by Tiwari Academy
NCERT Textbook Solutions for Class 9 Maths with MCQ Exercises Revised and Updated for Session 2025-26 for 9th Mathematics Exams in Hindi and English Medium. NCERT Class 9 Math Exercises and Multiple Choice Question Solutions provide a suitable guide for descriptive and objective questions.
Whether it’s solving the difficult concepts in NCERT Class 9 Maths Number Systems, students explore rational numbers, irrational numbers and their decimal expansions.
Class 9 Maths Chapter-wise Solutions for 2025-26
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
- Number Systems Exercises
- Polynomials Exercises
- Coordinate Geometry Exercises
- Linear Equations Exercises
- Euclid’s Geometry Exercises
- Lines and Angles Exercises
- Triangles Exercises
- Quadrilaterals Exercises
- Circles Exercises
- Heron’s Formula Exercises
- Surface Areas and Volumes Exercises
- Statistics Exercises
Class 9 Maths Chapter-wise MCQ Online Test
With growing demand for MCQ explanations, the NCERT 9th Maths Textbook MCQ Solutions has become a popular resource for Class 9 students. These objective question solutions offer more than just answers—they include detailed steps using mathematical terms like Cartesian coordinates, slope, variable, constant and coefficient.
Chapter 1 MCQ (Number Systems)
Chapter 2 MCQ (Polynomials)
Chapter 3 MCQ (Coordinate Geometry)
Chapter 4 MCQ (Linear Equations in Two Variables)
Chapter 5 MCQ (Introduction to Euclid’s Geometry)
Chapter 6 MCQ (Lines and Angles)
Chapter 7 MCQ (Triangles)
Chapter 8 MCQ (Quadrilaterals)
Chapter 9 MCQ (Circles)
Chapter 10 MCQ (Heron’s Formula)
Chapter 11 MCQ (Surface Areas and Volumes)
Chapter 12 MCQ (Statistics)
Chapter-wise solutions such as Chapter 8 (Quadrilaterals), dealing with properties of parallelograms and angle sum property, and Chapter 14 (Statistics), focusing on mean, median and mode, make revision easy and thorough. These guides cover the full syllabus with clarity. Class 9 Maths Chapter-wise Solutions include solved examples using algebraic identities, formulae and geometric theorems. Tiwari Academy’s solutions sharpen problem-solving techniques and develop strong conceptual understanding—essential for mastering mathematics.
Class 9 Maths Syllabus for 2025-26
In Class 9 Math NCERT Chapter 3 Coordinate Geometry, students learn about the Cartesian plane, plotting points and deriving the distance formula. NCERT Book Mathematics Chapter 15 Probability focuses on experimental probability and outcomes of random experiments. NCERT Maths solutions offer detailed explanations to help students build a strong foundation in mathematical reasoning and analytical skills. Step-by-step derivations of formulas and logical problem-solving techniques, such as in Exercise 1.1 Solutions and Exercise 2.2 Solutions, simplify even complex equations and theorems. The availability of Class 9 NCERT Mathematics textbook solutions in PDF format ensures students can conveniently access these resources for effective study.
Study Plan to Perform Well in Class 9 Exams
Class 9 Mathematics NCERT Solutions are an essential tool for students striving to strengthen their grasp of mathematical concepts. NCERT Class 9 Math textbook solutions cover all aspects of the curriculum, from Chapter-wise Solutions to Exercise Solutions, providing a detailed and structured learning path. Alongside the NCERT Class 9 Maths PDF, students can access additional resources like Class 9 Math Important Questions, Worksheets, and Practice Questions, making their preparation comprehensive. For those aiming for thorough revision, resources like Class 9 Maths Formulas, Revision Notes, and Sample Papers are incredibly helpful. By practicing problems from these solutions, students build the confidence needed to tackle their exams effectively. The class 9 mathematics solutions and answers have been suitably modified and revised taking into account the guidelines of CBSE and State board 9th Maths curriculum 2025-26. Your valuable feedback and Review would help us to improve further our answers.
