how to solve prove questions in maths class 9

NCERT Solutions for Class 9 Maths

Chapter Wise Class 9 Maths NCERT Solutions NCERT Solutions for Class 9 Maths in Hindi and English Medium are given here along with class 9th Maths current syllabus. Class 9 Maths Syllabus for 2024-25 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. Circles Chapter 10. Heron’s Formula Chapter 11. Surface Areas and Volumes Chapter 12. Statistics For other State Boards Chapter 13. Surface Areas and Volumes Chapter 14. Statistics Chapter 15. Probability

NCERT Solutions of Class 9 Maths

NCERT Solutions for Class 9 Maths in Hindi and English Medium have been updated for session 2024-25. We at Tiwari Academy have spared no effort in providing the best NCERT Solutions for Class 9 Maths keeping in mind needs of the students. Tiwari Academy’s NCERT Solutions are helpful to students by providing conceptual clarity and developing problem-solving ability.

The solutions and answers have been suitably modified and revised taking into account the guidelines of CBSE and State board 9th Maths curriculum 2024-25 . Your valuable feedback and Review would help us to improve further our answers. Class 9 Solution Apps Download Class 9 Math solutions can be found in various formats, including printed books, online resources, and mobile applications. Some websites like Tiwari Academy consider a sacred social responsibility by offering free access to NCERT solutions, so that education becomes accessible to one and all.

CBSE Syllabus for Class 9 Maths Revised for 2024-25

• CBSE Syllabus for Class 9 Maths

NCERT solutions are considered very useful for students as they are developed by subject experts based on curriculum prescribed by CBSE. If you are searching for the Class 9 Maths UP Board NCERT Solutions revised for 2024-25 exams, then do not worry. The good news is that Tiwari Academy has provided updated NCERT textbook solutions for Class 9 Mathematics here for all chapters. These are helpful in scoring more marks in the examination. They provide a solid foundation for understanding mathematical concepts and enable students to excel in their studies.

NCERT Solution Apps for 9th Class 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 question answers for the new Academic year based on latest NCERT book syllabus.

Tiwari Academy’s Educational App sends notifications and reminders for important dates, exams and study schedules. These help students to stay organized and on track with their studies. Students can monitor their scores, completion of exercises and areas where they need improvement.

How to Score well in class 9 Maths Exams For a Class 9 student aiming to excel in Maths, a structured approach to learning and practice is the key. Start by thoroughly understanding the current syllabus and the fundamental concepts it covers.

Physical exercise, hobbies, or even short walks can be refreshing and help in maintaining focus during study sessions. A positive mindset and belief in your ability to learn and improve will go a long way in improving your overall personality. Regular self-assessment mathematics through quizzes or timed practice sessions can be beneficial. This not only helps in identifying areas that need more attention but also builds confidence.

NCERT Solutions for Class 9 Maths All Chapters

These Chapter Wise NCERT Solutions for Class 9 Maths App is well designed so that class 9 students can easily understand each sum’s solutions. The Class 9th NCERT Math textbook has a total of 12 chapters which are divided into six units. Solving Class 9th Maths solution in each chapter will ensure positive results. Chapters covered in the NCERT 9th Math textbook are Number System, Polynomials, Introduction to Euclids Geometry, Quadrilaterals, Surface Areas, Heron’s Formula, and Volumes, Statistics etc. 

NCERT Class 9 Maths Chapters Solutions

Students who are facing any trouble in solving tough Class 9th Maths problems can get best help from these CBSE Maths Class 9 Solutions of NCERT (https://ncert.nic.in/) textbooks. The syllabus contains 12 chapters with important topics. Here all solutions build your fundamental very clear and efficiency by solving theses exercise-wise solutions.

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.

Class 9 Maths Chapter 1 for CBSE Board Class 9 Maths Exercise 1.1 in English Class 9 Maths Exercise 1.2 in English Class 9 Maths Exercise 1.3 in English Class 9 Maths Exercise 1.4 in English Class 9 Maths Exercise 1.5 in English

Class 9 Maths Chapter 1 Solution for State Boards Class 9 Maths Chapter 1 Exercise 1.1 Class 9 Maths Chapter 1 Exercise 1.2 Class 9 Maths Chapter 1 Exercise 1.3 Class 9 Maths Chapter 1 Exercise 1.4 Class 9 Maths Chapter 1 Exercise 1.5 Class 9 Maths Chapter 1 Exercise 1.6

Class 9 Maths Chapter 1 in Hindi Medium Class 9 Maths Exercise 1.1 in Hindi Class 9 Maths Exercise 1.2 in Hindi Class 9 Maths Exercise 1.3 in Hindi Class 9 Maths Exercise 1.4 in Hindi Class 9 Maths Exercise 1.5 in Hindi

There are five 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.

Topics to Study in Class 9 Maths Chapter 1 Number Systems Review of representation of natural numbers, integers, and rational numbers on the number line. Rational numbers as recurring/ terminating decimals. Operations on real numbers. 2. Examples of non-recurring/non-terminating decimals. Existence of non-rational numbers (irrational numbers) such as √2, √3 and their representation on the number line. Explaining that every real number is represented by a unique point on the number line and conversely, viz. every point on the number line represents a unique real number. 3. Definition of nth root of a real number. 4. Rationalization (with precise meaning) of real numbers of the type 1/(a + b√x) and 1/(√x + √y) (and their combinations) where x and y are natural number and a and b are integers. 5. Recall of laws of exponents with integral powers. Rational exponents with positive real bases (to be done by particular cases, allowing learner to arrive at the general laws.)

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. Class 9 Maths Chapter 2 for CBSE Board Class 9 Maths Exercise 2.1 in English Class 9 Maths Exercise 2.2 in English Class 9 Maths Exercise 2.3 in English Class 9 Maths Exercise 2.4 in English

Class 9 Maths Chapter 2 Solution for State Boards Class 9 Maths Chapter 2 Exercise 2.1 Class 9 Maths Chapter 2 Exercise 2.2 Class 9 Maths Chapter 2 Exercise 2.3 Class 9 Maths Chapter 2 Exercise 2.4 Class 9 Maths Chapter 2 Exercise 2.5

Class 9 Maths Chapter 2 in Hindi Medium Class 9 Maths Exercise 2.1 in Hindi Class 9 Maths Exercise 2.2 in Hindi Class 9 Maths Exercise 2.3 in Hindi Class 9 Maths Exercise 2.4 in Hindi

This chapter Polynomial consists of variables and coefficients, its operations of addition, subtraction, multiplication and also non-negative integer exponents of variables.

Topics of Class 9 Maths Chapter 2 Polynomials Definition of a polynomial in one variable, with examples and counter examples. Coefficients of a polynomial, terms of a polynomial and zero polynomial. Degree of a polynomial. Constant, linear, quadratic and cubic polynomials. Monomials, binomials, trinomials. Factors and multiples. Zeros of a polynomial. Motivate and State the Remainder Theorem with examples. Statement and proof of the Factor Theorem. Factorization of ax² + bx + c, a ≠ 0 where a, b and c are real numbers, and of cubic polynomials using the Factor Theorem. Recall of algebraic expressions and identities. Verification of identities: (x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx (x + y)³ = x³ + y³ + 3xy(x + y) (x – y)³ = x³ – y³ – 3xy(x – y) x³ + y³ = (x + y)(x² – xy + y²) x³ – y³ = (x – y)(x² + xy + y²) x³ + y³ + z³ – 3xyz = (x + y)(x² + y² + z² – xy – yz – 2zx) and their use in factorization of polynomials.

NCERT Solutions for Class 9 Maths Chapter 3 – Coordinate Geometry

Students can get NCERT exercises solutions for Class 9 Maths Chapter 3 with free of cost. This chapter 3 introduced 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.

Class 9 Maths Chapter 3 for CBSE Board Class 9 Maths Exercise 3.1 in English Class 9 Maths Exercise 3.2 in English

Class 9 Maths Chapter 3 for State Boards Class 9 Maths Chapter 3 Exercise 3.1 Class 9 Maths Chapter 3 Exercise 3.2 Class 9 Maths Chapter 3 Exercise 3.3

Class 9 Maths Chapter 3 in Hindi Medium Class 9 Maths Exercise 3.1 in Hindi Class 9 Maths Exercise 3.2 in Hindi

In NCERT Solutions for Class 9 Maths Chapter 3 Coordinate Geometry, students learn coordinate plane and the mutually perpendicular lines which are called axe. They downloads 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.

Class 9 Maths Chapter 3 Coordinate Geometry Main Points The Cartesian plane, coordinates of a point, names and terms associated with the coordinate plane, notations.

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, know about linear equations in two variables, such as ax + by + c = 0. Learn here how to graph of a linear equation in two variables.

Class 9 Maths Chapter 4 for CBSE Board Class 9 Maths Exercise 4.1 in English Class 9 Maths Exercise 4.2 in English

Class 9 Maths Chapter 4 for State Boards Class 9 Maths Chapter 4 Exercise 4.1 Class 9 Maths Chapter 4 Exercise 4.2 Class 9 Maths Chapter 4 Exercise 4.3 Class 9 Maths Chapter 4 Exercise 4.4

Class 9 Maths Chapter 4 in Hindi Medium Class 9 Maths Exercise 4.1 in Hindi Class 9 Maths Exercise 4.2 in Hindi

There are only two exercises in this NCERT Solutions for Class 9 Maths Chapter 9 Linear Equations in Two Variables. Download NCERT Solutions for Class 9 Maths PDF free of cost and study at any time anywhere. Students take the benefits clearing all the concepts of each math sum. Download free unlimited Chapter Linear Equations in Two Variables Class 9 Maths Solutions in Hindi Medium and English Medium.

Topics to be covered in Class 9 Maths Chapter 4 Linear Equations in Two Variables Recall of linear equations in one variable. Introduction to the equation in two variables. Focus on linear equations of the type ax + by + c = 0. Explain that a linear equation in two variables has infinitely many solutions and justify their being written as ordered pairs of real numbers, plotting them and showing that they lie on a line.

