# Mathematics Course for Class XI/IIT JEE

## About Course

# 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 sin
^{2}x + cos^{2}x = 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

### Course Content

#### Binomial Theorem

##### The Pascal Triangle

21:15##### Understanding Expansion formula

47:13

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