# NCERT Solutions for Class 9 Maths

NCERT Solutions for Class 9 Maths are provided here by the teachers with years of experience and which are extremely simple to understand. Most of the students of Class 9 face problems while solving the problem of Maths. And so they are searching for easy and effective steps of solving Maths problems. If you are searching for the Class 9 Maths UP Board NCERT Solutions, then not to worry, find NCERT Solutions for Class 9 Maths for all chapters which will help you a lot in scoring more marks in the examination. You can get to know about various concepts while solving Class 9 Maths NCERT Solutions, which will be useful in your higher classes.

Get Class 9th Maths solution for the Academic year 2020-2021 based on NCERT book syllabus. You just only need to click simply on the chapter name and get started learning. You can download offline app for Class 9 Maths NCERT Solutions and learn offline anywhere. Tiwari Academy website have facility to get both online and offline NCERT Solutions for Class 9 Maths PDF. And you can share these PDFs to your friend also.Page Contents

- 1 NCERT Solutions for Class 9 Maths All Chapters
- 2 NCERT Class 9 Maths Chapters
- 3 NCERT Solutions for Class 9 Maths Chapter 1 – Number System
- 4 NCERT Solutions for Class 9 Maths Chapter 2 – Polynomials
- 5 NCERT Solutions for Class 9 Maths Chapter 3 – Coordinate Geometry
- 6 NCERT Solutions for Class 9 Maths Chapter 4 – Linear Equations in Two Variables
- 7 NCERT Solutions for Class 9 Maths Chapter 5 – Introduction to Euclids Geometry
- 8 NCERT Solutions for Class 9 Maths Chapter 6 – Lines and Angles
- 9 NCERT Solutions for Class 9 Maths Chapter 7 – Triangles
- 10 NCERT Solutions for Class 9 Maths Chapter 8 – Quadrilaterals
- 11 NCERT Solutions for Class 9 Maths Chapter 9 – Areas of Parallelograms and Triangles
- 12 NCERT Solutions for Class 9 Maths Chapter 10 – Circles
- 13 NCERT Solutions for Class 9 Maths Chapter 11 – Constructions
- 14 NCERT Solutions for Class 9 Maths Chapter 12 – Heron’s Formula
- 15 NCERT Solutions for Class 9 Maths Chapter 13 – Surface Areas and Volumes
- 16 NCERT Solutions for Class 9 Maths Chapter 14 – Statistics
- 17 NCERT Solutions for Class 9 Maths Chapter 15 – Probability
- 18 How to Prepare Class 9 Maths all Chapters
- 18.1 Chapter 1: Number System
- 18.2 Chapter 2: Polynomials
- 18.3 Chapter 3: Coordinate Geometry
- 18.4 Chapter 4: Linear Equations in Two Variables
- 18.5 Chapter 5: Introduction to Euclid Geometry
- 18.6 Chapter 6: Lines and Angles
- 18.7 Chapter 7: Triangles
- 18.8 Chapter 8: Quadrilaterals
- 18.9 Chapter 9: Areas of Parallelograms and Triangles
- 18.10 Chapter 10: Circles
- 18.11 Chapter 11: Constructions
- 18.12 Chapter 12: Heron’s Formula
- 18.13 Chapter 13: Surface Areas and Volumes
- 18.14 Chapter 14: Statistics
- 18.15 Chapter 15: Probability

- 19 Importance of NCERT Solutions for Class 9 Maths
- 20 How are CBSE 9 Maths Solutions of NCERT Helpful for Final Exams?
- 20.0.0.1 What are the theorems that may be asked for proving in Exams for class 9 Chapter 6: Lines and Angles?
- 20.0.0.2 Which theorems may be asked for proving form class 9 Chapter 7: Triangles?
- 20.0.0.3 Is there any theorem in Chapter 10: Quadrilateral to prove?
- 20.0.0.4 How many theorems are there in Chapter 9: Areas of Parallelograms and Triangles to prove?
- 20.0.0.5 Is there only one theorem in Chapter 10: Circle, which is asked to prove in Examinations?
- 20.0.0.6 How many chapters are there in NCERT Class 9 Maths?
- 20.0.0.7 What Is A Polynomial Class 9?
- 20.0.0.8 Is class 9 maths tough?
- 20.0.0.9 How can I practice maths in Class 9?

## NCERT Solutions for Class 9 Maths All Chapters

These Chapter Wise NCERT Solutions for Class 9 Maths are well designed with a simple method so that class 9 students can easily understand each sums solutions. The Class NCERT 9th Math textbook has a total of 15 chapters which are divided into seven units. NCERT Class 9 Maths Solutions develop logical thinking skills so that students cable to solve all the sums once the concept is clear. Here students are also provided with online learning materials such as NCERT Exemplar Class 9 Maths Solutions. And the students are also advised to practice NCERT Exemplar Class 9 Maths Solutions to get an idea of question pattern in the final exam. Solving these Class 9th Maths solution in each chapter will assure positive results. Chapters covers in the NCERT 9th Math textbook are Number System, Polynomials, Introduction to Euclids Geometry, Quadrilaterals, Surface Areas, Heron’s Formula, Constructions and Volumes, Statistics, Probability etc.

