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