NCERT Solutions for Class 10 Maths

 Table of contents NCERT Solutions for Class 10 Maths Chapter Wise NCERT Solutions for Class 10 Maths CBSE Class  10 Maths Unit-wise Weightage for 2022-23 Internal Assessment for CBSE Class  10 Maths Importance of NCERT Solutions for Class  10 Maths Benefits of EduRev’s NCERT Maths Solutions for Class 10 Important Related Links for CBSE Class  10 Maths Frequently Asked Questions (FAQs): NCERT Solutions for Class 10 Maths

## NCERT Solutions for Class 10 Maths

Here you will find all of the Chapters 1 through Chapter 15 NCERT Solutions for Class 10 Maths Exercises. Our knowledgeable faculty has selected these Class 10 NCERT Solutions to aid students in their test preparation. In order to find a more effective way to approach the problems, students looking for Class 10 Maths NCERT Solutions can download all chapter-by-chapter PDFs.NCERT Solutions for Class  10 Mathematics

The best study materials available to students are without a doubt the answers to the questions found in the NCERT books. Additionally, these CBSE NCERT Solutions for Class 10 Maths 2022–23 will aid students in developing a deeper comprehension of the ideas provided in the NCERT Book. Students will be able to assess their level of preparation and concept mastery by practising the Book questions.

## Chapter Wise NCERT Solutions for Class 10 Maths

Chapter-wise NCERT Solutions for Class 10 Maths are a set of solutions designed to help students understand and prepare for the Mathematics subject at the Class 10 level. These solutions cover all the chapters of the NCERT textbook for Class 10 maths and are structured in a way that enables students to learn and revise the concepts thoroughly.

### NCERT Solutions for Class 10 Maths Chapter 1: Real Numbers

Students will study real numbers and irrational numbers in Chapter 1 of Class 10. The Euclid's Division Lemma asserts that "Given positive integers a and b, there exist unique integers q and r satisfying a = bq + r, 0rb," which is the first statement in the chapter. This lemma serves as the foundation for the Euclid's Division procedure, which determines the HCF of two positive integers. The Fundamental Theorem of Arithmetic, which is used to determine the LCM and HCF of two positive integers, is then defined. Following that, the theorem is used to describe the concepts of an irrational number, a rational number, and the decimal expansion of rational numbers.

Chapter 1 of the topics covered in class 10 Maths After examining past work and after illuminating and inspiring through examples, the Real Numbers: Fundamental Theorem of Arithmetic asserts, Evidence for the irrationality of 2, 3, and 5.

Class 10 Maths NCERT Solutions Chapter 1 Exercises

Also, access the following resources for NCERT Class 10 Chapter 1 Real Numbers, at EduRev:

### NCERT Solutions for Class 10 Maths Chapter 2: Polynomials

The definitions of the degree, linear, quadratic, and cubic polynomials are given at the beginning of the chapter on polynomials. There are a total of 4 exercises in this chapter, one of which is optional. Questions about calculating the number of zeros in a graph can be found in Exercise 2.1. Understanding the Geometrical Meaning of a Polynomial's Zeros is necessary. Students must locate the zeros of a quadratic polynomial in Exercise 2.2, which is based on the Relationship between Zeroes and Coefficients of a Polynomial. In some cases, they must also locate the quadratic polynomial. The division algorithm concept is defined in Exercise 2.3, where students can also find the questions that pertain to it.The questions in the optional exercise 2.4 are drawn from each of the Chapter 2 topics.

Topics Covered in Class 10 Maths Chapter 2 Polynomials :

Zeros of a polynomial. Relationship between zeros and coefficients of quadratic polynomials.

Class 10 Maths NCERT Solutions Chapter 2 Exercises

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### NCERT Solutions for Class 10 Maths Chapter 3: Pair of Linear Equations in Two Variables

Pair of Linear Equations in Two Variables is a concept that is explained in this chapter. There are a total of 7 tasks in this chapter, and they all involve solving a pair of linear equations using various strategies. How to represent a situation algebraically and graphically is explained in Exercise 3.1. Exercise 3.2 illustrates how to use the Graphical Method to solve the pair of linear equations. The Algebraic Method, Elimination Method, Cross-Multiplication Method, and Substitution Method are each covered in Exercises 3.3, 3.4, 3.5, and 3.6, respectively. Activity 3.7, an optional exercise, with questions of every description. In order to acquire the technique for solving linear equations, students must practice these tasks.

