# Maths NCERT solutions class 9

Whether you choose to be an engineer or a doctor, you will have to deal with Mathematics in every area. Making the concepts of maths concrete can immensely help you in securing good marks in the CBSE Class 6th to 12th exam as well as in various competitive exams.

## 1. Number system

• 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

Important formula

## 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

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## 3. COORDINATE GEOMETRY

• 3.1Introduction
• 3.2 Cartesian System
• 3.3 Plotting a Point in the Plane if its Coordinates are given
• 3.4 Summary

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## 4. LINEAR EQUATIONS IN TWO VARIABLES

• 4.1 Introduction
• 4.2 Linear Equation
• 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

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## 5. INTRODUCTION TO EUCLID’S GEOMETRY

5.1 Introduction
5.2 Euclid’s Definitions, Axioms and Postulate
5.3 Equivalent Versions of Euclid’s Fifth Postulate
5.4 Summary

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## 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

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## 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

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### Exercise 7.4

8.1 Introduction
8.2 Angle Sum Property of a Quadrilateral
8.4 Properties of a Parallelogram
8.5 Another Condition for a Quadrilteral to be a Parallelogram
8.6 The Mid-point Theorem
8.7 Summary

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## 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 Parallel
9.4 Triangles on the same Base and between the same Parallel
9.5 Summary

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## 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
10.9 Summary

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## 11. CONSTRUCTIONS

11.1 Introduction
11.2 Basic Constructions
11.3 Some Constructions of Triangles
11.4 Summary

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## 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

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## 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
13.9 Volume of a Sphere
13.10 Summary

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## 14. STATISTICS

14.1 Introduction
14.2 Collection of Data
14.3 Presentation of Data
14.4 Graphical Representation14.5 Measures of Central Tendency
14.6 Summary

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## 15. PROBABILITY

15.1 Introduction
15.2 Probability – an Experimental Approach
15.3 Summary

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