Business Mathematics (FBSM)

Syllabus overview 

This is a Foundation Level study in mathematical and statistical concepts and techniques. The first two sections, Basic Mathematics and Summarising and Analysing Data, include techniques which are fundamental to the work of the Chartered Management Accountant. The third section covers basic probability and is needed because Chartered Management Accountants need to be aware of and be able to estimate the risk and uncertainty involved in the decisions they make. The fourth section is an introduction to financial mathematics, a topic that is important to the study of financial management. Finally, there is an introduction to the mathematical techniques needed for forecasting, necessary in the area of business planning.

This syllabus aims to test the student’s ability to:

• explain and demonstrate the use of basic mathematics, including formulae and ratios;

• identify reasonableness in the calculation of answers;

• identify and apply techniques for summarising and analysing data;

• explain and demonstrate the use of probability where risk and uncertainty exist;

• explain and apply financial mathematical techniques;

• explain and demonstrate techniques used for forecasting.

There will be a written paper of two hours. Initially, objective testing will account for a minimum of 50% of the marks awarded on this paper. 

On completion of their studies students should be able to:

• demonstrate the order of operations in formulae, including the use of brackets, negative numbers, powers and roots;

• calculate percentages and proportions;
• calculate answers to appropriate significant figures or decimal places;
• calculate maximum absolute and relative errors;
• solve simple equations, including two variable simultaneous equations and quadratic equations;
• prepare graphs of linear and quadratic equations.

• Use of formulae.
• Percentages and ratios.
• Rounding of numbers.
• Basic algebraic techniques and the solution of equations, including simultaneous and quadratic equations.

On completion of their studies students should be able to:

• explain the difference between data and information;
• explain the characteristics of good information;
• explain the difference between primary and secondary data;
• identify the sources of secondary data;
• explain the different methods of sampling and identify where each is appropriate;
• tabulate data and explain the results;
• prepare a frequency distribution from raw data;
• prepare and explain the following graphs and diagrams: bar charts, time series graphs (not Z charts), scatter diagrams, histograms and ogives;
• calculate and explain the following summary statistics for ungrouped data: arithmetic mean, median, mode, range, standard deviation and variance;
• calculate and explain the following summary statistics for grouped data:
  arithmetic mean, median (graphical method only), mode (graphical method only), range, semi-interquartile range (graphical method only), standard deviation and variance;
• calculate and explain a simple index number, a fixed base and chain base series of index numbers;
• use index numbers to deflate a series and explain the results;
• calculate a simple weighted index number. Candidates will not have to decide whether to use base or current weights.

• Data and information.
• Primary and secondary data.
• Probability sampling (simple random sampling, stratified, systematic, multi-stage, cluster) and non-profitability sampling (quota).
• Tabulation of data.
• Frequency distributions.
• Graphs and diagrams: bar charts, time series graphs (not Z charts), scatter diagrams, histograms and ogives.
• Summary measures for both grouped and ungrouped data.
• Coefficient of variation.
• Index numbers.

On completion of their studies students should be able to:

• calculate a simple probability;

• demonstrate the use of the addition and multiplication rules of probability;

• calculate a simple conditional probability;

• calculate and explain an expected value;

• demonstrate the use of expected values to make decisions;

• explain the limitations of expected values;

• demonstrate the use of normal distribution and the CIMA Tables;

• demonstrate the application of the normal distribution to calculate probabilities.

• The relationship between probability, proportion and per cent.
• The addition and multiplication rules.
• Expected values.
• Normal distribution.

On completion of their studies students should be able to:

• calculate future values of an investment, using both simple and compound interest;
• calculate an annual percentage rate of interest, given a quarterly or monthly rate;
• calculate the present value of a future cash sum, using both a formula and CIMA Tables;
• calculate the present value of an annuity using both a formula and CIMA Tables;
• calculate loan/mortgage repayments and the value of an outstanding loan/mortgage;
• calculate the present value of a perpetuity;
• calculate the future value of regular savings (sinking funds) or find the savings given the future value, if necessary, using the sum of a geometric progression;
• calculate the NPV of a project and use this to decide whether a project should be undertaken, or to choose between mutually exclusive projects;
• calculate and explain the use of the IRR of a project.

• Simple and compound interest.
• Discounting to find the present value.
• Annuities and perpetuities.
• Loans and mortgages.
• Sinking funds and savings funds.
• Simple investment appraisal.

On completion of their studies students should be able to:

• calculate the correlation coefficient between two variables and explain the value;
• calculate the rank correlation coefficient between two sets of data and explain the value;
• explain the meaning of 100r² (the coefficient of determination);
• demonstrate the use of regression analysis between two variables to find the line of best fit, and explain its meaning;
• calculate a forecast of the value of the dependent variable, given the value of the independent variable;
• prepare a time series graph and identify trends and patterns;
• identify the components of a time series model;
• calculate the trend using a graph, moving averages or linear regression, and be able to forecast the trend;
• calculate the seasonal variations for both additive and multiplicative models;
• calculate a forecast of the actual value using either the additive or the multiplicative model;
• explain the difference between the additive and multiplicative models, and when each is appropriate;
• calculate the seasonally adjusted values in a time series;
• explain the reliability of any forecasts made.

• Correlation.
• Simple linear regression.
• Time series analysis – graphical analysis.
• Calculation of trend using graphs, moving averages and linear regression.
• Seasonal variations – additive and multiplicative.
• Forecasting.