CIMA - C3 Fundamentals Of Business Mathematics
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x Introduction
Moving on...
However you study, when you are ready to embark on the practice and revision phase of the BPP Learning Media
Effective Study Package, you should still refer back to this Study Text, both as a source of reference (you should
find the index particularly helpful for this) and as a way to review (the Fast forwards, Assessment focus points,
Chapter roundups and Quick quizzes help you here).
And remember to keep careful hold of this Study Text – you will find it invaluable in your work.
More advice on Study Skills can be found in BPP Learning Media's Learning to Learn Accountancy book.
Introduction xi
Learning outcomes and Syllabus
Paper C3 Fundamentals of Business Mathematics
Syllabus overview
This is a foundation level study in mathematical and statistical concepts and techniques. The first and third
sections, Basic Mathematics and Summarising and Analysing Data, include techniques which are fundamental to
the work of the Management Accountant. The second section covers basic probability and is needed because
Management Accountants need to be aware of and be able to estimate the risk and uncertainty involved in the
decisions they make. In the fourth and fifth sections, there is an introduction to the mathematical techniques
needed for forecasting, necessary in the area of business planning. The sixth section is an introduction to financial
mathematics, a topic that is important to the study of financial management. Finally, there is a section covering
how Chartered Management Accountants use spreadsheets in their day-to-day work.
Aims
This syllabus aims to test the student's ability to:
• Demonstrate the use of basic mathematics, including formulae and ratios
• Identify reasonableness in the calculation of answers
• Demonstrate the use of probability where risk and uncertainty exist
• Apply techniques for summarising and analysing data
• Calculate correlation coefficients for bivariate data and apply the technique of simple regression analysis
• Demonstrate techniques used for forecasting
• Apply financial mathematical techniques
• Use spreadsheets to facilitate the presentation of data, analysis of univariate and bivariate data and use of
formulae
xii Introduction
Assessment
There will be a computer based assessment of 2 hours duration, comprising 45 compulsory questions, each with
one or more parts.
Learning outcomes and syllabus content
A Basic mathematics – 15%
Learning outcomes
On completion of their studies students should be able to:
(i) Demonstrate the order of operations in formulae, including the use of brackets, powers and roots
(ii) Calculate percentages and proportions
(iii) Calculate answers to appropriate decimal places or significant figures
(iv) Solve simple equations, including 2 variable simultaneous equations and quadratic equations
(v) Prepare graphs of linear and quadratic equations
Syllabus content
Covered in chapter
(1) Use of formulae, including negative powers as in the formula for the learning curve 1b
(2) Percentages and ratios 1a
(3) Rounding of numbers 1a
(4) Basic algebraic techniques and the solution of equations – including simultaneous
and quadratic equations
1b
(5) Manipulation of inequalities 1b
Introduction xiii
B Summarising and analysing data - 15%
Learning outcomes
On completion of their studies students should be able to:
(i) Explain the difference between data and information
(ii) Identify the characteristics of good information
(iii) Tabulate data and prepare histograms
(iv) Calculate for both ungrouped and grouped data: arithmetic mean, median, mode, range, variance, standard
deviation and coefficient of variation.
