It is a fact that the 10th standard is one of the most important phases in everyone's lives. So, at Aakash, RD Sharma Solutions for Class 10 Maths are provided to help students enhance their knowledge on this particular subject and help them achieve success in their examinations. The expert faculty members at Aakash Institute prepare all these solutions for the exercise- wise problems. Moreover, these solutions are cross verified more than once to provide error- free contents to the students.
With the help of our materials, students can now solve any type of problems related to the topics in the curriculum. The main purpose of our institution is to create such resources for students that help them analyse their weak areas where they think they need improvement. Moreover, we also try to help them solve problems of advanced difficulty level in a very effective way.
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Mathematics is an unavoidably fundamental subject. The usage of this is very wide and growing. We need mathematics in almost every possible field, especially in the domain of science and technology. So, we provide students with the best possible way to study and enhance their knowledge quotient to be helpful for their examinations and their careers.
The Aakash RD Sharma Solutions for Class 10 Maths consists of 16 chapters that deal with multiple Units, namely Number System, Algebra, Geometry, Coordinate Geometry, Mensuration, Statistics and Probability.
Chapter 1 Real Numbers
Chapter 2 Polynomials
Chapter 3 Pair of Linear Equations in Two Variables
Chapter 4 Triangles
Chapter 5 Trigonometric Ratios
Chapter 6 Trigonometric Identities
Chapter 7 Statistics
Chapter 8 Quadratic Equations
Chapter 9 Arithmetic Progressions
Chapter 10 Circles
Chapter 11 Constructions
Chapter 12 Some Applications of Trigonometry
Chapter 13 Probability
Chapter 14 Coordinate Geometry
Chapter 15 Areas Related to Circles
Chapter 16 Surface Areas and Volumes
The first chapter of RD Sharma Solutions for Class 10 Maths is based on the principles, rules of real numbers. This chapter helps students comprehend the divisibility of integers and their three important properties, such as Euclid's division lemma, Euclid's division algorithm and the Fundamental Theorem of Arithmetic. To begin with, the concepts discussed, Euclid's division lemma can be understood by, let's say, if we have two positive integers m and n, there should be whole numbers x and y that satisfy the equation, m = nx + y,
where 0 ≤ y < n where m is the dividend and x is the divisor. Meanwhile, Euclid's division algorithm specifies the HCF (Highest Common Factor) of two given positive integers can be found using Euclid's Division Lemma. Lastly, the Fundamental Theorem of Arithmetic can be described as every composite number can be easily factorised as a product of its primes. This factorisation is termed to be unique, apart from the order in which the prime factor occurs.
In this chapter, students can gain knowledge on concepts related to polynomials and their solutions. Polynomials can easily be understood as algebraic expressions which have both coefficients and variables. This chapter teaches various topics based on the geometrical representation of linear and quadratic polynomials. Moreover, they also learn the geometric meaning of their results (the values of variables at which the polynomial attains the value zero) and the relationship between zeros and the coefficient of a polynomial. The Linear Polynomial is defined as a polynomial of degree one. In other words, it can be said that the highest exponent of the variable is one. Meanwhile, a Quadratic polynomial is considered a polynomial of degree two, i.e. the highest exponent of the given variable is two. Finally, the chapter sheds light on the geometric representation of linear and quadratic polynomials that deals with the graphical interpretations of polynomials and renders a better understanding of the concepts discussed in the chapter.
The RD Sharma Solutions for Class 10 Maths Chapter 3 consists of problems based on the following topics: systems of linear equations in two variables, graphical and algebraic methods of solving a linear equation in two variables, along with their applications. Firstly, linear equations in two variables can be understood by considering, if m, n and r are real numbers (m and n are not equal to zero), then "mx + ny = r" is called a linear equation in two variables. Secondly, Graphical and algebraic methods of solving linear equations in two variables are the two methods being taught in the chapter. Finally, the chapter also teaches us that these methods and the linear equations in two variables can also be used in our day-to- day lives.
This topic deals with some important concepts consisting of similarity of geometric figures, similar triangles and their properties, some basic results on proportionality and other fundamental theorems and criteria of proportionality. In the topic similarity of geometric figures, two figures are similar if they have the same sides, same angles, or the mirror image of the figures. And suppose the two pairs of corresponding angles in two triangles are congruent. In that case, we can say that they are similar triangles. Likewise, proportionality is nothing but the equality between two ratios. For instance, m/n = x/y where m and n are in the same proportion as x and y. The chapter bestows a thorough understanding of the various components of a triangle along with their related relationships. Thus, after learning all these concepts, it is easy for the students to solve exercise problems and arrive at the correct results, thereby cementing the concepts through practical applications.
