A transition from middle school to high school is seen in the promotion from class 8 to class 9th. Taking the next step in academic life can be daunting for many, and Aakash aims to simplify the process. Nevertheless, this is the best time for students to lay a strong foundation for their future. Many children find this step to be daunting, and Aakash strives to make it as easy as possible for them. CBSE Class 9 curriculum includes a majority of topics that are paramount in preparation for students' college years. It is designed to nudge the students towards the essential topics without depriving them of their enthusiasm for learning. Thus, each topic must be understood and mastered by the students.
Aakash provides RS Aggarwal Solutions for Class 9 Mathematics to guide students to comprehend every concept to the fullest. It is easy to score maximum marks in mathematics since it is a practice-based subject. Student assistance is the main objective. Solutions are prepared in a way, considering the recent changes in the classes of students. In order to increase the retention of concepts by the students, explanations are written in an easily comprehensible style of language.
Our Class 9 Mathematics RS Aggarwal Solutions are created by senior faculty and experts with a wealth of experience. The solutions PDF provides a detailed explanation and simplification of each topic and subtopic, allowing students to clear nearly all their doubts. Additionally, each question is analysed in detail, helping students better grasp and recognise the question's core concept and preparing them to answer every question correctly.
Before designing the solution, a comprehensive analysis of the current syllabus is conducted to ensure a format that will benefit the students. In class 9th mathematics, Aakash R. S. Aggarwal Solutions contain procedural working and answers for every question. The RS Aggarwal textbook for class 9th consists of 19 chapters. Using this solution, students gain a better understanding of the concept and are better prepared for exams. RS Aggarwal Class 9 Mathematics PDF Solutions are available at Aakash to ease students' workload. It is recommended that students download and effectively use the solutions PDF after studying the textbook. In this way, the students will gain in-depth knowledge of the subject.
A number is a mathematical entity that provides the basis of all operations (they are the operand), and they are used to count and measure things. A number system is a basis of representation of these numbers as per the rules defined by a certain system to denote a value or a quantity or even the place value of the number. The topics covered in Chapter 1 are the Introduction to Real Numbers, the concept of irrational numbers, exponent laws for real numbers, Representing Real Numbers on the Number Line, real numbers and their expansion in the decimal form and operations on real numbers.
The chapter is based on the basic definition of a polynomial. The chapter examines topics such as polynomials, properties of polynomials, types of polynomials, identifying whether a given expression is a polynomial or not and finding the degree of the polynomial. An algebraic expression is a collection of constants and variables connected by any or all of the operations addition, subtraction, multiplication, and division. The term "constant" refers to something that has a stable numerical value. A polynomial is an algebraic expression in which the variables have non-negative integral powers.
This chapter discusses Factorisation of Polynomials, which encompasses topics such as Factorisation of the Quadratic Polynomial of the kind ax2 + bx + c, where a ≠ 0, finding factors of third-degree polynomials and using remainder theorem to find the factors of a higher degree of polynomials. In this chapter, we also explore the idea of polynomials consisting of one variable, finding the values for zeros of polynomials (the value of the variable at which the polynomial returns the value of zero).
The chapter deals with the definition of linear equations in two variables, and as the name suggests, these are equations containing two variables, and if it were to be understood in simple words, the value of the equation would depend upon the value of both the variables. The chapter revolves around the methods to solve these equations. The solution of the equations is done by substituting the values of x and y. The chapter also contains exercises where the equations are simplified to find the values of the coefficients of x and y by comparing them to ax+by+c=0 (the general form of the linear equation in two variables). The chapter also contains some word problems where the solution is found by constructing a two-variable linear equation and substituting the values of both variables.
Chapter 5- Coordinate Geometry is the introduction of the Cartesian system, and it explains the rules regarding the system. It involves depicting lines or figures on the X-Y plane using the coordinates of the points or vertices of the figures. Coordinate geometry and charting a point in the plane if its coordinates are known are all concepts discussed in this chapter. The chapter lays the foundation of various important topics that would be taught in this section.
The Concepts related to classical Geometry are among the topics addressed in Chapter 6-Introduction To Euclid's Geometry. In addition, there are provisions for the topic of Euclid's Definitions and Axioms explained in detail for a thorough understanding. Finally, the chapter concludes with the introduction and explanations for Euclid's Postulates. The Euclidean Geometry contains four elements: solid shapes or 3-D figures, surfaces or 2-D figures, lines or curves, which comprise the 1-D figure and points that have no dimensions.
Chapter 7-Lines and Angles deal with the concepts related to lines and angles required to understand the related properties of angles, namely, the types of angles, complementary angles, and supplementary angles. The chapter includes questions where the angles formed by the transversal line to a pair of parallel lines is also calculated. In addition, there are questions where the value of unknown angles must be found by utilising the supplementary and complementary angle property. There are word problems based on the topics, and the chapter uses the algebraic expression to find the magnitude of the unknown angles.
Chapter 8- Triangles deal with the concepts related to the various properties and components of a triangle. The chapter explains in detail the sides, angles, vertices, interior and exterior of Triangles. Further topics discussed include the perimeter of the triangle, area of the triangle using the product of height and base and Heron's Formula, which uses the semi perimeter of the triangle. The chapter also informs the students about the types of triangles based on the interior angles. The questions in the chapter include finding the value of unknown angles using the sum of angles in a triangle property or the exterior and interior angle relation.
