Chapter-wise Class 9 Maths Questions and Answers Free PDF Download
Class 9 Maths is an important subject to master for students. In this class, they are introduced to concepts of Triangles, Polynomials, Number Systems, and much more. Also, the exercise questions are challenging, and thus we suggest the students to take guidance from reliable sources to prepare for the Class 9 Maths exam. In order to complete the vast syllabus in an easy and efficient way, Vedantu experts have compiled NCERT Class 9 Math Solution for students. These study materials act as guides that can help them progress in class. Students should download class 9th maths NCERT solutions PDF, for their preparation.


NCERT Solutions for Class 9 Maths - Chapter-wise List
Given below are the chapter-wise NCERT Solutions for Class 9 Maths. Go through these 9th maths solutions chapter-wise to be thoroughly familiar with the concepts.
S.No. | NCERT Solutions Class 9 Maths Chapter-wise List |
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Note: The chapters on Areas of Parallelograms and Triangles, Constructions and Probability have been excluded from the Class 9 Maths textbook for the 2024-25 academic year
Also Check for: The Concepts of NCERT Class 9 Maths
Glance on NCERT Solutions Class 9 Maths
NCERT Solutions for Class 9 Maths for all the chapters and exercises from Chapters 1 to 12 are provided.
Practising the textbook questions using these solutions can help students analyse their level of preparation and understanding of concepts.
Covering chapters like Number Systems, Algebraic Expressions, Linear Equations in Two Variables, Geometry, and Statistics.
The link also provides details about the exam pattern, marks weightage, and question paper design for CBSE Class 9 Maths.
The link also provides details about the exam pattern, marks weightage, and question paper design for CBSE Class 9 Maths.
This article also provides resources such as NCERT notes, important questions, exemplar solutions, RD Sharma, and RS Aggarwal solutions PDF for further reference.
NCERT Solutions for Class 9 Maths Chapter Details, Formulas and Exercises PDF
Chapter 1 - Number System
NCERT Class 9 Maths Chapter 1 sets the foundation for the subject. Solutions of text exercises and end exercise of Number are explained elaborately, to help understand the basic concepts. The chapter discusses the topics of rational, irrational numbers and representing the same on the number line. Students are also taught how to represent square roots, as well as terminating and non-terminating decimals on the number lines.
Exercise 1.1: Deals with basic classification of numbers. You might be asked to identify different types of numbers (natural, whole, integers, rational, irrational) from a given set.
Exercise 1.2: This exercise could involve applying properties of operations (addition, subtraction, multiplication, division) to various number systems. You might be asked to check if a specific property holds true for a particular operation on a given set of numbers.
Exercise 1.3: Here, the focus might be on representing numbers on the number line. You could be solving problems that involve plotting numbers, finding the distance between two numbers, or comparing their relative positions.
Exercise 1.4: Here, you might be challenged with problems that involve comparing and ordering numbers of different types (e.g., rational vs. irrational).
Exercise 1.5: This exercise could be a mix of concepts covered earlier. You might be presented with a scenario that requires applying various aspects of number systems and their properties to solve it.
In Class 9 Maths Chapter 1 on Number System, we cover the following:
Different Number Systems: natural, whole, integers, rational, irrational
Properties of operations (addition, subtraction, multiplication, division) on these systems
Representing numbers on the number line
Relating terminating/non-terminating recurring decimals to rational numbers
Understanding irrational numbers (e.g., √2, √3)
Every real number has a unique position on the number line (and vice versa)
Introduction to √x for positive real numbers
Brief review of exponent laws (integral & rational powers)
Brief introduction to rationalizing numbers
Chapter 1 - Number System Exercises in PDF Format | |
Class 9 Maths Chapter 1 Exercise 1.1 - 4 Questions & Solutions (4 short Answers) | |
Class 9 Maths Chapter 1 Exercise 1.2 - 4 Questions & Solutions (4 short Answers) | |
Class 9 Maths Chapter 1 Exercise 1.3 - 9 Questions & Solutions (8 short Answers, 1 long Answer) | |
Class 9 Maths Chapter 1 Exercise 1.4 - 5 Questions & Solutions (4 short Answers, 1 long Answer) | |
Class 9 Maths Chapter 1 Exercise 1.5 - 3 Questions & Solutions (3 short Answers) |
Along with this, students can also download additional study materials provided by Vedantu, for Chapter 1 of CBSE Class 9 Maths Solutions–
Chapter 2 - Polynomials
Chapter 2 of NCERT Solutions of Class 9 Maths is on Polynomials. Students are introduced to the concept of Polynomials, which are expressions consisting of variables and coefficients. Properties such as addition, subtraction, division, multiplication of polynomials are taught in this chapter along with their factorisation. The Factor Theorem and Remainder Theorem making use of these polynomials are also provided in this chapter.
