NCERT Solutions for Class 10 Maths PDF – Download Chapter wise
Check out the chapter-wise NCERT Maths Solutions PDFs for class 10 from the links provided below:
NCERT solutions class 10 maths chapter 1 to 15 are provided here. These solutions are prepared by our expert faculties to help students in their board exam preparations. The students looking for NCERT class 10 maths solutions can download all chapter-wise pdf to find a better approach of solving the questions. These solutions will also help students to have a deeper understanding of concepts covered in NCERT class 10 maths textbook. Practicing the textbook questions will help the students to analyze their level of preparation and the understanding of concepts. The solutions to these questions are provided here which can help students to clear their doubts easily.
The solution list comprises of all the chapter-wise answers to NCERT class 10 maths written in a very clear and lucid manner, keeping in the objective of textbooks. The students can refer these NCERT Solutions for class 10 maths pdf as their additional references and study materials. Practicing textbook exercises will surely help the students in their preparation for the examination.
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NCERT Solutions for Class 10 Maths
Chapter 1 – Real Numbers
In chapter 1 of class 10, students will explore real numbers and irrational numbers. The chapter starts 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<b”. The Euclid’s Division algorithm is based on this lemma and is used to calculate the HCF of two positive integers. Then, the Fundamental Theorem of Arithmetic is defined which is used to find the LCM and HCF of two positive integers. After that the concept of irrational number, rational number and decimal expansion of rational number is explained with the help of theorem
Chapter 2 – Polynomials
In Polynomials chapter begins with the definition of degree of the polynomial, linear polynomial, quadratic polynomial and cubic polynomial. This chapter has total 4 exercises including the optional exercise. The exercise 2.1 includes the questions on finding the number of zeroes through graph. It requires the understanding of Geometrical Meaning of the Zeroes of a Polynomial. The exercise 2.2 is based on the Relationship between Zeroes and Coefficients of a Polynomial where students have to find the zeros of quadratic polynomial and in some of the questions they have to find the quadratic polynomial. In exercise 2.3, the concept of division algorithm is defined and students will find the questions related to it. The optional exercise i.2 2.4 consists the questions from all the concepts of chapter 2.
Chapter 3 – Pair of Linear Equations in Two Variables
This chapter explains the concept of “Pair of Linear Equations in Two Variables”. This chapter has total 7 exercises and in these exercises different methods of solving the pair of linear equations is described. The exercise 3.1 describes how to represent a situation algebraically and graphically. The exercise 3.2 explains the methods of solving the pair of linear equation through Graphical Method. Exercise 3.3, 3.4, 3.5, 3.6 describes Algebraic Method, Elimination Method, Cross-Multiplication Method, Substitution Method respectively. The exercise 3.7 is optional exercise which contains all types of questions. Students must practice these exercise to master in the method of solving the linear equations.
Chapter 4 – Quadratic Equations
In this chapter students will get to know the standard form of writing a quadratic equation. Then this chapter will explain the method of solving the quadratic equation through factorisation method and completing the square method. Chapter ends with the topic on finding the nature of roots which states that, 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
Chapter 5 – Arithmetic Progressions
This chapter introduces students to a new topic that is Arithmetic Progression i.e AP. This chapter constitute of total 4 exercises. In exercise 5.1, students will find the questions related to representing a situation in form of AP, finding the first term and difference of an AP, finding out whether a series is AP or not. The 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 i.e 5.3, contains the questions on finding the sum of first n terms of an AP. The last exercise include higher level questions based on AP to enhance students analytical and power solving skills.
Chapter 6 – Triangles
In chapter 6 of class 10 CBSE maths, students will study about those figures which have the same shape but not necessary the same size. The chapter starts with the concept of similar and congruent figure. It further explains the condition for similarity of two triangles and theorems related to the similarity of triangles. After that, the areas of similar triangles has been explained with a theorem. At the end of this chapter the Pythagoras Theorem and converse of Pythagoras Theorem is described.
Chapter 7 – Coordinate Geometry
In this chapter students will learn how to find the distance between two points whose coordinates are given, and to find the area of the triangle formed by three given points. Along with this students will also study how to find the coordinates of the point which divides a line segment joining two given points in a given ratio. For this students will get introduced to Distance Formula, Section Formula and Area of a Triangle in this chapter.
