NCERT Solutions Class 10 Maths PDF – All Chapters Explained

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Class 10 Maths syllabus aims at helping you to build a strong base of topics, the basic knowledge about them, making them understand theorems and concepts and testing them enough in the form of exercise and examples in the textbook. The exercises given in the NCERT textbook are designed for the students to use their skills and learnings of each topic to the maximum. Before each exercise, you are also given enough examples to refer to and understand the questions with the help of the step-by-step explanations provided in the textbooks.

The CBSE Class 10 Maths board exam is directly based on the NCERT textbook. According to CBSE's official curriculum guidelines, almost all board exam questions — including the 80-mark written paper — are either directly from NCERT exercises or closely modelled on them. This means that a student who thoroughly solves every exercise in the NCERT textbook is already covering the widest portion of the exam.

The Class 10 Maths syllabus spans 14 chapters — from number theory and algebra to geometry, trigonometry, and probability. Each chapter builds on prior knowledge. A gap in Chapter 3 (Linear Equations) will slow you down in Chapter 5 (Arithmetic Progressions). This is why chapter-wise, step-by-step solutions are not just helpful — they are essential.

eSaral's NCERT Solutions are verified by faculty trained at IIT Bombay, ensuring every solution follows the correct method, uses the right notation, and meets CBSE's marking scheme. Whether you are solving Exercise 4.3 on quadratic equations or the optional Exercise 2.4 on polynomials, every answer here is aligned to what your examiner will be looking for.

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NCERT Class 10 Maths Chapter 1 Real Numbers

In Chapter 1 Real Numbers of Class 10, you will explore real numbers and irrational numbers. The chapter begins with the Euclid’s Division Lemma, which states that “Given positive integers a and b, there exist unique integers q and r satisfying a = bq + r, 0≤r

NCERT Class 10 Maths Chapter 2 Polynomials

In chapter 2 Polynomials, it begins with the definition of the degree of the polynomial, linear polynomial, quadratic polynomial and cubic polynomial. This chapter has a total of 4 exercises, including miscellaneous exercise. Exercise 2 includes questions on finding the number of zeroes through a graph. It requires a basic understanding of the Geometrical Meaning of the Zeroes of a Polynomial. Exercise 2.2 is based on the Relationship between Zeroes and Coefficients of a Polynomial, where you have to find the zeros of a quadratic polynomial and in some of the questions, they have to find the quadratic polynomial. In Exercise 2.3, the concept of the division algorithm is defined, and you will find the questions related to this topic. The optional exercise, 2.4, contains the questions from all the concepts of Chapter 2.

NCERT Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables

This chapter explains the concept of Pair of Linear Equations in Two Variables. This chapter consists of a total of 7 exercises, and in these exercises, different methods of solving the pair of linear equations are described. Exercise 3.1 explains how to represent a situation algebraically and graphically. Exercise 3.2 describes the methods of solving the pair of the linear equation along with the Graphical Method. Exercises 3.3, 3.4, 3.5 and 3.6 describe the Algebraic Method, Elimination Method, Cross-Multiplication Method, and Substitution Method, respectively. Exercise 3.7 is an optional exercise which contains all types of questions. You must practise these exercises to secure good marks in your board exams.

NCERT Class 10 Maths Chapter 4 Quadratic Equations

In chapter 4 Quadratic Equations, you will get to know the standard form of writing a Quadratic Equation. The chapter goes on to describe the method of solving the quadratic equation through completing the square method and factorization method . It ends with the topic on finding the nature of roots, where you will get to know what is 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

NCERT Class 10 Maths Chapter 5 Arithmetic Progressions

In this chapter you will introduced to a new topic, Arithmetic Progression, i.e. AP. This chapter has a total of 4 exercises. In Exercise 5.1, the questions related to representing a situation in the form of AP, finding the first term and difference of an AP, and finding out whether a series is AP or not. Exercise 5.2 includes the questions on finding out the nth term of an AP by using the following formula:

                              an = a + (n-1) d

The next exercise, which is 5.3, contains the questions on finding the sum of the first n terms of an AP. The last exercise contains miscellaneous questions which are high level questions based on AP to enhance your problem-solving skills and analytical.