Exercise 2.1: This exercise deals with identifying basic components of polynomials. You'll practice recognizing terms, coefficients, variables, and the degree of a polynomial expression.
Exercise 2.2: Here, the focus is on classifying polynomials based on their degree. You might be asked to identify polynomials as linear, quadratic, cubic, etc., based on the highest exponent of the variable.
Exercise 2.3: This exercise involves recognizing zeroes (or roots) of a polynomial. You might be presented with a polynomial equation and asked to find the values of the variable that make the equation true (where the expression evaluates to zero).
Exercise 2.4: This exercise covers on the Factor Theorem. This theorem relates the factors of a polynomial to its zeroes. You might be challenged with problems that involve finding factors based on zeroes or vice versa.
In Class 9 Maths Chapter 2 on Polynomials, we cover the following:
Explanation of a polynomial with one variable, its coefficients, along with examples and non-examples, its terms, and the zero polynomial.
Understanding the degree of a polynomial and types like constant, linear, quadratic, cubic polynomials; also monomials, binomials, and trinomials.
Concepts of factors, multiples, and zeros/roots of a polynomial/equation.
Introduction and rationale of the Remainder Theorem, with examples and comparisons to integers. Also, the statement and proof of the Factor Theorem.
Techniques for factorization of expressions like ax2 + bx + c, a ≠ 0 where a, b, c are real numbers, and of cubic polynomials using the Factor Theorem.
Definitions of the Remainder Theorem and the Factor Theorem.
Chapter 2 - Polynomials Exercises in PDF Format | |
Class 9 Maths Chapter 2 Exercise 2.1 - 5 Questions & Solutions (5 Short Answers) | |
Class 9 Maths Chapter 2 Exercise 2.2 - 4 Questions & Solutions (4 Short Answers) | |
Class 9 Maths Chapter 2 Exercise 2.3 - 3 Questions & Solutions (3 Short Answers) | |
Class 9 Maths Chapter 2 Exercise 2.4 - 5 Questions & Solutions (4 Short Answers, 1 Long Answer) |
Along with this, students can also download additional study materials provided by Vedantu, for Chapter 2 of CBSE Class 9 Maths Solutions–
Chapter 3 - Coordinate Geometry
Chapter 3 discusses the cartesian plane, coordinates of a point in the ‘xy’ plane, and several other significant terms associated with coordinate geometry. Students will learn how to plot points in the xy plane following the abscissa and ordinates, etc. With 3 exercises comprising both long and short questions, the exercises of NCERT Class 9 Solutions Maths for Chapter 3 are designed to test your application skills as well as cognizance.
Exercise 3.1: This exercise likely deals with the foundational concepts. You might be asked to explain how to describe the location of a point on a flat surface (like your desk) using coordinates. This involves understanding how perpendicular axes (X and Y) help pinpoint a position.
Exercise 3.2: Here, the focus is on translating coordinates into a visual representation. You'll probably practice plotting points on a graph based on their given coordinates (X and Y values).
In Class 9 Maths Chapter 3 on Coordinate Geometry, we cover the following:
The Cartesian Plane: A plane with a horizontal axis (x-axis) and a vertical axis (y-axis) that intersect at the origin (0,0).
