NCERT Class 10 Math Solutions for the 2022–23 School Year

 Here you will find all of the Chapters 1 through Chapter 15 NCERT Solutions for Class 10 Mathematical Exercises. Our knowledgeable faculty has selected these NCERT Solutions to aid students in their test preparation. In order to find a more effective way to approach the problems, students looking for the NCERT Solutions of Class 10 Maths can download all chapter-by-chapter PDFs.

The best study materials available to students are without a doubt the answers to the questions found in the NCERT books. Additionally, these CBSE NCERT Solutions for Class 10 Math 2022–23 will aid students in developing a deeper comprehension of the ideas provided in the textbook. Students will be able to assess their level of preparation and concept mastery by practising the textbook questions. The responses to these inquiries

NCERT Solutions Class 10 Maths Chapters

Chapter 1 Real Numbers

Chapter 2 Polynomials

Chapter 3 Pair of Linear Equations in Two Variables

Chapter 4 Quadratic Equations

Chapter 5 Arithmetic Progressions

Chapter 6 Triangles

Chapter 7 Coordinate Geometry

Chapter 8 Introduction to Trigonometry

Chapter 9 Some Applications of Trigonometry

Chapter 10 Circles

Chapter 11 Constructions

Chapter 12 Areas Related to Circles

Chapter 13 Surface Areas and Volumes

Chapter 14 Statistics

Chapter 15 Probability

Free PDF Download of NCERT Solutions for Class 10 Math

All of the chapter-by-chapter responses to the questions found in the NCERT Book for Class 10 Maths are included in the list of NCERT Solutions of Class 10 Maths, which is presented in a very clear and transparent manner while upholding the goal of textbooks. The NCERT Solutions for Class 10 are available to students as additional resources and study materials. The students' preparation for the test will undoubtedly benefit from practising the exercise solutions from NCERT textbooks.

Class 10 Maths Chapter Details and Exercises from NCERT Solutions

NCERT Mathematical Solutions for Class 10

Students will study real numbers and irrational numbers in Chapter 1 of Class 10. The Euclid's Division Lemma asserts that "Given positive integers a and b, there exist unique integers q and r satisfying a = bq + r, 0rb," which is the first statement in the chapter. This lemma serves as the foundation for the Euclid's Division procedure, which determines the HCF of two positive integers. The Fundamental Theorem of Arithmetic, which is utilised to determine the LCM and HCF of two positive integers, is then defined. Following that, the theorem is used to describe the concepts of an irrational number, a rational number, and the decimal expansion of rational numbers.

Class 10 Maths NCERT Solutions PDF Chapter 1 Exercises
☞NCERT Solutions Real Numbers Class 10 Exercise 1.1 – 5 Questions (4 Long Answers, 1 Short Answer)
☞NCERT Solutions Real Numbers Class 10 Exercise 1.2 – 7 Questions (4 Long Answers, 3 Short Answers)
☞NCERT Solutions Real Numbers Class 10 Exercise 1.3 – 3 Questions (3 Short Answers)
☞NCERT Solutions Real Numbers Class 10 Exercise 1.4 – 3 Questions (3 Short Answers)

NCERT Solutions for Class 10 Maths Chapter 2 Polynomials

The definitions of the degree, linear, quadratic, and cubic polynomials are given at the beginning of the chapter on polynomials. There are a total of 4 exercises in this chapter, one of which is optional. Questions about calculating the number of zeroes in a graph can be found in Exercise 2.1. Understanding the Geometrical Meaning of a Polynomial's Zeroes is necessary. Students must locate the zeros of a quadratic polynomial in Exercise 2.2, which is based on the Relationship between Zeroes and Coefficients of a Polynomial. In some cases, they must also locate the quadratic polynomial. The division algorithm concept is defined in Exercise 2.3, where students can also find the questions that pertain to it. Exercise 2.4, which is optional, consists of the the questions from all the concepts of Chapter 2.

Topics Covered in Class 10 Maths Chapter 2 Polynomials :

Zeros of a polynomial. Relationship between zeros and coefficients of quadratic polynomials.

Class 10 Maths NCERT Solutions PDF Chapter 2 Exercises
☞NCERT Solutions Polynomials Class 10 Exercise 2.1 – 1 Question (1 Short Answer)
☞NCERT Solutions Polynomials Class 10 Exercise 2.2 – 2 Questions (2 Short Answers)
☞NCERT Solutions Polynomials Class 10 Exercise 2.3 – 5 Questions (2 Short Answers, 3 Long Answers)
☞NCERT Solutions Polynomials Class 10 Exercise 2.4 – 5 Questions (2 Short Answers, 3 Long Answers)

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

Pair of Linear Equations in Two Variables is a concept that is explained in this chapter. There are a total of 7 tasks in this chapter, and they all involve solving a pair of linear equations using various strategies. How to represent a situation algebraically and graphically is explained in Exercise 3.1. Exercise 3.2 illustrates how to use the Graphical Method to solve the pair of linear equations. The Algebraic Method, Elimination Method, Cross-Multiplication Method, and Substitution Method are each covered in Exercises 3.3, 3.4, 3.5, and 3.6, respectively. Activity 3.7, an optional exercise, with questions of every description. In order to acquire the technique for solving linear equations, students must practise these tasks.

