II B - 5 - Hyperbola

5.0. Introduction

5.1 Equation of Hyperbola in Standard Form - Parametric Equations

5.1 Equation of Hyperbola in Standard Form - Parametric Equations

5.2 Equations of Tangent and Normal at a Point on the Hyperbola (Cartesian and Parametric)- Conditions for a Straight Line to be a Tangent - Asymptotes

5.2 Equations of Tangent and Normal at a Point on the Hyperbola (Cartesian and Parametric)- Conditions for a Straight Line to be a Tangent - Asymptotes

Maths II A - 1 - Algebra

01 Complex Numbers

01 Complex Numbers

1.1. Complex Number as an Ordered Pair of Real Numbers- Fundamental Operations

1.2 Representation of Complex Numbers in the form a+ib

1.3 Modulus and Amplitude of Complex Numbers –Illustrations

1.4 Geometrical and Polar Representation of Complex Numbers in Argand Plane- Argand Diagram

2 - De Moivre’s Theorem\

2.0. Introduction

2.1 De Moivre’s Theorem- Integral and Rational Indices

2.2 nth Roots of Unity- Geometrical Interpretations – Illustrations

3 - Quadratic Equations

3.0. Introduction

3.1 Quadratic Expressions, Equations in one variable

3.1 Quadratic Expressions, Equations in one variable

3.1 Quadratic Expressions, Equations in one variable

3.2 Sign of Quadratic Expressions – Change in Signs – Maximum and Minimum Values

3.2 Sign of Quadratic Expressions – Change in Signs – Maximum and Minimum Values

3.2 Sign of Quadratic Expressions – Change in Signs – Maximum and Minimum Values

3.3 Quadratic Inequations

4 - Theory of Equations

4.0. Introduction

4.1 The Relation between the Roots and Coefficients in an Equation

4.2 Solving the Equations when Two or More Roots of It are connected by Certain Relation

4.3 Equation with Real Coefficients, Occurrence of Complex Roots in Conjugate Pairs and Its Consequences

4.4 Transformation of Equations - Reciprocal Equations

5 - Permutations and Combinations

5.0. Introduction

5.1 Fundamental Principle of Counting - Linear and Circular Permutations

5.2 Permutations of ‘n’ Dissimilar Things Taken ‘r’ at a Time

5.3 Permutations When Repetitions Allowed

5.4 Circular Permutations

5.5 Permutations with Constraint Repetitions\

5.6 Combinations - Definitions and certain Theorems \

6 - Binomial Theorem

6.0. Introduction

6.1 Binomial Theorem for Positive Integral Index

6.2 Binomial Theorem for Rational Index

6.3 Approximations using Binomial Theorem

7 - Partial Fractions

7.0. Introduction

7.1 Partial Fractions of f(x)/g(x) when g(x) contains non –repeated Linear Factors

7.2 Partial Fractions of f(x)/g(x) when g(x) contains Repeated and/or Non-Repeated Linear Factors

7.3 Partial Fractions of f(x)/g(x) when g(x) contains Irreducible Factors

8 - Probability - Measures and Dispersion

8.0. Introduction

8.1 Range

8.2 Mean Deviation

8.3 Variance and Standard Deviation of Ungrouped/Grouped Data.

8.4 Coefficient of Variation and Analysis of Frequency Distribution with Equal Means but Different Variances

9 - Probability

9.0. Introduction

9.1 Random Experiments and Events

9.2 Classical Definition of Probability, Axiomatic Approach and Addition Theorem of Probability

9.2 Classical Definition of Probability, Axiomatic Approach and Addition Theorem of Probability

9.2 Classical Definition of Probability, Axiomatic Approach and Addition Theorem of Probability

9.3 Independent and Dependent Events; Conditional Probability- Multiplication Theorem and Bayee’s Theorem

9.3 Independent and Dependent Events; Conditional Probability- Multiplication Theorem and Bayee’s Theorem

9.3 Independent and Dependent Events; Conditional Probability- Multiplication Theorem and Bayee’s Theorem

9.3 Independent and Dependent Events; Conditional Probability- Multiplication Theorem and Bayee’s Theorem

10 - Random Variables and Probability Distributions

10.1 Random Variables

10.1 Random Variables

10.2 Theoretical discrete distributions – Binomial and Poisson Distributions

10.2 Theoretical discrete distributions – Binomial and Poisson Distributions

Maths II B - 1 - Coordinate Geometry

1.1. Circle - Equation of Circle - Standard Form - Center and Radius of a Circle with a given Line Segment as Diameter & Equation of Circle through Three Non Collinear Points - Parametric Equations of a Circle