Pair of Linear Equations in Two Variables is a topic covered in this chapter. There are seven tasks in this chapter that cover various strategies for resolving the linear equations.

The algebraic and graphical representation of a situation is explained in Exercise 3.1. In Exercise 3.2, the Graphical Method is used to solve a pair of linear equations. Exercises 3.3, 3.4, 3.5, and 3.6, respectively, provide descriptions of the Algebraic Method, Elimination Method, Cross-Multiplication Method, and Substitution Method.

All different kinds of questions are included in optional exercise 3.7. To master the process of solving linear equations, students must practice the activities.

Class 10 Maths NCERT Solutions Chapter 3 Exercises

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### NCERT Solutions for Class 10 Maths Chapter 4: Quadratic Equations

Students will learn about the usual form of writing a quadratic equation in this chapter. The chapter continues with describing how to solve a quadratic problem using the factorization approach and the square-root method. Finding the nature of roots is the final section of the chapter, and it explains that if :

• b2 - 4ac > 0, then the quadratic equation ax2 + bx + c = 0 has two unique real roots.
• If b2 - 4ac = 0, there are two equal roots.
• No roots at all if b2 - 4ac 0.

Topics Covered in Class 10 Maths Chapter 4 Quadratic Equations:

ax2 + bx + c = 0, (a 0) is the quadratic equation's conventional form. Using the quadratic formula and factorization, quadratic equations can be solved (only for real roots). Relationship between the roots' nature and the discriminant.

Daily activities-related situational problems based on quadratic equations have to be included.

Class 10 Maths NCERT Solutions PDF Chapter 4 Exercises

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### NCERT Solutions for Class 10 Maths Chapter 5: Arithmetic Progressions

Students are introduced to Arithmetic Progression, or AP, in this chapter. There are a total of 4 exercises in this chapter. Students will discover questions about modeling situations as APs, identifying the initial term and difference of an AP, and determining if a series is an AP in Exercise 5.1. The following formula can be used to get the nth term of an AP in the problems in Exercise 5.2: a = a + (n-1) d

Finding the sum of the first n terms of an AP is the topic of the next exercise, 5.3. Higher-level questions based on AP are included in the final activity to help students develop their analytical and problem-solving abilities.

Topics Covered in Class 10 Maths Chapter 5 Arithmetic Progressions:

Motivation for studying Arithmetic Progression Derivation of the nth term and sum of the first n terms of A.P. and their application in solving daily life problems.

Class 10 Maths NCERT Solutions Chapter 5 Exercises

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### NCERT Solutions for Class 10 Maths Chapter 6: Triangles

The figures with the same shape but different sizes are covered in Chapter 6 of the Class 10 CBSE Math Book. A comparable and congruent figure is the starting point of the chapter Triangles. It goes on to explain the prerequisites for the resemblance of two triangles as well as associated theorems. Following that, a theorem was used to explain how identical triangles' areas may be calculated. The Pythagoras Theorem and its Converse are discussed at the conclusion of this chapter.

Topics Covered in Class 10 Maths Chapter 6 Triangles:

Definitions, illustrations, and oppositional illustrations of related triangles.

• (Prove) The other two sides of a triangle are divided in the same ratio if a line parallel to one side of a triangle intersects the other two sides in clearly defined points.
• (Inspire) A line is parallel to the third side of a triangle if it divides the first two sides of the triangle in the same proportion.
• (Inspire) If the corresponding sides of two triangles are proportionate, the corresponding angles are equal, and the triangles are similar.
• (Inspire) Two triangles are comparable if their respective sides are proportionate, their corresponding angles are equal, and they have similar triangles.
• (Inspire) Two triangles are comparable if one of their angles is equal to another triangle's angle and the sides that include these angles are proportionate.