Topics Covered in Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables:

a pair of two-variable linear equations with a graphic representation of their consistency/inconsistency.
Algebraic requirements for the quantity of solutions. algebraic solution of two linear equations in two variables, using substitution and elimination. Situational issues that are easy..

Important Formulas –

The general form for a pair of linear equations in two variables, x and y, is

a1 x + b1 y + c1 = 0

and a2 x + b2 y + c2 = 0,

where a1, b1, c1, a2, b2, c2 are all real numbers and a12 + b12 ≠ 0, a22 + b22 ≠ 0.

Class 10 Maths NCERT Solutions PDF Chapter 3 Exercises
☞NCERT Solutions Pair of Linear Equations in Two Variables Class 10 Maths Exercise 3.1 – 3 Questions (2 Short Answers, 1 Long Answer)
☞NCERT Solutions Pair of Linear Equations in Two Variables Class 10 Maths Exercise 3.2 – 7 Questions (5 Short Answers, 2 Long Answers)
☞NCERT Solutions Pair of Linear Equations in Two Variables Class 10 Maths Exercise 3.3 – 3 Questions (2 Short Answers, 1 Long Answer)
☞NCERT Solutions Pair of Linear Equations in Two Variables Class 10 Maths Exercise 3.4 – 2 Questions (2 Long Answers)
☞NCERT Solutions Pair of Linear Equations in Two Variables Class 10 Maths Exercise 3.5 – 4 Questions (4 Short Answers)
☞NCERT Solutions Pair of Linear Equations in Two Variables Class 10 Maths Exercise 3.6 – 2 Questions (2 Long Answers)
☞NCERT Solutions Pair of Linear Equations in Two Variables Class 10 Maths Exercise 3.7 – 8 Questions (1 Short Answer, 7 Long Answers)

NCERT Solutions of Class 10 Maths Chapter 4 Quadratic Equations

Students will learn about the usual form of writing a quadratic equation in this chapter. The chapter continues with describing how to solve a quadratic problem using the factorization approach and the square-root method. Finding the nature of roots is the final section of the chapter, where it is stated that the quadratic equation ax2 + bx + c = 0 has

1. Two distinct real roots, if b² – 4ac > 0
2. Two equal roots, if b² – 4ac = 0
3. No real roots, if b² – 4ac < 0

Topics Covered in Class 10 Maths Chapter 4 Quadratic Equations :

the quadratic equation ax2 + bx + c = 0, (a 0), in standard form. Using the quadratic formula and factorization, quadratic equations can be solved (only for real roots). Relationship between the roots' nature and the discriminant.
Daily activities-related situational problems based on quadratic equations have to be included.

Important Formulas –

If b 2 – 4ac > 0, we get two distinct real roots

$-\frac{�}{2�}+\frac{\sqrt{{�}^2-4��}}{2�}���-\frac{�}{2�}-\frac{\sqrt{{�}^2-4��}}{2�}$

If b 2 – 4ac = 0, then

$$\begin{gathered} �=-\frac{�}{2�}\pm 0 \\ �=-\frac{�}{2�}��-\frac{�}{2�} \end{gathered}$$

So, the roots of the equation ax2 + bx + c = 0 are both -b/2a.

Therefore, we say that the quadratic equation ax2 + bx + c = 0 has two equal real roots in this case.

If b 2 – 4ac < 0, then there is no real number whose square is b 2 – 4ac. Therefore, there are no real roots for the given quadratic equation in this case.

Since b 2 – 4ac determines whether the quadratic equation ax2 + bx + c = 0 has real roots or not, b 2 – 4ac is called the discriminant of this quadratic equation.

So, a quadratic equation ax2 + bx + c = 0 has

(i) two distinct real roots, if b 2 – 4ac > 0,

(ii) two equal real roots, if b 2 – 4ac = 0,

(iii) no real roots, if b 2 – 4ac < 0.

Class 10 Maths NCERT Solutions PDF Chapter 4 Exercises
☞NCERT Solutions Maths Quadratic Equations Class 10 Exercise 4.1 – 2 Questions (1 Short Answer, 1 Long Answer)
☞NCERT Solutions Maths Quadratic Equations Class 10 Exercise 4.2 – 6 Questions (6 Short Answers)
☞NCERT Solutions Maths Quadratic Equations Class 10 Exercise 4.3 – 11 Questions (8 Short Answers, 3 Long Answers)
☞NCERT Solutions Maths Quadratic Equations Class 10 Exercise 4.4 – 5 Questions (2 Short Answers, 3 Long Answers)