NCERT Solutions for Class 9 Maths PDF Download
Browse all 9th NCERT Maths Solutions from your mobile or desktop and gain more marks in your exams. You can also go through the Chapterwise Important Questions for Class 9 Maths which will help you in extra practice and exams. This consists of 1 mark Questions, 2 Mark Numericals Questions, 3 Marks Numerical Questions, 4 Marks Questions, Word Problems, and previous year questions (VSAQ, SAQ, LAQ, and Value-Based Questions) from all chapters in class 9 maths designed according to CBSE Class 9 Maths Syllabus are laid in a sequential manner will help in scoring more marks in your Board Examinations.
This chapter is an extension of the number line you have studied in the previous standards. You will also get know how to place various types of numbers on the number line in this chapter. A total of 6 exercises in this chapter guides you through the representation of terminating or non terminating of the recurring decimals on the number line. Along with the rational numbers, you will also learn where to put the square roots of 2 and 3 on the number line. There are also laws of rational exponents and Integral powers taught in this chapter.
This chapter guides you through algebraic expressions called polynomial and various terminologies related to it. There is plenty to learn in this chapter about the definition and examples of polynomials, coefficient, degrees, and terms in a polynomial. Different types of polynomials like quadratic polynomials, linear constant, cubic polynomials, factor theorems, factorization theorem are taught in this chapter.
A total of 3 exercises in this chapter will help you understand coordinate geometry in detail. Along with there are concepts like concepts of a Cartesian plane, terms, and various terms associated with the coordinate plane are learned in this chapter. You will also learn about plotting a point in the XY plane and naming process of this point.
This chapter will introduce to a new equation, ax + by + c = 0 in two variables. The questions in this chapter will be related to proving that a linear number has infinite solutions, using ba graph to plot linear equation, and justifying any point on a line. A total of 4 exercises are there for your practice and understanding.
The chapter begins with the introduction of Indian geometry as it has some base in Euclid’s geometry. The Introduction of Euclid’s geometry in this chapter helps you with a process of defining geometrical terms and shapes. There are a total of 2 exercises where you will dwell into the relationship between theorems, postulates, and axioms.
This chapter in the NCERT textbook also has 2 exercises in it. There are various theorems on angles and lines in this chapter that can be asked in for proof. The first theorem which will be asked for proof is “If the two lines are intersecting each other, then the vertically opposite angles formed will be equal”. Also, the second proof that is asked is, “The sum of all the angles formed in a triangle is 180°”. There are other theorems also given, but these are based on only these two theorems.
The contents in this chapter will help in understanding the congruence of triangles along with the rules of congruence. This chapter also has two theorems in it and a total of 5 exercises for students to practice. These two theorems are given as proof while the other is used in the problems or applications. Besides this, there are many properties of inequalities and triangles in this chapter for students to learn.
This chapter is very interesting for students to learn and there are only 2 exercises in it. The questions in this chapter are related to the properties related to quadrilateral and their combinations with the triangles.
This chapter is important to understand the meaning of the area with this, the areas of the triangle, parallelogram, and their combinations are asked in this chapter along with their proofs. There are also examples of the an which are used as a proof of theorems in this chapter.
In this chapter, you will get to learn some interesting topics like equal chords and their distance from the center, the chord of a point and angle subtended by it, angles which are subtended by an arc of a circle, and cyclic quadrilaterals. There are also theorems in this chapter which are helpful to prove questions based on quadrilaterals, triangles, and circles.
This chapter will help you learn two different categories of construction. One of them is the construction of a triangle along with its base, difference or sum of the remaining two sides, and one base angle with base angle and parameters are given. The other is the construction of bisectors for the line segments and measuring angles that include 45/60/90, etc.
This chapter joins the long list NCERT chapters that also has 2 exercises in it. In this chapter, you will be learning the concepts that are an extension of concepts related to the area of a triangle. Furthermore, you will get to learn about finding the area of triangles, quadrilaterals, and various types of polygons. Along with the, is there is also knowledge of formula for the plane figures given in the chapter.
Every one of you has already studied mensuration in previous standards. Thus, you must be aware of surface areas and this chapter is on that. Along with this, this chapter also has a volume of cubes, cylinders, cuboids, cones, hemispheres, and spheres. Also, in this chapter, you will get to know about the conversion of one figure into another, and comparing volumes of two figures.
In this chapter, you will get the knowledge about the descriptive statistics and the collection of data based on different aspects of life. This is useful for interpretation and stating the inferences from the data. This chapter gives the basic knowledge of the collection of data as the data is available in raw form. As you move forward and study 5 exercises you will learn about presenting data in tabular form by keeping them together in regular intervals, polygon, histogram, or bar graph drawing. You will also get to the topics like mean, median, and mode and finding the central tendency with the raw data.
Probability in this book is based on the observation approach or finding the frequency. Questions in this chapter are very intuitive as they are based on daily life or day to day situations. For example, incidents like throwing dice, coin tossing, the probability for a deck of cards and simple events. If you are curious this chapter can be very interesting for you to learn and understand.
There may be a few times where you feel you are stuck and not getting the desired solutions. This is where we can you with NCERT solutions for class 9 maths. You can use this article as a reference for all the chapters in the NCERT book.
1. How do I study for the CBSE Class 9 Maths Solutions?
Practice the CBSE 9th Maths Solutions and try covering all the topics and questions carefully.
2. How could I learn Class 9 maths in an efficient and fast way?
The best way to learn fast is to solve NCERT. NCERT has few questions but has great importance in papers. If you can solve the whole NCERT with examples, you can easily score well. If you ample time try referring to RD Sharma too as it’s the best book.
