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NCERT Solutions For class 9 Maths

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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.

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

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 1 of CBSE Class 9 Maths Solutions–

Number System Important Questions

Number System Important Formulas

Number System Revision Notes

Number System NCERT Exemplar Solutions

Number System RD Sharma Solutions

Number Systems RS Aggarwal 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.

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 ax 2 + 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.

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 2 of CBSE Class 9 Maths Solutions–

Polynomials Important Questions

Polynomials Important Formulas

Polynomials Revision Notes

Polynomials NCERT Exemplar Solution

Polynomials RS Aggarwal 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).

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.

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

Coordinate Geometry Important Questions

Coordinate Geometry Important Formulas

Coordinate Geometry Revision Notes

Coordinate Geometry RD Sharma Solutions

Coordinate Geometry RS Aggarwal 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.

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.

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.

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.

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 4 of CBSE Class 9 Maths Solutions–

Linear Equations in Two Variables Important Questions

Linear Equations in Two Variables Important Formulas

Linear Equations in Two Variables Revision Notes

Linear Equations in Two Variables NCERT Exemplar Solutions

Linear Equations in Two Variables RD Sharma Solutions

Linear Equations in Two Variables RS Aggarwal 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.

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.

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 5 of CBSE Class 9 Maths Solutions–

Introduction to Euclids Geometry Important Questions

Introduction to Euclids Geometry Important Formulas

Introduction to Euclids Geometry Revision Notes

Introduction to Euclids Geometry NCERT Exemplar Solutions

Introduction to Euclids Geometry RD Sharma Solutions

Introduction to Euclids Geometry RS Aggarwal 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.

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.

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.

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 6 of CBSE Class 9 Maths Solutions

Lines and Angles Important Questions

Lines and Angles Important Formulas

Lines and Angles Revision Notes

Lines and Angles NCERT Exemplar Solutions

Lines and Angles RD Sharma Solutions

Lines and Angles RS Aggarwal 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.

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.

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 7 of CBSE Class 9 Maths Solutions–

Triangles Important Questions

Triangles Important Formulas

Triangles Revision Notes

Triangles NCERT Exemplar Solutions

Chapter 8: Triangles RS Aggarwal 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.

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 8 of CBSE Class 9 Maths Solutions–

Quadrilaterals Important Questions

Quadrilaterals Important Formulas

Quadrilaterals Revision Notes

Quadrilaterals NCERT Exemplar Solutions

Quadrilaterals RD Sharma Solutions

Quadrilaterals RS Aggarwal 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.

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

Circles Important Questions

Circles Important Formulas

Circles Revision Notes

Circles NCERT Exemplar Solutions

Circles RD Sharma Solutions

Circles RS Aggarwal 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.

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.

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

Heron’s Formula Important Questions

Heron’s Formula Important Formulas

Heron’s Formula Revision Notes

Heron’s Formula NCERT Exemplar Solutions

Heron’s Formula RD Sharma 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 - 11.5: 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.

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.

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

Surface Areas and Volumes Important Questions

Surface Areas and Volumes Formulas

Surface Areas and Volumes Revision Notes

Surface Areas and Volumes NCERT Exemplar 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.

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.

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.

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.

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.

Statistics Important Questions

Chapter 12: Statistics Formulas

Chapter 12: Statistics Revision Notes

CBSE Class 9 Maths Chapter-Wise Marks Weightage 

Internal Assessment for CBSE Class 9 Maths

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

Important Questions for CBSE Class 9 Math

RS Aggarwal Class 9 Solutions for Math book

NCERT Class 9 Math Formulas

NCERT Class 9 Maths Revision Notes

NCERT Class 9 Maths Exemplar Solutions

RD Sharma Solutions for NCERT Class 9

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

Surface Areas and Volume

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.

NCERT SOLUTIONS FOR CLASS 9

Cbse class 9 study materials.

• NCERT Solutions
• NCERT Class 9
• NCERT 9 Maths
• Chapter 1: Number Systems

NCERT Solutions for Class 9 Maths Chapter 1 Number Systems

Ncert solutions class 9 maths chapter 1 – cbse free pdf download.

Download Exclusively Curated Chapter Notes for Class 9 Maths Chapter – 1 Number Systems

Download most important questions for class 9 maths chapter – 1 number systems.

In NCERT Solutions for Class 9 Maths Chapter 1 , students are introduced to several important topics that are considered to be very crucial for those who wish to pursue Mathematics as a subject in their higher classes. Based on these NCERT Solutions , students can practise and prepare for their upcoming CBSE exams, as well as equip themselves with the basics of Class 10. These Maths Solutions of NCERT Class 9 are helpful as they are prepared with respect to the latest update on the CBSE syllabus for 2023-24 and its guidelines.

• Chapter 1- Number Systems
• Chapter 2 Polynomials
• Chapter 3 Coordinate Geometry
• Chapter 4 Linear Equations in Two Variables
• Chapter 5 Introduction to Euclids Geometry
• Chapter 6 Lines and Angles
• Chapter 7 Triangles
• Chapter 8 Quadrilaterals
• Chapter 9 Areas of Parallelograms and Triangles
• Chapter 10 Circles
• Chapter 11 Constructions
• Chapter 12 Heron’s Formula
• Chapter 13 Surface Areas and Volumes
• Chapter 14 Statistics
• Chapter 15 Inroduction to Probability

NCERT Solutions for Class 9 Maths Chapter 1 – Number Systems

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Access Answers to NCERT Class 9 Maths Chapter 1 – Number Systems

Exercise 1.1 page: 5.

1. Is zero a rational number? Can you write it in the form p/q where p and q are integers and q ≠ 0?

We know that a number is said to be rational if it can be written in the form p/q , where p and q are integers and q ≠ 0.

Taking the case of ‘0’,

Zero can be written in the form 0/1, 0/2, 0/3 … as well as , 0/1, 0/2, 0/3 ..

Since it satisfies the necessary condition, we can conclude that 0 can be written in the p/q form, where q can either be positive or negative number.

Hence, 0 is a rational number.

2. Find six rational numbers between 3 and 4.

There are infinite rational numbers between 3 and 4.

As we have to find 6 rational numbers between 3 and 4, we will multiply both the numbers, 3 and 4, with 6+1 = 7 (or any number greater than 6)

i.e., 3 × (7/7) = 21/7

and, 4 × (7/7) = 28/7. The numbers in between 21/7 and 28/7 will be rational and will fall between 3 and 4.

Hence, 22/7, 23/7, 24/7, 25/7, 26/7, 27/7 are the 6 rational numbers between 3 and 4.

3. Find five rational numbers between 3/5 and 4/5.

There are infinite rational numbers between 3/5 and 4/5.

