NCERT Solutions for Class 10 Maths

Class 10 being a whole new experience for you as it will be the very first time when you will be appearing for the board exams. Speaking of which, a thorough knowledge of all the chapters along with NCERT Solutions for Class 10 Maths can really help you to understand the subject better in less time. There are times when you might want to go through the chapters’ details first before starting off with the preparation. Indeed, it is a good practice to follow as you will be well-aware of what is there in that particular chapter beforehand. For the same reason, we have provided the chapters, topics and exercises included in each of them. There is a total of 15 chapters in class 10 Maths NCERT Book. Starting from chapter 1, Real Numbers to the last chapter, i.e. chapter 15, Probability, we have mentioned all the crucial details below. Scroll down to get well-versed with each and every chapter of CBSE Class 10 Maths.

Chapter 1 – Real Numbers

NCERT Class 10 Math Chapter 1, Real Numbers, is the extension of the topics learnt in 9th class. Sections 1.2 and 1.3 of this chapter contains some very important properties of positive integers, namely Euclid’s division algorithm and the Fundamental Theorem of Arithmetic. Furthermore, you will be revisiting Irrational Numbers in section 1.4 whereas Revisiting Rational Numbers and Their Decimal Expansions will be included in Section 1.5. Euclid’s division algorithm has a lot to do with divisibility of integers. It has plethora of applications associated with the divisibility properties of integers. NCERT Class 10 Maths Chapter 1, Real Numbers will be highly beneficial to compute the HCF of two positive integers

We cover all exercises in the chapter given below:-

EXERCISE 1.1 - 5 Questions with Solutions in PDF

EXERCISE 1.2 - 7 Questions with Solutions in PDF

EXERCISE 1.3 - 3 Questions with Solutions in PDF

EXERCISE 1.4 - 3 Questions with Solutions in PDF

Chapter 2 - Polynomials

Polynomials has total of four exercises however the last exercise is optional. In the first exercise, you need to find zeroes of polynomials p(x). In the second exercise, there are two questions. You have to verify the relationship between the zeroes and the coefficients in the first, while in the second, you have to find a quadratic polynomial. The third exercise has a total of five questions in which you have to do division of polynomials and obtain zeroes of polynomials. Then comes the optional exercise which has five questions in which you need to find zeroes of polynomials.

We cover all the exercises in the chapter given below:-

EXERCISE 2.1 - 1 Question with Solutions in PDF

EXERCISE 2.2 - 2 Questions with Solutions in PDF

EXERCISE 2.3 - 5 Questions with Solutions in PDF

EXERCISE 2.4 - 5 Questions with Solutions in PDF

Chapter 3 - Pair of Linear Equations in Two Variables

There is an introduction part in the beginning of this chapter explaining the concepts of Linear equations in two Variables. You will learn some further complex topics while revising concepts that you have learned in class 9. This chapter has a total of seven exercises in which the last exercise is optional again. You will see three world problems given in the first exercise. In the second exercise, there are a total of seven questions. The third exercise has three questions. The fourth exercise has two questions. The fifth exercise has a total of` five questions in which you have to solve the pair of linear equations through various methods given. The sixth exercise has two questions. The last exercise is optional. Some important topics covered in this chapter are graphical representations, Pair of Linear Equations in Two Variables, Algebraic Methods of Solving a Pair of Linear Equations, Graphical Method of Solution of a Pair of Linear Equations, Elimination Method, Substitution Method, Cross-Multiplication Method and Equations Reducible to a Pair of Linear Equations in Two Variables.

We cover all exercises in the chapter given below:-

EXERCISE 3.1 - 3 Questions with Solutions in PDF

EXERCISE 3.2 - 7 Questions with Solutions in PDF

EXERCISE 3.3 - 3 Questions with Solutions in PDF

EXERCISE 3.4 - 2 Questions with Solutions in PDF

EXERCISE 3.5 - 4 Questions with Solutions in PDF

EXERCISE 3.6 - 2 Questions with Solutions in PDF

EXERCISE 3.7 - 8 Questions with Solutions in PDF

Chapter 4 - Quadratic Equations

You will study quadratic equations and the number of ways to find their roots. You will also get to learn some applications of quadratic equations in our daily life situations. There is a total of four exercises in this chapter. The first exercise has two questions, in the first you will need to find check whether equations are quadratic equations or not while in the second you have to convert world problem into quadratic equations. You need to find the roots of quadratic equations by factorisation in the second exercise. You will be finding the roots of quadratic equations in the third exercise also. The fourth exercise has five questions based on finding the roots. A solution of a Quadratic Equation by Completing the Square, Solution of a Quadratic Equation by Factorisation, and Nature of Roots are the main topics studied in this chapter.

