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

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Content:

1. 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

2. POLYNOMIALS

• Introduction
• Polynomials in One Variable
• Zeroes of a Polynomial
• Remainder Theorem
• Factorisation of Polynomials
• Algebraic Identities
• Summary

3. COORDINATE GEOMETRY

• Introduction
• Cartesian System
• Plotting a Point in the Plane if its Coordinates are given
• Summary

4. 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

5. INTRODUCTIONTO EUCLID’S GEOMETRY

• Introduction
• Euclid’s Definitions, Axioms and Postulates
• Equivalent Versions of Euclid’s Fifth Postulate
• Summary

6. 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
• Summary

7. 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

8. 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

9. 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

10. 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

11. CONSTRUCTIONS

• Introduction
• Basic Constructions
• Some Constructions of Triangles
• Summary

12. HERON’S FORMULA

• Introduction
• Area of a Triangle – by Heron’s Formula
• Application of Heron’s Formula in finding Areas of Quadrilaterals
• Summary

13. 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

14. STATISTICS

• Introduction
• Collection of Data
• Presentation of Data
• Ggraphical Representation of Data
• Measures of Central Tendency
• Summary

15. 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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Courtesy: NCERT