To find out 5 rational numbers between 3/5 and 4/5, we will multiply both the numbers 3/5 and 4/5

with 5+1=6 (or any number greater than 5)

i.e., (3/5) × (6/6) = 18/30

and, (4/5) × (6/6) = 24/30

The numbers in between18/30 and 24/30 will be rational and will fall between 3/5 and 4/5.

Hence,19/30, 20/30, 21/30, 22/30, 23/30 are the 5 rational numbers between 3/5 and 4/5

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

(i) Every natural number is a whole number.

Natural numbers- Numbers starting from 1 to infinity (without fractions or decimals)

i.e., Natural numbers = 1,2,3,4…

Whole numbers – Numbers starting from 0 to infinity (without fractions or decimals)

i.e., Whole numbers = 0,1,2,3…

Or, we can say that whole numbers have all the elements of natural numbers and zero.

Every natural number is a whole number; however, every whole number is not a natural number.

(ii) Every integer is a whole number.

Integers- Integers are set of numbers that contain positive, negative and 0; excluding fractional and decimal numbers.

i.e., integers= {…-4,-3,-2,-1,0,1,2,3,4…}

Whole numbers- Numbers starting from 0 to infinity (without fractions or decimals)

i.e., Whole numbers= 0,1,2,3….

Hence, we can say that integers include whole numbers as well as negative numbers.

Every whole number is an integer; however, every integer is not a whole number.

(iii) Every rational number is a whole number.

Rational numbers- All numbers in the form p/q, where p and q are integers and q≠0.

i.e., Rational numbers = 0, 19/30 , 2, 9/-3, -12/7…

All whole numbers are rational, however, all rational numbers are not whole numbers.

Exercise 1.2 Page: 8

1. State whether the following statements are true or false. Justify your answers.

(i) Every irrational number is a real number.

Irrational Numbers – A number is said to be irrational, if it cannot be written in the p/q, where p and q are integers and q ≠ 0.

i.e., Irrational numbers = π, e, √3, 5+√2, 6.23146…. , 0.101001001000….

Real numbers – The collection of both rational and irrational numbers are known as real numbers.

i.e., Real numbers = √2, √5, , 0.102…

Every irrational number is a real number, however, every real number is not an irrational number.

(ii) Every point on the number line is of the form √m where m is a natural number.

The statement is false since as per the rule, a negative number cannot be expressed as square roots.

E.g., √9 =3 is a natural number.

But √2 = 1.414 is not a natural number.

Similarly, we know that there are negative numbers on the number line, but when we take the root of a negative number it becomes a complex number and not a natural number.

E.g., √-7 = 7i, where i = √-1

The statement that every point on the number line is of the form √m, where m is a natural number is false.

(iii) Every real number is an irrational number.

The statement is false. Real numbers include both irrational and rational numbers. Therefore, every real number cannot be an irrational number.

Every irrational number is a real number, however, every real number is not irrational.

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

No, the square roots of all positive integers are not irrational.

For example,

√4 = 2 is rational.

√9 = 3 is rational.

Hence, the square roots of positive integers 4 and 9 are not irrational. ( 2 and 3, respectively).

3. Show how √5 can be represented on the number line.

Step 1: Let line AB be of 2 unit on a number line.

Step 2: At B, draw a perpendicular line BC of length 1 unit.

Step 3: Join CA

Step 4: Now, ABC is a right angled triangle. Applying Pythagoras theorem,

AB 2 +BC 2 = CA 2

2 2 +1 2 = CA 2 = 5

⇒ CA = √5 . Thus, CA is a line of length √5 unit.

Step 4: Taking CA as a radius and A as a center draw an arc touching

the number line. The point at which number line get intersected by

arc is at √5 distance from 0 because it is a radius of the circle

whose center was A.

Thus, √5 is represented on the number line as shown in the figure.

4. Classroom activity (Constructing the ‘square root spiral’) : Take a large sheet of paper and construct the ‘square root spiral’ in the following fashion. Start with a point O and draw a line segment OP1 of unit length. Draw a line segment P1P2 perpendicular to OP 1 of unit length (see Fig. 1.9). Now draw a line segment P 2 P 3 perpendicular to OP 2 . Then draw a line segment P 3 P 4 perpendicular to OP 3 . Continuing in Fig. 1.9 :

Constructing this manner, you can get the line segment P n-1 Pn by square root spiral drawing a line segment of unit length perpendicular to OP n-1 . In this manner, you will have created the points P 2 , P 3 ,….,Pn,… ., and joined them to create a beautiful spiral depicting √2, √3, √4, …

Step 1: Mark a point O on the paper. Here, O will be the center of the square root spiral.

Step 2: From O, draw a straight line, OA, of 1cm horizontally.

Step 3: From A, draw a perpendicular line, AB, of 1 cm.

Step 4: Join OB. Here, OB will be of √2

Step 5: Now, from B, draw a perpendicular line of 1 cm and mark the end point C.

Step 6: Join OC. Here, OC will be of √3

Step 7: Repeat the steps to draw √4, √5, √6….

Exercise 1.3 Page: 14

1. Write the following in decimal form and say what kind of decimal expansion each has :

= 0.36 (Terminating)

= 4.125 (Terminating)

(vi) 329/400

= 0.8225 (Terminating)

2. You know that 1/7 = 0.142857. Can you predict what the decimal expansions of 2/7, 3/7, 4/7, 5/7, 6/7 are, without actually doing the long division? If so, how?

[Hint: Study the remainders while finding the value of 1/7 carefully.]

3. Express the following in the form p/q, where p and q are integers and q 0.

Assume that   x  = 0.666…

Then,10 x  = 6.666…

10 x  = 6 +  x

(ii) \(\begin{array}{l}0.4\overline{7}\end{array} \)

= (4/10)+(0.777/10)

Assume that  x  = 0.777…

Then, 10 x  = 7.777…

10 x  = 7 +  x

(4/10)+(0.777../10) = (4/10)+(7/90) ( x = 7/9 and x = 0.777…0.777…/10 = 7/(9×10) = 7/90 )

= (36/90)+(7/90) = 43/90

Assume that   x  = 0.001001…

Then, 1000 x  = 1.001001…

1000 x  = 1 +  x

4. Express 0.99999…. in the form p/q . Are you surprised by your answer? With your teacher and classmates discuss why the answer makes sense.

Assume that x  = 0.9999…..Eq (a)

Multiplying both sides by 10,

10 x  = 9.9999…. Eq. (b)

Eq.(b) – Eq.(a), we get

10 x  = 9.9999

– x  = -0.9999…

_____________

The difference between 1 and 0.999999 is 0.000001 which is negligible.

