NCERT Solutions For Class 10 Maths in PDF: Are you a student in search of NCERT Solutions for Class 10 Maths problem? Well, you don’t have to search further. On this page, you will get solutions to all the exercises, questions, and problems in the CBSE NCERT Class 10 Mathematics book. CBSE NCERT Class 10 Maths solution provided here is prepared by our teachers and academic experts at Embibe. NCERT free PDF exercise solutions provided here covers all the questions as per the CBSE NCERT textbooks. The NCERT exercise solutions are solved in simple steps which are very easy to understand.
In this article, we have provided you with NCERT Solutions for Class 10 Maths PDF. You can download solutions for all NCERT chapters (1 to 15) for free without any signup formalities. Scroll down to get the solutions and chapter-wise download links.
Chapter-wise NCERT Solutions For Class 10 Maths PDF
The links to the NCERT solutions for each chapter of Class 10 Maths are as under:
- 1st Chapter: Real Numbers
- 2nd Chapter: Polynomials
- 3rd Chapter: Pair of Linear Equations in Two Variables
- 4th Chapter: Quadratic Equations
- 5th Chapter: Arithmetic Progressions
- 6th Chapter: Triangles
- 7th Chapter: Coordinate Geometry
- 8th Chapter: Introduction to Trigonometry
- 9th Chapter: Some Applications of Trigonometry
- 10th Chapter: Circles
- 11th Chapter: Constructions
- 12th Chapter: Areas Related to Circles
- 13th Chapter: Surface Areas and Volumes
- 14th Chapter: Statistics
- 15th Chapter: Probability
CBSE NCERT Solutions For Class 10 Maths: Chapters & Exercise Solutions
Let us have a look at what each of the chapters in the NCERT syllabus of Class 10 Maths deals with. This will give you a better understanding of each chapter. After the chapter description, you will find a direct link to the solution PDF for that chapter. Just click on the link to view and download NCERT solution PDF.
NCERT Solutions For Class 10 Maths Chapter 1: Real Numbers
This chapter consists of four exercises based on the different topics of the chapter – Euclid’s Division Lemma, The Fundamental Theorem of Arithmetic, Revisiting Irrational Numbers, Revisiting Rational Numbers, and Their Decimal Expansions. There are two theorems in this chapter with examples and problems. In Class 9, you were introduced to the concept of irrational numbers and in Class 10 this discussion continues by revisiting irrational numbers. The sub-topics in this chapter are listed below:
- – 1.1 Introduction
- – 1.2 Euclid’s Division Lemma
- – 1.3 The Fundamental Theorem of Arithmetic
- – 1.4 Revisiting Irrational Numbers
- – 1.5 Revisiting Rational Numbers and Their Decimal Expansions
|Exercise 1.1||5 Questions|
|Exercise 1.2||7 Questions|
|Exercise 1.3||3 Questions|
|Exercise 1.4||3 Questions|
|Download Chapter 1 – Real Numbers Solutions PDF|
NCERT Solutions For Class 10 Maths Chapter 2: Polynomials
This chapter consists of four exercises with the last exercise as an optional one. The study of polynomials here is the continuation of topics studied in Class 9. The introduction of the chapter briefs polynomials with one variable and their degrees that were covered in Class 9.
This is further continued with the discussion of linear polynomials, quadratic polynomials, cubic polynomial. The geometrical meaning of the zeroes of a polynomial, the relationship between zeroes and coefficients of a polynomial, and division algorithm for polynomials are the main topics covered in this chapter. The sub-topics in this chapter are listed below:
- – 2.1 Introduction
- – 2.2 Geometrical Meaning of the Zeroes of a Polynomial
- – 2.3 Relationship between Zeroes and Coefficients of a Polynomial
- – 2.4 Division Algorithm for Polynomials
|Exercise 2.1||1 Question|
|Exercise 2.2||2 Questions|
|Exercise 2.3||5 Questions|
|Exercise 2.4||5 Questions|
|Download Chapter 2 – Polynomials Solutions PDF|
NCERT Solutions For Class 10 Maths Chapter 3: Pair Of Linear Equations In Two Variables
This chapter consists of seven exercises with the last exercise being optional. In this chapter, you will learn about pair of linear equations in two variables, graphical method of solution of a pair of linear equations, algebraic methods of solving a pair of linear equations (substitution method, elimination method, cross-multiplication method), and equations reducible to a pair of linear equations in two variables.
