CIE A LEVEL PURE MATHEMATICS 2 & 3 2nd EDITION BOOK AND WEBSITE LINK

Table of contents

Syllabus matching grid; 1 Algebra; 1.1 The modulus function; 1.2 Division of polynomials; 1.3 The remainder theorem; 1.4 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 TH + b cos TH in the form R sin(TH +- a) or R cos(TH +- a); Review exercise A - Pure 2; Review exercise A - Pure 3; Maths in real-life: Predicting tidal behaviour; 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 1 x + b; 5.3 Integration of sin (ax + b), cos (ax + b), ec2 (ax + b); 5.4 Extending integration of trigonometric functions; 5.5 Numerical integration using the trapezium rule; 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; Review exercise B - Pure 2; Review exercise B - Pure 3; Maths in real-life: Nature of Mathematics; 7 Further algebra; 7.1 Partial fractions; 7.2 Binomial expansions of the form (1 + x)n when n is not a positive integer; 7.3 Binomial expansions of the form (a + x)n where n is not a positive integer; 7.4 Binomial expansions and partial fractions; 8 Further integration; 8.1 Integration using partial fractions; 8.2 Integration of f(x) f'(x); 8.3 Integration by parts; 8.4 Integration using substitution; Review exercise C - Pure 3; 9 Vectors; 9.1 The equation of a straight line; 9.2 Intersecting lines; 9.3 The angle between two straight lines; 9.4 The equation of a plane; 9.5 Configurations of a line and a plane; 9.6 Configurations of two planes; 9.7 The distance from a point to a plane or 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; Review exercise D - Pure 3; Maths in real-life: Electrifying, magnetic and damp: how complex mathematics makes life simpler; Exam-style paper A - Pure 2; Exam-style paper B - Pure 2; Exam-style paper C - Pure 3; Exam-style paper D - Pure 3; Answers; Glossary of terms; Index