Hence, we can conclude that, 0.999 is too much near 1, therefore, 1 as the answer can be justified.

5. What can the maximum number of digits be in the repeating block of digits in the decimal expansion of 1/17 ? Perform the division to check your answer.

Dividing 1 by 17:

There are 16 digits in the repeating block of the decimal expansion of 1/17.

6. Look at several examples of rational numbers in the form p/q (q ≠ 0), where p and q are integers with no common factors other than 1 and having terminating decimal representations (expansions). Can you guess what property q must satisfy?

We observe that when q is 2, 4, 5, 8, 10… Then the decimal expansion is terminating. For example:

1/2 = 0. 5, denominator q = 2 1

7/8 = 0. 875, denominator q =2 3

4/5 = 0. 8, denominator q = 5 1

We can observe that the terminating decimal may be obtained in the situation where prime factorization of the denominator of the given fractions has the power of only 2 or only 5 or both.

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

We know that all irrational numbers are non-terminating non-recurring. three numbers with decimal expansions that are non-terminating non-recurring are:

• √3 = 1.732050807568
• √26 =5.099019513592
• √101 = 10.04987562112

8. Find three different irrational numbers between the rational numbers 5/7 and 9/11.

Three different irrational numbers are:

• 0.73073007300073000073…
• 0.75075007300075000075…
• 0.76076007600076000076…

9.  Classify the following numbers as rational or irrational according to their type:

√23 = 4.79583152331…

Since the number is non-terminating and non-recurring therefore, it is an irrational number.

√225 = 15 = 15/1

Since the number can be represented in p/q form, it is a rational number.

(iii) 0.3796

Since the number,0.3796, is terminating, it is a rational number.

(iv) 7.478478

The number,7.478478, is non-terminating but recurring, it is a rational number.

(v) 1.101001000100001…

Since the number,1.101001000100001…, is non-terminating non-repeating (non-recurring), it is an irrational number.

Exercise 1.4 Page: 18

1. Visualise 3.765 on the number line, using successive magnification.

Exercise 1.5 Page: 24

1. Classify the following numbers as rational or irrational:

We know that, √5 = 2.2360679…

Here, 2.2360679…is non-terminating and non-recurring.

Now, substituting the value of √5 in 2 –√5, we get,

2-√5 = 2-2.2360679… = -0.2360679

Since the number, – 0.2360679…, is non-terminating non-recurring, 2 –√5 is an irrational number.

(ii) (3 +√23)- √23

(3 + √ 23) –√23 = 3+ √ 23–√23

Since the number 3/1 is in p/q form, ( 3 +√23)- √23 is rational.

(iii) 2√7/7√7

2√7/7√7 = ( 2/7)× (√7/√7)

We know that (√7/√7) = 1

Hence, ( 2/7)× (√7/√7) = (2/7)×1 = 2/7

Since the number, 2/7 is in p/q form, 2√7/7√7 is rational.

Multiplying and dividing numerator and denominator by √2 we get,

(1/√2) ×(√2/√2)= √2/2 ( since √2×√2 = 2)

We know that, √2 = 1.4142…

Then, √2/2 = 1.4142/2 = 0.7071..

Since the number , 0.7071..is non-terminating non-recurring, 1/√2 is an irrational number.

We know that, the value of = 3.1415

Hence, 2 = 2×3.1415.. = 6.2830…

Since the number, 6.2830…, is non-terminating non-recurring, 2 is an irrational number.

2. Simplify each of the following expressions:

(i) (3+√3)(2+√2)

(3+√3)(2+√2 )

Opening the brackets, we get, (3×2)+(3×√2)+(√3×2)+(√3×√2)

= 6+3√2+2√3+√6

(ii) (3+√3)(3-√3 )

(3+√3)(3-√3 ) = 3 2 -(√3) 2 = 9-3

(iii) (√5+√2) 2

(√5+√2) 2 = √5 2 +(2×√5×√2)+ √2 2

= 5+2×√10+2 = 7+2√10

(iv) (√5-√2)(√5+√2)

(√5-√2)(√5+√2) = (√5 2 -√2 2 ) = 5-2 = 3

3. Recall, π is defined as the ratio of the circumference (say c) of a circle to its diameter, (say d). That is, π =c/d. This seems to contradict the fact that π is irrational. How will you resolve this contradiction?

There is no contradiction. When we measure a value with a scale, we only obtain an approximate value. We never obtain an exact value. Therefore, we may not realize whether c or d is irrational. The value of π is almost equal to 22/7 or 3.142857…

4. Represent (√9.3) on the number line.

Step 1: Draw a 9.3 units long line segment, AB. Extend AB to C such that BC=1 unit.

Step 2: Now, AC = 10.3 units. Let the centre of AC be O.

Step 3: Draw a semi-circle of radius OC with centre O.

Step 4: Draw a BD perpendicular to AC at point B intersecting the semicircle at D. Join OD.

Step 5: OBD, obtained, is a right angled triangle.

Here, OD 10.3/2 (radius of semi-circle), OC = 10.3/2 , BC = 1

OB = OC – BC

⟹ (10.3/2)-1 = 8.3/2

Using Pythagoras theorem,

OD 2 =BD 2 +OB 2

⟹ (10.3/2) 2 = BD 2 +(8.3/2) 2

⟹ BD 2 = (10.3/2) 2 -(8.3/2) 2

⟹ (BD) 2 = (10.3/2)-(8.3/2)(10.3/2)+(8.3/2)

⟹ BD 2  = 9.3

⟹ BD =  √9.3

Thus, the length of BD is √9.3.

Step 6: Taking BD as radius and B as centre draw an arc which touches the line segment. The point where it touches the line segment is at a distance of √9.3 from O as shown in the figure.

5. Rationalize the denominators of the following:

Multiply and divide 1/√7 by √7

(1×√7)/(√7×√7) = √7/7

(ii) 1/(√7-√6)

Multiply and divide 1/(√7-√6) by (√7+√6)

= (√7+√6)/(7-6)

= (√7+√6)/1

(iii) 1/(√5+√2)

Multiply and divide 1/(√5+√2) by (√5-√2)

= (√5-√2)/(5-2)

= (√5-√2)/3

(iv) 1/(√7-2)

Multiply and divide 1/(√7-2) by (√7+2)

1/(√7-2)×(√7+2)/(√7+2) = (√7+2)/(√7-2)(√7+2)

= (√7+2)/(7-4)

Exercise 1.6 Page: 26

64 1/2 = (8×8) 1/2

32 1/5 = (2 5 ) 1/5

(iii)125 1/3

(125) 1/3 = (5×5×5) 1/3

= 5 1 (3×1/3 = 3/3 = 1)

9 3/2 = (3×3) 3/2

= (3 2 ) 3/2

(ii) 32 2/5

32 2/5 = (2×2×2×2×2) 2/5

= (2 5 ) 2⁄5

(iii)16 3/4

16 3/4 = (2×2×2×2) 3/4

= (2 4 ) 3⁄4

(iv) 125 -1/3

125 -1/3 = (5×5×5) -1/3

= (5 3 ) -1⁄3

3. Simplify :

(i) 2 2/3 ×2 1/5

(ii) (1/3 3 ) 7

(iii) 11 1/2 /11 1/4

11 1/2 /11 1/4 = 11 (1/2)-(1/4)

(iv) 7 1/2 ×8 1/2

NCERT Solutions for Class 9 Maths Chapter 1 – Number Systems

As the Number System is one of the important topics in Maths, it has a weightage of 8 marks in Class 9 Maths CBSE exams. On an average three questions are asked from this unit.