Majorly you will learn to solve pair of linear equations by graphical method (which will be solved on graph sheets) and algebraic method (using the three methods mentioned above). Lastly, you will solve the equations which are reducible to a pair of linear equations. The chapter has plenty of examples and exercise questions. The sub-topics in this chapter are listed below:
- – 3.1 Introduction
- – 3.2 Pair of Linear Equations in Two Variables
- – 3.3 Graphical Method of Solution of a Pair of Linear Equations
- – 3.4 Algebraic Methods of Solving a Pair of Linear Equations
- Substitution Method
- Elimination Method
- Cross-Multiplication Method
- – 3.5 Equations Reducible to a Pair of Linear Equations in Two Variables
|Exercise 3.1||3 Questions|
|Exercise 3.2||7 Questions|
|Exercise 3.3||3 Questions|
|Exercise 3.4||2 Questions|
|Exercise 3.5||4 Questions|
|Exercise 3.6||2 Questions|
|Exercise 3.7||8 Questions|
|Download Chapter 3 Solutions PDF|
NCERT Solutions For Class 10 Maths Chapter 4: Quadratic Equations
Quadratic Equation is one of the most important and interesting chapters in the syllabus of the CBSE Class 10 syllabus for Maths. It consists of a total of four exercises. Here, students will initially learn the standard form of the quadratic equation with the help of examples. This will be followed by the study of the different methods of solving quadratic equations like the solution of a quadratic equation by factorization and solution of a quadratic equation by completing the square.
Lastly, students will learn about the nature of the roots. This chapter consists of plenty of exercises and examples which will help you to understand the topics. The sub-topics in this chapter are listed below:
- – 4.1 Introduction
- – 4.2 Quadratic Equations
- – 4.3 Solution of a Quadratic Equation by Factorisation
- – 4.4 Solution of a Quadratic Equation by Completing the Square
- – 4.5 Nature of Roots
|Exercise 4.1||2 Questions|
|Exercise 4.2||6 Questions|
|Exercise 4.3||11 Questions|
|Exercise 4.4||5 Questions|
|Download Chapter 4 Solutions PDF|
NCERT Solutions For Class 10 Maths Chapter 5: Arithmetic Progressions
An Arithmetic Progression (AP) is a sequence of numbers in which each term is obtained by adding a fixed number to the preceding term except the first term. In this chapter, students will learn the basics of AP – common difference, finite and infinite AP, nth term of an AP, the sum of first n terms of an AP, etc. The chapter consists of four exercises with the last exercise being an optional one. Also, there are examples of problems with detailed solutions to help you understand the various concepts in this chapter. The sub-topics in this chapter are listed below:
- – 5.1 Introduction
- – 5.2 Arithmetic Progressions
- – 5.3 Nth Term of an AP
- – 5.4 Sum of First n Terms of an AP
|Exercise 5.1||4 questions|
|Exercise 5.2||20 questions|
|Exercise 5.3||20 Questions|
|Exercise 5.4||5 Questions|
|Download Chapter 5 Solutions PDF|
NCERT Solutions For Class 10 Maths Chapter 6: Triangles
This chapter consists of 6 exercises with one being optional. In Class 9, congruence of triangles was discussed and here you will mainly learn about similar triangles with several theorems, proofs, and problems. First, you will learn the concept of similar triangles and the criteria for similarity of triangles. This will be followed by the study of the theorem on triangles. Thereafter, the area of similar triangles (with theorem) and the Pythagoras Theorem will be discussed. A total of 6 theorems are discussed in this chapter. The sub-topics in this chapter are listed below:
- – 6.1 Introduction
- – 6.2 Similar Figures
- – 6.3 Similarity of Triangles
- – 6.4 Criteria of Similarity of Triangles
- – 6.5 Areas of Similar of Triangles
- – 6.6 Pythagoras Theorem
|Exercise 6.1||3 Questions|
|Exercise 6.2||10 Questions|
|Exercise 6.3||16 Questions|
|Exercise 6.4||9 Questions|
|Exercise 6.5||17 Questions|
|Exercise 6.6||10 Questions|
|Download Chapter 6 – Triangles Solutions PDF|
NCERT Solutions For Class 10 Maths Chapter 7: Coordinate Geometry
Coordinate Geometry consists of a total of four exercises. In this chapter, you will learn how to find the distance between two points whose coordinates are given and how to find the area of the triangle formed by three given points. Besides, how to find the coordinates of the point which divides a line segment joining two given points in a given ratio will be discussed. The sub-topics in this chapter are listed below:
- – 7.1 Introduction
- – 7.2 Distance Formula
- – 7.3 Section Formula
- – 7.4 Area of a Triangle
|Exercise 7.1||10 Questions|
|Exercise 7.2||10 Questions|
|Exercise 7.3||5 Questions|
|Exercise 7.4||8 Questions|
|Download Chapter 7 Solutions PDF|
NCERT Solutions For Class 10 Maths Chapter 8: Introduction To Trignometry
Trigonometry is a very important chapter that holds significance not only in Class 10 but also in further grades. The chapter consists of a total of 4 exercises and example problems. The discussion starts with trigonometric ratios where you study sine, cosine, tangent, cosecant, secant, contingent.