Class 10 Maths NCERT Solutions Chapter 6 Exercises

Also, access the following resources for NCERT Class 10 Chapter 6 Triangles, at EduRev:

### NCERT Solutions for Class 10 Maths Chapter 7: Coordinate Geometry

In this chapter, students will learn how to determine the distance between any two locations whose coordinates are given, as well as how to determine the area of any triangle consisting of three given points. They will also learn how to find the coordinates of the point that divides a given line segment between two points in a particular ratio. Students will learn about the Area of a Triangle, Section Formula, and Distance Formula in this chapter on coordinate geometry.

Topics Covered in Class 10 Maths Chapter 7 Coordinate Geometry:
Review of linear equation graphs and coordinate geometry concepts. Distance calculation. Formula for Section (internal division).

Class 10 Maths NCERT Solutions Chapter 7 Exercises

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### NCERT Solutions for Class 10 Maths Chapter 8: Introduction to Trigonometry

In this chapter, students will study trigonometry. We'll research trigonometric ratios of the angles, or ratios of a right triangle to its acute angles. This chapter also defines the trigonometric ratios for angles of 00 and 900. Additionally, students will be able to compute trigonometric ratios for specific angles as well as build various trigonometric identities that include these ratios.

Topics Covered in Class 10 Maths Chapter 8 Introduction to Trigonometry:
Trigonometric ratios of the acute angle of a right-angled triangle. Motivate the ratios as proof of their existence, whichever ones are defined at 0° and 90° (clearly defined). the values of the trigonometric ratios of 300, 450, and 600. ratios and how they relate.

Class 10 Maths NCERT Solutions Chapter 8 Exercises

### NCERT Solutions for Class 10 Maths Chapter 9: Some Applications of Trigonometry

This chapter, which is a continuation of the previous one, will cover applications of trigonometry. It is used in geography, navigation, mapping, and determining the location of an island using longitudes and latitudes. In this chapter, students will learn how to use trigonometry to estimate the heights and distances of various objects without actually measuring them. They will be instructed on line of sight, angle of elevation, and angle of depression.

Topics Covered in Class 10 Maths Chapter 9 Some Applications of Trigonometry:
HEIGHTS AND DISTANCES – Angle of elevation, Angle of Depression.
Simple problems on heights and distances. Problems should not involve more than two right triangles. Angles of elevation/depression should be only 30°, 45°, and 60°.

Class 10 Maths NCERT Solutions Chapter 9 Exercise

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### NCERT Solutions for Class 10 Maths Chapter 10: Circles

Students have learned about circles and other concepts associated with them, such as chord, segment, arc, etc., in prior classes. Students will learn about the various circumstances that can occur when a circle and a line are presented in a plane in this chapter. The concepts of Tangent to a Circle and Number of Tangents from a Point on a Circle will thus be fully understood by them.

Topics Covered in Class 10 Maths Chapter 10 Circles:
At the point of contact, tangent to a circle

• Establish that the radius across the point of contact is perpendicular to the tangent at any point on a circle.
• (Show) Tangents drawn from an outside point to a circle have identical lengths.

Class 10 Maths NCERT Solutions Chapter 10 Exercises

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### NCERT Solutions for Class 10 Maths Chapter 11: Constructions

This chapter consists of a total of 2 exercises. Whatever students have learned about construction in earlier classes will also help them. In Exercise 11.1, students will study how to divide a line segment, whereas in Exercise 11.2, they will study the construction of tangents to a circle. Methods and steps for construction are explained, and also some examples are additionally given to make it clearer to the students.

Topics Covered in Class 10 Maths Chapter 11 Constructions:

• Division of a line segment in a given ratio (internally).
• Tangent to a circle from a point outside it.
• Construction of a triangle similar to a given triangle.