Coordinates of a Point: Each point on the Cartesian plane is defined by an ordered pair (𝑥,𝑦), representing its position along the x-axis and y-axis.
Names and Terms Associated with the Coordinate Plane: Terminology includes terms like origin, quadrants, axes, and coordinate points.
Notations Used in Coordinate Geometry: Symbols and notations such as (x,y) for points, and 𝑂 for the origin.
Plotting Points on the Plane: The process of marking points on the Cartesian plane based on their coordinates (𝑥,𝑦)
Graph of Linear Equations with Examples: Representation of linear equations on the Cartesian plane, typically resulting in a straight line.
Focusing on Linear Equations of the Form ax+by+c=0: Understanding and simplifying linear equations to the slope-intercept form 𝑦=𝑚𝑥+𝑐
Linking with the Chapter on Linear Equations in Two Variables: Connecting concepts from coordinate geometry with those from the study of linear equations involving two variables.
Chapter 3 - Coordinate Geometry Exercises | |
Class 9 Maths Chapter 3 Exercise 3.1 - 2 Questions & Solutions (1 Short Answer, 1 Long Answer) | |
Class 9 Maths Chapter 3 Exercise 3.2 - 2 Questions & Solutions (2 Short Answers) |
Along with this, students can also download additional study materials provided by Vedantu, for Chapter 3 of CBSE Class 9 Maths Solutions–
Chapter 4 - Linear Equations in Two Variables
Chapter 4 also discusses the concept of linear equations having two variables. Students already equipped with the knowledge of coordinate geometry will learn how to plot the graph of a linear equation with two variables.
NCERT 9th class Maths book solutions include 4 exercises with 16 questions in total. This chapter includes application-based questions to test your understanding of the chapter.
Exercise 4.1: This exercise focuses on writing linear equations in two variables. You'll likely be given worded problems describing relationships between two variables and asked to translate them into mathematical equations.
Exercise 4.2: Here, you'll practice solving linear equations in two variables. The problems might involve finding the values of the variables (x and y) that satisfy the given equation.
In Class 9 Maths Chapter 4 on Linear Equations in Two Variables, we cover the following:
Review of linear equations in one variable.
Introduction to equations involving two variables.
Demonstration that a linear equation in two variables has infinitely many solutions, represented as ordered pairs of real numbers.
Plotting these solutions to show they form a straight line.
Real-life examples and problems, including those on ratio and proportion, with both algebraic and graphical solutions presented simultaneously.
Chapter 4 - Linear Equations in Two Variables Exercises in PDF Format | |
Class 9 Maths Chapter 4 Exercise 4.1 - 2 Questions & Solutions (2 Short Answers) | |
Class 9 Maths Chapter 4 Exercise 4.2 - 4 Questions & Solutions (3 Short Answers, 1 Long Answer) |
Along with this, students can also download additional study materials provided by Vedantu, for Chapter 4 of CBSE Class 9 Maths Solutions–
Chapter 5 - Introduction to Euclid's Geometry
The 5th Chapter, Introduction to Euclid's Geometry tries to establish a link between present-day geometry with that of Euclidean geometry. The axioms, theorems and postulates have been provided to provide students with an in-depth understanding. Chapter 5 of Class 9 Maths NCERT Solutions has 2 exercises. The questions are based on analysis to test your analytical skills.
Exercise 5.1: This exercise might involve basic definitions and properties of points and lines. You could be asked to identify points and lines in diagrams, understand how many points two lines can intersect, or differentiate between intersecting and parallel lines.
In Class 9 Maths Chapter 5 on Introduction to Euclid's Geometry, we cover the following:
History – Euclid and the development of geometry in India.
Euclid’s method of transforming observed phenomena into precise mathematics using definitions, common notions, axioms/postulates, and theorems.
The five postulates of Euclid.
Equivalent interpretations of the fifth postulate.
Demonstrating the connection between axioms and theorems.
