**Description:**

**This resource is endorsed by
Cambridge Assessment International Education**.

Take mathematical understanding
to the next level with this accessible series, written by experienced authors,
examiners and teachers.

**Improve confidence as a mathematician** with clear explanations, worked examples, diverse activities and
engaging discussion points.**Advance problem-solving, interpretation and communication skills** through a wealth of questions that promote higher-order thinking.**Prepare for further study or life beyond the classroom** by applying mathematics to other subjects and modelling
real-world situations.**Reinforce learning** with
accompanying digital practice available on MEI’s Integral® online teaching and
learning platform.

This book covers the syllabus
content for **Further** **Pure Mathematics 2 **[9231], including
hyperbolic functions, matrices, differentiation, integration, complex numbers
and differential equations.

**Contents:**

Introduction

How to use this book

The Cambridge International AS
& A Level Further Mathematics 9231 syllabus

**Chapter 1: Hyperbolic functions** • Hyperbolic functions • Inverse Hyperbolic functions

**Chapter 2: Matrices** • Important results relating to 2 x 2 matrices • Finding the
inverse of a 3 x 3 matrix • Intersection of three planes • Eigenvalues and
eigenvectors

**Chapter 3: Differentiation** • Differentiating inverse trigonometric functions •
Differentiating hyperbolic functions •
Differentiating inverse hyperbolic functions • Finding the second
derivative for relations given implicitly • Finding the second derivative for
relations given parametrically • Polynomial approximations and Maclaurin series
• Using the Maclaurin series for standard functions

**Chapter 4: Integration** • Integration using the inverse sine function • Integrating
hyperbolic functions • Integration using inverse hyperbolic functions •
Integration using reduction formulae • Approximation of areas using rectangles
• Using areas under curves to approximate series sums • The arc length of a curve
• Surface area of a solid of revolution

**Chapter 5: Complex numbers** • The modulus and argument of a complex number • De Moivre’s
theorem • The *n*th roots of a complex number • Finding multiple angle
identities using de Moivre’s theorem • The form *z* = re^{i?}

**Chapter 6: Differential equations** • Integrating factors • Second order differential equations •
Auxiliary equations with complex roots • Non-homogeneous differential equations
• Use of substitutions to transform differential equations

Index

**Target Audience:**

This textbook is written for the
latest Cambridge International AS & A Level Further Mathematics syllabus
(9231).