Mathematics: Revision Guide for Pure Mathematics 3

ISBN-13: 9789675492075 / Angielski / Miękka / 2020 / 328 str.

Amy Khoo;Lip Seong Lee;Yau Yong

Opis

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.

Spis treści

• 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