### Free NCERT Solutions for Class 9 Maths All Chapters

- Chapter 1: Number Systems
- Chapter 2: Polynomials
- Chapter 3: Coordinate Geometry
- Chapter 4: Linear Equations in Two Variables
- Chapter 5: Introduction to Euclid’s Geometry
- Chapter 6: Lines and Angles
- Chapter 7: Triangles
- Chapter 8: Quadrilaterals
- Chapter 9: Areas of Parallelograms and Triangles
- Chapter 10: Circles
- Chapter 11: Constructions
- Chapter 12: Heron’s Formula
- Chapter 13: Surface Areas and Volumes
- Chapter 14: Statistics
- Chapter 15: Probability

### Free NCERT Solutions for Class 9 Maths in Hindi All Chapters

- पाठ 1: संख्या पद्धति
- पाठ 2: बहुपद
- पाठ 3: निर्देशांक ज्यामिति
- पाठ 4: दो चरों वाले रैखिक समीकरण
- पाठ 5: यूक्लिड की ज्यामिति का परिचय
- पाठ 6: रेखाएँ और कोण
- पाठ 7: त्रिभुज
- पाठ 8: चतुर्भुज
- पाठ 9: समांतर चतुर्भुजों और त्रिभुजों के क्षेत्रफल
- पाठ 10: वृत
- पाठ 11: रचनाएँ
- पाठ 12: हीरोन का सूत्र
- पाठ 13: पृष्ठीय क्षेत्रफल और आयतन
- पाठ 14: सांख्यिकी
- पाठ 15: प्रायिकता

## NCERT Class 9 Maths Chapters

Students who are facing trouble in solving tough Class 9th Maths problems can get best solutions from these CBSE Maths Class 9 Solutions of NCERT. The syllabus contains 15 chapters with important topics. Here all solutions are well solved with step by step solutions so students are suggested to do practice all sums so that they can understand the upcoming class maths syllabus easily. It builds your fundamental very clear and efficiency by solving theses exercise-wise solutions. You can also download 9th class NCERT book online here. And study it when you want.

## NCERT Solutions for Class 9 Maths Chapter 1 – Number System

NCERT Solutions for Class 9 Maths Chapter 1 introduce you different topics such as rational numbers and irrational numbers. You can learn how to represent the integers, rational and irrational numbers in a line. Here you get an overall knowledge of the number line. There are six exercises in this NCERT Solutions for Class 9 Maths Chapter 1 Number System, where you can also find all word problems based on 9th Class Maths NCERT Book. You can learn from these 9th Class Maths Book Solution, the representation of terminating and non-terminating recurring decimals, presentation of square roots of 2, 3, other non-rational numbers on the number line. You can deal with the laws of integral powers and rational exponents with positive real bases in Number Systems in this chapter. Download Chapter Number System Class 9 Maths Solutions in Hindi medium and English medium just by a simple click.

### Free NCERT Solutions for Class 9 Maths Chapter 1 in PDF

- Class 9 Maths Chapter 1 Exercise 1.1 Solutions in English
- Class 9 Maths Chapter 1 Exercise 1.2 Solutions in English
- Class 9 Maths Chapter 1 Exercise 1.3 Solutions in English
- Class 9 Maths Chapter 1 Exercise 1.4 Solutions in English
- Class 9 Maths Chapter 1 Exercise 1.5 Solutions in English
- Class 9 Maths Chapter 1 Exercise 1.6 Solutions in English
- Class 9 Maths Chapter 1 Exercise 1.1 Solutions in Hindi
- Class 9 Maths Chapter 1 Exercise 1.2 Solutions in Hindi
- Class 9 Maths Chapter 1 Exercise 1.3 Solutions in Hindi
- Class 9 Maths Chapter 1 Exercise 1.4 Solutions in Hindi
- Class 9 Maths Chapter 1 Exercise 1.5 Solutions in Hindi
- Class 9 Maths Chapter 1 Exercise 1.6 Solutions in Hindi
- Download Class 9 Maths Chapter 1 Exercise 1.1 Solutions In PDF
- Download Class 9 Maths Chapter 1 Exercise 1.2 Solutions In PDF
- Download Class 9 Maths Chapter 1 Exercise 1.3 Solutions In PDF
- Download Class 9 Maths Chapter 1 Exercise 1.4 Solutions In PDF
- Download Class 9 Maths Chapter 1 Exercise 1.5 Solutions In PDF
- Download Class 9 Maths Chapter 1 Exercise 1.6 Solutions In PDF

## Free NCERT Solutions for Class 9 Maths Chapter 1 videos

## NCERT Solutions for Class 9 Maths Chapter 2 – Polynomials

Get NCERT Solutions for Class 9 Maths Chapter 2 here with free of cost, and all solutions are solved by the professional Maths teacher. NCERT Solutions for Class 9 Maths Chapter 1 Polynomials introduced a particular type of algebraic expression, which are polynomial and terminology. This chapter Polynomial consists of variables and coefficients, its operations of addition, subtraction, multiplication and also non-negative integer exponents of variables. You can learn about the factorisation of polynomials. Here you can get knowledge about polynomial, degrees, coefficient, zeros and terms of a polynomial based on 9th Class Maths Book Solution. Download here Chapter Polynomials Class 9 Maths Solutions in Hindi medium and English medium by clicking the following links. Students who are searching for the 9th Class Maths Book Solution, get here easy solutions for all the exercises. You can learn offline in your desktop or mobile just downloading NCERT Solutions for Class 9 Maths PDF. You can also download Chapter Number System Class 9 Maths Solutions in Hindi medium and English medium here which are totally free.