We cover all the exercises in the chapter given below:-

EXERCISE 4.1 - 2 Questions with Solutions in PDF

EXERCISE 4.2 - 6 Questions with Solutions in PDF

EXERCISE 4.3 - 11 Questions with Solutions in PDF

EXERCISE 4.4 - 5 Questions with Solutions in PDF

Chapter 5 - Arithmetic Progressions

Arithmetic Progressions, chapter 5 of Class 10 Maths, deals with an introduction to Arithmetic Progression with the help of simple daily life examples and gradually deals with the topics entailed and their complexities. Four exercises are given in this chapter divided into various questions in which we have to find the term. Overall, you will learn how to find the nth terms and the sum of n consecutive terms, and in turn use the acquired knowledge in solving some daily life problems. 

We cover all the exercises in the chapter given below:-

EXERCISE 5.1 - 4 Questions with Solutions in PDF

EXERCISE 5.2 - 20 Questions with Solutions in PDF

EXERCISE 5.3 - 20 Questions with Solutions in PDF

EXERCISE 5.4 - 5 Questions with Solutions in PDF

Chapter 6 - Triangles

There are six exercises in chapter 6, Triangles, including one optional having a different set of questions based on the properties of triangles. This chapter has a total of 9 theorems and is very important for all the students of class 10 Maths for their class 10 Board exam. Triangles are one of the most important chapters of Class 10 Maths as there are a lot of subtopics derived from the concepts of this chapter in higher grades that not only helps you to excel in your school exams, but also in competitive level exams as well.

We cover all the exercises in the chapter given below:-

EXERCISE 6.1 - 3 Questions with Solutions in PDF

EXERCISE 6.2 - 10 Questions with Solutions in PDF

EXERCISE 6.3 - 16 Questions with Solutions in PDF

EXERCISE 6.4 - 9 Questions with Solutions in PDF

EXERCISE 6.5 -  17 Questions with Solutions in PDF

EXERCISE 6.6 - 10 Questions with Solutions in PDF

Chapter 7 - Coordinate Geometry

A total of four exercises are given in the chapter. The questions are based on finding the distance between the two points whose coordinates are provided and the area of a triangle formed by three given points. Coordinate Geometry one of the most important as well as interesting concepts of Class 10 Mathematics. Coordinate Geometry (or also called as the analytic geometry) takes us through the crucial link between geometry and algebra through graphs including lines and curves. It provides with the geometric concepts in Algebra and makes it easier for students to solve geometric problems. Coordinate geometry is a part of geometry where the position of points on the plane is described using an ordered pair of numbers. 

We cover all exercises in the chapter given below:-

EXERCISE 7.1 - 10 Questions with Solutions in PDF

EXERCISE 7.2 - 10 Questions with Solutions in PDF

EXERCISE 7.3 - 5 Questions with Solutions in PDF

EXERCISE 7.4 - 8 Questions with Solutions in PDF

Chapter 8 - Introduction to Trigonometry

This chapter has a total of four exercises comprising of various questions mainly on finding trigonometric ratios of the sides of a right triangle with respect to the acute angles of that triangle, called trigonometric ratios. Trigonometric Ratios, Trigonometric Ratios of Specific Angles, Trigonometric Identities and Trigonometric Ratios of Complementary Angles are the main topics you will learn in this chapter.

We cover all the exercises in the chapter given below:-

EXERCISE 8.1 - 11 Questions with Solutions in PDF

EXERCISE 8.2 - 4 Questions with Solutions in PDF

EXERCISE 8.3 - 7 Questions with Solutions in PDF

EXERCISE 8.4 - 5 Questions with Solutions in PDF

Chapter 9 - Some Applications of Trigonometry

In this chapter, you will be studying some very interesting ways in which trigonometry is used in daily life around you. This chapter has only one exercise and the questions of which are based on the practical applications of trigonometry.

We cover all the exercises in the chapter given below:-

EXERCISE 9.1 - 16 Questions with Solutions in PDF

Chapter 10 - Circles

Starting from the basics, that is the definition of Circle. A Circle is nothing but a closed shape with a certain set of points in a plane at a specific distance from the center of the circle. Circles of class 10 Maths has just two exercises. The first exercise contains basic questions, while the second has various questions in which you have to prove the given equations.

