Mathematics and Statistics 12th Board Exam HSC Commerce (Marketing and Salesmanship) Maharashtra State Board Topics and Syllabus

• Mathematical Logic 
  • Statements - Introduction in Logic 
  • Logical Connectives 
    • Conjunction (∧)
    • Disjunction (∨)
    • Negation (∼)
    • Conditional statement (Implication, →)
    • Biconditional (Double implication) (↔) or (⇔)
  • Statement Patterns and Logical Equivalence 

    tautology, contradiction, contingency, duality, negation of compound statement, contrapositive, converse, inverse

  • Algebra of Statements 

    idempotent law, associative law, commutative law, distributive law, identity law, complement law, involution law, DeMorgan’s laws

• Venn Diagrams 

• Statements
• Logical Connectives
• Statement patterns and logical equivalence
• Algebra of statements
• Venn diagrams

• Mathematical Logic 
  • Truth Value of Statement in Logic 
  • Logical Connectives 
    • Conjunction (∧)
    • Disjunction (∨)
    • Negation (∼)
    • Conditional statement (Implication, →)
    • Biconditional (Double implication) (↔) or (⇔)
  • Quantifier and Quantified Statements in Logic 
    • Universal quantifier (∀)
    • Existential quantifier (∃)
  • Statement Patterns and Logical Equivalence 

    tautology, contradiction, contingency, duality, negation of compound statement, contrapositive, converse, inverse

  • Algebra of Statements 

    idempotent law, associative law, commutative law, distributive law, identity law, complement law, involution law, DeMorgan’s laws

• Venn Diagrams 

• Determinant of a Matrix 
  • Introduction
  • Meaning
  • Definition
• Types of Matrices 
• Algebra of Matrices 
  • Transpose of a Matrix
  • Symmetric Matrix
  • Skew-Symmetric Matrix
  • Equality of Two matrices
  • Addition of Two Matrices
  • Scalar Multiplication of a Matrix
  • Multiplication of Two Matrices
• Properties of Matrices 
• Elementary Transformations 
• Inverse of Matrix 
• Application of Matrices 
  • Method of Inversion
  • Method of Reduction

• Derivatives of Composite Functions - Chain Rule 
• Derivatives of Inverse Functions 
• Derivative 
  • Derivatives of Logarithmic Functions 
• Derivatives of Implicit Functions 
• Derivatives of Parametric Functions 
• Second Order Derivative 

• Introduction of Derivatives 
• Increasing and Decreasing Functions 
• Maxima and Minima 
• Application of Derivatives to Economics 

• Integration 
• Methods of Integration - Integration by Substitution 
• Methods of Integration - Integration by Parts 
• Methods of Integration - Integration Using Partial Fractions 

• Fundamental Theorem of Integral Calculus 

  without proof

• Properties of Definite Integrals 

• Standard Forms of Parabola and Their Shapes 
• Standard Forms of Ellipse 
• Area Under Simple Curves 

• Differential Equations 
• Order and Degree of a Differential Equation 
• Formation of Differential Equation by Eliminating Arbitary Constant 
• Methods of Solving First Order, First Degree Differential Equations 
  • Differential Equations with Variables Separable Method 
  • Homogeneous Differential Equations 
  • Linear Differential Equations 
• Application of Differential Equations 
  • Population Growth and Growth of bacteria
  • Ratio active Decay
  • Newton's Law of Cooling
  • Surface Area

• Introduction of Matrices 
• Algebra of Matrices 
  • Transpose of a Matrix
  • Symmetric Matrix
  • Skew-Symmetric Matrix
  • Equality of Two matrices
  • Addition of Two Matrices
  • Scalar Multiplication of a Matrix
  • Multiplication of Two Matrices
• Inverse of Matrix 
• Solution of Equations 

• Definition and types of matrices
• Algebra of matrices
• Inverse of a matrix
• Solution of equations

• Commission and Brokerage Agent 
  • Principal
  • Commission
  • Commission Agents
  • Broker
  • Factor
  • Del Credere Agent
• Discount 
  • Drawer and Drawee
  • Date of bill and Face value
  • Nominal Due Date and Legal Due Date
  • Discounting a Bill
  • Banker’s Discount, Cash Value, Banker’s Gain

• Concept of Insurance 

  Meaning of Insurance

  Principles of Insurance : 

  • utmost good faith
  • insurable interest
  • indemnity
  • contribution
  • doctrine of subrogation
  • causa proxima
  • mitigation of loss

  Types of Insurance - Fire

  Types of Insurance - Life

  Types of Insurance - Marine

• Fire Insurance 
• Accident Insurance 
• Marine Insurance 
• Annuity 

  - Terminology of Annuity
  - Annuity Due
  - Sinking Fund

• Regression 
• Types of Linear Regression 
• Fitting Simple Linear Regression 
• The Method of Least Squares 
• Lines of Regression of X on Y and Y on X Or Equation of Line of Regression 
• Properties of Regression Coefficients 

• Introduction to Time Series 
• Uses of Time Series Analysis 
• Components of a Time Series 
  • Secular Trend
  • Seasonal Variation
  • Cyclical Variation
  • Irregular Variation
• Mathematical Models 
  • Additive Model
  • Multiplicative Model
• Measurement of Secular Trend 
  • Method of Freehand Curve ( Graphical Method)
  • Method of Moving Averages
  • Method of Least Squares

