PAPER NO. 7 BUSINESS MATHEMATICS AND STATISTICS UNIT DESCRIPTION

This unit covers the competencies required to record and manage business operations using mathematics. Competencies include: formulating and structuring relationships using algebraic expressions, determining cost and revenue using calculus, applying the concepts of commercial mathematics to compute cost and revenue, presenting statistical data using appropriate techniques, applying probability to anticipate potential business outcomes and using index numbers to compare related variables over time

LEARNING OUTCOMES

• Describe relationships using algebraic expressions

• Determine amounts using sequence and series and calculus

• Apply the concepts of commercial mathematics to compute costs and revenue

• Use statistics to analyse and present data

• Apply probability to anticipate potential business outcomes

• Use index numbers to compare related variables

CONTENT:

1. Describe relationships using algebraic expressions

1.1 Equations and Inequalities

1.1.1 Linear equations and inequalities; solving and graphing

1.1.2 Simultaneous equations and inequalities; solving and graphical presentation

1.1.3 Quadratic equations; solving and graphing

1.1.4 The function y = ex

1.1.5 Application of errors; absolute/relative

1.2 Algebraic Expressions

1.2.1 The number line

1.2.2 Known and unknowns (variables)

1.2.3 Algebraic terms and expressions operation

1.2.4 Factorisation

1.2.5 Simplification of algebraic expressions using BODMAS

1.2.6 Simplification of fractions

1.3 Matrices

1.3.1 Introduction: order of matrices, types of matrices

1.3.2 Matrix algebra: Addition, subtraction and multiplication of matrices

1.3.3 Determinants of 2×2 matrices

1.3.4 Inverses of 2×2 matrices

1.3.5 Application of matrices in solving business problems

1.4 Logarithms

1.4.1 Logarithms and anti-logarithms

1.4.2 Natural logarithm

1.4.3 Application of logarithms in business

2. Determine amounts using sequence and series and calculus

2.1 Sequences and series

2.1.1 Arithmetic progression (A.P): nth term, sum of first n terms including proofs

2.1.2 Geometric progression (G.P): nth term, sum of first n terms including proofs

2.1.3 Sum to infinity

2.1.4 Compound interest yield

2.1.5 Annuities and the sinking fund problems

2.2 Calculus: Differentiation and Integration

2.2.1 Basic calculus; differentiation: General polynomial rule, product rule, quotient rule and chain rule; integration: general polynomial rule, by parts and by partial fractions.

2.2.2 Solving total revenue, total cost and profit equations using calculus

3. Apply the concepts of commercial mathematics to compute costs and revenues

3.1 Buying and selling

3.1.1 Types of discounts

3.1.2 Percentage profit and loss

3.1.3 Mark-ups

3.1.4 Margins

3.2 Simple interest and compound interest computation

3.2.1 Basics of simple interest

3.2.2 Compound interest formulae

3.2.3 Finding principal, rate and time using simple interest formula and compound interest rate formula

3.2.4 Preparation of a loan amortisation schedule

3.3 Appreciation and depreciation calculation

3.3.1 Straight line method

3.3.2 Declining balance method

3.3.3 Sum of the year’s digits method correctly apply values and variables to any given formula

3.4 Wages and salaries computation

3.4.1 Piecework rate

3.4.2 Hourly rate

3.4.3 Commissions

3.5 Basic income tax calculations

3.5.1 Gross and net pay

3.5.2 Statutory deductions- PAYE, NHIF, NSSF

3.6 Foreign exchange rates computation

4. Use statistics to analyse and present data

4.1 Introduction

4.1.1 Definitions

4.1.2 Branches of statistics

4.2 Methods of data collection

4.2.1 Primary data

4.2.2 Secondary data

4.3 Sampling techniques

4.4 Data presentation techniques

4.4.1 Tables

4.4.2 Bar charts

4.4.3 Pie charts

4.4.4 Graphs: Time series graphs, Z-charts, Lorenz curves and semi- logarithmic graphs

4.4.5 Frequency distribution tables

4.4.6 Histograms and frequency polygon

4.5 Descriptive statistics

4.5.1 Measures of central tendency

4.5.2 Mean

4.5.3 Arithmetic mean

4.5.4 Weighted arithmetic mean

4.5.5 Geometric mean

4.5.6 Harmonic mean

4.5.7 Mode

4.5.8 Median

4.6 Measures of dispersion

4.6.1 Range

4.6.2 Quartile

4.6.3 Deciles

4.6.4 Percentiles

4.6.5 Mean deviation

4.6.6 Variance

4.6.7 Standard deviation

4.6.8 Coefficient of variation

4.7 Measures of skewness

4.7.1 Pearson’s coefficient of skewness

4.7.2 Product coefficient of skewness

4.8 Measures of kurtosis

4.8.1 Pearson’s coefficient of kurtosis

4.8.2 Product coefficient of kurtosis.

5. Apply probability to anticipate potential business outcomes

5.1 Set Theory

5.1.1 Types of sets; universal, empty/null, subsets, finite and infinite

5.1.2 Operation of set; unions, intersections, complements and set difference

5.1.3 Venn diagrams

5.1.4 Introduction to set theory

5.2 Basic Probability Theory

5.2.1 Definition

5.2.2 Sample space

5.2.3 Events

5.2.4 Experiment

5.2.5 Outcome

5.2.6 Types of events

5.2.6.1 Simple events

5.2.6.2 Compound events

5.2.6.3 Independent

5.2.6.4 Dependent events

5.2.6.5 Mutually exclusive events

5.2.6.6 Mutually inclusive

5.2.7 Explain rules/laws of probability

5.2.7.1 Additive rules

5.2.7.2 Multiplicative rules

5.2.8 Counting techniques

5.2.8.1 Combinations and permutations

5.2.9 Baye’s Theorem

5.2.10 Draw probability trees

5.2.11 Solving business problems using probability

6. Use index numbers to compare related variables

6.1 Define index numbers

6.2 Describe purpose of index numbers

6.3 Construct index numbers:

6.3.1 Simple index numbers (fixed base method and chain base method)

6.3.2 Weighted index numbers; Laspeyres, Paasche, Fisher’s ideal and Marshall- Edgeworth’s methods (both price and quantity index numbers)

6.3.3 Consumer Price Index (CPI)

6.4 Applications of CPI

6.5 Limitations of index numbers

Suggested Methods of Delivery

• Presentations and practical demonstrations by trainer;

• Guided learner activities and research to develop underpinning knowledge;

• Supervised activities and projects in a workshop;

The delivery may also be supplemented and enhanced by the following, if the opportunity allows:

• Visiting lecturer/trainer from the ICT sector;

• Industrial visits.

Recommended Resources Equipment

• Computer

• Financial calculators

Materials and supplies

• Digital instructional material including DVDs and CDs

Sample Reading and Reference materials

1. Swift, L., & Piff, S. (2014). Quantitative Methods: For Business, Management and Finance (4th edition). Palgrave Macmillan.

2. Jacques, I. (2018). Mathematics for Economics and Business (9th edition). Harlow: Pearson.

3. Andre, F. (2004). Business Mathematics and Statistics (6th edition) Australia: Thomson.

4. Lind, D. A., Marchal, W. G., & Wathen, S. A. (2021). Basic Statistics in Business and Economics (10th edition). New York: McGraw-Hill Education.

5. Clendenen, G., & Salzman, S. (2019). Business Mathematics (14th edition). Pearson.

6. Present value tables

7. Annuity tables

8. Kasneb e-learning resources (link on the Kasneb website).

9. Approved study packs.