PREFACE TO THE REVISED EDITION:

It gives me immense pleasure in presenting the thoroughly revised edition to my esteemed readers. In the present edition entire text has been re-written in a lucid manner without altering the basic structure and retaining the salient features of earlier editions. Illustrative examples and Exercises given at the end of every section/sub-section in each chapter have been arranged in the increasing order of difficulty level and have been categorized in to the following categories:

BASIC-Based on basic concepts and formulae

LOTS-Based on lower order thinking skills

HOTS - Based on higher order thinking skills

At the end of each chapter Exercises consisting of large number of Fill in the Blank Type Questions (FBQs) and Very Short Answer Type Questions (VSAQs) have been given.

Some new and unique features of this book are:

Detailed theory with illustrations

Algorithmic approach

Large number of Graded Solved Examples

Large number of FBQS, VSAQs

Large number of Graded Exercises

I also avail this opportunity to thank Sh. Ish Kanpur for his painstaking efforts and cooperation in bringing out this book in such an excellent form.

Every effort has been made to make this edition error free, some printing errors might have crept in inadvertently. I shall be grateful to the teachers and students if the same are brought to my notice. Any suggestions/criticism to enhance to quality of the book will be gratefully acknowledged. Feedback or queries can be sent through e-mail to

rdsmath.feedback@gmail.com.

Dr. R.D. SHARMA    

                                                          MATHEMATICS-IX                                                       

       CONTENTS IN BRIEF

          1. NUMBER SYSTEM...........................................................................................1.1-1.30

          2. EXPONENTS OF REAL NUMBERS..............................................................2.1-2.26

          3. RATIONALISATION........................................................................................3.1-3.16

          4. ALGEBRAIC IDENTITIES...............................................................................4.1-4.26

          5. FACTORIZATION OF ALGEBRAIC EXPRESSIONS..................................5.1-5.21

          6. FACTORIZATION OF POLYNOMIALS.........................................................6.1-6.28

          7. CO-ORDINATE GEOMETRY..........................................................................7.1-7.5

          8. LINEAR EQUATIONS IN TWO VARIABLES..............................................8.1-8.8

          9. INTRODUCTION TO EUCLID'S GEOMETRY..............................................9.1-9.9

         10. LINES AND ANGLES.....................................................................................10.1-10.34

         11. TRIANGLES......................................................................................................11.1-11.43

         12. QUADRILATERALS........................................................................................12.1-12.53

         13. CIRCLES............................................................................................................13.1-13.72

         14. HERON'S FORMULA......................................................................................14.1-14.21

         15. SURFACE AREA AND VOLUME OF A RIGHT CIRCULAR CONE........15.1-15.17

         16. SURFACE AREA AND VOLUME OF A SPHERE......................................16.1-16.19

         17. GRAPHICAL REPRESENTATION OF STATISTICAL DATA....................17.1-17.28

MATHEMATICS-IX

CONTENTS IN DELAIL

1. NUMBER SYSTEM............................................................................................................1.1-1.30

1.1 Introduction......................................................................................................................1.1

1.2 Brief review of numbers.........................................................................................................1.1

1.3 Decimal representation of rational numbers....................................................................1.5

1.4 Conversion of decimal numbers into rational numbers of the form..........................1.11

1.5 Irrational numbers.....................................................................................................................1.19

1.6 Some useful results on irrational numbers........................................................................1.21

1.7 Representing irrational numbers on the number line.....................................................1.27

1.8 Real numbers and real number line.....................................................................................1.28

1.9 Existence of square root of a positive real number.........................................................1.28

2. EXPONENTS OF REAL NUMBERS................................................................................2.1-2.26

2.1 Introduction.................................................................................................................................2.1

2.2 Integral exponents of a real number....................................................................................2.1

2.3 Laws of integral exponents....................................................................................................2.1

2.4 Rational exponents of a real number..................................................................................2.11

2.5 Laws of rational exponents....................................................................................................2.12

3. RATIONALISATION...........................................................................................................3.1-3.16

3.1 Introduction..................................................................................................................................3.1

3.2 Some identities...........................................................................................................................3.1

3.3 Rationalization of denominator..............................................................................................3.2

4. ALGEBRAIC IDENTITIES...................................................................................................4.1-4.26

4.1 Introduction...................................................................................................................................4.1

4.2 Recall of identities.......................................................................................................................4.1

4.3 Identity for the square of a trinomial......................................................................................4.7

4.4 Identity for the cube of a binomial..........................................................................................4.11

4.5 Sum and difference of cubes....................................................................................................4.18

4.6 One more identity.........................................................................................................................4.22

5. FACTORIZATION OF ALGEBRAIC EXPRESSIONS.......................................................5.1-5.21

5.1 Introduction.....................................................................................................................................5.1

5.2 Recall of work done earlier.........................................................................................................5.1

5.3 Factorization of algebraic expressions expressible as the sum or difference of two cubes...........................5.8