3. Can I get solved math questions for the Class 9 CBSE?
Yes, you can get solved math questions for Class 9 CBSE Exams from our page. Access the direct links available on our page and download them for free of cost.
4. Which is the best maths guide for 9th CBSE?
NCERT Solutions for Class 9 Maths will help you aid your preparation. Get a good grip over the subject by practicing more and more NCERT Solutions prevailing on our page.
5. How can I download the NCERT Solution Book for the CBSE Class 9 Maths?
Aspirants can download the CBSE Class 9 Maths NCERT Solutions by tapping on the direct links available. Lay a stronger foundation of the concepts by referring to the NCERT Solutions.
6. How long should a student of Class 9 practice math?
It’s not about the time limit. Try practicing as much as you can and revise the complete syllabus of Class 9 Maths for the exams to score well.
Now that you are provided all the necessary information regarding NCERT Solutions for class 9 Maths and we hope this detailed article on Class 9 Maths NCERT Solutions is helpful. If you have any doubt regarding this article or NCERT Class 9 Maths Solutions, leave your comments in the comment section below and we will get back to you as soon as possible.
by Editorial Team · Published December 13, 2021 · Updated June 13, 2023
Are you in need of Grade 9 Past Papers & Memos – All Subjects ? It can be a challenge to look for the latest question papers and their respective memorandums, let alone study Guides.
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NCERT Solutions for Class 9 Maths in Hindi and English Medium are given here along with class 9th Maths current syllabus. 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. 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
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.
Class: 9 | Mathematics |
Number of Chapters: | 12 (Twelve) |
Content: | NCERT Solutions and Extra Questions |
Content Mode: | Text, PDF and Videos Format |
Academic Session: | Year 2024-25 |
Medium: | Hindi and English Medium |
Chapters | Marks |
---|---|
1. Number Systems | 10 |
2. Polynomials and 4. Linear Equations in Two Variables | 20 |
3. Coordinate Geometry | 04 |
5. Introduction to Euclid’s Geometry, 6. Lines and Angles, 7. Triangles, 8. Quadrilaterals and 9. Circles | 27 |
10. Heron’s Formula and 11. Surface Areas and Volumes | 13 |
12. Statistics | 06 |
Pen Paper Test and Assessment | 10 |
Portfolio | 05 |
Lab Practical | 05 |
Total | 100 |
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.
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.
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 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.)
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.
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 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.
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 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.
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.
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.
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.
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 , 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.
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.
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
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
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
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.
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.
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 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..
According to new syllabus, there are a total of 12 chapters present in the NCERT Class 9 Maths.
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.
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.
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.
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.
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Chapter 1: number systems.
Representation of terminating/non-terminating recurring decimals on the number line (and successive magnification method). Presentation of square roots of 2, 3 and other non-rational numbers. Rationalization of real numbers, laws of integral powers and rational exponents with positive real bases in Number Systems .
Examples and definition of a polynomial, coefficient, degrees, zeroes and terms of a polynomial. Constant, linear, quadratic and cubic polynomials, monomials, binomials, trinomials. Factors and multiples, Remainder and factor theorems, factorization of a polynomials using factor theorem.
In this chapter Coordinate Geometry we will study the concept of cartesian plane, coordinates of a point in this xy – plane, name, terms, notations and other terms associated with the coordinate plane. Abscissa and ordinate of a points. Plotting a point in xy – plane and naming it.
This chapter provides the introduction to the equation in two variables of the type ax + by + c = 0. Proving a linear equation has infinite number of solutions. Plotting a linear equation on graph and justification of any point on line. Problems based on Linear Equations in Two Variables in daily life.
Euclid’s geometry and history of Indian geometry. Introduction to Euclid’s Geometry provides a way of defining the common geometrical shapes and terms. Euclid’s five postulates and redefining (equivalent versions) the fifth postulates. Relationship between axiom, postulates and theorems.
There are two theorems in Lines and Angles chapter which may be asked for proof. First is “If two lines intersect, vertically opposite angles are equal” and second is “The sum of the angles of a triangle is 180.”. Rest theorems are given for motivations and questions will be asked on the basis of all these theorems (Motivate/Prove).
In this chapter Triangles , two theorems (“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)” and “The angles opposite to equal sides of a triangle are equal.”) are given for proof and the rest will be asked in the form of applications/problems.
The chapter Quadrilaterals contains only one theorem( “The diagonal divides a parallelogram into two congruent triangles”) for proof. Other will be asked in the form of application and conceptual questions. Questions are on the basis of properties of quadrilaterals and combinations of it with triangles.
The combinations of areas of parallelograms and triangles are given to prove in most of the question. Proof and questions based on “Parallelograms on the same base and between the same parallels have the same area” will be asked. Example of median may be used as theorem in most of the questions.
“Equal chords of a circle subtend equal angles at the center” and “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” are given for proof in Circles . The other theorems are important for solving questions based on triangle, quadrilateral and circles.
There are two categories of constructions . One is Construction of bisectors of line segments and angles of measure 60, 90, 45 etc. The other is construction of a triangle given its base, sum/difference of the other two sides and one base angle & given perimeter and base angles.
Use of Heron’s formula to find the area of triangles, quadrilaterals (dividing it into two triangles) and other polygons. Knowledge of formulae of plane figures will also help in doing questions.
Students are familiar with surface areas and volumes as they have already studies mensuration in earlier classes. This chapter also contains problems based on surface areas and volumes of cube, cuboids, cylinders, cones, spheres and hemispheres. Conversion of one figure into the other comparing volumes is also given as an application of mensuration.