Class 10 Maths NCERT Solutions Chapter 11 Exercises

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### NCERT Solutions for Class 10 Maths Chapter 12: Areas Related to Circles

This chapter begins with the concepts of the perimeter and area of a circle. Using this concept, the chapter further explains how to find the area of a sector and segment of a circular region. Moreover, students will get clarity on finding the areas of some combinations of plane figures involving circles or their parts.

Topics Covered in Class 10 Maths Chapter 12 Areas Related to Circles:
Area of sectors and segments of a circle. Problems based on areas and perimeter/circumference of the above-said plane figures. (In calculating the area or segment of a circle, problems should be restricted to the central angle of 60°, 90° and 120° only.

Class 10 Maths NCERT Solutions Chapter 12 Exercises

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### NCERT Solutions for Class 10 Maths Chapter 13: Surface Areas and Volumes

In Chapter 13, there are a total of 5 exercises. The first exercise consists of questions based on finding the surface area of an object formed by combining any two of the basic solids, i.e. cuboid, cone, cylinder, sphere and hemisphere. In exercise 13.2, questions are based on finding the volume of objects formed by combining any two of a cuboid, cone, cylinder, sphere and hemisphere. Exercise 13.3 deals with the questions in which a solid is converted from one shape to another. Exercise 13.4 is based on finding the volume, curved surface area and total surface area of a frustum of a cone. The last exercise is optional and has high-level questions based on all the topics of this chapter.

Topics Covered in Class 10 Maths Chapter 13 Surface Areas and Volumes:
Surface areas and volumes of combinations of any two of the following: cubes, cuboids, spheres, hemispheres and right circular cylinders/cones.

Class 10 Maths NCERT Solutions Chapter 13 Exercises

Also, access the following resources for NCERT Class 10 Chapter 13 Surface Areas and Volumes, at EduRev:

### NCERT Solutions for Class 10 Maths Chapter 14: Statistics

Students will learn how to find the Mean, Mode, and Median and how to numerically depict ungrouped and grouped data. Additionally, the definition of cumulative frequency, its distribution, and how to create its curves will be covered.

Topics Covered in Class 10 Maths Chapter 14 Statistics:
Mean, median and mode of grouped data (bimodal situation to be avoided).

Class 10 Maths NCERT Solutions Chapter 14 Exercises

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### NCERT Solutions for Class 10 Maths Chapter 15: Probability

The final chapter covers probability. The theoretical approach to probability is where the chapter begins. The chapter then goes on to discuss the distinction between theoretical and experimental probability. It is effectively explained through a variety of instances. Students must complete the CBSE Math examples before moving on to the exercise problems.

Topics Covered in Class 10 Maths Chapter 15 Probability:
Classical definition of probability. Simple problems on finding the probability of an event.

Class 10 Maths NCERT Solutions Chapter 15 Exercises

Also, access the following resources for NCERT Class 10 Chapter 15 Probability, at EduRev:

## Importance of NCERT Solutions for Class  10 Maths

NCERT (National Council of Educational Research and Training) Solutions for Class 10 Maths are an essential resource for students studying in India. NCERT Solutions are designed to provide a comprehensive and thorough understanding of the concepts taught in the NCERT textbooks.

Here are some of the key benefits of using NCERT Solutions for Class 10 Maths:

• Accurate and Reliable: NCERT Solutions are prepared by subject matter experts with years of experience in teaching. Hence, these solutions are reliable and accurate, providing students with the right guidance to prepare for their exams.
• Complete coverage of syllabus: NCERT Solutions provide complete coverage of the syllabus prescribed by CBSE for Class 10 Maths. The solutions are designed to help students understand the concepts and topics in a detailed and comprehensive manner.
• Helps in revision: NCERT Solutions provide a quick and easy way for students to revise the entire syllabus in a short time. The solutions provide chapter-wise summaries, important points, and question answers that help students to revise and memorize the concepts effectively.
• Enhances problem-solving skills: NCERT Solutions are designed to help students enhance their problem-solving skills. The solutions provide step-by-step solutions to the questions, which helps students to understand the approach to solve a problem.
• Improves performance: Using NCERT Solutions for Class 10 Maths helps students to improve their performance in exams. The solutions provide an in-depth understanding of the concepts, which helps students to answer the questions accurately and confidently.

