CBSE Class XI Mathematics
Complete Syllabus 2025-26 | Subject Code: 041
Course Overview
Theory Paper
80
Marks
Internal Assessment
20
Marks
Duration
3
Hours
Total Units
5
Units
Key Learning Objectives
- Acquire knowledge and critical understanding of basic mathematical concepts through motivation and visualization
- Feel the flow of reasons while proving results or solving problems
- Apply knowledge and skills to solve problems using multiple methods
- Develop positive attitude to think, analyze and articulate logically
- Develop interest in Mathematics and participate in related competitions
- Understand different aspects of Mathematics used in daily life
- Develop awareness for national integration and social responsibility
- Develop reverence for great Mathematicians and their contributions
Unit-wise Marks Distribution
| Unit No. | Unit Name | Marks | Percentage |
|---|---|---|---|
| I | Sets and Functions | 23 | 28.75% |
| II | Algebra | 25 | 31.25% |
| III | Coordinate Geometry | 12 | 15% |
| IV | Calculus | 8 | 10% |
| V | Statistics and Probability | 12 | 15% |
| Total Theory | 80 | 100% | |
| Internal Assessment | 20 | - | |
Unit I: Sets and Functions (23 Marks)
Sets
- Sets and their representations
- Empty set, Finite and Infinite sets
- Equal sets, Subsets of real numbers
- Intervals with notations, Universal set
- Venn diagrams
- Union and Intersection of sets
- Difference of sets, Complement of a set
- Properties of Complement
Relations & Functions
- Ordered pairs, Cartesian product of sets
- Number of elements in Cartesian product
- Definition of relation, domain, co-domain and range
- Function as special type of relation
- Real valued functions and their types
- Constant, identity, polynomial, rational functions
- Modulus, signum, exponential, logarithmic functions
- Greatest integer functions with graphs
- Operations on functions
Trigonometric Functions
- Positive and negative angles
- Measuring angles in radians and degrees
- Conversion between degree and radian measures
- Definition using unit circle
- Fundamental identity: sin²x + cos²x = 1
- Signs of trigonometric functions
- Domain, range and graphs
- Sum and difference formulas
- Multiple angle identities (2x, 3x)
- Sum-to-product and product-to-sum identities
Unit II: Algebra (25 Marks)
Complex Numbers and Quadratic Equations
- Need for complex numbers, √−1
- Motivation by unsolvable quadratic equations
- Algebraic properties of complex numbers
- Argand plane representation
Linear Inequalities
- Algebraic solutions in one variable
- Representation on number line
- Linear inequality solving techniques
Permutations and Combinations
- Fundamental principle of counting
- Factorial notation (n!)
- Derivation of formulae for nPr and nCr
- Connection between permutations and combinations
- Simple applications and problems
Binomial Theorem
- Historical perspective
- Statement and proof for positive integral indices
- Pascal's triangle
- Simple applications
Sequence and Series
- Sequence and Series concepts
- Arithmetic Mean (A.M.)
- Geometric Progression (G.P.)
- General term of G.P.
- Sum of n terms of G.P.
- Infinite G.P. and its sum
- Geometric Mean (G.M.)
- Relation between A.M. and G.M.
Unit III: Coordinate Geometry (12 Marks)
Straight Lines
- Brief recall of 2D geometry
- Slope of a line
- Angle between two lines
- Various forms of line equations
- Point-slope form, slope-intercept form
- Two-point form, intercept form
- Lines parallel to axes
- Distance of point from line
Conic Sections
- Sections of a cone
- Circle, ellipse, parabola, hyperbola
- Degenerate cases: point, line, intersecting lines
- Standard equations and properties
- Standard equation of circle
- Basic properties of parabola, ellipse, hyperbola
Introduction to 3D Geometry
- Coordinate axes in three dimensions
- Coordinate planes in 3D
- Coordinates of a point in space
- Distance between two points in 3D
Unit IV: Calculus (8 Marks)
Limits and Derivatives
- Derivative as rate of change
- Distance function perspective
- Geometric interpretation
- Intuitive idea of limit
- Limits of polynomials and rational functions
- Limits of trigonometric functions
- Limits of exponential and logarithmic functions
- Definition of derivative
- Relation to slope of tangent
- Derivatives of sum, difference, product, quotient
- Derivatives of polynomial and trigonometric functions
Unit V: Statistics and Probability (12 Marks)
Statistics
- Measures of Dispersion
- Range calculation
- Mean deviation for ungrouped data
- Mean deviation for grouped data
- Variance for ungrouped data
- Variance for grouped data
- Standard deviation for ungrouped data
- Standard deviation for grouped data
Probability
- Events and occurrence of events
- 'Not', 'and' and 'or' events
- Exhaustive events
- Mutually exclusive events
- Axiomatic (set theoretic) probability
- Connection with earlier probability theories
- Probability of an event
- Probability of 'not', 'and' and 'or' events
Examination Pattern
| Typology of Questions | Marks | Percentage |
|---|---|---|
| Remembering & Understanding: Exhibit memory of previously learned material by recalling facts, terms, basic concepts. Demonstrate understanding by organizing, comparing, translating, interpreting, giving descriptions. | 44 | 55% |
| Applying & Analysing: Solve problems in new situations by applying acquired knowledge, facts, techniques and rules. Examine and break information into parts by identifying motives or causes. | 20 | 25% |
| Evaluating & Creating: Make judgments about information, validity of ideas based on criteria. Compile information in a different way by combining elements in new patterns. | 16 | 20% |
| Total | 80 | 100% |
Important Examination Features
No overall choice in the question paper, but 33% internal choices will be given in all sections
No chapter-wise weightage - Care to be taken to cover all chapters
Internal Assessment (20 Marks)
Periodic Tests
Best 2 out of 3 tests conducted throughout the year
10 Marks
Mathematics Activities
Based on NCERT Laboratory Manual activities
10 Marks
Assessment Breakdown for Activities
| S.No. | Assessment Component | Marks |
|---|---|---|
| 1 | Activities performed throughout the year and record keeping | 5 |
| 2 | Assessment of activity performed during year-end test | 3 |
| 3 | Viva-voce | 2 |
| Total Mathematics Activities | 10 | |
Formative Assessment Only Topics
The following topics are included for formative assessment only (not for board examination):
Sets
- Practical problems on Union and Intersection of two sets
Relations and Functions
- Composition of Functions
Trigonometric Functions
- General solution of trigonometric equations
- sin y = sin a, cos y = cos a, tan y = tan a
Algebra
- Principle of Mathematical Induction
- Polar representation of complex numbers
- Fundamental Theorem of Algebra
- Quadratic equations in complex number system
- Graphical solution of linear inequalities
- General and middle term in binomial expansion
- Special sums: ∑k, ∑k², ∑k³
Coordinate Geometry
- Normal form of line equations
- General equation of a line
- Section formula in 3D geometry
Calculus
- Derivatives of composite functions (Chain rule)
Probability
- Random experiments
- Outcomes and sample space
Prescribed Books
Primary Textbook
- Mathematics Textbook for Class XI
- Published by NCERT
Exemplar Problems
- Mathematics Exemplar Problems for Class XI
- Published by NCERT
Laboratory Manual
- Mathematics Lab Manual Class XI
- Published by NCERT