Class 10 is among the most important camps on your ascent to your academic summit. This is a very important class for the students, and it is the first time the students take up their first public exams. They are pitted against their batchmates from all across the country for the very first time in this class. The concepts taught in the class are very important as well because most of these topics will be there for their pre-college classes (11th and 12th). This is an important time for students to focus on the scoring subjects and make them their strong points because these subjects will eventually help them score a good rank in their board exams.
Mathematics is the prime candidate among these subjects. It is logic-based and completely dependent upon the understanding of concepts. The more a student has to practise, the better would be his scoring chances, yet mathematics is a difficult subject for many students, and this difficulty in comprehending the subject and the pressure of board exams compound the anxiety felt by the students of the students class 10
After a comprehensive study of the class 10th curriculum and the books available in the market, RS Aggarwal is considered among the best books to prepare for board exams. The book has been written by a famous mathematics professor, academician, and writer. Dr RS Aggarwal has compiled the book in easy language, and he has also provided some excellent questions for practice. However, despite the easy language of the book, the students still get stuck on the questions and here, Aakash Institute comes to the rescue. Aakash provides solutions to RS Aggarwal for class 10th maths. Aakash RS Aggarwal Solutions for Class 10 Mathematics cover every chapter and provide solutions to every question. In total, there are 20 chapters in the RS Aggarwal maths textbook for Class 10. Using the solution, students can gain a clear understanding of the concept and prepare for exams.
The priority of these solutions and the teachers preparing them is to help the students with their studies and lessen their anxiety. The solutions are prepared to keep in mind the current level of understanding of the students and their expected mental state in class 10th. Because of this, explanations are constructed at a level that is easy to understand, making it easier for students to comprehend information, follow and memorise. These solutions are prepared under the guidance of senior faculty members by the subject matter experts, both of whom have years of experience with them. The topic and subtopics are described and clarified in detail in each solution, which is beneficial for clearing most doubts. Furthermore, an in-depth analysis of each question is provided, so students learn how to approach any question correctly.
Students can download free PDF solutions for class 10 mathematics of RS Aggarwal from Aakash, which is the best way to ease their learning process. Once the students have gone through the textbook, Aakash Institute recommends that they download the PDF format and use it while practising questions to tally answers and cross-reference the procedures. Thus, understanding the topic at hand at a time in depth will ensure a solid understanding of the entire curriculum.
Chapter 1- Real numbers deal with the idea of irrational numbers, the concept of Euclid's division lemma, along with some major applications. The chapter also addresses the fundamental theorem of arithmetic motivating through examples, the introduction of real numbers, proofs of irrationality, real numbers examples and solutions. Finally, the chapter concludes with the revisiting of rational numbers and their decimal expansions.
Chapter 2- Polynomials deals with the definition of polynomials and explains the intricate details and concepts related to numerous properties of polynomials. In addition, the chapter addresses the division algorithm for polynomials which is paramount to solve the questions related to this topic. The geometrical meaning of a polynomial's zeros and the relationship between zeroes and coefficients of a polynomial are other aspects of a polynomial explained in this chapter.
Chapter 3- Linear equations in two variables deal with the fundamental properties of the equations, which have two variables. The chapter explains the various methods that are used to solve the linear equations in two variables. A new multiplication method, called cross- multiplication, is also introduced in the chapter. The chapter also includes methods like the elimination method, where one of the variables is eliminated to get the value of the other variable. The elimination method is also done by substitution, where one variable is expressed in the form of the other. The topic also discusses the graphical method of solving these questions. Consistency of the equations is one of the important topics where the chapter discusses whether the system of linear equations would have single solution infinite solutions or no solution. The chapter ends with word problems for the students.
The theorem of basic proportionality or Thales theorem is discussed in the chapter where it states that if a line parallels to any one side of the triangle and intersecting the other two sides will divide those two sides proportionally. The converse of this theorem is also possible where the line cutting any two sides of a triangle proportionally is parallel to the third side. The chapter has many questions based on similarity, and it gives an in-depth knowledge of properties of the triangles, classification of the triangles and how these properties are used to solve questions.
We will learn how to determine the values of trigonometric ratios in a triangle when the sides of a triangle are provided or any other trigonometric ratio. The chapter educates the students about the various trigonometric ratios, including sin, sec, cos, cosec, tan, and cot. These ratios are the ratios of their sides, and these can be used to calculate the related angles in the right- angled triangle. The chapter also teaches the students about the Pythagoras theorem and how to use them to find the length of missing sides.
