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NCERT Solutions For class 9 Maths

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Last updated date: 23rd May 2024
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NCERT Solutions for Class 9 Maths - 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.




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.

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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.


  1. 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.

  2. 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.

  3. 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.

  4. Exercise 1.4: This exercise might delve deeper into specific number systems. You could encounter questions related to properties of even and odd numbers, divisibility rules, or operations on fractions/decimals.

  5. Exercise 1.5: Here, you might be challenged with problems that involve comparing and ordering numbers of different types (e.g., rational vs. irrational).

  6. Exercise 1.6: 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 - 2 Questions & Solutions (2 long Answers)

Class 9 Maths Chapter 1 Exercise 1.5 - 5 Questions & Solutions (4 short Answers, 1 long Answer)

Class 9 Maths Chapter 1 Exercise 1.6 - 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.


  1. 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.

  2. 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.

  3. 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).

  4. 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.

  5. Exercise 2.5: This exercise introduces basic algebraic identities. These are equalities that hold true for all permissible values of the variables involved. You might be asked to prove or use such identities for simplification.


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)

Class 9 Maths Chapter 2 Exercise 2.5 - 16 Questions & Solutions (9 Short Answers, 5 Long Answer, 2 Very Long Answers)


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.


  1. 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.

  2. 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).

  3. Exercise 3.3: This exercise flips the script. You might be given a graph with points plotted and asked to determine their corresponding coordinates based on their position on the axes.


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)

Class 9 Maths Chapter 3 Exercise 3.3 - 2 Questions & Solutions (1 Short Answer, 1 Long Answer)



Along with this, students can also download additional study materials provided by Vedantu, for Chapter 3 of CBSE Class 9 Maths Solutions–



NCERT Solutions for Class 9 Maths 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.


  1. 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.

  2. 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.

  3. Exercise 4.3: This exercise introduces the concept of graphical representation of linear equations. You'll probably be asked to graph the solutions of the equations you practised solving in Exercise 4.2. This will help you visualize the relationship between the variables.

  4. Exercise 4.4: This exercise builds on your understanding from Exercise 4.3. You might be given the graph of a linear equation and asked to interpret it, write the corresponding equation, or answer questions based on the visual representation.


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)

Class 9 Maths Chapter 4 Exercise 4.3 - 8 Questions & Solutions (4 Short Answers, 4 Long Answers)

Class 9 Maths Chapter 4 Exercise 4.4 - 2 Questions & Solutions (2 Long Answers)



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.


  1. 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.

  2. Exercise 5.2: Here, you might encounter proofs related to the properties of points and lines introduced in the chapter. These proofs could involve establishing simple facts using the definitions and axioms presented in Euclid's Geometry.


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)

Class 9 Maths Chapter 5 Exercise 5.2 - 2 Questions & Solutions (1 Short Answer, 1 Long Answer)



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.


  1. 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.

  2. Exercise 6.2: Here, the focus might shift towards introducing transversals and understanding how they interact with parallel lines. You could be solving problems that involve finding corresponding angles, alternate interior angles, or alternate exterior angles formed by a transversal intersecting parallel lines.

  3. Exercise 6.3: This exercise could be a mix of concepts covered in the previous exercises. You might encounter problems that combine finding missing angles, identifying special angle pairs, and applying properties of parallel lines intersected by a transversal.


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)

Class 9 Maths Chapter 6 Exercise 6.2 - 3 Questions & Solutions (3 Short Answers, 3 Long Answers)

Class 9 Maths Chapter 6 Exercise 6.3 - 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.


  1. 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.

  2. 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).

  3. 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.

  4. Exercise 7.4: This exercise delves into the relationship between side lengths and angles in a triangle. You could be challenged with problems that involve proving that the longest side is opposite the largest angle in a right-angled triangle, or exploring relationships between side lengths in general triangles.


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)

Class 9 Maths Chapter 7 Exercise 7.4 - 6 Questions & Solutions (5 Short Answers, 1 Long Answer)

Class 9 Maths Chapter 7 Exercise 7.5 - 4 Questions & Solutions (3 Short Answers, 1 Long Answer)



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.


  1. 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.

  2. 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.


  1. 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.

  2. 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)

Class 9 Maths Chapter 9 Exercise 9.4 - 6 Questions & Solutions (6 Long Answers)

Class 9 Maths Chapter 9 Exercise 9.5 - 12 Questions & Solutions (12 Long Answers)

Class 9 Maths Chapter 9 Exercise 9.6 - 10 Questions & Solutions (10 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.


