CIMA - C3 Fundamentals Of Business Mathematics

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In this February 2010 new edition

• A user-friendly format for easy navigation

• Regular fast forward summaries emphasising the key points in each chapter

• Assessment focus points showing you what the assessor will want you to do

• Questions and quick quizzes to test your understanding

• Question bank containing objective test questions with answers

• A full index

BPP's i-Pass product also supports this paper.

FOR ASSESSMENTS IN 2010 and 2011

Certificate Paper C3

FUNDAMENTALS OF

BUSINESS MATHEMATICS

For assessments in 2010 and 2011

Study Text

First edition June 2006

Third edition February 2010

ISBN 9780 7517 8070 3

(previous edition 9780 7517 5281 6)

e-ISBN 9780 7517 8398 8

British Library Cataloguing-in-Publication Data

A catalogue record for this book

is available from the British Library

Published by

BPP Learning Media Ltd

Aldine House, Aldine Place

London W12 8AW

www.bpp.com/learningmedia

Printed in the United Kingdom

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without the prior written permission of BPP Learning

Media Ltd.

We are grateful to the Chartered Institute of

Management Accountants for permission to reproduce

past examination questions. The suggested solutions

in the Answer bank have been prepared by BPP

Learning Media Ltd.

BPP Learning Media Ltd

2010

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iii

Contents

Page

Introduction

The BPP Learning Media Study Text – The BPP Learning Media Effective Study Package – Help

yourself study for your CIMA assessment – Learning outcomes and syllabus content – The

assessment – Tackling multiple choice questions – Tackling objective choice questions

Part A Basic mathematics

1a Basic mathematical techniques...................................................................................................................................................3

1b Formulae and equations............................................................................................................................................................43

Part B Summarising and analysing data

2 Data and information.................................................................................................................................................................71

3 Data presentation ......................................................................................................................................................................85

4a Averages .................................................................................................................................................................................117

4b Dispersion ..............................................................................................................................................................................131

5 Index numbers ........................................................................................................................................................................149

Part C Probability

6 Probability ..............................................................................................................................................................................167

7 Distributions ...........................................................................................................................................................................189

Part D Financial mathematics

8 Compounding.........................................................................................................................................................................211

9 Discounting and basic investment appraisal...........................................................................................................................233

Part E Inter-relationships between variables

10 Correlation and linear regression............................................................................................................................................261

Part F Forecasting

11 Forecasting .............................................................................................................................................................................281

Part G Spreadsheets

12 Spreadsheets ..........................................................................................................................................................................305

Appendix: Tables and formulae.....................................................................................................................................313

Question bank .........................................................................................................................................................................325

Answer bank.............................................................................................................................................................................357

Index.............................................................................................................................................................................................395

Review form and free prize draw

iv Introduction

The BPP Learning Media Study Text

Aims of this Study Text

To provide you with the knowledge and understanding, skills and application techniques that you need if you are

to be successful in your exams

This Study Text has been written around the Fundamentals of Business Mathematics syllabus.

• It is comprehensive. It covers the syllabus content. No more, no less.

• It is written at the right level. Each chapter is written with CIMA's precise learning outcomes in

mind.

• It is targeted to the assessment. We have taken account of guidance CIMA has given and the

assessment methodology.

To allow you to study in the way that best suits your learning style and the time you have available, by following

our

ersonal Stud

Plan

(

see

(

vii

))

You may be studying at home on your own until the date of the exam, or you may be attending a full-time course.

You may like to (and have time to) read every word, or you may prefer to (or only have time to) skim-read and

devote the remainder of your time to question practice. Wherever you fall in the spectrum, you will find the BPP

Learning Media Study Text meets your needs in designing and following your personal Study Plan.

To tie in with the other components of the BPP Learning Media Effective Study Package to ensure you have the

best possible chance of passing the exam

(

see page

(

)

Learning to Learn Accountancy

BPP Learning Media's ground-breaking Learning to Learn Accountancy book is designed to be used both at the

outset of your CIMA studies and throughout the process of learning accountancy. It challenges you to consider

how you study and gives you helpful hints about how to approach the various types of paper which you will

encounter. It can help you focus your studies on the subject and exam, enabling you to acquire knowledge,

practise and revise efficiently and effectively.

