW Year 10 Advanced Maths Coursebook is designed to build strong conceptual understanding and problem-solving skills. Topics are explained clearly and explored in depth, helping students master the ideas required for success in Year 11 Advanced and Extension 1 Mathematics.
Why This Book Works
- Strong focus on conceptual understanding – not just applying formulas
- Extensive algebra coverage – essential for senior mathematics success
- Challenging and extension-style questions – preparing students for advanced pathways
- Fully worked solutions for every question – clear, logical methods students can learn from
- Hyperlinked solutions in the digital edition – move easily between questions and worked solutions
- Video support via QR codes – additional explanation for more demanding concepts
- Fully aligned to the NSW Year 10 Advanced Mathematics syllabus
- Instant digital access – or printed book with free shipping
Who This Book Is For
This book contains 16 chapters and includes the following topics:
- 1 Algebra Review
- 2 Surds
- 3 Earning Money
- 4 Straight Line Graphs
- 5 Measurement
- 6 Indices
- 7 Trigonometry
- 8 Quadratics
- 9 Probability
- 10 Simultaneous Equations
- 11 Single Variable and Bivariant Statistics
- 12 Geometric Figures
- 13 Logarithms and Polynomials
- 14 Circle Geometry
- 15 Non Linear Relationships Functions and Graphs
- 16 Networks
Each chapter includes clear theory, worked examples, graded practice questions, and fully worked solutions. QR codes throughout link to short video tutorials for additional support.
Algebra Review
- Adding and Subtracting Algebraic Fractions
- Multiplying and Dividing Algebraic Fractions
- Equations with Fractions
- Equation Problems
- Solving Inequalities
- Graphing Inequalities
Surds
- Simplifying Surds
- Surds and Rational Numbers
- Adding and Subtracting Surds
- Multiplying and Dividing Surds
- Binomial Products
- Rationalising the Denominator
Earning Money
- Earning an Income
- Income Tax
- Simple Interest
- Compound Interest
- Term Payments
- Depreciation
Straight Line Graphs
- Length of an Interval
- Midpoint of an Interval
- Gradient of an Interval
- Parallel and Perpendicular Lines
- Equation of Lines
- Graphing Linear Equations
- Finding the Equation of a Line Graphically
- Linear Models
Measurement
- Converting Units
- Accuracy of Measuring Instruments
- Pythagoras Theorem in 3D
- Area of Triangles and Quadrilaterals
- Area of Circles and Sectors
- Surface Area of Prisms
- Surface Area of Cylinders
- Surface Area of Pyramids
- Surface Area of Cones
- Surface Area of Composite Solids
- Volume of Prisms and Cylinders
- Volume of Pyramids and Cones
- Volume of Composite Solids
- Surface Area and Volume of Spheres
- Similar Solids
Indices
- Multiplication and Division Index Laws
- Power of a Power
- Zero and Negative Indices
- Scientific Notation
- Fractional Indices
- Exponential Equations
Trigonometry
- Trigonometric Ratios
- Finding Unknown Angles
- Finding Unknown Sides
- 2D Applications
- Bearings
- 3D Trigonometry
- Obtuse Angles and Exact Values
- Sine Rule
- Cosine Rule
- Area Rule
- The Four Quadrants
- Graphs of Trig Functions
Quadratics
- Expanding Quadratic Expressions
- Factorising Monic Quadratic Trinomials
- Factorising Non-Monic Quadratic Trinomials
- Factorising Special Binomial Products
- Factorising by Completing the Square
- Solving Quadratics by Factorising
- Solving Quadratics by the Quadratic Formula
- Solving Quadratics by Completing the Square
- Solving Higher Order Quadratics by Substitution
- Using Quadratics to Solve Problems
Probability
- Basic Concepts
- Venn Diagrams
- Two-Way Tables
- Mutually and Non-Mutually Exclusive Events
- Conditional Probability
- Arrays and Two-Step Experiments with Tables and Tree Diagrams
- Probability Tree Diagrams
- Dependent and Independent Events
- Sampling with Replacement
- Sampling without Replacement
Simultaneous Equations
- Substitution
- Elimination
- Graphically
- Non-Linear
- Simultaneous Equations Problems
Single Variable and Bivariant Statistics
- Shapes of Distributions
- Quartiles and Inter Quartile Range
- Boxplots
- Parallel Boxplots
- Standard Deviation
- Comparing Means and Standard Deviations
- Comparing Data Sets
- Scatter Plots
- Line of Best Fit
- Bivariant Data
Geometric Figures
- Basic Geometry
- Congruent Triangles
- Similar Figures
- Similar Triangles
- Network Diagrams
- Eulerian and Network Problems
- Shortest Path
Logarithms and Polynomials
- Logarithms Basics
- Logarithm Graphs
- Logarithm Laws
- Solving Equations using Logarithms
- Polynomials
- Expanding Polynomials
- Dividing Polynomials
- Remainder Theorem
- Factor Theorem
- Factoring Polynomials to find Zeros
- Graphs of Polynomials
Circle Geometry
- Circle Facts
- Angle Properties of Circles
- Tangent Properties
- Chord, Secant and Tangent Properties
Non Linear Relationships Functions and Graphs
- Travel Graphs
- Exploring Parabolas
- Sketching Parabolas Using Transformations
- Sketching Parabolas Using Factorisation
- Sketching Parabolas By Completing The Square
- Sketching Parabolas Using The Quadratic Formula And The Discriminant
- Applications of Parabolas
- Lines And Parabolas
- Functions and Notations
- Graphs of Circles
- Exponential Functions
- Hyperbola
- Cubic Equations
- Further Transformations
- Using Graphs to Describe Change
- Literal Equations
- Inverse Functions
- Direct Variation
- Inverse Variation
Networks
- Eulerian Trails and Circuits
- Networks
- Planar Graphs and Euler's formula
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