  1. 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.

  2. Exercise 10.2: This is a summary or review exercise. It revisits the key points of Heron's Formula, its application, or even ask you to solve problems similar to Exercise 10.1.


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)

Class 9 Maths Chapter 10 Exercise 10.2 - 9 Questions & Solutions (4 Long Answers, 5 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).


  1. 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.

  2. Exercises 11.2 - 11.5: 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.

  3. Exercises 11.6 - 11.8: Shifting focus to total surface area. You'll likely learn the formula for total surface area (TSA) of a cone (CSA + area of the base) and practice applying it to solve problems.

  4. Exercise 11.9: Introduction to volume of a cone. This exercise might involve the formula for the volume of a cone (1/3 * π * r² * h) and solving problems to find the volume based on cone dimensions.


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 (4 Short Answers, 4 Long Answers)

Class 9 Maths Chapter 11 Exercise 11.2 - 11 Questions & Solutions (5 Short Answers, 6 Long Answers)

Class 9 Maths Chapter 11 Exercise 11.3 - 8 Questions & Solutions

Class 9 Maths Chapter 11 Exercise 11.4 - 9 Questions & Solutions (4 Short Answers, 5 Long Answers)

Class 9 Maths Chapter 11 Exercise 11.5 - 9 Questions & Solutions (4 Short Answers, 5 Long Answers)

Class 9 Maths Chapter 11 Exercise 11.6 - 8 Questions & Solutions (8 Short Answers)

Class 9 Maths Chapter 11 Exercise 11.7 - 9 Questions & Solutions (9 Long Answers)

Class 9 Maths Chapter 11 Exercise 11.8 - 10 Questions & Solutions (5 Short Answers, 5 Long Answers)

Class 9 Maths Chapter 11 Exercise 11.9 - 3 Questions & Solutions (3 Long Answers)



Along with this, students can also download additional study materials provided by Vedantu, for Chapter 10 of CBSE Class 9 Maths Solutions



NCERT Solutions for Class 9 Maths 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.


  1. 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.

  2. Exercise 12.2: Here, you will be given a partially constructed bar graph with labels but missing bar heights. Based on the data provided, you'll likely practice calculating the heights of the bars and completing the graph.

  3. Exercise 12.3: This exercise introduces you to interpreting information from a completed bar graph. You will be asked to answer questions like identifying the category with the highest/lowest value or comparing values between different categories.

  4. Exercise 12.4: This exercise is a culmination of the previous ones. You might be presented with raw data or a partially completed graph, requiring you to use your understanding to create or interpret a complete bar graph and answer questions based on it.


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)

Class 9 Maths Chapter 12 Exercise 12.2 - 9 Questions & Solutions (9 Long Answers)

Class 9 Maths Chapter 12 Exercise 12.3 - 9 Questions & Solutions (6 Short Answers, 3 Long Answers)

Class 9 Maths Chapter 12 Exercise 12.4 - 6 Questions & Solutions (2 Short Answers, 4 Long 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

1. How to study NCERT Solutions for Class 9 Maths in an easy way?

Vedantu offers a free PDF for NCERT Solutions for Maths Class 9. In addition to being totally free, the NCERT Maths class 9 solutions PDF download can be accessed anytime as per your convenience and from anywhere and what’s more important is that these are designed by experienced teachers and thus, are error-free and reliable.

2. How to download NCERT Solutions for Class 9 Maths PDFs?

The latest edition of  Class 9 NCERT Solutions for Maths are available at Vedantu from where they can be downloaded by clicking on the links provided. Based on the CBSE syllabus, these solutions will enhance your ability for exam preparation and the option for convenient download makes things more hassle-free. You can now prepare for Class 9 Maths as per the latest syllabus and get all the necessary study material at your fingertips.

3. Which are the important chapters in CBSE Class 9 Maths?

The Class 9 Maths important chapters include:

  • Polynomials

  • Circles

  • Surface Areas and Volume

  • Triangles

  • Areas of Parallelograms and Triangles

  • Quadrilaterals

4. Which chapters and exercises are deleted from CBSE Class 9th Maths CBSE?

The chapters deleted from NCERT Class 9 CBSE Maths syllabus are Introduction to Euclid's Geometry and Areas of Parallelograms and Triangles. In addition to these, parts of various chapters are deleted as well.