Chapter 5 - Introduction to Euclid's Geometry Exercises in PDF Format | |
Class 9 Maths Chapter 5 Exercise 5.1 - 7 Questions & Solutions (4 Short Answers, 3 Long Answers) |
Along with this, students can also download additional study materials provided by Vedantu, for Chapter 5 of CBSE Class 9 Maths Solutions–
Chapter 6 - Lines and Angles
The 6th chapter in NCERT Solutions Class 9 Maths is on Lines and Angles. Students are mostly asked to prove the statements based on the axioms and theorems explained in the chapter. NCERT Solution Class 9 Maths of Chapter 6 includes 3 exercises.
Exercise 6.1: This exercise likely focuses on finding the measure of unknown angles based on given information. You might encounter problems where you need to use properties of angles (like a straight angle being 180 degrees) or identify special angle pairs (like linear pairs or verticals) to solve for missing angles.
In Class 9 Maths Chapter 6 on Lines and Angles, we cover the following:
Sum of Adjacent Angles on a Line: If a ray stands on a line, the sum of the two adjacent angles formed is 180°, and vice versa.
Vertically Opposite Angles: If two lines intersect, the vertically opposite angles are equal.
Angles Formed by a Transversal with Parallel Lines: Results on corresponding angles, alternate angles, and interior angles when a transversal intersects two parallel lines.
Parallel Lines: Lines parallel to a given line are also parallel.
Sum of Angles in a Triangle: The sum of the angles in a triangle is 180°.
Exterior Angle of a Triangle: If a side of a triangle is extended, the exterior angle formed is equal to the sum of the two opposite interior angles.
Chapter 6 - Lines and Angles Exercises in PDF Format | |
Class 9 Maths Chapter 6 Exercise 6.1 - 6 Questions & Solutions (5 Short Answers, 1 Long Answer) |
Along with this, students can also download additional study materials provided by Vedantu, for Chapter 6 of CBSE Class 9 Maths Solutions
Chapter 7 - Triangles
Triangles is the 7th Chapter in NCERT Maths Class 9 Solutions. The properties of triangles such as inequalities, congruence, rules of congruence have been explained in this chapter. Students are also taught about the application of the congruence rules while solving the exercise questions. NCERT Solution Class 9 Maths of Chapter 7 includes 5 exercises. These questions are designed to test your skills.
Exercise 7.1: This exercise deals with proving triangles congruent (having exactly the same size and shape) based on given criteria. You'll likely use properties like side-side-side (SSS) or angle-side-angle (ASA) congruence rules.
Exercise 7.2: Here, the focus is on properties of angles in triangles. You might encounter problems that involve finding the relationship between interior angles (angles inside the triangle) and exterior angles (angle formed by one side of the triangle and the extension of the other side).
Exercise 7.3: This exercise introduces the concept of midpoints and perpendicular bisectors (a line segment that bisects a side at a 90-degree angle). You might be asked to prove that a segment joining the midpoints of two sides of a triangle is parallel to the third side and half its length.
In Class 9 Maths Chapter 7 on Triangles, we cover the following:
SAS Congruence: Two triangles are congruent if two sides and the included angle of one triangle are equal to two sides and the included angle of the other triangle.
ASA Congruence: 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.
SSS Congruence: Two triangles are congruent if all three sides of one triangle are equal to all three sides of the other triangle.
Congruence in Right Triangles: Two right triangles are congruent if the hypotenuse and one side of one triangle are equal to the hypotenuse and one side of the other triangle.
Angles Opposite Equal Sides: The angles opposite equal sides of a triangle are equal.
Sides Opposite Equal Angles: The sides opposite equal angles of a triangle are equal.
Triangle Inequalities: Triangle inequalities and the relationship between an angle and the side opposite it; inequalities within a triangle.
Chapter 7 - Triangles Exercises in PDF Format | |
Class 9 Maths Chapter 7 Exercise 7.1 - 8 Questions & Solutions (6 Short Answers, 2 Long Answers) | |
Class 9 Maths Chapter 7 Exercise 7.2 - 8 Questions & Solutions (6 Short Answers, 2 Long Answers) | |
Class 9 Maths Chapter 7 Exercise 7.3 - 5 Questions & Solutions (3 Short Answers, 2 Long Answers) |
Along with this, students can also download additional study materials provided by Vedantu, for Chapter 7 of CBSE Class 9 Maths Solutions–
Chapter 8 - Quadrilaterals
In chapter 8 you will be introduced to Quadrilaterals and their various properties. A quadrilateral is a figure obtained by joining four distinct points on a plane. Students are provided in-depth knowledge about the topic in this chapter.