Introduction to statistics includes the presentation of data collected in raw form. Presentation of data in tabular form by grouping them in proper intervals, drawing a bar graph, histogram or polygon. Finding the measure of central tendency mean, mode and median of raw data.
Probability based on observation or frequency approach. Questions based on real life or day to day incidents. Toss of a coin, throwing a dice, based on deck of cards, etc. questions based on simple events.
Class 10 Maths Solutions Chapter 1 Class 10 Maths Solutions Chapter 2 Class 10 Maths Solutions Chapter 3 Class 10 Maths Solutions Chapter 4 Class 10 Maths Solutions Chapter 5
Class 10 Maths Solutions Chapter 6 Class 10 Maths Solutions Chapter 7 Class 10 Maths Solutions Chapter 8 Class 10 Maths Solutions Chapter 9 Class 10 Maths Solutions Chapter 10
Class 10 Maths Solutions Chapter 11 Class 10 Maths Solutions Chapter 12 Class 10 Maths Solutions Chapter 13 Class 10 Maths Solutions Chapter 14 Class 10 Maths Solutions Chapter 15
Class 9 Maths Solutions Chapter 1 Class 9 Maths Solutions Chapter 2 Class 9 Maths Solutions Chapter 3 Class 9 Maths Solutions Chapter 4 Class 9 Maths Solutions Chapter 5
Class 9 Maths Solutions Chapter 6 Class 9 Maths Solutions Chapter 7 Class 9 Maths Solutions Chapter 8 Class 9 Maths Solutions Chapter 9 Class 9 Maths Solutions Chapter 10
Class 9 Maths Solutions Chapter 11 Class 9 Maths Solutions Chapter 12 Class 9 Maths Solutions Chapter 13 Class 9 Maths Solutions Chapter 14 Class 9 Maths Solutions Chapter 15
NCERT Solutions for Class 9 Maths Chapter 1 Number Systems are provided here. Our NCERT Maths solutions contain all the questions of the NCERT textbook that are solved and explained beautifully. Here you will get complete NCERT Solutions for Class 9 Maths Chapter 1 all exercises Exercise in one place. These solutions are prepared by the subject experts and as per the latest NCERT syllabus and guidelines. CBSE Class 9 Students who wish to score good marks in the maths exam must practice these questions regularly.
Below we have provided the solutions of each exercise of the chapter. Go through the links to access the solutions of exercises you want. You should also check out our NCERT Class 9 Solutions for other subjects to score good marks in the exams.
Below we have listed the topics that have been discussed in this chapter. As Number System is one of the important topics in Maths, it has a weightage of 6 marks in class 9 Maths exams.
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9th Maths Assignment Answers 2021
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Ncert solutions for class 9 maths – free pdf updated for 2023-24 session.
NCERT Solutions for Class 9 Maths includes solutions to all the questions given in the NCERT textbook for Class 9. The students can download PDFs of chapter-wise solutions to these problems from the links provided below on this page. These NCERT Solutions for Class 9 cover all the topics included in the NCERT textbook, like Number System, Coordinate Geometry, Polynomials, Euclid’s Geometry, Quadrilaterals, Triangles, Circles, Constructions, Surface Areas and Volumes, Statistics, Probability, etc.
With the help of these Solutions of NCERT Books for Class 9 Maths , students can practise all types of questions from the chapters. The CBSE Class 9 Maths Solutions have been designed by our experts in a well-structured format to provide several possible methods of answering the problems and ensure a proper understanding of concepts. The students are suggested to practise all these solutions thoroughly for their exams. It will also help them in building a foundation for higher-level classes.
The following chapters have been removed from the NCERT Class 9 Maths textbook 2023-24.
Along with NCERT Solutions , students are also provided with other online learning materials available at BYJU’S, such as notes, books, question papers, exemplar problems, worksheets etc. These materials are designed with respect to the CBSE syllabus and NCERT curriculum. Students are also advised to practise CBSE Class 9 Sample Papers to get an idea of the question pattern in the final exam.
15 chapters are present in the NCERT Solutions for Class 9 Maths . These chapters given in the NCERT Class 9 Maths lay a foundation for the chapters present in Class 10. The PDFs given at BYJU’S are accessible to everyone and can be downloaded by the students for free.
Students having trouble solving tough Math problems can refer to these CBSE Maths Class 9 Solutions of NCERT for better guidance and for quick review. Solving these exercises in each chapter will ensure positive results.
This chapter discusses different topics, including rational numbers and irrational numbers. Students will also be learning the extended version of the number line and how to represent numbers (integers, rational and irrational) on it. A total of 6 exercises are present in this chapter that contains the problems based on all the topics asked in the chapter. This chapter also teaches students the representation of terminating/non-terminating recurring decimals (and successive magnification method) as well as the presentation of square roots of 2, 3 and other non-rational numbers on the number line. The chapter also deals with the laws of integral powers and rational exponents with positive real bases in the Number System.
Review of representation of natural numbers, integers, and rational numbers on the number line. Representation of terminating/non-terminating recurring decimals on the number line through successive magnification. Rational numbers as recurring/terminating decimals.
Examples of nonrecurring/non-terminating decimals such as √2, √3, √5 etc. 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, every point on the number line represents a unique real number.
Existence of √x for a given positive real number x (visual proof to be emphasised). Definition of n th root of a real number.
Recall of laws of exponents with integral powers. Rational exponents with positive real bases (to be done by particular cases, allowing the learner to arrive at the general laws).
Rationalisation (with precise meaning) of real numbers of the type (and their combinations) \(\begin{array}{l}\frac{1}{a+b\sqrt{x}}\: and\: \frac{1}{\sqrt{x}+\sqrt{\sqrt{y}}}\end{array} \) where x and y are natural numbers, and a and b are integers.