5. Are these NCERT Solutions enough to score better in the Class 9 Maths Board Exam?

NCERT Solutions for Class 9 Maths help students to find answers to the textbook exercise problems and clear all their doubts regarding the questions given in the NCERT book. The solutions are provided by expert teachers who are well versed in the curriculum. By referring to these, students can learn how to write answers in the exam that would fetch more marks. Students should, however, first make a habit of understanding the chapters and then refer to the NCERT Solutions if they are having trouble in solving the questions given in the textbook. Students are also encouraged to practise questions from previous years and solve sample papers to improve their scores in the exam.

6. Why is it important to refer to NCERT Solutions for Class 9 Maths?

Studying from the NCERT Solutions for Class 9 Maths is very important as they are a reliable way for you to cross-check your answers. You can use these as a guide on how your answers should appear in an examination. It will help you ensure that you don’t miss any steps and score the best possible marks.

7. Should I make notes while going through the NCERT Solutions for Class 9 Maths?

When you are creating notes, you are creating a simple guide that will help you build a thorough understanding of the subject as well as when you want to revise it. It helps you retain and recall concepts when needed. So, if you want to expedite your learning process, you need to make notes as well.

8. What is the best way to learn the concepts that are covered in the NCERT Solutions for Class 9 Maths?

The best way for you to learn the concepts that are covered in the solutions is through regular practice. If you are facing some difficulty with a concept and are unable to proceed further, you need to clarify your doubts immediately. This will ensure that there are no gaps in your learning.

9. Can you use any other method for solving questions apart from the one provided in the NCERT Solutions for Class 9 Maths pdf?

Yes, you can use some other method for solving problems as long as it is universally recognized. You cannot use any tricks to solve exam problems. You have to use standardized techniques.

10. Why should I refer to Vedantu’s NCERT Solutions Class 9 Maths?

Vedantu’s NCERT Solutions Class 9 Maths contains answers to all the questions in the NCERT Class 9 Maths book. The solutions are present in a simple manner so that students can understand easily. These solutions are framed by subject-matter experts and the solutions are updated according to the latest curriculum of the CBSE. Hence, these are very reliable. It will help students to clear their doubts and strengthen their concepts.

11. Should I practice NCERT Solutions for Class 9 Maths regularly?

Yes, you should practice NCERT Solutions for Class 9 Maths regularly. Solving questions daily will improve your speed and accuracy. Your fundamental concepts will be cleared, and you will understand chapters of higher classes easily. If you practice daily, you will gain sufficient confidence to attempt new questions, and you can even play around with the concepts, which will enhance your analytical skills.

12. What is the best reference book for Class 9 Maths?

Vedantu’s NCERT Solutions for Class 9 Maths is the best reference book for Class 9 Maths. It has detailed and comprehensive solutions to all questions in your NCERT Maths book. All the topics are covered in this book, and it focuses on strengthening your concepts. This is prepared by top faculties and is in accordance with the latest CBSE curriculum, and is very reliable.

13. Which is the hardest chapter in Maths Class 9?

The hardest chapter in Class 9 Maths often varies for different students based on their individual strengths and weaknesses. However, many students find "Chapter 8: Quadrilaterals" and "Chapter 10: Circles" challenging due to the abstract concepts and theorems involved. Additionally, "Chapter 13: Surface Areas and Volumes" can also be tough due to the complex calculations and spatial visualization required.

14. Which chapter is most important in Class 9 Maths?

All chapters in Class 9 Maths are important as they lay the foundation for higher classes. However, some particularly crucial chapters include "Chapter 1: Number Systems," "Chapter 6: Lines and Angles," "Chapter 8: Quadrilaterals," and "Chapter 14: Statistics." These chapters introduce fundamental concepts that are extensively used in higher-level mathematics.

15. Is Class 9 Maths easy?

Class 9 Maths can be easy for some students and challenging for others. It largely depends on a student's grasp of the basics, their interest in the subject, and the amount of practice they put in. Consistent study, understanding the core concepts, and regular practice can make Class 9 Maths manageable and even enjoyable.

16. Is Class 9 Maths important?

Yes, Class 9 Maths is very important. It builds the foundation for Class 10 and higher secondary level mathematics. The concepts learned in Class 9 are crucial for understanding more advanced topics in future classes. A strong understanding of Class 9 Maths also aids in various competitive exams and entrance tests later on.


By focusing on understanding the concepts thoroughly and practising regularly, students can excel in Class 9 Maths and find it to be a rewarding subject.