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Official syllabus

CBSE Class XI Applied Mathematics Syllabus 2026 – 27

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CBSEClass XIApplied Mathematics2026-27
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Overview

Course purpose: Applied Mathematics develops mathematical and statistical skills for higher study and applications in business, economics and the social sciences. It connects everyday situations with numerical, algebraic and graphical representations while strengthening reasoning, problem solving, data interpretation and mathematical communication.

Class XI focus: The syllabus covers numbers, quantification and numerical applications, algebra, calculus, combinatorics and probability, descriptive statistics, basics of financial mathematics and coordinate geometry, with emphasis on practical contexts and informed decision making.

Full syllabus

Course Introduction and Objectives instruction

Applied Mathematics
Subject Code – 241
Classes XI-XII

Secondary School Education prepares students to explore future career options after graduating from schools. Mathematics is an important subject that helps students to choose various fields of their choices. Mathematics is widely used in higher studies as an allied subject in the field of Economics, Commerce, Social Sciences and many others. It has been observed that the syllabus of Mathematics in senior secondary grades meant for science subjects may not be appropriate for the students who wish to pursue Commerce or Social Science-based subjects in university education. By keeping this in mind, one more elective course in the mathematics syllabus is developed for Senior Secondary classes with an aim to provide students relevant experience in Mathematics that can be used in fields other than Physical Sciences.

This course is designed to develop substantial mathematical skills and methods needed in other subject areas. Topics covered in two years aim to enable students to use mathematical knowledge in the field of business, economic and social sciences. It aims to promote appreciation of mathematical power and simplicity for its countless applications in diverse fields. The course continues to develop mathematical language and symbolism to communicate and relate everyday experiences mathematically. In addition, it reinforces the logical reasoning skills of formulating and validating mathematical arguments, framing examples, finding counterexamples. It encourages students to engage in mathematical investigations and to build connections within mathematical topics and with other disciplines. The course prepares students to use algebraic methods as a means of representation and as a problem-solving tool. It also enables students to interpret two-dimensional geometrical figures using algebra and to further deduce properties of geometrical figures in a coordinate system. The course content will help students to develop a sound understanding of descriptive and inferential statistics which they can use to describe and analyze a given set of data and to further make meaningful inferences out of it. Data based case studies from the field of business, economics, psychology, education, biology and census data will be used to appreciate the power of data in contemporary society.

It is expected that the subject is taught connecting concepts to the applications in various fields. The objectives of the course areas are as follows:

Course Objectives:

  • To develop an understanding of essential mathematical and statistical concepts that are relevant to areas such as business, economic and social sciences.
  • To enable students to interpret real-life situations into structured numerical, algebraic and graphical representations for analysis and decision making.
  • To develop ability to organise, analyse and interpret data, and to draw meaningful conclusions in practical contexts.
  • To strengthen logical thinking and reasoning by engaging students in problem-solving situations that require nuance understanding of qualification and relative change.
  • To develop clarity in mathematical communication, including the ability to justify solutions, examine assumptions and validate results.
  • To help students recognise connections between mathematics and other disciplines, and to use these connections meaningfully.

Purpose and objectives of CBSE Applied Mathematics for Classes XI-XII.

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Grade XI Examination Structure instruction

Grade XI (2026-27)

Number of Paper: 1
Time: 3 Hours
Max Marks: 80

No. Units Marks
I Numbers, Quantification and Numerical Applications 10
II Algebra 18
III Calculus 12
IV Combinatorics and Probability 10
V Descriptive Statistics 10
VI Basics of Financial Mathematics 15
VII Coordinate Geometry 05
Total 80
Internal Assessment 20

One three-hour written paper of 80 marks plus 20 marks Internal Assessment.

