It is quite common that the transition from primary school to secondary school is hard for students as they have to study a lot about various complicated concepts, especially when they move on to the 9 th grade. Due to this reason, students need not have to worry about scoring good marks in their examinations. Thus, here at Aakash Institute, we provide quality content for students in a very easily understandable language.
The Aakash Institute's RD Sharma Solutions for Class 9 Maths provides notes written in simple English, so even if a person doesn't have any previous knowledge on a certain topic, he/she can simply learn it with the help of our study materials. So, our main goal is to help students identify their weak areas and help them focus on that particular topic from an exam point of view.
Our institute also provides materials and notes for RD Sharma Solutions for Class 9 Maths in a freely downloadable PDF format. Using this feature, students can download whatever they need to make use of in their examinations. All our PDFs can be effortlessly downloaded using mobile phones, laptops as well as PCs. The materials are all prepared and evaluated by expert faculty members of our Aakash institution. So, students can expect error-free content from our side.
Mathematics is a fundamental analytical subject where one should know how to use it in their day-to-day lives. It is the most important key to all the science and engineering subjects. At our institution, we ensure we provide quality content for students where it is made interesting, so the students do not get bored or be forced to study something they don't like.
The Aakash RD Sharma Solutions for Class 9 Maths consists of 25 chapters, including Number System, Algebra, Geometry, Coordinate Geometry, Mensuration, Statistics, and Probability. Experts prepare these chapter-wise solutions in a step-by-step procedure to help students boost their confidence to prepare for their examinations.
With the help of RD Sharma Solutions for Class 9 Maths, students can not only solve practice problems in a very short duration but also with a clear idea of all the concepts. After a thorough analysis of the current syllabus, the solutions are designed to coordinate with the student's intellect. This will ensure an in-depth understanding of the topics provided in this subject.
Chapter 1 Number System
Chapter 2 Exponents of Real Numbers
Chapter 3 Rationalisation
Chapter 4 Algebraic Identities
Chapter 5 Factorisation of Algebraic Expressions
Chapter 6 Factorisation of Polynomials
Chapter 7 Introduction to Euclid's Geometry
Chapter 8 Lines and or Angles
Chapter 9 Triangles and its Angles
Chapter 10 Congruent Triangles
Chapter 11 Coordinate Geometry
Chapter 12 Heron's Formula
Chapter 13 Linear Equations in Two Variables
Chapter 14 Quadrilaterals
Chapter 15 Area of Parallelograms and Triangles
Chapter 16 Circles
Chapter 17 Constructions
Chapter 18 Surface Area and Volume of a Cuboid and Cube
Chapter 19 Surface Area and Volume of a Right Circular Cylinder
Chapter 20 Surface Area and Volume of a Right Circular Cone
Chapter 21 Surface Area and Volume of a Sphere
Chapter 22 Tabular Representation of Statistical Data
Chapter 23 Graphical Representation of Statistical Data
Chapter 24 Measures of Central Tendency
Chapter 25 Probability
This is the very first chapter of RD Sharma Solutions for Class 9 Maths. It deals with improving the knowledge of the number system. They include rational and irrational numbers, representing the numbers on a number line, laws of exponents, rationalisation and real numbers. Apart from all this, various shortcut methods and tricks are also provided. Those tricks include formulae that are used in solving topic-wise problems as per the updated CBSE syllabus.
This chapter contains various problems related to topics like Laws of Integral Exponents, Integral Exponents of a Real Number and Rational Exponents of a Real Number. All these topics are being taught to the students and exercise problems so that they can understand the concepts in a detailed manner. Students also get a chance to work out these problems and clarify any doubts they have to perform well in their examinations.
This chapter contains step-wise explanations of related topics and concepts. This chapter has solved problems that include identities and the rationalisation of a denominator. Apart from this, this chapter also contains various illustrative examples before each exercise. This will play a major role in helping the students understand the correct method for solving the problem. It also helps identify two or more methods to solve any given equation, which helps the students think from a much wider perspective.
In this chapter, concepts like Identities are taught to the students. Few other topics related to this are Identity of a binomial and Sum and Difference of Cubes are also being explained to the students. Moreover, problems based on Identities and their concepts are also taught. Thus, students obtain knowledge that can be very useful in their career even after their examinations if they want to pursue their dreams in science or engineering.