Important Formulas –
Operations on Real Numbers
√(a/b) = √a/√b
√ab = √a √b
(√a + √b) (√a – √b) = a – b
(a + √b) (a – √b) = a 2 – b
(√a + √b) (√c + √d) = √ac + √ad + √bc + √bd
(√a + √b) 2 = a + 2√ab + b
Laws of Exponents for Real Numbers
a m . a n = a m + n
(a m ) n = a mn
a m /a n = a m – n , m > n
a m b m = (ab) m
Class 9 Maths NCERT Solutions Chapter 1 Exercises |
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☞ – 4 Questions (4 short answers) ☞ – 4 Questions (4 short answers) ☞ – 9 Questions (8 short answers, 1 long answer) ☞ – 2 Questions (2 long answers) ☞ – 5 Questions (4 short answers, 1 long answer) ☞ – 3 Questions (3 short answers) |
Also, access the following resources for Class 9 Chapter 1 Number System, at BYJU’S:
We just saw all the solutions to the exercises given in the NCERT math textbook for class 9 for chapter 1 – Number System. Do you want to learn this and all other math concepts in a fun way, with engaging videos? BYJU’S The Learning App has you covered.
BYJU’S The Learning App for grade 9 math contains:
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This chapter discusses a particular type of algebraic expression called polynomial and the terminology related to it. Polynomial is an expression that consists of variables and coefficients involving the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. The chapter also deals with the Remainder Theorem and the Factor Theorem with the uses of these theorems in the factorisation of polynomials. Students will be taught several examples as well as the definition of different terms like polynomials, degrees, coefficients, zeros and terms of a polynomial. A total of 5 exercises are present in this chapter, which includes problems related to all the topics mentioned in the chapter.
Definition of a polynomial in one variable, its coefficients, with examples and counter examples, its terms, zero polynomial. Degree of a polynomial. Constant, linear, quadratic, cubic polynomials; monomials, binomials, trinomials. Factors and multiples. Zeros/roots of a polynomial/equation. State and motivate the Remainder Theorem with examples and analogy to integers. Statement and proof of the Factor Theorem. Factorisation of ax 2 + bx + c, a ≠ 0 where a, b, c are real numbers, and of cubic polynomials using the Factor Theorem.
Recall algebraic expressions and identities. Further identities of the type:
(x + y + z) 2 = x 2 + y 2 + z 2 + 2xy + 2yz + 2zx
(x ± y) 3 = x 3 ± y 3 ± 3xy (x ± y)
x 3 + y 3 + z 3 – 3xyz = (x + y + z) (x 2 + y 2 + z 2 – xy – yz – zx)
and their use in the factorisation of polynomials. Simple expressions are reducible to these polynomials.
Important Formulas –
(x + y) 2 = x 2 + 2xy + y 2
(x – y) 2 = x 2 – 2xy + y 2
x 2 – y 2 = (x + y) (x – y)
(x + y + z) 2 = x 2 + y 2 + z 2 + 2xy + 2yz + 2zx
(x + y) 3 = x 3 + y 3 + 3xy(x + y)
(x – y) 3 = x 3 – y 3 – 3xy(x – y)
x 3 + y 3 + z 3 – 3xyz = (x + y + z) (x 2 + y 2 + z 2 – xy – yz – zx)
Dividend = (Divisor × Quotient) + Remainder
Remainder Theorem
Let p(x) be any polynomial of degree greater than or equal to one, and let a be any real number. If p(x) is divided by the linear polynomial x – a, then the remainder is p(a).
Factor Theorem
If p(x) is a polynomial of degree n > 1 and a is any real number, then (i) x – a is a factor of p(x), if p(a) = 0, and (ii) p(a) = 0, if x – a is a factor of p(x).
Class 9 Maths NCERT Solutions Chapter 2 Exercises |
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☞ – 5 Questions (5 short answers) ☞ – 4 Questions (4 short answers) ☞ – 3 Questions (3 short answers) ☞ – 5 Questions (4 short answers, 1 long answer) ☞ – 16 Questions (9 short answers, 5 long answers, 2 very long answers) |
Also, access the following resources for Class 9 Chapter 2 Polynomials, at BYJU’S:
The chapter Coordinate Geometry includes the concepts of the cartesian plane, coordinates of a point in xy–plane, terms, and notations associated with the coordinate plane, including the x-axis, y-axis, x- coordinate, y-coordinate, origin, quadrants and more. Students, in this chapter, will also be studying the concepts of abscissa and ordinates of a point as well as plotting and naming a point in xy–plane. There are 3 exercises in this chapter that contain questions revolving around the topics mentioned in the chapter, helping the students get thorough with the concepts.
The Cartesian plane, coordinates of a point, names and terms associated with the coordinate plane, notations, plotting points in the plane, graph of linear equations as examples; focus on linear equations of the type ax + by + c = 0 by writing it as y =mx + c and linking with the chapter on linear equations in two variables.
Important Points –
Class 9 Maths NCERT Solutions Chapter 3 Exercises |
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☞ – 2 Questions (1 short answer, 1 long answer) ☞ – 2 Questions (2 short answers) ☞ – 2 Questions (1 short answer, 1 long answer) |
Also, access the following resources for Class 9 Chapter 3 Coordinate Geometry, at BYJU’S:
Along with recalling the knowledge of linear equations in one variable, this chapter will introduce the students to the linear equation in two variables, i.e. ax + by + c = 0. Students will also learn to plot the graph of a linear equation in two variables. There are 4 exercises in this chapter that consist of questions related to finding the solutions of a linear equation, plotting a linear equation on the graph and other topics discussed in the chapter.
