# Wiley's Decoding Mathematics For JEE, Vol I

ISBN: 9788126522927

1228 pages

## Description

Fundamentals of Mathematics, Volume – I (as per Class 11 syllabus) offers a compelling solution for all CBSE students preparing for JEE and other engineering entrance examinations. The content has been organized to provide a more structured approach to meet the requirements of both JEE and CBSE syllabi. The book offers multidimensional approach of the subject through clear and engaging explanation of concepts aided with interesting coloured figures. Also, the book deals with application-based approach through qualitative problem sets. This book empowers students' concept building and enhances critical thinking skills in mathematics and its fundamentals.

Chapter 1 Sets, Relations and Functions

1.1 Introduction

1.2 Set 3

1.3 Relations

1.4 Functions

1.5 Binary Operations

Chapter 2 Trigonometric Ratios and Identities

2.1 Introduction

2.2 Measurement of Angles and Sign Convention (The Amount of Turning)

2.3 Trigonometric Ratios

2.4 Trigonometric Identities

2.5 Values of Trigonometric Ratios of Standard Acute Angles

2.6 Reduction Formulas

2.7 Trigonometric Ratios of Compound Angles

2.8 Sum and Product Transformations

2.9 Trigonometric Ratios of Multiple and Sub-Multiple Angles

2.10 Continued Product of Cosine Series

2.11 Applications of Trigonometry

2.12 Conditional Identities

2.13 Graphs of Trigonometric Functions and Applications

2.14 Summation of Trigonometric Series

2.15 Inequalities of Triangles

2.16 Elimination of Trigonometric Variables

Chapter 3 Trigonometric Equations and Inverse Trigonometry

3.1 Introduction

3.2 Solving Trigonometric Equations – General Solutions

3.3 General Solution of Trigonometric Equations

3.4 Solution of Different Types of Trigonometric Equation

3.5 Solving Simultaneous Equations

3.6 Inverse Trigonometric Functions

3.7 Domain and Range of the Inverse Trigonometric Functions

3.8 Graphs of the Inverse Trigonometric Functions

3.9 Properties of Inverse Trigonometric Functions

Chapter 4 Solutions of Triangles

4.1 Introduction

4.2 Relations Between Sides and Angles of a Triangle

4.3 Area of Triangles

4.4 Relation Between the Sides and the Half-Angles of a Triangle

4.5 Solving a Triangle

4.6 Circles Linked with Triangles

4.7 Orthocentre and Pedal Triangle

4.8 Medians and Centroid of a Triangle

4.9 Regular Polygon

4.10 Definitions

4.11 Some Important Properties of Triangle

4.12 Some Properties Related to Circle

4.13 Some Important Theorems

Chapter 5 Quadratic Equations and Expressions

5.1 Introduction

5.2 Wavy-Curve Method of Solving Inequalities

5.3 Quadratic Equations

5.4 Roots of a Quadratic Equation

5.5 Relation between Roots and Coefficients of Quadratic Equation

5.6 Equations Reducible to Quadratic

5.7 Conclusions about Roots of Quadratic Equations

5.8 Condition for Two Quadratic Equations to Have a Common Root

5.9 Maximum and Minimum Values of Quadratic Expression

5.10 Location of Roots

5.11 Applications of Quadratic Equation

Chapter 6 Complex Numbers

6.1 Introduction

6.2 Imaginary and Complex Numbers

6.3 Properties of Complex Numbers

6.4 Conjugate of a Complex Number

6.5 Modulus of a Complex Number

6.6 Argument of a Complex Number

6.7 Geometrical Representation of Complex Numbers

6.8 Representation of Complex Numbers

6.9 De Moivre’s Theorem

6.10 Rotation Theorem

6.11 Vectorial Representation of a Complex Number

6.12 Geometry of Complex Numbers

6.13 Condition for Right-Angled Isosceles Triangle

6.14 Straight Line in Complex Plane

6.15 Circle in Complex Plane

6.16 Some Special Properties

6.17 Conic Section in Complex Plane

6.18 Some Important Results of Locus

Chapter 7 Permutations and Combinations

7.1 Introduction

7.2 Fundamental Principle of Counting

7.3 Factorials

7.4 Permutation

7.5 Combination

7.6 Division and Distribution into Groups

7.7 Multinomial Theorem

7.8 Exponent of Prime p in n!

7.9 Derangement

7.10 Application of Permutation and Combination – Navigate a Grid

Chapter 8 Binomial Theorem

8.1 Introduction

8.2 Binomial Theorem

8.3 General Term in a Binomial Expansion

8.4 Middle Terms in Binomial Expansion

8.5 Term Independent of x

8.6 Greatest Coefficient in Binomial Expansion

8.7 Numerically Greatest Term in Binomial Expansion

8.8 Binomial Coefficients and Its Properties

8.9 Applications of Binomial Expansions

Chapter 9 Sequences and Series

9.1 Introduction

9.2 Series

9.3 Progression

9.4 Arithmetic Progression

9.4.4 Properties of AP

9.5 Arithmetic Mean (AM)

9.6 Geometrical Progression

