Category: ### Sets

1
Sets and Their Representations
2
Empty Set
3
Finite and Infinite Sets
4
Equal Sets
5
Subsets
6
Subsets of a Set of Real Numbers Especially Intervals
7
Power Set
8
Universal Set
9
Venn Diagrams
10
Union and Intersection of Sets

### Relations & Functions

1
Ordered Pairs
2
Cartesian Product of Sets
3
Number of Elements in the Cartesian Product of Two Finite Sets
4
Cartesian Product of the Set of Reals with Itself
5
Definition of Relation
6
Pictorial Diagrams
7
Domain, Co-Domain and Range of a Relation
8
Function as a Special Type of Relation
9
Pictorial Representation of a Function, Domain, Co-Domain and Range of a Function.
10
Real Valued Functions

### Trigonometric Functions

1
Positive and Negative Angles
2
Measuring Angles in Radians and Conversion From one Measure to Another
3
Definition of Trigonometric Functions with the Help of Unit Circle
4
Truth of the Identity sin2x + cos2x = 1, for all x
5
Signs of Trigonometric Functions
6
Domain and Range of Trigonometric Functions and their Graphs
7
Expressing sin (x±y) and cos (x±y) in Terms of sinx, siny, cosx & cosy and Their Simple Applications
8
Deducing Identities
9
General Solution of Trigonometric Equations

### Principle of Mathematical Induction

1
Process of the Proof by Induction
2
Application of the Method
3
The Principle of Mathematical Induction and Simple Applications

### Complex Numbers and Quadratic Equations

1
Need for Complex Numbers
2
Algebraic Properties of Complex Numbers
3
Argand Plane Polar Representation
4
Statement of Fundamental Theorem of Algebra
5
6
Square Root of a Complex Number.

### Linear Inequalities

1
Linear Inequalities
2
Algebraic Solutions of Linear Inequalities
3
Graphical Solution of Linear Inequalities in two Variables
4
Graphical Method of Finding Solution of System of Linear Inequalities

### Permutations and Combinations

1
Fundamental Principle of Counting
2
Factorial n
3
Permutations and Combinations
4
Derivation of Formulae form nPr and nCr and their Connections
5
Simple Applications

### Binomial Theorem

1
Historical Perspective
2
Binomial Theorem
3
Pascal’s Triangle
4
General and Middle Term in Binomial Expansion
5
Simple Applications

### Sequence and Series

1
Sequence and Series
2
Arithmetic Progression
3
Arithmetic Mean
4
Geometric Progression
5
General Term of a G.P., Sum of n Terms of a G.P.
6
Infinite G.P. and its Sum
7
Geometric Mean (G.M.)
8
Relation Between A.M. and G.M
9
Formulae for Special Sums

### Straight Lines

1
Two Dimensional Geometry
2
Slope of a Line and Angle Between Two Lines
3
Various Forms of Equations of a Line
4
General Equation of a Line
5
Equation Lines passing Through the Point of Intersection of two Lines
6
Distance of a Point From a Line

### Conic Sections

1
Sections of a Cone : Circles
2
Ellipse
3
Parabola
4
Hyperbola
5
A Point, a Straight line and a Pair of Intersecting Lines
6
Standard Equations of Parabola, Ellipse and Hyperbola
7
Standard Equation of a Circle

### Introduction to Three-dimensional Geometry

1
Coordinate Axes and Coordinate Planes in 3D
2
Coordinates of a Point
3
Distance Between two Points and Section Formula

### Limits and Derivatives

1
Derivative Introduced as Rate of Change
2
Intuitive Idea of Limit
3
Limits of Polynomials and Rational Functions
4
Definition of Derivative Relate it to Scope of Tangent of the Curve
5
Derivative of Sum, Difference, Product and Quotient of Functions
6
Derivatives of Polynomial and Trigonometric Functions

### Mathematical Reasoning

1
Mathematically Acceptable Statements
2
Connecting Words/ Phrases
3
Variety of Examples Related to Real Life and Mathematics
4
Validating the Statements Involving the Connecting Words
5
Difference Among Contradiction, Converse and Contrapositive

### Statistics

1
Measures of Dispersion: Range
2
Mean Deviation, Variance
3
Standard Deviation of Ungrouped/Grouped Data
4
Analysis of Frequency Distributions

### Probability

1
Random Experiments
2
Outcomes, Sample Spaces
3
Events Occurrence of Events, ‘not’, ‘and’ and ‘or’ Events
4
Exhaustive Events, Mutually Exclusive Events
5
Axiomatic Probability
6
Connections with other Theories of Earlier Classes
7
Probability of an Event, Probability of ‘not’, ‘and’ and ‘or’ Events