(v) Explain the concept of a frequency distribution
(vi) Prepare graphs/diagrams of normal distribution, explain its properties and use tables of normal distribution
(vii) Apply the Pareto distribution and the '80:20 rule'
(viii) Explain how and why indices are used
(ix) Calculate indices using either base or current weights
(x) Apply indices to deflate a series
Syllabus content
Covered in chapter
(1) Data and information 2
(2) Tabulation of data 3
(3) Graphs and diagrams: bar charts, scatter diagrams, histograms and ogives 3
(4) Summary measures of central tendency and dispersion for both grouped and
ungrouped data
4a, 4b
(5) Frequency distributions 3
(6) Normal distribution, the Pareto distribution and the '80:20 rule' 7
(7) Index numbers 5
C Probability – 15%
Learning outcomes
On completion of their studies students should be able to:
(i) Calculate a simple probability
(ii) Demonstrate the addition and multiplication rules of probability
(iii) Calculate a simple conditional probability
(iv) Calculate an expected value
(v) Demonstrate the use of expected value tables in decision making
(vi) Explain the limitations of expected values
(vii) Explain the concepts of risk and uncertainty
xiv Introduction
Syllabus content
Covered in chapter
(1) The relationship between probability, proportion and percent 6
(2) Addition and multiplication rules in probability theory 6
(3) Venn diagrams 6
(4) Expected values and expected value tables 6
(5) Risk and uncertainty 6
D Financial Mathematics - 15%
Learning outcomes
On completion of their studies students should be able to:
(i) Calculate future values of an investment using both simple and compound interest
(ii) Calculate an Annual Percentage Rate of interest given a quarterly or monthly rate
(iii) Calculate the present value of a future cash sum, using both a formula and CIMA tables
(iv) Calculate the present value of an annuity and a perpetuity using formula and CIMA tables
(v) Calculate loan/mortgage repayments and the value of an outstanding loan/mortgage
(vi) Calculate the future value of regular savings and/or the regular investment needed to generate a required
future sum, using the formula for the sum of a geometric progression
(vii) Calculate the NPV and IRR of a project and explain whether and why it should be accepted
Syllabus content
Covered in chapter
(1) Simple and compound interest 8
(2) Annuities and perpetuities 9
(3) Loans and mortgages 8, 9
(4) Sinking funds and savings funds 8, 9
(5) Discounting to find net present value and internal rate of return and interpretation of
NPV and IRR
9
E Inter-relationships between variables – 15%
Learning outcomes
On completion of their studies students should be able to:
(i) Prepare a scatter diagram
(ii) Calculate the correlation coefficient and the coefficient of determination between two variables
(iii) Calculate the regression equation between two variables
(iv) Apply the regression equation to predict the dependent variable, given a value of the independent variable
Introduction xv
Syllabus content
Covered in chapter
(1) Scatter diagrams and the correlation coefficient 3, 10
(2) Simple linear regression 10
F Forecasting – 15%
Learning outcomes
On completion of their studies students should be able to:
(i) Prepare a time series graph
(ii) Identify trends and patterns using an appropriate moving average
(iii) Identify the components of a time series model
(iv) Prepare a trend equation using either graphical means or regression analysis
(v) Calculate seasonal factors for both additive and multiplicative models and explain when each is appropriate
(vi) Calculate predicted values given a time series model
(vii) Identify the limitations of forecasting models
Syllabus content
Covered in chapter
(1) Time series analysis – graphical analysis 11
(2) Trends in time series – graphs, moving averages and linear regression 11
(3) Seasonal variations using both additive and multiplicative models 11
(4) Forecasting and its limitations 11
G Spreadsheets – 10%
Learning outcomes
On completion of their studies students should be able to:
(i) Explain the features and functions of spreadsheet software
(ii) Explain the use and limitations of spreadsheet software in business
(iii) Apply spreadsheet software to the normal work of a Chartered Management Accountant
Indicative Syllabus content
Covered in chapter
(1) Features and functions of commonly-used spreadsheet software: workbook,
worksheet, rows, columns, cells, data, text, formulae, formatting, printing, graphics
and macros. Note: Knowlegde of Microsoft Excel type spreadsheet
vocabulary/formulae syntax is required. Formula tested will be that which is
constructed by users rather than pre-programmed formulae
1, 12
(2) Advantages and disadvantages of spreadsheet software, when compared to manual
analysis and other types of software application packages
12
(3) Use of spreadsheet software in the day-to-day work of the Chartered Management
Accountant: budgeting, forecasting, reporting performance, variance analysis, what-if
analysis, discounted cashflow calculations
1, 3, 4b, 9, 10, 12
xvi Introduction
The assessment
Format of computer-based assessment (CBA)
The CBA will not be divided into sections. There will be a total of 45 objective test questions and you will need to
answer ALL of them in the time allowed, 2 hours.
Frequently asked questions about CBA
Q
What are the main advantages of CBA?
A • Assessments can be offered on a continuing basis rather than at six-monthly intervals
• Instant feedback is provided for candidates by displaying their results on the computer screen
Q
Where can I take CBA?
A
• CBA must be taken at a 'CIMA Accredited CBA Centre'. For further information on CBA, you can
email CIMA at cba@cimaglobal.com.
Q
How does CBA work?
A • Questions are displayed on a monitor
• Candidates enter their answers directly onto a computer
• Candidates have 2 hours to complete the Business Mathematics examination
• The computer automatically marks the candidate's answers when the candidate has completed the
examination
• Candidates are provided with some indicative feedback on areas of weakness if the candidate is
unsuccessful
Q
What sort of questions can I expect to find in CBA?
