RD Sharma Class 9 Maths Solutions - Free PDF Download
RD Sharma Class 9 Solutions provided by Vedantu are reviewed by subject experts and arranged in a sequential manner. Class 9 is a very important academic year for all the students. This is where students start exploring the fundamentals of core subjects that they will have to study for the critical class 10 board exams, and the RD Sharma class 9 solutions are considered one of the best preparation materials for students. It is free to download the solution of RD Sharma class 9 PDFs and they provide a comprehensive and easy-to-understand resource to help prepare for exams.
The advantage of these solutions is that they cover all the subjects that students have to cover in school and they are based on NCERT textbooks. They are thus aligned with the syllabuses of almost all schools. One of the most difficult subjects according to most students in mathematics. Being a very precise subject, it can actually be a very easy subject to understand when the basics are integrated firmly. So how does one go about changing this fear of a tough subject and give students the resources to improve their mathematics knowledge? The RD Sharma class 9 maths book solutions are very thorough. There are detailed solutions that cover the core principles and theories – important formulas and fundamentals that will help students solve all kinds of problems. Algebra, arithmetic, and geometry are full-fledged subjects in themselves and balancing the different topics along with other subjects can sometimes be difficult. The RD Sharma mathematics class 9 solutions will go a long way in helping students learn, and they are free. But that is not all – online lessons in the core science subjects are now available on our online learning platform to ensure that students are able to keep up with the competition.
You can also Download NCERT Solutions to help you to revise complete Syllabus and score more marks in your examinations
RD Sharma Solutions for Class 9 Maths
As technology improves, teaching methods need to change accordingly. Nowadays, young students spend a lot of time on gadgets and they take in a lot of information on the internet. At Vedantu we aim to ensure that the time children spend with gadgets helps them in their education. Apart from resources like the RD Sharma class 9 solutions free download, we offer a thorough and well-planned online lessons in the core science subjects. These lessons provide all the benefits of home tutoring at a much lower cost. It offers students a comprehensive learning experience delivered via a platform that fits naturally into their daily routine. Let us explore the many benefits of online classes delivered by our team. In addition to that, you can also download NCERT Solutions for Class 9 Maths from Vedantu.com.
Tuitions are an important part of school preparations now. This is because India’s academic framework is one of the most competitive in the world. Tuitions provide a more customised approach compared to school classrooms where teachers have to attend to very large groups. At the same time, getting hold of good tutors has become a challenge for many parents nowadays. Home tutors are expensive and scheduling with them can be impossible if they are in high demand. Group-tuitions can have their own disadvantages. In large cities, students already have to spend a lot of time in commuting. our online classes give students the home tuition experience while allowing them to gain control of their own routine. Pressure can be one of the main reasons why students fail to grasp concepts – but our lessons allow more time for students, reducing the pressure. Students get to learn at their own pace - this is very important when they are learning a tough subject. The one-on-one style of learning ensures that all the attention is on the student and there are no distractions.
RD Sharma is considered the best preparation guide book for boards by academicians all across the country. Vedantu offers detailed RD Sharma Class 9 Solutions online in an easy to understand manner. Following are the chapters that this study material covers.
Chapter 1 – Number system
The number system is a foundational concept, essential to progress with the rest of the class 9 math. Starting with the number line, here, you’ll learn mathematical tools like the magnification of a number line, presentation of square roots of 2, 3, etc. and more. You’ll learn the difference between rational and irrational numbers. It also covers the method of rationalising the denominator, a handy technique indispensable for solving complex calculations further in the syllabus.
Chapter 2 – Exponents of real numbers
Exponents, also called Powers or Indices, are a requisite concept for algebra. This chapter provides concepts on the representation of a number in exponent form. The powers or exponents of real numbers follow the same laws as that of rational numbers. Students will be able to solve simplification problems involving powers with the product law, quotient law, and power law.
Chapter 3 – Rationalisation
An important concept for solving complex calculations without the help of a calculator, rationalisation helps you to convert a difficult-to-divide fraction into a simpler form. You’ll learn to apply techniques like multiplying the numerator and denominator by root, or a conjugation. Solving problems involving the same will help you to solidify these concepts.
Chapter 4 – Algebraic identities
Algebraic identities offer a shortcut to solving some of the cumbersome and lengthy problems. An algebraic identity is an equality that holds true for any value of the variables in the entire expression. With the concepts in this chapter, you’ll be able to formulate algebraic relations from word problems. You’ll also learn some of the commonly used binomial, factoring and three-variable identities.
Chapter 5 – Factorisation of algebraic expressions
Factorisation is the opposite of expansion and is an essential concept for class 9 students. It builds on the previous concepts of algebra like identities and exponents. You’ll learn how to factorise lengthy expression by using common factors, difference of squares, grouping in pairs, etc.
Chapter 6 – Factorisation of polynomials
Most algebraic expressions take the form of a polynomial. Learning to factorise a polynomial expression into irreducible factors with coefficients in the same domain is essential. This chapter teaches you to factorise polynomials with degrees greater than 2 as well, which will help you later on in the class 9 curriculum.
Chapter 7 – Introduction to Euclid’s Geometry
The chapter helps you to form the base for geometry. Euclidean geometry is based on axioms and theorems to find out relations between lines, figures and angles in space. It presents a student with a deductive, comprehensive, and logical approach. You can develop the basics required to progress further into the intricate and intriguing world of geometry.
