Tamil Nadu Board of Secondary EducationHSC Commerce Class 12

# Business Mathematics and Statistics HSC Commerce Class 12 Tamil Nadu Board of Secondary Education Syllabus 2024-25

Tamil Nadu Board of Secondary Education Syllabus 2024-25 Class 12: The Tamil Nadu Board of Secondary Education Class 12 Business Mathematics and Statistics Syllabus for the examination year 2024-25 has been released by the , Tamil Nadu Board of Secondary Education. The board will hold the final examination at the end of the year following the annual assessment scheme, which has led to the release of the syllabus. The 2024-25 Tamil Nadu Board of Secondary Education Class 12 Business Mathematics and Statistics Board Exam will entirely be based on the most recent syllabus. Therefore, students must thoroughly understand the new Tamil Nadu Board of Secondary Education syllabus to prepare for their annual exam properly.

The detailed Tamil Nadu Board of Secondary Education Class 12 Business Mathematics and Statistics Syllabus for 2024-25 is below.

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

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

## Syllabus

1 Applications of Matrices and Determinants
• 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)
1. A system of equations with exactly one solution
2. A system of equations with infinitely many solutions
3. 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
• Transition Probability Matrices
• Forecasting the succeeding state when the initial market share is given
1. One stage Transition Probability
2. Transition Matrix
2 Integral Calculus – 1
• 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
3 Integral Calculus – 2
• 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
1. Inventory
2. Amount of an Annuity
3. Consumption of a Natural Resource
• The demand functions from elasticity of demand
• Consumer’s surplus
• Producer surplus
4 Differential Equations
• 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
5 Numerical Methods
• 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
6 Random Variable and Mathematical Expectation
• 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
7 Probability Distributions
• Distribution
• Binomial distribution
• Poisson Distribution
• Normal Ditribution
1. Standard Normal Distribution
8 Sampling Techniques and Statistical Inference
• Concepts of Sampling
• Basic concepts of sampling
1. Lottery method
2. Table of Random number
• Sampling and Non-Sampling Errors
• Sampling distribution
• Computing standard error in simple cases
• Estimation
• Point and Interval Estimation
1. Point estimation
2. 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
9 Applied Statistics
• Time Series Analysis
• Meaning, Uses and Basic Components
• Why should we learn Time Series?
• Components of Time Series
1. Secular Trend
2. Seasonal variations
3. Cyclic variations
4. Irregular variations
• Measurements of Trends
1. Freehand or Graphic Method
2. Method of Semi-Averages
3. Method of Moving Averages
4. Method of Least Squares
• Method of Moving Averages
• Method of Least Squares
• Methods of measuring Seasonal Variations By Simple Averages
• Index Numbers
• Statistical Quality Control (SQC)
• Meaning
• Causes of Variation
• Process Control and Product Control
• Construction of X and R charts
10 Operations Research
• 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