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12th Standard Business Maths English Medium Chapters / Lessons 2022-2023


APPLICATIONS OF MATRICES AND DETERMINANTS

ANALYTICAL GEOMETRY

APPLICATIONS OF DIFFERENTIATION - I

APPLICATIONS OF DIFFERENTIATION - II

APPLICATIONS OF INTEGRATION

DIFFERENTIAL EQUATIONS

INTERPOLATION AND FITTING A STRAIGHT LINE

PROBABILITY DISTRIBUTIONS

SAMPLING TECHNIQUES AND STATISTICAL INFERENCE

APPLIED STATISTICS



12th Standard Business Maths English Medium Chapters / Lessons 2022-2023


APPLICATIONS OF MATRICES AND DETERMINANTS
ANALYTICAL GEOMETRY
APPLICATIONS OF DIFFERENTIATION - I
APPLICATIONS OF DIFFERENTIATION - II
APPLICATIONS OF INTEGRATION
DIFFERENTIAL EQUATIONS
INTERPOLATION AND FITTING A STRAIGHT LINE
PROBABILITY DISTRIBUTIONS
SAMPLING TECHNIQUES AND STATISTICAL INFERENCE
APPLIED STATISTICS

12th Standard Business Maths English Medium Chapters / Lessons 2022-2023 Syllabus

APPLICATIONS OF MATRICES AND DETERMINANTS

Inverse of a Matrix - Minors and Cofactors of the elements of a determinant - Adjoint of a square matrix - Inverse of a non singular matrix. Systems of linear equations - Sub matrices and minors of a matrix - Rank of a matrix - Elementary operations and equivalent matrices - Systems of linear equations - Consistency of equations - Testing the consistency of equations by rank method. Solution of linear equations - Solution by Matrix method - Solution by Cramer’s rule Input - Output Analysis - Transition Probability Matrices

ANALYTICAL GEOMETRY

Conics - The general equation of a conic - Parabola - Standard equation of parabola - Tracing of the parabola - Ellipse - Standard equation of ellipse - Tracing of the ellipse - Hyperbola Standard equation of hyperbola - Tracing of the hyperbola - Asymptotes - Rectangular hyperbola - Standard equation of rectangular hyperbola

APPLICATIONS OF DIFFERENTIATION - I

Functions in economics and commerce - Demand function - Supply function - Cost function - Revenue function - Profit function - Elasticity - Elasticity of demand - Elasticity of supply - Equilibrium price - Equilibrium quantity - Relation between marginal revenue and elasticity of demand. Derivative as a rate of change - Rate of change of a quantity - Related rates of change Derivative as a measure of slope - Slope of the tangent line - Equation of the tangent - Equation of the normal

APPLICATIONS OF DIFFERENTIATION - II

Maxima and Minima - Increasing and decreasing functions - Sign of the derivative - Stationary value of a function - Maximum and minimum values - Local and global maxima and minima - Criteria for maxima and minima - Concavity and convexity - Conditions for concavity and convexity - Point of inflection - Conditions for point of inflection. Application of Maxima and Minima - Inventory control - Costs involved in inventory problems - Economic order quantity - Wilson’s economic order quantity formula. Partial Derivatives - Definition - Successive partial derivatives - Homogeneous functions - Euler’s theorem on Homogeneous functions. Applications of Partial Derivatives - Production function - Marginal productivities - Partial Elasticities of demand.

APPLICATIONS OF INTEGRATION

Fundamental Theorem of Integral - Calculus Properties of definite integrals - Geometrical Interpretation of Definite Integral as Area Under a Curve Application of Integration in Economics and Commerce - The cost function and average cost function from marginal cost function - The revenue function and demand function from marginal revenue function - The demand function from elasticity of demand. Consumers’ Surplus - Producers’ Surplus

DIFFERENTIAL EQUATIONS

Formation of Differential Equations - Order and Degree of a Differential Equation - Family of curves Formation of Ordinary Differential Equation First order Differential Equations - Solution of a differential equation - Variables Separable Homogeneous differential equations - Solving first order homogeneous differential equations - First order linear differential equation - Integrating factor Second order Linear Differential Equations with constant coefficients - Auxiliary equations and Complementary functions-Particular Integral - The General solution

INTERPOLATION AND FITTING A STRAIGHT LINE

Interpolation - Graphic method of interpolation - Algebraic methods of interpolation - Finite differences-Derivation of Gregory - Newton's forward formula-Gregory - Newton's backward formula-Lagrange's formula Fitting a straight line Scatter diagram-Principle of least squares - Derivation of normal equations by the principle of least squares

PROBABILITY DISTRIBUTIONS

Random variable and Probability function - Discrete Random Variable - Probability function and Probability distribution of a Discrete random variable - Cumulative Distribution function-Continuous Random Variable-Probability function - Continuous Distribution function Mathematical expectation - Discrete Distributions Binomial distribution-Poisson distribution - Continuous Distributions Normal Distribution - Properties of Normal Distribution Standard Normal Distribution

SAMPLING TECHNIQUES AND STATISTICAL INFERENCE

Sampling and Types of Errors Sampling and sample - Parameter and Statistic - Need for Sampling - Elements of Sampling Plan - Types of Sampling - Sampling and non-sampling errors Estimation Estimator - Point Estimate and Interval Estimate - Confidence Interval for population mean and proportion Hypothesis Testing Null Hypothesis and Alternative Hypothesis - Types of Error - Critical region and level of significance - Test of significance

APPLIED STATISTICS

Linear Programming - Structure of Linear programming problem - Formulation of the Linear Programming Problem - Applications of Linear programming - Some useful Definitions -Graphical method Correlation and Regression - Meaning of Correlation - Scatter Diagram-Co-efficient of Correlation - Regression - Dependent Variable - Independent Variable - Two Regression Lines Time Series Analysis - Uses of analysis of Time Series - Components of Time Series Models-Measurement of secular trend Index Numbers - Classification of Index Numbers - Uses of Index Numbers Method of construction of Index Numbers - Weighted Index Numbers - Test of adequacy for Index Number - Cost of living index - Methods of constructing cost of living index - Uses of cost of living index number Statistical Quality - Control Causes for variation-Role and advantages of SQC - Process and Product control - Control Charts

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12th Standard Business Maths English Medium Chapters / Lessons 2022-2023

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