Chapter 8 – Lines and angles
Angles in a geometric figure form various relations with each other. Chapter 8 is all about these relations. Concepts of vertically opposite, complementary and supplementary angles are presented here with clarity. Additionally, with the knowledge of the properties of parallel lines and transversal arrangement, you’ll be able to find the values of unknown angles in complex 2D geometries.
Chapter 9 – Triangles and its angles
Here, you are introduced to the various types of triangles and the properties of their three angles. You learn how to figure out the values of unknown angles in a geometry composed by triangles. Properties like exterior angles, linear pairs, vertically opposite angles, alternate angles, etc. are demystified.
Chapter 10 – Congruent triangles
Suppose you see two similar objects and state to a friend that the two are geometrically same. But your friend refuses to believe so. How do you prove it? Studying congruency of triangles provides with an insight on how you can do so. Here, you build the logic to prove that two triangular 2D bodies are a replica of each other, using Euclidean theorems.
Chapter 11 – Coordinate geometry
Named after Rene Descartes, this branch of mathematics that combines geometry with algebra is called Cartesian coordinate geometry. You’ll learn about the rectangular coordinate plane, and methods to find out the distance between two points in the same. Plotting points in planes with its coordinates and notations is an essential concept covered in this chapter. Line equations and Apollonius theorems are included as well.
Chapter 12 – Herons Formula
Useful in finding out the area of any triangle where only the length of its sides is given, Herons formula is an essential tool to learn. Further, the chapter discusses the application of this formula to find areas of quadrilaterals.
Chapter 13 - Linear equation in two variables
With the concept of the equation of a straight line, one can solve many other simple real-life problems. Linear equations are an essential tool to do the same. In this chapter, a student learns to present the geometric representation of various straight line equations.
Chapter 14 – Quadrilaterals
A quadrilateral is a polygon with four edges and four vertices. Here, you learn about the various properties of a quadrilateral and the relation between its angles. After developing the concept of convex and concave triangles, you get to solve problems involving a variety of quadrilaterals with unknown values of edges. Formulae of area and volumes of different quadrilaterals are also introduced here.
Chapter 15 – Areas of Parallelograms and Triangles
It’s easy to find the area of a right angle triangle, but how do you find the area of an obtuse or acute-angled triangle? This chapter covers the formulae and methods of calculating the areas of various triangles and other parallelograms like rhombus and trapezium.
Chapter 16 – Circles
Understanding the properties of a circle is essential for anyone who’ll choose higher studies that involve mathematics. Students learn about the various properties of circles and related theorems such as Thales’, alternate segment, and perpendicular tangent. One also learns their application by solving problems involving circles with other inscribed geometrical figures.
Chapter 17 – Constructions
In this chapter, you acquire the skills to construct geometric figures only using a scale and a compass. You learn to construct various angles, bisect lines, inscribe triangles into figures and do much more.
Chapter 18 – Surface area and volume of cuboid and cube
Learning to calculate a cuboid’s surface area and volume and solving various problems with the formula is essential to score high grades successfully. An easy yet scoring chapter, practising the problems here can lead you to get better grades tomorrow.
Chapter 19 – Surface area and volume of a right circular cylinder
A right circular cylinder is a commonly occurring geometrical figure in many other areas of science like physics and biology. So, you need to learn the ways of measuring its dimensions. That is what you learn in this chapter.
Chapter 20 – Surface area and volume of a right circular cone
Here, a student learns to solve problems involving volume and surface area of a right circular cone. You also learn to calculate a cone’s slant height and other dimensions using provided ratios.
Chapter 21 – Surface area and volume of a sphere
Learning the formulas for volumes of spheres is a part of the entire curriculum. You’ll learn to understand complex problems that involve various circular bodies. The chapter falls under the topic of analytical geometry.
Chapter 22 – Tabular representation of statistical data
Statistics is the science of collection, presentation, analysis and interpretation of numerical data. It’s an important branch of mathematics that finds application in various other fields. Here, you are introduced to the basic concepts like primary and secondary data, discrete and continuous frequency distribution, etc.
Chapter 23 – Graphical representation of statistical data
To understand the relationship between variables, it’s important to understand graphs. They offer a visual representation of statistical data. Chapter 23 teaches a student various ways to visually represent huge volumes of statistical data through graphs.
Chapter 24 - Measures of central tendencies
In this chapter, you learn about the different measures of central tendencies such as the mean, median and mode. With these measures, you can identify the location of maximum number values in a distribution. It’s also an easy and scoring chapter.
Chapter 25 – Probability
The measure of the possibility of an event’s occurrence is called Probability. Here, one understands the essential concepts like different types of events (mutually exclusive, complementary, equally likely, etc.), and sample space. One also learns the theorems of compound probability, and other axioms and their application in solving complex problems.
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Even though we use the latest technology in interactive and live online education, the lessons maintain the personal touch and interaction of a traditional class environment. Students get familiar with their tutors who come with a very good reputation and expertise. Our faculty comprises of leading teachers chosen from across the country – leaders in their respective fields. Class 9 students will get first-hand knowledge and tips from Ph.D. holders and tutors who have graduated from top colleges like IIMs and IITs. This kind of exposure is priceless at such an important juncture of school life. Along with high-quality resources like the RD Sharma class 9 solutions PDF free download, online classes in the core science subjects our website provide the best launch pad for students.