NCERT Solutions for Class 9 Maths Chapter 5 – Introduction to Euclid’s 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 NCERT exercises for Class 9 Maths Introduction to Euclid’s Geometry defining common geometrical shapes and terms.

Class 9 Maths Chapter 5 for CBSE Board Class 9 Maths Exercise 5.1 in English

Class 9 Maths Chapter 5 for State Boards Class 9 Maths Chapter 5 Exercise 5.1 Class 9 Maths Chapter 5 Exercise 5.2

Class 9 Maths Chapter 5 in Hindi Medium Class 9 Maths Exercise 5.1 in Hindi

There is only one exercise in this 9th Class Maths Book Solution which teach you deeper knowledge relation between axiom, postulates, and theorems. Download here Chapter Euclid’s Geometry Class 9 Maths Solutions in Hindi medium and English medium.

Syllabus of Class 9 Maths Chapter 5 Introduction to Euclid’s Geometry History – Geometry in India and Euclid’s geometry. Euclid’s method of formalizing observed phenomenon into rigorous Mathematics with definitions, common/obvious notions, axioms/postulates and theorems. The five postulates of Euclid. Showing the relationship between axiom and theorem, for example: (Axiom) 1. Given two distinct points, there exists one and only one line through them. (Theorem) 2. (Prove) Two distinct lines cannot have more than one point in common.

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.

Class 9 Maths Chapter 6 Solutions for CBSE Board Class 9 Maths Exercise 6.1 in English Class 9 Maths Exercise 6.2 in English

Class 9 Maths Chapter 6 Solutions for State Boards Class 9 Maths Chapter 6 Exercise 6.1 Class 9 Maths Chapter 6 Exercise 6.2 Class 9 Maths Chapter 6 Exercise 6.3

Class 9 Maths Chapter 6 in Hindi Medium Class 9 Maths Exercise 6.1 in Hindi Class 9 Maths Exercise 6.2 in Hindi

9th Maths Book Solution are provided here are well-reviewed. Get free NCERT Solutions for Class 9 Maths in PDF for offline study. Practice these solutions thoroughly to get maximum marks in the final exam. Download Chapter Lines and Angles Class 9 Maths Solutions in Hindi medium and English medium.

Class 9 Maths Chapter 6 Lines and Angles Topics 1. (Motivate) If a ray stands on a line, then the sum of the two adjacent angles so formed is 180° and the converse. 2. (Prove) If two lines intersect, vertically opposite angles are equal. 3. (Motivate) Lines which are parallel to a given line are parallel.

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.

Class 9 Maths Chapter 7 Solutions for CBSE Board Class 9 Maths Exercise 7.1 in English Class 9 Maths Exercise 7.2 in English Class 9 Maths Exercise 7.3 in English

Class 9 Maths Chapter 7 Solutions for State Boards Class 9 Maths Chapter 7 Exercise 7.1 Class 9 Maths Chapter 7 Exercise 7.2 Class 9 Maths Chapter 7 Exercise 7.3 Class 9 Maths Chapter 7 Exercise 7.4 Class 9 Maths Chapter 7 Exercise 7.5

Class 9 Maths Chapter 7 in Hindi Medium Class 9 Maths Exercise 7.1 in Hindi Class 9 Maths Exercise 7.2 in Hindi Class 9 Maths Exercise 7.3 in Hindi

In this 9th Maths Book Solution, we have to prove the properties of the triangle which you learn about in previous classes. Apply the various congruence rules while solving the problems. In this chapter, students learn about eight theorems. There are three exercises which cover in this NCERT Solutions for Class 9 Maths Chapter 7 Triangles. Get Chapter Triangles Class 9 Maths Solutions in Hindi medium and English medium.

Class 9 Maths Chapter 7 Triangles Main Points to Study 1. (Motivate) Two triangles are congruent if any two sides and the included angle of one triangle is equal to any two sides and the included angle of the other triangle (SAS Congruence). 2. (Prove) 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). 3. (Motivate) Two triangles are congruent if the three sides of one triangle are equal to three sides of the other triangle (SSS Congruence). 4. (Motivate) Two right triangles are congruent if the hypotenuse and a side of one triangle are equal (respectively) to the hypotenuse and a side of the other triangle. (RHS Congruence) 5. (Prove) The angles opposite to equal sides of a triangle are equal. 6. (Motivate) The sides opposite to equal angles of a triangle are equal.

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.

Class 9 Maths Chapter 8 for CBSE and State Boards Class 9 Maths Exercise 8.1 in English Class 9 Maths Exercise 8.2 in English

Class 9 Maths Chapter 8 in Hindi Medium Class 9 Maths Exercise 8.1 in Hindi Class 9 Maths Exercise 8.2 in Hindi

Class 9 Maths chapter 8 contains two exercises that contain only one theorem to prove. These Solutions include 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.

Class 9 Maths Chapter 8 Quadrilaterals Focus Points 1. (Prove) The diagonal divides a parallelogram into two congruent triangles. 2. (Motivate) In a parallelogram opposite sides are equal, and conversely. 3. (Motivate) In a parallelogram opposite angles are equal, and conversely. 4. (Motivate) A quadrilateral is a parallelogram if a pair of its opposite sides is parallel and equal. 5. (Motivate) In a parallelogram, the diagonals bisect each other and conversely. 6. (Motivate) In a triangle, the line segment joining the mid points of any two sides is parallel to the third side and in half of it and (motivate) its converse.

NCERT Solutions for Class 9 Maths Chapter 9 – Circles

Here get well explained NCERT Solutions for Class 9 Maths Chapter Circles with free of cost and no need to login and register to get solutions for all exercises. In this NCERT Solutions for Class 9 Maths Chapter 9 Circle, learn that circle is a collection of all the points in a plane at a fixed distance.

Class 9 Maths Chapter 9 for CBSE Board Class 9 Maths Exercise 9.1 in English Class 9 Maths Exercise 9.2 in English Class 9 Maths Exercise 9.3 in English

Class 9 Maths Chapter 9 Solutions for State Boards Class 9 Maths Chapter 9 Exercise 9.1 Class 9 Maths Chapter 9 Exercise 9.2 Class 9 Maths Chapter 9 Exercise 9.3 Class 9 Maths Chapter 9 Exercise 9.4

Class 9 Maths Chapter 9 in Hindi Medium Class 9 Maths Exercise 9.1 in Hindi Class 9 Maths Exercise 9.2 in Hindi Class 9 Maths Exercise 9.3 in Hindi

Get knowledge about circle including a Chord at a Point, Equal Chords. There are a total of twelve theorems present in this chapter. Download  NCERT Solutions for Class 9 Maths PDF without any cost and registration. Get Chapter 9 Circles Class 10 Maths Solutions in Hindi medium and English medium here.

Class 9 Maths Chapter 9 Circles Curriculum for 2024-25 1.(Prove) Equal chords of a circle subtend equal angles at the center and (motivate) its converse. 2.(Motivate) The perpendicular from the center of a circle to a chord bisects the chord and conversely, the line drawn through the center of a circle to bisect a chord is perpendicular to the chord. 3. (Motivate) Equal chords of a circle (or of congruent circles) are equidistant from the center (or their respective centers) and conversely. 4. (Prove) 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. 5. (Motivate) Angles in the same segment of a circle are equal. 6. (Motivate) If a line segment joining two points subtends equal angle at two other points lying on the same side of the line containing the segment, the four points lie on a circle. 7. (Motivate) The sum of either of the pair of the opposite angles of a cyclic quadrilateral is 180° and its converse.

NCERT Solutions for Class 9 Maths Chapter 10 – Heron’s Formula

Students get NCERT Solutions for Class 9 Maths Chapter 10 , 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, find out distances in the triangle without calculating.

Class 9 Maths Chapter 10 for CBSE Board Class 9 Maths Exercise 10.1 in English

Class 9 Maths Chapter 10 for State Boards Class 9 Maths Chapter 10 Exercise 10.1 Class 9 Maths Chapter 10 Exercise 10.2 Class 9 Maths Chapter 10 Exercise 10.3 Class 9 Maths Chapter 10 Exercise 10.4 Class 9 Maths Chapter 10 Exercise 10.5 Class 9 Maths Chapter 10 Exercise 10.6

Class 9 Maths Chapter 10 in Hindi Medium Class 9 Maths Exercise 10.1 in Hindi

This formula is used to find out the areas of quadrilaterals, the area of triangles and other polygons. There is only one exercise in this NCERT Solutions for Class 9 Maths Chapter 10 Heron’s Formula. Download NCERT Solutions for Class 9 Maths Chapter 12 PDF and learn anytime in desktop or mobile while offline.

Class 9 Maths Chapter 10 Heron’s Formula Main Points To Study Area of a triangle using Heron’s formula (without proof)

NCERT Solutions for Class 9 Maths Chapter 11 – Surface Areas and Volumes

NCERT Solutions for Class 9 Maths Chapter 11 , learn to find the surface areas and volumes of cuboids and cylinders in details. In this NCERT Solutions for Class 9 Maths Chapter 11 Surface Areas and Volumes, learn the surface areas of some other solids such as cones and spheres.

Class 9 Maths Chapter 11 for CBSE Board Class 9 Maths Exercise 11.1 in English Class 9 Maths Exercise 11.2 in English Class 9 Maths Exercise 11.3 in English Class 9 Maths Exercise 11.4 in English

Class 9 Maths Chapter 11 Solutions for State Boards Class 9 Maths Chapter 11 Exercise 11.1 Class 9 Maths Chapter 11 Exercise 11.2

Class 9 Maths Chapter 11 in Hindi Medium Class 9 Maths Exercise 11.1 in Hindi Class 9 Maths Exercise 11.2 in Hindi Class 9 Maths Exercise 11.3 in Hindi Class 9 Maths Exercise 11.4 in Hindi

Here students get detailed knowledge about the surface areas and volumes in earlier classes. There are four exercises in chapter 11 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. Get Chapter Surface Areas and Volumes  Class 9 Maths Solutions in Hindi medium and English medium.