• One out of three questions in part A (1 marks).
• One out of three questions in part B (2 marks).
• One out of three questions in part C (3 marks).

This chapter talks about:

• Introduction of Number Systems
• Irrational Numbers
• Real Numbers and their Decimal Expansions
• Representing Real Numbers on the Number Line.
• Operations on Real Numbers
• Laws of Exponents for Real Numbers

List of Exercises in NCERT Solutions for Class 9 Maths Chapter 1:

Exercise 1.1 Solutions 4 Questions ( 2 long, 2 short)

Exercise 1.2 Solutions 4 Questions ( 3 long, 1 short)

Exercise 1.3 Solutions 9 Questions ( 9 long)

Exercise 1.4 Solutions 2 Questions ( 2 long)

Exercise 1.5 Solutions 5 Questions ( 4 long 1 short)

Exercise 1.6 Solutions 3 Questions ( 3 long)

NCERT Solutions for Class 9 Maths Chapter 1- Number Systems

NCERT Solutions for Class 9 Maths Chapter 1 Number System is the first chapter of Class 9 Maths. The Number System is discussed in detail in this chapter. The chapter discusses the Number Systems and their applications. The introduction of the chapter includes whole numbers, integers and rational numbers.

The chapter starts with the introduction of Number Systems in section 1.1, followed by two very important topics in sections 1.2 and 1.3

• Irrational Numbers – The numbers which can’t be written in the form of p/q.
• Real Numbers and their Decimal Expansions – Here, you study the decimal expansions of real numbers and see whether it can help in distinguishing between rational and irrational.

Next, it discusses the following topics.

• Representing Real Numbers on the Number Line – In this, the solutions for 2 problems in Exercise 1.4.
• Operations on Real Numbers – Here, you explore some of the operations like addition, subtraction, multiplication and division on irrational numbers.
• Laws of Exponents for Real Numbers – Use these laws of exponents to solve the questions.

Explore more about Number Systems and learn how to solve various kinds of problems only on  NCERT Solutions For Class 9 Maths . It is also one of the best academic resources to revise for your CBSE exams.

Key Advantages of NCERT Solutions for Class 9 Maths Chapter 1 – Number Systems

• These NCERT Solutions for Class 9 Maths help you solve and revise the whole CBSE syllabus of Class 9.
• After going through the step-wise solutions given by our subject expert teachers, you will be able to score more marks in the board exams.
• It follows NCERT guidelines.
• It contains all the important questions from the examination point of view.

The faculty have curated the solutions in a lucid manner to improve the problem-solving abilities of the students. For a more clear idea about Number Systems, students can refer to the study materials available at BYJU’S.

• RD Sharma Solutions for Class 9 Maths Number Systems

Disclaimer: 

Dropped Topics – 1.4 Representing real numbers on the number line.

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On our website we have provided assignments for all subjects in Grade 9, all topic wise test sheets have been provided in a logical manner so that you can scroll through the topics and download the worksheet that you want.

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Yes all test papers for Mathematics Class 9 are available for free, no charge has been put so that the students can benefit from it. And offcourse all is available for download in PDF format and with a single click you can download all assignments.

https://www.assignmentsbag.com is the best portal to download all assignments for all classes without any charges.

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CBSE Class 9 Maths PDF – Download Free Updated for 2023-2024

CBSE Class 9 Maths Book is a very significant study material for students, as it lays the foundation for many of the basic concepts covered in higher classes. The Class 9 students also realise the importance of the NCERT book for Class 9 Maths, for the reason that the book gives an insight into the complete Maths subject, according to the CBSE syllabus.

Download NCERT PDF for Class 9 Maths

Students can download NCERT Class 9 Maths pdf for the year 2023-2024 from the below-given links.

NCERT PDF for Class 9 Maths Chapter-wise in English

NCERT PDF for Class 9 Maths Chapter in Hindi

Why One Should Read NCERT PDF for Class 9 Maths?

NCERT Book for Class 9 Maths helps students by providing thorough knowledge to them about the main topics and concepts covered in the subject. The book also helps students to clarify their doubts about Class 9 Maths. The other benefits include the following:

• Subject experts explain every concept and topic clearly and in an easy way
• Students can get in-depth knowledge and information about Class 9 Maths
• Difficult problems are solved using easy simple steps
• Help students prepare ahead for the class and exams
• Students can gain practice by solving the Class 9 Maths problems

NCERT PDFs Related Links:  

NCERT Books

NCERT Books for Class 9 Maths PDF Download [2020- 21 Edition Revised Syllabus]

NCERT Books Class 9 Maths : The National Council of Educational Research and Training (NCERT) publishes Maths textbooks for Class 9. The NCERT Class 9th Maths textbooks are well known for it’s updated and thoroughly revised syllabus. The NCERT Maths Books are based on the latest exam pattern and CBSE syllabus.

NCERT keeps on updating the Maths books with the help of the latest question papers of each year. The Class 9 Maths books of NCERT are very well known for its presentation. The use of NCERT Books Class 9 Maths is not only suitable for studying the regular syllabus of various boards but it can also be useful for the candidates appearing for various competitive exams, Engineering Entrance Exams, and Olympiads.

NCERT Class 9 Maths Books in English PDF Download

NCERT Class 9 Maths Books are provided in PDF form so that students can access it at any time anywhere. Class 9 NCERT Maths Books are created by the best professors who are experts in Maths and have good knowledge in the subject.

