# Unit-I: Sets and Functions

#### Sets

• Sets and their representation
• Types of sets: empty sets, finite and infinite sets, power set, universal set
• Cardinality of sets
• Subset and superset
• Venn diagram
• Operation on sets: union of sets
• Operation on sets: intersection and difference of sets
• Complement of sets
• Practical problems on union and intersection of two sets

#### Relations & Functions

• Cartesian product of sets
• Relations
• Function: domain and range
• identity function, constant function and modulus function
• Graphs of polynomial function
• Algebra of real functionsn

#### 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 trignometric functions and their graphs
• Expressing sin (x±y) and cos (x±y) in terms of sinx, siny, cosx & cosy and their simple application
• Deducing identities like the following:
• Identities related to sin 2x, cos 2x, tan 2x, sin 3x, cos 3x and tan 3x
• General solution of trigonometric equations of the type sin y = sin a, cos y = cos a and tan y = tan a.

# UNIT II: ALGEBRA

#### 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
• Simple Application of principle of mathematical induction

#### Complex Numbers and Quadratic Equations

• Need for complex numbers, especially √1, to be motivated by inability to solve some of the quardratic equations
• Algebraic properties of complex numbers
• Modulus and conjugate 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
• Euler's formula and De Moivre's theorem
• Square root of a complex number.

#### 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.

#### Permutations and Combinations

• Fundamental principle of counting
• Permutations
• Combinations

#### 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.

#### Sequence and Series

• Sequence and Series
• Arithmetic Progression (A.P.).
• Geometric progression
• Relationship between Aithmetic mean and geometric mean
• Formula for the following special sum:

# UNIT III: COORDINATE GEOMETRY

#### 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
• AEquation of family of lines passing through the point of intersection of two lines
• Distance of a point from a line.

#### Conic Sections

• Sections of cone
• Circle
• Parabola
• Ellipse
• 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.

#### Introduction to Three–dimensional Geometry

• Coordinates of point in space
• Distance between two points
• Section formula

# Unit-IV: Calculus & Mathematical Reasoning

#### Limits and Derivatives

• Derivative introduced as rate of change both as that of distance function and geometrically.
• Intutive idea of limit
• Limits of polynomials and rational functions, trignometric, 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 trignometric functions

#### Mathematical Reasoning

• Introduction
• Statements
• New statements from old
• Special word/phrase
• Implications
• validating statements

# Unit-VI: Statistics and Probability

#### Statistics

• Measures of dispersion and range
• Mean deviation
• mean deviation for ungrouped data
• mean deviation for discrete frequency distribution
• mean deviation for continuous frequency distribution
• Variance and standard deviation
• Shortcut method for finding variance and standard deviation
• Analysis of frequency distribution

#### Probability

• Random experiments; outcomes, sample spaces
• Event and types of event
• Algebra of event
• Axiomatic approach to probability