# NCERT solutions for class 10 maths

NCERT Solutions for Class 10 Maths is prepared by highly experienced teachers of the Physics Wallah academic team. All questions given in the exercise of the NCERT textbook are solved with the required step as per the CBSE guideline for the Board exam.

The advent of class 10th leads to stress among students. The team at Physics Wallah has developed solutions for class 10 maths for them. The team is dedicated to ensuring students don’t feel any type of stress. The team is dedicated to bringing on solutions to problems with a unique approach to solving problems. Most of the students are unable to score decent marks in the examination.

The NCERT Solutions help students to score great marks with smart study. Physics Wallah teachers wish students to have crystal clear concepts. Students looking forward to grasping concepts can learn through solved questions for class 10 maths provided. Do refer to NCERT Solutions for Class 10 Science.The students can enhance their problem-solving skills through a stringent schedule of solving questions.

## NCERT Solutions for Class 10 Maths Free PDF Download ### Chapter 1 Real Numbers

In class 10 chapter 1 , students will explore real and irrational numbers. The chapter begins with Euclid's division lemma, which states that "given positive integers a and b, there exist unique integers qar satisfying a = bq + r, 0≤r<b". The Euclidean division algorithm is based on this lemma and is used to compute the HCF of two given positive integers. Therefore, the Fundamental Theorem of Arithmetic is defined, which is used to find the LCM and HCF of two positive integers. Then the concept of irrational number, rational number and decimal expansion of rational numbers is explained using the theorem.

Topics Covered in this chapter are- Fundamental Theorem of Arithmetic – statements after reviewing work done before and after illustrating and motivating through examples, Proofs of irrationality of √2, √3, √5. NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Exercises Exercise 1.1 Exercise 1.2 Exercise 1.3 Exercise 1.4

Also, access the helpful resources for Class 10 Maths Chapter 1 Real Numbers at Physics Wallah

### Chapter 2 Polynomials

In Polynomials, the chapter begins by defining the degree of a polynomial, a linear polynomial, a quadratic polynomial, and a cubic polynomial. This chapter consists of 4 exercises, including an optional exercise. Exercise 2.1 contains questions about finding the number of zeros in a graph. It requires understanding the geometric meaning of the zeros of a polynomial. Exercise 2.2 is based on the Relationship between Zeros and Coefficients of a Polynomial, where students must find the zeros of a quadratic polynomial. In some questions, they have to find a quadratic polynomial. In Exercise 2.3, the term division algorithm is defined, and students will find related questions. Additional exercise 2.4 consists of questions from all concepts of chapter 2.

Topics Covered in this chapter are- Zeros of a polynomial, Relationship between zeros and coefficients of quadratic polynomials.

 NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Exercises Exercise 2.1 Exercise 2.2 Exercise 2.3 Exercise 2.4

Also, access the helpful resources for Class 10 Maths Chapter 2 Polynomials at Physics Wallah

### Chapter 3 Pair of Linear Equations in Two Variables

This chapter explains the concept of a pair of linear equations in two variables. This chapter contain a total of 7 exercises, and in these exercises, different methods of solving a pair of linear equations are described. Exercise 3.1 describes how to represent the situation algebraically and graphically. Exercise 3.2 explains methods for solving a pair of linear equations using the graphical method. And exercises 3.3, 3.4, 3.5, and 3.6 describe the algebraic method, the elimination method, the cross-multiplication method, and the substitution method. Exercise 3.7 is an optional exercise that contains all types of questions. Students must practice these exercises to master the method of solving linear equations.

Topics Covered in this chapter are- Pair of linear equations in two variables and graphical method of their solution, consistency/ inconsistency. Algebraic conditions for number of solutions. Pair of linear equations in two variables solution – by substitution, by elimination. Simple situational problems.

 NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Exercise 3.1 Exercise 3.2 Exercise 3.3 Exercise 3.4 Exercise 3.5 Exercise 3.6 Exercise 3.7

Also, access the helpful resources for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables at Physics Wallah

### Chapter 4 Quadratic Equations

In this chapter, students will discuss the standard form of writing a Quadratic Equation. The chapter properly explain the method of solving the quadratic equation through the completing the square method and factorization method. The chapter finish with the topic on finding the nature of roots which means, a quadratic equation ax² + bx + c = 0 has:

• Two distinct real roots, if b² – 4ac > 0
• Two equal roots, if b² – 4ac = 0
• No real roots, if b² – 4ac < 0

Topics Covered in this chapter are- Standard form of a quadratic equation ax2 + bx + c = 0, (a ≠ 0). Solutions of quadratic equations (only real roots) by factorization, and by using quadratic formula. Relationship between discriminant and nature of roots.

 NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations Exercises Exercise 4.1 Exercise 4.2 Exercise 4.3 Exercise 4.4

Also, access the helpful resources for Class 10 Maths Chapter 4 Quadratic Equations at Physics Wallah

### Chapter 5 Arithmetic Progressions

This chapter introduces students to the new topic of Arithmetic Progression or AP. The chapter contains a total of 4 exercises. In Exercise 5.1, students will find questions about representing a situation in AP form, finding the first term and difference of an AP, and determining whether a series is an AP or not. Exercise 5.2 contains questions on finding the nth term of an AP using the following formula:

an = a + (n-1) d

In the next exercise i.e., 5.3, contains the questions on finding the sum of first n terms of an AP. The last exercise includes higher-level questions based on AP to enhance students’ analytical and problem-solving skills.

Topics Covered in this chapter are- Arithmetic Progression, Derivation of the nth term and the sum of the first n terms of A.P. and their application in solving daily life problems.

 NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions Exercises Exercise 5.1 Exercise 5.2 Exercise 5.3 Exercise 5.4

Also, access the helpful resources for Class 10 Maths Chapter 5 Arithmetic Progressions at Physics Wallah

### Chapter 6 Triangles

In Class 10 CBSE Maths chapter 6, students will study figures of the same shape but not necessarily the same size. The Triangles chapter begins with the concept of a similar and congruent figure. It further explains the condition of the similarity of two triangles and theorems related to the similarity of triangles. Then the areas of similar triangles were explained by using the theorem. At the end of this chapter, the Pythagorean theorem and the inversion of the Pythagorean theorem are discussed.

Topics Covered in this chapter are- Definitions, examples, counter examples of similar triangles.

1. Prove that if a line is drawn parallel to the one side of a triangle to intersect the other two sides in the distinct points and the other two sides are divided in the same ratio.
2. If a line divides the two sides of a triangle in the same ratio, the line is parallel to the third side.
3. If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar.
4. If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar.
5. If one angle of a triangle is equal to one angle of the another triangle and sides including these angles are proportional, and the two triangles are similar.
 NCERT Solutions for Class 10 Maths Chapter 6 Triangles Exercises Exercise 6.1 Exercise 6.2 Exercise 6.3 Exercise 6.4 Exercise 6.5 Exercise 6.6

Also, access the helpful resources for Class 10 Maths Chapter 6 Triangles at Physics Wallah

### Chapter 7 Coordinate Geometry

In the chapter 7, students will learn how to find the distance between two points whose coordinates are given and the area of ​​the triangle formed by the three given points. Students will also learn how to find the coordinates of a point that bisects a line joining the two given points in a given ratio. In the end, students will be introduced to the distance formula, the section formula, and the area of ​​a triangle in this Coordinate Geometry chapter.

Topics Covered in this chapter are- the concepts of coordinate geometry, graphs of linear equations. Distance formula. Section formula (internal division). NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Exercises Exercise 7.1 Exercise 7.2 Exercise 7.3 Exercise 7.4

Also, access the helpful resources for Class 10 Maths Chapter 7 Coordinate Geometry at Physics Wallah

### Chapter 8 Introduction to Trigonometry

This chapter introduces students about trigonometry. They will study about some ratios of a right triangle with respect to its acute angles, called trigonometric ratios of angles. The chapter also defines trigonometric ratios for angles 00 and 900. Furthermore, students will know how to calculate trigonometric ratios for specific angles and establish some identities involving these ratios, called trigonometric identities.

Topics Covered in this chapter are- Trigonometric ratios of an acute angle of a right-angled triangle. Proof (well defined); motivate the ratios whichever are defined at 0o and 90o. Values of the trigonometric ratios of 300, 450 and 600. Relationships between the ratios. Trignometric Identities: Proof and applications of the identity sin2A + cos2A = 1. Only simple identities to be given.

 NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Exercises Exercise 8.1 Exercise 8.2 Exercise 8.3 Exercise 8.4

Also, access the helpful resources for Class 10 Maths Chapter 8 Introduction to Trigonometry at Physics Wallah

### Chapter 9 Some Applications of Trigonometry

In this chapter, students will study the applications of trigonometry here. It is used in geography, navigation, map construction, and determining the position of an island in relation to latitudes and longitudes. Students will see how trigonometry is used to find the heights and distances of various objects without actually measuring them. They will become familiar with the topics of the line of sight, angle of elevation, and angle of depression.

Topics Covered in this chapter are- Height and Distance: Angle of elevation, and Angle of Depression. Basic problems on heights and distances. Problems should not contain more than two right triangles. Angles of elevation/depression should be only 30°, 45°, or 60°.

 NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry Exercises Exercise 9.1

Also, access the helpful resources for Class 10 Maths Chapter 9 Some Applications of Trigonometry at Physics Wallah

### Chapter 10 Circles

In earlier classes, students learned about a circle and various terms related to a circle, such as chord, segment, arc, etc. In chapter 10, students will study the various problem that occur when a circle and a line are placed in a plane. So they get thoroughly acquainted with the concept of a tangent to a circle and the number of tangents from the point on a circle.

Topics Covered in this chapter are- Tangent to a circle, point of contact

• Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.
• Prove that lengths of tangents drawn from an external point to a circle are equal.
 NCERT Solutions for Class 10 Maths Chapter 10 Circles Exercises Exercise 10.1 Exercise 10.2

Also, access the helpful resources for Class 10 Maths Chapter 10 Circles at Physics Wallah

### Chapter 11 Constructions

This chapter consists of a total of two exercises. Students who have learned about construction in earlier lessons will also help them. In Exercise 11.1, students will discuss how to bisect a line, while in Exercise 11.2, they will also learn the construction of tangents to a circle. The methods and steps for the construction are explained, and some examples are additionally given to make it more clear to the students.

Topics Covered in this chapter are- Division of a line segment in a given ratio (internally), Tangent to a circle from the point outside it, and construction of a triangle similar to a given triangle.

 NCERT Solutions for Class 10 Maths Chapter 11 Constructions Exercises Exercise 11.1 Exercise 11.2

Also, access the helpful resources for Class 10 Maths Chapter 11 Constructions at Physics Wallah

### Chapter 12 Areas Related to Circles

This chapter begins with the concepts of circumference and area of ​​a circle. Using this concept, the chapter goes on to explain how to find the area of ​​a sector and a segment of a given circular region. In addition, students will learn to calculate the areas of some combinations of plane figures involving circles or their parts.

Topics Covered in this chapter are- Area of sectors and segments of a circle. Problems based on areas and perimeter/circumference. Calculating the area of segment of a circle, problems should be restricted to central angle of 60°, 90° and 120° only.

 NCERT Solutions for Class 10 Maths Chapter 12 Areas Related to Circle Exercises Exercise 12.1 Exercise 12.2 Exercise 12.3

Also, access the helpful resources for Class 10 Maths Chapter 12 Areas Related to Circles at Physics Wallah

### Chapter 13 Surface Areas and Volumes

There are five exercises in Chapter 13. The first exercise consists of questions based on determining the surface area of ​​an object created by joining any two basic bodies, i.e., a cuboid, a cone, a cylinder, a sphere, and a hemisphere. In the exercise, question 13.2 are based on finding the volume of objects formed by combining any of the cuboid, cone, cylinder, sphere, and hemisphere. Exercise 13.3 deals with questions in which a body is transformed from one shape to another. Exercise 13.4 is based on determining the volume, curved surface, and total surface of a frustum of a cone. The final exercise is optional and contains high-level questions based on all the topics in the chapter.

Topics Covered in this chapter are- Surface areas and volumes of combinations of any two of the following: cubes, cuboids, spheres, hemispheres, and right circular cylinders/cones.

 NCERT Solutions for Class 10 Maths Chapter 13 Surface Areas and Volumes Exercises Exercise 13.1 Exercise 13.2 Exercise 13.3 Exercise 13.4 Exercise 13.5

Also, access the helpful resources for Class 10 Maths Chapter 13 Surface Areas and Volumes at Physics Wallah

### Chapter 14 Statistics

Here, students will discuss the numerical representation of ungrouped data into grouped data and find the mean, mode, and median. The concept of cumulative frequency, cumulative frequency distribution, and how to draw cumulative frequency curves will also be explained.

