# NCERT Solutions for Class 10 Maths

NCERT Solutions for Class 10 Maths: The class 10 Mathematics contains 15 interesting chapters. All the chapters are important for CBSE board exam. At least one question is sure from a chapter. So there is no scope of skipping any chapter. NCERT Solutions for Class 10 Maths of each chapter consist of many exercises for practice and an optional exercise. It is mandatory to solve all the exercises including the optional exercises to get a good score on the board exam. If you are through with the concept and problems of NCERT and by practicing previous 5 years questions you can easily score good mark in CBSE board exams.

Here we will cover NCERT Solutions for Class 10 Maths in detail. In these mathematics, the following are the chapters:-

Chapter-1 Real Numbers

Chapter-2 Polynomials

Chapter-3 Pair of Linear Equations in Two Variables

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

## CBSE Class 10 Weightage Distribution Of Mathematics-

 Unit Title Weightage 1. Number system 06 2. Algebra 20 3. Co-ordinate Geometry 06 4. Geometry 15 5. Trigonometry 12 6. Mensuration 10 7. Statistics And Probability 11 Total Marks 80

The main chapters with a brief outline of the topics are given below-

1. Real Numbers: The main topics of NCERT Solutions of this chapter include Euclid’s Division Lemma and uses this concept to find the HCF of given numbers, LCM of numbers and the relation between HCF and LCM,  fundamental theorem of arithmetic and use of this theorem to prove the given number is rational or irrational and the last topic is testing if the given rational number is terminating or non terminating repeating. There are many real-life examples of LCM and HCF mentioned in the NCERT Solutions for Class 10 of this chapter.

2. Polynomials: The chapter starts with an explanation of polynomials referring to the previous classes and then explains the geometrical interpretation of the zeroes of the polynomial. Then it gives the relation between zeroes and coefficient of a given polynomial and also explains about how to carry out the polynomial divisions.

3. Pair of Linear Equations in Two Variables: There are many real-life examples which can be formulated using the concept of linear equations in two variables. Many such problems are mentioned in the NCERT Solutions for Class 10 Maths. The chapter covers various algebraic methods to solve a given pair of linear equations and geometrical way of solving the pair of linear equations.

4. Quadratic Equations: We gets a quadratic equation if a quadratic polynomial is equated to zero with the condition that the coefficient of the variable with power two not equal to zero. The main content of the chapter includes the various methods of solving the quadratic equations and how to determine the consistency of quadratic equations from the value of discriminants.

5. Arithmetic Progressions: The NCERT Solutions for Class 10 of this chapter introduces the concept of arithmetic progression, how to find the nth term of an arithmetic progression and also the expression for the sum of n terms of an arithmetic progression. There are some real-life situations mentioned in the NCERT  solutions of this chapter. Studying a chapter by correlating to real-life example will be interesting.

6. Triangles: The NCERT Class 10 Chapter 6 starts with the explanation of the difference between the congruent figures and similar figures. The main topic of the chapter is the similarity of triangles, criteria for similarity, area of triangles and understanding of Pythagoras Theorem using the similarity of triangles. There are many interesting examples which can be solved using the similarity of triangles.

7. Coordinate Geometry: This is one of the chapters which you will use in almost all the areas your higher studies, whether it is Science, Commerce or Arts. The NCERT Solutions for Class 10 Maths of this chapter includes the distance formulae, section formulae and the concept of finding the area of triangles if the coordinate of the vertex is given.

8. Introduction to Trigonometry: In this chapter, there is a total of 4 exercise and questions of these exercises mainly on finding trigonometric ratios of the sides of a right-angled triangle. The NCERT Solutions for Class 10 Maths of this chapter covers important concepts like the find trigonometric ratios, trigonometric ratios of some specific angles, trigonometric ratios of complementary angles and trigonometric Identities.

9. Some Applications of Trigonometry: This chapter is the continuation of chapter 8 and here the student will study some applications of trigonometry. "Trigonometry" unit holds 12 marks out of 80 marks in the CBSE final maths paper and we can expect one question of 3 or 4 marks from this concept. IN this we will learn how trigonometry is helpful in finding the distance and height of different objects without actually measuring them.

10. Circles: A circle is nothing but a closed figure with a collection of points in a plane which are at a specific distance (radius) from a fixed point (centre). In this chapter, we will discuss tangent to a circle and number of tangents from a point on the circle. In chapter 10 circles, there is a total of 2 exercises with 17 questions in them.

11. Constructions: This chapter, deals with the problems constructions. It is a part of the geometry unit and geometry holds 15 marks in the final CBSE exams and construction is a scoring topic for students. In this chapter, there is a total of 2 exercises with 14 questions. There is a total of 2 exercises in this chapter. In the first exercise, we learn how to divide a line segment and in the second exercise, we will learn the construction of tangents to a circle.

12. Areas Related to Circles: In this chapter, we will deal with areas related to circles. This chapter is a part of Mensuration unit, which holds 10 marks in the CBSE Class 10 final exam. In this chapter, there are 3 exercises with 35 questions in them. In this chapter, we will learn the perimeter and area of a circle, areas of sector and segment of a circle, areas of combinations of plane figures.

13. Surface Areas and Volumes: In this chapter, we will discuss how to find surface areas and volumes of combinations, which are formed by two or more than two of the basic solids such as cone, cuboid, cylinder, sphere and hemisphere. In this chapter, there is a total of 5 exercises with 38 questions in them. In all the exercises, we will deal with questions on finding surface areas and volumes of solids.

14. Statistics: In this chapter, we will discuss how to find the measures of central tendency namely, mean, mode and median from the ungrouped data to that of grouped data. In this chapter, there is a total of 4 exercises with 25 questions. In NCERT Class 10 Maths Chapter 14 Statistics students also get to know about the concept of cumulative frequency, it's distribution and how to draw cumulative frequency curves.

15. Probability: In 9th Class, we learned about empirical probabilities or experimental probabilities of events which are based on the results of actual experiments. In this class, we will discuss the theoretical probability (also called classical probability) of an event, and solve simple questions based on this concept. In this chapter, there are 2 exercises with 30 questions in them.

Here we are going to provide detailed NCERT Solutions for Class 10 which will help students in the preparation of class 10 CBSE board exam. The NCERT Solutions for Class 10 Maths prepared by subject experts to facilitate easy understanding and smooth of concepts.