# Complete Pure Mathematics 2/3 for Cambridge International AS & A Level

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
• 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
• Glossary