### Free NCERT Solutions for Class 9 Maths Chapter 2 in PDF

- Class 9 Maths Chapter 2 Exercise 2.1 Solutions in English
- Class 9 Maths Chapter 2 Exercise 2.2 Solutions in English
- Class 9 Maths Chapter 2 Exercise 2.3 Solutions in English
- Class 9 Maths Chapter 2 Exercise 2.4 Solutions in English
- Class 9 Maths Chapter 2 Exercise 2.5 Solutions in English
- Class 9 Maths Chapter 2 Exercise 2.1 Solutions in Hindi
- Class 9 Maths Chapter 2 Exercise 2.2 Solutions in Hindi
- Class 9 Maths Chapter 2 Exercise 2.3 Solutions in Hindi
- Class 9 Maths Chapter 2 Exercise 2.4 Solutions in Hindi
- Class 9 Maths Chapter 2 Exercise 2.5 Solutions in Hindi
- Download Class 9 Maths Chapter 2 Exercise 2.1 Solutions In PDF
- Download Class 9 Maths Chapter 2 Exercise 2.2 Solutions In PDF
- Download Class 9 Maths Chapter 2 Exercise 2.3 Solutions In PDF
- Download Class 9 Maths Chapter 2 Exercise 2.4 Solutions In PDF
- Download Class 9 Maths Chapter 2 Exercise 2.5 Solutions In PDF

## Free NCERT Solutions for Class 9 Maths Chapter 2 videos

## NCERT Solutions for Class 9 Maths Chapter 3 – Coordinate Geometry

Students who are confused about Class 9 Maths syllabus, here they can get NCERT Solutions for Class 9 Maths Chapter 3 with free of cost. This chapter 3 introduced the student the concepts of the cartesian plane, coordinates of a point in the plane, terms, coordinate plan notations, x-axis, y-axis, x- coordinate, y-coordinate, quadrants, origin and many more. A student has knowledge of the concepts of Abscissa and ordinates of a point as well plotting in XY – plane in this 9th Class Maths Book Solution. In NCERT Solutions for Class 9 Maths Chapter 3 Coordinate Geometry, You can also learn coordinate plane and the mutually perpendicular lines which are called axe. You can also download NCERT Solutions for Class 9 Maths PDF to learn offline anywhere. Get Chapter Number System Class 9 Maths Solutions in Hindi medium and English medium.

### Free NCERT Solutions for Class 9 Maths Chapter 3 in PDF

- Class 9 Maths Chapter 3 Exercise 3.1 Solutions in English
- Class 9 Maths Chapter 3 Exercise 3.2 Solutions in English
- Class 9 Maths Chapter 3 Exercise 3.3 Solutions in English
- Class 9 Maths Chapter 3 Exercise 3.1 Solutions in Hindi
- Class 9 Maths Chapter 3 Exercise 3.2 Solutions in Hindi
- Class 9 Maths Chapter 3 Exercise 3.3 Solutions in Hindi
- Download Class 9 Maths Chapter 3 Exercise 3.1 Solutions In PDF
- Download Class 9 Maths Chapter 3 Exercise 3.2 Solutions In PDF
- Download Class 9 Maths Chapter 3 Exercise 3.3 Solutions In PDF
- Class 9th Maths Study Material for 2020-21 – English Medium
- Class 9th Maths Study Material for 2020-21 – Hindi Medium
- Class 9 Mathematics Solutions Main Page

## Free NCERT Solutions for Class 9 Maths Chapter 3 videos

## NCERT Solutions for Class 9 Maths Chapter 4 – Linear Equations in Two Variables

NCERT Solutions for Class 9 Maths Chapter 4 teaches you here about the knowledge of linear equations in one variable. In this chapter, you can know about linear equation in two variables, such as ax + by + c = 0. You know how to the graph of a linear equation in two variables. There are four exercises in this NCERT Solutions for Class 9 Maths Chapter 9 Linear Equations in Two Variables. You can download NCERT Solutions for Class 9 Maths PDF with free of cost and study at any time anywhere. These 9th Class Maths Book Solution are solved by the skilled Math teachers with easy method. So that students can clear all the concept of each math sum. Download free unlimited Chapter Linear Equations in Two Variables Class 9 Maths Solutions in Hindi medium and English Medium. Share these links to your classmates and let them help to score good marks in the final exam.

### Free NCERT Solutions for Class 9 Maths Chapter 4 in PDF

- Class 9 Maths Chapter 4 Exercise 4.1 Solutions in English
- Class 9 Maths Chapter 4 Exercise 4.2 Solutions in English
- Class 9 Maths Chapter 4 Exercise 4.3 Solutions in English
- Class 9 Maths Chapter 4 Exercise 4.4 Solutions in English
- Class 9 Maths Chapter 4 Exercise 4.1 Solutions in Hindi
- Class 9 Maths Chapter 4 Exercise 4.2 Solutions in Hindi
- Class 9 Maths Chapter 4 Exercise 4.3 Solutions in Hindi
- Class 9 Maths Chapter 4 Exercise 4.4 Solutions in Hindi
- Download Class 9 Maths Chapter 4 Exercise 4.1 Solutions In PDF
- Download Class 9 Maths Chapter 4 Exercise 4.2 Solutions In PDF
- Download Class 9 Maths Chapter 4 Exercise 4.3 Solutions In PDF
- Download Class 9 Maths Chapter 4 Exercise 4.4 Solutions In PDF
- Class 9th Maths Study Material for 2020-21 – English Medium
- Class 9th Maths Study Material for 2020-21 – Hindi Medium

## Free NCERT Solutions for Class 9 Maths Chapter 4 videos

## NCERT Solutions for Class 9 Maths Chapter 5 – Introduction to Euclids Geometry

Get NCERT Solutions for Class 9 Maths Chapter 5 for all exercises. This chapter includes Euclid’s approach to geometry which is used the present-day geometry. In this NCERT Solutions for Class 9 Maths chapter Introduction to Euclids Geometry defining common geometrical shapes and terms. There are two exercises in this 9th Class Maths Book Solution which teach you deeper knowledge relation between axiom, postulates, and theorems. You can download here Chapter Euclids Geometry Class 9 Maths Solutions in Hindi medium and English medium.

