CBSE Class XI 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
Applied Mathematics Learning Objectives
- Develop practical mathematical skills for real-world applications
- Understand mathematical concepts in business, finance, and economics
- Apply statistical methods for data analysis and interpretation
- Master financial mathematics for practical problem-solving
- Develop logical reasoning and analytical thinking
- Use spreadsheet applications for mathematical computations
- Connect mathematics with various career opportunities
- Build foundation for higher studies in commerce and social sciences
Unit-wise Marks Distribution
| Unit No. | Unit Name | Marks | Percentage |
|---|---|---|---|
| I | Numbers, Quantification and Numerical Applications | 09 | 11.25% |
| II | Algebra | 15 | 18.75% |
| III | Mathematical Reasoning | 06 | 7.5% |
| IV | Calculus | 10 | 12.5% |
| V | Probability | 08 | 10% |
| VI | Descriptive Statistics | 12 | 15% |
| VII | Basics of Financial Mathematics | 15 | 18.75% |
| VIII | Coordinate Geometry | 05 | 6.25% |
| Total Theory | 80 | 100% | |
| Internal Assessment | 20 | - | |
Note: Algebra and Financial Mathematics carry highest weightage (15 marks each - 18.75%)
Unit I: Numbers, Quantification and Numerical Applications (09 Marks)
Binary Numbers
- Definition and concept of binary system
- Decimal to binary conversion
- Binary to decimal conversion
- Applications in computer science
Indices, Logarithm and Antilogarithm
- Definitions and basic concepts
- Laws of indices
- Properties of logarithms
- Antilogarithm calculations
- Applications in real-life problems
Numerical Applications
- Clock problems (angles, rotations, meeting points)
- Calendar problems (odd days, day determination)
- Time and work problems
- Seating arrangement (linear and circular)
- Problem-solving strategies
Unit II: Algebra (15 Marks)
HIGHEST WEIGHTAGE UNIT - 18.75% of Total Marks
Sets
- Definitions and representations
- Types and notations of sets
- Subsets and intervals
- Venn diagrams
- Operations on sets (union, intersection, complement)
- Practical applications
Relations
- Ordered pairs concept
- Cartesian product
- Relation definition
- Domain and range
- Types of relations
- Applications in real-life scenarios
Sequences and Series
- Sequences vs. series
- Arithmetic Progression (nth term, sum, mean)
- Geometric Progression (nth term, sum, mean)
- Relation between AM and GM
- Applications in finance and business
Permutations and Combinations
- Factorial notation
- Fundamental principle of counting
- Definition of permutation
- Definition of combination
- Applications in probability
- Real-life problem solving
Unit III: Mathematical Reasoning (06 Marks)
Logical Reasoning
- Odd man out problems
- Syllogism concepts and applications
- Blood relations problems
- Coding-decoding techniques
- Pattern recognition
- Logical sequence problems
Unit IV: Calculus (10 Marks)
Functions
- Dependent and independent variables
- Graphical representation of functions
- Domain, range, and co-domain
- Types: constant, identity, polynomial, rational
- Composite, logarithmic, exponential functions
- Modulus and algebraic functions
Limits and Differentiation
- Limits and continuity concepts
- Instantaneous rate of change
- Differentiation (non-trigonometric functions)
- Chain rule for differentiation
- Applications in real-life problems
- Rate problems in economics
Unit V: Probability (08 Marks)
Applied Probability
- Use of probability in real life
- Random experiments
- Sample space concepts
- Events and types of events
- Conditional probability definition
- Applications in business decisions
- Risk assessment problems
Unit VI: Descriptive Statistics (12 Marks)
Measures of Dispersion
- Range calculation
- Quartile deviation
- Mean deviation
- Standard deviation for ungrouped data
- Standard deviation for grouped data
- Variance calculations
Percentile and Correlation
- Percentile rank definition
- Calculation of percentiles
- Interpretation of results
- Correlation definition
- Spearman's rank correlation
- Applications for ungrouped data
Unit VII: Basics of Financial Mathematics (15 Marks)
HIGHEST WEIGHTAGE UNIT - 18.75% of Total Marks
Interest and Interest Rates
- Simple interest calculations
- Compound interest applications
- Nominal vs. effective rates
- Real interest rates
- Equivalency problems
- Annual equivalency rate
Annuities
- Concept of annuities
- General annuity calculations
- Due annuities
- Deferred annuities
- Applications up to three periods
- Real-life financial planning
Taxation
- GST calculation and applications
- Income tax computations
- Direct vs. indirect taxes
- Tax computation methods
- Deductions and exemptions
- Tax planning strategies
Bills and Tariffs
- Types of bills
- Tariff rate structures
- Fixed charges and service charges
- Surcharge calculations
- Electricity bill interpretation
- Water bill calculations
Unit VIII: Coordinate Geometry (05 Marks)
Straight Line
- Slope of a line
- Various forms of equations
- Angle between lines
- Perpendicular distance from point to line
- Distance between parallel lines
- Applications in economics
Circle and Parabola
- Circle definition and properties
- Forms of circle equations
- Applications of circles
- Parabola definition
- Standard equation of parabola
- Real-life applications
Practical Component - Spreadsheet Usage
Data Analysis and Visualization
- Calculating averages and interest
- Creating pictographs
- Pie charts and bar graphs
- Central tendency measures
- Graph plotting and visualization
Practical Exercises
- Budgeting and financial planning
- Product comparison analysis
- Smart purchasing decisions
- Report card analysis
- Statistical data interpretation
Real Data Projects
- Weather data collection
- Price analysis studies
- Inflation rate calculations
- Pollution data analysis
- Market research projects
Examination Pattern
Examination Structure
Single Theory Paper - 3 Hours Duration - 80 Marks
Internal Assessment - 20 Marks (Projects & Practicals)
Total Maximum Marks: 100
Assessment Features
- Application-oriented questions with real-life contexts
- Emphasis on practical problem-solving skills
- Integration of mathematical concepts with business scenarios
- Use of spreadsheet tools for computational work
- Project-based learning and assessment
- Focus on data analysis and interpretation
- Financial literacy through mathematical applications
Internal Assessment (20 Marks)
Projects & Activities
Excel-based projects and mathematical explorations
15 Marks
Viva-Voce
Oral assessment of project understanding
5 Marks
Suggested Project Areas
Financial Projects
- Personal budget planning
- Investment analysis
- Loan calculation studies
- Tax planning exercises
Data Analysis Projects
- Market survey analysis
- Weather pattern studies
- Sports statistics analysis
- Population data interpretation
Business Applications
- Profit-loss calculations
- Break-even analysis
- Inventory management
- Sales forecasting
Key Success Tips
Preparation Strategy
- Focus on Algebra and Financial Mathematics (highest weightage - 15 marks each)
- Master spreadsheet applications for practical work
- Practice real-life problem-solving scenarios
- Understand financial concepts with mathematical applications
- Develop strong logical reasoning skills
- Work on data analysis and interpretation regularly
- Complete all practical exercises using Excel/spreadsheets
- Connect mathematical concepts with business applications
- Practice numerical problems from various life situations
- Maintain a project portfolio throughout the year
Career Connections
Commerce & Business
- Chartered Accountancy
- Business Administration
- Banking and Finance
- Investment Analysis
Data & Analytics
- Data Science
- Business Analytics
- Market Research
- Statistical Analysis
Social Sciences
- Economics
- Psychology (Statistics)
- Sociology (Research)
- Public Administration