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.
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
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
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
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:
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
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:
a_{n} = 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
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.
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
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
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 0^{0} and 90^{0}. 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 0^{o} and 90^{o}. Values of the trigonometric ratios of 30^{0}, 45^{0} and 60^{0}. 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
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
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
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
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
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
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
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
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
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 |
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.
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.
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.
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.
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.