Topics Covered in this chapter are- Mean, median, and mode of grouped data (bimodal situation to be avoided).

 NCERT Solutions for Class 10 Maths Chapter 14 Statistics Exercises Exercise 14.1 Exercise 14.2 Exercise 14.3 Exercise 14.4

Also, access the helpful resources for Class 10 Maths Chapter 14 Statistics at Physics Wallah

### Chapter 15 Probability

The final chapter deals with Probability. The chapter begins with a theoretical approach to probability. Subsequently, the chapter explains the difference between experimental probability and theoretical probability. Various examples are given for effective explanation. So, before going through the practice problems, students must first solve the CBSE Maths examples.

Topics Covered in this chapter are- Classical definition of probability. and simple problems on the probability of an event.

 NCERT Solutions for Class 10 Maths Chapter 15 Probability Exercises Exercise 15.1 Exercise 15.2

Also, access the helpful resources for Class 10 Maths Chapter 15 Probability at Physics Wallah

### How NCERT Solutions for Class 10 Maths help you in the New Pattern of CBSE Board

Recently CBSE announced its new pattern of board exam for class 10. Now onwards students will appear for two exams in their class 10. Maths is the most scoring subject for all students and it needs practice of questions and understanding the applications of formulas and concepts in the numerical.

Exercise of NCERT is most important and NCERT solutions for class 10 Maths prepared by experts of Physics Wallah can help you a lot. According to the new pattern of CBSE board Maths, the subject consists of the following weightage.

 Unit Title Marks Weightage 1 Number System 06 2 Algebra 20 3 Coordinate Geometry 06 4 Geometry 15 5 Trigonometry 12 6 Mensuration 10 7 Statistics And Probability 11 Total Marks 80

### Why are NCERT Solutions for Class 10 Maths important?

The complete study material has been prepared after deeply analyzing the subject. Students can find the NCERT solutions for class 10 maths as per the latest NCERT council guidelines. Since many students face a great amount of difficulty in solving typical numerical problems. Through the guidance of faculty through study material, they can solve typical examples.

1. Class 10th maths also comprises tough theories and numerical which needs special attention. The team at Physics Wallah has also made efforts to provide students with special notes on topics needing special attention.
2. The students are provided with detailed explanations to questions most asked in previous years. At times solving us might be difficult for students.
3. The explanation of each question is prepared with a step-by-step guide to solving typical sums. Extra concept notes are also provided in the study material by our team.
4. The team at Physics Wallah comprises experts who have already topped the national-level exams. The guidance provided by subject experts in the form of notes is highly valuable. Students can find a systematic approach to questions and study material. Students facing any kind of issue can directly reach our faculties.

### How to Study NCERT Solutions for Class 10 Maths effectively?

• The diversified nature of the maths syllabus makes it necessary to have a unidirectional approach.
• The students can easily prepare with solutions for class 10 maths provided by the team at Physics Wallah.
• It can be effective in terms of revision.
• The Physics Wallah study material is very concise and effective. In order to maximize benefit to students, the team has made a wide range of detailed analyses of previous year questions.
• These Physics Wallah study materials are prepared in such a manner that can be shared among friends.

### Why Physics Wallah is best for NCERT Solutions for Class 10 Maths?

• The students looking to score top marks in their examination can go through questions given in the exercise well in advance. We have made it available in Pdf format.
• This solution can be accessed on multiple devices. The very ideology upon which the study material is based is strengthening concept foundations.

### Chapter-wise NCERT Solutions for Class 10 Maths

Do not worry about your difficulties in Mathematics, I assure you that mine are greater. (Albert Einstein) The essence of mathematics is not to make simple things complicated, but to make complicated things simple.The most important year of a student’s life starts from class 10. This is the year from which your subject's interest and foundation build-up. The most important subject in class 10 in terms of subject difficulty is class 10 Maths.

Questions of Physics Wallah for Maths and NCERT books are extremely helpful to fulfil your requirements. On this page, the academic team of Physics Wallah uploaded question solution of NCERT solutions for class 10 maths also another theoretical requirement of the subject we have uploaded all chapter detail theory and questions like objective questions, subjective question, solved question for class 10 which is extremely helpful for your board exam as well as entrance exam preparation like NTSE, a foundation for JEE & NEET.

