SSC BOARD PAPERS IMPORTANT TOPICS COVERED FOR BOARD EXAM 2024

### SYLLABUS FOR MATHEMATICAL AND STATISTICAL TECHNIQUES AT F.Y.B.Com. EXAMINATION

Revised Course
(WITH EFFECT FROM THE ACADEMIC YEAR 2012-2013)

# The main objective of this course is to introduce mathematics and statistics to undergraduate students of commerce, so that they can use them in the field of commerce and industry to solve the real life problems.

Distribution of topics and lectures
Semester I
 Course UBCOMFSI.6 Mathematical and Statistical Techniques-I Topic No. of lectures Unit I 15 Unit II 15 Unit III 15 Unit IV 15 Unit V 15 Total 75

Total number of lectures 75 +Notional75=150 lectures =  3 CREDITS

Semester II
 Course UBCOMFSII.6 Mathematical and Statistical Techniques-II Topic No. of lectures Unit I 15 Unit II 15 Unit III 15 Unit IV 15 Unit V 15 Total 75

Total number of lectures 75 +Notional 75=150 lectures =  3 CREDITS

MATHEMATICAL AND STATISTICAL TECHNIQUES
WORKLOAD: MATHEMATICS     :   2 lectures per week
STATISTICS        :  3 lectures per week
TUTORIAL          :  1  per week
Tutorial batch size : 25 Students
Semester I
Course: UBCOMFSI.6
Mathematical and Statistical Techniques-I
MATHEMATICS: (24 marks)
Unit I
Shares and Mutual Funds:
Concept of share, face value, market value, dividend, equity shares, preferential shares, bonus shares. Simple examples.
Mutual Funds: Simple problems on calculation of Net income after considering entry load, dividend, change in Net Asset Value(N.A.V.) and exit load. Averaging of price under the Systematic Investment Plan(S.I.P.)
Unit II
Permutations & Combinations:
Factorial Notation, Fundamental Theorem,Definition of Permutations, Simple examples.
Definition of Combinations, Simple examples. Statement of theorems on Combination. Examples of commercial application of permutations and combinations.

Linear Programming Problems:
Sketching of graphs of (i) linear equation Ax + By + C = 0  (ii) linear inequalities.
Mathematical Formulation of Linear Programming Problems upto 3 variables. Solution of Linear Programming Problems using  graphical method up to 2 variables.

STATISTICS: (36 marks)
Unit III
Measures of Central Tendency:
Arithmetic mean, Weighted mean, Median, Mode, Quartiles, Deciles and Percentiles. Locating median and quartiles through ogives.  Histogram to locate mode, combined mean and weighted mean.
Measures of Dispersion:
Range, Quartile deviation, Mean deviation from mean, Standard deviation and their coefficients. Combined standard deviation.
Unit IV
Elementary Probability Theory:
Concept of random experiment/trial and possible outcomes; Sample Space and Discrete Sample Space; Events their types, Algebra of Events, Mutually Exclusive and Exhaustive Events, Complimentary  events.
Classical definition of Probability, Addition theorem (without proof), conditional probability.
Independence of Events: P(A∩B) = P(A) P(B)  Simple examples.
Random Variable: Probability distribution of a discrete random variable; Expectation and Variance; Simple examples on probability distributions.
Unit V
Decision Theory: Decision making situation, Decision maker, Courses of Action, States of Nature, Pay-off and Pay-off matrix; Decision making under uncertainty, Maximin, Maximax, Minimax regret and Laplace criteria; simple examples to find optimum decision. Formulation of Payoff Matrix.
Decision making under Risk, Expected Monetory Value(EMV); Decision tree; simple Examples based on EMV, Expected Opportunity Loss(EOL), simple Examples based on EOL.

Semester II
Course: UBCOMFSII.6
Mathematical and Statistical Techniques-II

MATHEMATICS : (24 marks)
Unit I
Functions, Derivatives and Their Applications
Concept of real functions: constant function, linear function, xn , ex, ax, log x.
Demand, Supply, Total Revenue, Average Revenue, Total cost, Average cost and Profit function. Equilibrium Point, Break-even point.
Derivative as rate measure.
Derivatives  of functions: Constant function,  xn , ex, ax, log x.
Rules of derivatives: Scalar multiplication, sum, difference, product, quotient (Statements only), simple problems.
Second Order derivatives
Applications: Derivative as rate of change , Marginal Cost, Marginal Revenue, Elasticity of Demand. Maxima and Minima for functions in Economics and Commerce.
(Examination Questions on this unit should be application oriented only.)

