Table Of ContentCIMA Official
Learning System
Relevant for
Computer-Based Assessments
C3 – Fundamentals
of Business
Mathematics
CIMA Certifi cate in
Business Accounting
Graham Eaton
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First edition 2008
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09 10 11 11 10 9 8 7 6 5 4 3 2 1
Contents
The CIMA Learning system ix
How to use your CIMA Learning System ix
Study technique xi
Computer-Based Assessments xii
Fundamentals of Business Mathematics and Computer-Based Assessments xiii
Learning outcomes and indicative syllabus content xiv
Mathematical Tables xix
1 Basic Mathematics 1
Learning Outcomes 3
1.1 Introduction 3
1.2 Mathematical operations and brackets 3
1.3 Different types of numbers 4
1.4 Rounding 5
1.4.1 Rounding to the nearest whole number 5
1.4.2 Signifi cant fi gures 5
1.4.3 Decimal places 6
1.4.4 Rounding up or rounding down 6
1.5 Powers and roots 7
1.5.1 Defi nitions 7
1.6 Mathematical operations in Excel 8
1.6.1 Rounding numbers in Excel 8
1.7 Variables and functions 10
1.8 Formulae 11
1.9 Exponential numbers 13
1.10 Solving equations 14
1.10.1 Linear equations with only one variable 14
1.10.2 Quadratic equations with only one variable 15
1.10.3 Simultaneous linear equations 16
1.11 Manipulating inequalities 18
1.12 Percentages and ratios 19
1.13 Accuracy and approximation 20
1.14 Errors from rounding 21
1.15 Using Excel to produce graphs of Linear and Quadratic Equations 21
1.15.1 Producing a single linear equation in Excel 21
1.15.2 Drawing multiple equations on a single graph 22
1.15.3 Single quadratic equation 23
1.15.4 Two quadratic equations on one graph 24
1.16 Using Excel to produce the graph of a hyperbola 25
1.17 Summary 26
Revision Questions 27
Solutions to Revision Questions 33
iii
iv FUNDAMENTALS OF BUSINESS MATHEMATICS C3
TS 2 Obtaining Data 39
N
TE Learning Outcomes 41
N
O 2.1 Introduction 41
C
2.1.1 The difference between information and data 42
2.2 Primary data: sampling 43
2.3 Probability sampling methods 44
2.3.1 Simple random sampling 44
2.3.2 Stratifi ed random sampling 44
2.4 Other sampling methods 46
2.5 Multistage sampling 47
2.6 Secondary data: sources 48
2.7 Questionnaires 48
2.8 Contact with respondents 49
2.9 Importing data to Excel 50
2.9.1 Importing data from Word 50
2.9.2 Using the Excel Text to Columns feature 51
2.10 Summary 52
Revision Questions 53
Solutions to Revision Questions 59
3 Presentation of Data 63
Learning Outcomes 65
3.1 Introduction 65
3.2 Linear graphs 65
3.3 Solving simultaneous linear equations using graphs 70
3.4 Quadratic graphs 71
3.5 Tallying frequency distributions 72
3.6 Discrete and continuous variables 75
3.7 Cumulative frequency distribution 76
3.8 Histograms and ogives 78
3.9 Pie charts 85
3.10 Bar charts 87
3.10.1 Creating Bar charts using Excel 90
3.11 Tabulation 95
3.12 Pareto analysis – The 80-20 rule 96
3.13 Using spreadsheets to produce histograms, ogives and pie charts 98
3.13.1 Creating a histogram in Excel 98
3.13.2 Creating an ogive in Excel 101
3.13.3 Creating a Pie chart in Excel 102
3.14 Summary 103
Readings 105
Revision Questions 109
Solutions to Revision Questions 117
FUNDAMENTALS OF BUSINESS MATHEMATICS v
4 Descriptive Statistics 125 C
O
N
Learning Outcomes 127
T
E
4.1 Introduction 127 N
T
S
4.2 The arithmetic mean 127
4.3 The median 131
4.4 The mode 135
4.5 A comparison of the three averages 137
4.6 Measures of spread 139
4.7 The range 139
4.8 The interquartile range; the quartile deviation 140
4.9 Deciles 142
4.10 The mean absolute deviation 144
4.11 The standard deviation 145