NCERT Solution Class 9 Maths of Chapter 8 includes 2 exercises. These questions are based on your application skills and analysis skills.
Exercise 8.1: This exercise involves using theorems related to quadrilaterals, especially parallelograms. You might encounter problems that ask you to prove properties of a quadrilateral based on given information about its sides or angles. For instance, you could be asked to show that a quadrilateral with opposite sides equal and parallel is a parallelogram.
Exercise 8.2: Here, the focus shifts towards applying the Mid-Point Theorem. This theorem states that the line segment joining the midpoints of any two sides of a triangle is parallel to the third side and half its length. You might be solving problems that involve using this theorem to prove properties of quadrilaterals or find missing lengths and angles within them.
In Class 9 Maths Chapter 8 on Triangles, we cover the following:
Diagonals of a Parallelogram: The diagonal of a parallelogram divides it into two congruent triangles.
Equality of Opposite Sides in a Parallelogram: In a parallelogram, opposite sides are equal, and vice versa.
Equality of Opposite Angles in a Parallelogram: In a parallelogram, opposite angles are equal, and conversely.
Conditions for a Parallelogram: A quadrilateral is a parallelogram if a pair of its opposite sides are both parallel and equal.
Bisection of Diagonals in a Parallelogram: In a parallelogram, the diagonals bisect each other, and conversely.
Midpoint Theorem in Triangles: The line segment joining the midpoints of any two sides of a triangle is parallel to the third side, and its converse can be motivated.
Chapter 8 - Quadrilaterals Exercises in PDF Format | |
Class 9 Maths Chapter 8 Exercise 8.1 - 12 Questions & Solutions (2 Short Answers, 6 Long Answers, 4 Very Long Answers) | |
Class 9 Maths Chapter 8 Exercise 8.2 - 7 Questions & Solutions (2 Short Answers, 3 Long Answers, 3 Very Long Answers) |
Along with this, students can also download additional study materials provided by Vedantu, for Chapter 8 of CBSE Class 9 Maths Solutions–
Chapter 9 - Circles
In this chapter of Class 9 Maths, you will learn about circles. Definition of a circle, tangent, chord, arc, etc., are described in this chapter. Various other concepts such as the angle subtended by the arc of a circle, cyclic quadrilaterals, etc., are also explained. 9th class Maths book solutions Chapter 9 includes 6 exercises and solutions to all 35 questions given in your NCERT Textbook. These questions are based on your numerical abilities, application skills, and memory skills.
Exercise 9.1: Deals with theorems about equal chords subtending equal central angles and vice versa (converse). You'll practice identifying these relationships and their implications.
Exercise 9.2: This exercise involves problems applying these central angle and chord relationships to solve for missing measures (angles or chord lengths) based on the given information.
In Class 9 Maths Chapter 9 on Circles, we cover the following:
Defining Circle-related Concepts: Understanding the terms radius, circumference, diameter, chord, arc, and subtended angle through examples.
Equal Chords and Central Angles: Equal chords of a circle subtend equal angles at the centre, and vice versa.
Perpendicular Bisector of a Chord: The perpendicular from the centre of a circle to a chord bisects the chord, and conversely, a line drawn through the centre of a circle to bisect a chord is perpendicular to the chord.
Uniqueness of Circles through Three Points: There is one and only one circle passing through three given non-collinear points.
Equal Chords and Distance from Center: Equal chords of a circle (or of congruent circles) are equidistant from the centre(s), and vice versa.
Angle Subtended by an Arc: 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.
Angles in the Same Segment: Angles in the same segment of a circle are equal.