The Points to be covered in Class 9 Maths Chapter 11 Surface Areas and Volumes Surface areas and volumes of spheres (including hemispheres) and right circular cones.

NCERT Solutions for Class 9 Maths Chapter 12 – Statistics

These best easy NCERT Solutions for Class 9 Maths Chapter 12 , deals with Statistics which the extraction of meaningful information is studied is known as Statistics.

Class 9 Maths Chapter 12 for CBSE Board Class 9 Maths Exercise 12.1 in English

Class 9 Maths Chapter 12 Solutions for State Boards Class 9 Maths Chapter 12 Exercise 12.1 Class 9 Maths Chapter 12 Exercise 12.2

Class 9 Maths Chapter 12 in Hindi Medium Class 9 Maths Exercise 12.1 in Hindi

Statistics is used in our daily life such as aspects of the life of people, useful to the State etc. These NCERT Solutions for Class 9 Maths Chapter 12 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 learn to Mean, Mode and median as well. Get Chapter Statistics Class 9 Maths Solutions in Hindi medium and English medium.

Class 9 Maths Chapter 12 Statistics Main Points Bar graphs, histograms (with varying base lengths), and frequency polygons.

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

Tiwari Academy NCERT solutions on Surface Areas and Volumes based on state board syllabus, Hindi and English medium, 2024-25 session. Achieve mastery in geometry with Tiwari Academy’s expert NCERT Solutions for Class 9 Maths Exercise 13.8, tailored for students in the 2024-2025 session, available in both Hindi and English. Class 9 Maths Chapter 13 for State Boards Class 9 Maths Chapter 13 Exercise 13.1 Class 9 Maths Chapter 13 Exercise 13.2 Class 9 Maths Chapter 13 Exercise 13.3 Class 9 Maths Chapter 13 Exercise 13.4 Class 9 Maths Chapter 13 Exercise 13.5 Class 9 Maths Chapter 13 Exercise 13.6 Class 9 Maths Chapter 13 Exercise 13.7 Class 9 Maths Chapter 13 Exercise 13.8 Class 9 Maths Chapter 13 Exercise 13.9

NCERT Solutions for Class 9 Maths Chapter 14 Statistics

Access Class 9 Maths Chapter 14 Statistics solutions in Hindi and English. Perfect for CBSE students, our resources at Tiwari Academy are comprehensive and user-friendly. Class 9 Maths Chapter 1 Solution for State Boards Class 9 Maths Chapter 14 Exercise 14.1 Class 9 Maths Chapter 14 Exercise 14.2 Class 9 Maths Chapter 14 Exercise 14.3 Class 9 Maths Chapter 14 Exercise 14.4

NCERT Solutions for Class 9 Maths Chapter 15 Probability

Master Class 9 Maths with Chapter 15 Probability solutions, available in English and Hindi. Excel in CBSE exams with Tiwari Academy’s expert resources. Clear, concise, and free – your key to understanding Probability concepts. Class 9 Maths Chapter 15 Solutions for State boards Class 9 Maths Chapter 15 Exercise 15.1

Importance of NCERT Solutions for Class 9 Maths

NCERT stands for National Council of Educational Research and Training. NCERT was formed to provide standardised textbooks along with research and training in the field of 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 learn these subjects offline also by just downloading these PDFs. You can study anywhere and anytime.

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 clear your all doubts and concepts clear.

Created the Best Subject Experts in Field Class 9 Maths solution provided by an expert math teacher who has been created by the high-quality subject matter experts. So get more marks with these high-quality study materials. All solutions are designed by following extensive research on the Math subject. Be able to solve a wide range of problems at any difficulty level.

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 .

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 2024-25 having classical approach of constructions and geometrical chapters. Get here UP Board Secondary Education (High School) Solution, Sample Papers, Notes and other study material.

How to practice Class 9 Maths using NCERT Solutions?

According to new NCERT Textbooks published for academic session 2024-25, the syllabus for class 9 Maths is reduced significantly. That is why, the NCERT Solutions for class 9 Maths is also modified and revised as per new session. NCERT Solutions play a significant role in helping students score well in their Class 9 CBSE (Central Board of Secondary Education) Mathematics exams. Follow the steps given here to know how you can score well in exams using class 9 Maths solutions.

Step 1: Use NCERT Solutions for Comprehensive Coverage of class 9 Maths textbook.

Step 2: verify your answers and learn about the exam pattern., step 3: revise the syllabus and use class 9 maths ncert solution as a revision aid., step 4: make effective self study in 9th maths using ncert solutions., step 5: confined to new rationalised ncert textbooks and solve it using ncert solutions..

How many chapters are there in NCERT Class 9 Maths?

According to new syllabus, there are a total of 12 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- Circles, 
• Chapter 10- Heron’s Formula, 
• Chapter 11- Surface Areas and Volumes, 
• Chapter 12- Statistics, 

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.

How can I get more than 80% marks in Class 9 Maths Exams?

Most of the chapters in Class 9 Maths are easy to understand. If we try to learn by doing, the mathematics become simple and interesting subject otherwise it would be a burden for us. Get concentrated on your NCERT Textbook 2024-25 and start practicing with understanding to score well with less efforts. How to practice questions: Read the preface of the chapter and see the pattern of each example given before the exercises. Now taking the hints from these solved example, try to solve the questions of exercises by own. Don’t take help from teachers or online website when your are solving the questions. After trying many time if still not getting the correct answers, then consult your respective teacher or visit to Tiwari Academy to take help from PDF Solutions or videos solutions.

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 perform best in Terminal exams of Class 9 Maths?

There are so many chapters in class 9 Maths which are easy and interesting to work with. When you are in energetic mood, start doing the chapter which you considered as difficult one but if you are tired and still want to practice mathematics, start with an easier chapter. Studying in this manner make the mathematics interesting and easier.

Sushant Mukherjee

Providing help in science for class 6 to 10. Adviser in Tiwari Academy for the science related subjects subject as well as videos contents. Ample teaching experience in schools. I am not only working for Tiwari Academy but also provide new ideas for the website and apps.

Copyright 2024 by Tiwari Academy | A step towards Free Education

NCERT Solutions for Class 9 Maths

NCERT solutions for class 9 maths comprise the analysis and explanation of all the problems covered by the NCERT textbook for 9th grade. The solutions are provided in a detailed manner to ensure that students can understand concepts as they go through them. These class 9 maths NCERT solutions are prepared by some of the most accomplished experts in the field of Mathematics.

Class 9th Maths NCERT Solutions are extremely helpful for students preparing for CBSE exams and state or national competitive tests such as Olympiads. The CBSE examinations follow the structure provided by the NCERT textbooks. Additionally, CBSE NCERT solutions for class 9 maths help in getting students ready to face class 10th and the corresponding board exams.

NCERT Maths Class 9 Solutions PDF Download

Practicing these class 9 maths NCERT solutions can help students to increase their theoretical skills and practical knowledge. The solutions to all NCERT class 9 maths sums are available for free pdf download. You can find tips and tricks included with the solutions. The links to these pdf solutions are given below.

Class 9th Maths NCERT Solutions Chapter 1 to 15

As a student, you must indulge in constant revision and practice all the solutions. Thus, revisiting the above-mentioned links periodically is a must. Start by attempting the questions in the NCERT book and then have a look at these class 9th maths NCERT solutions. You can download the NCERT textbook given below and begin your learning journey.

☛ Download Class 9 Maths NCERT Book

NCERT Solutions for Class 9 Maths Chapter 1

NCERT solutions for class 9 maths chapter 1 number systems help students amass the tools required to identify rational and irrational numbers , locate real numbers on a number line , and convert a real number to its decimal form. The solutions to this chapter also give students a good understanding of simplifying expressions using certain identities and laws of exponents .

Important Formulas:

• √(ab) = √a √b
• √(a/b) = √a/√b
• (√a + √b)(√a - √b) = a - b
• (√a + √b)2 = a + b + 2√(ab)

Class 9 Maths Chapter 1 Real Numbers

Topics Covered: NCERT solutions for class 9 maths cover questions based on rationalizing the denominator , the rules of exponentiation, identities applied to positive real numbers, expanding a real number into its decimal form, and vice versa.

Total Questions: Chapter 1 has a total of 27 questions, out of which 5 are easy, 7 are moderate and 10 are difficult.

NCERT Solutions for Class 9 Maths Chapter 2

NCERT solutions for class 9 maths chapter 2 polynomials help students form the basics of polynomials that will be used in higher classes. Students learn about the types of polynomials in one variable, degree and zeros of a polynomial , the remainder theorem , factorization of polynomials , and the application of algebraic identities.

• (x + y) 2 = x 2 + 2xy + y 2
• x 2 - y 2 = (x + y) (x - y)
• (x + a) (x + b) = x 2 + (a + b)x + ab
• (x - y) 2 = x 2 - 2xy + y 2
• (x + y + z) 2 = x 2 + y 2 + z 2 + 2xy + 2yz + 2zx

Class 9 Maths Chapter 2 Polynomials

Topics Covered: Factorization of different polynomials using the splitting method and factor theorem , finding the remainder of a polynomial, applying algebraic identities to simplify sums, and determining the zeros of a polynomial.

Total Questions: Class 9 maths chapter 2 polynomials have 33 questions. 10 are of a moderate level, 14 are easy and 9 are challenging sums.

NCERT Solutions for Class 9 Maths Chapter 3

NCERT solutions for class 9 maths chapter 3 coordinate geometry help students to get a grasp on how to describe the position of an object using coordinates and explanation of the cartesian system . It acts as a foundation for further chapters that require students to use their knowledge to solve geometrical problems.

Class 9 Maths Chapter 3 Coordinate Geometry

Topics Covered: Determining the x and y coordinates of a point in a cartesian plane, identifying quadrants, locating an object, and expressing it in the form of coordinates are the topics under class 9 maths NCERT solutions.

Total Questions: There are 6 questions in class 9 maths chapter 3 coordinate geometry. 3 are difficult, 2 are medium level and 1 is an easy question.

