Tamil Nadu Board of Secondary Education Syllabus For Class 12th Business Mathematics and Statistics: Knowing the Syllabus is very important for the students of Class 12th. Shaalaa has also provided a list of topics that every student needs to understand.

The Tamil Nadu Board of Secondary Education Class 12th Business Mathematics and Statistics syllabus for the academic year 2021-2022 is based on the Board's guidelines. Students should read the Class 12th Business Mathematics and Statistics Syllabus to learn about the subject's subjects and subtopics.

Students will discover the unit names, chapters under each unit, and subtopics under each chapter in the Tamil Nadu Board of Secondary Education Class 12th Business Mathematics and Statistics Syllabus pdf 2021-2022. They will also receive a complete practical syllabus for Class 12th Business Mathematics and Statistics in addition to this.

## Tamil Nadu Board of Secondary Education Class 12th Business Mathematics and Statistics Revised Syllabus

Tamil Nadu Board of Secondary Education Class 12th Business Mathematics and Statistics and their Unit wise marks distribution

### Tamil Nadu Board of Secondary Education Class 12th Business Mathematics and Statistics Course Structure 2021-2022 With Marking Scheme

## Syllabus

- Rank of a Matrix
- Concept
- Elementary Transformations and Equivalent matrices
- Echelon form and finding the rank of the matrix (upto the order of 3×4)

- A system of equations with exactly one solution
- A system of equations with infinitely many solutions
- A system of equations that has no solution

- Testing the consistency of non homogeneous linear equations (two and three variables) by rank method

- Application of Determinants
- Cramer’s Rule
- Non Homogeneous linear equations upto three variables

- Cramer’s Rule
- Transition Probability Matrices
- Forecasting the succeeding state when the initial market share is given

- One stage Transition Probability
- Transition Matrix

- Indefinite Integrals
- Concept of Indefinite Integral
- Two important properties of Integral Calculus
- Integration by decomposition
- Integration by parts
- Integration by substitution (or) change of variable method
- Some special types of Integrals

- Definite Integrals
- The fundamental theorems of Integral Calculus
- Properties of defi nite integrals
- Gamma Integral
- Definite integral as the limit of a sum

- The Area of the Region Bounded by the Curves
- Geometrical Interpretation of De nite Integral as Area under a curve

- Application of Integration in Economics and Commerce
- Cost functions from marginal cost functions
- Revenue functions from Marginal revenue functions

- Inventory
- Amount of an Annuity
- Consumption of a Natural Resource

- The demand functions from elasticity of demand
- Consumer’s surplus
- Producer surplus

- Formation of Ordinary Differential Equations
- Definition of ordinary differential equation
- Order and degree of a differential equation
- Formation of ordinary differential equation

- Solution of a Differential Equation

- Solution of First Order and First Degree Differential Equations
- Variables Separable Method
- Substitution Method
- Homogeneous Form or Homogeneous Differential Equation
- General solution and particular solution
- Differential Equation in which variables are separable
- Linear differential equations of first order

- Second Order First Degree Differential Equations with Constant Coefficients
- A general second order linear differential equation with constant coefficients is of the form

- Finite Differences
- Forward Diff erence Operator, Backward Diff erence Operator and Shift ing Operator
- Finding the missing terms

- Interpolation
- Methods of interpolation
- Graphical method
- Algebraic method
- Lagrange’s interpolation formula

- Random Variable
- Definition of a random variable
- Types of Random Variable
- Discrete random variable
- Continuous random variable

- Mathematical Expectation
- Mean
- Variance
- Expected value and Variance
- Properties of Mathematical expectation

- Distribution
- Binomial distribution
- Poisson Distribution
- Normal Ditribution

- Standard Normal Distribution

- Concepts of Sampling
- Basic concepts of sampling

- Lottery method
- Table of Random number

- Sampling and Non-Sampling Errors
- Sampling distribution
- Computing standard error in simple cases

- Estimation
- Point and Interval Estimation

- Point estimation
- Interval estimation

- Hypothesis Testing
- Meaning : Null Hypothesis and Alternative Hypothesis - Level of Significants and Type of Errors
- Testing Procedure : Large sample theory and test of significants for single mean

- Time Series Analysis
- Meaning, Uses and Basic Components

- Why should we learn Time Series?
- Components of Time Series

- Secular Trend
- Seasonal variations
- Cyclic variations
- Irregular variations

- Measurements of Trends

- Freehand or Graphic Method
- Method of Semi-Averages
- Method of Moving Averages
- Method of Least Squares

- Method of Moving Averages
- Method of Least Squares
- Methods of measuring Seasonal Variations By Simple Averages

- Index Numbers
- Meaning, Classifications and Uses
- Weighted Index Number
- Test of adequacy for an Index Number

- Construction of Cost of Living Index Number

- Uses of Cost of Living Index Number
- Methods of constructing Cost of Living Index Number
- Aggregate Expenditure Method
- Family Budget Method

- Statistical Quality Control (SQC)
- Meaning
- Causes of Variation
- Process Control and Product Control
- Construction of X and R charts

- Transportation Problem
- Definition and formulation
- Methods of finding initial Basic Feasible Solutions

- Assignment Problem
- Definition and formulation
- Solution of assignment problems (Hungarian Method)

- Decision Theory
- Meaning
- Situations- Certainty and uncertainty
- Maximin and Minimax Strategy