FUNDAMENTALS OF BUSINESS MATHEMATICS AND - THE INSTITUTE OF ...

4 FOUNDATION : PAPER -

FUNDAMENTALS

OF BUSINESS

MATHEMATICS AND

STATISTICS

FOUNDATION

STUDY NOTES

The Institute of Cost Accountants of India CMA Bhawan, 12, Sudder Street, Kolkata - 700 016

First Edition : January 2013 Second Edition : September 2014

Published by : Directorate of Studies The Institute of Cost Accountants of India (ICAI) CMA Bhawan, 12, Sudder Street, Kolkata - 700 016 icmai.in

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Copyright of these Study Notes is reserved by the Institute of Cost Accountants of India and prior permission from the Institute is necessary

for reproduction of the whole or any part thereof.

Syllabus

PAPER 4: FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS (FBMS) Syllabus Structure

A

Fundamentals of Business Mathematics

40%

B

Fundamentals of Business Statistics

60%

A 40%

B 60%

ASSESSMENT STRATEGY There will be written examination paper of three hours. OBJECTIVES To gain understanding on the fundamental concepts of mathematics and statistics and its application in business decisionmaking Learning Aims The syllabus aims to test the student's ability to: Understand the basic concepts of basic mathematics and statistics Identify reasonableness in the calculation Apply the basic concepts as an effective quantitative tool Explain and apply mathematical techniques Demonstrate to explain the relevance and use of statistical tools for analysis and forecasting Skill sets required Level A: Requiring the skill levels of knowledge and comprehension

CONTENTS

Section A: Fundamentals of Business Mathematics

40%

1. Arithmetic

2. Algebra

3. Calculus

Section B: Fundamentals of Business Statistics

60%

4. Statistical representation of Data

5. Measures of Central Tendency and Dispersion

6. Correlation and Regression

7. Index Numbers

8.Time Series Analysis- basic applications including Moving Average

9. Probability

10. Theoretical Distribution

SECTION A: FUNDAMENTALS OF BUSINESS MATHEMATICS [40 MARKS] 1. Arithmetic

(a) Ratios and Proportions (b)Simple and Compound interest including application of Annuity

(c) Bill Discounting and Average Due Date (d) Mathematical reasoning ? basic application

2. Algebra (a)Set Theory and simple application of Venn Diagram (b) Variation, Indices, Logarithms

(c) Permutation and Combinations ? basic concepts

(d) Linear Simultaneous Equations ( 3 variables only) (e) Quadratic Equations (f)Solution of Linear inequalities (by geometric method only) (g) Determinants and Matrices 3. Calculus (a)Constant and variables, Functions, Limit & Continuity (b)Differentiability & Differentiation, Partial Differentiation (c)Derivatives ? First order and Second order Derivatives (d)Maxima & Minima ? without constraints and with constraints using Lagrange transform (e) Indefinite Integrals: as primitives, integration by substitution, integration by part (f) Definite Integrals: evaluation of standard integrals, area under curve SECTION B: FUNDAMENTALS OF BUSINESS STATISTICS [60 MARKS]

4. Statistical Representation of Data (a) Diagrammatic representation of data (b) Frequency distribution (c)Graphical representation of Frequency Distribution ? Histogram, Frequency Polygon, Ogive, Pie-chart

5. Measures of Central Tendency and Dispersion (a) Mean, Median, Mode, Mean Deviation (b) Quartiles and Quartile Deviation (c) Standard Deviation (d) Co-efficient of Variation, Coefficient of Quartile Deviation

6. Correlation and Regression (a) Scatter diagram (b) Karl Pearson's Coefficient of Correlation (c) Rank Correlation (d) Regression lines, Regression equations, Regression coefficients

7. Index Numbers (a) Uses of Index Numbers (b)Problems involved in construction of Index Numbers (c) Methods of construction of Index Numbers

8.Time Series Analysis ? basic application including Moving Average (a) Moving Average Method (b) Method of Least Squares

9. Probability (a)Independent and dependent events; Mutually exclusive events (b)Total and Compound Probability; Baye's theorem; Mathematical Expectation

10. Theoretical Distribution (a)Binomial Distribution, Poisson Distribution ? basic application (b) Normal Distribution ? basic application

4 I FUNDAMENTALS OF LAWS AND ETHICS

Content

SECTION - A

BUSINESS MATHEMATICS

Study Note 1 : Arithmetic

1.1

Ratio & Proportion

1.1

1.2

Simple & Compound Interest (Including Application of Annuity)

1.6

1.3

Discounting of Bills and Average Due Date

1.19

1.4

Mathematical Reasoning - Basic Application

1.37

Study Note 2 : Algebra

2.1

Set Theory

2.1

2.2

Inequations

2.15

2.3

Variation

2.18

2.4

Logarithm

2.23

2.5

Laws of Indices

2.33

2.6

Permutation & Combination

2.39

2.7

Simultaneous Linear Equations

2.51

2.8

Matrices & Determinants

2.56

Study Note 3 : Calculus

3.1

Function

3.1

3.2

Limit

3.6

3.3

Continuity

3.17

3.4

Derivative

3.23

3.5

Integration

3.57

SECTION - B

STATISTICS

Study Note 4 : Statistical Representation of Data

4.1

Diagramatic Representation of Data

4.1

4.2

Frequency Distribution

4.5

4.3

Graphical Representation of Frequency Distribution

4.10

Study Note 5 : Measures Of Central Tendency and Measures of Dispersion

5.1

Measures of Central Tendency or Average

5.1

5.2

Quartile Deviation

5.42

5.3

Measures of Dispersion

5.44

5.4

Coefficient Quartile & Coefficient variation

5.61

Study Note 6 : Correlation and Regression

6.1

Correlation & Co-efficient

6.1

6.2

Regression Analysis

6.20

Study Note 7 : Index Numbers

7.1

Uses of Index Numbers

7.1

7.2

Problems involved in construction of Index Numbers

7.2

7.3

Methods of construction of Index Numbers

7.2

7.4

Quantity Index Numbers

7.12

7.5

Value Index Number

7.13

7.6

Consumber Price Index

7.13

7.7

Aggregate Expenditure Method

7.14

7.8

Test of Adequacy of the Index Number Formulae

7.15

7.9

Chain Index Numbers

7.19

7.10

Steps in Construction of Chain Index

7.20

Study Note 8 : Time Series Analysis

8.1

Definition

8.1

8.2

Components of Time Series

8.1

8.3

Models of Time Series Analysis

8.2

8.4

Measurement of Secular Trend

8.3

8.5

Method of Semi Averages

8.3

8.6

Moving Average Method

8.3

8.7

Method of Least Squares

8.6

Study Note 9 : Probability

9.1

General Concept

9.2

Some Useful Terms

9.3

Measurement of Probability

9.4

Theorems of Probability

9.5

Bayes' Theorem

9.6

Odds

Study Note 10 : Theoretical Distribution

10.1

Theoretical Distribution

10.2

Binomial Distribution

10.3

Poisson Distribution

10.4

Normal Distribution

9.1 9.1 9.3 9.8 9.11 9.15

10.1 10.1 10.13 10.19

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