It is one of the most important chapters that are taught in the 9th grade. The chapter revolves around the congruence of figures and states that any two shapes that are the same in size and shape are congruent to each other. The chapter mainly focuses on the congruence of triangles and explains the criterion for various triangles (scalene, isosceles, equilateral and right angles triangle) to be congruent. The chapter explains each other criterions, including the SAS, ASA, SSS, and RHS criterion for congruence of triangles. The next topic discussed in the chapter is inequality in triangles, where important rules regarding triangles are explained. The inequality states that if two sides in a triangle are not equal to each other, then the angle opposite to the lengthier side will have the greatest angle, and the converse of this theorem is also there, which states the side opposite to the greatest angles is longest. The last inequality states that the sum of two sides of a triangle will always be greater than their third side. These inequalities are the basic requirements for the formation of triangles.
The chapter is based on quadrilaterals and the various types of quadrilaterals. The chapter defines a quadrilateral as a figure formed by joining four line segments to form a closed figure. The chapter also includes the special types of quadrilaterals, including the parallelogram, rhombus, square and rectangle. A parallelogram is defined by the figure having opposite sides parallel and equal. The opposite angles in the figure are also equal. The chapter contains theorems that deal with the specification and identification of parallelograms from quadrilaterals. The chapter discusses the features and properties of these special quadrilaterals, and apart from all these topics, this chapter also teaches the students about the midpoint theorem.
Chapter 11- Areas Of Parallelogram And Triangles deals with the Areas of Parallelograms and Triangles and also includes the concepts of area and the concepts of a Corollary: The area of a rectangle and a parallelogram with the same base and parallels is the same. There is an explicit mention of a Corollary that states that "The area of triangles with the same base and parallels is the same". Another corollary explained with examples and the proof is that "Parallelograms with the Same Base and between the Same Parallels have the same area". These concepts are based on Euclid's Area Axioms. The chapter contains questions on the base and altitude of a parallelogram. The solutions to questions in this chapter include using theorems like midpoint theorem and the formulae for various figures to calculate the numerical questions and the question where it is required to prove a statement or a condition.
Chapter 12- Circles deal with the circles' concepts and define a circle with respect to a point and a fixed distance. The chapter also contains the position of a point with respect to a circle and the measurement of the angle made by an arc. The chapter also explores the concept of minor and major arcs and the angles subtended by these arcs. The congruence of a circle is also discussed in the chapter, along with the properties of the chords in a circle. The chapter also mentions the cyclic quadrilaterals, and there are various questions on these concepts discussed.
The chapter has three important concepts to be discussed. First, the bisector of a line segment is taught to the students. Second, drawing the bisector of a line segment and drawing the perpendicular bisector of a line segment is also discussed. Next, the chapter also includes the bisector of angles and the construction of angles using the compass and ruler only. The chapter also includes the section on triangles and how to construct the triangles with different magnitudes of angles.
This chapter walks you through the process of using Heron's formula to calculate the area of a triangle. The chapter revolves around the area of two figures which include the triangle and quadrilaterals. There are formulae discussed and used for finding the area of the isosceles triangle and equilateral triangle. It also shows us how to find the perimeter of a triangle, the area of quadrilaterals by dividing the figure into triangles and finding the area of the triangle.
Chapter 15-Volume And Surface Area of solids are based on finding the total surface area, curved surface area and the volume of the solid shapes (3-D figures). The chapter deals with the explanation of boxed figures like cuboids and cubes. It explains their geometry, faces, vertices and edges. The formulae for volume and surface area are provided, along with the questions for practice. The chapter also discusses cones and cylinders, their geometry. The total surface area for these figures is discussed, along with their curved surface area and volume. The topic of hollow cylinders is also discussed, and the chapter ends with the discussion of shapes like hollow sphere, hemisphere and solid sphere.
Chapter 16- Representation of Data in Tabular Form deals with the concepts related to collecting data and the various methods to organise this set of data for methodical usage. The chapter also deals with the concepts of statistics. Methods to depict the organised or unorganised data along with the frequency of the collected data are an important topic addressed in this chapter. The important concepts related to data handling mentioned in this chapter include the frequency distribution, types of frequency distribution and methods of forming classes to represent data.
Chapter 17- Histogram and Frequency Polygon deals with the methods for the representation of data. The important topics discussed in this chapter are the Concepts of data arrangement and the graphical Representation of Data. The chapter begins by introducing a bar graph and moves on to a histogram similar to the bar graph. The chapter also teaches the students to read a bar graph and a histogram. The chapter concludes with solved numerical examples for understanding the Presentation of Data in the form of a histogram and Frequency polygons.
The Collection of data, measures of central tendency, concepts of statistics, and data analysis are all covered in Chapter 18- Mean, Median, and Mode of Ungrouped Data. Therefore the topics taught in this chapter are arithmetic mean, the properties related to the arithmetic mean, median and mode.
Probability is a study based on chance, and it is the core concept studied in this course. Chapter 19-Probability covers some terms related to probability and its history. This chapter also talks about events, experiments and outcomes. Probability can be defined as the possibility of the occurrence of a particular outcome. The probability of the occurrence of an event is always 1 or less than one. The probability of an event equivalent to one is called a sure event.
Ques 1: What is the cost of the Aakash RS Aggarwal Solutions for class 9th maths?
The RS Aggarwal solutions provided by the Aakash Institute for class 9th maths are free of cost. It is an initiative by the Aakash Institute where they are trying to bridge the gap between the people who can afford the high-grade education and the people who have no access to it. The solutions PDF found on the official website of Aakash institute levels the playing field as they provide the clarity of concepts and make the students independent of any other source.
Ques 2: What is the ideal way to use the RS Aggarwal Solutions for class 9th maths?
The ideal way to use the RS Aggarwal solutions for class 9th maths is to use it in combination with the textbook. To obtain the maximum benefit from the solutions, the students should first go through the textbook material, and after understanding the theoretical part, they should start practising the questions and consult the solutions PDF when they get stuck on the questions. In the end, they should compare their procedure and the procedure provided by the solutions PDF and choose the simpler and faster method for the future.