The RD Sharma Solutions for Class 9 Maths Chapter 5 consists of topics like the different types of factorisation and factorisation as a sum or difference of two cubes. Additionally, along with these concepts, students also get a chance to study factorisation using a formula for the cube of a binomial. Students are taught how to use the formula and how to arrive at the final answer. Moreover, they get the knowledge of the factorisation of algebraic expressions, which is the last topic they will study in this chapter.
This chapter contains a topic on zeros of a polynomial where students get in-depth knowledge on this concept and solve the practice problems. Furthermore, they are taught some important theorems, such as the Reminder theorem and the Factorial theorem, which are fundamental for solving some basic problems in this chapter. Lastly, a concept called Factorisation of Polynomials using Factor theorem is being deeply discussed along with its exercise problems.
This chapter is the first chapter in geometry, which covers various theorems and properties essential to solving geometrical equations. First, students get a deep understanding of Axioms and Theorems where they learn the concepts and get familiarised with them by solving the problems. Additionally, they also learn Incidence Properties. Then, the next topic after completing this would be Parallel and Intersecting Lines, where they study how to construct those lines using the theorems and properties they learnt before. Moreover, they also happen to study other topics such as Line Segment, Length Axioms and Plane.
The RD Sharma Solutions for Class 9 Maths Chapter 8 deals with Lines and Angles. This is the type of topic where students learn how to construct lines with the help of angles. They also get to know about the different types of angles and their relations and results on parallel lines. More than just grasping the concept, our experts also help students with exercise problems to understand how to use the concepts they have studied in an analytical representation.
This is one of the most fundamental chapters in geometry. Here, students gain knowledge on constructing triangles with the help of angles. They also study different concepts required to determine the angles and sides deeply discussed on our platform in a very easy language. This chapter also covers different concepts like triangles based on the side, angles and exterior and interior angles. All the solutions contain a pictorial representation, making it very easy for the students to grasp the ideas.
The RD Sharma Solutions for Class 9 Maths Chapter 10 helps students understand the congruence of line segments. Lines segments are said to be congruent if they have the same length. In other words, congruence is also called equals. So, other than this, they gain a wide knowledge of the congruence of angles where they study how to construct and use them in solving the problems. Furthermore, students also learn the concept called the congruence of triangles. Moreover, they are taught other topics also, such as congruence criteria and inequality relations.
This chapter is the beginning of a whole new unit called Coordinate Geometry. Here, students can learn about the rectangular Cartesian coordinates of a point and the plotting of points. Additionally, students get to know the definition of geometry and identify the coordinates and meaning of the coordinate plane. Moreover, some formulae are also being discussed. The common ones are the distance formula and the section formula that help students understand the concept and solve these formulae's problems. Lastly, the mid-point theorem is also being taught.
The RD Sharma Solutions for Class 9 Maths Chapter 12 teaches the students basic concepts like introduction, Heron's formula and its applications. Heron's formula is often used in finding the area of a triangle when the lengths of all sides are known. This can also be said as Hero's formula. Only the lengths need to be known, and it is not that necessary to know the angle measurement of a triangle to calculate its area.
All the concepts given in this chapter are written in a simple language where anyone can understand easily. The RD Sharma Solutions for Class 9 Maths Chapter 13 primarily deals with Linear Equations in two variables. First, students get to know about this concept and enhance their knowledge further by solving the exercise problems. Then, the solution of a linear equation is being taught. Moreover, they learn the Graph of a linear equation in two variables and then lastly, they learn the equations of lines parallel to the X-axis and Y-axis.
This is among the essential concepts in RD Sharma Solutions for Class 9 Maths because it acts as a piece of basic knowledge and will be further learned in higher classes. Quadrilaterals are nothing but plane figures with four sides or edges and four corners or vertices. They will typically be of standard shapes with four sides: rectangle, square, trapezoid, parallelogram and kite, or some irregular and uncharacterised. This chapter deals with topics such as terms associated with the quadrilateral. Moreover, the properties of a Parallelogram, namely the Properties of a Rectangle, the Properties of a Rhombus, the Angle sum property, and the Properties of a Square, are also being taught. Other than this, Types of Quadrilaterals are also being discussed, along with some useful facts about triangles.
Chapter 15 of the RD Sharma Solutions for Class 9 Maths has 3 exercises based on some fundamental topics such as figures on the same base. The chapter also teaches about figures between the parallel lines. In addition, this chapter covers topics related to understanding the areas of parallelograms and triangles. Moreover, another topic called polygon regions is also being taught to the students. Additionally, they get to learn Area Axioms also. These concepts will enhance the students' knowledge and help them get improved marks in their examinations.
