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Cambridge International AS & A Level Mathematics: Revision Guide for Pure Mathematics 3

Cambridge International AS & A Level Mathematics: Revision Guide for Pure Mathematics 3

Cambridge International AS & A Level Mathematics: Revision Guide for Pure Mathematics 3 is 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.

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 polynomials

   Polynomial 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 sign

   Iterative 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


Author Yong Yau, Lee Lip Seong, Amy Khoo
Pages 328
Published 2020

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Tags: Mathematics, Cambridge, Sunway University Press