To enhance their understanding further, students can utilize interactive resources like NCERT Class 9 Maths Video Lectures and Online Tests. These are complemented by Mock Tests, MCQs and Doubt Clearing Sessions, ensuring that all learning gaps are addressed. For exam preparation, Class 9 NCERT Math Exam Pattern and Syllabus guides offer clarity on what to expect. With tools like Problem Solving Techniques, Tips and Tricks and Conceptual Questions, students develop critical thinking skills. Whether through Online Coaching or Interactive Learning Platforms, these solutions ensure students excel academically while enjoying the process of learning mathematics.
Class 9 Solution Apps Download
Class 9 Math solutions are available in multiple formats such as printed books, online resources and mobile apps. Platforms like Tiwari Academy take their social responsibility seriously by providing free access to NCERT solutions, ensuring that quality education is accessible to everyone. These free resources help students learn and succeed without financial barriers.
| Class: 9 | Mathematics Textbook |
| Number of Chapters: | 12 (Twelve) |
| Content: | NCERT Solutions and Extra Questions |
| Content Mode: | Online PDF and Videos |
| Academic Session: | Current Year 2025-26 |
| Medium: | Hindi Medium and English Medium |
CBSE Syllabus for Class 9 Mathematics Revised for 2025-26
The Class 9 Maths NCERT Solutions are a vital resource for students looking to master the fundamentals of mathematics. These solutions, designed according to the latest CBSE Class 9 Math Syllabus, cover all chapters with clear, step-by-step explanations. Students can enhance their preparation by solving Sample Papers, practicing Important Questions and reviewing Previous Year Papers. The inclusion of Math Formulas and Revision Notes ensures that students can quickly revise essential concepts before exams. Resources like NCERT Class 9 Mathematics Worksheets and Practice Questions provide ample opportunities for hands-on learning, helping students identify and improve weak areas effectively.
Class 9 Math Chapter wise Marking Scheme for 2025-26 Exams
| 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 |
The Need of a Perfect Study Plan for Class 9 Maths
Following a study timetable in NCERT Class 9 Maths ensures consistent learning, better time management, and reduced stress. It helps prioritize subjects, focus on weak areas and balance schoolwork with leisure. A structured plan builds discipline, enhances productivity and prepares students effectively for mathematics exams, setting a strong foundation for future academic success in math.
Success is the sum of small efforts, repeated day in and day out. – Robert Collier
| Time Slot | Topic/Activity | Notes |
|---|---|---|
| 6:00 AM – 6:30 AM | Revision of Formulas | Focus on key formulas from Algebra and Geometry. |
| 6:30 AM – 7:30 AM | Solve Practice Questions | Work on previous day’s topics to strengthen concepts. |
| 5:00 PM – 5:30 PM | New Concepts | Learn a new topic like Trigonometry or Probability. |
| 5:30 PM – 6:30 PM | Practice Numericals | Solve numerical problems from textbooks or guides. |
| 8:00 PM – 8:30 PM | Doubt Clearing | Review doubts and seek help if needed. |
| 8:30 PM – 9:00 PM | Quick Revision | Revisit key concepts and formulas of the day. |
To support diverse learning needs, students can explore NCERT Class 9 Math Video Lectures and participate in Online Tests to build their confidence. For personalized guidance, Doubt Clearing Sessions and Online Coaching help clarify challenging topics. Tools like NCERT Maths MCQs and Interactive Learning Platforms make preparation engaging and interactive. With access to Study Material, Assignments and insights into the Exam Pattern, students gain a well-rounded understanding of the subject. Whether it’s solving complex problems or learning through Tips and Tricks, these resources ensure that Class 9 Mathematics students excel in math and approach the subject with confidence.