Unit II
Interest and Annuity
Simple Interest and Compound Interest    ,Interest  compounded more than once a year. Calculations involving upto 4 time periods.
Annuity Immediate and its Present value, Future value. Equated Monthly Installments (EMI) using reducing balance method & amortization of loans.  Simple problems involving up to 4 time periods.
STATISTICS: (36 marks)
Unit III
Bivariate Linear Correlation: Scatter Diagram, Computation of Karl Pearson’s Coefficient of Correlation(Case of Bivariate Frequency Table to be excluded), Computation of Spearman’s Rank Correlation Coefficient (case of repeated ranks upto 2 repetitions only)
Bivariate Linear Regression: Finding Regression lines by method of least squares. Properties of Regression Coefficients- i) r = √byx­­xy          ii) (x̅ , y̅ ) is the point of intersection of two regression lines.
Unit IV
Time series: Concepts and components of a time series. Estimation of Trend using Moving Average Method and Least Squares Method(only Linear Trend)
Estimation of Seasonal Component using Simple Arithmetic Mean (For Trend free data only)
Concept of Forecasting using Least Squares Method.
Index Numbers: Concept and uses. Simple and Composite Index Nos. (unweighted, weighted), Laspeyre’s Price Index No, Paasche’s Price Index No, Fisher’s Price Index No., Cost of living Index No., Real Income, Simple Examples.
Concept of Wholesale Price Index No. (Examples on missing values should not be done)
Unit V
Probability Distributions:
Discrete Probability Distribution: Binomial ,Poisson (Properties and applications only, no derivations are expected)
Continuous Probability distribution: Normal Distribution. (Properties and applications only, no derivations are expected)

Tutorial:
Two tutorials to be conducted on each unit  i.e. 10 tutorials per term. At the end of each term one Tutorial assignment of 10 marks should be given.

Examination:
Internal Assessment 40% (40 marks)
(i)                Two periodical class tests -                                                           20 marks
(ii)              One Tutorial Assignment  -                                                           10 marks
(iii)             Active participation in class instructional deliveries -              05 marks
(iv)             Overall conduct as a responsible student, mannerism etc.    05 marks.

Semester End Examination 60% (60 marks)
At the end of each semester, there will be a Semester  End Examination of 60 marks , 2 hours duration and question paper pattern as shown below.
Question Paper Pattern:( Course: UBCOMFSI.6 and Course: UBCOMFSII.6)
1)In Section I (based on Mathematics), Two questions carrying 12 marks each. First question should be on Unit I and Second question should be from Unit II.
In each question there should be three sub-questions carrying 6 marks each . Students should be asked to answer any 2 sub questions from each question.
2) In Section II (based on Statistics), Three questions carrying 12 marks each. First question should be on Unit III , Second question should be from Unit IV and third question should be from Unit V.
In each question there should be three sub-questions carrying 6 marks each . Students should be asked to answer any 2 sub questions from each question.

Reference Books:
1)      Mathematics for Economics and Finance Methods and Modelling by Martin Anthony and Norman Biggs,
Cambridge University Press, Cambridge low-priced edition, 2000, Chapters 1, 2, 4, 6 to 9 & 10.
2)      Applied Calculus  By Stephen Waner and Steven Constenoble,         Brooks/Cole Thomson Learning, second edition, Chapter 1 to 5.
3)      Business Mathematics By D. C. Sancheti and V. K. Kapoor, Sultan Chand & Sons, 2006, Chapter 1, 5, 7, 9 &10.
By J. D. Gupta, P. K. Gupta and Man Mohan, Tata Mc-Graw Hill Publishing Co. Ltd., 1987, Chapters 9 to 11 & 16.
5)      Quantitative Methods-Part-I  By S. Saha and S. Mukerji, New Central Book Agency, 1996, Chapters 7 & 12.
6)      Mathematical Basis of Life Insurance By S.P. Dixit, C.S. Modi and R.V. Joshi,
Insurance Institute of India, Chapters 2: units 2.6, 2.9, 2.20 & 2.21.
7)      Securities Laws & Regulation of Financial Market
Intermediate Course Paper 8, Institute of Company Secretaries of India, Chapter 11.
8)      Investments  By J.C. Francis & R.W. Taylor, Schaum’s Outlines, Tata Mc-Graw Hill Edition 2000, Chapters 2,4 & section 25.1.
9)      Indian Mutual Funds Handbook
By Sundar Shankaran, Vision Books, 2006, Sections 1.7,1.8.1, 6.5 & Annexures  1.1to 1.3.
10)   STATISTICS by Schaum Series.
11)   Operations Research by Gupta and Kapoor
12)   Operations Research by Schaum Series