CBSE Syllabus

CBSE Syllabus For Class 11,Detailed Syllabus of CBSE For Class 11 Maths

CBSE Syllabus For Class 11,Detailed Syllabus of CBSE For Class 11

NCERT Syllabus for class 11 Maths is important for the students of class 11, as it gives a brief idea about topics in Maths.

Practicing solved and unsolved questions from NCERT Maths textbooks helps students to have a better understanding of the subject, which helps to excel in the board examination as well as in the competitive examination, such as JEE etc. NCERT syllabus helps students to prepare a strategic plan for studying. As maths requires a lot of practice, it is important for the students to have a thorough practice of all the questions. Students can visit our site to know more practice important maths question.

Syllabus of CBSE Class 11 Maths contains all topics which you will study this session. You should refer to the official CBSE Syllabus only to study Maths when you are in Class 11. Central Board of Secondary Education (CBSE) changes Class 11 Maths Syllabus from time to time. 

Unit

Topic

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

Unit-I: Sets and Functions

1. Sets

  • Sets and their representations.
  • Finite and Infinite sets.
  • Empty set. Power set. Equal sets. Subsets.
  • Properties of Complement Sets.
  • Venn diagrams. Difference of sets.
  • Complement of a set.
  • Universal set. Subsets of a set of real numbers especially intervals (with notations).
  • Union and Intersection of sets.
  • Practical Problems based on sets.

2. Relations & Functions

  • Ordered pairs, Cartesian product of sets.
  • Cartesian product of the sets of real (up to R x R).
  • Pictorial representation of a function, domain, co-domain, and range of a function. Function as a special kind of relation from one set to another.
  • Definition of relation, pictorial diagrams, domain, co-domain, and range of a relation. Number of elements in the cartesian product of two finite sets.
  • Sum, difference, product and quotients of functions.
  • Real-valued functions, domain and range of these functions: modulus, exponential, constant, polynomial, identity, rational, Signum, logarithmic and greatest integer functions, with their graphs.

3. Trigonometric Functions

  • Positive and negative Angles.
  • Definition of trigonometric functions with the help of the unit circle.
  • Truth of the sin2x+cos2x=1, for all x.
  • Signs of trigonometric functions
  • Domain and range of trigonometric functions and their graphs.
  • Measuring angles in radians and in degrees and conversion of one into other. Expressing sin (x±y) and cos (x±y) in terms of sin x, sin y, cos x & cos y and their simple application.
  • Deducing identities like the following: 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

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.

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.

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.

4. Permutations and Combinations

  • Fundamental principle of counting.
  • Factorial n. (n!)Permutations and combinations,
  • Derivation of formulae and their connections, simple applications.

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.

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.
  • Formula for the following special sum

Unit-III: Coordinate Geometry

1. Straight Lines

 

  • Brief recall of two dimensional geometry 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 and 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.

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 and hyperbola.
  • Standard equation of a circle.

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

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

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

1. Statistics

  • Measures of dispersion; Range, mean deviation, variance and standard deviation of ungrouped/grouped data.
  • Analysis of frequency distributions with equal means but different variances.

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.

Important Topics to focus in Maths Exam Chapterwise

Chapter Name

Important Topics and Tips

Relations and Functions

  • Types of Relations
  • Composite of two functions
  • Invertible Functions
  • Frequently asked question are from ‘Equivalence relations’ and composite of functions

Inverse Trigonometric Functions

  • Properties of Inverse Trigonometric functions
  • Write down domain and range of all trigonometric function and related graphs on paper and revise them on daily basis

Matrices

  • Multiplication of Matrices
  • Symmetric and Skew Symmetric Properties
  • Finding Inverse of a Matrix using elementary transformation
  • Most of the students get stuck in elementary transformation

Determinants

  • Properties of determinants
  • Adjoint and Inverse of a Matrix
  • Solution of system of linear equations
  • Always mark the question while you get stuck, because all questions cannot be practised before exams

Continuity and Differentiability

  • Continuity of a function
  • Logarithmic Differentiation
  • Second order derivatives
  • Differentiation of Parametric form of functions
  • Logarithmic, trigonometric functions, exponential should be at tip

Application of Derivatives

  • Rate of change
  • Increasing and decreasing functions
  • Tangents and Normal to Curves
  • First and Second Derivatives Test for finding Local Maxima and Minima

Integrals

  • Integration by method of Substitution
  • Integration by Method of Partial Fractions
  • Integration by Parts
  • Definite Integral as Limit of a sum
  • Properties of Definite Integrals

Application of Integrals

  • Area under curves
  • Area bounded by a curve and a line
  • Area bounded by 2 Curves
  • It always better to draw the curve and shade the area to be calculated

Differential Equations

  • Formation of differential equation
  • Method of Solving Differential Equation with variable separable
  • Homogeneous Differential Equation
  • Linear differential equation

Vector Algebra

  • Scalar Product of Vectors and Projection of Vectors on a line
  • Vector Product of Vectors

3-D Geometry

  • Direction Cosines and Direction Ratio of line
  • Equation of line
  • Coplanarity of line
  • Angle between 2 lines
  • Shortest distance between 2 skew lines
  • Equation of plane in normal form
  • Equation of plane perpendicular to given vector and passing through a given point
  • Equation of plane passing through 3 non-collinear points
  • Plane passing through the intersection of two planes
  • Angle between 2 planes
  • Distance of a point from a plane
  • Angle between a line and a plane

Linear Programming

  • Graphical Solution to linear problems

Probability

  • Multiplication Theorem of Probability
  • Independent Events
  • Bayes’ Theorem
  • Random Variable and its probability distribution
  • Mean and Variance of Random Variable
  • Binomial Distribution
  • Try to revise the concepts of permutation and combination before getting into the chapter