CBSE Class XII Applied Mathematics
Complete Syllabus 2025-26 | Subject Code: 241
Course Overview
Theory Paper
80
Marks
Internal Assessment
20
Marks
Duration
3
Hours
Total Units
8
Units
Course Objectives
- Apply mathematical concepts and techniques to solve real-world problems in business and economics
- Develop analytical and logical thinking skills through quantitative applications
- Understand statistical methods for data analysis and interpretation
- Learn financial mathematics for business decision making
- Master numerical methods and computational techniques
- Develop skills in linear programming for optimization problems
- Integrate technology tools like spreadsheets for mathematical applications
- Build foundation for higher studies in commerce, economics, and management
Unit-wise Marks Distribution
| Unit No. | Unit Name | Marks | Percentage |
|---|---|---|---|
| I | Numbers, Quantification and Numerical Applications | 11 | 13.75% |
| II | Algebra | 10 | 12.5% |
| III | Calculus | 15 | 18.75% |
| IV | Probability Distributions | 10 | 12.5% |
| V | Inferential Statistics | 05 | 6.25% |
| VI | Time-based Data | 06 | 7.5% |
| VII | Financial Mathematics | 15 | 18.75% |
| VIII | Linear Programming | 08 | 10% |
| Total Theory | 80 | 100% | |
| Internal Assessment | 20 | - | |
Note: Calculus and Financial Mathematics carry highest weightage (15 marks each - 18.75% each)
Unit I: Numbers, Quantification and Numerical Applications (11 Marks)
Modulo Arithmetic
- Define modulus of an integer
- Apply arithmetic operations using modular arithmetic rules
- Congruence modulo concepts
- Apply the definition in various problems
- Properties of modular arithmetic
Alligation and Mixture
- Understand alligation concepts
- Mixture at a given price
- Determine mean price of a mixture
- Apply rule of allegation
- Weighted average applications
Numerical Problems
- Boats and Streams (upstream and downstream)
- Pipes and Cisterns
- Races and Games
- Time, work and distance problems
- Speed and relative motion
Numerical Inequalities
- Describe and write numerical inequalities
- Application of algebraic inequations
- Linear inequalities
- Quadratic inequalities
- Real-life inequality applications
Unit II: Algebra (10 Marks)
Matrices
- Matrices and types of matrices
- Equality of matrices
- Transpose of a matrix
- Symmetric and Skew symmetric matrix
- Addition, subtraction, scalar multiplication
- Matrix multiplication
Determinants and Applications
- Determinants (singular, non-singular)
- Properties of determinants
- Inverse of a matrix (by cofactors)
- Properties of inverse matrices
- Solving system of simultaneous equations
- Matrix method and Cramer's rule
Unit III: Calculus (15 Marks)
Differentiation and Applications
- Derivatives up to second order
- Differentiation of simple functions
- Parametric and implicit functions
- Rate of change applications
- Marginal cost and revenue
- Increasing/Decreasing functions
- Maxima and Minima (first and second derivative tests)
- Local and global extrema
- Applied optimization problems
Integration and Applications
- Integration as anti-derivatives
- Simple algebraic functions
- Methods: substitution, partial fractions, by parts
- Indefinite Integrals as family of curves
- Definite Integrals as area under curve
- Fundamental theorem of calculus
- Consumer surplus and producer surplus
Differential Equations
- Order and degree of differential equations
- Formation of differential equations
- Solving simple differential equations
- Separable variable method
- Applications in real-world problems
Unit IV: Probability Distributions (10 Marks)
Probability Distribution
- Concepts of random variables
- Discrete probability distribution
- Mathematical Expectation
- Mean, variance, SD of random variable
Specific Distributions
- Binomial Distribution - characteristics, mean, variance, SD
- Poisson Distribution - definition, mean, variance
- Normal Distribution - properties, areas under curve
- Standard normal variate
Unit V: Inferential Statistics (05 Marks)
Population and Sample
- Population and Sample definitions
- Representative sample concepts
- Sampling methods
- Parameter and Statistics definitions