### Free NCERT Solutions for Class 9 Maths Chapter 5 in PDF

- Class 9 Maths Chapter 5 Exercise 5.1 Solutions in English
- Class 9 Maths Chapter 5 Exercise 5.2 Solutions in English
- Class 9 Maths Chapter 5 Exercise 5.1 Solutions in Hindi
- Class 9 Maths Chapter 5 Exercise 5.2 Solutions in Hindi
- Download Class 9 Maths Chapter 5 Exercise 5.1 Solutions In PDF
- Download Class 9 Maths Chapter 5 Exercise 5.2 Solutions In PDF
- Class 9th Maths Chapter 5 Study Material for 2020-21 in English
- Class 9th Maths Chapter 5 Study Material for 2020-21 in Hindi

## Free NCERT Solutions for Class 9 Maths Chapter 5 videos

## NCERT Solutions for Class 9 Maths Chapter 6 – Lines and Angles

NCERT Solutions for Class 9 Maths Chapter 6 revolves around the theorems present in the topics of Lines and Angles. In this NCERT Solutions for Class 9 Maths Chapter 6 Lines and Angles, there are three exercises which clear the chapter thoroughly about Lines and Angles. The sum of angles of a triangle is 180 and theorems are explained here with all related questions. 9th Class Maths Book Solution are provided here are well-reviewed. You can download free NCERT Solutions for Class 9 Maths PDF for offline study. You are advised to practice these solutions thoroughly to get maximum marks in the final exam. You can download Chapter Lines and Angles Class 9 Maths Solutions in Hindi medium and English medium. Choose the particular medium links solution below as per your need.

### Free NCERT Solutions for Class 9 Maths Chapter 6 in PDF

- Class 9 Maths Chapter 6 Exercise 6.1 Solutions in English
- Class 9 Maths Chapter 6 Exercise 6.2 Solutions in English
- Class 9 Maths Chapter 6 Exercise 6.3 Solutions in English
- Class 9 Maths Chapter 6 Exercise 6.1 Solutions in Hindi
- Class 9 Maths Chapter 6 Exercise 6.2 Solutions in Hindi
- Class 9 Maths Chapter 6 Exercise 6.3 Solutions in Hindi
- Download Class 9 Maths Chapter 6 Exercise 6.1 Solutions In PDF
- Download Class 9 Maths Chapter 6 Exercise 6.2 Solutions In PDF
- Download Class 9 Maths Chapter 6 Exercise 6.3 Solutions In PDF
- Class 9th Maths Chapter 6 Study Material 2020-21 in English
- Class 9th Maths Chapter 6 Study Material 2020-21 in Hindi

## Free NCERT Solutions for Class 9 Maths Chapter 6 videos

## NCERT Solutions for Class 9 Maths Chapter 7 – Triangles

Get NCERT Solutions for Class 9 Maths Chapter 7, and students will study detail knowledge about the triangle, congruence of triangles, rules of congruence, and its properties of triangles and many more. In this 9th Class Maths Book Solution, you will also prove the properties of the triangle which you learn about in previous classes. Here you can also apply the various congruence rules while solving the problems. In this chapter, you can learn about eight theorems. There are five exercises which cover in this NCERT Solutions for Class 9 Maths Chapter 7 Triangles. Here you can download free unlimited NCERT Solutions for Class 9 Maths PDF to learn offline anywhere. Get Chapter Triangles Class 9 Maths Solutions in Hindi medium and English medium.

## NCERT Solutions for Class 9 Maths Chapter 8 – Quadrilaterals

Find NCERT Solutions for Class 9 Maths Chapter 8, which covers the topic Quadrilaterals. The joining four points in order is called a quadrilateral. The NCERT Solutions for Class 9 Maths Chapter 8 Quadrilaterals provides you with the students to the depth of the topics of Quadrilaterals. This chapter 8 contains two exercises that contain only one theorem to prove. Here you learn about the total of nine theorems includes the application or conceptual level questions. This 9th Class Maths Book Solution includes Angle sum property of a Quadrilateral, properties of a parallelogram, and types of quadrilaterals etc. Download here Chapter Quadrilaterals Class 9 Maths Solutions in Hindi medium and English medium.

## NCERT Solutions for Class 9 Maths Chapter 9 – Areas of Parallelograms and Triangles

Find the NCERT Solutions for Class 9 Maths Chapter 9 with all exercises. Here you get the knowledge about the formulae for finding the areas of different figures. Learn here relationships between the areas of geometric figures in this 9th Class Maths Book Solution. This NCERT Solutions for Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles have the same base and between the same parallels which are equal in area. Area of parallelograms and triangle and their combinations are explained in this chapter with related questions. Download NCERT Solutions for Class 9 Maths PDF with free of cost and do practice anytime. Find Chapter Areas of Parallelograms and Triangles Class 9 Maths Solutions in Hindi medium and English medium.

