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• 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 *C + b cos *C in the form R sin(*C ± a) or R cos(*C ± 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