9.7 Geometrical Mean (GM)

9.8 Arithmetic-Geometric Progression (AGP)

9.9 Harmonic Progression

9.10 Harmonic Mean (HM)

9.11 Some Special Series

9.12 Summation Using Sigma Notation

9.13 Inequalities

9.14 Relation between AM and GM

9.15 Relation between AM, GM and HM

9.16 Weighted Means

Chapter 10 Cartesian Coordinates and Straight Lines

10.4 Deductions of Simple Geometrical Theorems Using Section/Distance Formula

10.5 Area of a Triangle

10.6 Area of Quadrilateral

10.7 Area of Polygon

10.8 Locus

10.9 Translation and Rotation of Axes

10.10 Introducing Straight Lines

10.11 Slope Formula of a Straight Line

10.12 Angle Between Two Lines

10.13 Equation of a Line Parallel to the x-Axis

10.14 Equation of a Line Parallel to the y-Axis

10.15 Equation of the x-Axis and the y-Axis

10.16 x-Intercept and y-Intercept of a Line

10.17 Different Forms of Equation of a Line

10.18 Equation of Lines Parallel and Perpendicular to a Given Line

10.19 Position of Two Points with Respect to a Line

10.20 Perpendicular Distance of a Point from a Line

10.21 Distance Between Two Parallel Lines

10.22 Area of Parallelogram

10.23 Point of Intersection of Two Lines

10.24 Condition for Concurrency of Three Lines

10.25 Equation of Lines Passing through a Point that Makes an Angle with the Line

10.26 Equation of Angle Bisector

10.26.2 Bisector of Angle Containing Origin

10.27 Bisectors Between Two Lines Expressed in Parametric Form

10.28 Bisectors in Case of Triangle

10.29 Concurrency of Three Angles Bisectors

10.30 Family of Straight Lines

10.31 Pair of Straight Lines

Chapter 11 Circles

11.1 Introduction

11.2 Standard Equation of a Circle

11.3 General Equation of a Circle

11.4 Diametrical Equation of a Circle

11.5 Intercepts of a Circle on Coordinate Axes

11.6 Parametric Equation of a Circle

11.7 Position of a Point with Respect to a Circle

11.8 Position of a Line with Respect to a Circle

11.9 Tangents

11.10 Power of a Point

11.11 Director Circle

11.12 Chord of Contact

11.13 Normal

11.14 Family of Circles

11.15 Pole and Polars

11.16 Diameter of Circle

11.17 Angle of Intersection of Two Circles

11.18 Radical Axis and Radical Centre

11.19 Coaxial System of Circles

11.20 Limiting Points

Chapter 12 Parabola

12.1 Introduction

12.2 Parabola

12.3 Standard Equation of Parabola

12.4 General Equation of Parabola

12.5 Parametric Equations of a Parabola

12.6 Position of a Point Relative to a Parabola

12.7 Chord of Parabola

12.8 Position of a Line Relative to a Parabola

12.9 Tangents to the Parabola

12.10 Director Circle

12.11 Normal to the Parabola

12.12 Subtangent and Subnormal

12.13 Pair of Tangents

12.14 Chord of Contact

12.15 Equation of Chord in Terms of Midpoint

12.16 Polar and Pole

12.17 Diameter of Parabola

12.18 Important Properties of Parabola

Chapter 13 Ellipse

13.1 Introduction

13.2 Definition of Ellipse

13.3 Equation of Ellipse

13.4 Eccentricity of an Ellipse

13.5 Terms Related to Ellipse

13.6 Directrix and Focal Directrix Property

13.7 Auxiliary Circle and Eccentric Angle

13.8 Parametric Equation of Ellipse

13.9 Position of a Point with Respect to Ellipse

13.10 Interaction of Line and Ellipse

13.11 Equation of Chord of an Ellipse

13.12 Tangents to an Ellipse

13.13 Normal to an Ellipse

13.14 Pair of Tangent

13.15 Chord of Contact

13.16 Equation of Chord in Terms of Its Midpoint

13.17 Polar and Pole

13.18 Diameter of Ellipse

13.19 Conjugate Diameter

13.20 Properties of Ellipse

13.21 Important Highlights of Ellipse

Chapter 14 Hyperbola

14.1 Introduction

14.2 Standard Equation of Hyperbola

14.3 Eccentricity

14.4 Length of Latus of Rectum

14.5 Conjugate Hyperbola

14.6 Directrix and Focal Directrix Property

14.7 Auxiliary Circle and Eccentric Angle

14.8 Parametric Equation of Hyperbola

14.9 Position of a Point with Respect to Hyperbola

14.10 Interaction of Line and Hyperbola

14.11 Equation of Chord of Hyperbola

14.12 Tangents to Hyperbola

14.13 Important Highlights of Tangents and Normals

14.14 Pair of Tangent

14.15 Chord of Contact

14.16 Equation of Chord in Terms of Its Midpoint

14.17 Polar and Pole

14.18 Diameter of Hyperbola

14.19 Conjugate Diameter

14.20 Asymptotes of Hyperbola

14.21 Important Points on Asymptotes

14.22 Rectangular Hyperbola

14.23 Asymptotes as Coordinate Axes

Solved Examples

Practice Questions

Answer with Explanation

Important Formulas

Solved Previous Years' JEE Main Questions (2008–2018)

Solved Previous Years’ JEE Advanced Questions (2008–2018)

Chapter Exercises

Answer Key

Concept Map