Concyclic Points and Cyclic Quadrilaterals: 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. The sum of either pair of opposite angles of a cyclic quadrilateral is 180°, and vice versa.
Chapter 9 - Circles Exercises in PDF Format | |
Class 9 Maths Chapter 9 Exercise 9.1 - 2 Questions & Solutions (2 Short Answers) | |
Class 9 Maths Chapter 9 Exercise 9.2 - 2 Questions & Solutions (2 Long Answers) | |
Class 9 Maths Chapter 9 Exercise 9.3 - 3 Questions & Solutions (3 Long Answers) |
Along with this, students can also download additional study materials provided by Vedantu, for Chapter 9 of CBSE Class 9 Maths Solutions
Chapter 10 - Heron’s Formula
Heron’s formula, the 10th chapter of Class 9 Maths, is used to calculate the area of a triangle when the lengths of its sides are given. Students are also taught how to calculate the area of quadrilaterals and other polygons by dividing them into triangles and applying Heron’s formula. NCERT Solution Class 9 Maths of Chapter 10 includes 2 exercises designed on your ability to decipher and apply the formula.
Exercise 10.1: This exercise involves practice problems where you'll be given the side lengths of a triangle and asked to find its area using Heron's Formula.
In Class 9 Maths Chapter 10 on Heron’s Formula, we cover the following:
Area of a Triangle with Heron’s Formula: Finding the area of a triangle using Heron’s Formula, without going into the proof.
Application in Quadrilaterals: Using Heron’s Formula to find the area of a quadrilateral.
Chapter 10 - Heron’s Formula Exercises in PDF Format | |
Class 9 Maths Chapter 10 Exercise 10.1 - 6 Questions & Solutions (2 Short Answers, 2 Long Answer, 2 Very Long Answers) |
Along with this, students can also download additional study materials provided by Vedantu, for Chapter 10 of CBSE Class 9 Maths Solutions
Chapter 11 - Surface Areas and Volumes
In this chapter, you will understand the significance of surface areas and volumes of cubes, cuboids, cones, etc. This chapter teaches students how to calculate the same. NCERT Solution Class 9 Maths of Chapter 11 includes 9 exercises and these questions will test your understanding ability and memory skills (required to retain the different formulae).
Exercise 11.1: Introduction to finding the curved surface area (CSA) of a cone. You'll be introduced to the relevant formula and practice using it on cones with different measurements.
Exercises 11.2 - 11.3: Further exploration of CSA. These exercises might involve variations like calculating CSA when the slant height or radius is missing, or solving problems with right cones vs. slanted cones.
In Class 9 Maths Chapter 11 on Surface Areas and Volumes, we cover the following:
Introduction to Surface Areas and Volumes
Surface Area of a Cuboid and a Cube:
Surface Area of a Right Circular Cylinder
Surface Area of a Right Circular Cone
Surface Area of a Sphere
Volume of a Cuboid
Volume of a Cube
Volume of a Right Circular Cylinder
Volume of a Right Circular Cone
Volume of a Sphere
Chapter 11 - Surface Areas and Volumes Exercises in PDF Format | |
Class 9 Maths Chapter 11 Exercise 11.1 - 8 Questions & Solutions | |
Class 9 Maths Chapter 11 Exercise 11.2 - 11 Questions & Solutions | |
Class 9 Maths Chapter 11 Exercise 11.3 - 8 Questions & Solutions | |
Class 9 Maths Chapter 11 Exercise 11.4 - Questions & Solutions |
Along with this, students can also download additional study materials provided by Vedantu, for Chapter 10 of CBSE Class 9 Maths Solutions
Chapter 12 - Statistics
Statistics is the 12th chapter in Class 9 Maths. Students are introduced to the concept of statistics and its significance and application in different fields. Concepts of data, data distribution, and representation, different types of graphs, etc., are also explained. Students will mainly learn to calculate mean, median, and mode in this chapter. NCERT Solution Class 9 Maths of Chapter 12 contains 4 exercises. The questions judge your comprehensive ability and analytical skills.
Exercise 12.1: This exercise involves interpreting data presented in a textual format (like percentages) and converting it into a suitable format for creating a bar graph.
