Tailored for students undertaking Pure Mathematics 3 (Paper 3) of the Cambridge International AS & A Level Mathematics (9709) examination. Written by seasoned lecturers and complete with step-by-step worked examples, useful tips, and questions from actual past examination papers, this book covers the latest 2020-2022 syllabus for Pure Mathematics 3.
Yong Yau has taught Mathematics and Further Mathematics at pre-university level for 45 years. An experienced trainer and examiner, he is Master Teacher, Principal Lecturer and Head of the A Level Mathematics/Further Mathematics department at Sunway College, Malaysia. Lee Lip Seong is Senior Lecturer and Deputy Head of the A Level Mathematics/Further Mathematics department at Sunway College, Malaysia. Since 2017, he is also examiner for the Cambridge IGCSE Additional Mathematics and Singapore GCE O Level Mathematics papers. Amy Khoo has been teaching A Level Mathematics and Further Mathematics for over 10 years. Formerly a lecturer at Sunway College, Malaysia, she is now based in China.
Cambridge International AS & A Level Mathematics 9709 Syllabus How to use this book 1 The Modulus Function Definition of modulus function Sketching graphs of modulus functions Solving equations involving modulus functions Solving inequalities involving modulus functions 2 Polynomials and Polynomial Equations Definition of polynomials Equality and operations Remainder theorem and factor theorem Factorisation of polynomialsPolynomial equations and inequalities 3 The Binomial Series Binomial theorem Expressing rational expressions in partial fractions Using partial fractions in binomial expansion 4 Exponential and Logarithmic Functions Exponential functions Logarithmic functions Graphs of exponential and logarithmic functions Solving exponential and logarithmic equations Transforming a non-linear relationship into linear form 5 Trigonometry Graphs of secant, cosecant and cotangent functions Fundamental identities Harmonic form Use of harmonic form 6 Differentiation Derivative of logarithmic function Derivative of exponential function Derivative of trigonometric function Techniques of differentiation Derivative of Implicit and parametric differentiations Applications of differentiation 7 Integration Standard formulae and rules Integrating rational functions Integrating exponential functions Integrating trigonometric functions Integration by parts Integration by substitution 8 Differential Equations General and particular solution Rate of change 9 Numerical Solutions of Equations The graphical method and change of signIterative method 10 Vectors Definition of vectors Vectors in two-dimensional space Vectors in three-dimensional space Scalar product of two vectors The vector equation of a straight line Parallel, intersecting or skew lines The perpendicular distance from a point to a line The angle between two lines 11 Complex Numbers Definition of complex numbers Fundamental processes The conjugate of complex numbers Argand diagram, modulus and argument Square roots of complex numbers Solving polynomial equations with complex roots Solving quadratic equations with non-real coefficients Geometrical effects Locus problems Inequalities of a complex number Answers