## NCERT Solutions for Class 9 Maths Chapter 10 – Circles

Here get well explained NCERT Solutions for Class 9 Maths Chapter Circles with free of cost. And also you no need to login and register to get solutions for all exercises. In this NCERT Solutions for Class 9 Maths Chapter 10 CHAPTER Circle, you learn about the circle which can be defined as a collection of all the points in a plane at a fixed distance. You get knowledge about circle including a Chord at a Point, Equal Chords. There are a total of twelve theorems present in this chapter. And there are six exercises in this chapter includes questions from all the concepts present in the chapter. Download NCERT Solutions for Class 9 Maths PDF without any cost and registration. You also get Chapter Circles Class 10 Maths Solutions in Hindi medium and English medium here. Choose your medium solutions link accordingly.

## NCERT Solutions for Class 9 Maths Chapter 11 – Constructions

From these NCERT Solutions for Class 9 Maths, Chapter 11 students will learn some basic constructions. Here you learn methods to construct certain kinds of triangles. These two exercises in this NCERT Solutions for Class 9 Maths Chapter 11 Constructions. In the first exercise, you know about the construction of a certain angle and how to bisect of a given angle. And the second exercise teaches you the constructions of triangles when different parameters are given. Get download unlimited NCERT Solutions for Class 9 Maths chapter Constructions PDF. Here students can get both medium solutions such as Chapter Constructions Class 9 Maths Solutions in Hindi Medium and English Medium.

## NCERT Solutions for Class 9 Maths Chapter 12 – Heron’s Formula

Students get NCERT Solutions for Class 9 Maths Chapter 12, which covers Heron’s formula which is used to calculate the area of a triangle with all three sides length is given. By the help of Heron’s Formula, you can find out distances in the triangle without calculating. This formula is used to find out the areas of quadrilaterals, the area of triangles and other polygons. There are two exercises in these NCERT Solutions for Class 9 Maths Chapter12 Heron’s Formula. This chapter 4 help the student to better understand the method of solving the problems based on Heron’s formula. You can also download NCERT Solutions for Class 9 Maths Chapter 12 PDF and learn anytime in your desktop or mobile while offline. You can also get Chapter Heron’s Formula Class 9 Maths Solutions in Hindi medium and English medium here.

## NCERT Solutions for Class 9 Maths Chapter 13 – Surface Areas and Volumes

NCERT Solutions for Class 9 Maths Chapter 13, learn to find the surface areas and volumes of cuboids and cylinders in details. In this NCERT Solutions for Class 9 Maths Chapter 13 Surface Areas and Volumes, you learn the surface areas of some other solids such as cones and spheres. Here you can get detailed knowledge about the surface areas and volumes in earlier classes. There are eight exercises in this chapter that covers surface areas and volumes of different solids such as cubes, cuboids, hemispheres, spheres, cylinders, cones etc. Download NCERT Solutions for Class 9 Maths PDF here without paying any cost and required no login detail. You can also get Chapter Surface Areas and Volumes Class 9 Maths Solutions in Hindi medium and English medium.

## NCERT Solutions for Class 9 Maths Chapter 14 – Statistics

These best easy NCERT Solutions for Class 9 Maths Chapter 14, deals with Statistics which the extraction of meaningful information is studied is known as Statistics. Statistics is used in our daily life such as aspects of the life of people, useful to the State etc. This NCERT Solutions for Class 9 Maths Chapter 14 Statistics teaches the different presentation of the data, including the frequency distribution too. Presentation data in tubular and row form and grouping them in a regular interval. Here you learn to Mean, Mode and median as well. NCERT Solutions for Class 9 Maths chapter Statistics PDFs are available here to learn offline. And get Chapter Statistics Class 9 Maths Solutions in Hindi medium and English medium.

## NCERT Solutions for Class 9 Maths Chapter 15 – Probability

NCERT Solutions for Class 9 Maths Chapter 15 are here provided by the expert math teacher with an easy strategy. Here you learn about “Probability” which is the chances of occurrence of the collection of some outcomes of an experiment or event. In this NCERT Solutions for Class 9 Maths Chapter 15 Probability, you learn how to measure the chance of occurrence of a particular outcome. There is only one topic in this chapter. This chapter is very interesting, which is based on our daily life such as throwing dices, tossing, card probability etc. Download unlimited NCERT Solutions for Class 9 Maths Chapter Probability PDF, and you can also share with your parents. Find here Chapter Probability Class 9 Maths Solutions in Hindi medium and English medium for all exercises.

NCERT Solutions for Class 9 Maths Chapter 15 in PDF

## How to Prepare Class 9 Maths all Chapters

### Chapter 1: Number System

In this NCERT Solutions for Class 9 Maths Chapter 1, Number System, you study about the Number System with its definition and types of numbers. Here you learn the definition of all the types Number System along with their properties. The Number system includes natural numbers, whole numbers, integers, rational numbers and irrational numbers. Every Rational number is expressible either as a terminating decimal or as a repeating decimal. Every Terminating decimal is a rational number. Here you can learn properties of Irrational Numbers such as: commutative, associative and distributive etc. The process of converting the denominator to a rational number by multiplying the numerator and denominator.

**Summary:** Natural Numbers, Whole Numbers, Integers, Rational Numbers, Irrational Numbers, Real Numbers, Difference between Terminating and Recurring Decimals, Properties of Irrational Numbers etc.