Class 9 Maths Chapter 3 Summary:

Class 9 maths NCERT solutions chapter 3 gives a brief overview of the definition of the origin, how to use the horizontal x-axis and vertical y-axis to pinpoint the position of an object. It also helps students determine what quadrant does a point lies in depending upon the signs of the coordinates.

NCERT Solutions for Class 9 Maths Chapter 4

NCERT solutions for class 9 maths chapter 4 linear equations in two variables introduce students to a linear equation in two variables by helping them understand the concepts behind it. The solutions include solving linear equations , graphical representation methods, and the depiction of parallel lines.

Linear equations are one of the most important chapters covered in class 9 maths NCERT solutions . The following are a few tips that can help you power through these solutions quickly and efficiently.

• Build an understanding of the concepts
• Revision of the topic at regular intervals
• Understanding the general form of a line

Class 9 Maths Chapter 4 Linear Equations in Two Variables

Topics Covered: Finding solutions to a linear equation by substituting values, representing a linear equation in two variables graphically, and how to write the equation of lines parallel to the x-axis.

Total Questions: Chapter 4 linear equations in two variables have a total of 16 questions. 8 require students to carefully think and attempt the problem, 5 are moderate and 4 are easy sums.

NCERT Solutions Class 9 Maths Chapter 5

NCERT solutions class 9 maths chapter 5 introduction to Euclid’s geometry gives students an insight into the definitions of points, lines, surfaces, and so on. Students also get an idea of the 5 postulates given by Euclid that are used to solve geometry problems.

Class 9 Maths Chapter 5 Introduction to Euclid’s Geometry

Topics Covered: Euclid’s five postulates dealing with line segments, radii, perpendicular lines , and the variation of the fifth postulate are the topics covered under NCERT solutions class 9 maths.

Total Questions: Chapter 5 introduction to Euclid’s Geometry has 9 questions, 4 are simple, 3 are intermediate and 2 are tough sums.

The chapter deals with five postulates given by Euclid regarding a straight line, a terminating line, a circle, and its radius, as well as right angles . Students also learn about the two equivalent versions of Euclid’s fifth postulate that led to the discovery of other theorems.

Class 9 Maths NCERT Solutions Chapter 6

Class 9 maths NCERT solutions chapter 6 lines and angles give students an understanding of the basic definitions of various terms that are used in geometry . Students learn about the different types of angles, pairs of angles, transversals, parallel lines , angle sum property of triangles, and axioms associated with these concepts.

Class 9 Maths NCERT Solutions Chapter 6 Preparation Tips

There are a number of properties taught in this chapter that students must learn. The following points can help in streamlining this process.

• Practice several questions on properties of angles that get formed when a transversal intersects 2 or 3 parallel lines.
• Understand the reasoning behind theorems such as the angle sum property of a triangle.
• Make a note of the relationship between pairs of angles.

Cuemath is one of the world's leading math learning platforms that offers LIVE 1-to-1 online math classes for grades K-12 . Our mission is to transform the way children learn math, to help them excel in school and competitive exams. Our expert tutors conduct 2 or more live classes per week, at a pace that matches the child's learning needs.

Class 9 Maths Chapter 6 Lines and Angles

Topics Covered: Adjacent angles, vertically opposite angles, linear pairs of angles, alternate angles , corresponding angles , parallel lines, and transversal are topics falling under Class 9 maths NCERT solutions. In addition to this, problems based on the angle sum property of a triangle are also included in these solutions.

Total Questions: There are a total of 18 questions in class 9 maths chapter 6 lines and angles. 10 are very easy property-based questions, 5 require some thinking on a student’s part and 3 are difficult sums.

NCERT Solutions for Class 9 Maths Chapter 7

NCERT solutions for class 9 maths chapter 7 triangles are a fantastic way for students to learn about the congruence of triangles using the SAS, SSS, ASA, RHS criteria. Several properties of triangles along with concepts on the inequality of triangles also fall under the scope of this chapter.

Class 9 Maths Chapter 7 Triangles

Topics Covered: Questions based on applying properties of triangles, proving the congruence of two triangles using different methods, and theorems on the inequality of triangles are the topics covered.

Total Questions: Class 9 maths chapter 7 has 31 questions. 10 are simple questions based on applying the properties of triangles, 9 are complex sums and 12 are moderate problems.

Chapter Summary:

In this chapter, students learn about the SSS, SAS, ASA, and RHS congruence criteria. Students can get a good grasp on properties of triangles such as sides opposite to equal angles are equivalent, the sum of any two sides of a triangle is greater than the third side, and so on. Thus, after studying this chapter students can master the basic concepts of a triangle.

NCERT Solutions for Class 9 Maths Chapter 8

NCERT solutions for class 9 maths chapter 8 quadrilaterals comprise questions that teach students about the different types of quadrilaterals such as squares , rhombuses , rectangles , parallelograms, and their properties.

Class 9 Maths Chapter 8 Quadrilaterals

Topics Covered: Angle sum property of quadrilaterals, properties of a parallelogram , square, and rhombus that depend upon different factors such as length of diagonals, the measure of sides, etc. It also includes the mid-point theorem .

Total Questions: 19 sums - 8 are simple problems, 6 are of an intermediate level and 5 are challenging questions.

Class 9 Maths NCERT Solutions Chapter 9

Class 9 maths NCERT solutions chapter 9 areas of parallelograms and triangles include various theorems that help to simplify finding the area of complex parallelograms as well as triangles, properties to find the area of triangles divided by a median, and area of planar regions.

• Area of a triangle = ½ × base × height
• Area of a parallelogram = base × height

Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles

Topics Covered: Topics covered incorporate questions on finding the area of two or more triangles and parallelograms with the same base between the same parallels, determining the area of triangles that are split by a median as well as the area of congruent figures.

Total Questions: Chapter 9 areas of parallelograms and triangles have a total of 31 questions. 8 questions belong to an optional exercise with a high difficulty level, 14 are intermediate and 9 are simple sums.

NCERT Solutions for Class 9 Maths Chapter 10

NCERT solutions for class 9 maths chapter 10 circles build a foundation for students by introducing them to the various terms related to circles. Students get the opportunity to build their knowledge base on properties of chords, the angle subtended by chord and arc, perpendicular to a point, the distance of a chord from the center as well as cyclic quadrilaterals .

Preparation Tips:

NCERT solutions for class 9 maths chapter 10 are purely based on the properties of various elements of a circle. To memorize these theorems you can follow the topics listed below.

• Make a note of all the properties so that you can skim through them when required.
• Solve all NCERT textbook questions.
• Regularly revise the solutions so that you can recall them when necessary.

Class 9 Maths Chapter 10 Circles

Topics Covered: NCERT solutions class 9 maths encompass topics such as angles subtended by a chord at a point, perpendiculars dropped from the center to a chord, and how to calculate the distance of equal chords from the center. Other discussions include angles subtended by an arc of the circle, cyclic quadrilaterals, and their attributes.

Total Questions: There are a total of 35 questions in this chapter out of which 15 are relatively simpler, 10 are complex and 10 are of moderate complexity.

NCERT Solutions for Class 9 Maths Chapter 11

NCERT solutions for class 9 maths chapter 11 constructions will teach students how to precisely use geometrical instruments for basic constructions. Students learn to construct different angles , perpendicular bisectors , and triangles with a few given restraints.

Class 9 Maths Chapter 11 Constructions

Topics Covered: Constructing an angle from a ray, bisector of a given angle, and techniques to construct triangles when certain constraints such as the perimeter are mentioned, are the topics explained in this chapter.

Total Questions: Chapter 11 constructions have a total of 10 questions. 3 can be simply solved, 5 are moderate questions and 2 are difficult.

After studying NCERT solutions class 9 maths chapter 11 students will be adept at using a ruler and compass to bisect a given angle, construct angles of discrete values, draw the perpendicular bisector of a line segment , and building triangles.

NCERT Solutions for Class 9 Maths Chapter 12

NCERT solutions for class 9 maths chapter 12 heron’s formula is a formula given by the Hero of Alexandria to calculate the area of a triangle when the lengths of all three sides are known. In this chapter, students will learn more about the application of this formula to find the area of triangles and quadrilaterals .

• Semi Perimeter s = (a + b + c)/2
• Area of a Triangle = √[s (s - a) (s - b) (s - c)]

Class 9 Maths Chapter 12 Heron’s Formula

Topics Covered: NCERT Solutions class 9 maths chapter 12 cover the complete scope of Heron’s formula and how to apply it to questions for determining the area of a triangle. Additionally, this formula is also used for computing the area of a quadrilateral .

Total Questions: Chapter 12 heron’s formula consists of 15 well-curated questions out of which 5 are simple, 3 and medium level and 7 are difficult problems.

Class 9 Maths NCERT Solutions Chapter 13

Class 9 maths NCERT solutions chapter 13 surface areas and volumes introduce students to the concepts required to find the total surface areas, lateral or curved surface areas, and volumes of different shapes. The concepts and formulas in this chapter are very important as they form the basis of topics covered in higher education.

• TSA of a Cuboid = 2(lb + bh + hl)
• TSA of a Cube = 6a 2
• TSA of a Cylinder = 2πr(r + h)
• TSA of a Cone = πr(l + r)
• TSA of a Sphere = 4πr 2
• TSA of a Hemisphere = 3πr 2

Class 9 Maths Chapter 13 Surface Areas and Volumes

Topics Covered: Finding the TSA, LSA/CSA, along with the volume of shapes such as cubes, cuboids, right circular cylinder , right circular cone , sphere, and hemisphere.

Total Questions: Chapter 13 surface areas and volumes have 75 questions. 25 are easy formula-based sum, 31 are medium level and 10 are difficult problems that challenge a student’s thinking abilities.

Class 9 Maths NCERT Solutions Chapter 14

Class 9 maths NCERT solutions chapter 14 statistics provide an in-depth analysis of problems that are based on the collection and presentation of data for analytical purposes, graphical representation of data using different types of graphs, and measures of central tendency . This chapter enables students to develop their calculation speed and visualization skills.

