Welcome to one of the most important years of your academic life. The yearend would bring you in competition with your peers from across the country for the very first time in your life. CBSE Class 10 becomes the foundation stone on which the palace of your academics is built, and this is the year when students are under a lot of pressure from the upcoming board examinations.
Keeping all other subjects aside for a while, mathematics takes an important role because this is the time where the subjects transform drastically to include the core topics that would be taught in the higher classes and be used in real life. Thus, the understanding of these topics becomes all the more important because concepts left out here would lead to problems in the entire units in further classes and professional courses. To help the students understand the concepts that are essential to the class 10th mathematics, we at Aakash Institute provide all the solutions with a detailed explanation in NCERT Solutions for Class 10 Maths.
NCERT Solutions for Class 10 Maths contains all the answers in a stepwise manner. The language used in NCERT Solutions for Class 10 Maths is easy and understandable, which ensures the students become selfsufficient when equipped with the solutions. The Aakash NCERT Solutions for Class 10 Maths is prepared by industry experts and experienced faculty members which is the testimony of its quality.
The chapter starts with Euclid’s division theorem, which states that “for given set of integers a and b, there exist precise integers q and r, which fulfil the equation “a = bq + r”, where ‘r’ lies between 0 and b. HCF and LCM are based on divisibility. Other included topics are Fundamental Arithmetic Theorem, properties of positive integers, conversion of a fraction to decimal and decimal to a fraction. The chapter has four exercises. 1st exercise discusses Euclid’s division lemma, 2nd exercise is based on HCF & LCF, the 3rd exercise is talking about proving the rational or irrational number, and the last mean 4th exercise is based on fractions to decimal and decimal to fractions.
The chapter starts with the definition of the degree of a polynomial, linear polynomial, quadratic polynomial, and cubic polynomial. In this chapter, there are four exercises, including one optional exercise as well. The chapter teaches about the use of a graph to calculate the roots of the polynomial or the value at which the polynomial would return zero value. The chapter also delves into the relationship between zeroes and the coefficient of a polynomial. It helps students locate the zeroes of a quadratic polynomial and cubic polynomial. The chapter also teaches the remainder theorem to divide a polynomial by another polynomial.
This chapter explains the idea of pairs of linear equations. This chapter begins with linear equations in two variables, using the graphical method of their solution, algebraic conditions for linear equations. The chapter further elaborates on the solutions of a pair of linear equations in two variables algebraically by substitution, elimination and cross multiplication method. Students can find different methods of solving these equations easily. This chapter contains seven practice sets, including an algebraic method, elimination method, crossmultiplication methods, and substitution method. NCERT Solutions for Class 10 Maths help the students get a comprehensive understanding of such topics.
In this chapter, the student will be able to know about the writing of quadratic equations in a standard form. The chapter proceeds to explain the method of solving the quadratic equations through the factorisation method and Shreedharacharya’s formula. This chapter also talks about the basics of a quadratic equation. It additionally integrated everyday sports primarily based totally on the situational troubles of quadratic equations. This chapter includes four exercises, where you have to solve whether the equation is quadratic or not and conversion of the word problem in quadratic equation, find the roots of the quadratic equation factorisation, and the chapter also tells about the nature of roots whether they are real and distinct, real and equal or nonreal roots. The chapter also defines the relationships between the roots and the coefficient in the quadratic equation.
This chapter introduces students to a new topic which is an arithmetic progression. This chapter deals with the concept of sequence and series. The chapter elaborates on arithmetic progression, which is a series in which two consecutive terms have a constant difference. The chapter increases the analytical and problemfixing talents of students. This chapter constitutes four exercises related to the general form of arithmetic progression, finding the 1st term and the difference of an AP. Questions are also based on finding whether the series is arithmetic progression or not, and it also includes finding out the nth term of arithmetic progression by using the formula provided in the chapter. This chapter will help you get the concepts and help you build the capability to solve problems related to sequences and series. The chapter forms the base of various advanced concepts to come in the higher classes.