1.1. Circle - Equation of Circle - Standard Form - Center and Radius of a Circle with a given Line Segment as Diameter & Equation of Circle through Three Non Collinear Points - Parametric Equations of a Circle

1.1. Circle - Equation of Circle - Standard Form - Center and Radius of a Circle with a given Line Segment as Diameter & Equation of Circle through Three Non Collinear Points - Parametric Equations of a Circle

1.1. Circle - Equation of Circle - Standard Form - Center and Radius of a Circle with a given Line Segment as Diameter & Equation of Circle through Three Non Collinear Points - Parametric Equations of a Circle

1.1. Circle - Equation of Circle - Standard Form - Center and Radius of a Circle with a given Line Segment as Diameter & Equation of Circle through Three Non Collinear Points - Parametric Equations of a Circle

1.2 Position of a Point in the Plane of a Circle – Power of a Point - Definition of Tangent - Length of Tangent

1.2 Position of a Point in the Plane of a Circle – Power of a Point - Definition of Tangent - Length of Tangent

1.2 Position of a Point in the Plane of a Circle – Power of a Point - Definition of Tangent - Length of Tangent

1.2 Position of a Point in the Plane of a Circle – Power of a Point - Definition of Tangent - Length of Tangent

1.3 Position of a Straight Line in the Plane of a Circle - Conditions for a Line to be Tangent – Chord Joining Two Points on a Circle – Equation of the Tangent at a Point on the Circle - Point of Contact - Equation of Normal.

1.3 Position of a Straight Line in the Plane of a Circle - Conditions for a Line to be Tangent – Chord Joining Two Points on a Circle – Equation of the Tangent at a Point on the Circle - Point of Contact - Equation of Normal.

1.3 Position of a Straight Line in the Plane of a Circle - Conditions for a Line to be Tangent – Chord Joining Two Points on a Circle – Equation of the Tangent at a Point on the Circle - Point of Contact - Equation of Normal.

1.3 Position of a Straight Line in the Plane of a Circle - Conditions for a Line to be Tangent – Chord Joining Two Points on a Circle – Equation of the Tangent at a Point on the Circle - Point of Contact - Equation of Normal.

1.3 Position of a Straight Line in the Plane of a Circle - Conditions for a Line to be Tangent – Chord Joining Two Points on a Circle – Equation of the Tangent at a Point on the Circle - Point of Contact - Equation of Normal.

1.3 Position of a Straight Line in the Plane of a Circle - Conditions for a Line to be Tangent – Chord Joining Two Points on a Circle – Equation of the Tangent at a Point on the Circle - Point of Contact - Equation of Normal.

1.4 Chord of Contact - Pole and Polar - Conjugate Points and Conjugate Lines - Equation of Chord with given Middle Point

1.4 Chord of Contact - Pole and Polar - Conjugate Points and Conjugate Lines - Equation of Chord with given Middle Point

1.4 Chord of Contact - Pole and Polar - Conjugate Points and Conjugate Lines - Equation of Chord with given Middle Point

1.4 Chord of Contact - Pole and Polar - Conjugate Points and Conjugate Lines - Equation of Chord with given Middle Point

1.5 Relative Position of Two Circles - Circles Touching Each Other Externally, Internally; Common Tangents – Centers of Similitude - Equation of Pair of Tangents from an External Point

1.5 Relative Position of Two Circles - Circles Touching Each Other Externally, Internally; Common Tangents – Centers of Similitude - Equation of Pair of Tangents from an External Point

1.5 Relative Position of Two Circles - Circles Touching Each Other Externally, Internally; Common Tangents – Centers of Similitude - Equation of Pair of Tangents from an External Point

1.5 Relative Position of Two Circles - Circles Touching Each Other Externally, Internally; Common Tangents – Centers of Similitude - Equation of Pair of Tangents from an External Point

1.5 Relative Position of Two Circles - Circles Touching Each Other Externally, Internally; Common Tangents – Centers of Similitude - Equation of Pair of Tangents from an External Point