NCERT solutions for Class 9 Mathematics are incredibly useful for students because they are created by subject experts based on the CBSE curriculum. If you’re searching for the revised Class 9 Maths UP Board NCERT Solutions for the 2025-26 exams, Tiwari Academy has you covered. They offer updated solutions for all chapters, making it easier for students to understand key concepts and score higher in exams. These solutions not only strengthen mathematical understanding but also help students 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.
| Class 9 All Subjects iOS App for iPad & iPhone |
Our Educational App offers notifications and reminders for important dates, exams and study schedules, helping students stay organised and focused. The app also allows students to track their scores, monitor exercise completion and identify areas for improvement, making it a valuable tool for staying on track with their studies.
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 short walks can refresh your mind and improve focus while studying. Staying positive and believing in yourself helps you grow. Regular quizzes or timed math practice show weak areas and build confidence.
Solutions for NCERT Class 9 Mathematics All Chapters
These Chapter Wise Class 9 Mathematics Solutions App is well designed so that class 9 students can easily understand each sum’s solutions. 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 of 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 Textbook Solutions for Class 9 Math Chapter 1 Number System
NCERT Solutions for Class 9 Maths Chapter 1 introduces key topics like rational numbers and irrational numbers. You will learn how to represent integers, rational numbers and irrational numbers on a number line. This chapter provides a comprehensive understanding of the number line, helping students grasp these fundamental concepts effectively.
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 Exercises 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 Book Solutions for Class 9 Mathematics Chapter 3 Coordinate Geometry
Students can get NCERT exercises solutions for Class 9 Maths Chapter 3 with free of cost. Chapter 3 introduces the concepts of the Cartesian plane, including coordinates of a point, terms, coordinate plane notations, x-axis, y-axis, x-coordinate, y-coordinate, quadrants, origin and more. It provides a thorough understanding of these fundamental terms, helping students navigate and plot points on the coordinate plane effectively.
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 about the coordinate plane and the mutually perpendicular lines, known as axes. They can download the NCERT Solutions for Class 9 Maths PDF to study offline anytime, making it convenient for learning on the go. 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 Topic-wise Solutions for Class 9 Math Chapter 4 Linear Equations in Two Variables
NCERT Solutions for Class 9 Maths Chapter 4 4 covers linear equations in one variable and introduces linear equations in two variables, like ax + by + c = 0. In this chapter, students will also learn how to plot the graph of a linear equation in two variables, gaining a solid understanding of these key concepts.
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
NCERT Solutions for Class 9 Maths Chapter 9, Linear Equations in Two Variables, includes just two exercises. Students can download the free NCERT Solutions for Class 9 Maths PDF to study anytime, anywhere. These solutions help students clear all concepts for each math problem. Download unlimited free solutions for Chapter 9 Linear Equations in Two Variables in both 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 Detailed 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 covers Euclid’s approach to geometry, which forms the foundation of present-day geometry. In the NCERT exercises for Class 9 Maths, Introduction to Euclid’s Geometry, students will learn about defining common geometrical shapes and terms, providing a solid understanding of the basics of geometry.
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
This 9th Class Maths Book Solution includes only one exercise that provides a deeper understanding of the relationship between axioms, postulates, and theorems. Download Chapter Euclid’s Geometry Class 9 Maths Solutions in both Hindi Medium and English Medium for free to enhance your learning experience.
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 Exercises Solutions for Class 9 Mathematics 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
The 9th Maths Book Solutions provided here are carefully reviewed for accuracy. Get free NCERT Solutions for Class 9 Maths in PDF format for offline study. Practice these solutions thoroughly to score your best in the final exams. Download Chapter Lines and Angles Class 9 Maths Solutions in both Hindi 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 Textbook Topics 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, students will prove the properties of triangles learned in previous classes. While solving problems, they will apply various congruence rules. This chapter includes eight theorems, and there are three exercises covered in the NCERT Solutions for Class 9 Maths Chapter 7, Triangles. Download Chapter Triangles Class 9 Maths Solutions in both Hindi Medium and English Medium for a comprehensive understanding.