Recall of linear equations in one variable. Introduction to the equation in two variables. Prove 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 seem to lie on a line. Examples, problems from real life, including problems on Ratio and Proportion and with algebraic and graphical solutions being done simultaneously.
Important Points –
Class 9 Maths NCERT Solutions Chapter 4 Exercises |
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☞ – 2 Questions (2 short answers) ☞ – 4 Questions (3 short answers, 1 long answer ) ☞ – 8 Questions (4 short answers, 4 long answers) ☞ – 2 Questions (2 long answers) |
Also, access the following resources for Class 9 Chapter 4 Linear Equations in Two Variables, at BYJU’S:
This chapter discusses Euclid’s approach to geometry and tries to link it with present-day geometry. Introduction to Euclid’s Geometry provides the students with a method of defining common geometrical shapes and terms. Students will be taken deeper into the topic of axioms, postulates and theorems with the two exercises present in the chapter.
History – Euclid and geometry in India. Euclid’s method of formalising observed phenomenon into rigorous mathematics with definitions, common/obvious notions, axioms/postulates, and theorems. The five postulates of Euclid. Equivalent versions of the fifth postulate. Showing the relationship between axiom and theorem. 1. Given two distinct points, there exists one and only one line through them. 2. (Prove) Two distinct lines cannot have more than one point in common.
Important Axioms and Postulates –
Some of Euclid’s axioms are:
(1) Things which are equal to the same thing are equal to one another.
(2) If equals are added to equals, the wholes are equal.
(3) If equals are subtracted from equals, the remainders are equal.
(4) Things which coincide with one another are equal to one another.
(5) The whole is greater than the part.
(6) Things which are double of the same things are equal to one another.
(7) Things which are halves of the same thing are equal to one another.
Euclid’s Five Postulates
Postulate 1 – A straight line may be drawn from any one point to any other point.
Postulate 2 – A terminated line can be produced indefinitely.
Postulate 3 – A circle can be drawn with any centre and any radius.
Postulate 4 – All right angles are equal to one another.
Postulate 5 – If a straight line falling on two straight lines makes the interior angles on the same side of it taken together less than two right angles, then the two straight lines, if produced indefinitely, meet on that side on which the sum of angles is less than two right angles.
Class 9 Maths NCERT Solutions Chapter 5 Exercises |
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☞ – 7 Questions (4 short answers, 3 long answers) ☞ – 2 Questions (1 short answer, 1 long answer) |
Also, access the following resources for Class 9 Chapter 5 Introduction to Euclid’s Geometry, at BYJU’S:
This chapter revolves around the theorems present in the topics of Lines and Angles. Students might often be asked to prove the statements given in the questions. There are 3 exercises in the chapter, solving which students would be able to understand the concepts covered in the chapter thoroughly. There are four axioms and eight theorems covered in the chapter.
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, the vertically opposite angles are equal. 3. (Motivate) Results on corresponding angles, alternate angles, and interior angles when a transversal intersects two parallel lines. 4. (Motivate) Lines, which are parallel to a given line, are parallel. 5. (Prove) The sum of the angles of a triangle is 180°. 6. (Motivate) If a side of a triangle is produced, the exterior angle so formed is equal to the sum of the two interior opposite angles.
(i) each pair of corresponding angles is equal,
(ii) each pair of alternate interior angles is equal,
(iii) each pair of interior angles on the same side of the transversal is supplementary.
(i) any one pair of corresponding angles is equal, or
(ii) any one pair of alternate interior angles is equal, or
(iii) any one pair of interior angles on the same side of the transversal is supplementary, then the lines are parallel.
Class 9 Maths NCERT Solutions Chapter 6 Exercises |
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☞ – 6 Questions (5 short answers, 1 long answer) ☞ – 6 Questions (3 short answers, 3 long answers) ☞ – 6 Questions (5 short answers, 1 long answer) |
Also, access the following resources for Class 9 Chapter 6 Lines and Angles, at BYJU’S:
In this chapter, students will study in detail the congruence of triangles, rules of congruence, some properties of triangles and the inequalities in triangles. The chapter has a total of 5 exercises, in which the students are asked “to-prove” as well as application-level problems. With this chapter, students will also learn to prove the properties that they learnt in earlier classes. The chapter also teaches the students to apply the various congruence rules while solving the problems. There are about eight theorems covered in this chapter.
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 the 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. 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. 7. (Motivate) Triangle inequalities and the relation between ‘angle and facing side’; inequalities in a triangle.
Important Axioms and Theorems –
Axiom 7.1 (SAS congruence rule) – Two triangles are congruent if two sides and the included angle of one triangle are equal to the two sides and the included angle of the other triangle.
Theorem 7.1 (ASA congruence rule) – Two triangles are congruent if two angles and the included side of one triangle are equal to two angles and the included side of the other triangle.
Theorem 7.2 – Angles opposite to equal sides of an isosceles triangle are equal.
Theorem 7.3 – The sides opposite to equal angles of a triangle are equal.
Theorem 7.4 (SSS congruence rule) – If the three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent.
Theorem 7.5 (RHS congruence rule) – If in two right triangles, the hypotenuse and one side of one triangle are equal to the hypotenuse and one side of the other triangle, then the two triangles are congruent.
Theorem 7.6 – If two sides of a triangle are unequal, the angle opposite to the longer side is larger (or greater).
Theorem 7.7 – In any triangle, the side opposite to the larger (greater) angle is longer.
Theorem 7.8 – The sum of any two sides of a triangle is greater than the third side.
