# 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

Answers

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

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