This chapter is entirely based on the values of trigonometric ratios for certain angles. These angles include 90°, 45°, 60° and 30°. The numerical values of the various trigonometric ratios for these angles are provided, and these numerical values are used to solve questions by means of substitution. In addition, the chapter includes the evaluation of values and the required to prove type questions.
Chapter 7- Trigonometric ratios of complementary angles deal with complementary angles, and each angle is converted to and difference of their complementary angle (for example, 68° = 90° -22°). The chapter also elaborates on the trigonometric identities for complementary angles like sin(90- θ)= cosθ. Finally, the chapter contains questions that are solved using identities similar to these.
Chapter 8- Trigonometric identities explain various theorems concerning trigonometric ratios and provide proofs for them. These trigonometric identities form the basis of the chapter, and these are used to solve the question given in the chapter. In essence, trigonometric identities are equations that involve trigonometric ratios. In a trigonometric identity, a trigonometric ratio (square of the ratio) is expressed in the form of other trigonometric ratios. As part of this course, we examine how our trigonometric identities can prove other certain conditions. Answering these questions correctly requires remembering the identities.
Chapter 9 deals with the concept of statistics. The chapter revolves around the arithmetic mean, mode and median. The chapter also discusses the representation of data in the form of grouped data and converting the ungrouped and grouped. The calculation of the mean from the grouped data and the process of multiplication of the midpoint of the group and the value of x is also covered in the chapter. The chapter also gives a graphical representation of median and cumulative frequency graphs. The chapter also teaches the students to draw an Ogive.
Chapter 10- Quadratic equations deal with the nature of roots, the quadratic equations concepts, and some well explained examples and solutions. The chapter also discusses the relationship between the discriminant and the nature of roots. Some situational problems based on the quadratic equations relevant to day-to-day activities have been included in the chapter to concrete the concepts and learn how to apply them flawlessly. The solutions of quadratic equations by the method of factorisation and the solutions of quadratic equations by the quadratic formula are some of the important methods that mark the chapter's conclusion.
Chapter 11- Arithmetic progressions deal with the concepts that can be applied to solve logical and mathematical problems. The concepts in this chapter are the basis of a lot of computational and coding studies. An important topic discussed in this chapter is arithmetic progressions, a series in which the next digit is obtained by adding a certain number to the previous term. This number remains constant and is termed as the common difference. The chapter concludes with detailed explanations and solved questions based on applying the formulas to find the value of the n th term, the general term of an arithmetic progression, and the sum of the first n terms of the progression.
A comprehensive chapter on circles is included in RS Aggarwal's book for class 10. You'll learn about how to solve problems related to circles. The chapter also deals with the definitions of the various parts and subsections of a circle. This entire section revolves around the chords, radii, diameters, tangents to a point, tangents from a point, normal and angles subtended by the chords. This chapter teaches the student some theorems related to the components of the circle, and these prove helpful in solving the questions and proving the entities required in the practice problems given in the textbook.
In chapter 13- Construction, students learn to divide a line segment using a specific ratio, make triangles similar to each other, and build tangents to a circle. Students will be taught how to draw tangents to a circle from a point on the circle without using the centre and do so from outside the circle when the circle's centre is given. The chapter also requires the students to divide a line in certain ratios and thus form a similar triangle. The solutions provided by the Aakash Institute for RS Aggarwal class 10th maths helps the students greatly in this chapter.
The application of trigonometric ratios and other concepts along with the Pythagoras theorem is the basis of chapter 14- Heights and Distances. The students will learn how to build an imaginary right angle utilising the information given in the question. This right-angled triangle will be further used to determine the entities asked in the question, including a certain height, the base length, or the angle of inclination of some entity. The base can be defined as the distance between the upright entity and the inclined entity.
Chapter 15- Probability will discover the chapter's basic rules and elaborate on the study of chance. The students will be exposed to the terminology, including words like outcomes, events, favourable outcomes, and the chance of certain things happening. The chapter finds out how likely a certain thing or outcome would be obtained if a certain experiment is done with or without limiting conditions. Probability could be found out as the ratio of favourable outcomes to the total possible outcomes. The chapter holds tremendous value as it forms the basis of fields like analytics, forecasting and planning.
Coordinate geometry includes topics such as triangle area, simple geometric configurations, distance formula, equations graphs, and section formula. The chapter on coordinate geometry also covers the crucial topic midpoint formula, application of the section formula, application of the distance formula to calculate the triangle area. Plotting points on the cartesian plane to form a triangle is also covered in the chapter, along with finding the coordinates of the points that lie on the circle.