II B - 2 - System of Circles

2.1 Angle between Two Intersecting Circles

2.2 Radical Axis of Two Circles – Properties - Common Chord and Common Tangent of Two Circles – Radical Center

2.2 Radical Axis of Two Circles – Properties - Common Chord and Common Tangent of Two Circles – Radical Center

2.2 Radical Axis of Two Circles – Properties - Common Chord and Common Tangent of Two Circles – Radical Center

2.2 Radical Axis of Two Circles – Properties - Common Chord and Common Tangent of Two Circles – Radical Center

2.3 Intersection of a Line and a Circle

II B - 3 - Parabola

3.0. Introduction

3.1 Conic Sections – Parabola; Equation of Parabola in Standard Form - Different Forms of Parabola- Arametric Equations

3.1 Conic Sections – Parabola; Equation of Parabola in Standard Form - Different Forms of Parabola- Arametric Equations

3.2 Equations of Tangent and Normal at a Point on the Parabola ( Cartesian and Parametric) - Conditions for Straight Line to be a Tangent

3.2 Equations of Tangent and Normal at a Point on the Parabola ( Cartesian and Parametric) - Conditions for Straight Line to be a Tangent

3.2 Equations of Tangent and Normal at a Point on the Parabola ( Cartesian and Parametric) - Conditions for Straight Line to be a Tangent

II B - 4 - Ellipse

4.0. Introduction

4.1 Equation of ? Ellipse in Standard Form - Parametric Equations

4.1 Equation of ? Ellipse in Standard Form - Parametric Equations

4.1 Equation of ? Ellipse in Standard Form - Parametric Equations

4.1 Equation of ? Ellipse in Standard Form - Parametric Equations

4.1 Equation of ? Ellipse in Standard Form - Parametric Equations

4.2 Equation of Tangent and Normal at a Point on the ellipse (Cartesian and Parametric) - Condition for a Straight Line to be a Tangent

4.2 Equation of Tangent and Normal at a Point on the ellipse (Cartesian and Parametric) - Condition for a Straight Line to be a Tangent

Calculus - II B - 6 - Integration

6.0. Introduction

6.1 Integration as the Inverse Process of Differentiation - Standard Forms - Properties of Integrals

6.1 Integration as the Inverse Process of Differentiation - Standard Forms - Properties of Integrals

6.1 Integration as the Inverse Process of Differentiation - Standard Forms - Properties of Integrals

6.2 Method of Substitution - Integration of Algebraic, Exponential, Logarithmic, Trigonometric and Inverse Trigonometric Functions. Integration by Parts.

6.2 Method of Substitution - Integration of Algebraic, Exponential, Logarithmic, Trigonometric and Inverse Trigonometric Functions. Integration by Parts.

6.2 Method of Substitution - Integration of Algebraic, Exponential, Logarithmic, Trigonometric and Inverse Trigonometric Functions. Integration by Parts.

6.2 Method of Substitution - Integration of Algebraic, Exponential, Logarithmic, Trigonometric and Inverse Trigonometric Functions. Integration by Parts.

6.2 Method of Substitution - Integration of Algebraic, Exponential, Logarithmic, Trigonometric and Inverse Trigonometric Functions. Integration by Parts.

6.2 Method of Substitution - Integration of Algebraic, Exponential, Logarithmic, Trigonometric and Inverse Trigonometric Functions. Integration by Parts.

6.2 Method of Substitution - Integration of Algebraic, Exponential, Logarithmic, Trigonometric and Inverse Trigonometric Functions. Integration by Parts.

6.3 Integration - Partial Fractions Method

6.4 Reduction Formulae

II B - 7 - Definite Integrals

7.0. Introduction

7.1 Definite Integral as the Limit of Sum

7.2 Interpretation of Definite Integral as an Area

7.3 Fundamental Theorem of Integral Calculus

7.4 Properties

7.5 Reduction Formulae

7.6 Application of Definite Integral to Areas

II B - 8 - Differential Equations

8.1 Formation of Differential Equation - Degree and Order of an Ordinary Differential Equation

8.2 Solving Differential Equation by a) Variables Separable Method

b) Homogeneous Differential Equation

c) Non - Homogeneous Differential Equation

d) Linear Differential Equations