Introduction v

The BPP Learning Media Effective Study Package

Recommended

period of use

The BPP Learning Media Effective Study Package

From the outset and

throughout

Learning to Learn Accountancy

Read this invaluable book as you begin your studies and refer to it as you work through the

various elements of the BPP Learning Media Effective Study Package. It will help you to

acquire knowledge, practise and revise, efficiently and effectively.

Three to twelve

months before the

assessment

Study Text

Use the Study Text to acquire knowledge, understanding, skills and the ability to apply

techniques.

Throughout

i-Pass

i-Pass, our computer-based testing package, provides objective test questions in a variety of

formats and is ideal for self-assessment.

One to six months

before the assessment

Practice & Revision Kit

Try the numerous assessment-format questions, for which there are full worked solutions

where relevant prepared by BPP Learning Media's own authors. Then attempt the two mock

assessments.

From three months

before the assessment

until the last minute

Passcards

Work through these short, memorable notes which are focused on what is most likely to

come up in the assessment you will be sitting.

vi Introduction

Help yourself study for your CIMA assessment

Assessments for professional bodies such as CIMA are very different from those you have taken at college or

university. You will be under greater time pressure before the assessment – as you may be combining your

study with work. There are many different ways of learning and so the BPP Study Text offers you a number of

different tools to help you through. Here are some hints and tips: they are not plucked out of the air, but based on

research and experience. (You don't need to know that long-term memory is in the same part of the brain as

emotions and feelings - but it's a fact anyway.)

The right approach

1 The right attitude

Believe in yourself

Yes, there is a lot to learn. Yes, it is a challenge. But thousands have

succeeded before and you can too.

Remember why you're doing it

Studying might seem a grind at times, but you are doing it for a reason: to

advance your career.

2 The right focus

Read through the Syllabus and

learning outcomes

These tell you what you are expected to know and are supplemented by

Assessment focus points in the text.

3 The right method

The whole picture

You need to grasp the detail - but keeping in mind how everything fits into

the whole picture will help you understand better.

• The Introduction of each chapter puts the material in context.

• The Syllabus content, Learning outcomes and Assessment focus

points show you what you need to grasp.

In your own words

To absorb the information (and to practise your written communication

skills), it helps to put it into your own words.

• Take notes.

• Answer the questions in each chapter. You will practise your written

communication skills, which become increasingly important as you

progress through your CIMA exams.

• Draw mindmaps.

• Try 'teaching' a subject to a colleague or friend.

Give yourself cues to jog your

memory

The BPP Learning Media Study Text uses bold to highlight key points.

• Try colour coding with a highlighter pen.

• Write key points on cards.

Introduction vii

4 The right review

Review, review, review It is a fact that regularly reviewing a topic in summary form can fix it in your

memory. Because review is so important, the BPP Learning Media Study

Text helps you to do so in many ways.

• Chapter roundups summarise the 'fast forward' key points in each

chapter. Use them to recap each study session.

• The Quick quiz is another review technique you can use to ensure that

you have grasped the essentials.

• Go through the Examples in each chapter a second or third time.

Developing your personal Study Plan

BPP Learning Media's Learning to Learn Accountancy book emphasises the need to prepare (and use) a study

plan. Planning and sticking to the plan are key elements of learning success.

There are four steps you should work through.

Step 1 How do you learn?

First you need to be aware of your style of learning. The BPP Learning Media Learning to Learn

Accountancy book commits a chapter to this self-discovery. What types of intelligence do you

display when learning? You might be advised to brush up on certain study skills before launching

into this Study Text.

BPP Learning Media's Learning to Learn Accountancy book helps you to identify what intelligences

you show more strongly and then details how you can tailor your study process to your preferences.

It also includes handy hints on how to develop intelligences you exhibit less strongly, but which

might be needed as you study accountancy.