The chapter is entirely based on the areas of the 2-D figures, and it contains all the formulas used to calculate the areas of the triangle. The first section of the chapter is based on the area and perimeter of the triangle. The next section is based on the area and perimeter of the rectangle and square. This portion contains the question based on the cost for covering a certain area or the cost for fencing the area. The chapter also contains the MCQ type questions based on the area and perimeter for these figures.
Chapter 18 discusses the circles, and this chapter deals with the region enclosed by a circle. The chapter has questions based on the entire circle, semicircle, quadrant, or arc separated from a circle. The chapter also talks about the area enclosed within a segment of a circle. Since circles are very important figures and are crucial from a scientific study point of view and the real-life aspect. Thus, the concepts, properties and theorems taught in this chapter become very important for the students to retain in their minds.
As the name suggests, the chapter is based on the 3-D solids and deals with volume, total surface area, and certain figures' curved surface area. The figures discussed include the cube and cuboid primarily. Apart from that, the chapter also focuses on the sphere, cylinder and cone. Furthermore, the chapter deals with simple volume and surface area questions and includes volume change questions and shape conversion from one figure to another. The questions are all formula based which makes this chapter slightly easy and scoring.
Ques 1: Why are the RS Aggarwal solutions for class 10th important?
The solutions hold value because the 10th grade is very important in the academic journey and because these solutions have a very high-quality standard. Experienced faculty members prepare the solutions, and they are very easy to understand, which makes the students independent of any other help required to understand the subject. The PDF solutions help the students with quick revision during the examinations, but it helps them throughout practice. It helps them with their confusion, their speed of solving the questions, and it provides them with simpler solutions that are easy to remember and replicate for similar questions.
Ques 2: How much do these RS Aggarwal Solutions by the Aakash Institute cost, and where can they be found?
These solutions are free of cost, and they can be easily found on the official website of Aakash Institute. The solutions are provided in a chapter-wise manner and for the entire syllabus, and students can choose accordingly. These solutions go a long way in helping students who cannot afford expensive education or high-quality study material. As these are free of cost, everyone can access good quality material to understand mathematics and work hard to achieve more marks and succeed.
Class 10 is among the most important camps on your ascent to your academic summit. This is a very important class for the students, and it is the first time the students take up their first public exams. They are pitted against their batchmates from all across the country for the very first time in this class. The concepts taught in the class are very important as well because most of these topics will be there for their pre-college classes (11th and 12th). This is an important time for students to focus on the scoring subjects and make them their strong points because these subjects will eventually help them score a good rank in their board exams.
Mathematics is the prime candidate among these subjects. It is logic-based and completely dependent upon the understanding of concepts. The more a student has to practise, the better would be his scoring chances, yet mathematics is a difficult subject for many students, and this difficulty in comprehending the subject and the pressure of board exams compound the anxiety felt by the students of the students class 10
After a comprehensive study of the class 10th curriculum and the books available in the market, RS Aggarwal is considered among the best books to prepare for board exams. The book has been written by a famous mathematics professor, academician, and writer. Dr RS Aggarwal has compiled the book in easy language, and he has also provided some excellent questions for practice. However, despite the easy language of the book, the students still get stuck on the questions and here, Aakash Institute comes to the rescue. Aakash provides solutions to RS Aggarwal for class 10th maths. Aakash RS Aggarwal Solutions for Class 10 Mathematics cover every chapter and provide solutions to every question. In total, there are 20 chapters in the RS Aggarwal maths textbook for Class 10. Using the solution, students can gain a clear understanding of the concept and prepare for exams.
The priority of these solutions and the teachers preparing them is to help the students with their studies and lessen their anxiety. The solutions are prepared to keep in mind the current level of understanding of the students and their expected mental state in class 10th. Because of this, explanations are constructed at a level that is easy to understand, making it easier for students to comprehend information, follow and memorise. These solutions are prepared under the guidance of senior faculty members by the subject matter experts, both of whom have years of experience with them. The topic and subtopics are described and clarified in detail in each solution, which is beneficial for clearing most doubts. Furthermore, an in-depth analysis of each question is provided, so students learn how to approach any question correctly.
Students can download free PDF solutions for class 10 mathematics of RS Aggarwal from Aakash, which is the best way to ease their learning process. Once the students have gone through the textbook, Aakash Institute recommends that they download the PDF format and use it while practising questions to tally answers and cross-reference the procedures. Thus, understanding the topic at hand at a time in depth will ensure a solid understanding of the entire curriculum.