Your assessment will consist entirely of a number of different types of objective test question. Here are some
possible examples.
• MCQs. Read through the information on page (xvi ii) about MCQs and how to tackle them.
• Data entry. This type of OT requires you to provide figures such as the correct figure.
• Hot spots. This question format might ask you to identify which cell on a spreadsheet contains a particular
formula or where on a graph marginal revenue equals marginal cost.
• Multiple response. These questions provide you with a number of options and you have to identify those
which fulfil certain criteria.
Introduction xvii
This text provides you with plenty of opportunities to practise these various question types. You will find OTs
within each chapter in the text and the Quick quizzes at the end of each chapter are full of them. The Question
Bank contains more than one hundred objective test questions similar to the ones that you are likely to meet in
your CBA.
Further information relating to OTs is given on page (xix).
The Practice and Revision Kit for this paper was published in December 2009 and is full of OTs, providing you
with vital revision opportunities for the fundamental techniques and skills you will require in the assessment.
BPP Learning Media's MCQ Cards were also published in February 2010 and can provide you with 100 MCQs to
practice on, covering the whole syllabus.
xviii Introduction
Tackling multiple choice questions
In a multiple choice question on your paper, you are given how many incorrect options?
A Two
B Three
C Four
D Five
The correct answer is B.
The MCQs in your exam contain four possible answers. You have to choose the option that best answers the
question. The three incorrect options are called distracters. There is a skill in answering MCQs quickly and
correctly. By practising MCQs you can develop this skill, giving you a better chance of passing the exam.
You may wish to follow the approach outlined below, or you may prefer to adapt it.
Step 1 Skim read all the MCQs and identify what appear to be the easier questions.
Step 2 Attempt each question – starting with the easier questions identified in Step 1. Read the question
thoroughly. You may prefer to work out the answer before looking at the options, or you may prefer
to look at the options at the beginning. Adopt the method that works best for you.
Step 3 Read the four options and see if one matches your own answer. Be careful with numerical
questions, as the distracters are designed to match answers that incorporate common errors. Check
that your calculation is correct. Have you followed the requirement exactly? Have you included every
stage of the calculation?
Step 4 You may find that none of the options matches your answer.
• Re-read the question to ensure that you understand it and are answering the requirement.
• Eliminate any obviously wrong answers.
• Consider which of the remaining answers is the most likely to be correct and select the
option.
Step 5 If you are still unsure make a note and continue to the next question.
Step 6 Revisit unanswered questions. When you come back to a question after a break you often find you
are able to answer it correctly straight away. If you are still unsure have a guess. You are not
penalised for incorrect answers, so never leave a question unanswered!
Exam focus. After extensive practice and revision of MCQs, you may find that you recognise a question when you
sit the exam. Be aware that the detail and/or requirement may be different. If the question seems familiar read the
requirement and options carefully – do not assume that it is identical.
BPP Learning Media's i-Pass for this paper provides you with plenty of opportunity for further practice of MCQs.
Introduction xix
Tackling objective test questions
Of the total marks available for the paper, objective test questions (OTs) comprise 20/50 per cent. Questions will be
worth between 2 to 4 marks.
What is an objective test question?
An OT is made up of some form of stimulus, usually a question, and a requirement to do something.
(a) Multiple choice questions
(b) Filling in blanks or completing a sentence
(c) Listing items, in any order or a specified order such as rank order
(d) Stating a definition
(e) Identifying a key issue, term, figure or item
(f) Calculating a specific figure
(g) Completing gaps in a set of data where the relevant numbers can be calculated from the information given
(h) Identifying points/zones/ranges/areas on graphs or diagrams, labelling graphs or filling in lines on a graph
(i) Matching items or statements
(j) Stating whether statements are true or false
(k) Writing brief (in a specified number of words) explanations
(l) Deleting incorrect items
(m) Choosing right words from a number of options
(n) Complete an equation, or define what the symbols used in an equation mean
OT questions in CIMA assessments
CIMA has offered the following guidance about OT questions in the assessments.
• Credit may be given for workings where you are asked to calculate a specific figure.
• If you exceed a specified limit on the number of words you can use in an answer, you will not be awarded
any marks.
Examples of OTs are included within each chapter, in the quick quizzes at the end of each chapter and in the
objective test question bank.
BPP Learning Media's i-Pass for this paper provides you with plenty of opportunity for further practice of OTs.