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# RD Sharma Class 9 Solutions

RD Sharma Class 9 Maths Solutions are the best study material available for learning all significant topics covered in the CBSE Class 9 Maths syllabus. Our Maths experts have drafted RD Sharma Solutions for Class 9 Solutions in a comprehensive yet crisp and concise manner. It helps you learn quickly and effectively and score high marks in your exam.

RD Sharma Class 9 Maths Book comprises 25 chapters. Here you will learn about number systems, exponents of real numbers, rationalisation, polynomials, coordinate geometry, linear equations in two variables, Euclid’s geometry, lines and angles, triangles, quadrilaterals, areas of parallelograms and triangles, circles, constructions, Heron’s formula, surface areas and volumes of various three-dimensional objects, statistics and probability in a holistic manner.

Our RD Sharma Class 9 Solutions are curated using the best ways to solve problems in arithmetic, geometry, algebra and statistics. These solutions give you an in-depth understanding of the topics discussed in the chapter. Thorough knowledge of these topics prepares you well for your Class 9 exams and also strengthens your concepts for learning more complex concepts in higher classes. Our RD Sharma solutions are best for practising all types of questions and revising during your exams. They comprise step by step, easy to understand and a hundred percent accurate solutions.

Class 9

## RD Sharma Class 9 Solutions Chapter 1: Number Systems

RD Sharma Class 9 Number Systems is an important chapter of arithmetic, you learn about whole numbers, integers and rational numbers. The topics are well explained with the help of real number lines. As a real number can be rational or irrational, so every real number is represented by a unique point on the number line. Further, you learn about decimal expressions of rational and irrational numbers, how to represent real numbers on the number lines, the process of successive magnification, and operations on real numbers. There are 4 exercises and 23 questions in chapter 1. All the questions have been answered in a step by step manner.

## RD Sharma Class 9 Solutions Chapter 2: Exponents of Real Numbers

Chapter 2 of this book teaches you about the laws of exponents for real numbers. It teaches you that when a, n and m are natural numbers and a is called the base and m and n are the exponents; the following relations hold true: (i) am. an = am+n; (ii) (am)n = amn; (iii) am / an = am-n, given m>n; (iv) ambn = abmn. These rules can be applied to a number whose base is a positive real number, and the exponents are rational or fractional numbers. This chapter consists of 2 exercises and 36 questions of different difficulty levels. Practising these exercises, you will become thorough with the chapter and ace your exams.

## RD Sharma Class 9 Solutions Chapter 3: Rationalisation

Rationalisation is chapter 3 of RD Sharma Class 9 Maths Solutions. This chapter introduces you to the concept of rationalisation, which is a process of eliminating the radicals of the denominator of a fraction.   Further, you learn about some important algebraic identities and how to simplify algebraic expressions using identities. You can practise all these concepts through 15 questions given in 2 exercises of the chapter 3.

## RD Sharma Class 9 Solutions Chapter 4: Algebraic identities

Chapter 4 of RD Sharma Class 9 Maths Book teaches you about algebraic identity for the square of a trinomial and sum and difference of cubes identities. In this chapter, you will come across writing equations in expanded form, evaluating equations, simplifying equations and finding cubes of binomial expressions using the identities learnt. The chapter consists of 26 questions in 5 exercises. There is one more exercise that consists of 4 short answer questions. Our RD Sharma Class 9 Maths Solutions answers all questions of all exercises in a step by step manner.

## RD Sharma Class 9 Solutions Chapter 5: Factorisation of Algebraic Expressions

RD Sharma Class 9 Chapter 5 Solutions provides detailed answers for all the 85 questions in 4 exercises. In this chapter, you learn about the method of factorisation and how to simplify an algebraic expression using the factorisation method. A term is broken into smaller factors in the process of factorisation of algebraic expressions, which are made up of different variables, integer constants, and basic arithmetic operations of algebra.

## RD Sharma Class 9 Solutions Chapter 6: Factorisation of Polynomials

Chapter 6 is a very important chapter based on algebra. Here you learn about polynomials and concepts on the factorisation of Polynomials, terms and coefficients. You learn that polynomials of degree one, two and three are called a linear, quadratic and cubic polynomials respectively, and polynomials of one, two and three terms are called monomial, binomial and trinomial respectively. You also learn about the remainder theorem and factor theorem and their use in the factorisation of polynomials. In this chapter there are 5 exercises and 63 questions for you to practice and

## RD Sharma Class 9 Solutions Chapter 7: Introduction to Euclid’s geometry

Chapter 7 has 1 exercise and 6 questions. Euclid’s geometry covers knowledge about properties of point and lines, parallel lines, intersecting lines, line segment, interior point of a line segment, congruence of line segments, length axioms of a line segment and distance between two points.

