Fundamentals of Business Mathematics

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Syllabus outline

The syllabus comprises:

Topic and Study Weighting
A - Basic Mathematics    15%
B - Probability     15%
C - Summarising and Analysing Data  15% 
D - Inter-relationships between Variables  15%
E - Forecasting     15%
F - Financial Mathematics    15%
G - Spreadsheets     10%

Learning 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;
• apply spreadsheets to facilitate the presentation of data, analysis of univariate and bivariate data and use of formulae.

Assessment strategy

There will be a computer based assessment of 2 hours duration, comprising 45 compulsory questions, each with one or more parts.

A variety of objective test question styles and types will be used within the assessment.

Learning outcomes and indicative 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 brackets, powers and roots;

(ii) calculate percentages and proportions;

(iii) calculate answers to an appropriate number of decimal places or significant figures;

(iv) solve simple equations, including two variable simultaneous equations and quadratic equations;

(v) prepare graphs of linear and quadratic equations.

Indicative syllabus content

• Use of formulae, including negative powers as in the formula for the learning curve.
• Percentages and ratios.
• Rounding of numbers.
• Basic algebraic techniques and solution of equations, including simultaneous equations and quadratic equations.
• Manipulation of inequalities

B 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.

Indicative syllabus content

• The relationship between probability, proportion and percent.
• Addition and multiplication rules in probability theory.
• Venn diagrams.
• Expected values and expected value tables.
• Risk and uncertainty.

C 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.

Indicative syllabus content

• Data and information.
• Tabulation of data.
• Graphs and diagrams: scatter diagrams, histograms, bar charts and ogives.
• Summary measures of central tendency and dispersion for both grouped and ungrouped data.
• Frequency distributions.
• Normal distribution, the Pareto distribution and ‘80:20 rule’.
• Index numbers

D 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.

Indicative syllabus content

• Scatter diagrams and the correlation coefficient.
• Simple linear regression.

E 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.

Indicative syllabus content

• Time series analysis – graphical analysis.
• Trends in time series – graphs, moving averages and linear regression.
• Seasonal variations using both additive and multiplicative models.
• Forecasting and its limitations.

F 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 monthly or quarterly rate;

(iii) calculate the present value of a future cash sum using 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 the loan/mortgage outstanding;

(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 net present value (NPV) and internal rate of return (IRR) of a project and explain whether and why it should be accepted;

Indicative syllabus content

• Simple and compound interest.
• Annuities and perpetuities.
• Loans and mortgages.
• Sinking funds and savings funds.
• Discounting to find NPV and IRR and interpretation of NPV and IRR.

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

• Features and functions of commonly-used spreadsheet software: workbook, worksheet, rows, columns, cells, data, text, formulae, formatting, printing, graphics and macros. Note: Knowledge of Microsoft Excel type spreadsheet vocabulary/formulae syntax is required. Formulae tested will be that which is constructed by users rather than pre-programmed formulae.
• Advantages and disadvantages of spreadsheet software, when compared to manual analysis and other types of software application packages.
• 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.
  

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