• Class 9 Maths NCERT Book English Medium
• Class 9 Maths NCERT Book Hindi Medium
• Class 9 Maths Proofs in Mathematics
• Class 9 Maths Introduction to Mathematical Modelling

NCERT Books for Class 9 Maths English Medium

NCERT Books for Class 9th Maths (Ganit) – Hindi Medium

• Class 9 Maths NCERT Book Introduction
• पाठ 1:  संख्या पद्धति
• पाठ 2:  बहुपद
• पाठ 3:  निर्देशांक ज्यामिति
• पाठ 4:  दो चरों वाले रैखिक समीकरण
• पाठ 5:  यूक्लिड की ज्यामिति का परिचय
• पाठ 6:  रेखाएँ और कोण
• पाठ 7:  त्रिभुज
• पाठ 8:  चतुर्भुज
• पाठ 9:  समांतर चतुर्भुजों और त्रिभुजों के क्षेत्रफल
• पाठ 10:  वृत
• पाठ 11:  रचनाएँ
• पाठ 12:  हीरोन का सूत्र
• पाठ 13:  पृष्ठीय क्षेत्रफल और आयतन
• पाठ 14:  सांख्यिकी
• पाठ 15:  प्रायिकता
• Proofs in Mathematics Hindi
• Class 9 Maths Hindi Medium Introduction to Mathematical Modelling

The NCERT syllabus mainly focuses on this book to make it student-friendly to make it useful for both the students and the competitive exam aspirants. The book covers a detailed Maths based on the syllabuses of various boards. NCERT Maths Books for Class 9 is perfectly compatible with almost every Indian education state and central boards.

We hope that this detailed article on NCERT Books Class 9 Maths helps you in your preparation and you crack the Class 9 exams or competitive exams with excellent scores.

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NCERT Solutions for Class 6, 7, 8, 9, 10, 11 and 12

NCERT Solutions for Class 9 Maths – Class 9 Maths NCERT Solutions

If you are searching for NCERT Solutions for Class 9 Maths , you have reached the correct place. LearnCBSE.in has created most accurate and detailed solutions for Class 9 Maths NCERT solutions. NCERT Class 9 Maths Solutions includes all the questions provided as per new revised syllabus in Class 9 math NCERT textbook.  You can download PDFs of Maths NCERT Solutions Class 9 without LOGIN. You can also practice Extra Questions for Class 9 Maths  on LearnCBSE.in

NCERT Class 9 Maths Solutions –  NCERT Solutions Class 9 Maths

• Chapter 1 Number systems
• Chapter 2 Polynomials
• Chapter 3 Coordinate Geometry
• Chapter 4 Linear Equations in Two Variables
• Chapter 5 Introduction to Euclid Geometry
• Chapter 6 Lines and Angles
• Chapter 7 Triangles
• Chapter 8 Quadrilaterals
• Chapter 9 Areas of Parallelograms and Triangles
• Chapter 10 Circles
• Chapter 11 Constructions
• Chapter 12 Heron’s Formula
• Chapter 13 Surface Areas and Volumes
• Chapter 14 Statistics
• Chapter 15 Probability
• Class 9 Maths (Download PDF)

There are 15 chapters in class 9 maths. These chapters lay a foundation for the chapters that will come in class 10. This pdf is accessible to everyone and they can use this pdf based on their convenience. Here below we are helping you with the overview of each and every chapter appearing in the textbook.

NCERT Solutions for Class 9 Maths Chapter 1

• Class 9 Maths Number systems Exercise 1.1
• Class 9 Maths Number systems Exercise 1.2
• Class 9 Maths Number systems Exercise 1.3
• Class 9 Maths Number systems Exercise 1.4
• Class 9 Maths Number Systems Exercise 1.5
• Class 9 Maths Number Systems Exercise 1.6
• Number Systems Class 9 Extra Questions

NCERT Solutions for Class 9 Maths Chapter 2

• Class 9 Maths Polynomials Exercise 2.1
• Class 9 Maths Polynomials Exercise 2.2
• Class 9 Maths Polynomials Exercise 2.3
• Class 9 Maths Polynomials Exercise 2.4
• Class 9 Maths Polynomials Exercise 2.5
• Polynomials Class 9 Extra Questions

NCERT Solutions for Class 9 Maths Chapter 3

• Class 9 Maths Coordinate Geometry Exercise 3.1
• Class 9 Maths Coordinate Geometry Exercise 3.2
• Class 9 Maths Coordinate Geometry Exercise 3.3
• Coordinate Geometry Class 9 Extra Questions

NCERT Solutions for Class 9 Maths Chapter 4

• Class 9 Maths Linear Equations in Two Variables Exercise 4.1
• Class 9 Maths Linear Equations in Two Variables Exercise 4.2
• Class 9 Maths Linear Equations in Two Variables Exercise 4.3
• Class 9 Maths Linear Equations in Two Variables Exercise 4.4
• Linear Equations for Two Variables Class 9 Extra Questions
• Linear Equations in Two Variables Class 9 Word Problems and Important Questions

NCERT Solutions for Class 9 Maths Chapter 5

• Class 9 Maths Introduction to Euclid Geometry Exercise 5.1
• Chapter 5 Introduction to Euclid’s Geometry Ex  5.2
• Introduction to Euclid’s Geometry Class 9 Extra Questions

NCERT Solutions for Class 9 Maths Chapter 6

• Class 9 Maths Lines and Angles Exercise 6.1
• Class 9 Maths Lines and Angles Exercise 6.2
• Class 9 Maths Lines and Angles Exercise 6.3
• Lines and Angles Class 9 Extra Questions

NCERT Solutions for Class 9 Maths Chapter 7

• Class 9 Maths Triangles Exercise 7.1
• Class 9 Maths Triangles Exercise 7.2
• Class 9 Maths Triangles Exercise 7.3
• Class 9 Maths Triangles Exercise 7.4
• Chapter 7 Triangles Ex 7.5
• Triangles Class 9 Extra Questions

NCERT Solutions for Class 9 Maths Chapter 8

• Class 9 Maths Quadrilaterals Exercise 8.1
• Class 9 Maths Quadrilaterals Exercise 8.2
• Quadrilaterals Class 9 Extra Questions
• Quadrilaterals Class 9 Maths Important Questions

NCERT Solutions for Class 9 Maths Chapter 9

• Class 9 Maths Areas of Parallelograms and Triangles Exercise 9.1
• Class 9 Maths Areas of Parallelograms and Triangles Exercise 9.2
• Class 9 Maths Areas of Parallelograms and Triangles Exercise 9.3
• Chapter 9 Areas of Parallelograms and Triangles Ex 9.4
• Areas of Parallelograms and Triangles Class 9 Extra Questions

NCERT Solutions for Class 9 Maths Chapter 10

• Class 9 Maths Circles Exercise 10.1
• Class 9 Maths Circles Exercise 10.2
• Class 9 Maths Circles Exercise 10.3
• Class 9 Maths Circles Exercise 10.4
• Class 9 Maths Circles Exercise 10.5
• Chapter 10 Circles Ex 10.6
• Circles Class 9 Extra Questions
• Circles Class 9 Maths Important Questions with Answers