Class 9 Maths Chapter 14 Statistics

Topics Covered: Representation of data in the form of frequency tables and drawing inferences from them, plotting data points using bar graphs , histograms , and frequency polygons, finding the mean , median , and mode of the given data .

Total Questions: Chapter 14 statistics have 26 problems that can be split into 8 long answer-type questions, 11 moderate, and 7 simple sums.

Once students finish practicing class 9 maths NCERT solutions chapter 14 they will have a good understanding of the purpose of well-organized data, the three measures of central tendency for ungrouped data namely mean, median, and mode. Students can effectively apply these formulas to all levels of problems after studying this topic.

NCERT Solutions Class 9 Maths Chapter 15

NCERT solutions class 9 maths chapter 15 probability help students deal with daily-life problems that require the use of probability concepts. This chapter helps students explore more about empirical probability, the definition of an event, and how to calculate the probability of different events.

NCERT Maths Class 9 Chapter 15 Study Tips

NCERT solutions class 9 maths chapter 6 probability is a widely used topic that people require to perform their day-to-day operations. Given below are some study tips that can help in comprehending this chapter in a better manner.

• Apply the concept to simple daily life questions.
• Practice the solutions regularly to get the best results.
• Read the question carefully and break it down to get a better idea of what has to be done.

NCERT Maths Class 9 Chapter 15 Probability

Topics Covered: Finding the probability of the occurrence of heads or tails when a coin is flipped, tossing a die, and drawing conclusions from the result obtained are the topics covered in NCERT solutions class 9 maths.

Total Questions: Chapter 15 probability has 13 questions. 4 are short answer problems, 3 are difficult and 6 are moderate sums.

Class 9 Maths NCERT Solutions Important Formulas

Class 9 maths covers several topics such as polynomials, number systems, geometry, probability, etc. The formulas and concepts behind these topics are required to understand higher grade mathematics. Formulas are required to reduce the time taken to solve questions and increase accuracy. Given below is an overview of the important maths formulas encompassed in the NCERT solutions for class 9 maths.

• Area of a triangle = ½ * b × h
• Perimeter of a triangle = a + b + c
• Area of parallelogram = b × h
• Perimeter of a parallelogram = 2(a + b)

Surface Area and volume:

• TSA of a cuboid = 2(lb + bh +lh)
• Volume of a cuboid = l×b×h
• TSA of a cube = 6a 2
• Volume of a cube = a 3
• (a + b) 2 = a 2 + b 2 + 2ab
• (a - b) 2 = a 2 + b 2 - 2ab
• (a + b) (a - b) = a 2 - b 2

Importance of NCERT Solutions for Class 9 Maths

Class 9 Maths NCERT Solutions are extremely helpful for CBSE students as they give a means for efficient time management and improving auxiliary abilities. The following are the advantages of these solutions.

• Practical Applications: Many of the sums provided by the NCERT textbook are similar to real-life examples, especially when word problems are considered. By following the class 9 maths NCERT solutions students can come up with precise solutions that can also be applied to daily life problems.
• Practice: To solve the toughest sums within a matter of minutes you need due diligence and regular practice. These NCERT solutions for class 9 maths are very helpful for this purpose as they give students a detailed overview of how to solve different types of sums. They can also help a student to complete the syllabus well within the given time frame.
• Regular Revision: On examination days, students do not have the time to solve each and every question. Thus, these NCERT solutions class 9 maths help students with a quick revision of the entire syllabus. This also helps to free up time so that students can focus on ensuring that their concept formation is correct and can be accurately applied to sums.

FAQs on NCERT Solutions for Class 9 Maths

Why are ncert solutions for class 9 maths important.

NCERT solutions for class 9 maths are vital for students as they provide reliable solutions that students can use to cross-check their answers. These class 9 maths NCERT solutions also guide students on how to appear for an examination so that students can write their answers without missing any steps and get the best possible score.

Where Can I Get Chapter-wise Solutions for NCERT Class 9 Maths?

The chapter-wise solutions for NCERT class 9 maths can be accessed by the links mentioned above. They are further segregated into exercise-wise pdfs that are available for free download. These pdfs are also compatible with mobile screens and are in a scrollable format for easy use.

How CBSE Students can utilize Class 9 Maths NCERT Solutions?

To effectively utilize class 9 maths NCERT solutions students need to ensure that they have an understanding of the concepts used to solve the problems. Thus, when they start consulting these solutions students will comprehend them in a better manner and will be able to retain what they learned more efficiently.

Do I Need to Make Notes while Referring to NCERT Solutions Class 9 Maths?

Notes act as a simplified guide for students when they are trying to build an understanding of the subject or if they are revising that question. It is a good way of retaining and recalling concepts when required. Thus, it is crucial that students make notes of the NCERT solutions class 9 maths to expedite their learning process.

What are the Best Ways to Learn Concepts Covered in NCERT Solutions Class 9th Maths?

The most impactful way to learn concepts covered in NCERT solutions class 9th maths is by constantly practicing these solutions. If a student finds some concept difficult and cannot proceed further while attempting a problem he needs to immediately clarify his doubts so that there is no gap in learning.

Can We Use Other Methods to Solve Problems Apart From Those Mentioned in NCERT Solutions for Class 9 Maths?

You may not want to use the method given in the NCERT solutions for class 9 maths however, the approach used and the answer obtained need to be universally recognized. Having said that you cannot use the tricks that are useful in solving competitive exam problems as these are not standardized techniques.

Why Choose Cuemath for Class 9 Maths NCERT Solutions?

The best website for class 9 maths NCERT solutions is Cuemath. These solutions are prepared by IITians and certified math experts. Thus, they are reliable, precise and give the best techniques to solving any problem. They also include some tips to enable students to solve sums with speed and accuracy.

How Many Chapters are there in NCERT Solutions for Class 9 Maths?

There are 15 chapters in class 9 maths NCERT solutions. The problems covered by these are fantastic to improve a student’s understanding of different concepts. The NCERT solutions give an in-depth analysis of all exercise problems.

Do I Need to Practice all Questions Provided in NCERT Solutions Class 9 Maths?

All questions that are included in the CBSE home examinations are based on the NCERT class 9 maths. Thus, in order to get good marks, it is necessary to be well-versed with all the questions covered in class 9 maths NCERT solutions that can only be achieved through regular practice and due diligence.

Are NCERT Solutions for Class 9 Maths Sufficient for CBSE Exams?

The NCERT solutions for class 9 maths are sufficient for all CBSE exams. As the school teachers set the paper they include questions from the NCERT textbook. The language or values given in the problem may differ however, the approach to solving it is more or less the same. As long as a student has a robust understanding of all chapters, he can successfully clear the examination.

What are the Important Topics Covered in NCERT Solutions for Class 9 Maths?

All the topics such as construction, circles , surface area , volume , statistics, etc. that are covered in the NCERT solutions for class 9 maths are required for class 10th. Thus, skipping a topic is not advisable. In addition to this, all topics within the scope of mathematics are interlinked making it necessary to give equal attention without leaving out anything.

What are the Important Formulas in NCERT Class 9 Maths Solutions?

The questions in NCERT solutions class 9 maths are mostly based on the application of theorems and axioms to prove a certain point. Thus, as there are a fewer number of formulas it is not only easy but necessary to memorize them all.

What are the Benefits of Class 9 Maths NCERT Solutions for CBSE Students?

The class 9 maths NCERT solutions help students to finish their syllabus on time giving them enough room for revision. They also provide a quick overview of all the problems that students can use as a reference while skimming through the chapter.

Why Should I Practice NCERT Solutions for Class 9 Maths Regularly?

The practice of NCERT solutions for class 9 maths will help a student achieve the goal of perfection. It helps students get comfortable with the covered concepts. Thus, during an examination students can keep their cool and breeze through the paper without getting flustered.

How is Class 9 Maths NCERT Solutions Promoting Problem Solving in Students?

NCERT solutions for class 9 maths start by explaining the questions and then breaking the problem down to elucidate it in a better way. It teaches students to think of the why and how behind a sum. These solutions encourage students to use a similar approach enabling them to harness their problem-solving skills and computational mindset.

NCERT Solutions for Class 9 Maths

Ncert solutions for class 9 maths – free pdf.

All the solutions of Ncert maths class 9 are available here for free download. Maths NCERT is usually prescribed to all CBSE schools, though even some state board schools also follow them. Ncert solution for class 9 maths is very important as it is the foundation on which mathematics of higher grades will be based on. Unlike class 8 maths, the syllabus of Maths in class 9th is very vast and may feel a bit difficult. The concepts which you will study in class 9th is also important because of another reason as it also compromises the basic concepts you need in order to crack any competitive exam. Whether it is an Olympiad, JEE, NEET, NDA, RBI or any other government exam, you require strong class 9 th maths base.

Mathongo provides free PDF download Ncert solutions of Class 9 Maths. We provide you the best solutions of NCERT Class 9 online. All the mathematics solutions have been made with the aid of the best teachers, academicians and subject experts. NCERT solutions are very beneficial for students as many times questions come directly from NCERT textbooks itself. Students who use Ncert solutions for class 9 maths pdf are more prepared as the answers given in these free pdfs are crisp and well structured. All the answers are based on the guidelines of CBSE curriculum which will help the students to score good marks.

NCERT Class 9 Maths Chapterwise Solutions

• Chapter 1 – Number Systems
• Chapter 2 – Polynomials
• Chapter 3 – Coordinate Geometry
• Chapter 4 – Linear Equations in Two Variables
• Chapter 5 – Introduction to Euclids 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

Why Go for Mathongo’s NCERT Maths Solutions for Class 9

Mathongo provides NCERT class 9 maths solution at free of cost online and it’s easily accessible in the form of PDF. Each PDF constitutes of the chapter in which exercise-wise solutions are given. It is very easy for the students to locate any answer from the exercise. All the solutions are made with the help of the best teachers and academicians. The solutions are plain easy and can be understood by anyone. The approaches and the methods used to solve the questions are also given in step by step method so that students score well in the paper. For additional conceptual clarity, diagrams and formulas are also used.

