 # Class 11 Syllabus

Class 11 Maths Syllabus is given below. Students can get to know the weightage of all the chapters and can be able to prepare with suitable strategies to excel in the examination.

## Class 11 Maths Syllabus 2019-20

One Paper
Three Hours                                                         Total Period= 240 [35 Minutes Each] Max. Marks -80

 Unit Topic No.of Periods Marks I. Sets and Functions 60 23 II. Algebra 70 30 III. Co-ordinate Geometry 40 10 IV. Calculus 30 05 V. Mathematical Reasoning 10 02 VI. Statistics and Probability 30 10 Total 240 80 Internal Assessment – 20

#### 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.

#### 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

#### 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.li>

#### 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.

#### 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.

#### 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.