Class 9 Maths NCERT Solutions Chapter 7 Exercises |
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☞ – 8 Questions (6 short answers, 2 long answers) ☞ – 8 Questions (6 short answers, 2 long answers) ☞ – 5 Questions (3 short answers, 2 long answers) ☞ – 6 Questions (5 short answers, 1 long answer) ☞ – 4 Questions (3 short answers, 1 long answer) |
Also, access the following resources for Class 9 Chapter 7 Triangles, at BYJU’S:
A figure obtained by joining four points in order is called a quadrilateral. This chapter takes the students to the depth of the topics of Quadrilaterals. The chapter contains 2 exercises that contain only one theorem to prove. However, there are a total of nine theorems that can be used to solve the application or conceptual-level questions asked. The angle sum property of a quadrilateral, types of quadrilaterals, properties of a parallelogram, and the mid-point theorem are explained in this chapter to help the students in learning the concepts thoroughly.
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 are parallel and equal. 5. (Motivate) In a parallelogram, the diagonals bisect each other conversely. 6. (Motivate) In a triangle, the line segment joining the midpoints of any two sides is parallel to the third side and (motivate) its converse.
Important Theorems –
A quadrilateral has four sides, four angles and four vertices.
Angle Sum Property of a Quadrilateral – The sum of the angles of a quadrilateral is 360 o .
Theorem 8.1 – A diagonal of a parallelogram divides it into two congruent triangles
Theorem 8.2 – In a parallelogram, opposite sides are equal.
Theorem 8.3 – If each pair of opposite sides of a quadrilateral is equal, then it is a parallelogram.
Theorem 8.4 – In a parallelogram, opposite angles are equal.
Theorem 8.5 – If in a quadrilateral, each pair of opposite angles is equal, then it is a parallelogram.
Theorem 8.6 – The diagonals of a parallelogram bisect each other.
Theorem 8.7 – If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.
Theorem 8.8 – A quadrilateral is a parallelogram if a pair of opposite sides are equal and parallel.
Theorem 8.9 – The line segment joining the mid-points of two sides of a triangle is parallel to the third side.
Theorem 8.10 – The line drawn through the mid-point of one side of a triangle, parallel to another side, bisects the third side.
Class 9 Maths NCERT Solutions Chapter 8 Exercises |
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☞ – 12 Questions (2 short answers, 6 long answers, 4 very long answers) ☞ – 7 Questions (2 short answers, 2 long answers, 3 very long answers) |
Also, access the following resources for Class 9 Chapter 8 Quadrilaterals, at BYJU’S:
In this chapter, an attempt has been made to consolidate the knowledge about the formulae to find the areas of different figures by studying relationships between the areas of geometric figures, provided they lie on the same base and between the same parallels. This study will also be useful in understanding some results on the ‘similarity of triangles’. The chapter contains 4 exercises, of which most of the questions ask the students to prove the statements given.
Review the concept of area and recall the area of a rectangle. 1. (Prove) Parallelograms on the same base and between the same parallels have the same area. 2. (Motivate) Triangles on the same base and between the same parallels are equal in area and its converse.
Theorem 9.1 – Parallelograms on the same base and between the same parallels are equal in area.
Theorem 9.2 – Two triangles on the same base (or equal bases) and between the same parallels are equal in area.
Theorem 9.3 – Two triangles having the same base (or equal bases) and equal areas lie between the same parallels.
Class 9 Maths NCERT Solutions Chapter 9 Exercises |
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☞ – 1 Question (1 short answer) ☞ – 6 Questions (5 short answers, 1 long answer) ☞ – 16 Questions (12 short answers, 4 long answers) ☞ – 8 Questions (4 short answers, 1 long answer, 3 very long answers) |
Also, access the following resources for Class 9 Chapter 9 Areas of Parallelograms and Triangles, at BYJU’S:
A circle can be defined as a collection of all the points in a plane at a fixed distance from a fixed point in the plane. Topics like Angle Subtended by a Chord at a Point, Equal Chords and their respective distances from the Centre, the Angle Subtended by an Arc of a Circle, Cyclic Quadrilaterals and other terms related to circles are covered in this chapter. A total of twelve theorems are present in this chapter, learning which the students will get a clearer idea of the concepts taught. There are 6 exercises in this chapter which consist of questions from all the concepts present in the chapter.
Through examples, arrive at definitions of circle-related concepts, radius, circumference, diameter, chord, arc, and subtended angle. 1. (Prove) Equal chords of a circle subtend equal angles at the centre and (motivate) its converse. 2. (Motivate) The perpendicular from the centre of a circle to a chord bisects the chord, and conversely, the line drawn through the centre of a circle to bisect a chord is perpendicular to the chord. 3. (Motivate) There is one and only one circle passing through three given non-collinear points. 4. (Motivate) Equal chords of a circle (or of congruent circles) are equidistant from the centre(s) and conversely. 5. (Prove) The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle. 6. (Motivate) Angles in the same segment of a circle are equal. 7. (Motivate) If a line segment joining two points subtends equal angles at two other points lying on the same side of the line containing the segment, the four points lie on a circle. 8. (Motivate) The sum of either pair of opposite angles of a cyclic quadrilateral is 180 0 and its converse.
Theorem 10.1 – Equal chords of a circle subtend equal angles at the centre.
Theorem 10.2 – If the angles subtended by the chords of a circle at the centre are equal, then the chords are equal.
Theorem 10.3 – The perpendicular from the centre of a circle to a chord bisects the chord.
Theorem 10.4 – The line drawn through the centre of a circle to bisect a chord is perpendicular to the chord.
Theorem 10.5 – There is one and only one circle passing through three given non-collinear points.
Theorem 10.6 – Equal chords of a circle (or of congruent circles) are equidistant from the centre (or centres).