Mathongo has provided the best solutions for class 9 maths Ncert textbooks. Students can refer to these solutions which will help them in solving the previous year question papers. These NCERT maths class 9solution will help the students to study more effectively and also present the answers in the most effective way to get the highest scores.

The back-end exercise questions given in NCERT books are very important for the class 9 finals. These exercises often test the conceptual clarity and the subject knowledge of the student. NCERT Solutions will help you to understand these concepts better. On the other hand, the students who have a problem in solving maths and require assistance and guidance can also refer to class 9 Ncert Maths Solutions to clarify the concepts of the complex question. Maths is all about practice. The more you practice, the better you will be. Ncert maths class 9 pdf download can help students to solve all their problems and also save their time as everything is in one place, one click away.

How to score 90℅ or above in class 9 maths?

Getting above 90% score is not difficult. Believe me. You just need to do these steps.

Step 1: Focus in Class

Step 2: Study what concept was taught in that day itself.

Step 3: Practice the questions of NCERT. Don’t leave any.

Step 4: Study from another reference book like RD Sharma for more conceptual clarity and further practice.

What are the best books for class 9 maths?

NCERT Maths is more than enough for all the concepts. But if you wish to score high marks and have a strong foundation, it is advisable to refer books like RD Sharma or RS Aggarwal.

How to improve maths in class 9?

In order to improve maths, you can do nothing apart from practice. Solve previous year question papers. Give mock tests. Analyze your mistakes and try to correct them by understanding why were you going wrong in the first place. Solve a variety of questions. Refer to different books, if necessary.

Share with friends:

NCERT Solutions for Class 9 Maths Free PDF Download

Ncert solutions for class 9 maths.

NCERT solutions for class 9 Maths is available to download for free from the links below. NCERT solutions are really helpful when it comes to a complicated subject like Mathematics. NCERT solutions for class 9 Maths will help you to understand and solve complex problems easily. It is time-saving and best study materials to follow for all the boards and especially CBSE boards.

NCERT solutions also help in cracking many competitive entrance exams like JEE Main, JEE Advanced, NEET, etc.

Class 9 Maths NCERT Solutions are available chapterwise on the app Toppr. Toppr app provides you a lot of free study materials, 1000+ hours of video lectures, mock tests, live doubt solving and more. You can signup or download Toppr app for Android or iOS .

Download NCERT solutions for all subjects of Class 9 here .

NCERT Solutions for Class 9 Maths Chapterwise

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 – Area 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

Class 9 Maths NCERT Solutions Chapterwise

Ncert solutions for class 9 maths chapter 1 number systems.

Rational numbers, Irrational numbers, Irrational numbers between two number are the topics covered under this chapter. We have solved more than 20 problems in this chapter. Download NCERT solutions for this chapter here .

NCERT Solutions for Class 9 Maths Chapter 2 Polynomials

In this chapter, you will learn more about polynomials, degree of polynomials, and theorem related to it. We have solved more than 70 problems in this chapter. Download NCERT Solutions for this chapter here .

NCERT Solutions for Class 9 Maths Chapter 3 Coordinate Geometry

In this chapter, we have covered Distance formula, section formula, and more about the area of triangles and quadrilaterals. Download NCERT solutions for this chapter here .

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

We covered Linear equations in one variable in the previous Class, now it is time to solve two variables in equations. We have solved more than 30 problems in this chapter. Download NCERT Solutions for this chapter here .

NCERT Solutions for Class 9 Maths Chapter 5 Introduction to Euclid’s Geometry

Euclid’s postulates, Axioms, Conjectures are the topics covered under this chapter. Download NCERT solutions for this chapter here .

NCERT Solutions for Class 9 Maths Chapter 6 Lines and Angles

In this chapter, you will learn about Geometry, Lines, and different types of angles. Geometry is one of the most important parts of Mathematics and NCERT solutions will help you understand it easily. Download NCERT Solutions for this chapter here .

NCERT Solutions for Class 9 Maths Chapter 7 Triangles

In this chapter, you will learn about the topics like properties of triangles, Pythagoras theorem, Basic proportionality theorem and more. This is one of the important chapters in CBSE Class 9 Maths. We have solved more than 50 solutions for this chapter. Download CBSE NCERT solutions for this chapter here .

NCERT Solutions for Class 9 Maths Chapter 8 Quadrilaterals

In this chapter, you will learn about Quadrilaterals and its properties and some theorems related to the quadrilateral. We have solved more than 50 solutions for this chapter. Download CBSE NCERT solutions for this chapter here .

NCERT Solutions for Class 9 Maths Chapter 9 Area of Parallelograms and Triangles

In this chapter, we will learn about calculating the area of triangles and parallelograms. Download NCERT solutions for this chapter here .

NCERT Solutions for Class 9 Maths Chapter 10 Circles

In this chapter, you will learn about the Arc of circle, tangents, cyclic quadrilateral and more. Download NCERT solutions for this chapter here .

NCERT Solutions for Class 9 Maths Chapter 11 Constructions

In this chapter, you will learn about the constructions of triangles, segments, tangent to a circle and more. Download NCERT solutions for this chapter here .

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

Heron’s formula will help in measuring the surface area of Triangles. We have solved more than 20 problems in this chapter. Download NCERT Solutions for this chapter here .

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

In this chapter, you will learn about the surface area and volumes of different shapes like Cuboid, cubes, cylinder, etc. This chapter will help you to understand how to measure the dimensions of different shapes. Download CBSE NCERT solutions for this chapter here .

NCERT Solutions for Class 9 Maths Chapter 14 Statistics

Graphs, Charts, Frequency Distribution, Mean-Median-Mode are the topics covered under this chapter. This chapter will also help you in understand some of the business mathematics concepts. Download NCERT Solutions for this chapter here .

NCERT Solutions for Class 9 Maths Chapter 15 Probability

Probability is a complicated concept and also one of the most important. Probability is a topic which will also help you in solving real-life problems, business mathematics, and also important for many competitive entrance exams. Download NCERT Solutions for this chapter here .

Download Toppr – Best Learning App for Class 5 to Class 12

On Toppr app we provide study materials, 1000+ hours of video lectures, mock test, live doubts solving, and more. Download Toppr app for Android and iOS and join our 7 Million+ students.

Solved Questions For You:

Question 1. State whether the following statements are true or false. Give reasons for your answers.

(i) Every natural number is a whole number. (ii) Every integer is a whole number. (iii) Every rational number is a whole number.

(i) True every natural is a whole number because natural number start from     1  and whole number start from  0 , so every natural number is a whole number.

Question 2. Write three numbers whose decimal expansions are non-terminating non-recurring.

Answer:  All irrational numbers have non-terminating and non-recurring decimal expression.

So, \(\sqrt{2}\), \(\sqrt{3}\), and \(\sqrt{5}\) will give such expressions.

Question 3.  Are the square roots of all positive integers irrational? If not, give an example of the square root of a number that is a rational number.

Answer:  No,

for example \(\sqrt{4}\) = 2 is a rational number.

Question 4. Is zero a rational number? Can you write it in the form \(\frac{p}{q}\) ​ , where  p  and  q  are integers and  q \(\neq\)  = 0 ?

We know that a rational number is a number which can be written in the form of \(\frac{p}{q}\) , where  q  is not equal to zero. 

Thus, yes,  zero is a rational number, as it can be written in the form of \(\frac{p}{q}\) .

Customize your course in 30 seconds

Which class are you in.

NCERT Solutions for Class 9

• NCERT Solutions for Class 9 History Chapter 3 Free PDF Download
• NCERT Solutions for Class 9 History Chapter 6 Free PDF Download
• NCERT Solutions for Class 9 Maths Chapter 15 Free PDF Download
• NCERT Solutions for Class 9 Maths Chapter 7 Free PDF Download
• NCERT Solutions for Class 9 Maths Chapter 14 Free PDF Download
• NCERT Solutions for Class 9 Maths Chapter 12 Free PDF Download
• NCERT Solutions for Class 9 Maths Chapter 1 Free PDF Download
• NCERT Solutions for Class 9 Maths Chapter 9 Free PDF Download
• NCERT Solutions for Class 9 Maths Chapter 4 Free PDF Download
• NCERT Solutions for Class 9 Maths Chapter 11 Free PDF Download

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

Download the App

FREE CBSE Online Coaching for Class 9 Maths. No Conditions

Extra questions for class 9 maths chapter 1, number systems | real numbers | rational & irrational numbers.

NCERT Class 9 Math / Number System Extra Questions

C hapter 1 of CBSE NCERT Class 9 Math covers number systems. Concepts covered in chapter 1 include rational numbers, irrational numbers, rationalizing irrational numbers by multiplying with their conjugates, decimal expansion of real numbers, operations on real numbers and laws of exponents or rules of indices. The extra questions given below include questions akin to HOTS (Higher Order Thinking Skills) questions and exemplar questions of NCERT.

Here is a quick recap of the key concepts that are covered in this chapter in the CBSE NCERT Class 9 Math text book.

What are rational numbers?

A number that can be written in the form \\frac{p}{q}\\) where p and q are integers and p ≠ 0 is a rational number.

Possibility 1 : If the decimal expansion of the number is terminating it is a rational number. Note: Integers are terminating decimals and are therefore, rational numbers.

Possibility 2 : If the decimal expansion of the number is non-terminating but is recurring , it is rational. Example \\frac{1}{3}\\) = 0.333.. is a non-terminating recurring decimal and is a rational number.

What are irrational numbers?

A number that CANNOT be written in the form \\frac{p}{q}\\) where p and q are integers and p ≠ 0 is an irrational number.

If the decimal expansion of the number is non-terminating AND non-recurring it is an irrational number. Example: \\sqrt{2}\\), π

How to Rationalize Irrational Numbers?

For an irrational number of the form a + √b, a - √b is its conjugate. And for an irrational number of the from a - √b, a + √b is its conjugate.