### Chapter 2: Polynomials

In this NCERT Solutions for Class 9 Maths Chapter 2, Polynomials, you learn about the definition of Polynomials which comes from the word “poly” which means “many” and the word “nominal” which means “term”. Variables and expression are called as indeterminate and coefficients. The coefficients involve the operations of subtraction, addition, non-negative integer are the exponents of variable & multiplication. The real numbers can also be expressed as polynomials. Polynomials without any variables called constant polynomials. The constant polynomial 0 is known polynomials. The highest power of the polynomial is called the degree of the polynomial.

**Summary:** Polynomial Definition, Polynomials in One Variable, Zeros of Polynomials, Remainder Theorem, Factorisation of Polynomials, Algebraic Identities.

### Chapter 3: Coordinate Geometry

Here in this NCERT Solutions for Class 9 Maths Chapter 3, Coordinate Geometry, student study about the complete concept of coordinate geometry such as cartesian system, coordinate points etc. You know how to plot the points in the coordinate axes, quadrants with signs and many more. A Cartesian is a plane which is defined by two perpendicular number lines, i.e. a horizontal line (x−axis) and a vertical line (y−axis). Where coordinate axes intersect each other at right angles and the point of intersection of these two axes is called Origin.

And when the cartesian plane is divided into four equal parts, called quadrants. You also learn the representation of a point on the Cartesian plane here.

**Summary:** Cartesian System, Quadrants, Points in different Quadrants, Plotting on a Graph, Representation of a point on the Cartesian plane, plotting a point etc.

### Chapter 4: Linear Equations in Two Variables

Here in this NCERT Solutions for Class 9 Maths Chapter 4, Linear Equations in Two Variables, you learn about Linear Equations which form as ax + by + c = 0. a, b and c are real numbers, and a & b does not equal to zero. Linear Equations with x and y which further makes the two sides of an equation equal. In this chapter, you also learn about the example of a linear equation in two variables.

**Summary:** Linear Equations in Two Variables Definition, Linear Equations in Two Variables Example, Linear Equations in Two Variables Questions, Linear Equations in Two Variables Word Problems etc.

### Chapter 5: Introduction to Euclid Geometry

Here in this NCERT Solutions for Class 9 Maths Chapter 5, Introduction to Euclid Geometry, you learn about Euclidean geometry which is the study of geometry. According to the mathematician Euclid who has explained in his book on geometry which is known as Elements. And geometry is called Euclid geometry. He explained geometric shapes and figures such as euclidean geometry, its elements, axioms and five important postulates etc. Construction of Pyramids by the Egyptians is the example of extensive use of geometrical techniques used by the people. Mathematician Euclid made the evolutions in geometry and compiled it into his famous treatise, which is known as ‘Elements’.

**Summary:** Definition, Introduction to Euclid Geometry, Euclid’s Element, Axioms, Euclid’s Five Postulates, Worksheet etc.

### Chapter 6: Lines and Angles

Here you study about Lines And Angles in this NCERT Solutions for Class 9 Maths Chapter 6, Lines and Angles. Lines are defined as a straight and have negligible depth or width. There are many types of lines: perpendicular lines, intersecting lines, transversal lines, etc. An angle is a figure where two rays emerge from a common point. A line segment is a part of a line which have two end-points. It is the shortest distance and has a fixed length. Two lines are said to be parallel when they do not meet at any point known as Parallel Lines. And when a line intersects two lines at distinct points known as Transversal Line.

**Summary:** Lines and Angles – Definition and Properties, Line Segment, Perpendicular Lines, Parallel Lines, Transversal Line, Properties of Lines, Acute Angle, Straight Angle etc.

### Chapter 7: Triangles

In this NCERT Solutions for Class 9 Maths Chapter 7, Triangles, you learn about the concept of triangles. Here you learn about such as congruency, criteria for the congruency such as SAS, SSS, ASA, AAS etc. When three sides of one triangle are equally known as SSS Criteria for Congruency. If two sides and the included angle of one triangle are equal to the corresponding sides known as SAS Criteria for Congruency. And where two triangles are congruent if two angles and the included side of one triangle are equal known as ASA Criteria for Congruency. Here you know all about Properties of Isosceles triangle.

**Summary:** Properties of Isosceles triangle, Inequalities in Triangles, AAS Criteria for Congruency, Criteria for Congruency, SSS Criteria for Congruency, Congruent Triangles etc.

### Chapter 8: Quadrilaterals

In this NCERT Solutions for Class 9 Maths Chapter 8, Quadrilaterals complete notes on quadrilaterals, you learn complete notes on quadrilaterals. A quadrilateral is a shape which has four sides. Here you learn about different types of quadrilateral including square, rectangle, parallelogram properties etc. Opposite angles in a parallelogram are equal. Diagonals of a rhombus bisect each other at right angles. And also learn about The Mid-Point Theorem.

**Summary:** Introduction to Quadrilaterals, square, rectangle, parallelogram properties, Properties of diagonal of a parallelogram, important results related to parallelograms, The Mid-Point Theorem

### Chapter 9: Areas of Parallelograms and Triangles

This NCERT Solutions for Class 9 Maths Chapter 9, Areas of Parallelograms and Triangles teaches you parallelogram, which is a quadrilateral with two pairs of parallel sides. Where the opposite sides and opposite angles of a parallelogram are equal. The formula of an area of parallelogram Area = base × height. And The area of a triangle ½ * base * height.