We cover all the exercises in the chapter given below:-

EXERCISE 10.1 - 4 Questions With Solutions in PDF

EXERCISE 10.2 - 13 Questions With Solutions in PDF

Chapter 11 - Constructions

In class 9, you must have carried out certain constructions and calculations using a straight edge (ruler) and compass, for example, drawing the perpendicular bisector of a line segment, bisecting any angle, some constructions of triangles and much more. In this chapter of class 10, i.e. Constructions, we shall study some more constructions by using the idea of the earlier constructions. You might also have to give the mathematical reasoning behind why such constructions work. In this chapter, there is two exercises where you have to draw various constructions such as division of line segments, construction of Tangents to a Circle and the questions are based on them.

We cover all the exercises in the chapter given below:-

EXERCISE 11.1 - 7 Questions With Solutions in PDF

EXERCISE 11.2 - 7 Questions With Solutions in PDF

Chapter 12 - Areas related to Circles

You must be already familiar with some of the methods of finding the perimeters and areas of simple plane figures such as squares, rectangles, parallelograms, triangles and circles from your previous classes. Many objects that we come across in our day to day life are related to some of the circular shapes in some form or the other. In this chapter, you will be learning about areas related to triangles. There are three exercises that cover all the questions of the area of a circle and finding the areas of two special ‘parts’ of a circular region.

We cover all the exercises in the chapter given below:-

EXERCISE 12.1 - 5 Questions with Solutions in PDF

EXERCISE 12.2 - 14 Questions with Solutions in PDF

EXERCISE 12.3 - 16 Questions. with Solutions in PDF

Chapter 13 - Surface Areas and Volumes

We assume that from class 9, you are familiar with some of the solids like cone, cuboid, cylinder, and sphere. You have also learned how to find surface areas and volumes. In our daily life, we come across a number of solids made up of combinations of two or more of the basic solids such as cuboid, Cylinder, Sphere or cone. In this chapter, there are five exercises and all of them will deal with the problems of finding areas and volumes of different solids such as a cube, cuboid and cylinder.

We cover all exercises in the chapter given below:-

EXERCISE 13.1 - 9 Questions with Solutions in PDF

EXERCISE 13.2 - 8 Questions with Solutions in PDF

EXERCISE 13.3 - 9 Questions with Solutions in PDF

EXERCISE 13.4 - 5 Questions with Solutions in PDF

EXERCISE 13.5 - 7 Questions with Solutions in PDF

Chapter 14 - Statistics

You will see a total of four exercises in this chapter. The questions will be based on finding mean, median and mode from ungrouped data to that of grouped data. You will also be solving questions related to cumulative frequency, how to draw cumulative frequency curves and the cumulative frequency distribution topics.

We cover all exercises in the chapter given below:-

EXERCISE 14.1 - 9 Questions with Solutions in PDF

EXERCISE 14.2 - 6 Questions with Solutions in PDF

EXERCISE 14.3 - 7 Questions with Solutions in PDF

EXERCISE 14.4 - 3 Questions with Solutions in PDF

Chapter 15 - Probability

Probability deals with the occurrence of a random event. The value of probability is expressed between zero and one. Probability helps you to estimate how likely events are to happen. If we take a coin as an example, the result of tossing a coin, will either be Head OR Tails, only two possible outcomes are possible. Out of the two exercises in this chapter, one is optional. The questions are based on finding the probability of getting a situation mostly on coins and dice.

We cover all exercises in the chapter given below:-

EXERCISE 15.1 - 25 Questions with Solutions in PDF

EXERCISE 15.2 - 5 Questions with Solutions in PDF

Importance of Class 10 Mathematics NCERT Solutions

Class 10 is the most crucial stage in every student life since the next course or the career path they would like to choose in future days all depends on their score in Class 10. Maths is a subject known for its difficulty and students find it hard to find the relevant study materials while they are preparing for their exam. The struggle of finding the right study materials end here as Vedantu provides NCERT Solutions for Class 10 Mathematics which help the students in their preparation for board exam as well as the competitive exam. Since NCERT solutions provide an in-detail explanation for various concepts of Class 10 Maths, it indeed helps the student in understanding concepts easily. Download the NCERT Class 10 Mathematics Solutions Free PDF now and redefine your preparation for class 10 Maths.

