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The module given below is regarding the syllabus of applied mathematics compiled for standard 12th students as per the CBSE notifications and guidelines for a better and quick understanding of the unit-wise syllabus.
Unit-1: Numbers, Quantification and Numerical Applications
- Congruence Modulo
- Modulo Arithmetic
- Numerical Inequalities
- Alligation And Mixture
- Numerical Problems
- Boats and Streams (Upstream And Downstream)
- Races and Games
- Pipes and Cisterns
Unit-2: Algebra
- Inverse of A Matrix
- Solving system of simultaneous equations using matrix method
- Cramer’s Rule
- Algebra of Matrices
- Matrices and types of Matrices
- Determinants
- Equality of Matrices
- Transpose of a Matrix
- Symmetric and Skew Symmetric Matrix
Unit- 3: Calculus
Differentiation and its Applications
- Marginal Cost and Marginal Revenue using Derivatives
- Maxima and Minima
- Application of Derivatives
- Higher-Order Derivatives
- Increasing /Decreasing Functions
Integration and Its Applications
- Definite Integrals as area under the Curve
- Application of Integration
- Integration
- Indefinite Integrals as Family of Curves
Differential Equations and Modeling
- Application of Differential Equations
- Differential Equations
- Formulating and Solving Differential Equations
Unit- 4: Probability Distributions
- Variance
- Mathematical Expectation
- Normal Distribution
- Probability Distribution
- Poisson Distribution
- Binomial Distribution
Unit – 5: Inferential Statistics
- Population and Sample
- t-Test (One-Sample T-Test and Two Independent Groups T-Test)
- Parameter and Statistics and Statistical Interferences
Unit -6: Index Numbers and Time-Based Data
- Components of Time Series
- Methods of Measuring Trend
- Time Series
- Secular Trend
- Time Series Analysis for Univariate Data
Unit – 7: Financial Mathematics
- Calculation of Emi
- Linear Method of Depreciation
- Perpetuity
- Sinking Funds
- Compound Annual Growth Rate
- Calculation of Returns
- Nominal Rate of Return
Unit – 8: Linear Programming
- Feasible and Infeasible Solutions
- Optimal Feasible Solution
- Introduction and Related Terminology
- Feasible and Infeasible Regions
- Mathematical Formulation of linear programming problem
- Graphical method of solution for problems in two variables
- Different types of linear programming problems
