NSW Year 12 Maths Extension 2 - Coursebook
Extension 2 is the most demanding maths offered in NSW — complex numbers, advanced calculus, three-dimensional vectors and rigorous proof. Every step is shown, 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 12 Mathematics Extension 2 is the highest level of school mathematics offered in NSW and demands a deep level of mathematical understanding, precision, and logical reasoning. Students are required to work fluently with complex numbers, advanced calculus, three-dimensional vectors, and rigorous proof techniques.
Many students find Extension 2 challenging not because of a lack of ability, but because explanations are often brief, working is condensed, and links between concepts are not made explicit.
Our Solution
The Class Mathematics NSW Year 12 Mathematics Extension 2 Coursebook is designed as a comprehensive and structured guide through the entire Extension 2 syllabus. Each topic is developed carefully, with clear explanations and step-by-step worked solutions that emphasise mathematical reasoning and method.
This coursebook supports students in mastering complex ideas by breaking them into logical steps, helping students build confidence, accuracy, and depth of understanding required for Extension 2 assessments and the HSC.
Why This Book Works
- Complete coverage of the NSW Year 12 Mathematics Extension 2 syllabus
- Strong emphasis on proof, algebraic manipulation, and reasoning
- Fully worked solutions for every question – , showing complete and rigorous methods
- Clear explanations of advanced concepts – including complex numbers and integration techniques
- Past HSC questions included – and organised by topic
- Ideal for assessment preparation and HSC revision
Who This Book Is For
This book contains 5 chapters and includes the following topics:
- 1 Complex Numbers
- 2 Proof
- 3 Further Work With Vectors
- 4 Integration
- 5 Mechanics
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.
Complex Numbers
- Arithmetic and Quadratic Equations
- Argand Diagram
- Eulers Theorem
- De Moivres Theorem
- Complex Numbers and Polynomials
- Zeros of a Polynomial
- Complex Coefficients of a Polynomial
- Vector Problems
- Roots of Complex Numbers
- Curves and Regions
Proof
- Language of Proof
- Methods of Proof
- Inequalities Proof
- Induction Series
- Induction Divisibility
- Induction Inequalities
- Induction Other
- Induction Recursive
Further Work With Vectors
- Coordinates in 3D
- Vectors in Three Dimensions
- The Dot Product
- Applications of the Dot Product
- Vector Proofs in Geometry
- Vector Equation of a Line
- Vector Equations of Circles, Spheres and Planes
Integration
- Trig Functions
- Inverse Trig Functions
- Log Functions
- t Formulae
- Partial Fractions
- Integration by Parts
- Recurrence Relations
- Applications
Mechanics
- Velocity, Acceleration as a Function of x
- Simple Harmonic Motion (SHM)
- Motion in Physical Terms
- Resisted Motion
- Projectiles in Resisted Motion
- Resistance Proportional to v^2
- Projectile Motion Without Resistance
Inside the book
See exactly how a topic is explained and how a solution is worked, before you buy.
SAMPLESample teaching pages — how a topic is explained
SAMPLESample worked answers — every question, fully solved