NCERT Solutions for Class 9 Maths Chapter 11

• Class 9 Maths Constructions Exercise 11.1
• Class 9 Maths Constructions Exercise 11.2
• Constructions Class 9 Extra Questions
• Class 9 Maths Constructions Important Questions

NCERT Solutions for Class 9 Maths Chapter 12

• Class 9 Maths Heron’s Formula Exercise 12.1
• Class 9 Maths Heron’s Formula Exercise 12.2
• Heron’s Formula Class 9 Extra Questions
• Class 9 Areas of Parallelograms and Triangles Worksheets with Solutions

NCERT Solutions for Class 9 Maths Chapter 13

• Class 9 Maths Surface Areas and Volumes Exercise 13.1
• Class 9 Maths Surface Areas and Volumes Exercise 13.2
• Class 9 Maths Surface Areas and Volumes Exercise 13.3
• Class 9 Maths Surface Areas and Volumes Exercise 13.4
• Class 9 Maths Surface Areas and Volumes Exercise 13.5
• Class 9 Maths Surface Areas and Volumes Exercise 13.6
• Class 9 Maths Surface Areas and Volumes Exercise 13.7
• Class 9 Maths Surface Areas and Volumes Exercise 13.8
• Chapter 13 Surface Areas and Volumes Ex 13.9
• Surface Areas and Volumes Class 9 Extra Questions
• Surface Areas and Volumes Word Problems and Important Questions

NCERT Solutions for Class 9 Maths Chapter 14

• Class 9 Maths Statistics Exercise 14.1
• Class 9 Maths Statistics Exercise 14.2
• Class 9 Maths Statistics Exercise 14.3
• Class 9 Maths Statistics Exercise 14.4
• Statistics Class 9 Extra Questions
• Maths Class 9 Statistics Important Questions with solutions

NCERT Solutions for Class 9 Maths Chapter 15

• Class 9 Maths Probability Exercise 15.1
• Probability Class 9 Extra Questions
• Class 9 Probability Important Questions

Maths NCERT Solutions

In this article, we will provide you all the necessary information regarding Class 9th Maths NCERT Solutions. NCERT Maths Class 9 Textbook Solutions is solved by expert teachers provide you a strong foundation in the subject Maths. The 9th CBSE Maths Solutions are solved keeping various parameters in mind such as stepwise marks, formulas, mark distribution, etc., This in turn, helps you not to lose even a single mark.

It is important to build a strong base in maths. This is one subject that will be useful for every student irrespective of their branch. And thus we are helping you with NCERT Solutions of Class 9 Maths. This pdf can guide you to all the solutions given in the NCERT textbook along with the exercise.

Maths plays a major role in every student’s life. Working on NCERT Solutions Class 9 Maths Notes will not only help you to score good marks in the grade 9 but also helps you to clear the toughest competitive exams like JEE, NEET, JEE Advanced etc., Further it is CBSE Class 9 Maths Solutions will also be helpful to clear the exams like Olympiad, NTSE, through which you can easily avail scholarship and make your education journey hassle free. Read on to find out everything about NCERT Class 9th Maths Solutions to secure colorful marks in CBSE grade 9.

CBSE Class 9 Maths Unit Wise Weightage

NCERT Solutions for Class 9 Maths PDF Download

Browse all 9th NCERT Maths Solutions from your mobile or desktop and gain more marks in your exams. You can also go through the Chapterwise Important Questions for Class 9 Maths which will help you in extra practice and exams. This consists of 1 mark Questions, 2 Mark Numericals Questions, 3 Marks Numerical Questions, 4 Marks Questions, Word Problems, and previous year questions (VSAQ, SAQ, LAQ, and Value-Based Questions) from all chapters in class 9 maths designed according to CBSE Class 9 Maths Syllabus are laid in a sequential manner will help in scoring more marks in your Board Examinations.

Class 9 Maths Chapter 1 Number Systems

This chapter is an extension of the number line you have studied in the previous standards. You will also get know how to place various types of numbers on the number line in this chapter. A total of 6 exercises in this chapter guides you through the representation of terminating or non terminating of the recurring decimals on the number line. Along with the rational numbers, you will also learn where to put the square roots of 2 and 3 on the number line. There are also laws of rational exponents and Integral powers taught in this chapter.

Class 9 Maths Chapter 2 Polynomials

This chapter guides you through algebraic expressions called polynomial and various terminologies related to it. There is plenty to learn in this chapter about the definition and examples of polynomials, coefficient, degrees, and terms in a polynomial. Different types of polynomials like quadratic polynomials, linear constant, cubic polynomials, factor theorems, factorization theorem are taught in this chapter.

Class 9 Maths Chapter 3 Coordinate Geometry

A total of 3 exercises in this chapter will help you understand coordinate geometry in detail. Along with there are concepts like concepts of a Cartesian plane, terms, and various terms associated with the coordinate plane are learned in this chapter. You will also learn about plotting a point in the XY plane and naming process of this point.

Class 9 Maths Chapter 4 Linear Equations in Two Variables

This chapter will introduce to a new equation, ax + by + c = 0 in two variables. The questions in this chapter will be related to proving that a linear number has infinite solutions, using ba graph to plot linear equation, and justifying any point on a line. A total of 4 exercises are there for your practice and understanding.

Class 9 Maths Chapter 5 Introduction to Euclid’s Geometry

The chapter begins with the introduction of Indian geometry as it has some base in Euclid’s geometry. The Introduction of Euclid’s geometry in this chapter helps you with a process of defining geometrical terms and shapes. There are a total of 2 exercises where you will dwell into the relationship between theorems, postulates, and axioms.

Class 9 Maths Chapter 6 Lines and Angles

This chapter in the NCERT textbook also has 2 exercises in it. There are various theorems on angles and lines in this chapter that can be asked in for proof. The first theorem which will be asked for proof is “If the two lines are intersecting each other, then the vertically opposite angles formed will be equal”. Also, the second proof that is asked is, “The sum of all the angles formed in a triangle is 180°”. There are other theorems also given, but these are based on only these two theorems.

Class 9 Maths Chapter 7 Triangles

The contents in this chapter will help in understanding the congruence of triangles along with the rules of congruence. This chapter also has two theorems in it and a total of 5 exercises for students to practice. These two theorems are given as proof while the other is used in the problems or applications. Besides this, there are many properties of inequalities and triangles in this chapter for students to learn.

Class 9 Maths Chapter 8 Quadrilaterals

This chapter is very interesting for students to learn and there are only 2 exercises in it. The questions in this chapter are related to the properties related to quadrilateral and their combinations with the triangles.