**Summary:** Parallelogram, Triangles, Area of Parallelogram, Area of a Triangle.

### Chapter 10: Circles

In this NCERT Solutions for Class 9 Maths Chapter 10, a circle is a special kind of ellipse which eccentricity is zero and the two foci are coincident. The distance from the centre of the circle to the outer line is known as radius. And where Diameter is the line which divides the circle into two equal parts. The circles divide the plane into two regions such as interior and exterior regions which has area and perimeter.

**Summary:** Circle Definition, How to draw a circle, Circles Terminologies, Radius of Circle (r), Diameter (d) of Circle, Circle Formulas for Area and Circumference etc.

### Chapter 11: Constructions

In this NCERT Solutions for Class 9 Maths Chapter 11, Constructions, you know how to construct the different shapes are drawn using the compass and ruler. Here you also learn about how to draw bisector of the given angle, construction of a perpendicular. Here you take the guide with construction steps and clear diagram.

**Summary:** Introduction, Basic constructions, some constructions of triangles, Constructions Class with Examples

### Chapter 12: Heron’s Formula

In this NCERT Solutions for Class 9 Maths Chapter 12, Heron’s Formula, according to this formula triangle is a closed three-dimensional figure. By using this formula Heron’s Formula, we can find out the area of the triangle, polygons etc. without calculating. A triangle.is a closed figure, with three sides and three angles.

**Summary:** Types of triangles, Area of an equilateral triangle, Area of an isosceles triangle, Area of a triangle – By Heron’s formula, Area of any polygon – By Heron’s formula etc.

### Chapter 13: Surface Areas and Volumes

In this NCERT Solutions for Class 9 Maths Chapter 13, Surface Areas and Volumes, Here you learn about complete surface area, and volume formulas for different three-dimensional shapes such as Cuboid, cone, cylinder, Surface Area(CSA), Lateral Surface Area (LSA), A cuboid is a three dimensional Shape.

**Summary:** Cuboid, Total Surface Area of a Cuboid, Lateral Surface Area of a Cuboid, Cube, Total Surface Area of a cube, Lateral Surface area of a cube, Right Circular Cylinder, The curved Surface area of a right circular cylinder etc.

### Chapter 14: Statistics

In this NCERT Solutions for Class 9 Maths Chapter 14, Statistics, all the important topics covered in this chapter. You learn about Statistics, that means: the extraction of meaningful information from a given set of data is called Statistics. Statistics is used in many fields, such as business in the market. And also used in daily life such as in the field of Engineering, Medicine, Weather forecasting, etc. In this chapter, you know about Collection of Data, Presentation of Data, representation of Data with graph, Measures of Central Tendency etc.

**Summary:** Collection of Data, Presentation of Data, Graphical representation of Data, Measures of Central Tendency, Measure of central tendency, Mean, Median, Mode etc.

### Chapter 15: Probability

This NCERT Solutions for Class 9 Maths Chapter 15, Probability, students get knowledge about Introduction to Probability, and Probability is the measurement of the likelihood of an event or experiment to occur. It can range between 0 and 1, 0 probability means the event or experiment be an impossible and probability of 1 means a certain event. The formula of the Probability of experiments to happen P(E)=Number of favourable outcomes/Total number of outcomes. Here you learn all about Probability, its Experiment, Sum of Probabilities of Favourable and unfavourable events etc. Probability is used in many fields in our daily life.

**Summary:** Introduction to Probability, Experimental/Empirical Probability, Sum of Probabilities of Favourable and unfavourable events

## Importance of NCERT Solutions for Class 9 Maths

NCERT stands for National Council of Educational Research and Training. NCERT was formed to give standardise the education system of India. NCERT Solutions for Class 9 Maths is very helpful will provide you with a detailed and in-depth understanding of all the questions and concepts of NCERT Textbooks. Excluding that there are so many other benefits of NCERT Solutions for Class 9 Maths.

### Explain Each And Every Concept in Detail

NCERT Solutions for Class 9 Maths explain each and every concept in detail and in easy language. It helps you and so important for better understanding and scoring good marks in 9 class exams.

### Most Accurate Solutions

All the NCERT Solutions for Class 9 Maths for all chapters are provided by the many years experienced teachers. All solutions are well-reviewed before provided. Students who have misguided by the wrong study materials before can study with these most accurate NCERT Solutions for Class 9 Maths.

### Student can learn Offline

NCERT Solutions for Class 9 Maths for all chapters PDFS are available, so you can learn these subjects offline also by just downloading these PDFs. You can study anywhere and anytime. You can also share these PDF links to your classmates as well.

### Clear all Doubts

Class 9 Students who have confusion with many topics in class 9 Maths, they can learn with these NCERT Solutions for Class 9 Maths for all chapters. These solutions are given in easy method, and it may clear your all doubts and concepts clear.

### Created the Best Subject Experts in Field

NCERT Solutions for Class 9 Maths provided by an expert math teacher who has been created by the high-quality subject matter experts. So you can get more marks with these high-quality study materials. All solutions are designed by following extensive research on the Math subject. So you will able to solve a wide range of problems at any difficulty level.

### What is the Exam pattern of CBSE Class 9 Maths in 2020

Maths is an important subject which also scoring subject for CBSE Class 9 students. If the students practice thoroughly and revise with all syllabus, then they can score even 100 out of 100 marks. To score highest, you should have clear all concept. So students are advised to know all CBSE Syllabus for Class 9 Maths right from the beginning of the academic year of 2020-2021, that can help them to prepare a study plan for the final exam. There six units in CBSE Class 9 Maths. And there are 15 chapters in 9th Maths subjects. The annual exam, theory covers a total of 80 marks and where internal assessment includes 20 marks.