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Numbers, Quantification and Numerical Applications unit

UNIT – 1 NUMBERS, QUANTIFICATION AND NUMERICAL APPLICATIONS

Numbers & Quantification

Chapter Details of content Learning Outcomes
1.1 Binary Numbers
  • Introduction to Binary Number System
  • Conversion of decimal numbers to binary system and vice-versa and its applications.
 Students will be able to

  • Understand the relation between decimal and binary number system.
  • Able to convert from one system to another.
  • Understand the application of Binary number system in programming, coding, machine learning etc.
1.2 Indices, Logarithm and Antilogarithm
  • Indices and its properties
  • Common and Natural logarithm
  • Laws of logarithms
  • Logarithm and exponential as inverse operations
  • Procedure of finding logarithm and antilogarithms of given number
  • Applications of logarithms
 Students will be able to

  • Apply rules of indices to simplify expressions and solve problems involving powers
  • Define logarithms and antilogarithms as inverse operations
  • Distinguish between common logarithms and natural logarithms
  • Apply logarithmic and antilogarithmic techniques to simplify complex calculations, and solve practical problems
1.3 Introduction To Bhartiya System of Numeration
  • Introduction To Bhartiya System of Numeration
 Students will be able to

  • Gain acquaintance with traditional way of expressing numbers

Numbers in day-to-day Life

Chapter Details of content Learning Outcomes
1.4 Clocks
  • Evaluate the angular value of a minute
  • Measure of angle formed between two hands of clock at given time
  • Calculation of the time for which hands of clock meet
 Students will be able to

  • Calculate the angular displacement of hour and minute hands
  • Find the exact time when clock hands coincide, are opposite, or form a specific angle
  • Understand the practical utility of calendar
1.5 Calendar
  • Odd days in a month/ year/ century
  • Decode the day for the given date
 Students will be able to

  • Calculate odd days in any given month, year, or century
  • Find the day of the week for any given date
1.6 Time and Work
  • Relationship between work and time
  • Comparison of the work done by the individual / group w.r.t. time
 Students will be able to

  • Solve time-work problems
  • Represent time-work relationship graphically
1.7 Speed, Distance and Time
  • The time taken/ distance covered from the given data.
 Students will be able to

  • Represent distance-time relationship graphically
1.8 Seating arrangement
  • Creation of seating plan/ draft as per given conditions (Linear/circular).
  • Locating the position of a person in a seating arrangement.
 Students will be able to

  • Design and create seating plans in linear and circular arrangements
  • Determine the exact position of any person in a seating arrangement by analysing the given conditions and applying logical reasoning
  • Apply seating arrangement concepts to real-life situations

Binary numbers, logarithms, Bhartiya numeration, clocks, calendars, time and work, speed and seating arrangements.

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Algebra unit

UNIT – 2 ALGEBRA

Sets

Chapter Details of content Learning Outcomes
2.1 Introduction to Sets – Sets and their representation
  • Set as well-defined collection of objects.
  • Representation of a set in Roster form and Set builder form
  • Different types of sets on the basis of number of elements in the set
  • Differentiate between equal set and equivalent set
 Students will be able to

  • understand the systematic development of set theory.
  • represent sets accurately using both roster form and set-builder form
  • differentiate between the two methods of expressing the same set.
2.2 Subsets, Intervals as subsets
  • Subsets
  • Power set and its elements
  • Universal Set
  • Subset of real numbers as intervals
 Students will be able to

  • list all possible subsets of a given set, calculate the total number of subsets
  • justify why the empty set is a subset of every set through logical reasoning.
  • define power sets, construct the power set of a given set by identifying all its subsets
  • Get an idea about the special sets i.e., intervals which have vide utility in the study of analysis.
2.3 Venn Diagrams and Operations on Sets
  • Concept of Venn diagram to understand the relationship between sets
  • Problems using Venn diagram
  • Operations on sets
 Students will be able to

  • Use set operations to solve problems in various fields, such as probability, and data analysis.
  • Develop problem-solving skills using set theory and Venn diagrams.
  • Perform operations on sets to solve practical problems

Relations

Chapter Details of content Learning Outcomes
2.4 Ordered pairs — Cartesian product of two sets
  • Significance of specific arrangement of elements in a pair
  • Cartesian product of two sets
 Students will be able to

  • Understand the concept of ordered pairs
  • Find the Cartesian product of two finite sets
  • Calculate the number of elements in a Cartesian product
2.5 Relations
  • Expressing relation as a subset of Cartesian product
  • Domain and range of a relation
 Students will be able to

  • Identify and express relations as subsets of Cartesian products
  • Determine the domain and range of any relation
  • Create and analyse custom relations from everyday situations

Mathematical Logic

2.6 Mathematical Logic
  • Logical problems involving odd man out, syllogism, blood relation and coding-decoding
 Students will be able to