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 all Exercises 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 includes two exercises and focuses on proving one theorem. These solutions cover important concepts such as the angle sum property of a quadrilateral, properties of a parallelogram, and different types of quadrilaterals. Download Chapter Quadrilaterals Class 9 Maths Solutions in both Hindi Medium and English Medium for free.
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 Book Exercises Solutions for Class 9 Math Chapter 9 Circles
Get well-explained NCERT Solutions for Class 9 Maths Chapter Circles for free, with no need to log in or register. Access solutions for all exercises at no cost, making learning easy and convenient. 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
Learn about circles, including Chord at a Point and Equal Chords, with twelve theorems in total. Download NCERT Solutions for Class 9 Maths for free, with no registration needed. Get Chapter 9 Circles Solutions in both Hindi and English Medium at no cost.
Class 9 Maths Chapter 9 Circles Curriculum for 2025-26
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 Based 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 helps calculate the area of a triangle when the lengths of all three sides are given. With Heron’s Formula, you can find the area of a triangle without needing to calculate the heights or distances directly.
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
Heron’s Formula is used to find the areas of quadrilaterals, triangles, and other polygons. There is only one exercise in NCERT Solutions for Class 9 Maths Chapter 10, Heron’s Formula. You can download the NCERT Solutions for Class 9 Maths Chapter 12 PDF for free and study anytime, offline, on your desktop or mobile.
Class 9 Maths Chapter 10 Heron’s Formula Main Points To Study
Area of a triangle using Heron’s formula (without proof)
NCERT Related Exercises 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 detail. In NCERT Solutions for Class 9 Maths Chapter 11, Surface Areas and Volumes, you will also explore the surface areas of 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
In this chapter, students will deepen their understanding of surface areas and volumes, building on concepts from earlier classes. Chapter 11 includes four exercises covering the surface areas and volumes of various solids such as cubes, cuboids, hemispheres, spheres, cylinders and cones. Download the NCERT Solutions for Class 9 Maths PDF for free without any login or registration required. 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 New Textbook 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 plays an important role in daily life, influencing various aspects like people’s lives and state functions. NCERT Solutions for Class 9 Maths Chapter 12, Statistics, teaches how to present data in different ways, including frequency distribution. You’ll also learn how to organize data in tabular and row form, group it in regular intervals and calculate the mean, mode and median. 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 Revised Solutions for Class 9 Math Chapter 13 Surface Areas and Volumes
Tiwari Academy offers NCERT solutions on Surface Areas and Volumes, based on the state board syllabus for the 2025-26 session, in both Hindi and English mediums. Master geometry with Tiwari Academy’s expert NCERT Solutions for Class 9 Maths Exercise 13.8, specifically designed for students of the 2024-2025 session, available in both languages.
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 Previous Book Solutions for Class 9 Maths Chapter 14 Statistics
Access Class 9 Maths Chapter 14 Statistics solutions in both Hindi and English at Tiwari Academy. Perfect for CBSE students, our resources are comprehensive, user-friendly and designed to help you improve in your studies.
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 Exercise Solution for Class 9 Maths Chapter 15 Probability
Master Class 9 Maths Chapter 15, Probability, with our solutions in English and Hindi. Clear and concise, these expert resources help you excel in CBSE exams and understand Probability easily.
Class 9 Maths Chapter 15 Solutions for State boards
Class 9 Maths Chapter 15 Exercise 15.1
Importance of NCERT Textbook Solutions for Class 9 Mathematics Exercises
NCERT or the National Council of Educational Research and Training, creates standard textbooks and supports education in India. NCERT Class 9 Mathematics Exercise Solutions give clear, detailed answers to textbook questions, helping students understand concepts better. These solutions improve learning and boost exam performance with many added benefits.
Explain Each and Every Concept in Detail
Class 9 Maths Question Answers explain every concept in detail using simple language, making it easier for students to understand. These solutions are essential for a better grasp of the subject and help in scoring good marks in Class 9 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 are available as downloadable PDFs for all chapters, allowing you to study offline. You can access these solutions anytime and anywhere, making learning more convenient and flexible.