In Class 9 Maths Chapter 12 on Surface Areas and Volumes, we cover the following:
Gathering data.
Presenting data in various formats such as tables, ungrouped and grouped data.
Creating bar graphs, histograms (with varying base lengths), and frequency polygons.
Analysing data qualitatively to determine the appropriate method of presentation.
Calculating mean, median, and mode for ungrouped data.
Chapter 12 - Statistics Exercises in PDF Format | |
Class 9 Maths Chapter 12 Exercise 12.1 - 2 Questions & Solutions (2 Short Answers) |
Along with this, students can also download additional study materials provided by Vedantu, for Chapter 10 of CBSE Class 9 Maths Solutions
CBSE Class 9 Maths Chapter-Wise Marks Weightage
Sr.No | Chapter Name | Marks |
1 | Number Systems | 10 |
2 | Algebra | 20 |
3 | Coordinate Geometry | 4 |
4 | Geometry | 27 |
5 | Mensuration | 13 |
6 | Statistics & Probability | 6 |
Total | 80 | |
Internal Assessment | 20 | |
Total | 100 |
Internal Assessment for CBSE Class 9 Maths
Internal Assessment | |
Pen Paper Test and Multiple Assessment | 10 Marks |
Portfolio | 5 Marks |
Lab Practical | 5 Marks |
Total | 20 Marks |
Benefits of Vedantu’S NCERT Solutions for Class 9 Maths
NCERT or National Council of Educational Research and Training was created to standardize India’s education system. The NCERT solutions can help you get an in-depth and detailed understanding of the concepts and questions from the NCERT textbooks. Here are some more benefits of Vedantu’s NCERT Solutions for Class 9 Maths:
1. All the Concepts are Explained in Detail
In these solutions, you will find that all the concepts have been explained in easy language and in detail. It will help you get a better understanding of the concepts and score well in your exams.
2. Accurate Solutions
The NCERT solutions for class 9 maths PDF by Vedantu have been created by experienced teachers. The solutions are well-reviewed so that students don’t get misguided by inaccurate study materials.
3. Learn Online and Offline
Vedantu’s NCERT Solutions for Class 9 Maths are available in PDF format online. You can download these PDFs and learn offline as well. This means you can study anytime and anywhere. It is also possible to share the links of the NCERT Maths class 9 solutions PDF download with your friends.
4. Get Your Doubts Cleared
If you are confused about any topic from your class 9 Maths syllabus, you can use these NCERT solutions for getting your doubts cleared. All the solutions are provided in an easy way so that you can have your concepts cleared.
5. Created by the Best Teachers
Vedantu’s NCERT Solutions for Class 9 Maths have been created by teachers who are subject matter experts. By studying through these high-quality study materials, you will be able to score more marks. The solutions have been designed after performing extensive research on the subject. Once you are done, you will be able to solve problems of varying difficulty levels.
6. Helps with Preparation For Exams
The NCERT Solutions contain a Chapter Wise List Of Class 9 Maths so that students can easily identify the important chapters that have significant weightage in the examinations. Thus, they can prepare for their exams well and score more marks by focusing on chapters that are crucial.
7. Makes Revision Easier
While revising the chapters, students don’t have to go through the entire book. The NCERT solutions have explained all the topics and concepts in a very easy manner. While solving the problems, students will learn about the theorems, formulas, and descriptions that are used. Thus, they will easily be able to complete the chapter without any interruptions.
Important Related Links for CBSE Class 9 Maths
Conclusion
Vedantu's NCERT Solutions for Class 9 Maths provide comprehensive guidance and practice for each curriculum chapter. These solutions are essential for students aiming to understand concepts thoroughly and perform well in exams. Key areas to focus on include mastering formulas, practicing exercises, and understanding theorems and their applications. Additionally, topics such as Polynomials, Coordinate Geometry, Linear Equations, and Probability are crucial and often challenging, requiring extra attention and regular practice. Utilizing these solutions can significantly enhance a student's problem-solving skills and conceptual clarity.