5.4 Factorization by using the formulae for the cube of a binomial......................................5.12

5.5 Factorization of algebraic expressions of the form a² + b²+c²-3abc.............................5.14

5.6 Factorization of sum of the cubes when their sum is zero................................................5.17

6. FACTORIZATION OF POLYNOMIALS................................................................................6.1-6.28

6.1 Some definitions.............................................................................................................................6.1

6.2 Zeros (roots) of a polynomial......................................................................................................6.4

63 Remainder theorem........................................................................................................................6.8

6.4 Factor theorem................................................................................................................................6.13

6.5 Factorization of polynomials by using factor theorem........................................................6:21

7. CO-ORDINATE GEOMETRY.................................................................................................7.1-7.5   

7.1 Introduction......................................................................................................................................7.1

7.2 Rectangular or Cartesian Co-ordinates of a point...............................................................7.2

8. LINEAR EQUATIONS IN TWO VARIABLES....................................................................8.1-8.8

8.1 Introduction......................................................................................................................................8.1

8.2 Linear equations in two variables..............................................................................................8.1

8.3 Solution of a linear equation........................................................................................................8.3

9. INTRODUCTION TO EUCLID'S GEOMETRY.....................................................................9.1-99

9.1 Introduction........................................................................................................................................9.1

9.2 Axioms (postulates) and theorems.............................................................................................9.1

9.3 Some undefined terms....................................................................................................................9.1

9.4 Incidence properties of points and lines....................................................................................9.2

9.5 Parallel lines and intersecting lines..............................................................................................9.3

9.6 Line segment......................................................................................................................................9.5

9.7 Length axioms of line segments...................................................................................................9.6

9.8 Ray, half-line, line separation.........................................................................................................9.6

9.9 Half-plane.............................................................................................................................................9.7

10. LINES AND ANGLES..............................................................................................................10.1-10.34

10.1 Angles..................................................................................................................................................10.1

10.2 Measure of an angle........................................................................................................................10.2

10.3 Types of angles.................................................................................................................................10.2

10.4 Some angle relations.......................................................................................................................10.5

10.5 Angles made by a transversal with two lines..........................................................................10.17

11. TRIANGLES................................................................................................................................11.1-11.43

11.1 Introduction.........................................................................................................................................11.1

11.2 Triangle.................................................................................................................................................11.2

11.3 Congruence of line segments........................................................................................................11.2

11.4 Congruence of angles......................................................................................................................11.2

11.5 Congruence of triangles..................................................................................................................11.2

11.6 Sufficient conditions (criteria) for congruence of triangles...................................................11.4

12. QUADRILATERALS...................................................................................................................12.1-12.53

12.1 Introduction..........................................................................................................................................12.1

12.2 Quadrilateral and some terms associated to it..........................................................................12.1

12.3 Various types of quadrilaterals.......................................................................................................12.2

12.4 Properties of a parallelogram..........................................................................................................12.2

12.5 Sufficient conditions for a Quadrilateral to be a Parallelogram............................................12.15

12.6 Properties of Rectangles, Rhombi and a Squares....................................................................12.27

12.7 The mid-point theorem.....................................................................................................................12.34

13. CIRCLES.......................................................................................................................................13.1-13.72

13.1 Introduction............................................................................................................................................13.1

13.2 Circle and terms related to a circle..................................................................................................13.1

13.3 Chord and arc properties of circles.................................................................................................13.6

13.4 Some useful properties of equal chords........................................................................................13.24

13.5 Arcs and angles subtended by them..............................................................................................13.32

13.6 Properties of a cyclic quadrilateral...................................................................................................13.50

14. HERON'S FORMULA....................................................................................................................14.1-14.21

14.1 Introduction..............................................................................................................................................14.1

14.2 Heron's formula.......................................................................................................................................14.2

14.3 Some applications of Heron's formula.............................................................................................14.10

15. SURFACE AREA AND VOLUME OF A RIGHT CIRCULAR CONE.......................................15.1-15.17

15.1 Introduction..............................................................................................................................................15.1

15.2 Right circular cone..................................................................................................................................15.1

15.3 Surface area of a right circular cone.................................................................................................15.2

15.4 Volume of a right circular cone...........................................................................................................15.7

16. SURFACE AREA AND VOLUME OF A SPHERE.....................................................................16.1-16.19

16.1 Introduction...............................................................................................................................................16.1

16.2 Sphere.........................................................................................................................................................16.1

16.3 Section of a sphere by a plane.............................................................................................................16.1

16.4 Surface area of a sphere, hemi-sphere and spherical shell........................................................16.2

16.5 Volumes of a sphere, a hemisphere and a spherical shell...........................................................16.7

17. GRAPHICAL REPRESENTATION OF STATISTICAL DATA....................................................17.1-17.28

17.1 Introduction.................................................................................................................................17.1

17.2 Bar graph.......................................................................................................................................17.1

17.3 Reading and interpretation of bar graphs............................................................................17.2

17.4 Construction of bar graphs........................................................................................................17.10

17.5 Bar graphs and their constructions..........................................................................................17.10

17.6 Histogram.........................................................................................................................................17.17

17.7 Frequency polygon........................................................................................................................17.23