4.12 The coeffi cient of variation 148
4.13 A comparison of the measures of spread 150
4.14 Descriptive statistics using Excel 150
4.15 A practical example of descriptive statistical analysis using Excel 152
4.15.1 The questionnaire 153
4.15.2 Data capture 153
4.15.3 Preliminary analysis 155
4.15.4 Descriptive statistics 157
4.15.5 Worked Example Conclusions 161
4.16 Summary 162
Readings 165
Revision Questions 169
Solutions to Revision Questions 179
5 Index Numbers 185
Learning Outcomes 187
5.1 Introduction 187
5.2 Defi nitions 187
5.3 Interpretation of index numbers 188
5.4 Choice of base year 189
5.5 Change of base year 190
5.6 Combining series of index numbers 191
5.7 Chain-base index numbers 192
5.8 Composite index numbers 194
5.9 Relative price indices 196
5.10 Aggregative price indices 198
5.11 Choice of base weighting or current weighting 199
5.12 Quantity indices 200
5.13 The construction of the UK retail price index 202
5.14 Using the RPI 202
5.15 Summary 206
Readings 207
Revision Questions 209
Solutions to Revision Questions 217
vi FUNDAMENTALS OF BUSINESS MATHEMATICS C3
TS 6 Financial Mathematics 223
N
TE Learning Outcomes 225
N
O 6.1 Introduction 225
C
6.2 Simple interest 225
6.3 Compound interest 227
6.4 Equivalent rates of interest 228
6.5 Depreciation 230
6.6 More complex investments 231
6.7 Geometric progressions 233
6.8 Present values 234
6.9 Net present values – practical examples 236
6.10 Problems using NPV in practice 239
6.11 Annuities 239
6.12 PV of a perpetuity 241
6.13 Loans and mortgages 242
6.14 Internal rate of return 243
6.15 Financial functions in Excel 246
6.15.1 The investment reports 246
6.16 Summary 248
Readings 251
Revision Questions 253
Solutions to Revision Questions 263
7 Correlation and Regression 271
Learning Outcomes 273
7.1 Introduction 273
7.2 Correlation 274
7.3 Pearson’s correlation coeffi cient 278
7.4 Interpreting correlation coeffi cients 279
7.5 Rank correlation: Spearman’s coeffi cient 280
7.6 Which correlation coeffi cient to use 282
7.7 Regression 282
7.8 The least-squares criterion 283
7.9 Interpreting a and b 286
7.10 Forecasting 287
7.11 Which variable to denote by y 289
7.12 Judging the validity of forecasts 290
7.13 Summary 292
Revision Questions 293
Solutions to Revision Questions 301
8 Time Series 307
Learning Outcomes 309
8.1 Introduction 309
8.2 Components and models of time series 309
FUNDAMENTALS OF BUSINESS MATHEMATICS vii
8.3 Forecasting linear trends 312 C
O
8.4 Forecasting seasonal components 314 N
T
8.5 Producing the fi nal forecast 317 EN
T
8.6 Seasonal adjustment 318 S
8.7 Moving average trends 319
8.8 Other types of data 322
8.9 Judging the validity of forecasts 324
8.10 Computations involving the additive model 325
8.11 Summary 328
Readings 329
Revision Questions 331
Solutions to Revision Questions 339
9 Probability 345
L earning Outcomes 347
9.1 Introduction 347
9.2 Defi nitions of probability 348
9.3 Addition rules of probability 349
9.4 The probability of opposites 351
9.5 The multiplication rules of probability 351
9.6 More conditional probabilities 355
9.7 Discrete probability distributions; expectations 356
9.8 Expectation and decision-making 358
9.9 Limitations of this approach 361
9.10 Characteristics of the normal distribution 362
9.11 Use of the tables of normal distribution 363
9.12 Further normal distribution examples 368
9.13 Venn diagrams 370
9.13.1 Using Venn diagrams to assist with probability 371
9.14 Uncertainty and risk 372
9.15 Summary 375
Revision Questions 377
Solutions to Revision Questions 385
