Applied Mathematics Class 12 Syllabus 2025
There are eight units - (i) Numbers, Quantification and Numerical Applications (ii) Algebra (iii) Calculus (iv) Probability Distributions (v) Inferential Statistics (vi) Index Numbers and Time-based data (vii) Financial Mathematics (viii) Linear Programming.
Exam Structure
| # | Unit | Marks |
| I | Numbers, Quantification and Numerical Applications | 11 |
| II | Algebra | 10 |
| III | Calculus | 15 |
| IV | Probability Distributions | 10 |
| V | Inferential Statistics | 5 |
| VI | Index Numbers and Time-based data | 6 |
| VII | Financial Mathematics | 15 |
| VIII | Linear Programming | 8 |
| Total | 80 |
Unit 1: Numbers, Quantification and Numerical Applications
- Modulo Arithmetic
- Congruence modulo
- Simple arithmetic functions
- Alligation and Mixture
- Numerical problems
- Boats and Streams (upstream and downstream)
- Pipes and Cistern
- Races and Games
- Numerical inequalities
Unit 2: Algebra
- Matrices and types of matrices
- Equality of matrices, Transpose of a matrix, Symmetric and Skew symmetric matrix
- Algebra of matrices
- Determinants
- Inverse of a matrix
- Solving system of simultaneous equations using matrix method, Cramer's rule
Unit 3: Calculus
Differentiation and its Applications
- Higher Order Derivatives
- Application of derivatives
- Marginal Cost and Marginal Revenue using derivatives
- Increasing / Decreasing functions
- Maxima and Minima
Integration and its Applications
- Integration
- Indefinite Integrals as family of curves
- Definite integral as area under the curve
- Application of Integration
Differential Equations and Modeling
- Differential Equations
- Formulating and Solving Differential Equations
- Application of Differential Equations
Unit 4: Probability Distributions
- Probability Distribution
- Mathematical Expectation
- Variance
- Binomial Distribution
- Poisson distribution
- Normal distribution
Unit 5: Inferential Statistics
- Population and sample
- Parameter and Statistics and statistical inferences
- t-Test (one sample t-test and two independent groups t-test)
Unit 6: Index numbers and Time-based data
- Time series
- Components of Time Series
- Time Series analysis for univariate data
- Secular Trend
- Methods of Measuring trend
Unit 7: Financial Mathematics
- Perpetuity, Sinking funds
- Calculation of EMI
- Calculation of returns, nominal rate of return
- Compound annual growth rate
- Linear method of depreciation
Unit 8: Linear Programming
- Introduction and related terminologies
- Mathematical formulation of linear programming problems
- Different types of linear programming problems
- Graphical method of solution for problems in two variables
- Feasible and infeasible regions
- Feasible and infeasible solutions, optimal feasible solutions