FAQs on NCERT Solutions For Class 9 Maths All Chapters - 2025-26
1. What is the correct method to use NCERT Solutions for Class 9 Maths effectively?
First, attempt to solve the NCERT textbook problems on your own. If you get stuck or wish to verify your approach, then refer to the solutions. Focus on understanding the step-by-step method used, not just memorising the final answer. This strategy helps in building genuine problem-solving abilities and ensures you learn the underlying concepts.
2. Why is it crucial to refer to the Class 9 Maths NCERT Solutions for exam preparation?
The NCERT Solutions are designed strictly according to the official CBSE 2025–26 curriculum and exam pattern. They provide the most standard and accepted methods for solving problems, which aligns perfectly with the board's evaluation criteria. Using them ensures your preparation is focused and relevant for scoring well in exams.
3. Are there any deleted chapters or topics in the Class 9 Maths syllabus for the 2025-26 session?
Yes, for the 2025-26 academic session, CBSE has rationalised the syllabus. Key chapters like 'Areas of Parallelograms and Triangles' have been removed entirely. It is essential to refer to the latest syllabus to ensure you focus your efforts only on the prescribed topics that will be part of the final examination.
4. How should I make notes when using the NCERT Solutions?
When studying with NCERT Solutions, avoid copying the entire solution. Instead, use a notebook to jot down key information that aids in revision. This includes:
- The specific formula or theorem applied in a particular step.
- Any tricky calculation or a common mistake you are likely to make.
- Alternative methods for solving the same problem, if applicable.
This practice helps in better retention and faster revision.
5. For which chapters in Class 9 Maths are the step-by-step NCERT Solutions particularly beneficial?
While solutions are helpful for all chapters, they are especially useful for chapters that involve complex proofs and multi-step problems. These include:
- Chapter 7: Triangles (for understanding congruence criteria).
- Chapter 8: Quadrilaterals (for applying properties and theorems correctly).
- Chapter 10: Circles (for solving complex theorem-based questions).
- Chapter 12: Surface Areas and Volumes (for accurate formula application and calculations).
6. Can I use a different method to solve a problem than the one shown in the NCERT Solutions and still get full marks?
Absolutely. As long as your method is mathematically sound, logically correct, and part of the recognised CBSE curriculum, you will receive full marks. The NCERT Solutions provide a standard, reliable approach, but examiners are trained to award marks for any valid alternative method that leads to the correct result.
7. Is practicing only the NCERT textbook questions using these solutions enough to score over 95% in Class 9 Maths?
Mastering the NCERT textbook with the help of solutions is the most critical first step and builds a strong conceptual foundation. However, to score above 95%, it is highly recommended to also solve problems from NCERT Exemplar, sample papers, and previous years' question papers. This exposes you to a wider variety of question types and improves your speed and confidence under exam conditions.
8. How do NCERT Solutions help in understanding the application of theorems in chapters like Triangles or Circles?
NCERT Solutions do more than provide answers; they demonstrate the practical application of complex theorems. By showing exactly how a theorem like the Mid-point Theorem or the 'angle subtended by an arc at the centre' is used to solve a specific problem, the solutions bridge the gap between theoretical knowledge and its application, making abstract concepts much clearer.
9. What is the best way to handle a problem when my answer doesn't match the NCERT Solution?
If your answer differs, avoid the impulse to immediately copy the provided solution. Instead, carefully re-examine your own steps to identify the error. Check for calculation mistakes, incorrect formula application, or a flaw in your logic. Comparing your method with the correct one is an excellent way to pinpoint and fix specific weaknesses in your understanding.
10. Beyond getting the correct answer, what should I look for in the NCERT Solutions to improve my problem-solving skills?
To truly enhance your skills, analyse the structure of the solution. Ask yourself 'why' a particular step was taken or 'how' a specific formula was chosen. Notice the efficiency of the method used. Understanding the reasoning ('the why') behind the procedure ('the how') is essential for developing strong analytical skills that can be applied to new and unfamiliar problems.