### How NCERT Solutions for Class 10 Maths can help you

All of you know that nowadays almost all entrance exams in India are conducted by NTA, and NTA follows NCERT books so it is the most important book for your academic journey. For class 10 board NCERT books are highly recommended to solve the NCERT books, now you must wonder how to read or use NCERT class 10 maths and NCERT solutions for class 10 maths?

So in this article, we will discuss the best way to use NCERT solutions for class 10 maths, and this method will not only help you to complete the NCERT book for maths but also helps you to have a solid foundation of class 10 maths.

### Tips to excel in class 10 maths

1. Always attend your school maths class or coaching maths class never miss your class, understand the difference between urgency vs important. If there is urgency then only miss the lecture else never miss the classes.
2. If you miss any class maths in class 10 make a backup plan to cover that.
3. Before maths class in class 10 try to read the topics from your textbook it will help you to understand the concept quickly.
4. After the class, read the NCERT book theory, spend time with theory, make your notes for class 10 maths and make a separate notebook for note down the important formula of the chapter. Use the different color pen to highlight the important formula and try to learn the important formula. You can note down all math formulas from Physics Wallah.
5. After doing all the steps from 1 to 4, now solve the questions from the NCERT book and try to solve all questions of NCERT. Take help from NCERT solutions for class 10 maths prepared by Physics Wallah. Don’t jump into NCERT solutions for class 10 maths immediately, always try to solve by yourself before taking the reference of NCERT solutions for class 10 maths.
6. When you complete the entire questions from the NCERT exercise of NCERT. After that, you required more good-quality questions to excel in the chapter. To do so Physics Wallah uploaded a huge number of questions for the class 10 maths chapter-wise. Solve all questions after doing questions and taking reference of solutions.
7. Finally, go for chapter wise online tests of the particular chapter from the Physics Wallah online test session and get your score. If the score is less than 70 percent, revise once more the entire chapter and again go for the same chapter online test.

### Frequently Asked Question (FAQs)

Q1. How to score Good marks in class 10 Maths?

Ans. To score Good Marks in class 10 Maths one must follow NCERT text book thoroughly. Read the theory from the text book try to build your own concepts. prepare your notes from NCERT class 10 Maths text book ensure you have mentioned all important formulas of the chapter.

Try to solve all Numerical given in the Exercise by yourself and use NCERT solutions for class 10 Maths only for reference. Build your understanding and understand the pattern from previous year class 10 Questions papers and do practice from class 10 Maths sample papers. Always remember doing practice good Maths numerical is best way out to score full marks in class 10 Maths.

Q2. What are the Important chapters of class 10 Maths for CBSE Board Exam?

Ans. As far as Important questions for class 10 Maths is concern there is no specific chapter because questions are asked from all chapters. So prepare a strategies to find out the important chapter of class 10 Maths of which 5 marks questions are asked. Such chapters are Some Applications of Trigonometry, Probability , Pair of Linear Equations in Two Variables.

Q3. How to use NCERT Solutions for class 10 Maths effectively?

Ans. NCERT solutions for class 10 Maths must be use with the following instructions such as.

1. Do not copy any solution for your homework form NCERT solutions for class 10 Maths.
2. Try to find out the answer and best solution of each and every question asked in the exercise do not go for solution immediately.
3. Use NCERT solutions for class 10 Maths only for the reference purposes not for solving the home work.

Q4. How many chapters are in NCERT class 10 Maths and in CBSE class 10 Maths syllabus?

Ans. NCERT class 10 Maths consist 15 Chapters and each chapter having two to three exercise consist of Questions of type Long Answers, Short Answer and MCQ based questions. There are almost 30 to 45 question in each chapter. Students must solve NCERT exemplar for more practice.

Q5. Is NCERT class 10 Maths is sufficient for CBSE board exam?

Ans. Yes if you are preparing for CBSE class 10 board exam than NCERT text book is more than enough however if you are preparing for NTSE or foundation for JEE than you need additional recourses like Physics Wallah Class 10 Maths notes for JEE. For NTSE you need to solve additional questions from Maths section of Physics Wallah.