# Mathematics Course for Class XI/IIT JEE

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# A course in mathematics for class XIth/IIT JEE students.

## 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

### What Will You Learn?

• You will be able to solve questions from NCERT syllabus.

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