Trigonometry is considered a prerequisite for higher grade mathematics, and thus, it is a very important topic in Mathematics. The chapter deals with the relationship between the lengths of the sides and the angles of triangles. In this chapter, students study the basic concepts such as trigonometric ratios and the relations between them. Additionally, they are also taught about trigonometric ratios of some specific angles and trigonometric ratios of complementary angles. Trigonometric ratios are of six types. They are cosine, sine, tangent, cotangent, secant and cosecant. Furthermore, trigonometric ratios of complementary angles are described as, if the sum of two angles is 90 degrees, then one is termed to be complementary of another angle. This introductory chapter comprises important fundamental concepts that will be applied in the following chapters, and thus, it holds great value.
In RD Sharma Solutions for Class 10 Mathematics Chapter 6, students are set to study some fundamental trigonometric identities that form the framework of the entire concept of trigonometry. They also get to know about the Trigonometric identities formula. Trigonometric identities can be useful whenever some trigonometric functions are involved either in an equation or an expression. Geometrically, these identities include certain functions of one or more angles. These are considered to be various distinct identities that involve the side length and triangle angle. The following are the list of trigonometric identities discussed in the chapter; Reciprocal Identities, Pythagorean Identities, Ratio Identities, Opposite Angle Identities, Complementary Identities and Angle Sum and Difference identities. Understanding these concepts is paramount for the chapters that follow and applications of these as mathematical tools in other subjects.
Chapter 7 is the first Chapter in Statistics. Statistics can be described as the collection, organisation, analysis, interpretation and presentation of numerical data. In this chapter, students will learn methods for finding the mean, median and mode of a grouped data. They will also learn about cumulative frequency graphs of a frequency distribution. Meanwhile, the mean is found out by adding all the numbers in the data set and then dividing them by the number of values, whereas the median is considered the middle value when a data set is ordered from least to greatest. Mode is the data that occurs most frequently in a data set. Lastly, the frequency distribution is nothing but the overview of all different values in some variable and the number of times they occur.
The RD Sharma Solutions for Class 10 Maths Chapter 8 deals with Quadratic equations and their related topics. As discussed in the previous chapters on polynomials, quadratic equations are considered second-degree polynomial equations. A quadratic equation in one variable is of the type Where m, n, p, This is the general form of a quadratic equation where m is denoted as the leading coefficient, and p is considered the absolute term of the given quadratic equation. So, the values of x (α,β) satisfying the quadratic equation are the roots of that same equation Commonly, the quadratic equation will always consist of two roots, one is real, and the other is imaginary. Chapter 8-Quadratic Equations holds great value in solving equations related to physics and mechanics in the higher levels of education. Thus, acing this chapter is a necessity.
Chapter 9-Arithmetic Progressions deals with the concepts of series and patterns in a mathematical string of data. A sequence is said to be an arrangement of numbers in a definite order based on some rule. Arithmetic Progression is also a sequence of numbers in which the difference of any two successive terms is always a constant. The RD Sharma Solutions for Class 10 Maths Chapter 9 consists of various concepts such as general form, nth term, and the sum of an AP. The generic term of AP is denoted as the formula for the nth term of the AP with 'a' as its first term and 'd' as the common difference, a n = a + (n – 1) d
In this form, the nth term (a n ) is termed an AP's general term. Students also gain knowledge on the sum of the terms of an AP, which is also considered to be the addition of the first n terms of the arithmetic sequence. In addition, solutions for questions related to practical applications that will cement the understanding of concepts is provided by the Aakash institute, with detailed explanations that do not omit a single step and enable an easily understandable study session.
Chapter 10 Circles deal with the definitions and the components of a circle. Circles are obtained with the locus of all points which are equidistant from the centre. The RD Sharma Solutions for Class 10 Maths Chapter 10 gives the students ideas about the secant of a circle and its tangent and properties. For example, the secant of a circle intersects the circle at exactly two points, whereas the tangent to a circle is a straight line that touches the circle at a single point. More than this, students also do exercise problems based on circles, triangles and quadrilaterals. The students who study the solutions will get a clear-cut idea of how to construct circles using the mentioned methods. They will also understand the various properties of the circles. The experts validate the study materials provided by the Aakash Institute to the students, and they are easily understandable.
