2.Relations & Functions

2.1. Introduction

2.2. Cartesian Product of Sets

2.2. Cartesian Product of Sets

2.2. Cartesian Product of Sets

2.3. Relations

2.3. Relations

2.3. Relations

2.3. Relations

2.3. Relations

2.4. Functions

2.4.1. Some Functions and their Graphs

i- Identity Function

ii- Constant Function

iii- Polynomial Function

iv- Rational Function

v- The Modulus Function

vi- Signum Function

vii- Greatest Integer Function

2.4.2. Algebra of Real Numbers

2.4.2. Algebra of Real Numbers

2.4.2. Algebra of Real Numbers

i- Addition of Two Real Numbers

ii- Subtraction of Real Function from Another

iii- Multiplication by a Scalar

iv- Multiplication of Two Real Functions

v- Quotient of Two Real Functions

1.Sets

1.1. Introduction

1.2. Sets and their Representation

1.2. Sets and their Representation

1.2. Sets and their Representation

1.3. The Empty Set

1.4. Finite and Infinite Sets

1.5. Equal Sets

1.6. Sub-Sets

1.6.1. Subsets of Set of Real Numbers

1.6.2. Intervals as Subsets of R

1.7. Power Set

1.8. Universal Set

1.9. Venn Diagrams

1.9. Venn Diagrams

1.9. Venn Diagrams

1.10. Operations of Sets

1.10. Operations of Sets

1.10. Operations of Sets

1.10.1. Union of Sets

1.10.2. Intersection of Sets

1.10.3. Difference of Sets

1.11. Compliment of a Set

1.12. Practical Problems on Union and Intersection of Two Sets

3.Trigonometric Functions

3.1. Introduction

3.1. Introduction

3.2. Angles

3.2.1. Degree Measurement

3.2.2. Radian Measure

3.2.3. Relation Between Radian and Real Numbers

3.2.4. Relation between Degree and Radian

3.3 Trigonometric Functions

3.3 Trigonometric Functions

3.3 Trigonometric Functions

3.3.1. Sign of Trigonometric Functions

3.3.2. Domain and Range of Trigonometric Functions

3.4. Trigonometric Functions of Sum and Difference of Two Angles

3.5. Trigonometric Equations

3.5. Trigonometric Equations

3.5. Trigonometric Equations

3.5. Trigonometric Equations

3.5. Trigonometric Equations

4.Principle of Mathematical Induction

4.1. Introduction

4.2. Motivation

4.3. The Principle of Mathematical Induction

4.3. The Principle of Mathematical Induction

4.3. The Principle of Mathematical Induction

4.3. The Principle of Mathematical Induction

5.Complex Numbers and Quadratic Equations

5.1. Introduction

5.2. Complex Numbers

5.3. Algebra of Complex Numbers

5.3.1. Addition of Two Complex Numbers

5.3.2. Difference of Two Complex Numbers

5.3.3. Multiplication of Two Complex Numbers

5.3.4. Division of Two Complex Numbers

5.3.5. Power of I

5.3.6. The Square Roots of Negative Real Number

5.3.6. The Square Roots of Negative Real Number

5.3.6. The Square Roots of Negative Real Number

5.3.7. Identities

5.4. The Modulus and Conjugate of a Complex Number

5.5. Argand Plane and Polar Representation

5.5.1. Polar Representation of a Complex Number

5.6. Quadratic Equations

5.6. Quadratic Equations

5.6. Quadratic Equations

6.Linear Inequalities

6.1. Introduction

6.2. Inequalities

6.3. Algebra Solutions of Linear Inequalities in One Variable and their Graphical Representation

6.4. Graphical Solution of Linear Inequalities in Two Variables

6.5. Solution of System of Linear Inequalities in Two Variables

6.5. Solution of System of Linear Inequalities in Two Variables

6.5. Solution of System of Linear Inequalities in Two Variables

8.Binomial Theorem

8.1. Introduction

8.1. Introduction

8.2. Binomial Theorem for Positive Integral Indices

8.2. Binomial Theorem for Positive Integral Indices

8.2. Binomial Theorem for Positive Integral Indices

8.2.1. Binomial Theorem for any Positive Integral n

8.2.2. Some Special Cases

8.3. General and Middle Terms

8.3. General and Middle Terms

8.3. General and Middle Terms

8.3. General and Middle Terms

8.3. General and Middle Terms

8.3. General and Middle Terms

8.3. General and Middle Terms

8.3. General and Middle Terms

8.3. General and Middle Terms

9.Sequence and Series

9.1. Introduction

9.2. Sequences

9.3. Series

9.4. Arithmetic Progression

9.4. Arithmetic Progression

9.4. Arithmetic Progression

9.4. Arithmetic Progression

9.4.1. Arithmetic Mean

9.4.1. Arithmetic Mean

9.4.1. Arithmetic Mean