Class 9 Maths Chapter 9 Areas of Triangles and Parallelogram

This chapter is important to understand the meaning of the area with this, the areas of the triangle, parallelogram, and their combinations are asked in this chapter along with their proofs. There are also examples of the an which are used as a proof of theorems in this chapter.

Class 9 Maths Chapter 10 Circles

In this chapter, you will get to learn some interesting topics like equal chords and their distance from the center, the chord of a point and angle subtended by it, angles which are subtended by an arc of a circle, and cyclic quadrilaterals. There are also theorems in this chapter which are helpful to prove questions based on quadrilaterals, triangles, and circles.

Class 9 Maths Chapter 11 Constructions

This chapter will help you learn two different categories of construction. One of them is the construction of a triangle along with its base, difference or sum of the remaining two sides, and one base angle with base angle and parameters are given. The other is the construction of bisectors for the line segments and measuring angles that include 45/60/90, etc.

Class 9 Maths Chapter 12 Heron’s Formula

This chapter joins the long list NCERT chapters that also has 2 exercises in it. In this chapter, you will be learning the concepts that are an extension of concepts related to the area of a triangle. Furthermore, you will get to learn about finding the area of triangles, quadrilaterals, and various types of polygons. Along with the, is there is also knowledge of formula for the plane figures given in the chapter.

Class 9 Maths Chapter 13 Surface Areas and Volume

Every one of you has already studied mensuration in previous standards. Thus, you must be aware of surface areas and this chapter is on that. Along with this, this chapter also has a volume of cubes, cylinders, cuboids, cones, hemispheres, and spheres. Also, in this chapter, you will get to know about the conversion of one figure into another, and comparing volumes of two figures.

Class 9 Maths Chapter 14 Statistics

In this chapter, you will get the knowledge about the descriptive statistics and the collection of data based on different aspects of life. This is useful for interpretation and stating the inferences from the data. This chapter gives the basic knowledge of the collection of data as the data is available in raw form. As you move forward and study 5 exercises you will learn about presenting data in tabular form by keeping them together in regular intervals, polygon, histogram, or bar graph drawing. You will also get to the topics like mean, median, and mode and finding the central tendency with the raw data.

Class 9 Maths Chapter 15 Probability

Probability in this book is based on the observation approach or finding the frequency. Questions in this chapter are very intuitive as they are based on daily life or day to day situations. For example, incidents like throwing dice, coin tossing, the probability for a deck of cards and simple events. If you are curious this chapter can be very interesting for you to learn and understand.

There may be a few times where you feel you are stuck and not getting the desired solutions. This is where we can you with NCERT solutions for class 9 maths. You can use this article as a reference for all the chapters in the NCERT book.

FAQs on NCERT Solutions for Class 9 Maths

1.  How do I study for the CBSE Class 9 Maths Solutions?

Practice the CBSE 9th Maths Solutions and try covering all the topics and questions carefully.

2. How could I learn Class 9 maths in an efficient and fast way?

The best way to learn fast is to solve NCERT. NCERT has few questions but has great importance in papers. If you can solve the whole NCERT with examples, you can easily score well. If you ample time try referring to RD Sharma too as it’s the best book.

3. Can I get solved math questions for the Class 9 CBSE?

Yes, you can get solved math questions for Class 9 CBSE Exams from our page. Access the direct links available on our page and download them for free of cost.

4.  Which is the best maths guide for 9th CBSE?

NCERT Solutions for Class 9 Maths will help you aid your preparation. Get a good grip over the subject by practicing more and more NCERT Solutions prevailing on our page.

5. How can I download the NCERT Solution Book for the CBSE Class 9 Maths?

Aspirants can download the CBSE Class 9 Maths NCERT Solutions by tapping on the direct links available. Lay a stronger foundation of the concepts by referring to the NCERT Solutions.

6. How long should a student of Class 9 practice math?

It’s not about the time limit. Try practicing as much as you can and revise the complete syllabus of Class 9 Maths for the exams to score well.

Now that you are provided all the necessary information regarding NCERT Solutions for class 9 Maths and we hope this detailed article on Class 9 Maths NCERT Solutions is helpful. If you have any doubt regarding this article or NCERT Class 9 Maths Solutions, leave your comments in the comment section below and we will get back to you as soon as possible.

Free Resources

NCERT Solutions

Quick Resources

Assignment - Number System, Class 9 Math PDF Download

TRUE / FALSE TYPE QUESTION 1. The sum of two rational numbers in rational 2. The sum of two irrational numbers is irrational. 3. The product of two rational numbers is rational. 4. The product of two irrational numbers is irrational. 5. The sum of a rational number and an irrational number is irrational. 6. The product of a non zero rational number and an irrational number is a rational number. 7. Every real number is rational. 8. π is irrational and 22/7 is rational. 9. Every rational number must be a whole number. 10. The number zero is both positive and negative. 11. The sum of two prime numbers is always even. 12. The product of two odd numbers is always odd.

VERY SHORT ANSWER TYPE QUESTION

22. Express the following in the form of p/q.

23. Examine, whether the following numbers are rational or an irrational :

24. Write two irrational numbers between 0.2 and 0.21. 25. Write three irrational numbers between 0.202002000200002.... and 0.203003000300003.... . 26. (i) Write two irrational numbers between 0.21 and 0.2222.... (ii) Find three different irrational numbers between the rational numbers 5/7 and 5/9 27. Write three irrational numbers between √3 and √5 . 28. Find two irrational numbers between 0.5 and 0.55.

Express as a pure surd :-

Express each of the following as a mixed surd :-

45. Simplify :-

50. Find the rationalising factor of

SHORT ANSWER TYPE QUESTION

TRUE & FALSE TYPE QUESTIONS 1. True

FILL IN THE BALANKS

13. Real, Rational number, irrational number

14. Terminating, recurring

16. Rational

20. 718/1665

21. Rational, irrational

VERY SHORT ANSWERS

22. (i) 1/3   (ii) 37/99    (iii) 6/11   (iv) 5/99    (v) 4/3    (vi) 23/37      (vii) 311/99    (viii) 9/55    (ix) 49/37    (x)295/9

23. (i) Irrational (ii) Rational (iii) Irrational (iv)Irrational (v) Irrational (vi)Irrational (vii) Rational (viii) Irrational (ix) Irrational (x) Irrational (xi) Irrational

24. 0.2010010001...., 0.2020020002.... 25. 0.20201001000100001...., 0.202020020002..., 0.202030030003.... 26. (i) 0.21010010001.... , 0.21020020002..... (ii) 0.2010010001 ............., 0.2020020002 ..........., 27. 1.8010010001....., 1.9010010001..., 2.010010001...