Chapter 8 – Introduction to Trigonometry
This chapter will introduce students to Trigonometry. They will study some ratios of a right triangle with respect to its acute angles, called trigonometric ratios of the angles. The chapter also defines the trigonometric ratios for angles of 00 and 900. Further, students will also know how to calculate trigonometric ratios for some specific angles and establish some identities involving these ratios, called trigonometric identities.
Chapter 9 – Some Applications of Trigonometry
This chapter is the continuation of the previous chapter as here student will study the application of trigonometry. It is used in geography, navigation, construction of maps, determining the position of an island in relation to the longitudes and latitudes. In this chapter students will see how trigonometry is used for finding the heights and distances of various objects, without actually measuring them. They will get introduced to the term line of sight, angle of elevation, angle of depression.
Chapter 10 – Circles
In earlier classes students have studied about circle and various terms related to a circle like chord, segment, arc etc. In this chapter, students will study the different situations that arises when a circle and a line are given in a plane. So, they will get thorough with the concept of Tangent to a Circle and Number of Tangents from a Point on a Circle.
Chapter 11 – Constructions
In this chapter consist of total 2 exercises. Whatever students have learned about construction in earlier classes will also help them. In exercise 11.1, students will study how to divide a line segment. Whereas in exercise 11.2 they will study the construction of tangents to a circle. Method and steps for construction are explained and also some example are given to make it more clear to the students.
Chapter 12 – Areas Related to Circles
This chapter begins with the concepts of perimeter and area of a circle. Using this concept the chapter further explains, how to find the area of sector and segment of a circular region. Moreover, students will get to know how to find the areas of some combinations of plane figures involving circles or their parts.
Chapter 13 – Surface Areas and Volumes
In chapter 13, there are total 5 exercises. The first exercise consist the questions based on finding the surface area of an object formed by combining any two of the basic solids i.e cuboid, cone, cylinder, sphere and hemisphere. In exercise 13.2 questions are based on finding the volume of objects formed by combining any two of a cuboid, cone, cylinder, sphere and hemisphere. The exercise 13.3 deals with the questions in which solid is converted from one shape to another. The exercise 13.4 is based on finding the volume, curved surface area and total surface area of frustum of a cone. The last exercise is optional and has high level questions based on all the topics of this chapter.
Chapter 14 – Statistics
Here students will learn numerical representation of ungrouped data to grouped data and finding the Mean, Mode and Median. Also the concept of cumulative frequency, cumulative frequency distribution and how to draw cumulative frequency curves will be explained.
Chapter 15 – Probability
The last chapter deals with the probability. The chapter starts with the theoretical approach of probability. Then the chapter explains the difference between experimental probability and theoretical probability. There are various example are given to explain it in a better way. So, before going through the exercise problems students must solve the examples of CBSE Maths first.
Benefits of NCERT Solutions Class 10 Maths:
The class 10 NCERT maths solutions given here in PDFs have several benefits like:
- The solutions given here are very easy to understand.
- Solutions are provided in steps for better understanding.
- Diagrams are given to help the students in visualizing the solutions.
- All the questions from each chapter are covered.
The students are advised to prepare all the chapters covered in the solution modules which will eventually help them to have a deeper knowledge of concepts. For effective preparations, it is important for students to understand all the steps provided in the solutions.
How CBSE 10 Maths Solutions of NCERT Helpful for Board Exams?
CBSE Class 10 Maths is an important subject for students. Here we have provided complete assistance to students for its preparation. Class 10 is the first benchmark for any student that will reflect in the future records of achievement. Central Board of Secondary Education (CBSE) always prescribes the NCERT books for board exam preparation.
Exam preparation is a rigorous process that requires an overall understanding of individual chapters. This process demands hard work towards studies and an effective approach to get through the solutions. This significant role is played by class 10 NCERT solutions to equip students in the preparation of competitive entrance exams. NCERT books are best known for putting forth the concepts in a simple way for better understanding.
The NCERT exemplar questions have strategically placed after every topic to check the conceptual understanding of students. The students are then made to answer them to check their conceptual understanding. NCERT class 10 books for mathematics are written in the most lucid and clear manner that helps to break the complex problems in the most efficient way.
Keep visiting to get complete chapter-wise solutions in PDF for all the classes. Students can even download BYJU’S App to get a personalized learning experience and prepare for the exams more effectively.