This chapter deals with the definitions and examples of similar triangles. Through this chapter, a student will learn about the same shape but not essentially the same size. It starts with the concept of a similar and congruent figure. The chapter also explains the condition for the similarity of two triangles and theorems according to the similarity of triangular shapes. Further, the areas of similar triangles are explained with a theorem, and at last, Pythagoras theorem and converse of Pythagoras theorem are also covered in the chapter. In this chapter, there are six exercises based on the properties of triangles. Various theorems are also there, which form the basis of the exercises. This chapter also helps you with the concepts involved in higher studies.
This chapter starts with standards of coordinate geometry, graphs of linear equations. The chapter in the class 10th maths revolves around the Distance formula and Section formula. There are sections on the area of the triangle as well. From this chapter, students will know how to calculate the distance between the two points whose coordinates are given. The chapter also teaches them to discover the location and area of the triangle fashioned out of three particular given points that do not lie on the same line. Also, students will get to know how to find the coordinates of the point which divides a line segment joining two given points in a particular ratio. NCERT Solutions for Class 10 Maths introduce the students to Distance Formula, Section Formula and Area of a Triangle in this chapter.
From this chapter, students will be able to study some ratios of a right triangle with respect to one of its acute angles, which is known as trigonometric ratios of the angles. The chapter also constitutes the trigonometric ratios for angles of 00 to 900. Students also get to know how to calculate trigonometric ratios for some particular angles and establish some particular points involving these ratios, known as trigonometric specification. In this chapter, four exercises consist of various questions on finding Trigonometric Ratios, Trigonometric Identities, and Trigonometric Ratios of Complementary Angles are primary subtopics of this chapter.
In this chapter, students will be able to study the applications of trigonometry. It is mainly 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 locating the heights and distances of diverse objects without measuring them. Students get to learn about the line of sight, attitude of elevation, attitude of depression. Questions are mainly based on the realistic applications of trigonometry. The angle of elevation, Angle of Depression are considered tougher portions of this chapter. In Chapter 9, students should know about trigonometry to find the heights and distances of various objects without realtime measuring of these objects.
Students have a basic idea about circles and various terms related to a circle like a chord, segment, arc, etc. In this chapter, students will be able to study the different situations that arise when a circle and a line are given in a plane. They get accustomed to the idea of Tangent to a Circle and Number of Tangents from a Point on a Circle. The chapter deals with the circle theorems, which help solve various questions in geometry. The chapter contains various questions based on the tangent to the circle and the chords in a circle which make use of the circle theorems, and the solutions of these have been provided in an understandable way in the NCERT Solutions for Class 10 Maths.
This chapter starts with the division of a line segment in a given ratio. Then tangents to a circle from a point outside it and after that the construction of a triangle similar to a given triangle. From this chapter, students can learn about the construction of various geometrical figures. There are two exercises in this chapter from that, student will able to study how to divide a line segment, and also they will understand the construction of tangents to a circle. Methods and steps for construction are explained in understandable language, and also some examples are additionally incorporated to make it clearer to the students. This chapter also talks about Thales Theorem, which is also known as Basic Proportionality theorem.
This chapter constitutes the concepts of perimeter and area of a circle. Applying this concept, the chapter further explains how to find the area of sector and segment of a circular region. Moreover, students will be able to get clarity on finding the areas of some combinations of plane figures involving circles. This chapter has Three exercises regarding questions of the area of a circle and reallife questions, and costrelated questions on areas related to the circular region.
This chapter deals with finding areas and volumes of different solids such as cube, cuboid and cylinder, and so on. The chapter includes a total of five exercises, consisting of questions based on finding the surface area of an object formed by combining any two of the basic solids like the cuboid, cone, cylinder, sphere and hemisphere. The questions in the chapter are based on finding the volume of objects formed by combining various solid figures or conversion of one shape to another. The NCERT Solutions for Class 10 Maths provided by the Aakash institute provides the answers to the easy as well as the tough question of the topic.
Here, students will learn the numerical representation of individual data to grouped data and find the Mean, Mode and Median. Also, this chapter contains the idea of cumulative frequency, cumulative frequency distribution and a way to draw cumulative frequency curves. You will also learn the relation between Mean, Mode, and Median. This chapter forms the basis of data science and analytics. The chapter teaches the students the pictorial representation of the raw, unorganised data from which tangible results can be obtained. There are generally four exercises in the chapter wherein you need to resolve questions primarily based totally on locating mean, median and mode from individual records to that of group records. You must be able to recognise and resolve the questions associated with cumulative frequency, the cumulative frequency distribution, and a process to draw cumulative frequency curves after going through this chapter.