  • Identify patterns and solve odd man out problems
  • Draw valid conclusions using syllogism
  • Decode blood relations and solve coding-decoding problems
  • Apply logical reasoning skills to real-life decision-making situations

Sequences and Series

Chapter Details of content Learning Outcomes
2.7 Sequence and Series
  • Differentiate between sequence and series
 Students will be able to

  • Distinguish between sequences and series
2.8 Arithmetic Progression
  • Arithmetic mean (AM) of two positive numbers
 Students will be able to

  • Calculate and apply arithmetic mean (AM) of two positive numbers to find average values in real-life situations
2.9 Geometric Progression
  • Introduction of Geometric Progression (GP)
  • nᵗʰ term of a GP
  • sum of n terms and sum of infinite terms of a GP
  • Problems based on applications of GP
  • Geometric mean (GM) of two positive numbers
  • Relation between AM and GM and related problems
  • Application problems based on AP and GP
 Students will be able to

  • Identify and construct geometric progressions
  • Calculate geometric mean (GM) of two positive numbers
  • Analyse and prove the AM-GM inequality relationship
  • Apply formulas of arithmetic and geometric progressions strategically to solve real-world problems

Sets, relations, mathematical logic, sequences, arithmetic progression and geometric progression.

View official PDF page 4 ↗

Calculus unit

UNIT – 3 CALCULUS

Functions

Chapter Details of content Learning Outcomes
3.1 Functions and their graphs
  • Dependent and independent variables
  • Definition of function using dependent and independent variable
  • Domain, range and co-domain of a given function
  • Types of functions
  • Graphical representation of function
 Students will be able to

  • Define dependent and independent variables
  • Define and differentiate between domain, co-domain, and range of functions
  • Classify and define various types of functions
  • Determine domain, co-domain, and range of given functions
  • Represent functions graphically on coordinate planes
  • Apply function concepts to solve real-life problems involving mapping relationships like student enrolment systems, profit-loss calculations, and designing input-output models for business.

Limits, Continuity and Derivatives

Chapter Details of content Learning Outcomes
3.2 Limits and continuity of functions
  • Limit of a function
  • Continuity of a function
 Students will be able to

  • Define and understand the concept of limit of a function by analysing the behaviour of functions.
  • Solve problems based on the algebra of limits.
  • Define continuity of a function at a point and over an interval
3.3 Differentiation
  • Instantaneous rate of change
  • Finding the derivative of the functions
 Students will be able to

  • Define the derivative of a function and relate it to the slope of the tangent to a curve.
3.4 Algebra of derivatives
  • Differentiation of addition, subtraction, multiplication and division of two or more functions
  • Differentiation of a function of a function
 Students will be able to

  • state and apply the fundamental rules of differentiation for sum, difference, product, and quotient of two or more functions
  • understand the chain rule as the method for differentiating composite functions.

Functions, limits, continuity, differentiation and the algebra of derivatives.

View official PDF page 6 ↗

Permutations and Combinations & Probability unit

UNIT – 4 PERMUTATIONS AND COMBINATIONS & PROBABILITY

Combinatorics

Chapter Details of content Learning Outcomes
4.1 Combinatorics
  • Factorial of a number
  • Fundamental Principle of Counting
  • Concept of Permutation
  • Simple problems based on permutations
  • Define combination
  • Difference between permutation and combination
  • Problems based on Combinations
 Students will be able to

  • Understand and calculate factorials of numbers
  • Appreciate how to count without counting
  • Define permutation and apply the concept to solve problems
  • Define combination and differentiate it from permutation
  • Apply permutation and combination formulas strategically
  • Model complex counting situations using permutation and combination concepts

Probability

Chapter Details of content Learning Outcomes
4.2 Probability
  • Random experiment and sample space with suitable examples
  • Event and its Types
  • Concept of Probability
  • Problems based on calculating probabilities in real life situations
  • Concept of conditional probability
 Students will be able to

  • Define random experiment and sample space with suitable examples
  • Recognize and differentiate different types of events and find their probabilities
  • Appreciate the use of probability in daily life situations
  • Apply reasoning skills to solve problems based on conditional probability

Counting principles, permutations, combinations and probability including conditional probability.

