CambridgeMATHS Stage 6 : Mathematics Extension 2 Year 12

Introduction
Rationale
About the authors
1 Complex numbers I
	1A The arithmetic of complex numbers
	1B Quadratic equations
	1C The Argand diagram
	1D Modulus-argument form
	1E Vectors and the complex plane
	1F Curves and regions in the Argand diagram
	1G Polynomials and complex numbers
	1H Chapter review exercise
2 Proof
	2A The language of proof
	2B Number proofs
	2C Proof by contraposition and by contradiction
	2D Algebraic inequalities
	2E Induction
	2F Inequalities in geometry and calculus
	2G Chapter review exercise
	Appendix: The fundamental theorem of arithmetic
3 Complex numbers II: de Moivre and Euler
	3A Powers of complex numbers
	3B Trigonometric identities
	3C Roots of complex numbers
	3D Exponential form: Euler’s formula
	3E Applications of exponential form
	3F Chapter review exercise
4 Integration
	4A The standard integrals
	4B Algebraic manipulation
	4C Substitution
	4D Partial fractions
	4E Denominators with quadratics
	4F Integration by parts
	4G Trigonometric integrals
	4H Reduction formulae
	4I Miscellaneous integrals
	4J Chapter review exercise
	Appendix: A short table of integrals
5 Vectors
	5A Coordinates in three dimensions
	5B Vectors in three dimensions
	5C The dot product
	5D Applications of the dot product
	5E Vector proofs in geometry
	5F The vector equation of a line
	5G Vector equations of circles, spheres and planes
	5H Chapter review exercise
	Appendix: Some Geometry in 3D
6 Mechanics
	6A Forces and acceleration
	6B Simple harmonic motion and time
	6C Simple harmonic motion and displacement
	6D Horizontal resisted motion
	6E Vertical resisted motion
	6F Projectile motion
	6G Miscellaneous problems
	6H Chapter review exercise
Answers
	Chapter 1
	Chapter 2
	Chapter 3
	Chapter 4
	Chapter 5
	Chapter 6
Index