Chapter 1- Real numbers deal with the idea of irrational numbers, the concept of Euclid's division lemma, along with some major applications. The chapter also addresses the fundamental theorem of arithmetic motivating through examples, the introduction of real numbers, proofs of irrationality, real numbers examples and solutions. Finally, the chapter concludes with the revisiting of rational numbers and their decimal expansions.
Chapter 2- Polynomials deals with the definition of polynomials and explains the intricate details and concepts related to numerous properties of polynomials. In addition, the chapter addresses the division algorithm for polynomials which is paramount to solve the questions related to this topic. The geometrical meaning of a polynomial's zeros and the relationship between zeroes and coefficients of a polynomial are other aspects of a polynomial explained in this chapter.
Chapter 3- Linear equations in two variables deal with the fundamental properties of the equations, which have two variables. The chapter explains the various methods that are used to solve the linear equations in two variables. A new multiplication method, called cross- multiplication, is also introduced in the chapter. The chapter also includes methods like the elimination method, where one of the variables is eliminated to get the value of the other variable. The elimination method is also done by substitution, where one variable is expressed in the form of the other. The topic also discusses the graphical method of solving these questions. Consistency of the equations is one of the important topics where the chapter discusses whether the system of linear equations would have single solution infinite solutions or no solution. The chapter ends with word problems for the students.
The theorem of basic proportionality or Thales theorem is discussed in the chapter where it states that if a line parallels to any one side of the triangle and intersecting the other two sides will divide those two sides proportionally. The converse of this theorem is also possible where the line cutting any two sides of a triangle proportionally is parallel to the third side. The chapter has many questions based on similarity, and it gives an in-depth knowledge of properties of the triangles, classification of the triangles and how these properties are used to solve questions.
We will learn how to determine the values of trigonometric ratios in a triangle when the sides of a triangle are provided or any other trigonometric ratio. The chapter educates the students about the various trigonometric ratios, including sin, sec, cos, cosec, tan, and cot. These ratios are the ratios of their sides, and these can be used to calculate the related angles in the right- angled triangle. The chapter also teaches the students about the Pythagoras theorem and how to use them to find the length of missing sides.
This chapter is entirely based on the values of trigonometric ratios for certain angles. These angles include 90°, 45°, 60° and 30°. The numerical values of the various trigonometric ratios for these angles are provided, and these numerical values are used to solve questions by means of substitution. In addition, the chapter includes the evaluation of values and the required to prove type questions.
Chapter 7- Trigonometric ratios of complementary angles deal with complementary angles, and each angle is converted to and difference of their complementary angle (for example, 68° = 90° -22°). The chapter also elaborates on the trigonometric identities for complementary angles like sin(90- θ)= cosθ. Finally, the chapter contains questions that are solved using identities similar to these.
Chapter 8- Trigonometric identities explain various theorems concerning trigonometric ratios and provide proofs for them. These trigonometric identities form the basis of the chapter, and these are used to solve the question given in the chapter. In essence, trigonometric identities are equations that involve trigonometric ratios. In a trigonometric identity, a trigonometric ratio (square of the ratio) is expressed in the form of other trigonometric ratios. As part of this course, we examine how our trigonometric identities can prove other certain conditions. Answering these questions correctly requires remembering the identities.
Chapter 9 deals with the concept of statistics. The chapter revolves around the arithmetic mean, mode and median. The chapter also discusses the representation of data in the form of grouped data and converting the ungrouped and grouped. The calculation of the mean from the grouped data and the process of multiplication of the midpoint of the group and the value of x is also covered in the chapter. The chapter also gives a graphical representation of median and cumulative frequency graphs. The chapter also teaches the students to draw an Ogive.
Chapter 10- Quadratic equations deal with the nature of roots, the quadratic equations concepts, and some well explained examples and solutions. The chapter also discusses the relationship between the discriminant and the nature of roots. Some situational problems based on the quadratic equations relevant to day-to-day activities have been included in the chapter to concrete the concepts and learn how to apply them flawlessly. The solutions of quadratic equations by the method of factorisation and the solutions of quadratic equations by the quadratic formula are some of the important methods that mark the chapter's conclusion.
