Revision Guide for Pure Mathematics 3 (Second Edition)

Mathematics: Revision Guide for Pure Mathematics 3 is the 2nd edition study guide tailored for students undertaking Pure Mathematics 3 of the Cambridge International AS & A Level Mathematics (9709) examination. It provides in-depth coverage of the latest syllabus and serves to help students prepare for the examination more effectively.

Written by a seasoned lecturer with 50 years of experience, this book is filled with step-by-step worked examples, clear and concise explanations, insightful study tips, alternative methods to finding a solution, and questions from actual past examination papers for self-assessment.

This book is suitable for students taking the Pure Mathematics 3 component of Cambridge International AS & A Level Economics (9709).

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 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


Yong Yau has taught Mathematics and Further Mathematics at pre-university level for 50 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.