The final chapter deals with Probability. The chapter begins with the general approach of probability. It is the study of obtaining the chances of success or failure in a particular experiment. The chapter also includes the different aspects of experimental probability and theoretical probability. There are many examples given to explain it effectively. But before solving the exercise problems, students have to solve the examples of textbooks, and after that, it will be easy to understand and solve.
Given below is the Exam pattern for CBSE Class 10 Maths Exam Pattern 20202021, the current session.
Q. How do NCERT Solutions for Class 10 Maths help grab the important concepts covered in the NCERT Class 10 Maths?
A. Students who are willing to score good marks in the Class 10th board exams are suggested to practice exercises of each chapter, and as you know, math is not an easy subject, and it’s totally based on concepts, but if you understand the aspects of every fact, then you can easily score good marks in the subject. Each and every detail is explained in NCERT Solutions for Class 10 Maths in a way to makes it easier for the students. While studying, the solutions, which are constructed by keeping in mind the NCERT guidelines, help the students understand the correct way to solve the questions expected of them in the board examinations.
Q. Can the NCERT Solutions for Class 10 Maths really solve your math problems?
A.You see the tenthgrade test is a test that usually holds a very important place in the academics of your life. A subject like math that has no place to memorize or write, and it is never possible to pass without understanding, becomes all the more important. But only marks are not important, and understanding the concepts is also required because these concepts would help you throughout your life. NCERT Solutions for Class 10 Maths provides the support needed to understand the solution to the questions provided in the books. This way, if a student practices his school book well, he/she will develop a very good understanding of the concepts that are crucial to the curriculum.
Q. Are the NCERT Solutions for Class 10 Maths good for the students of other boards?
A.NCERT Solutions for Class 10 Maths are designed for the NCERT books, and they follow the CBSE and NCERT guidelines; thus, they may not be according to the guidelines and specifications of other boards, but the students can still gain the same knowledge on the concepts and the topics that have been discussed in the NCERT books. Since the majority of the syllabus is similar across all boards in the subject of maths thus, the NCERT Solutions for Class 10 Maths prove beneficial to the students of all boards
Q. Are the NCERT Solutions for Class 10 Maths available at a price?
A. The NCERT Solutions for Class 10 Maths is available at the website of the Aakash Institute. The PDF of the solutions is available free of cost, and it is available to everyone regardless of the board, you are a student of Aakash institute or not.
Q. Is it necessary to read or practice the NCERT solutions for CLASS 10 MATHS?
A. NCERT books as all of us know are the base of any class, any school, board, or competitive exam for school students. In this scenario, what is needed is to have a proper understanding of the concepts behind the topics and chapters included in the NCERT syllabus of any particular class? Most of the time, students do not get it in the classroom or during selfstudy. In such cases, NCERT solutions act as recorded help to students looking out to clear their concepts. One can just download the PDF and consult it whenever required.
The NCERT solutions for CLASS 10 MATHS by Aakash specifically provide detailed answers for all subjects and stepbystep solutions for Maths. Accessing the NCERT Solutions by Aakash can give you an edge over others. Moreover, it is based on the exact syllabus which covers not only the CBSE board but also the Olympiads.
Q. Where and how can a student download CLASS 10 MATHS NCERT Solutions?
A. For the ease of students, we at Aakash have provided a PDF file for NCERT Solutions 2020 of all subjects, all topics for all classes. The detailed solutions are prepared by our senior and experienced faculty which gives students an indepth understanding of the concepts rather than the particular question.
CLASS 10 MATHS NCERT Solutions are also provided in PDF format for the ease of students.
Q. Why CLASS 10 MATHS NCERT Solutions are recommended?
A. Well, it’s a fact that NCERT books are the best for CBSE board exam preparation. It is not just because this council is recommended by CBSE itself but the content and syllabus of NCERT books are the best across the country.
Syllabus and Topics CLASS 10 MATHS NCERT Solutions are curated after thorough research keeping in mind the development perspective of students which helps them excel in board exams.
Thus, it gets extremely important for students to thoroughly go through the recommended NCERT syllabus for a particular exam.
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