Are you a theorist or are you more practical? If you would rather get to grips with a theory before

trying to apply it in practice, you should follow the study sequence on page (ix). If the reverse is true

(you like to know why you are learning theory before you do so), you might be advised to flick

through Study Text chapters and look at examples, case studies and questions (Steps 8, 9 and 10 in

the suggested study sequence) before reading through the detailed theory.

Step 2 How much time do you have?

Work out the time you have available per week, given the following.

• The standard you have set yourself

• The time you need to set aside later for work on the Practice & Revision Kit and Passcards

• The other exam(s) you are sitting

• Very importantly, practical matters such as work, travel, exercise, sleep and social life

Hours

Note your time available in box A. A

viii Introduction

Step 3 Allocate your time

• Take the time you have available per week for this Study Text shown in box A,

multiply it by the number of weeks available and insert the result in box B. B

• Divide the figure in box B by the number of chapters in this text and insert the

result in box C. C

Remember that this is only a rough guide. Some of the chapters in this book are longer and more

complicated than others, and you will find some subjects easier to understand than others.

Step 4 Implement

Set about studying each chapter in the time shown in box C, following the key study steps in the

order suggested by your particular learning style.

This is your personal Study Plan. You should try and combine it with the study sequence outlined

below. You may want to modify the sequence a little (as has been suggested above) to adapt it to

your personal style.

BPP Learning Media's Learning to Learn Accountancy gives further guidance on developing a study

plan, and deciding where and when to study.

Suggested study sequence

It is likely that the best way to approach this Study Text is to tackle the chapters in the order in which you find

them. Taking into account your individual learning style, you could follow this sequence.

Key study steps Activity

Step 1

Topic list

Each numbered topic is a numbered section in the chapter.

Step 2

Introduction

This gives you the big picture in terms of the context of the chapter, the learning outcomes the

chapter covers, and the content you will read. In other words, it sets your objectives for study.

Step 3

Fast forward

Fast forward boxes give you a quick summary of the content of each of the main chapter

sections. They are listed together in the roundup at the end of each chapter to provide you with

an overview of the contents of the whole chapter.

Step 4

Explanations

Proceed methodically through the chapter, reading each section thoroughly and making sure

you understand.

Step 5

Key terms and

Assessment focus

points

• Key terms can often earn you easy marks if you state them clearly and correctly in an

appropriate exam answer (and they are highlighted in the index at the back of the text).

• Assessment focus points state how we think the examiner intends to examine certain

topics.

Step 6

Note taking

Take brief notes, if you wish. Avoid the temptation to copy out too much. Remember that being

able to put something into your own words is a sign of being able to understand it. If you find

you cannot explain something you have read, read it again before you make the notes.

Introduction ix

Key study steps Activity

Step 7

Examples

Follow each through to its solution very carefully.

Step 8

Questions

Make a very good attempt at each one.

Step 9

Answers

Check yours against ours, and make sure you understand any discrepancies.

Step 10

Chapter roundup

Work through it carefully, to make sure you have grasped the significance of all the fast

forward points.

Step 11

Quick quiz

When you are happy that you have covered the chapter, use the Quick quiz to check how much

you have remembered of the topics covered and to practise questions in a variety of formats.

Step 12

Question(s) in the

question bank

Either at this point, or later when you are thinking about revising, make a full attempt at the

Question(s) suggested at the very end of the chapter. You can find these at the end of the

Study Text, along with the Answers so you can see how you did.

Short of time: Skim study technique?

You may find you simply do not have the time available to follow all the key study steps for each chapter, however

you adapt them for your particular learning style. If this is the case, follow the skim study technique below.

• Study the chapters in the order you find them in the Study Text.

• For each chapter:

– Follow the key study steps 1-2

– Skim-read through step 4, looking out for the points highlighted in the fast forward boxes (step 3)

– Jump to step 10

– Go back to step 5

– Follow through step 7

– Prepare outline answers to questions (steps 8/9)

– Try the Quick quiz (step 11), following up any items you can't answer

– Do a plan for the Question (step 12), comparing it against our answers

– You should probably still follow step 6 (note-taking), although you may decide simply to rely on the

BPP Leaning Media Passcards for this.