Why Vedantu

Vedantu NCERT Solutions for Class 10 Maths enables you to understand all the basic & advance level concepts after solving each & every exercise question. Our Maths teachers especially focus on clearing out your concepts and providing you with a thorough understanding of all the topics. You are taught on a one-to-one basis by our most dedicated teachers. We at Vedantu don't believe in just recorded lectures as they don't prove helpful in solving doubts related to any of the book solutions.

To assess your progress on a regular basis, you are also tested by our maths tutors at a definite interval of time. The results are shared with your parents to keep them on the same page as well. Another benefit of Vedantu is that you get to choose the pace of the learning of the lesson and the timing of the live tutoring session. The lesson plan is customized according to your requirements. The live sessions are also recorded and are available free of cost to all the students and their parents later for review and revision purposes. Another biggest advantage of studying with Vedantu is that you can choose to study class 10 maths NCERT solutions either on your PC or through your Android mobile devices after downloading our Instant doubt solving app! You can either join us as a regular student or contact us whenever you have doubts and want to prepare for your tests or examinations! We want our NCERT solutions for class 10 maths to prove highly beneficial for you!

There are several ways with which you can avail the benefits of our NCERT Class 10 Maths Solutions. Let’s see what they are after a brief description. Stepping into Class 10 is the best experience of your life as you will be experimenting and facing new things which might appear very exciting to you. As mentioned already that it will be the first time in your life when you will be appearing for the class 10 board exams. Maths is counted among the most dreadful subjects which is feared by a lot of the students. This is the reason why along with NCERT Solutions for Class 10 Maths, we have provided the detailed chapter-wise content so that you face no problem while solving the tricky questions of class 10 Maths. Students are advised to keep the Maths NCERT Solutions class 10 handy so that they can prepare short notes that are highly beneficial for class 10 Maths exam. You can include important formulas and theorems and make short notes of it. Chapters like Coordinate Geometry and Constructions need undivided attention which can be gained by solving NCERT Solutions for Class 10 Maths and going through the root cause of each and every problem you are facing a problem with. 

Studying hard alone won’t get you top grades in the examination; you also need to adopt a smart study strategy and thus we have uploaded NCERT Solutions for Class 10 Maths to facilitate the students with the benefit of stepwise solutions. NCERT solutions give the top edge to your efforts and practice and help you in understanding the concepts in an interesting, easy and better way. For additional guidance, you can enroll at Vedantu and find excellent tutorials, through the learning experience and useful study material. Solutions of NCERT books provide an effortful challenge to the students trying to get their concepts straightened out. A good understanding and strong foundation in all major maths topics help students to solve the hardest of problems. These solutions are based on the latest topics involved in the book and are written with the utmost care. 

Mathematics is that subject which is required at every step of life. A thorough understanding of the concept of basic calculations is required for a student to comprehend his mathematical skills. However, it is seen that children often detest the subject owing to the various formulas, figures and calculations. Studying and teaching mathematics can at times become tiresome but here’s a solution to it. At Vedantu, mathematics as a subject is made easy to learn and understand with NCERT Solutions for class 10 Maths. Here, the concepts beginning from practicing the sums are also provided to help students learn with clarity and also test their understanding of the concepts.

Mathematics is all about having a strong knowledge of the basics. Hence, topics which give a firm foundation to the knowledge of mathematics of a student are discussed here. Each of these topics is explained and discussed with great precision and elaboration. A proper introduction to every topic is given and all terminologies are well defined. Children learn better with illustrations, and therefore, Vedantu uses various illustrations and examples to explain the various concepts. At every step appropriate and real-life example are given thus making it relatable for the student and providing him with a clear picture of whatever he has read or understood so far.

The main focus of ours is to make learning easy and eliminate the fear of numbers from the minds of the students. The explanation of the various topics is done in an organised and simple manner in NCERT Solutions for Class 10 Maths PDF so as to make it easy for the students to understand the concepts in clear light. Apart from giving a theoretical explanation to the topics, the provision of contacting our experts is also made accessible for the students. With Vedantu, Mathematics can be made easy to learn as its approach is student friendly. The more you practice, the better you get at solving mathematics problems. Download NCERT Solutions for Class 10 Maths now and study at your own pace. Join Vedantu and make learning pleasurable. We wish you all the best for your journey along with the preparation of Class 10 Maths and good fortune to all your endeavours.