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 solutions are prepared by expert teachers and subject specialists to help you score higher. Each solution is carefully crafted after thorough research, allowing you to tackle problems of any difficulty.
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.
NCERT PDF Solutions for Class 9 Maths simplify complex mathematical concepts, helping students understand formulas, equations and problem-solving techniques thoroughly, improve analytical skills and boost confidence, which is crucial for anyone aiming to score good in their exams. To maximise success in CBSE Class 9 Maths, it is essential to cover all exercises, proofs and thoroughly learn every theorem, postulate and corollary in the syllabus. Skipping any topic could impact your overall understanding of geometry, algebra and trigonometry foundation and performance in exams. NCERT Textbook solutions provide step-by-step explanations for each exercise, ensuring you master every concept with precision. By staying consistent and covering all topics in CBSE 9th Maths syllabus, students can build a strong foundation and perform well in both school assessments and final exams.
Feedback & Suggestions
A panel of experts at Tiwari Academy recently conducted a two-day workshop to thoroughly review and enhance the content quality of their educational materials. During this workshop, they meticulously analysed both the English and Hindi versions of the content, providing valuable suggestions for improvements. Based on these expert recommendations, necessary amendments were made to ensure that the solutions meet high educational standards and offer clear, concise explanations for students.
Following these discussions, the final draft of the solutions is prepared, adhering to the new syllabus for 2025-26. We offer well-structured materials with a classical approach to geometry and constructions, making key concepts easier to grasp. For UP Board High School students, complete solutions, sample papers and notes are available for the 2025-26 syllabus in Hindi and English. These resources support exam success and concept mastery.
How to practice Class 9 Maths using NCERT Solutions?
For the academic session 2025-26, NCERT has significantly reduced the syllabus for Class 9 Maths in the latest textbooks. As a result, the NCERT Solutions for Class 9 Maths have also been updated and revised accordingly. These solutions are essential for students aiming to excel in their CBSE Class 9 Mathematics exams. Follow the steps below to learn how you can effectively use the updated Class 9 Maths solutions to improve your exam performance.
- 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.
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.
Which chapters are most important in Class 9 NCERT Maths for final exams?
In Class 9 NCERT Maths, several chapters hold significant importance for the final exams due to their weightage and foundational value. Number Systems, Polynomials and Linear Equations in Two Variables are essential for developing algebraic thinking. Coordinate Geometry introduces plotting points on the Cartesian plane, which is crucial for future geometry concepts. Geometry-based chapters like Triangles, Quadrilaterals and Circles are also very important, as they include theorem-based questions and constructions. Mensuration chapters such as Surface Areas and Volumes frequently appear in exams with application-based problems. Statistics and Probability focus on data handling and basic probability concepts, which are easy to score. Focusing on these chapters ensures a strong performance in the final exams.
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 score full marks in Class 9 Maths?
To score full marks in Class 9 Maths, regular practice and a clear understanding of concepts are crucial. Begin by solving all NCERT textbook questions as they are designed to cover the entire syllabus comprehensively. Also, make sure to understand and practice each theorem, as many problems are based on applying these mathematical principles.
In addition, revising formulas regularly, solving sample papers and taking mock tests can help boost your confidence and time management skills during the exam. It’s important to identify weak areas and work on them through additional exercises or reference materials. With consistent effort and the right strategy, scoring full marks is achievable.
Where can I find free NCERT Solutions for Class 9 Maths?
Free NCERT Solutions for Class 9 Maths are widely available on various educational websites like Tiwari Academy, etc. These platforms provide chapter-wise solutions in a clear, step-by-step format. Additionally, you can download the official Tiwari Academy app, which offers solutions and textbooks for free.
These resources not only help in solving textbook problems but also provide practice questions and mock tests. For students looking to excel in their exams, having access to these solutions ensures a thorough understanding of each topic and helps in revising important questions quickly.