Theorem 10.7 – Chords equidistant from the centre of a circle are equal in length.
Theorem 10.8 – The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.
Theorem 10.9 – Angles in the same segment of a circle are equal.
Theorem 10.10 – If a line segment joining two points subtends equal angles at two other points lying on the same side of the line containing the line segment, the four points lie on a circle (i.e. they are concyclic).
Theorem 10.11 – The sum of either pair of opposite angles of a cyclic quadrilateral is 180º.
Theorem 10.12 – If the sum of a pair of opposite angles of a quadrilateral is 180º, the quadrilateral is cyclic.
Class 9 Maths NCERT Solutions Chapter 10 Exercises |
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☞ – 2 Questions (2 short answers) ☞ – 2 Questions (2 long answers) ☞ – 3 Questions (3 long answers) ☞ – 6 Questions (6 long answers) ☞ – 12 Questions (12 long answers) ☞ – 10 Questions (10 long answers) |
Also, access the following resources for Class 9 Chapter 10 Circles, at BYJU’S:
In this chapter, students will learn some basic constructions. The method learnt will then be used to construct certain kinds of triangles. There are 2 exercises present in this chapter, of which the first exercise deals with the construction of a certain angle or the bisector of a given angle. On the other hand, the second exercise deals with the constructions of triangles when different parameters are given.
1. Construction of bisectors of a line segment and angle, 60°, 90°, 45° angles etc., equilateral triangles. 2. Construction of a triangle given its base, sum/difference of the other two sides and one base angle. 3. Construction of a triangle of given perimeter and base angles.
Construction 11.1 – To construct the bisector of a given angle.
Construction 11.2 – To construct the perpendicular bisector of a given line segment.
Construction 11.3 – To construct an angle of 600 at the initial point of a given ray.
Construction 11.4 – To construct a triangle, given its base, a base angle and the sum of the other two sides.
Construction 11.5 – To construct a triangle given its base, a base angle and the difference between the other two sides.
Construction 11.6 – To construct a triangle, given its perimeter and its two base angles.
Class 9 Maths NCERT Solutions Chapter 11 Exercises |
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☞ – 5 Questions (2 short answers, 2 long answers, 1 very long answer) ☞ – 5 Questions (5 very long answers) |
Also, access the following resources for Class 9 Chapter 11 Constructions, at BYJU’S:
The chapter discusses Heron’s formula, which can be used to calculate the area of a triangle when the length of all three sides is given. In this method, there is no need to calculate the angles or other distances in the triangle. This formula can be used not only to find the area of triangles but also to find the areas of quadrilaterals and other polygons by dividing them into triangles. There are 2 exercises in this chapter which help the student understand the method of solving the problems based on Heron’s formula.
Area of a triangle using Heron’s formula (without proof) and its application in finding the area of a quadrilateral.
Area of a triangle = 1/2 × base × height
Where a, b and c are the sides of a triangle
s is the semi-perimeter, i.e. half of the perimeter of a triangle = (a + b + c)/2
Class 9 Maths NCERT Solutions Chapter 12 Exercises |
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☞ – 6 Questions (2 short answers, 2 long answers, 2 very long answers) ☞ – 9 Questions (4 long answers, 5 very long answers) |
Also, access the following resources for Class 9 Chapter 12 Heron’s Formula, at BYJU’S:
In this chapter, students shall learn to find the surface areas and volumes of cuboids and cylinders in detail and broaden the study to some other solids, such as cones and spheres. This chapter is just an extended version of the chapter mensuration, in which the students learnt about the surface areas and volumes in earlier classes. There are 8 exercises in this chapter, and these exercises contain problems that are based on surface areas and volumes of different solids such as cubes, cuboids, spheres, cylinders, cones, and hemispheres.
Surface areas and volumes of cubes, cuboids, spheres (including hemispheres) and right circular cylinders/cones.
Surface Area of a Cuboid = 2(lb + bh + hl)
where l, b and h are, respectively, the three edges of the cuboid
Surface Area of a Cube = 6a 2
where a is the edge of the cube.
Curved Surface Area of a Cylinder = 2πrh
where r is the radius of the base of the cylinder and h is the height of the cylinder
Total Surface Area of a Cylinder = 2πr(r + h)
where h is the height of the cylinder and r is its radius
Curved Surface Area of a Cone = 1/2 × l × 2πr = πrl
where r is its base radius, and l is its slant height
Total Surface Area of a Cone = πrl + πr 2 = πr(l + r)
Surface Area of a Sphere = 4 π r 2
where r is the radius of the sphere.
Curved Surface Area of a Hemisphere = 2πr 2
where r is the radius of the sphere of which the hemisphere is a part.
Total Surface Area of a Hemisphere = 3πr 2
Volume of a Cuboid = base area × height = length × breadth × height
Volume of a Cube = edge × edge × edge = a 3
Volume of a Cylinder = πr 2 h
where r is the base radius, and h is the height of the cylinder.
Volume of a Cone = 1/3 πr 2 h
where r is the base radius, and h is the height of the cone.
Volume of a Sphere = 4/3 πr 3
Volume of a Hemisphere = 2/3 πr 3
where r is the radius of the hemisphere.
Class 9 Maths NCERT Solutions Chapter 13 Exercises |
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☞ – 8 questions ☞ – 11 questions ☞ – 8 questions ☞ – 9 questions ☞ – 9 questions ☞ – 8 questions ☞ – 9 questions ☞ – 10 questions ☞ – 3 questions |
Also, access the following resources for Class 9 Chapter 13 Surface Areas and Volumes, at BYJU’S:
The branch of Mathematics in which the extraction of meaningful information is studied is known as Statistics. It can also be defined as the collection of data on different aspects of the life of people useful to the State. The chapter teaches about the different presentations of the data, including the frequency distribution as well. The chapter also helps the students learn the graphical representation of data using different graphs such as Bar graphs, Histograms, Frequency polygons, etc. The chapter also lets the students learn the measure of central tendency mean, median and mode of the raw data. A total of 4 exercises are present in the chapter that includes problems related to all these concepts.
