Mathematics: Textbook for Class IX

1. NUMBER SYSTEMS
    1.1 Introduction
    1.2 Irrational Numbers
    1.3 Real Numbers and their Decimal Expansions
    1.4 Representing Real Numbers on the Number Line
    1.5 Operations on Real Numbers
    1.6 Laws of Exponents for Real Numbers
    1.7 Summary

2. POLYNOMIALS
    2.1 Introduction
    2.2 Polynomials in One Variable
    2.3 Zeroes of a Polynomial
    2.4 Remainder Theorem
    2.5 Factorisation of Polynomials
    2.6 Algebraic Identities
    2.7 Summary

3. COORDINATE GEOMETRY
    3.1 Introduction
    3.2 Cartesian System
    3.3 Plotting a Point in the Plane if its Coordinates are given
    3.4 Summary

4. LINEAR EQUATIONS IN TWO VARIABLES
    4.1 Introduction
    4.2 Linear Equations
    4.3 Solution of a Linear Equation
    4.4 Graph of a Linear Equation in Two Variables
    4.5 Equations of Lines Parallel to x-axis and y-axis
    4.6 Summary

5. INTRODUCTION TO EUCLID’S GEOMETRY
    5.1 Introduction
    5.2 Euclid’s Definitions, Axioms and Postulates
    5.3 Equivalent Versions of Euclid’s Fifth Postulate
    5.4 Summary

6. LINES AND ANGLES
    6.1 Introduction
    6.2 Basic Terms and Definitions
    6.3 Intersecting Lines and Non-intersecting Lines
    6.4 Pairs of Angles
    6.5 Parallel Lines and a Transversal
    6.6 Lines Parallel to the same Line
    6.7 Angle Sum Property of a Triangle
    6.8 Summary

7. TRIANGLES
    7.1 Introduction
    7.2 Congruence of Triangles
    7.3 Criteria for Congruence of Triangles
    7.4 Some Properties of a Triangle
    7.5 Some More Criteria for Congruence of Triangles
    7.6 Inequalities in a Triangle
    7.7 Summary

8. QUADRILATERALS
    8.1 Introduction
    8.2 Angle Sum Property of a Quadrilateral
    8.3 Types of Quadrilaterals
    8.4 Properties of a Parallelogram
    8.5 Another Condition for a Quadrilateral to be a Parallelogram
    8.6 The Mid-point Theorem
    8.7 Summary
9. AREAS OF PARALLELOGRAMS AND TRIANGLES
    9.1 Introduction
    9.2 Figures on the same Base and Between the same Parallels
    9.3 Parallelograms on the same Base and between the same Parallels
    9.4 Triangles on the same Base and between the same Parallels
    9.5 Summary

10. CIRCLES
    10.1 Introduction
    10.2 Circles and its Related Terms : A Review
    10.3 Angle Subtended by a Chord at a Point
    10.4 Perpendicular from the Centre to a Chord
    10.5 Circle through Three Points
    10.6 Equal Chords and their Distances from the Centre
    10.7 Angle Subtended by an Arc of a Circle
    10.8 Cyclic Quadrilaterals
    10.9 Summary

11. CONSTRUCTIONS
    11.1 Introduction
    11.2 Basic Constructions
    11.3 Some Constructions of Triangles
    11.4 Summary
12. HERON’S FORMULA
    12.1 Introduction
    12.2 Area of a Triangle – by Heron’s Formula
    12.3 Application of Heron’s Formula in finding Areas of Quadrilaterals
    12.4 Summary

13. SURFACE AREAS AND VOLUMES
    13.1 Introduction
    13.2 Surface Area of a Cuboid and a Cube
    13.3 Surface Area of a Right Circular Cylinder
    13.4 Surface Area of a Right Circular Cone
    13.5 Surface Area of a Sphere
    13.6 Volume of a Cuboid
    13.7 Volume of a Cylinder
    13.8 Volume of a Right Circular Cone
    13.9 Volume of a Sphere
    13.10 Summary

14. STATISTICS
    14.1 Introduction
    14.2 Collection of Data
    14.3 Presentation of Data
    14.4 Graphical Representation of Data
    14.5 Measures of Central Tendency
    14.6 Summary

15. PROBABILITY
    15.1 Introduction
    15.2 Probability – an Experimental Approach
    15.3 Summary

APPENDIX – 1 PROOFS IN MATHEMATICS
    A1.1 Introduction
    A1.2 Mathematically Acceptable Statements
    A1.3 Deductive Reasoning
    A1.4 Theorems, Conjectures and Axioms
    A1.5 What is a Mathematical Proof?
    A1.6 Summary

APPENDIX – 2 INTRODUCTION TO MATHEMATICAL MODELLING
    A2.1 Introduction
    A2.2 Review of Word Problems
    A2.3 Some Mathematical Models
    A2.4 The Process of Modelling, its Advantages and Limitations
    A2.5 Summary

ANSWERS/HINTS