How many exercises are there in the NCERT Class 9 Maths book?
The NCERT Class 9 Maths book contains a total of 15 chapters, each consisting of multiple exercises. The number of exercises varies across chapters, but on average, each chapter has around 3-4 exercises, amounting to over 80 exercises in the entire book. Some chapters like Triangles and Quadrilaterals have more exercises due to the complexity of the topics.
These exercises cover various types of questions, from easy to difficult, ensuring students develop a comprehensive understanding of each topic. By solving all these exercises, students can build a strong foundation and effectively prepare for their exams.
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 2025-26 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.
What is the importance of the theorems in Class 9 Maths?
Theorems in Class 9 Maths play a crucial role as they lay the foundation for understanding geometry and problem-solving techniques. Important theorems like Pythagoras’ theorem, properties of triangles and circles not only appear in exams but also form the base for higher-level Maths. Understanding the proof of these theorems helps students apply them effectively to solve complex questions.
Learning these theorems thoroughly enhances logical thinking and analytical skills, which are essential not only for Maths but also for subjects like Physics. These theorems appear frequently in exams, so knowing them well can contribute to scoring full marks in related questions.
Is class 9 maths difficult?
In real Maths of class, 9th and 10th are both very easy. But practically you can say class 9th mathematics 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 math 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.
What is the best way to practice Class 9 Maths?
The best way to practice Class 9 Maths is through consistent problem-solving from the NCERT textbook and additional reference materials. Start by solving all the textbook exercises and then move on to sample papers and previous years’ question papers. This helps in familiarising yourself with the exam pattern and types of questions that are commonly asked.
Regular revision of key concepts and formulas ensures that you retain important information. Online platforms offering practice tests can also be beneficial for testing your speed and accuracy. Time management and regular revision are key to mastering the subject.
Is Class 9 Maths easy?
Class 9 Maths can feel challenging for some students due to the introduction of more complex concepts like algebraic expressions, geometry and coordinate geometry. However, with consistent practice and a clear understanding of concepts, it becomes easy. The difficulty level depends largely on how well students grasp the foundational topics and apply them to solve problems.
Students who regularly practice the NCERT exercises and seek help for difficult areas often find that the subject becomes easier over time. Proper guidance and use of supplementary resources like NCERT Solutions can make the subject less daunting.
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.
Are the NCERT solutions enough for scoring well in Class 9 Maths?
NCERT Solutions are a great resource and can be sufficient for scoring well in Class 9 Maths if studied thoroughly. The solutions cover all the essential concepts and types of questions that could appear in the exam. They are structured in a step-by-step manner to help students grasp the logic behind each problem.
However, for students aiming for perfection, practicing additional questions from reference books or mock tests might provide the extra edge. Solving a variety of problems ensures familiarity with different question formats, boosting overall performance in exams.
How can I improve my problem-solving skills in Class 9 Maths?
Improving problem-solving skills in Class 9 Maths requires regular practice and a strategic approach to tackling different types of questions. Start by understanding the concepts behind each topic and then apply them to solve NCERT textbook problems. After mastering the basics, move on to solving sample papers and taking timed mock tests to improve speed and accuracy.
Analysing mistakes and reviewing difficult problems is equally important for improvement. Revising key formulas and practicing mental Maths can also enhance problem-solving efficiency. Engaging in group discussions and seeking help from teachers or peers can further improve understanding and performance.
Can I download Class 9 Maths solutions for offline study?
Yes, you can easily download Class 9 Maths solutions for offline study from various websites like Tiwari Academy and other similar websites or the official NCERT website. These platforms offer downloadable PDFs of chapter-wise solutions, which can be saved for offline access. Tiwari Academy Offline mobile apps also provide NCERT solutions, allowing you to study without the need for an internet connection.
Offline access to solutions is helpful for revising anytime and anywhere, making it convenient for students who may not always have internet access. Having these solutions on hand ensures you can practice regularly and clarify doubts as they arise.
