## 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.

*Cambridge International AS & A Level Mathematics: Revision Guide for Pure Mathematics 3 *is a study guide that aims to support students preparing for the Cambridge International AS & A Level Mathematics (9709) examination.

Written by seasoned lecturers, this book provides in-depth coverage of the latest 2020–2022 syllabus for the Pure Mathematics 3 component of the examination. This book is filled with step-by-step worked examples, clear and concise explanations, insightful study tips, and questions from actual past examination papers for self-assessment.

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

*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

*Answers*

**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.