## Mathematics #### 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
Acknowledgements

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