Thereafter, you will learn about trigonometric ratios of some specific angles (0, 30, 45, 60, and 90 degrees) followed by trigonometric ratios of complementary angles and trigonometric identities. There are plenty of problems to understand the chapter better. The sub-topics in this chapter are listed below:
- – 8.1 Introduction
- – 8.2 Trigonometric Ratios
- – 8.3 Trigonometric Ratios of Some Specific Angles
- – 8.4 Trigonometric Ratios of Complementary Angles
- – 8.5 Trigonometric Identities
|Exercise 8.1||11 Questions|
|Exercise 8.2||4 Questions|
|Exercise 8.3||7 Questions|
|Exercise 8.4||5 Questions|
|Download Chapter 8 Solutions PDF|
NCERT Solutions For Class 10 Maths Chapter 9: Some Applications Of Trigonometry
In this chapter, you will learn about some interesting ways to implement trigonometry and solve real-life problems. This chapter has only one exercise. The questions are based on real-life applications of trigonometry. You will have to visualize and mathematically represent it to solve the problems. The sub-topics in this chapter are listed below:
- – 9.1 Introduction
- – 9.2 Tangent to a Circle
|Exercise 9.1||16 Questions|
|Download Chapter 9 Solutions PDF|
NCERT Solutions For Class 10 Maths Chapter 10: Circles
The basic definition and other fundamentals of circles were discussed in the previous class. Here we will continue with further discussion on circles. The chapter consists of only two theorems and two exercises. The discussion in this chapter is mainly based on the tangent to a circle and the number of tangents from a point on a circle. The sub-topics in this chapter are listed below:
- – 10.1 Introduction
- – 10.2 Tangent to a Circle
- – 10.3 Number of Tangents from a Point on a Circle
|Exercise 10.1||4 Questions|
|Exercise 10.2||13 Questions|
|Download Chapter 10 Solutions PDF|
NCERT Solutions For Class 10 Maths Chapter 11: Constructions
NCERT Class 10 Chapter 11 is a continued discussion from Class 9 where you came across some basic constructions. In this chapter, you will learn a few more constructions using your past knowledge of the basic constructions. The two major discussions are about the division of a line segment and the construction of tangents to a circle. Besides, you will also be expected to give mathematical reasoning behind why such constructions work. Also, you will have to be good at using geometrical instruments. The sub-topics in this chapter are listed below:
- – 11.1 Introduction
- – 11.2 Division of a Line Segment
- – 11.3 Construction of Tangents to a Circle
|Exercise 11.1||7 Questions|
|Exercise 11.2||7 Questions|
|Download Chapter 11 Solutions PDF|
NCERT Solutions For Class 10 Maths Chapter 12: Areas Related To Circles
NCERT Class 10 Maths Chapter 12 – Area Related to Circles – mainly deals with finding the areas of the sector, a segment of a circle, and areas of a combination of plane figures. In this chapter, our discussion will begin with the revision of the perimeter and area of circles.
Later, the discussion will extend to finding the area of a segment and section of a segment. Lastly, you will also learn to calculate the area of a combination of plane figures. In our daily life, we find many objects to be round or circular in shape. Thus, having knowledge of Areas Related to Circles is of great significance. The sub-topics in this chapter are listed below:
- – 12.1 Introduction
- – 12.2 Perimeter and Area of a Circle
- – 12.3 Areas of Sector and Segment of a circle
- – 12.4 Areas of Combination of Plane Figures
|Exercise 12.1||5 Questions|
|Exercise 12.2||14 Questions|
|Exercise 12.3||16 Questions|
|Download Chapter 12 Solutions PDF|
NCERT Solutions For Class 10 Maths Chapter 13: Surface Areas And Volumes
In this chapter, you will learn about surface areas and volumes of combinations of solids which is a continuation of the discussion in Class 9 on cuboid, cone, cylinder, and sphere. The chapter begins with the understanding of solid figures as a combination of solids and continues to calculate their surface area and volume.