Chapter 11 Construction is another important topic in geometry. The RD Sharma Solutions for Class 10 Maths Chapter 11 Construction helps students construct a triangle similar to a given triangle and the tangents to a circle. Construction in geometry is nothing but drawing shapes, angles or lines accurately based on the given data. Construction of such figures involves the usage of a compass, a ruler and a pencil. Angles can be observed as the amount of turn between two lines from their common point, whereas the length, on the other hand, indicates the size of a line segment. These are some of the basic concepts that a student will come across while studying this chapter. This chapter enlightens the students with real-life applications and, thus, is inevitable.
The RD Sharma Solutions for Class 10 Maths Chapter 12 covers basic problems related to heights and distances. The students are exclusively taught how the height of certain objects and the distance from certain points work to help them understand the basic concepts. For example, the height of a triangle is the length of a perpendicular line segment that originates on a side and intersects at the opposite angle. Trigonometry is the section of mathematics that deals with the relationship between angles and the side lengths of triangles. The chapter Application of Trigonometry also deals with the concepts of the angle of elevation and the angle of depression that help understand the distance of a structure from a certain location and the height of structures by incorporating various trigonometry concepts. Other than this, students also get a chance to obtain knowledge related to some of its applications in exercise problems.
Chapter 13 Probability deals with the prediction of the occurrence of certain events based on certain mathematical principles. There is always a degree of certainty or uncertainty about what has happened or what will happen in almost every event. This is the main reason we study this chapter, as it leads to finding the probability of any particular event. This is one of the most fundamental topics in mathematics, which deals with numerical notations of how likely an event is to occur or how likely a proposition is true. An event is nothing but an outcome or defined set of outcomes of any random experiment that has already taken place or will take place. So, with the help of materials provided on our platform, students can obtain a strong grasp on this concept and gain a good amount of knowledge on this particular chapter which will also be useful to them for their exams. The chapter is also crucial in real-life problems as it governs forecasting, analytics, and probability distribution.
Coordinate Geometry is defined as the study of geometry using coordinate points. The RD Sharma Solutions for Class 10 Maths Chapter 14 covers some basic concepts like understanding rectangular coordinates, the distance between two points, the sections formulae and its applications, co-linearity of points, and the area of a triangle quadrilateral by implementing the concepts of coordinate geometry. These concepts are used to find the distance between two points (vertices in this case) on the x-y plane. Distance between two points on a cartesian plane can be found by using the distance formula, an application of the Pythagoras theorem. The chapter also sheds light on the concept of the section formula used to identify the ratio in which a line segment is divided by a point either internally or externally. Students also get to solve some exercise problems to get a firmer grip on the concepts, and the practical application helps structure the theories they learned in this chapter.
In Chapter 15 Areas Related to Circles, students get to study concepts related to finding the area of circular regions and knowledge about two other special parts of the region known to be the sector and the segment of a circle. The circle's area is defined as pi times the square of its radius. This is how we can describe the area of circular regions. Meanwhile, the sector is nothing but a part of the circle, made up of an arc of the circle and its two radii. On the other hand, the segment is the region bounded by the arc and the intercepted area of the circle. These concepts are thoroughly explained in the chapter and are facilitated with practical applications by virtue of numerical problems. All the solutions provided by the Aakash Institute are given in a step-by-step manner that is very easily understandable so that the students won't find any difficulty in understanding all these concepts.
The RD Sharma Solutions for Class 10 Maths Chapter 16 Surface Areas and Volumes deals with questions related to the mensuration of three-dimensional figures. The chapter also deals with the problems related to converting one solid into another and finding the surface areas and volumes of a combination of two or more solids. The surface area is the region occupied by its surface and the areas on all the surfaces in a three-dimensional figure. On the other hand, volume is nothing but the total amount of space occupied by a shape or a substance. Students also get to solve the practice problems and get familiarised with all the concepts that they have learned. There is a special mention of the term 'frustum', which is obtained by hypothetically slicing a cone along a horizontal axis. With the help of the experts at the Aakash institution, we ensure to provide high-quality content to the students that will help them gain a thorough understanding of the innumerable concepts and prepare them to acquire good grades in their examinations.
Q. How did RD Sharma Solutions help students prepare for their board exam?
A. All the solutions to the problems in RD Sharma provided by the Aakash institute are written in a very straightforward language where one can easily go through and understand the context without any difficulties. Moreover, the solutions are methodologically explained without omitting steps that help the students gain confidence in their learning journey and help them work harder to achieve success.
Q. Where to download the PDF for RD Sharma Solutions for Class 10 Maths?
A. The RD Sharma Solutions for Class 10 Maths are provided on the Aakash institute's website. The solutions are provided and evaluated by our Subject Matter Experts, which facilitates a smooth and precise understanding of every concept. All these are explained in detail and are given in a step-wise manner.