**Complete Pure Mathematics 2/3 Second Edition for Cambridge International AS & A Level by Jean Linsky, James Nicholson, and Brian Western**

## Contents of Complete Pure Mathematics 2/3

- Algebra
- The modulus function
- Division of polynomials
- The remainder theorem
- The factor theorem
- Logarithms and exponential functions
- Continuous exponential growth and decay
- The logarithmic function and logarithms to base e
- Equations and inequalities using logarithms
- Using logarithms to reduce equations to linear form
- Trigonometry
- Secant, cosecant, and cotangent
- Further trigonometric identities
- Addition formulae
- Double angle formulae
- Expressing a sin bcos in the form
- R sin(+a) or R cos(@ta)
- Maths in real-life: Predicting tidal behaviour
- Differentiation
- Differentiating the exponential function
- Differentiating the natural logarithmic function
- Differentiating products
- Differentiating quotients
- Differentiating sinx,cos x, and tanx
- Implicit differentiation
- Parametric differentiation
- Integration
- Integration of sin(ax + b), cos(ax + b), sec (ax + b)
- Extending integration of trigonometric functions
- Numerical integration using the trapezium rule – Pure
- Numerical solution of equations
- Finding approximate roots by change of sign or graphical methods
- Finding roots using iterative relationships
- Convergence behaviour of iterative functions
- Maths in real-life: Nature of mathematics
- Further algebra
- Partial fractions
- Binomial expansions
- Binomial expansions and partial fractions
- Further integration
- Integration using partial fractions
- Integration by parts
- Integration using substitution
- Vectors
- Vector notation
- The magnitude of a vector
- Addition and subtraction of vectors: a geometric approach
- The vector equation of a straight line
- Intersecting lines
- Scalar products
- The angle between two straight lines
- The distance from a point to a line
- Differential equations
- Forming simple differential equations (DE)
- Solving first-order differential equations with separable variables
- Finding particular solutions to differential equations
- Modelling with differential equations
- Complex numbers
- Introducing complex numbers
- Calculating with complex numbers
- Solving equations involving complex numbers
- Representing complex numbers geometrically
- Polar form and exponential form
- Loci in the Argand diagram
- Maths in real-life: Electrifying, magnetic and damp: how complex mathematics makes life simpler
- Exam-style paper A – Pure
- Exam-style paper – Pure
- Exam-style paper A – Pure
- Exam-style paper – Pure
- Answers
- Glossary