Thereafter, the conversion of solid from one shape to another and related concepts are discussed. Lastly, the concept of Frustum of a cone is discussed. A total of five exercises are there in this chapter with the last one being optional. The sub-topics in this chapter are listed below:
- – 13.1 Surface Area of a Combination of Solids
- – 13.2 Volume of a Combination of Solids
- – 13.3 Conversion of Solid from One Shape to Another
- – 13.4 Frustum of a Cone
|Exercise 13.1||9 Questions|
|Exercise 13.2||8 Questions|
|Exercise 13.3||9 Questions|
|Exercise 13.4||5 Questions|
|Exercise 13.5||7 Questions|
|Download Chapter 13 Solutions PDF|
NCERT Solutions For Class 10 Maths Chapter 14: Statistics
This chapter consists of four exercises with more of arithmetic calculations. Here you will be calculating the mean, median and mode of grouped and ungrouped data. Also, you will be solving problems on the cumulative frequency and how to draw cumulative frequency curves and cumulative frequency distribution topics. The sub-topics in this chapter are listed below:
- – 14.1 Introduction
- – 14.2 Mean of Grouped Data
- – 14.3 Mode of Grouped Data
- – 14.4 Median of Grouped Data
- – 14.5 Graphical Representation of Cumulative Frequency Distribution
|Exercise 14.1||9 Questions|
|Exercise 14.2||6 Questions|
|Exercise 14.3||7 Questions|
|Exercise 14.4||3 Questions|
|Download Chapter 14 Solutions PDF|
NCERT Solutions For Class 10 Maths Chapter 15: Probability
This chapter deals with the study and calculation of the probability of occurrence of an event, which is very common in our daily life. This chapter gives a mathematical approach to understanding this. The chapter consists of only two exercises of which one is optional. The sub-topics in this chapter are listed below:
- – 15.1 Introduction
- – 15.2 Probability: A Theoretical Approach
|Exercise 15.1||25 Questions|
|Exercise 15.2||5 Questions|
|Download Chapter 15 Solutions PDF|
Advantages Of NCERT Solutions By Embibe For Class 10 Maths
The NCERT Class 10 Maths solution provided here will be of great help to students. The advantages are listed as follows:
- Better Understanding of Concepts: The NCERT Class 10 solutions will help you develop a better understanding of the topics. This will help you to have a strong command over the subject. The step-by-step precise and elaborate solutions will help students understand the problem-solving method better.
- Acts as a Reference to Solve and Practice: Students can refer to the solutions in case of any doubt. It also helps in knowing the correct way to solve problems. You can also use it for practice and quick revision.
- Assignment Completion: Candidates may have to solve the problems as a part of an assignment and thus these NCERT solutions will help you in this task.
- On Spot Learning: For many students, Mathematics gradually becomes hard to understand as they do not clear their doubts and understand the problem-solving method. Thus, using the Class 10 Maths NCERT solutions, students can understand the solving method then and there. This saves them from getting stuck in a single question without any hint or clue.
- Will Lay a Strong Foundation for Future Grades: Eventually, the concepts and problems will lay a strong foundation for higher classes. Be it cracking competitive exams, applying for government exams, or any other opportunity, this basic knowledge will help you a lot.
Significance Of Class 10 Maths NCERT Solutions
Class 10 board exams are the first public exams faced by students and thorough preparation is very much needed right from the beginning of the year. Among all the subjects, Mathematics is one of the important subjects and requires a proper understanding of all the chapters & topics. A thorough understanding of the concepts and developing problem-solving skills will not only help you score excellent marks in the upcoming exams but also will also act as a strong foundation for future studies.
Preparing for Class 10 Maths is very crucial and any negligence will affect your overall percentage in the board exams. Thus students must prepare for the exam consistently using the Class 10 Maths NCERT Exercise solutions. The solutions will act as a guide when you solve the exercise questions on your own.
How To Study For Class 10 Maths?
Many students find Maths as a difficult subject and often do not pay attention as much as they do for other subjects. However, it is very important to understand that Maths is not difficult to learn and understand. For many students, the first thing that comes to their mind when they think of Maths is that it is very difficult. Thus, it first thing is to remove the mental block by the action which you take.
To begin with, you first need to read and understand the topics. If you feel you are not able to understand the concept after the class approach your teachers and elders for help. Thereafter, take easy problems first and solve them. Thereafter start solving more challenging problems. This exercise will help you overcome your fear of Maths subject. Now, when you approach the next chapter, you just need to repeat the same.