Class 9th Chapter-Wise Marks Weightage

| Unit Name | Marks | |

I | Number System | 08 | |

II | Algebra | 17 | |

III | Coordinate Geometry | 04 | |

IV | Geometry | 28 | |

V | Mensuration | 13 | |

VI | Statistics & Probability | 10 | |

Total | 80 |

## How are CBSE 9 Maths Solutions of NCERT Helpful for Final Exams?

CBSE 9 Maths Solutions of NCERT is sufficient to score more in 9th boards exams. With NCERT Solutions for Class 9 Maths, students will get complete guidance on every topics and sub-topics related to the respective chapter. It is an effective and the best way to make students understand the subject and exclusively to perform well in the final exams. CBSE 9 Maths Solutions of NCERT are very helpful to get full marks in the final exam, but Just make sure you cover all the exercise and learn the theorems of the whole syllabus. Also, do not skip any topic of CBSE 9th Maths syllabus.

##### What are the theorems that may be asked for proving in Exams for class 9 Chapter 6: Lines and Angles?

The following theorems may be asked to prove in exams, rest are for application and motivation:

1. If two lines intersect, vertically opposite angles are equal.

2. The sum of the angles of a triangle is 180.

##### Which theorems may be asked for proving form class 9 Chapter 7: Triangles?

The following theorems may be asked to prove in exams, rest are for application and motivation:

1. Two triangles are congruent if any two angles and the included side of one triangle is equal to any two angles and the included side of the other triangle (ASA Congruence).

2. The angles opposite to equal sides of a triangle are equal.

##### Is there any theorem in Chapter 10: Quadrilateral to prove?

Yes, there is only one important theorem (The diagonal divides a parallelogram into two congruent triangles), that may be asked to prove.

##### How many theorems are there in Chapter 9: Areas of Parallelograms and Triangles to prove?

There is only one theorem (Parallelograms on the same base and between the same parallels have equal area.) asked for proving. This theorem is quite important one for all examinations.

##### Is there only one theorem in Chapter 10: Circle, which is asked to prove in Examinations?

No, there are two theorems (1. Equal chords of a circle subtend equal angles at the center. 2. The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.) for the examination point of view.

###### Feedback & Suggestions

A panel of experts from Tiwari Academy held a workshop of two days and thoroughly discussed the content quality and made some suggestions. Amendments were carried out in the English as well as Hindi draft accordingly.

The final draft was thus prepared. The solutions are prepared according to new syllabus for 2019-20 having classical approach of constructions and geometrical chapters. उत्तर प्रदेश में भी NCERT की किताबें लगने के बाद हम लोग UP बोर्ड के लिए भी अध्धयन सामग्री बना रहे हैं। अगर UP Board NCERT Solutions प्राप्त करने में विद्यार्थियों को किसी प्रकार की परेशानी हो रही है तो हमें Contact करें या फोन पर भी बता सकते हैं। UP Board Secondary Education (High School) के लिए अध्ययन सामग्री, Sample Papers, Notes तथा पश्नों के हल यहाँ से प्राप्त करें।

## FAQs

##### How many chapters are there in NCERT Class 9 Maths?

There are a total of 15 chapters present in the NCERT Class 9 Maths.

- Chapter 1- Number System,
- Chapter 2- Polynomials,
- Chapter 3- Coordinate Geometry,
- Chapter 4- Linear Equations in Two Variables,
- Chapter 5- Introduction to Euclid’s Geometry,
- Chapter 6- Lines and Angles,
- Chapter 7- Triangles,
- Chapter 8- Quadrilaterals,
- Chapter 9- Areas of Parallelograms and Triangles,
- Chapter 10- Circles,
- Chapter 11- Constructions,
- Chapter 12- Heron’s Formula,
- Chapter 13- Surface Areas and Volumes,
- Chapter 14- Statistics,
- Chapter 15- Probability

These are the chapters in Class 9 of NCERT Maths. And you need to cover all the chapters to get full marks in your final exam.

##### What Is A Polynomial Class 9?

Polynomials refer to Poly (means many) and nominals (means terms). Thus, a polynomial contains many terms. Thus, a type of algebraic expression with many terms having variables and coefficients is called a polynomial. Polynomial Based on the Number of Its Terms such as monomial, binomial and trinomial. A polynomial equation is an equation which can be written in the form: axn + bxn-1 + . . . + rx + s = 0. (Where a,b, r,s are constant). And the types of a polynomial function are: Degree One (Linear), Degree Two (Quadratic), Degree Four (Quartic), Degree Five (Quintic) and so on.

##### Is class 9 maths tough?

In real maths of class, 9th and 10th are both very easy. But practically you can say class 9th maths is tough for you because you introduced some new topics and topics in the advanced level study here. In previous classes like 8th, 7th and 6th, the maths you study is very basic and somehow simple. So your mindset is for that simple maths method with very fewer logics and formulas. Some student class 9 get confusion with the syllabus.

##### How can I practice maths in Class 9?

The practice is the key to scoring good marks in the exam. So students need to practice different types of questions for Maths, including the syllabus. Solve the previous CBSE practice papers and sample papers in one sitting within the time constraint. Give more importance to the topics which have high weightage. And skip any topic if you want to score more marks in the exam. And make sure you have done 3-4 time revision before your exam.