The Class 11 Maths index page provided here includes all the chapters and sub-topics as outlined in the NCERT textbook, strictly following the CBSE syllabus. Each concept is presented in a clear and student-friendly manner to help learners develop a strong conceptual understanding.
Class 11 marks a crucial academic phase, as the topics not only form the foundation for school exams but also play a significant role in competitive exams like JEE. This topic-wise index serves as a quick and comprehensive reference, enabling students to navigate the entire syllabus with ease and efficiency.
Unit – I: Sets and Functions
Chapter 1: Sets
• Sets and Their Representations
• Empty Set
• Finite and Infinite Sets
• Equal Sets
• Subsets
• Subsets of a set of real numbers especially intervals (with notations)
• Power Set
• Universal Set
• Venn Diagrams
• Union and Intersection of Sets
• Difference of Sets
• Complement of a Set
• Properties of Complement
Chapter 2: Relations & Functions
• Ordered pairs and Cartesian product of sets
• Number of elements in the cartesian product of two finite sets
• Cartesian product of the sets of real (up to R × R)
• Definition of −
• Relation
• Pictorial diagrams
• Domain, Co-domain and Range of a relation
• Function as a special kind of relation from one set to another
• Pictorial representation of a function, domain, co-domain and range of a function
• Real valued functions, domain and range of these functions −
• Constant
• Identity
• Polynomial
• Rational
• Modulus
• Signum
• Exponential
• Logarithmic
• Greatest integer functions (with their graphs)
• Sum, difference, product and quotients of functions
Chapter 3: Trigonometric Functions
• Introduction to Trigonometric Functions
• Positive and negative angles
• Measuring angles in radians and in degrees and conversion of one into other
• Definition of trigonometric functions with the help of unit circle
• Truth of the sin2x + cos2x = 1, for all x
• Signs of trigonometric functions
• Domain and range of trigonometric functions
• Graphs of Trigonometric Functions
• Expressing sin (x±y) and cos (x±y) in terms of sinx, siny, cosx & cosy and their simple application
• Identities related to sin 2x, cos2x, tan 2x, sin3x, cos3x and tan3x
• General solution of trigonometric equations of the type sin y = sin a, cos y = cos a and tan y = tan a
Unit – II: Algebra
Chapter 4: Principle of Mathematical Induction
• Introduction to Principle of Mathematical Induction
• Process of the proof by induction −
• Motivating the application of the method by looking at natural numbers as the least inductive subset of real numbers
• The principle of mathematical induction and simple applications
Chapter 5: Complex Numbers and Quadratic Equations
• Need for complex numbers, especially √1, to be motivated by inability to solve some of the quadratic equations
• Algebraic properties of complex numbers
• Argand plane and polar representation of complex numbers
• Statement of Fundamental Theorem of Algebra
• Solution of quadratic equations in the complex number system
• Square root of a complex number
Chapter 6: Linear Inequalities
• Introduction to Linear inequalities
• Algebraic solutions of linear inequalities in one variable and their representation on the number line
• Graphical solution of linear inequalities in two variables
• Graphical solution of system of linear inequalities in two variables
Chapter 7: Permutations and Combinations
• Introduction to Permutations and Combinations
• Fundamental principle of counting
• Factorial n
• (n!) Permutations and combinations
• Derivation of formulae and their connections
• Simple applications
Chapter 8:Â Binomial Theorem
• History
• Statement and proof of the binomial theorem for positive integral indices
• Pascal’s triangle
• General and middle term in binomial expansion
• Simple applications
Chapter 9: Sequence and Series
• Sequence and Series
• Arithmetic Progression (A.P.)
• Arithmetic Mean (A.M.)
• Geometric Progression (G.P.)
• Arithmetic and Geometric series infinite G.P. and its sum
• Geometric mean (G.M.)
• Relation between A.M. and G.M.
Unit – III: Coordinate Geometry
Chapter 10: Straight Lines
• Introduction to Straight Lines
• Brief recall of two dimensional geometries from earlier classes
• Shifting of origin
• Slope of a line and angle between two lines
• Various forms of equations of a line −
• Parallel to axis
• Point-slope form
• Slope-intercept form
• Two-point form
• Intercept form
• Normal form
• General equation of a line
• Equation of family of lines passing through the point of intersection of two lines
• Distance of a point from a line
Chapter 11: Conic Sections
• Sections of a cone −
• Circles
• Ellipse
• Parabola
• Hyperbola − a point, a straight line and a pair of intersecting lines as a degenerated case of a conic section.
• Standard equations and simple properties of −
• Parabola
• Ellipse
• Hyperbola
• Standard equation of a circle
Chapter 12: Introduction to Three–dimensional Geometry
• Three–dimensional Geometry
• Coordinate axes and coordinate planes in three dimensions
• Coordinates of a point
• Distance between two points
• Section Formula
Unit-IV: Calculus
Chapter 13: Limits and Derivatives
• Limits
• Derivatives
• Limits of the trigonometric functions
• Algebra of the derivative of the function
Unit-V: Mathematical Reasoning
Chapter 14: Mathematical Reasoning
• Introduction to Mathematical Reasoning
• Mathematically acceptable statements
• Connecting words/ phrases
• Validating the statements involving the connecting words difference between contradiction, converse and contrapositive
Unit-VI: Statistics and Probability
Chapter 15: Statistics
• Introduction to Statistics
• Measures of dispersion −
• Range
• Mean deviation
• Variance
• Standard deviation of ungrouped/grouped data
• Analysis of frequency distributions with equal means but different variances.
Chapter 16: Probability
• Probability Introduction
• Random experiments −
• Outcomes
• Sample spaces (set representation)
• Types of Events
• Occurrence of events, ‘not’, ‘and’ and ‘or’ events
• Exhaustive events
• Mutually exclusive events
• Axiomatic (set theoretic) probability
• Connections with the theories of earlier classes
• Probability of −
• An event
• Probability of ‘not’, ‘and’ and ‘or’ events
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