RD Sharma Class 9 Solutions
RD Sharma Solutions for class 9 provides vast knowledge about the concepts through the chapter-wise solutions. These solutions help to solve problems of higher difficulty and to ensure students have a good practice of all types of questions that can be framed in the examination. Referring to the solution also helps the students to encourage them to the learning process through easy ways.
Chapter 1: Number Systems
The chapter Number Systems in this book is an important chapter of arithmetic. This helps to 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, the 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 are discussed in its total four exercises present in this chapter.
Chapter 2: Exponents and Powers of Real Numbers
Chapter 2 of this book is the exponents and powers of real numbers that help to learn about the laws of exponents for real numbers. It explains that when a, n, and m are natural numbers and a is called the base and m and n are the exponents; there are rules that 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 two exercises and of different difficulty levels.
Chapter 3: Rationalisation
Chapter 3, Rationalisation is chapter introduces the concept of rationalisation, which is a process of eliminating the radicals of the denominator of a fraction. Here, are a total of two exercises in this chapter that helps to learn about some important algebraic identities and how to simplify algebraic expressions using identities.
Chapter 4: Algebraic Identities
Chapter 4 of this book discusses the concept of the algebraic identity for the square of a trinomial and the sum and difference of cubes identities. In this chapter, the concepts of writing equations in expanded form, evaluating equations, simplifying equations, and finding cubes of binomial expressions using the identities learned. The chapter consists of a total of four exercises only.
Chapter 5: Factorization of Algebraic Expressions
This chapter provides detailed knowledge in four exercises about the methods of factorization and how to simplify an algebraic expression using the factorization method. A term is broken into smaller factors in the process of factorization of algebraic expressions, which are made up of different variables, integer constants, and basic arithmetic operations of algebra.
Chapter 6: Factorization of Polynomials
The present chapter is based on algebra that is it helps to learn about polynomials and concepts on the factorization of Polynomials, terms, and coefficients. Further, it also helps to learn the concept of the remainder theorem and factor theorem and their use in the factorization of polynomials. In this chapter, there are five exercises that consist of the problems related to the mentioned topics.
Chapter 7: Introduction to Euclid’s Geometry
Chapter 7 has only one exercise that 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.
Chapter 8: Lines and Angles
In this chapter, the basic terms, definitions, and symbols about lines and angles are learned. The problems are basically covered on the topics like the intersecting and non-intersecting or parallel lines, linear pair of angles and axioms, and theorems related to it. Further, the topics like parallel lines and transversals followed by the interior and exterior angles made by the intersection and the related axioms and theorems are also covered. These topics are covered in four exercises only.
Chapter 9: Triangle and Its Angles
There are only two exercises based on the congruency in the geometrical figures like triangles, circles, and squares. This chapter helps to learn about the equalities of angles and sides in a triangle.
Chapter 10: Congruent Triangles
In this chapter 10, there some other criteria for the congruence of triangles are discussed. This chapter has six exercises that help to learn about side-angle-side (SAS), angle-side-angle (ASA), angle-angle-side (AAS), side-side-side (SSS), and RHS congruence rules in triangles and the inequalities in a triangle.
Chapter 11: Coordinate Geometry
The coordinate Geometry chapter discussed in this book introduces a very important topic of coordinate geometry covered in its one exercise, the Cartesian system and the terms origin, positive and negative directions, planes, coordinate axes, and quadrants.
Chapter 12: Heron’s Formula
Chapter 12 of this book introduced Heron’s formula, which is used for finding the area of different types of triangles with respect to their three sides discussed through its two exercises. Also, this chapter helps to learn how to apply Heron’s formula for obtaining formulas for plane figures such as quadrilaterals, squares, rectangles, and some combination figures.
Chapter 13: Linear Equations in Two Variables
This chapter discusses the concept of linear equations and their solution techniques. There are total four exercises that help to learn the plot of 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, this provides the knowledge 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.
Chapter 14: Quadrilaterals
This is an important chapter from geometry, that helps to learn about the types of quadrilaterals such as trapezium, rhombus, and square. Here you will also learn about the angle sum property of quadrilaterals. Further, this chapter helps to learn about several theorems related to the properties of a parallelogram and the mid-point theorem. All of these concepts are covered in detail in the total four exercises given in this chapter.
Chapter 15: Areas of Parallelograms and Triangles
This chapter covered several rules and theorems related to the determination of the area of parallelograms and triangles, which include these figures on the same base and between the same parallels, other geometric figures, regions, and some area axioms. Such concepts are asked in a total of three exercises in this chapter.
Chapter 16: Circles
Circles chapter in this book contains four exercises based on the important topic like the definition of a circle and the terms circumference, segments, sector, chord, and semicircle. There are some theorems related to the angle subtended by a chord at a point, and perpendicular from the Centre to a chord discussed in this chapter.
Chapter 17: Constructions
Construction is a crucial chapter from geometry, as this chapter helps to 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). There are only three exercises based on the mentioned topics covered in this chapter.
Chapter 18: Surface Area and Volume of a Cuboid and a Cube
This is an important chapter from geometry, as this helps to learn about the volume of a cuboid is given by the product of length, height, and width of the cuboid. Further, the total surface area of a cuboid is the sum of the areas of its six faces, the surface area and volume of a cube can be learned through a total of two exercises.
Chapter 19: Surface Area and Volume of a Right Circular Cylinder
Chapter 19 introduces the concept of the right circular cylinder and some important definitions of the related terms such as base, axis, radius, height, and lateral surface. This chapter discusses each and every topic covered through the problems mentioned in its two exercises.
Chapter 20: Surface Area and Volume of a Right Circular Cone
There are two exercises that are based on the concepts of the cone and its dimensions. Here in this chapter, the questions are asked to determine the terms like the 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.
Chapter 21: Surface Area and Volume of a Sphere
This chapter contains the problems that need to find the surface area and volume of the sphere, to find the surface area of a sphere when its radius (r) or diameter is given. This chapter comprises two exercises that covered the mentioned topics thoroughly.
Chapter 22: Tabular Representation of Statistical Data
This chapter explains an important portion of statistics like the statistical data may be of primary or secondary types, and the collection of data needs to be followed by an effective arrangement in tabular form for study. Further, the methods of data are presented in an array in either ascending or descending way or can be presented in alphabetical order. These mentioned topics are so covered in two exercises only.
Chapter 23: Graphical Representation of Statistical Data
Chapter 23 covers the important and practical concepts of statistics. This chapter has two exercises that help to learn the graphical representation of data in the form of bar graphs and histograms. It also explains 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.
Chapter 24: Measures of Central Tendency
This chapter contains four exercises based on the concept of measure of central tendency which 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. This chapter helps to learn about these terms and their properties in detail.
Chapter 25: Probability
There is only one exercise present in this chapter. The chapter first introduces the concept of probability and various approaches related to it. Further, the experimental or empirical approach to probability and important terms such as a trial, an elementary event, and a compound event are also learned in this chapter.