9.5. Geometric Progression

9.5. Geometric Progression

9.5. Geometric Progression

9.5. Geometric Progression

9.5. Geometric Progression

9.5.1. General Term of GP

9.5.2. Sum to n Terms of a GP

9.5.3. Geometric Mean

9.5.3. Geometric Mean

9.5.3. Geometric Mean

9.6. Relationship between A.M. And G.M.

9.6. Relationship between A.M. And G.M.

9.6. Relationship between A.M. And G.M.

9.7. Sum to n Terms of Special Series

10.Straight Lines

10.1. Introduction

10.1. Introduction

10.1. Introduction

10.2. Slope of a Line

10.2. Slope of a Line

10.2. Slope of a Line

10.2.1. Slope of a Line when coordinates any two points on the Line Given

10.2.2. Conditions for Parallelism and Perpendicularity of Lines in Terms of their Slopes

10.2.3. Angle between Two Lines

10.2.3. Angle between Two Lines

10.2.3. Angle between Two Lines

10.2.4. Collinearity of Three Points

10.2.4. Collinearity of Three Points

10.3. Various Forms of the Equation of a Line

10.3.1. Horizontal and Vertical Lines

10.3.2. Point-Slope Form

10.3.3. Two Point Form

10.3.4. Slope-Intercept Form

10.3.5. Intercept Form

10.3.6. Normal Form

10.4. General Equation of a Line

10.4.1. Different Forms

10.5. Distance of Point From a Line

10.5. Distance of Point From a Line

10.5. Distance of Point From a Line

10.5.1. Distance between Two Parallel Lines

10.5.1. Distance between Two Parallel Lines

10.5.1. Distance between Two Parallel Lines

11. Conic Sections

1.1. Introduction

11.2. Sections of a Cone

11.2.1. Circle, Ellipse, Parabola and Hyperbola

11.2.2. Degenerated Conic Sections

11.3. Circle

11.3. Circle

11.3. Circle

11.4. Parabola

11.4.1. Standard Equations of Parabola

11.4.1. Standard Equations of Parabola

11.4.1. Standard Equations of Parabola

11.4.2. Latus Rectum

11.5. Ellipse

11.5.1. Relationship between Semi-Major Axis, Semi-Minor Axis and the Distance of the Focus from the Center of the Ellipse

11.5.2. Special Cases of an Ellipse

11.5.3. Eccentricity

11.5.4. Standard Equations of an Ellipse

11.5..5. Latus Rectum

11.6. Hyperbola

11.6.1. Eccentricity

11.6.2. Standard Equation of Hyperbola

11.6.3. Latus Rectum

12.Introduction to Three Dimensional Geography

12.1. Introduction

12.2. Coordinate Axes and Coordinate Planes in Three Dimensional Space

12.3. Coordinate Point in Space

12.4. Distance between Two Points

12.5. Section Formula

13.Limits and Derivatives

13.1. Introduction

13.2. Intuitive Idea of Derivatives

13.3. Limits

13.3. Limits

13.3. Limits

13.3.1. Algebra of Limits

13.3.2. Limits of Polynomials and Rational Functions

13.4. Limits of Trigonometric Functions

13.5. Derivatives

13.5.1. Algebra of Derivative of Functions

13.5.2. Derivative of Polynomials and Trigonometric Functions

14.Mathematical Reasoning

14.1. Introduction

14.2. Statements

14.3. New Statements from Old

14.3.1. Negation of a Statement

14.3.2. Compound Statements

14.4. Special Words / Phrases

14.4.1. The Word “And”

14.4.2. The Word “or”

14.4.3. Quantifiers

14.5. Implications

14.5.1. Contra positive and Converse

14.6. Validating Statements

14.6.1. By Contradiction

15.Statistics

15.1. Introduction

15.2. Methods of Dispersion

15.3. Range

15.4. Mean Deviation

15.4.1. Mean Deviation for Ungrouped Data

15.4.2. Mean Deviation for Grouped Data

15.4.3. Limitations of Mean Deviation

15.5. Variance and Standard Deviation

15.5.1. Standard Deviation

15.5.2. Standard Deviation of a Discrete Frequency Distribution

15.5.3. Standard Deviation of a Continuous Frequency Distribution

15.5.4. Shortcut Method to Find Variance and Standard Deviation

15.6. Analysis of Frequency Distribution

15.6.1. Comparison of Two Frequency Distributions with Same Mean

16.Probability

16.1. Introduction

16.1. Introduction

16.1. Introduction

16.2. Random Experiments

16.2.1. Outcomes and Sample Space

16.3. Event

16.3.1. Occurrence of an Event

16.3.2. Types of Event

16.3.3. Algebra of Events

16.3.4. Mutually Exclusive Events

16.3.5. Exhaustive Events

16.4. Axiomatic Approach to Probability

16.4.1. Probability of an Event

16.4.2. Probabilities of Equally Likely Outcomes

16.4.3. Probability of the Event 'A or B'

16.4.4. Probability of Even 'Not A'