- Central limit theorem
- Statistical inference
Statistical Testing
- t-Test (one sample t-test)
- Small group sample testing
- Hypothesis formulation
- Null and alternate hypotheses
- Degree of freedom
- Statistical test and interference
Unit VI: Time-based Data (06 Marks)
Time Series
- Time Series - chronological data
- Components of Time Series
- Secular trend
- Seasonal variation
- Cyclical variation
- Irregular variation
Trend Analysis
- Time Series analysis for univariate data
- Secular Trend - long-term tendency
- Methods of Measuring Trend
- Moving average method
- Least squares method
Unit VII: Financial Mathematics (15 Marks)
HIGHEST WEIGHTAGE UNIT - 18.75% of Total Marks
Perpetuity and Sinking Funds
- Perpetuity concepts
- Sinking Funds definition
- Differentiation from savings
- Applications in financial planning
Valuation of Bonds
- Bond definition and characteristics
- Present value approach
- Bond pricing calculations
- Yield to maturity
EMI Calculations
- Calculation of EMI
- Flat-rate method
- Reducing-balance method
- Loan amortization
Growth and Depreciation
- Compound Annual Growth Rate (CAGR)
- CAGR concepts and differences
- CAGR calculations
- Linear method of Depreciation
- Depreciation advantages and disadvantages
- Depreciation calculations
Unit VIII: Linear Programming (08 Marks)
Linear Programming Problem
- Introduction and related terminology
- Mathematical formulation of LPP
- Different types (Manufacturing, Diet problem, etc.)
- Constraint formulation
- Objective function identification
Graphical Method
- Graphical method for 2 variables
- Feasible region identification
- Bounded and unbounded regions
- Infeasible regions
- Corner Point Method for optimal solution
- Optimization techniques
Practical Work
Use of Spreadsheet
- Graphs of exponential functions on Excel
- Demand and supply functions plotting
- Matrix operations using spreadsheets
- Probability simulations
- Collection and analysis of real data
- Maxima and minima studies
Suggested Projects
- Application-based explorations related to coding
- Financial calculations using logarithms
- Set theory applications
- Graphical data interpretation
- Population analysis
- Rainfall prediction models
- Shop inventory management
- Stock market analysis
- Insurance calculations
- Sports statistics
- Crop and rainfall analysis
Examination Pattern
Examination Structure
Single Paper - 3 Hours Duration - 80 Marks
All eight units covered in the theory paper
Internal Assessment (20 Marks)
Practical Applications
Based on spreadsheet activities and project work
Marks allocation as per CBSE guidelines
Data Analysis Projects
Real-world data collection and analysis using mathematical tools
Includes graphical interpretation
Assessment Components
- Activities performed throughout the year and record keeping
- Assessment of activity performed during year-end test
- Viva-voce based on practical understanding
- Project work evaluation and presentation
- Use of technology tools and software
Prescribed Books
Note on Textbooks
- No explicit prescribed books are listed in the official CBSE syllabus document
- Teachers may refer to NCERT and other standard textbooks
- Focus on practical applications and real-world problems
- Use of digital resources and online materials encouraged
Digital Resources
- CBSE official website materials
- Online mathematical tools and calculators
- Spreadsheet software (Microsoft Excel, Google Sheets)
- Educational videos and tutorials
- Practice problems from various sources
Key Success Tips
Preparation Strategy
- Focus equally on Calculus and Financial Mathematics (15 marks each)
- Master numerical applications for real-world problem solving
- Practice matrix operations and determinant calculations regularly
- Understand probability distributions with practical examples
- Learn spreadsheet applications for data analysis
- Practice linear programming graphical methods
- Understand time series analysis for trend prediction
- Complete practical projects to strengthen conceptual understanding
- Use technology tools effectively for mathematical computations
- Connect mathematical concepts to business and economic applications