## RD Sharma Class 9 Solutions Chapter 8: Lines and Angles

In this chapter, you learn about basic terms, definitions and symbols about line and angles. Next, you learn about the intersecting and non-intersecting or parallel lines, linear pair of angles and axioms and theorems related to it. Here you also learn about parallel lines and transversal followed by the interior and exterior angles made by the intersection and the related axioms and theorems. This chapter has 4 exercises with 73 questions. Our comprehensive RD Sharma Class 9 Maths chapter 8 solutions cover all concepts of the chapter in detail.

## RD Sharma Class 9 Solutions Chapter 9: Triangles and its Angles

There are 2 exercises and 26 questions in chapter 9 of RD Sharma Class 9 Maths Book. In this chapter, you learn about congruency in the geometrical figures like triangles, circles and squares. Next, you learn about the equalities of angles and sides in a triangle. Our smart and well-structured RD Sharma Class 9 Maths Triangles and its Angles solutions answer all questions of all exercises in a simple language and in an easy to understand manner.

## RD Sharma Class 9 Solutions Chapter 10: Congruent Triangles

In the chapter 10 of RD Sharma Class 9th Maths solutions, you learn some other criteria for congruence of triangles. You learn about side-angle-side (SAS), angle-side-angle (ASA), angle-angle-side (AAS), side-side-side (SSS) and RHS congruence rules in triangles. Further, you learn about inequalities in a triangle. This chapter has 6 exercises with 39 questions.

## RD Sharma Class 9 Solutions Chapter 11: Coordinate Geometry

Coordinate Geometry chapter of RD Sharma Class 9 Maths introduces you to a very important topic of coordinate geometry. Here you learn about the cartesian system and the terms origin, positive and negative directions, planes, coordinate axes and quadrants. This chapter consists of 1 exercise with 2 questions.

## RD Sharma Class 9 Solutions Chapter 12: Heron’s Formula

Chapter 12 of RD Sharma Class 9 Maths Book introduces you to Heron’s formula, which is used for finding the area of different types of triangles with respect to their three sides. Also, you will learn how to apply Heron’s formula for obtaining formulas for plane figures such as quadrilaterals, squares, rectangles and some combination figures. This chapter has 2 exercises containing 25 questions based on the determination of the area of the above-mentioned geometrical figures.

## RD Sharma Class 9 Maths Solutions Chapter 13: Linear Equations in two Variables

RD Sharma Class 9 chapter 13 tells you about linear equations and their solution techniques. Here you also learn to plot a graph of a linear equation in two variables and that every point (a, b) on the line AB gives a solution x = a, y = b of the equation and any point, which does not lie on the line AB, is not a solution of the given equation. Next, you learn about equations of lines parallel to the x-axis and y-axis and how the equation y = mx represents a line passing through the origin. This chapter of RD Sharma Class 9 Maths Book consists of 4 exercises 36 questions covering all the concepts learnt.

## RD Sharma Class 9 Maths Solutions Chapter 14: Quadrilaterals

In this important chapter from geometry, you will learn about types of quadrilaterals such as trapezium, rhombus, and square. Here you will also learn about the angle sum property of quadrilaterals. Further, you learn about several theorems related to the properties of a parallelogram. You also learn that a quadrilateral is a parallelogram if a pair of opposite sides is equal and parallel and the mid-point theorem. All of these concepts are covered in detail in the 43 questions of 4 exercises given in this chapter. Our RD Sharma Class 9 Solutions methodically and logically answer all questions from all the exercises to help you learn effectively and efficiently.

## RD Sharma Class 9 Maths Solutions Chapter 15: Area of Parallelograms and Triangles

Here you learn about several rules and theorems related to the determination of the area of parallelogram and triangles, which include these figures on the same base and between the same parallels, other geometric figures, regions and some area axioms. There are 35 questions asked in 3 exercises of this chapter and are based on the above concepts.

## RD Sharma Class 9 Maths Solutions Chapter 16: Circles

RD Sharma Class 9 Circles chapter contains 4 exercises and 30 questions based on the important topic of circles from the Class 9 Maths Syllabus. Here you learn the definition of a circle and the terms circumference, segments, sector, chord and semicircle. You also learn theorems related to the angle subtended by a chord at a point, and perpendicular from the centre to a chord. Next, you learn here about equal chords and their distances from the centre, the angle subtended by an arc of a circle, cyclic quadrilaterals and congruence of circles and arcs.