Chapter 16 of the RD Sharma Solutions for Class 9 Maths consists of important topics and definitions, namely arcs of a circle, a segment of a circle, arcs, congruence of circles, and chord of a circle, where students are taught how to determine different types of notations that are present in a circle. They also get to understand a few more concepts, such as some results on equal chords, arcs, and angles subtended by them. Finally, another important concept named cyclic quadrilateral is also being discussed.
In RD Sharma Solutions for Class 9 Maths Chapter 17, students attain knowledge on simple and complex constructions, which make use of a ruler and a pair of compasses. In this chapter, students are taught some basic concepts, such as constructing standard angles. Then, they can learn how to construct how lines are based on angles in a step-by-step manner and construct triangles, where they understand how triangles are being made using appropriate methods.
In this chapter, students obtain some basic ideas on units of measurements. Firstly, they learn how to measure volume and surface area, in which they use some methods and formulae to arrive at the final results. Then, they are taught the measurements of cubes and cuboids. Additionally, they are also exposed to solving problems based on surface area and later practical problems on the cuboidal and cubic area. Moreover, another topic called the volume of a cube and cuboid is also being discussed.
The RD Sharma Solutions for Class 9 Maths Chapter 19 consists of some important formulae and problems used to determine the surface area and volume of a right circular cylinder. A right circular cylinder is nothing but a cylinder that has a closed circular surface that has two parallel bases on both the ends and whose elements are perpendicular to its base. This one is also called the right cylinder.
In this chapter, some main concepts, such as the right circular cone and the surface area of conical shapes and structure and volume of similar shapes, are discussed. A right circular cone is a type of cone where the axis lies in the line, meeting the vertex to the midpoint of the circular base, i.e. the centre point of the circular base is joined with the apex of the cone to form a right angle. A cone is nothing but a three-dimensional shape having a circular base and narrowing smoothly to a point above the base. The point is considered as the apex.
In RD Sharma Solutions for Class 9 Maths Chapter 21, students can eye a solid geometrical shape called a sphere. A sphere is a 3-D circular shape that has some volume and some surface area. This chapter also consists of a sphere, surface area, the section of a sphere by a plane, and volume. With the help of expert-validated study materials from our platform, students can grasp the knowledge on all these fundamental concepts and perform well in their examinations.
Effective representation of data is very important, and the tabular form is used for the statistical data for the ease of the observers' understanding. In RD Sharma Solutions for Class 9 Maths Chapter 22, students learn about the steps involved in tabular form representation of data. This is the first topic under Statistics. Students also gain knowledge on various other concepts such as Statistics and Statistical data. In addition, they also get to know some additional topics such as presentation of data, construction of frequency distribution tables, frequency distribution, and cumulative frequency distribution.
In this chapter, students study topics related to the graphical representation of statistical data. So, they can dive deep into some of its sub-topics. To start with, they first get to know about constructing a bar graph and histogram. Furthermore, they are also taught on the topic called the frequency polygon and its construction. Finally, there are plenty of exercise problems available in this chapter to practice and use during their examinations.
This topic deals with concepts related to measuring the central tendency. First, students get an idea of arithmetic mean and grouped data. Meanwhile, they also learn about the median. The concept of mode is also taught in this chapter. After understanding each concept, they get their hands on the practice problems to completely master this topic.
The RD Sharma Solutions for Class 9 Maths Chapter 25 consists of a very fundamental topic called probability. This will be an important chapter for students at this grade because they will have to study this in their upcoming years in a much more advanced manner and use this in their future for day-to-day purposes. In this chapter, students learn about probability which is also determined as an event that is most likely to occur and operations related to it.
Q. Why is RD Sharma Solutions for Class 9 Maths provided by the Aakash Institute important?
A. Mathematics is a completely analytical subject, where students must get a good amount of knowledge on various concepts and formulae before solving the problems. Aakash's RD Sharma Solutions for Class 9 Maths provides top quality study materials and gives the students motivation to succeed in their examinations by providing their notes in a very understandable language. Moreover, the questions are solved in a very easy method in this solutions PDF which makes the student independent in terms of study, and they do not need help from anywhere else.
Q. Where to find and download RD Sharma Solutions for Class 9 th Maths?
A. They are all easily available on the Aakash website, and the topics are given in the order so that no one gets confused while looking for what they want. In addition, they can download these files as a PDF file either chapter wise or for the whole class. One other impressive thing about these solutions is that Aakash provides these solutions free of cost.