28. 0.501001.001..., 0.5020020002..... 29. 0.101001000100001, 0.1020020002....

47. 33 

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FAQs on Assignment - Number System, Class 9 Math

Assignment - Number System

Extra questions, video lectures, semester notes, past year papers, class 9 math, objective type questions, viva questions, shortcuts and tricks, sample paper, mock tests for examination, important questions, previous year questions with solutions, practice quizzes, study material.

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• CBSE Class 10

CBSE Class 10 Syllabus 2024-25: Download Latest and Revised FREE PDFs

Cbse class 10 syllabus: the central board of secondary education (cbse) curriculum is out for the academic year 2024–25 on the official website, cbseacademic.nic.in. students and teachers can download the direct pdf of the latest and revised cbse class 10 syllabus 2025 here for maths, science, social science, hindi, english, and other elective subjects..

CBSE Syllabus 2025 for Class 10: The Central Board of Secondary Education (CBSE) 2024 board exams for Class 10 are over, and the new academic session has begun.  This new syllabus or curriculum will be followed for the academic session 2024–25. In the CBSE-released syllabus, you will find the PDFs of the compulsory and optional subjects in free downloadable format. 

The new syllabus for CBSE 10th is a new initiative to improve the classroom and school environment by encouraging the holistic development of students. According to CBSE, “the secondary education curriculum is a major step in giving shape to the nation’s vision of education. It aims to provide education that addresses local, national, and global needs.”

Here, the CBSE Class 10 syllabus 2024–25 is provided for Maths, Science, Social Science, Hindi, English, and other elective subjects in PDF format. You can scroll down and download the PDFs from the link provided below. 

CBSE Class 10 Curriculum Areas

CBSE Class 10 Syllabus 2024-25

Here, you will get the subject-wise 2024 CBSE Class 10 syllabus. These syllabi are the latest and include all the revisions that CBSE would have thought of for the new academic year. Download these files and keep them for future reference. 

CBSE Secondary School Curriculum Salient Features

• i. provide ample scope for holistic i.e., physical, intellectual and social development of students;
• ii. emphasize constructivist rather than rote learning by highlighting the importance of hands-on experience;
• iii. enlist general and specific teaching and assessment objectives to make learning competency-based and attain mastery over laid down competencies;
• iv. encourage the application of knowledge and skills in real-life problem-solving scenarios;
• v. uphold the ‘Constitutional Values’ by encouraging values-based learning activities;
• vi. promote 21st Century Skills, Life Skills, Financial Literacy, Digital Literacy, Health and Wellness, Road Safety, Citizenship Education, Disaster Management and multilingualism;
• vii. integrate innovations in pedagogy such as experiential, activity-centered, joyful learning, Sport & Art-Integrated Learning, toy-based pedagogy, storytelling, gamification etc. with technological innovations (ICT integration) to keep pace with the global trends in various disciplines;
• viii. promote inclusive practices as an overriding consideration in all educational activities;
• ix. enhance and support learning by different types of assessments; and
• x. strengthen knowledge and attitude related to livelihood skills;
• xi. foster multilingual and multicultural learning and national understanding in an interdependent society;
• xii. integrate environmental education in various disciplines from classes I- XII.
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How to Download CBSE Class 10 Syllabus 2025?

The CBSE 2024–25 curriculum is out! Students and teachers can download the syllabus PDF for all the subjects by following the steps mentioned below:

Step 1: Visit the official website of the Central Board of Secondary Education (CBSE) at cbseacademic.nic.in. 

Step 2: Click on the section labelled “Curriculum.”

Step 3: Click on the link or tab mentioning "Curriculum 2024-25."

Step 4: Download the syllabus PDF.

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Features of CBSE Class 10 Syllabus 2024-25

• The CBSE Class 10 syllabus is designed in such a that it help students know the latest question paper pattern. 
• The typology of questions and their weightage is also provided through the syllabus.
• The syllabus involves all the topics and units with proper marking scheme.
• Simple language makes it easy to understand and comprehend. 
• CBSE Class 10 Mock Test Videos For Quick Revision
• CBSE Class 10 Science Lab Manual PDF

Having the latest syllabus is mandatory and is the first resource you need to crack your board exams. Thus, students should always keep a copy of the syllabus with them. 

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• Is CBSE Class 10 syllabus 2025 out? + Yes, the Central Board of Secondary Education (CBSE) has updated its curriculum section for the academic year 2024-25. Students can download the syllabus PDFs from CBSE's official website.
• Is there any change in CBSE Class 10 syllabus 2024-25? + The CBSE Board has not updated any information regarding the change in the Class 10 syllabus. It is advised for students to follow the 2025 syllabus for their 2024–25 academic session. After comparing the 2024 and 2025 syllabi, the detailed information will be updated on the official website of Jagran Josh. 
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CBSE NCERT Solutions

NCERT and CBSE Solutions for free

Class 9 Mathematics Quadrilateral Assignments

We have provided below free printable Class 9 Mathematics Quadrilateral Assignments for Download in PDF. The Assignments have been designed based on the latest NCERT Book for Class 9 Mathematics Quadrilateral . These Assignments for Grade 9 Mathematics Quadrilateral cover all important topics which can come in your standard 9 tests and examinations. Free printable Assignments for CBSE Class 9 Mathematics Quadrilateral , school and class assignments, and practice test papers have been designed by our highly experienced class 9 faculty. You can free download CBSE NCERT printable Assignments for Mathematics Quadrilateral Class 9 with solutions and answers. All Assignments and test sheets have been prepared by expert teachers as per the latest Syllabus in Mathematics Quadrilateral Class 9. Students can click on the links below and download all Pdf Assignments for Mathematics Quadrilateral class 9 for free. All latest Kendriya Vidyalaya Class 9 Mathematics Quadrilateral Assignments with Answers and test papers are given below.

Mathematics Quadrilateral Class 9 Assignments Pdf Download

We have provided below the biggest collection of free CBSE NCERT KVS Assignments for Class 9 Mathematics Quadrilateral . Students and teachers can download and save all free Mathematics Quadrilateral assignments in Pdf for grade 9th. Our expert faculty have covered Class 9 important questions and answers for Mathematics Quadrilateral as per the latest syllabus for the current academic year. All test papers and question banks for Class 9 Mathematics Quadrilateral and CBSE Assignments for Mathematics Quadrilateral Class 9 will be really helpful for standard 9th students to prepare for the class tests and school examinations. Class 9th students can easily free download in Pdf all printable practice worksheets given below.

Topicwise Assignments for Class 9 Mathematics Quadrilateral Download in Pdf

Advantages of Class 9 Mathematics Quadrilateral Assignments

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