1 Algebra; 1.1 Operations with polynomials; 1.2 Solution of polynomial equations; 1.3 The modulus function; 2 Logarithms and exponentials; 2.1 Exponential functions; 2.2 Logarithms; 2.3 Graphs of logarithms; 2.4 Modelling curves; 2.5 The natural logarithm function; 2.6 The exponential function; 3 Trigonometry; 3.1 Reciprocal trigonometrical functions; 3.2 Compound-angle formulae; 3.3 Double-angle formulae; 3.4 The forms r cos(±), r sin(±). 3.5 The general solutions of trigonometrical equations 4 Differentiation; 4.1 The product rule; 4.2 The quotient rule; 4.3 Differentiating natural logarithms and exponentials; 4.4 Differentiating trigonometrical functions; 4.5 Differentiating functions defined implicitly; 4.6 Parametric equations; 4.7 Parametric differentiation; 5 Integration; 5.1 Integrals involving the exponential function; 5.2 Integrals involving the natural logarithm function; 5.3 Integrals involving trigonometrical functions; P2 5.4 Numerical integration; 6 Numerical solution of equations. 6.1 Interval estimation? change-of-sign methods6.2 Fixed-point iteration; 6.3 Problems with the fixed-point iteration method; 7 Further algebra; 7.1 The general binomial expansion; 7.2 Review of algebraic fractions; 7.3 Partial fractions; 7.4 Using partial fractions with the binomial expansion; 8 Further calculus; 8.1 Differentiating tan-1 x; 8.2 Integration by substitution; 8.3 Integrals involving exponentials and natural logarithms; 8.4 Integrals involving trigonometrical functions; 8.5 The use of partial fractions in integration; 8.6 Integration by parts; 8.7 General integration. 9 Differential equations9.1 Forming differential equations from rates of change; 9.2 Solving differential equations; 10 Vectors; 10.1 Vectors in two dimensions; 10.2 Vectors in three dimensions; 10.3 Vector calculations ; 10.4 The angle between two vectors; 10.5 The vector equation of a line; 10.6 The intersection of two lines; 10.7 The angle between two lines; 10.8 The perpendicular distance from a point to a line; 11 Complex numbers; 11.1 Extending the number system; 11.2 Working with complex numbers; 11.3 Sets of points in an Argand diagram. 11.4 The modulus?argument form of complex numbers11.5 Sets of points using the polar form; 11.6 Working with complex numbers in polar form; 11.7 Complex exponents; 11.8 Complex numbers and equations

Endorsed by Cambridge Assessment International Education to provide full support for Paper 2 and 3 of the syllabus for examination from 2020. Take mathematical understanding to the next level with this accessible series, written by experienced authors, examiners and teachers. - Improve confidence as a mathematician with clear explanations, worked examples, diverse activities and engaging discussion points. - Advance problem-solving, interpretation and communication skills through a wealth of questions that promote higher-order thinking.