Front cover — NSW Year 12 Maths Extension 1 - Coursebook

Inside cover — NSW Year 12 Maths Extension 1 - Coursebook

Contents — NSW Year 12 Maths Extension 1 - Coursebook

Sample theory pages — NSW Year 12 Maths Extension 1 - Coursebook

Sample practice questions — NSW Year 12 Maths Extension 1 - Coursebook

Sample worked answers — NSW Year 12 Maths Extension 1 - Coursebook

NSW Year 12 Maths Extension 1 - Coursebook

Extension 1 asks students to handle complex algebra, formal proof, calculus and vectors in unfamiliar settings. Every step is shown, with a fully worked solution for every question.

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Hyperlinked solutions — tap any question, jump straight to its worked answer
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Both formats: a fully worked solution for every question · QR-code video tutorials · aligned to the NSW Year 7 syllabus

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Fully aligned to the NSW Year 7 Mathematics syllabus

Written by John Kinny-Lewis — 45+ years teaching maths

A fully worked solution for every question

The Challenge

Year 12 Mathematics Extension 1 builds on Advanced Mathematics and introduces a significant increase in difficulty, abstraction, and mathematical reasoning. Students are expected to manipulate complex algebra, construct formal proofs, and apply calculus and vectors in unfamiliar contexts.

Many students struggle when explanations are brief, working steps are skipped, or questions are not clearly linked to the syllabus outcomes assessed in the HSC.

Our Solution

The Class Mathematics NSW Year 12 Mathematics Extension 1 Coursebook is designed as a complete, structured guide through the entire Extension 1 syllabus. Each topic is clearly explained, with methods broken down step by step to help students develop confidence and accuracy.

The book focuses heavily on algebraic manipulation, proof, vectors, and calculus — the core skills required to succeed in Extension 1 and perform strongly in the HSC.

Why This Book Works

Complete coverage of the NSW Year 12 Mathematics Extension 1 syllabus
Strong emphasis on algebraic reasoning and proof
Fully worked solutions for every question – , showing full logical working
Past HSC questions included – and organised by topic
Clear explanations of complex concepts – such as vectors, calculus, and differential equations
Ideal for assessment preparation and HSC revision

Who This Book Is For

Students completing NSW Year 12 Mathematics Extension 1

Students aiming for strong HSC performance in Extension 1 mathematics

Students who want clear structure and fully explained solutions

Parents supporting high-performing mathematics students

This book contains 7 chapters and includes the following topics:

1 Trig Equations
2 Proof
3 Vectors
4 Calculus
5 Differential Equations
6 Projectile Motion
7 Binomial Distribution

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.

Trig Equations

Compound Angle Equations
Auxiliary Angle Method
t Formulae Method

Proof

Series
Divisibility

Vectors

Vector Basics
Vectors in Two Dimensions
Vectors in Component Form
Scalar Product of Vectors
Projection of Vectors
Vectors in Geometry

Calculus

Integration by Substitution
Trig Integration
Derivative of Inverse Functions
Integrations that give Inverse Trig Functions
Volumes of Solids of Revolution

Differential Equations

Introduction to Differential Equations (DEs)
Direction Fields
Solving y=f(x)
Solving y=g(y)
Solving y=f(x)g(y)
Modelling First Order

Projectile Motion

Time Equations
Equation of Path

Binomial Distribution

Bernoulli Trials
Binomial Distribution
Mean and Variance of a Binomial Distribution
Normal Approximation of the Sample Proportion

See how it teaches

Inside the book

See exactly how a topic is explained and how a solution is worked, before you buy.

SAMPLE

Sample teaching pages — how a topic is explained

SAMPLE

Sample worked answers — every question, fully solved

The author

Written by John Kinny-Lewis

45+ years in the classroom. He wrote this book because students were hitting Year 7 algebra with no way to check their own work — and parents couldn't help once the methods changed.