Chapter 11- Arithmetic progressions deal with the concepts that can be applied to solve logical and mathematical problems. The concepts in this chapter are the basis of a lot of computational and coding studies. An important topic discussed in this chapter is arithmetic progressions, a series in which the next digit is obtained by adding a certain number to the previous term. This number remains constant and is termed as the common difference. The chapter concludes with detailed explanations and solved questions based on applying the formulas to find the value of the n th term, the general term of an arithmetic progression, and the sum of the first n terms of the progression.
A comprehensive chapter on circles is included in RS Aggarwal's book for class 10. You'll learn about how to solve problems related to circles. The chapter also deals with the definitions of the various parts and subsections of a circle. This entire section revolves around the chords, radii, diameters, tangents to a point, tangents from a point, normal and angles subtended by the chords. This chapter teaches the student some theorems related to the components of the circle, and these prove helpful in solving the questions and proving the entities required in the practice problems given in the textbook.
In chapter 13- Construction, students learn to divide a line segment using a specific ratio, make triangles similar to each other, and build tangents to a circle. Students will be taught how to draw tangents to a circle from a point on the circle without using the centre and do so from outside the circle when the circle's centre is given. The chapter also requires the students to divide a line in certain ratios and thus form a similar triangle. The solutions provided by the Aakash Institute for RS Aggarwal class 10th maths helps the students greatly in this chapter.
The application of trigonometric ratios and other concepts along with the Pythagoras theorem is the basis of chapter 14- Heights and Distances. The students will learn how to build an imaginary right angle utilising the information given in the question. This right-angled triangle will be further used to determine the entities asked in the question, including a certain height, the base length, or the angle of inclination of some entity. The base can be defined as the distance between the upright entity and the inclined entity.
Chapter 15- Probability will discover the chapter's basic rules and elaborate on the study of chance. The students will be exposed to the terminology, including words like outcomes, events, favourable outcomes, and the chance of certain things happening. The chapter finds out how likely a certain thing or outcome would be obtained if a certain experiment is done with or without limiting conditions. Probability could be found out as the ratio of favourable outcomes to the total possible outcomes. The chapter holds tremendous value as it forms the basis of fields like analytics, forecasting and planning.
Coordinate geometry includes topics such as triangle area, simple geometric configurations, distance formula, equations graphs, and section formula. The chapter on coordinate geometry also covers the crucial topic midpoint formula, application of the section formula, application of the distance formula to calculate the triangle area. Plotting points on the cartesian plane to form a triangle is also covered in the chapter, along with finding the coordinates of the points that lie on the circle.
The chapter is entirely based on the areas of the 2-D figures, and it contains all the formulas used to calculate the areas of the triangle. The first section of the chapter is based on the area and perimeter of the triangle. The next section is based on the area and perimeter of the rectangle and square. This portion contains the question based on the cost for covering a certain area or the cost for fencing the area. The chapter also contains the MCQ type questions based on the area and perimeter for these figures.
Chapter 18 discusses the circles, and this chapter deals with the region enclosed by a circle. The chapter has questions based on the entire circle, semicircle, quadrant, or arc separated from a circle. The chapter also talks about the area enclosed within a segment of a circle. Since circles are very important figures and are crucial from a scientific study point of view and the real-life aspect. Thus, the concepts, properties and theorems taught in this chapter become very important for the students to retain in their minds.
As the name suggests, the chapter is based on the 3-D solids and deals with volume, total surface area, and certain figures' curved surface area. The figures discussed include the cube and cuboid primarily. Apart from that, the chapter also focuses on the sphere, cylinder and cone. Furthermore, the chapter deals with simple volume and surface area questions and includes volume change questions and shape conversion from one figure to another. The questions are all formula based which makes this chapter slightly easy and scoring.
Ques 1: Why are the RS Aggarwal solutions for class 10th important?
The solutions hold value because the 10th grade is very important in the academic journey and because these solutions have a very high-quality standard. Experienced faculty members prepare the solutions, and they are very easy to understand, which makes the students independent of any other help required to understand the subject. The PDF solutions help the students with quick revision during the examinations, but it helps them throughout practice. It helps them with their confusion, their speed of solving the questions, and it provides them with simpler solutions that are easy to remember and replicate for similar questions.
Ques 2: How much do these RS Aggarwal Solutions by the Aakash Institute cost, and where can they be found?
These solutions are free of cost, and they can be easily found on the official website of Aakash Institute. The solutions are provided in a chapter-wise manner and for the entire syllabus, and students can choose accordingly. These solutions go a long way in helping students who cannot afford expensive education or high-quality study material. As these are free of cost, everyone can access good quality material to understand mathematics and work hard to achieve more marks and succeed.