Important Laws of Exponents (Rules of Indices)

If a > 0 is a real number and m and n are rational numbers, the following laws of exponents hold good.

• a m × a n = a m + n Example .: 10 3 × 10 2 = 10 3 + 2 = 10 5
• (a m ) n = a mn Example : (10 3 ) 2 = 10 (3 \\times\\) 2) = 10 6
• \\frac{a^m}{a^n}\\) = a (m - n) Example : \\frac{10^3}{10^2}\\) = 10 (3 - 2) = 10
• a m b m = (ab) m Example : 2 2 × 5 2 = (2 × 5) 2 = 10 2

Extra Questions for Class 9 Maths - Number Systems

Prime Factorise & Rationalise Denominator: \\frac{14}{{\sqrt {108}} - {\sqrt {96}} + {\sqrt {192}} - {\sqrt {54}}}\\)

Rational numbers - Fractions: Find 5 rational numbers between \\frac{3}{4}) and \\frac{4}{5}).

Express as Fractions Express 1.363636... in the form \\frac{p}{q}), where p and q are integers and q ≠ 0.

Express in the form \\frac{p}{q}) Express 0.4323232… in the form \\frac{p}{q}), where p and q are integers and q ≠ 0.

Simplify the following (a) \({8 + \sqrt{5})}) \({8 - \sqrt{5})}) (b) \({10 + \sqrt{3})}) \({6 + \sqrt{2})}) (c) \{(\sqrt {3} + \sqrt {11})}^2) + \{(\sqrt {3} - \sqrt {11})}^2)

Rationalize the denominator: (a) \\frac{2}{\sqrt{3} - 1}) (b) \\frac{7}{\sqrt{12} - \sqrt{5}}) (c) \\frac{1}{8 + 3\sqrt{5}}) (d) \\frac{1}{4 + \sqrt{2} + \sqrt{5}})

Simplify and find the value of (a) \{(729)}^{\frac{1}{6}}) (b) \{(64)}^{\frac{2}{3}}) (c) \{(243)}^{\frac{6}{5}}) (d) \{(21)}^{\frac{3}{2}} \times {(21)}^{\frac{5}{2}}) (e) \\frac{{(81)}^{\frac{1}{3}}}{{(81)}^{\frac{1}{12}}})

Operation on real numbers & Algebraic identities If x = \\frac{3 - {\sqrt{13}}}{2}\\), what is the value of \x^2 + \frac{1}{x^2}\\)?

Rationalise & find value of cubic expression If x = \\frac{1}{8-\sqrt{60}}\\), what is the value of (x 3 - 5x 2 + 8x - 4) ?

Question 10

Rationalise the denominator \\frac{1}{9 + {\sqrt{5} + \sqrt{6}}}\\)

Free CBSE Online Coaching Class 9 Maths

Register in 2 easy steps and Start learning in 5 minutes!

★ Sign up for Free

Already have an Account?

★ Login to Continue

NCERT Solutions For Class 9 Math

• Number Systems
• Polynomials
• Coordinate Geometry
• Linear Equations
• Euclid's Geometry
• Lines and Angles
• Quadrilaterals
• Areas: Parallelograms & Triangles
• Construction
• Heron's Formula
• Surface Areas & Volumes

Copyrights © 2016 - 22 All Rights Reserved by Maxtute.com - An Ascent Education Initiative . Privacy Policy | Terms & Conditions

Phone: (91) 44 4500 8484 Mobile: (91) 93822 48484

WhatsApp: WhatsApp Now Email: [email protected]

Wizako GMAT Preparation

GMAT Online Course

GMAT Coaching in Chennai

GMAT Sample Questions

GMAT Preparation Online Videos

Wizako GRE Preparation

GRE Online Courses

GRE Coaching in Chennai

GRE Questions

GRE Preparation Videos

2IIM CAT Preparation

CAT Coaching Online

CAT Coaching in Chennai

CAT Questions

CAT Preparation Videos

Ascent TANCET Coaching

TANCET Classes Online

TANCET Coaching Centres in Chennai

TANCET Previous Year Question Papers

TANCET Questions

Intuitive Math learning

School Math Videos

2IIM | How to prepare for CAT?

Talk to our experts

1800-120-456-456

NCERT Solutions for Class 9 Maths Exercises

• NCERT Solutions
• Maths All Exercises

NCERT Solutions for Class 9 Maths Exercises - PDF Solutions

Class 9 Maths has a vivid CBSE syllabus covering excellent topics in Mathematics. The CBSE board has formulated the syllabus for the development of respective mathematical concepts and skills among the students. To prepare these chapters, refer to the NCERT Class 9 Maths All Exercises Solutions developed by the subject experts of Vedantu and learn how the fundamental questions can be solved accurately.

Learn the best approaches to solve such problems and score more in the exams.

Vedantu is a platform that provides free NCERT Solution and other study materials for students. Students can register and get access to the best and reliable source of study materials specially made by master teachers at Vedantu. You can download NCERT Solutions Class 9 Maths to help you to revise the complete Syllabus and score more marks in your examinations. Subjects like Science, Maths, English will become easy to study if you have access to NCERT Solution for Class 9 Science , Maths solutions, and solutions of other subjects that are available on Vedantu only.

NCERT Solutions for Class 9 Maths - Chapter-wise List

Given below are the chapter-wise NCERT Solutions for Class 9 Maths . These solutions are provided by the Maths experts at Vedantu in a detailed manner. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.

NCERT Solutions for Class 9 Maths Chapter 1

NCERT Solutions for Class 9 Maths Chapter 2

Ncert solutions for class 9 maths chapter 3, ncert solutions for class 9 maths chapter 4, ncert solutions for class 9 maths chapter 5, ncert solutions for class 9 maths chapter 6, ncert solutions for class 9 maths chapter 7, ncert solutions for class 9 maths chapter 8, ncert solutions for class 9 maths chapter 9, ncert solutions for class 9 maths chapter 10, ncert solutions for class 9 maths chapter 11, ncert solutions for class 9 maths chapter 12, ncert solutions for class 9 maths chapter 13, ncert solutions for class 9 maths chapter 14, ncert solutions for class 9 maths chapter 15.

NCERT Solutions for Class 9 Maths All Exercises

What could be better if you get the simpler and readymade solutions of your Class 9 NCERT textbook exercises ? Moreover, all these are created by an experienced subject matter expert. Can you imagine how beneficial these could be? Sounds amazing, right! You must opt for these NCERT solutions for Class 9 Maths All Exercises right away. You can download NCERT solutions Class 9 Maths All Exercises from Vedantu official website (vedantu.com) by registering yourself with your phone number/ email address. You can also access the same study materials from Vedantu app as well. In that case, you need to download the Vedantu app first from Google play store.

You will get Class 9 Maths All Exercises NCERT solutions written in a simple and lucid manner. Solve all the problems/questions given in the exercises and evaluate your performance with these 100% accurate solutions so that you can learn how to write answers to the questions from any perspective during the final exam. Each of the answers in the Maths All Exercises NCERT solutions Class 9 is student-friendly and customized by the experts.

These NCERT solutions Class 9 Maths All Exercises contain step-by-step answers to all the questions from the exercise which are considered as an invaluable aid to the students when it comes to regular study, exam preparation or doing homework. Class 9 Maths All Exercises NCERT solutions will clear all your doubts in very less time. Hence your confidence will be boosted. By practising the questions from these books, you will be able to improve your time management skills. That will help you in solving all the questions in the stipulated time frame during the final exam.

NCERT Solutions for Class 9 Maths All Exercises are designed as per the latest CBSE curriculum and guidelines. Vedantu’s study materials are updated regularly as per the latest changes. Hence students of Class 9 who are referring to these materials will be able to score the best marks in the final exam. Once you start using these materials, the preparation for Class 9 exam and scoring the highest percentile amongst your peers will seem like a cakewalk at the end of the day.

NCERT Solutions for Class 9 Maths Chapter 1 Number System

6 exercises are included in the NCERT Solutions for Class 9 Maths Chapter 1 which are Exercise 1.1 to 1.6. Most of the questions are application based and a few are memory-based questions to test students’ application skills and cognizance.

NCERT Solutions for Class 9 Maths Chapter 2 Polynomials

Chapter 2 of NCERT Solutions for Class 9 Maths includes 5 exercises. The majority of questions are practical and application-based which allows you to improve the understanding of the chapter.

Class 9 Maths NCERT Solutions Chapter 3 Coordinate Geometry

With 3 exercises comprising both long and short questions, the exercises of NCERT Class 9 Solutions Maths for Chapter 3 are designed to test your application skills as well as cognizance.

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

NCERT 9th class Maths book solutions include 4 exercises with 16 questions in total. This chapter includes application-based questions to test your understanding of the chapter.

NCERT Solutions for Class 9 Maths Chapter 5 Introduction to Euclid's Geometry

Chapter 5 of Class 9 Maths NCERT Solutions has 2 exercises. The questions are based on analysis to test your analytical skills and cognizance.

NCERT Solutions for Class 9 Maths Chapter 6 Lines and Angles

NCERT Solution Class 9 Maths of Chapter 6 includes 3 exercises.

NCERT Solutions for Class 9 Maths Chapter 7 Triangles

NCERT Solution Class 9 Maths of Chapter 7 includes 5 exercises . These questions are designed to test your cognizance.

NCERT Solutions for Class 9 Maths Chapter 8 Quadrilaterals

NCERT Solution Class 9 Maths of Chapter 8 includes 2 exercises. These questions are based on your application skills and analysis skills.

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

NCERT Solution Class 9 Maths of Chapter 9 includes 4 questions to test your application skills, numerical skills and memory skills.

NCERT Solutions for Class 9 Maths Chapter 10 Circles

9th class Maths book solutions Chapter 10 includes 6 exercises and solutions to all 35 questions given in your NCERT Textbook. These questions are based on your numerical abilities, application skills, and memory skills.

NCERT Solutions for Class 9 Maths Chapter 11 Constructions

Ncert solutions for class 9 maths chapter 12 heron’s formula.