NCERT Class 10 Maths Chapter 6 Triangles

In Chapter 6 of Class 10 Maths, you will learn about triangles, triangles with same shape but with different angles. This chapter starts with the concept of a similar and congruent figure. It will  explain the condition for the similarity and theorems  of two triangles and theorems related to the similarity of triangles. further, the areas of similar triangles have been explained with a theorem. At the end you will learn about the Pythagoras Theorem and the Converse of Pythagoras Theorem.

Important theorems that you should know thoroughly while preparing for the exam include:

Theorem 1: If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.

Theorem 2: If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.

Theorem 3: If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion) and hence the two triangles are similar.

Theorem 4: If in two triangles, sides of one triangle are proportional to (i.e., in the same ratio of) the sides of the other triangle, then their corresponding angles are equal and hence the two triangles are similar.

Theorem 5: If one angle of a triangle is equal to one angle of the other triangle and the sides including these angles are proportional, then the two triangles are similar.

NCERT  Class 10 Maths Chapter 7 Coordinate Geometry

In chapter 7, you will learn how to find the distance between two points whose coordinates are already given, and to find the area of the triangle formed by three given points. Along with this, you will also know how to find the coordinates of the point which divides a line segment joining two given points in a given ratio.

NCERT  Class 10 Maths Chapter 8 Introduction to Trigonometry

Trigonometry Introduced in chapter 8 to the student in NCERT textbook. You will study some ratios of a right triangle with respect to its acute angles called trigonometric ratios of the angles. Also, the trigonometric ratios for angles 0∘ and 90∘. You will also learn to calculate trigonometric ratios for the given angles and also a few trigonometric identities.

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

This chapter 9 is the continuation of the previous chapter; here, you will study the applications of trigonometry. It is used in so many ways such as: geography, navigation, construction of maps, and determining the position of an island in relation to the latitudes and  longitudes. In this chapter, we will see how trigonometry is used for finding the heights and distances of several objects without actually measuring them. 

NCERT Solutions for Class 10 Maths Chapter 10 Circles

In chapter 10, you will be introduced to the concept of tangents and the number of tangents from a point on a circle. 

 Important Theorems –

Theorem 1: The tangent at any point of a circle is perpendicular to the radius through the point of contact.

Theorem 2: The lengths of tangents drawn from an external point to a circle are equal.

NCERT Class 10 Maths Chapter 11 Areas Related to Circles

As per the name of the chapter, it is all about the perimeter and area of a circle. The concepts of finding the area of a sector and segment of a circle are discussed here. Further, this chapter explains how to find the area of the figures that contain a circle or part of a circle.

NCERT Class 10 Maths Chapter 12 Surface Areas and Volumes

Chapter 13  is about the surface areas and volumes of different shapes and objects. There are a total of 5 exercises in this chapter. Find the surface area of any object which is 2-dimensional or 3-dimensional. The 3-dimensional shapes include cuboid, cone, sphere, hemisphere and cylinder. After that, there are questions on finding the volume of the objects that are made up of two different solid shapes. Also, in this chapter, you will get questions on conversion from one shape to another. This chapter discusses how to find the volume, curved surface area and total surface area of a frustum of a cone.

NCERT Solutions for Class 10 Maths Chapter 13 Statistics

In this chapter 13, you will learn the numerical representation of ungrouped data to grouped data and you will get to know how to find the Mean, Mode and Median. Also, the concept of cumulative frequency, cumulative frequency distribution and how to draw cumulative frequency curves will be clarified.

NCERT Class 10 Maths Chapter 14 Probability

This is the last chapter of class 10 NCERT Maths which deals with Probability. This chapter starts with the theoretical approach of probability. Later, the chapter explains the difference between experimental probability and theoretical probability. There are several examples given to explain it in an effective way. So, before going through the exercise problems, you must solve the examples of  this book first

Benefits of NCERT Solutions Class 10 Maths

The Class 10 NCERT Solutions of Maths provided on our page in PDFs formate have several benefits, which include:

• The solutions are easily understandable.

• Solutions are provided for each chapter in steps for better understanding.

• Diagrams are given to help you to understand the solutions better.

• Each question from each chapter is covered.