Introduction to Statistics: Collection of data, presentation of data – tabular form, ungrouped/grouped, bar graphs, histograms (with varying base lengths), frequency polygons, qualitative analysis of data to choose the correct form of presentation for the collected data. Mean, median, and mode of ungrouped data.
Statistics deals with the collection, presentation, and analysis of data, as well as the drawing of meaningful conclusions from the data.
Mean – It is found by adding all the values of the observations and dividing it by the total number of observations. It is denoted by \(\begin{array}{l}\overline{x}\end{array} \) .
Median – It is the value of the middle-most observation (s).
If n is an odd number, the median = value of the [(n + 1)/2] th observation
If n is an even number, median = Mean of the values of the (n/2) th and [(n/2) + 1] th observations.
Mode – The mode is the most frequently occurring observation.
Class 9 Maths NCERT Solutions Chapter 14 Exercises |
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☞ – 2 questions (2 short answers) ☞ – 9 questions (9 long answers) ☞ – 9 questions (6 short answers, 3 long answers) ☞ – 6 questions (2 short answers, 4 long answers) |
Also, access the following resources for Class 9 Chapter 14 Statistics, at BYJU’S:
The collection of some outcomes of an experiment is known as an event of an experiment. The chances of occurrence of an event are known as probability. In this chapter, students will learn to measure the chance of occurrence of a particular outcome in an experiment. This chapter contains only 1 exercise. The problems covered in this exercise are based on real-life incidents, enhancing the interest of the students in solving the questions.
History, Repeated experiments and observed frequency approach to probability. Focus is on empirical probability. (A large amount of time to be devoted to group and to individual activities to motivate the concept; the experiments to be drawn from real-life situations and from examples used in the chapter on statistics).
The empirical probability P(E) of an event E happening is given by
P (E) = Number of trials in which the event happened/The total number of trials
Class 9 Maths NCERT Solutions Chapter 15 Exercises |
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☞ – 10 Questions ( 4 short answers, 3 long answers, 3 very long answers) |
Also, access the following resources for Class 9 Chapter 15 Probability, at BYJU’S:
I | Number Systems | 10 |
II | Algebra | 20 |
III | Coordinate Geometry | 04 |
IV | Geometry | 27 |
V | Mensuration | 13 |
VI | Statistics and Probability | 06 |
Total | 80 | |
Internal Assessment | 20 | |
Total | 100 |
Pen Paper Test and Multiple Assessment (5+5) | 10 Marks |
Portfolio | 05 Marks |
Lab Practical (Lab activities to be done from the prescribed books) | 05 Marks |
During the exam preparation, students should first complete the units carrying more weightage and then move on to the lower weightage. This helps students to first cover the important concepts and improves their confidence level to perform well in the annual exam.
The students are advised to analyse all the concepts covered in the Syllabus of Class 9 Maths and prepare a proper preparation strategy. It’s merely impossible to score well in Maths by simply reading and memorising the concepts. Students should always try to understand the concept and logic given in any particular topic. The students are suggested to practise these NCERT Solutions Class 9 materials on a regular basis to develop a strong understanding of basic mathematics concepts.
Along with the NCERT Solutions, we have also provided a brief summary of important formulas and different methods of solving similar problems to help students understand the concepts thoroughly. Keep visiting BYJU’S to get more updated learning materials, and download the BYJU’S app for a better and personalised learning experience with engaging video lessons.
How can i learn the class 9 maths chapters in a fast and efficient way, can i get solved answers for the questions from the ncert class 9 maths chapters, should i daily solve the questions from the ncert solutions for class 9 maths , how can i download the ncert solutions for class 9 maths at byju’s, leave a comment cancel reply.
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Class 9 General Math Assignment solution with right answer 2021 with PDF. Class 9 Higher Math & Math assignment answer 2021 11th week solution is available on admissionwar.com. Today we will try to give you Class 9 math assignment question and answer. In this post, we have arranged for your class 9 mathematics (Gonit) all week assignment solve so stay with us
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Grade 9 edwardsmaths assignment 2020 term 1.
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Expert Teachers at SamacheerKalvi.Guru has created Tamilnadu State Board Samacheer Kalvi 9th Maths Book Answers and Solutions Guide Pdf Free Download in English Medium and Tamil Medium are part of Samacheer Kalvi 9th Books Solutions . Here we have given TN State Board New Syllabus Samacheer Kalvi 9th Std Maths Guide Pdf of Book Back Questions and Answers, Chapter Wise Important Questions, Study Material, Question Bank, Notes, Formulas, Term 1, 2, 3.
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Grade 9 Math Project and Memo Term 3 2021. 16596 Download. 995.58 KB File Size. 1 File Count. August 23, 2021 Create Date. August 23, 2021 Last Updated. File. Action. Gr 9 Area, Surface Area and Volume project Term 3.pdf.
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NCERT Solutions for Class 9 Maths CBSE 2023-24 in PDF format, solved by subject experts as per the latest edition NCERT books and CBSE Syllabus, can be downloaded for free at BYJU'S. ... ☞ Exercise 12.2 - 9 Questions (4 long answers, 5 very long answers) Also, access the following resources for Class 9 Chapter 12 Heron's Formula, at BYJU'S:
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