• Index Numbers 
• Types of Index Numbers 
  • Price Index Number
  • Quantity Index Number
  • Value Index Number
• Index Numbers - Terminology and Notation 
• Construction of Index Numbers 
  • Simple Aggregate Method 
  • Weighted Aggregate Method 
    • Laspeyre's Price Index Number
    • Paasche’s Price Index Number
    • Dorbish-Bowley’s Price Index Number
    • Fisher’s Ideal Price Index Number
    • Marshall-Edgeworth’s Price Index Number
    • Walsh’s Price Index Number
• Cost of Living Index Number 

  Steps in Construction of Cost of Living Index Numbers

  • Choice of Base Year
  • Choice of Commodities
  • Collection of Prices
  • Choice of Average
  • Choice of Weights
  • Purpose of Index Numbers
• Method of Constructing Cost of Living Index Numbers - Aggregative Expenditure Method 
• Method of Constructing Cost of Living Index Numbers - Family Budget Method 
• Uses of Cost of Living Index Number 

• Introduction of Linear Programming 
• Linear Programming Problem (L.P.P.) 
• Mathematical Formulation of Linear Programming Problem 

• Assignment Problem 
• Hungarian Method of Solving Assignment Problem 
• Special Cases of Assignment Problem 
  • Unbalanced assignment problem
  • Maximization Problem
  • Restricted assignment problem
  • Alternative optimal solutions
• Sequencing Problem 
• Types of Sequencing Problem 
  • Sequencing n jobs on Two Machine
  • Sequencing n jobs on three machine
• Finding an Optimal Sequence 

• Mean of a Random Variable 
• Types of Random Variables 
  • Discrete random variable
  • Continuous random variable
• Random Variables and Its Probability Distributions 
• Probability Distribution of Discrete Random Variables 
  • Probability mass function
  • Cumulative distribution function
  • Expected values and variance
• Probability Distribution of a Continuous Random Variable 
  • Probability density function
  • Cumulative distribution function
• Binomial Distribution 
• Bernoulli Trial 
• Mean of Binomial Distribution (P.M.F.) 
• Variance of Binomial Distribution (P.M.F.) 
• Poisson Distribution 

• Continuous Function of Point 

  Continuous left hand limit

  Continuous right hand limit
  

Continuity of a function at a point

• Derivatives of Implicit Functions 
• Logarithmic Differentiation 
• Derivatives of Functions in Parametric Forms 
• Second Order Derivative 
• Derivative 
  • Derivative of Inverse Function 

• Derivative of Inverse function
• Logarithmic Differentiation
• Derivative of implicit function
• Derivative of parametric function
• Second order derivative

• Increasing and Decreasing Functions 
• Maxima and Minima 

• Increasing and decreasing functions
• Maxima and minima

• Indefinite Integration 
  • Definition of an Integral 
  • Integral of Standard Functions 
  • Rules of Integration 
  • Methods of Integration 
  • Integration by Parts 

    Integral of the types

    `int e^x{f(x)+f^'(x)}dx`

    `intsqrt(x^2+a^2)dx, intsqrt(x^2-a^2)dx`

    `int (px+q) sqrt(ax^2+bx+c)" "dx`

• Definition of an integral
• Integral of standard functions
• Rules of Integration
• Methods of Integration
• Integration by parts

• Properties of Definite Integrals 
• Applications of Definite Integrals 

• Definite Integral
• Properties
• Applications

• Ratio, Proportion and Partnership 

Ratio, proportion and partnership

• Commission, Brokerage and Discount 

• Commission and Brokerage
• Discount

• Insurance and Annuity 

Insurance and Annuity

• Concept of Demography 
• Uses of Vital Statistics in Demography 
• Measurements of Mortality 
• Life Tables 

• Introduction, Definition
• Uses of vital statistics
• Measurements of Mortality
• Life tables

• Statistics 
  • Bivariate Frequency Distribution 

    bivariate data, tabulation of bivariate data

  • Karl Pearson’s Coefficient of Correlation 
• Rank Correlation 

• Bivariate frequency distribution
• Karl Pearson’s coefficient of correlation
• Rank correlation

• Lines of Regression of X on Y and Y on X Or Equation of Line of Regression 
• Regression Coefficient of X on Y and Y on X 
• Regression Propertise 

• Equation of line of regression
• Regression coefficients and their properties

• Random Variables and Its Probability Distributions 
• Binomial Theorem and Binomial Distribution 
• Poisson Distribution 
• Normal Distribution 
• Probability Distribution of a Discrete Random Variable 
• Probability Distribution 
  • Distribution Function of a Continuous Random Variable 

• Definition and types of random variables
• Probability Distribution of a Discrete Random Variable
• Probability Distribution of a Continuous Random Variable
• Binomial Theorem
• Binomial Distribution
• Poisson Distribution
• Normal Distribution

• Inequations in Management Mathematics 
• Linear Programming Problem in Management Mathematics 
• Assignment Problem 
• Sequencing in Management Mathematics 

• Inequations
• Linear Programming Problem
• Assignment Problem
• Sequencing