NCERT Solution Class 9 Maths of Chapter 12 includes 2 exercises designed on your ability to decipher and apply the formula.

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

NCERT Solution Class 9 Maths of Chapter 13 includes 9 exercises and these questions will test your understanding ability and memory skills (required to retain the different formulae).

NCERT Solutions for Class 9 Maths Chapter 14 Statistics

NCERT Solution Class 9 Maths of Chapter 14 contains 4 exercises. The questions judge your comprehensive ability and analytical skills.

NCERT Solutions Class 9 Maths Chapter 15 Probability

NCERT Solution Class 9 Maths Chapter 15 comprises just a single exercise that will assess your comprehensive ability. To prepare for the exams, make sure to read the chapter thoroughly and practise all the exercise questions. This will help you to score better.

CBSE Class 9 Maths Chapter-Wise Marks Weightage 

Internal assessment for cbse class 9 maths, importance of cbse chapter wise list of class 9 maths all exercises.

The experts have formulated the exercise solutions following the latest CBSE syllabus of Class 9 Maths so that students can find them conveniently here. The 9th Maths All Exercises Book Answers for all the exercises have been simplified so that students can easily grab hold of the concepts and use them to develop their answering skills.

The Maths chapters included in this syllabus are all crucial for the conceptual development of the students. They will need these fundamental concepts and skills in the future to study advanced Mathematics in higher classes. Hence, the foundation needs to be strong enough to carry these skills.

This is where the solutions can act as the right guide for the students to develop such skills in a profound way.

Download NCERT Maths All Exercises Book Class 9 Solutions PDF

Perform the NCERT Maths All Exercises Book Class 9 Solutions PDF free download to complete your study material. Find out how the experts have skillfully solved all the questions utilising mathematical principles. Develop your skills accordingly and learn how to ace the Class 9 Maths exams .

Important Related Links for CBSE Class 9 Maths

Important Questions for CBSE Class 9 Math

RS Aggarwal Class 9 Solutions for Math book

NCERT Solutions for Class 9 Maths

CBSE Class 9 Maths Revision Notes

FAQs on NCERT Solutions for Class 9 Maths Exercises

1. How can I prepare all the Class 9 Maths chapters?

Complete preparing a chapter by solving its exercises. Compare your answers to the solutions to find the preparation gaps to fix them. Proceed to the next chapter. This is how you can complete the whole syllabus.

2. How many chapters are there in Class 9 Maths?

There are 15 chapters in the CBSE Class 9 Maths syllabus.

3. What is the best way to remember the Class 9 Maths formulas?

The best way to remember the Class 9 Maths formulas is to prepare and apply them. The more your practice the easier you can remember them all.

4. How can I revise the Class 9 Maths exercises before an exam?

Follow the solutions and revise the answers before an exam and reduce your preparation time.

5. Can I use the exercise solutions for doubt resolution?

The answers in the solutions can be used to resolve your doubts related to the exercise problems. All the answers are accurate and follow the latest CBSE guidelines .

NCERT Solutions for Class 9

Cbse study materials for class 9, cbse study materials.

• CBSE Maths Important Questions
• Class 9 Maths
• Chapter 8: Quadrilaterals

Important Questions CBSE Class 9 Maths Chapter 8 Quadrilaterals

Important Questions Class 9 Maths Chapter 8 Quadrilaterals are provided here that cover different question variations which will help the students to get thoroughly acquainted with all the concepts. These CBSE class 9 questions for quadrilaterals include several short answers, long answer and HOTS type questions which will let the students develop their problem-solving skills.

These CBSE Class 9 Maths Chapter 8 Important Questions on Quadrilateral help students to prepare most effectively for the final exams and face it most confidently. Solving these important questions is the best practise for students.

Also Check:

• Important 2 Marks Questions for CBSE 9th Maths
• Important 3 Marks Questions for CBSE 9th Maths
• Important 4 Marks Questions for CBSE 9th Maths

Important Questions Class 9 Maths Chapter 8 Quadrilaterals with Solutions

Go through the following important questions for class 9 Maths Chapter 8 Quadrilateral to understand the concepts quickly and it helps to solve the problems having similar patterns.

1. What is a quadrilateral? Mention 6 types of quadrilaterals.

A quadrilateral is a 4 sided polygon having a closed shape. It is a 2-dimensional shape.

The 6 types of quadrilaterals include:

• Parallelogram

2. The diagonals of which quadrilateral are equal and bisect each other at 90°?

Square. The diagonals of a square are equal and bisect each other at 90°.

3. Identify the type of quadrilaterals:

(i) The quadrilateral formed by joining the midpoints of consecutive sides of a quadrilateral whose diagonals are perpendicular.

(ii) The quadrilateral formed by joining the midpoints of consecutive sides of a quadrilateral whose diagonals are congruent.

(i) The quadrilateral formed by joining the midpoints of consecutive sides of a quadrilateral whose diagonals are perpendicular is a rectangle .

(ii) The quadrilateral formed by joining the midpoints of consecutive sides of a quadrilateral whose diagonals are congruent is a rhombus .

4. Find all the angles of a parallelogram if one angle is 80°.

For a parallelogram ABCD, opposite angles are equal.

So, the angles opposite to the given 80° angle will also be 80°.

It is also known that the sum of angles of any quadrilateral = 360°.

So, if ∠A = ∠C = 80° then,

∠A + ∠B + ∠C + ∠D = 360°

Also, ∠B = ∠D

80° + ∠B + 80° + ∠D = 360°

Or, ∠B +∠ D = 200°

Hence, ∠B = ∠D = 100°

Now, all angles of the quadrilateral are found which are:

5. In a rectangle, one diagonal is inclined to one of its sides at 25°. Measure the acute angle between the two diagonals.

Let ABCD be a rectangle where AC and BD are the two diagonals which are intersecting at point O.

Now, assume ∠BDC = 25° (given)

Now, ∠BDA = 90° – 25° = 65°

Also, ∠DAC = ∠BDA, (as diagonals of a rectangle divide the rectangle into two congruent right triangles)

So, ∠BOA = the acute angle between the two diagonals = 180° – 65° – 65° = 50°

6. Is it possible to draw a quadrilateral whose all angles are obtuse angles?

It is known that the sum of angles of a quadrilateral is always 360°. To have all angles as obtuse, the angles of the quadrilateral will be greater than 360°. So, it is not possible to draw a quadrilateral whose all angles are obtuse angles.

7. Prove that the angle bisectors of a parallelogram form a rectangle. 

LMNO is a parallelogram in which bisectors of the angles L, M, N, and O intersect at P, Q, R and S to form the quadrilateral PQRS. LM || NO (opposite sides of parallelogram LMNO) L + M = 180 (sum of consecutive interior angles is 180o) MLS + LMS = 90 In LMS, MLS + LMS + LSM = 180 90 + LSM = 180 LSM = 90 RSP = 90 (vertically opposite angles) SRQ = 90, RQP = 90 and SPQ = 90 Therefore, PQRS is a rectangle.

8. In a trapezium ABCD, AB ∥ CD. Calculate ∠ C and ∠ D if ∠ A = 55° and ∠ B = 70°

In a trapezium ABCD, ∠A + ∠D = 180° and ∠B + ∠C = 180°

So, 55° + ∠D = 180°

Or, ∠D = 125°

70° + ∠C = 180°

Or, ∠C = 110°

9. Calculate all the angles of a parallelogram if one of its angles is twice its adjacent angle.

Let the angle of the parallelogram given in the question statement be “x”.

Now, its adjacent angle will be 2x.

It is known that the opposite angles of a parallelogram are equal.

So, all the angles of a parallelogram will be x, 2x, x, and 2x

As the sum of interior angles of a parallelogram = 360°,

x + 2x + x + 2x = 360°

Or, x = 60°

Thus, all the angles will be 60°, 120°, 60°, and 120°.

10. Calculate all the angles of a quadrilateral if they are in the ratio 2:5:4:1.

As the angles are in the ratio 2:5:4:1, they can be written as-

2x, 5x, 4x, and x

Now, as the sum of the angles of a quadrilateral is 360°,

2x + 5x + 4x + x = 360°

Or, x = 30°

Now, all the angles will be,

2x =2 × 30° = 60°

5x = 5 × 30° = 150°

4x = 4 × 30° = 120°, and

Important Question Class 9 Maths Chapter 8 Quadrilaterals for Practice

Solve the following important questions for class 9 Maths chapter 8 quadrilaterals to score good marks.

• The angles of a quadrilateral are in the ratio of 3: 5: 9: 13. Determine all the angles of a quadrilateral.
• A quadrilateral is a _____, if its opposite sides are equal.  (a)  Trapezium (b)  Kite (c)  Parallelogram (d)  Cyclic quadrilateral.
• If one angle of a parallelogram is 30° less than twice the smallest angle, then determine the measurement of each angle.
• Prove that the diagonal of a parallelogram divides it into two congruent triangles.
• ABCD is a rhombus with ∠ABC = 50°.  Determine ∠ACD.
• ABC is a triangle. D, E, and F are the midpoints of AB, BC and CA respectively. Show that by joining these midpoints D, E and F,  a triangle ABC is divided into four congruent triangles.
• ABCD is a rhombus with ∠ABC = 40°. The measure of ∠ACD is ____. (a)  20° (b)  40° (c)  70° (d)  90°
• ABCD is a quadrilateral in which P, Q, R, S are the midpoints of the sides AB, BC, CD and DA respectively. AC is the diagonal. Prove that: (a)  PQRS is a parallelogram (b)  PQ = SR (c)  SR || AC and SR = ½ AC.
• Show that the diagonals of a rectangle are equal in length.
• Prove that the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.

More Topics Related to Class 8 Quadrilaterals

Stay tuned with BYJU’S – The Learning App and download the app to get all class-wise important questions with solutions and learn all Maths-related topics quickly by watching videos.

Leave a Comment Cancel reply

Your Mobile number and Email id will not be published. Required fields are marked *

Request OTP on Voice Call

Post My Comment

Register with BYJU'S & Download Free PDFs

Register with byju's & watch live videos.