Complete Pure Mathematics 2 & 3 for Cambridge International AS & A Level
$36.24

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

By Jean Linsky, Brian Western, James Nicholson
US$ 36.24
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Book Description

Providing complete syllabus support (9709), this stretching and practice-focused course builds the advanced skills needed for the latest Cambridge assessments and the transition to higher education. Engaging, real world examples make mathematics relevant to real life.

Table of Contents
  • Front Cover
  • Title Page
  • Contents
  • Introduction
  • 1 Algebra
    • 1.1 The modulus function
    • 1.2 Sketching linear graphs of the form y = a|x| + b
    • 1.3 Division of polynomials
    • 1.4 The remainder theorem
    • 1.5 The factor theorem
  • 2 Logarithms and exponential functions
    • 2.1 Continuous exponential growth and decay
    • 2.2 The logarithmic function
    • 2.3 ex and logarithms to base e
    • 2.4 Equations and inequalities using logarithms
    • 2.5 Using logarithms to reduce equations to linear form
  • 3 Trigonometry
    • 3.1 Secant, cosecant, and cotangent
    • 3.2 Further trigonometric identities
    • 3.3 Addition formulae
    • 3.4 Double angle formulae
    • 3.5 Expressing a sin θ + b cos θ in the form R sin(θ ± α) or R cos(θ ± α)
    • Maths in real-life
  • 4 Differentiation
    • 4.1 Differentiating the exponential function
    • 4.2 Differentiating the natural logarithmic function
    • 4.3 Differentiating products
    • 4.4 Differentiating quotients
    • 4.5 Differentiating sin x, cos x, and tan x
    • 4.6 Implicit differentiation
    • 4.7 Parametric differentiation
  • 5 Integration
    • 5.1 Integration of eax+b
    • 5.2 Integration of 1ax + b
    • 5.3 Integration of sin (ax + b), cos (ax + b), sec2 (ax + b)
    • 5.4 Extending integration of trigonometric functions
    • 5.5 Numerical integration using the trapezium rule – Pure 2
  • 6 Numerical solution of equations
    • 6.1 Finding approximate roots by change of sign or graphical methods
    • 6.2 Finding roots using iterative relationships
    • 6.3 Convergence behaviour of iterative functions
    • Maths in real-life
  • 7 Further algebra
    • 7.1 Partial fractions
    • 7.2 Binomial expansions of the form (1 + x)n when nis not a positive integer
    • 7.3 Binomial expansions of the form (a + x) n where n is nota positive integer
    • 7.4 Binomial expansions and partial fractions
  • 8 Further integration
    • 8.1 Integration using partial fractions
    • 8.2 Integration of 1x2+a2
    • 8.3 Integration of kf ′(x)f(x)
    • 8.4 Integration by parts
    • 8.5 Integration using substitution
  • 9 Vectors
    • 9.1 Vector notation
    • 9.2 The magnitude of a vector
    • 9.3 Addition and subtraction of vectors: a geometric approach
    • 9.4 The vector equation of a straight line
    • 9.5 Intersecting lines
    • 9.6 Scalar products
    • 9.7 The angle between two straight lines
    • 9.8 The distance from a point to a line
  • 10 Differential equations
    • 10.1 Forming simple differential equations (DEs)
    • 10.2 Solving first-order differential equations with separable variables
    • 10.3 Finding particular solutions to differential equations
    • 10.4 Modelling with differential equations
  • 11 Complex numbers
    • 11.1 Introducing complex numbers
    • 11.2 Calculating with complex numbers
    • 11.3 Solving equations involving complex numbers
    • 11.4 Representing complex numbers geometrically
    • 11.5 Polar form and exponential form
    • 11.6 Loci in the Argand diagram
    • Maths in real-life
  • Exam-style paper 2A – Pure 2
  • Exam-style paper 2B – Pure 2
  • Exam-style paper 3A – Pure 3
  • Exam-style paper 3B – Pure 3
  • Answers
  • Glossary
  • Index
  • Index
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