View official PDF page 6 ↗

Descriptive Statistics unit

UNIT – 5 DESCRIPTIVE STATISTICS

Measures of Dispersion and Percentiles

Chapter Details of content Learning Outcomes
5.1 Measures of Dispersion
  • Meaning of dispersion in a data set
  • Range, mean deviation, standard deviation and variance
 Students will be able to

  • Understand the meaning of dispersion in a data set
  • Differentiate between range, mean deviation and standard deviation
  • Calculate range, range standard deviation and variance, and standard deviation for ungrouped and grouped data set
  • Choose appropriate measure of dispersion to calculate spread of data
5.2 Percentiles
  • Concept of Percentile rank
  • Calculate and interpret Percentile rank of scores in a given ungrouped data set.
 Students will be able to

  • Calculate, analyze and interpret Percentile rank of scores in a given ungrouped data set.

Correlation

5.3 Correlation
  • Concept of Correlation
  • Karl Pearson’s coefficient of Correlation for ungrouped data
  • Spearman’s Rank Correlation for ungrouped data
 Students will be able to

  • Analyze relationships between variables by calculating and interpreting Karl Pearson's coefficient of correlation and Spearman's rank correlation coefficient for ungrouped data.

Regression

5.4 Regression
  • Concept of Regression analysis
  • Dependent and Independent variables
  • Regression Coefficients
  • Regression Equations
  • Properties of Regression Equations
 Students will be able to

  • Distinguish between correlation and regression analysis.
  • Compute regression coefficients.
  • Solve real-world problems by selecting and applying appropriate correlation or regression techniques.

Dispersion, percentiles, correlation and regression.

View official PDF page 7 ↗

Financial Mathematics unit

UNIT – 6 FINANCIAL MATHEMATICS

Interests and Annuities

Chapter Details of content Learning Outcomes
6.1 Interest and Interest Rates
  • Concept of Interest Rates
  • Comparison between Nominal Interest Rate, Effective Rate and Real Interest Rate
  • Practical applications of interest rate w.r.t simple and compound interest
  • Concept of effective rate of interest
 Students will be able to

  • Understand the concept of interest rates
  • Differentiate between nominal interest rate, effective rate, and real interest rate
  • Calculate and compare simple and compound interest
  • Apply interest rate concepts to solve real-life financial problems
  • Define with examples the concept of effective rate of interest
  • Analyze and evaluate financial products and investment schemes
6.2 Annuities
  • Meaning of Immediate Annuity, Annuity due and Deferred Annuity
  • Future and present value of ordinary annuity, annuity due (up to 3 period)
  • Concept of Annuity in real life situations
 Students will be able to

  • Understand and differentiate between immediate annuity, annuity due, and deferred annuity
  • Calculate the future and present value of regular annuity and annuity due
  • Apply annuity concepts to real-life financial situations

Tax and Utility Bills

6.3 Taxes and Utility Bills
  • Concept of Income tax and GST w.r.t. tax new tax guidelines
  • Utility bills and its various types – Electricity, Water and PNG Bills
 Students will be able to

  • Understand the concept of income tax and GST
  • Calculate income tax and GST liabilities using applicable tax brackets
  • Analyse and calculate types of utility bills – Electricity and Water Bills
  • Apply taxation and utility billing concepts to real-life situations.

Interest rates, annuities, taxes and utility bills.

View official PDF page 8 ↗

Coordinate Geometry unit

UNIT – 7 COORDINATE GEOMETRY

Straight Lines

Chapter Details of content Learning Outcomes
7.1 Straight lines
  • Concept of slope of a line
  • Various forms of equation of line
 Students will be able to

  • Understand the gradient as the measure of steepness and calculate it using coordinates
  • Derive and apply various algebraic forms to represent lines in a Cartesian plane.
  • Apply linear equations to model real-world scenarios like demand and supply curves in economics.

Circles and Parabola

Chapter Details of content Learning Outcomes
7.2 Circles and Parabola
  • Determination of the equations of circle and parabola as a locus of a point in a plane under certain conditions
  • Different form of equations of a circle
  • Solve problems based on applications of circle
 Students will be able to

  • Define circles and parabolas as sets of points satisfying specific geometric conditions in a plane.
  • Formulate and solve equations of circles in standard, central, diameter, and general forms.
  • Identify the properties of a parabola and express its standard form equation based on its focus and directrix.
  • Utilize the properties of circles to solve practical and coordinate-based mathematical problems.

