Complete Pure Mathematics 2 & 3

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
  • 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

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