Class 11th Mathematics part - 1 NCERT

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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
  •  based on sets
Chapter 2: Relations & Functions
  • Ordered pairs
    • Cartesian product of sets
  • Definition of −
    • Relation
    • Pictorial diagrams
    • Domain
    • Co-domain
    • Range of a relation
    • 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
  • 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

Unit-II: Algebra

Chapter 1: 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 2: 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 3: Linear Inequalities
  • 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 4: Permutations and Combinations
  • Fundamental principle of counting
  • Factorial n
  • (n!) Permutations and combinations
  • Derivation of formulae and their connections
  • Simple applications.
Chapter 5: 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 6: Sequence and Series
  • Sequence and Series
  • Arithmetic Progression (A.P.)
  • Arithmetic Mean (A.M.)
  • Geometric Progression (G.P.)
  • General term of a G.P.
  • Sum of n terms of a 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 1: 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
Chapter 2: 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 3. Introduction to Three–dimensional Geometry
  • Coordinate axes and coordinate planes in three dimensions
  • Coordinates of a point
  • Distance between two points and section formula

Unit-IV: Calculus

Chapter 1: Limits and Derivatives
  • Derivative introduced as rate of change both as that of distance function and geometrically
  • Intuitive idea of limit
  • Limits of −
    • Polynomials and rational functions
    • Trigonometric, exponential and logarithmic functions
  • Definition of derivative, relate it to slope of tangent of a curve, derivative of sum, difference, product and quotient of functions
  • The derivative of polynomial and trigonometric functions

Unit-V: Mathematical Reasoning

Chapter 1: Mathematical Reasoning
  • Mathematically acceptable statements
  • Connecting words/ phrases - consolidating the understanding of "if and only if (necessary and sufficient) condition", "implies", "and/or", "implied by", "and", "or", "there exists" and their use through variety of examples related to real life and Mathematics
  • Validating the statements involving the connecting words difference between contradiction, converse and contrapositive

Unit-VI: Statistics and Probability

Chapter 1: 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 2: Probability
  • Random experiments −
    • Outcomes
    • Sample spaces (set representation)
  • 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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