Straight lines, circles and parabola.

View official PDF page 8 ↗

Marks & examination pattern

Official assessment structure
AssessmentMarksWeightage
Written Examination80.00
Internal Assessment20.00

Written Examination

Duration
3 hours

Number of Paper: 1. Time: 3 Hours. Max Marks: 80.

Internal Assessment

Internal Assessment: 20 Marks.

Practical & Projects

Suggested Practicals using spreadsheet

  1. Visualizing Functions and Their Properties: Plotting graphs of functions in GeoGebra to observe how coefficients change the graph’s shape and to find out their domain and range graphically.
  2. Understanding Derivatives: Constructing a tangent line to a curve in GeoGebra and observing its slope as the point moves and demonstrating the derivative as the instantaneous rate of change.
  3. Personal Budgeting: Designing a comprehensive monthly budget tracker in a spreadsheet to manage income and expenditures using summation and percentage formulas.
  4. Comparative Cost-Benefit Analysis: Building a decision-making model to identify the most economical purchase for a high-value product by comparing cost, shipping charges, tax and other hidden costs.
  5. Descriptive Measures of Data: Using spreadsheet functions (e.g., AVERAGE, STDEV.P etc.) to compute the mean, median, mode, variance, and standard deviation of a raw dataset.
  6. Interest Growth Analysis: Developing a comparative sheet for Simple vs. Compound Interest to track the growth of an investment over time.
  7. Environmental & Economic Data Modelling: Analysing real-world datasets regarding local weather, inflation or AQI by generating and interpreting scatter plots, histograms, bar graphs etc. to identify correlations and seasonal trends.

Suggested Projects

List of Suggested projects (Class XI /XII)

  1. Use of prime numbers in coding and decoding of messages
  2. Prime numbers and divisibility rules
  3. Logarithms for financial calculations such as interest, present value, future value, profit/loss etc. with large values)
  4. The cardinality of a set and orders of infinity
  5. Comparing sets of Natural numbers, rational numbers, real numbers and others
  6. Use of Venn diagram in solving practical problems
  7. Fibonacci sequence: Its' history and presence in nature
  8. Testing the validity of mathematical statements and framing truth tables
  9. Investigating Graphs of functions for their properties
  10. Visit the census site of India http://www.censusindia.gov.in/Census_Data_2001/Census_Data_Online/Language/Statement3.html Depict the information given there in a pictorial form
  11. Prepare a questionnaire to collect information about money spent by your friends in a month on activities like travelling, movies, recharging of the mobiles, etc. and draw interesting conclusions
  12. Check out the local newspaper and cut out examples of information depicted by graphs. Draw your own conclusions from the graph and compare it with the analysis given in the report
  13. Analysis of population migration data – positive and negative influence on urbanization
  14. Each day newspaper tells us about the maximum temperature, minimum temperature, and humidity. Collect the data for a period of 30 days and represent it graphically. Compare it with the data available for the same time period for the previous year
  15. Analysis of career graph of a cricketer (batting average for a batsman and bowling average for a bowler). Conclude the best year of his career. It may be extended for other players also – tennis, badminton, athlete
  16. Vehicle registration data – correlating with pollution and the number of accidents
  17. Visit a village near Delhi and collect data of various crops over the past few years from the farmers. Also, collect data about temperature variation and rain over the period for a particular crop. Try to find the effect of temperature and rain variations on various crops
  18. Choose any week of your ongoing semester. Collect data for the past 10 – 15 years for the amount of rainfall received in Delhi during that week. Predict the amount of rainfall for the current year
  19. Weather prediction (prediction of monsoon from past data)
  20. Visit Kirana shops near your home and collect the data regarding the sales of certain commodities over a month. Try to figure out the stock of a particular commodity which should be in the store in order to maximize the profit
  21. Stock price movement
  22. Risk assessments by insurance firms from data
  23. Predicting stock market crash
  24. Predicting the outcome of an election – exit polls
  25. Predicting mortality of infants

Prescribed Books

Refer to the official source; no separate requirements have been recorded.

Version Changes

Official PDF

Official syllabus documentCBSE-Class-11-12-Applied-Mathematics-2026-27
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