Overall, NCERT Solutions for Class 10 Maths are an essential resource for students studying in India. The solutions provide a comprehensive understanding of the concepts taught in the NCERT textbooks and help students to prepare effectively for their exams.

## Benefits of EduRev’s NCERT Maths Solutions for Class 10

EduRev’s NCERT Maths Solutions for Class 10 offer several benefits for students. Some of the key advantages are:

• Comprehensive coverage: The solutions provide comprehensive coverage of all the topics included in the CBSE curriculum for Class 10 Maths. This means that students can use these solutions to prepare for exams and gain a better understanding of the concepts.
• Interactive practice material: EduRev’s NCERT Maths Solutions for Class 10 include interactive practice material such as quizzes, tests, and flashcards, which help students to test their understanding of the concepts and identify their areas of weakness.
• Clear explanations: The solutions are written in a clear and concise manner, making it easy for students to understand even complex concepts. The step-by-step approach used in these solutions helps students to learn the problem-solving process, which is an essential skill for success in Maths.
• Multiple solutions: EduRev’s NCERT Maths Solutions for Class 10 provide multiple solutions to each question, helping students to understand different approaches to solving the same problem. This can help to broaden their understanding of the subject and improve their problem-solving skills.
• Free of cost: EduRev’s NCERT Maths Solutions for Class 10 are available for free, making them accessible to all students regardless of their financial background.
• Mobile app: EduRev’s NCERT Maths Solutions for Class 10 are also available as a mobile app, which makes it convenient for students to access the solutions anytime, anywhere.

Overall, EduRev’s NCERT Maths Solutions for Class 10 are an excellent resource for students who want to improve their Maths skills and achieve success in the subject. The solutions provide a solid foundation of knowledge and problem-solving skills, which can help students to develop a positive attitude towards the subject and become more motivated to learn.

Students can also access NCERT Solutions of all subjects of Class 10:

## Frequently Asked Questions (FAQs): NCERT Solutions for Class 10 Maths

### How to grasp the important concepts covered in the NCERT Solutions for Class 10 Maths?

Students who aspire to score good marks in the Class 10 exams are advised to study the NCERT Solutions from the EduRev App. The solutions are curated with utmost care by a set of faculty having vast experience in the respective subject. Each and every minute detail is explained in an interactive manner to make it easier for the students while learning. The step-wise solutions are designed by keeping in mind the marks weightage allotted as per the CBSE guidelines.

### Will the NCERT Solutions for Class 10 Maths help me to solve problems easily?

The Class 10 exam is one of the major turning points in the life of students. Maths is a subject which mainly contains numericals, and understanding of concepts helps to score more marks. Students are recommended to first understand the syllabus for the academic year and learn the concepts based on them for better performance. Solving the Book problems by referring to the solutions will improve the logical thinking and analytical skills among students.

### Where will I get the NCERT Solutions for Class 10 Maths?

Students can get the NCERT Solutions for Class 10 Maths at the EduRev App. The solutions are prepared by the subject matter experts keeping in mind the understanding capacity of students. The main objective of creating solutions is to help students learn complex concepts without any difficulty. Students can also cross-check their answers while solving the Book problems to get an idea about the other methods of answering the questions efficiently.

### Are the NCERT Solutions for Class 10 Maths useful for the students under the CBSE board?

Given below are some of the uses of the NCERT Maths Solutions for Class 10 –

1. It builds a strong foundation of fundamental concepts and improves confidence to face exams.

2. The method of solving complex problems can be learnt easily.

3. It is a perfect study material for the students to finish their assignments on time and to score more marks in the exams.

### How to get an idea about the important concepts in the NCERT Solutions for Class 10 Maths?

Before the start of an academic year, students should download the CBSE syllabus and go through it for a clear idea about the concepts which are important for the exams. Students must solve the NCERT Book problems by choosing the correct study material which satisfies their needs. Practising the problems on a regular basis by referring to the NCERT Solutions for Class 10 Maths improves the problem-solving abilities of students.

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