CBSE Class 10 Maths Unit-wise Marks
In this section, you will get the weightage of each chapter/unit in the CBSE Class 10 Maths syllabus. The unit-wise marks weightage is compiled in accordance with CBSE Class 10 Maths exam paper 2020.
|Unit Number||Unit Name||Marks Weightage|
|7||Statistics & Probability||11|
CBSE Class 10 Maths Exam Pattern
The total marks allotted for CBSE Class 10 Maths exam paper is 100. The theory paper will be of 80 marks and 20 marks will be taken from the internal assessments of students. CBSE has revised the exam pattern and increased the number of questions in the paper from 30 to 40. This implies that the marks allotted per question have reduced. Now, the majority of the questions (about 25%) in the paper are objective type/very short answer type questions.
You can check the latest CBSE Class 10 Maths exam pattern to understand the step-wise allotment of marks for every answer.
|Sections||Number of Questions||Marking Scheme|
|A||20 (1 mark per question)||20|
|B||6 (2 marks per question)||12|
|C||8 (3 marks per question)||24|
|D||6 (4 marks per question)||24|
*The paper will be of 80 marks and will contain 40 questions in total.
Ask Your Doubts On Embibe Ask
Are you looking for solutions for Maths problems? Is there a reaction in Chemistry that you cannot understand? Do you have any academic questions? Embibe offers you a platform where you can put all your queries and get them resolved by experts. At Embibe Ask, you will get solutions to all your queries. You can post your queries/questions on the portal or you can check the questions/queries asked by others. The academic experts at Embibe will resolve your queries at the earliest.
FAQs On Class 10 Maths NCERT Solutions
The FAQs on Class 10 Maths NCERT Solutions are provided below. This will help you to answer your queries:
A. The Class 10 Maths NCERT Solutions can be downloaded online. Students can click on this page to download the solutions in PDF format. The solutions are solved by the experts at Embibe.
A. NCERT Books are the best source for class 10 board exam preparations. In this context, solving Class 10 Maths NCERT exercise questions is very essential for regular preparation, practice, and revision.
A. Solving the NCERT exercise solutions will help you a lot with your exam preparations. Besides that, you can also solve some different type of questions and solve the previous year papers.
A. Solve the exercise questions on your own. If you are taking some time to solve it then try your best and give that time. However, if you are really stuck and not able to solve then you can refer to the solutions provided here to check the problem-solving method. Directly referring to the solutions is not advisable as it will impact your ability to seek different methods to solve a problem.
A. Embibe’s NCERT Solutions for 10th Maths are prepared by academic experts with decades of experience. These solutions have been prepared as a complete package and you will not need any other solutions or guides to prepare for CBSE Class 10 exams. And the best part is you can download these solutions for free and refer to them anytime, anywhere.
A. Many experts and toppers recommend NCERT textbook for Class 10 Maths as the book to follow while preparing for CBSE 10th board exams.
A. Other than the Class 10 Maths NCERT textbook, you can refer to Class 10 Mathematics textbooks by R.D. Sharma and R.S. Aggarwal.
A. The most important thing is to practice sums and problems every day. You can pay special attention to units like Algebra, Trigonometry, Statistics & Probability as these topics have the highest weightage and can help you score maximum marks in the exam.
Learn & Practice Class 10 Lessons Online With Embibe
Embibe not only offers you books and solutions to practice and study but also other resources like practice questions and mock tests. You can solve Class 10 Practice Questions on Embibe and check the solutions if needed. You can also take a Class 10 Foundation Mock Test. These are available for free and will help you improve your conceptual knowledge and test-taking skills. You can follow the below-mentioned steps to take a mock test or practice questions at Embibe:
- – 1st Step: Visit embibe.com. We advise you to take the test or practice questions after logging in.
- – 2nd Step: Click on the ‘Take a Test’ button beneath the search tab.
- – 3rd Step: Click on the ‘change your goal’ button on the top-right corner of the screen. Select your goal as ‘Foundation-10’.
- – 4th Step: Choose the subject you want to take the test in.
- – 5th Step: Click on the ‘Start Test’ button to start taking the test.
- – 6th Step: You can select the chapter from the list if you want to take a test on a particular chapter.
- – 6th Step: Click on the ‘Start Practice’ tab to practice Class 10 Maths questions before taking a test.
We have now provided you with the complete NCERT Solutions for Class 10 Maths. Make the best use of it by solving and practicing the problems. You can use these solutions as and when you complete a lesson. You can also attempt to solve model test papers and previous years’ papers. Maths is all about practice and solving test papers and previous years’ papers will help you in performing better.
We hope this article helps you. If you have any questions, feel free to post it in the comment box below. We will get back to you at the earliest. Stay tuned to embibe.com for more on CBSE NCERT Solutions For Class 10.1822 Views