10 Spreadsheet Skills using Excel 393
L earning Outcomes 395
10.1 Introduction 395
10.2 Spreadsheet terminology 396
10.2.1 Workbooks and Worksheets 396
10.2.2 Cells 396
10.3 A note on macros and application development 396
10.4 Getting started with Excel 397
10.4.1 Workbooks of fi les 397
10.4.2 Worksheets 397
10.4.3 Scroll bars 398
viii FUNDAMENTALS OF BUSINESS MATHEMATICS C3
S 10.4.4 Status bar 398
T
N
E 10.4.5 Toolbars 398
T
N 10.5 Good spreadsheet design 398
O
C 10.6 Getting started 399
10.6.1 Problems with this spreadsheet 399
10.6.2 Positive aspects of this spreadsheet 399
10.7 Ownership and version 399
10.7.1 Problems with this spreadsheet 400
10.7.2 Positive aspects of this spreadsheet 400
10.8 Formatting 400
10.8.1 Problems with this spreadsheet 400
10.8.2 Positive aspects of this spreadsheet 401
10.9 Documentation 402
10.10 Minimising absolute values 403
10.10.1 Problems with this spreadsheet 404
10.11 Control checks for auditing 405
10.12 Charts 406
10.13 Tips for larger plans 406
10.14 Templates 407
10.14.1 Data input forms 408
10.15 The use of spreadsheets by management accountants 409
10.16 Summary 410
Preparing for the Assessment 411
R evision technique 413
Format of the assessment 414
R evision Questions 417
Solutions to Revision Questions 453
Mock Assessment 1 481
Mock Assessment 2 505
Index 535
The CIMA
Learning System
How to use your CIMA Learning System
This Fundamentals of Business Mathematics Learning System has been devised as a resource
for students attempting to pass their CIMA computer-based assessments, and provides:
● a detailed explanation of all syllabus areas;
● extensive ‘ practical ’ materials;
● generous question practice, together with full solutions;
● a computer-based assessments preparation section, complete with computer-based assess-
ments standard questions and solutions.
This Learning System has been designed with the needs of home-study and distance-
learning candidates in mind. Such students require very full coverage of the syllabus topics,
and also the facility to undertake extensive question practice. However, the Learning
System is also ideal for fully taught courses.
This main body of the text is divided into a number of chapters, each of which is organ-
ised on the following pattern:
● Detailed learning outcomes expected after your studies of the chapter are complete. You
should assimilate these before beginning detailed work on the chapter, so that you can
appreciate where your studies are leading.
● Step-by-step topic coverage. This is the heart of each chapter, containing detailed explana-
tory text supported where appropriate by worked examples and exercises. You should
work carefully through this section, ensuring that you understand the material being
explained and can tackle the examples and exercises successfully. Remember that in
many cases knowledge is cumulative: if you fail to digest earlier material thoroughly, you
may struggle to understand later chapters.
● Activities. Some chapters are illustrated by more practical elements, such as comments
and questions designed to stimulate discussion.
● Question practice. The test of how well you have learned the material is your ability to
tackle exam-standard questions. Make a serious attempt at producing your own answers,
but at this stage do not be too concerned about attempting the questions in computer-
based assessments conditions. In particular, it is more important to absorb the material
thoroughly by completing a full solution than to observe the time limits that would
apply in the actual computer-based assessments.
ix