## RD Sharma Class 9 Maths Solutions Chapter 17: Constructions

Chapter 17 of RD Sharma Class 9 Maths Solutions is a crucial chapter from geometry. Here you learn about the constructions of the bisector of a line segment, bisector of a given angle, triangles with accuracy using only a compass and a ruler (without using protractors). All the 11 questions asked in 3 exercises of RD Sharma Class 9 Constructions chapter have been solved in a descriptive manner accompanying related figures for easy understanding.

## RD Sharma Class 9 Maths Solutions Chapter 18: Surface Area and Volume of a Cuboid and Cube

This is an important chapter from geometry. Here you learn that the volume of a cuboid is given by the product of length, height and width of the cuboid. You also learn that the total surface area of a cuboid is the sum of the areas of its six faces. Here you will also learn how to calculate the surface area and volume of a cube. There are a total of 47 questions asked in 2 exercises of this chapter. Our RD Sharma Class 9 Solutions cover all concepts of this chapter in detail.

## RD Sharma Class 9 Maths Solutions Chapter 19: Surface Area and Volume of a Right Circular Cylinder

Chapter 19 introduces you to a right circular cylinder and some important definitions of the related terms such as base, axis, radius, height and lateral surface. Here you will also learn that the surface area of a cylinder is calculated with the formula: 2πr (r + h), and the volume of a cylinder is calculated by the formula:  πr2h, where r = radius of the cylinder and h = height of the cylinder. This chapter consists of 2 exercises and 46 questions. Our RD Sharma Class 9 Maths Solutions answer all questions of the exercises and give you ample practise to become thorough with the concepts of the chapter.

## RD Sharma Class 9 Maths Solutions Chapter 20: Surface Area and Volume of a Right Circular Cone

There are 2 exercises and 38 questions in this chapter of RD Sharma Class 9 Maths Book. Here you come across cone and its dimensions. Here you learn that Curved Surface Area (CSA) of the cone is occupied by the surface, excluding the base, and its total surface area (TSA) is the area occupied by the surface, including the curved part and the base. This chapter also teaches you in detail about the volume of a right circular cone.

## RD Sharma Class 9 Maths Solutions Chapter 21: Surface Area and Volume of a Sphere

In this chapter, you learn to find the surface area and volume of the sphere (shape of a ball). Here you learn how to find the surface area of a sphere when its radius (r) or diameter is given. The surface area of a sphere is given by 4πr2, the surface area of a hemisphere is given by 2πr2, and the volume of a sphere is given by 4/3πr3. This chapter comprises 2 exercises and 45 questions. All the questions of both the exercises have been answered in an easy to understand manner in our smart and systematic RD Sharma Solutions.

## RD Sharma Class 9 Maths Solutions Chapter 22: Tabular Representation of Statistical Data

RD Sharma Class 9 chapter 22 is an important portion of statistics. Here you learn that statistical data may be of primary or secondary types, and collection of data need to be followed by an effective arrangement in tabular form for study. Further, you come to know that data may be presented in an array in either ascending or descending way or can be presented in alphabetical order. Next, you learn here that data can be studied using different methods such as tally marks and frequency distribution. This chapter consists of 32 questions in 2 exercises. Our RD Sharma Class 9 Maths Solutions answer all questions of all exercises in a comprehensive manner.

## RD Sharma Class 9 Maths Solutions Chapter 23: Graphical Representation of Statistical Data

Chapter 23 covers the important and practical concepts of statistics. Here you learn the graphical representation of data in the form of bar graph and histogram. It tells you how graphs help us to understand the relationship between variables and measure the position or values of one variable when the other variable is changed by a certain value. In this chapter, you will also learn about frequency polygon and its algorithm. This chapter has 2 exercises and 36 questions. Our RD Sharma Class 9 Maths Solutions answer all questions of the exercises in a step by step manner.

## RD Sharma Class 9 Maths Solutions Chapter 24: Measures of central tendency

This chapter contains 54 questions in 4 exercises based on the concept of measure of central tendency that is the typical or central value of a probability distribution. The measure of central tendency is used to signify a group of data by a single value representative of the central location. These measures are mean, average, median and mode. You learn about these terms and their properties in this chapter in detail.

## RD Sharma Class 9 Maths Solutions Chapter 25: Probability

There are 14 questions in 1 exercise of RD Sharma Class 9 Probability chapter. The chapter first introduces you to the concept of probability (a measure of the possibility that an event will occur) and various approaches to it. Further, you learn about the experimental or empirical approach to probability.  Here you will also learn important terms such as a trial, an elementary event and a compound event.