CBSE 11th Class Mathematics Syllabus


Course Structure

Units Topics Marks
I Sets and Functions 29
II Algebra 37
III Co-ordinate Geometry 13
IV Calculus 6
V Mathematical Reasoning 3
VI Statistics and Probability 12
Total 100

Course Syllabus

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 Sets
  • Practical Problems based on sets

Chapter 2: Relations & Functions

  • Ordered pairs

    • 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

    • 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

  • 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 and their graphs

  • 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 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

  • 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 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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