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Class IX: Mathematics

Download NCERT Books for UPSC & State PSC Exams: Class IX (Mathematics)

NUMBER SYSTEMS
Introduction
Irrational Numbers
Real Numbers and their Decimal Expansions
Representing Real Numbers on the Number Line
Operations on Real Numbers
Laws of Exponents for Real Numbers
Summary
POLYNOMIALS
Introduction
Polynomials in One Variable
Zeroes of a Polynomial
Remainder Theorem
Factorisation of Polynomials
Algebraic Identities
Summary
COORDINATE GEOMETRY
Introduction
Cartesian System
Plotting a Point in the Plane if its Coordinates are given
Summary
LINEAR EQUATIONS IN TWO VARIABLES
Introduction
Linear Equations
Solution of a Linear Equation
Graph of a Linear Equation in Two Variables
Equations of Lines Parallel to x-axis and y-axis
Summary
INTRODUCTIONTO EUCLID’S GEOMETRY
Introduction
Euclid’s Definitions, Axioms and Postulates
Equivalent Versions of Euclid’s Fifth Postulate
Summary
LINES AND ANGLES
Introduction
Basic Terms and Definitions
Intersecting Lines and Non-intersecting Lines
Pairs of Angles
Parallel Lines and a Transversal
Lines Parallel to the same Line
Angle Sum Property of a Triangle
TRIANGLES
Introduction
Congruence of Triangles
Criteria for Congruence of Triangles
Some Properties of a Triangle
Some More Criteria for Congruence of Triangles
Inequalities in a Triangle
Summary
QUADRILATERALS
Introduction
Angle Sum Property of a Quadrilateral
Types of Quadrilaterals
Properties of a Parallelogram
Another Condition for a Quadrilteral to be a Parallelogram
The Mid-point Theorem
Summary
AREAS OF PARALLELOGRAMS AND TRIANGLES
Introduction
Figures on the same Base and Between the same Parallels
Parallelograms on the same Base and between the same Parallels
Triangles on the same Base and between the same Parallels
Summary
CIRCLES
Introduction
Circles and its Related Terms : A Review
Angle Subtended by a Chord at a Point
Perpendicular from the Centre to a Chord
Circle through Three Points
Equal Chords and their Distances from the Centre
Angle Subtended by an Arc of a Circle
Cyclic Quadrilaterals
Summary
CONSTRUCTIONS
Introduction
Basic Constructions
Some Constructions of Triangles
Summary
HERON’S FORMULA
Introduction
Area of a Triangle – by Heron’s Formula
Application of Heron’s Formula in finding Areas of Quadrilaterals
Summary
SURFACE AREAS AND VOLUMES
Introduction
Surface Area of a Cuboid and a Cube
Surface Area of a Right Circular Cylinder
Surface Area of a Right Circular Cone
Surface Area of a Sphere
Volume of a Cuboid
Volume of a Cylinder
Volume of a Right Circular Cone
Volume of a Sphere
Summary
STATISTICS
Introduction
Collection of Data
Presentation of Data
Ggraphical Representation of Data
Measures of Central Tendency
Summary
PROBABILITY
Introduction
Probability – an Experimental Approach
Summary
APPENDIX – 1 PROOFS IN MATHEMATICS
Introduction
Mathematically Acceptable Statements
Deductive Reasoning
Theorems, Conjectures and Axioms
What is a Mathematical Proof?
Summary
APPENDIX – 2 INTRODUCTION TO MATHEMATICAL MODELLING
Introduction
Review of Word Problems
Some Mathematical Models
The Process of Modelling, its Advantages and Limitations
Summary
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