NCERT solutions for class 9 maths- Do you spend more time than the expected while doing homework and preparing for exams? Then detailed solutions from experts is your answer. NCERT class 9 maths contains 15 chapters. NCERT solutions for class 9 maths will make a strong base for the upcoming NCERT class 10 maths. Chapters in NCERT class 9 maths will help in your daily life calculations and also for scoring good marks in the examination. There are solved examples and exercises for practice in each chapter of CBSE NCERT class 9 maths. If you want to score good, then a good understanding of all the solved examples and practicing all the exercise questions mentioned in the class 9 maths NCERT is necessary. CBSE NCERT solutions for class 9 maths, will help you as a reference while solving the exercise problems. Many of these chapters are basics for competitive exams like Olympiad, CAT and many other government jobs and entrance exams. NCERT solutions for chapters, statistics and probability are very important in engineering, science, maths, economics, and business, etc. Solutions of NCERT class 9 maths will be easily available here with a detailed explanation and you can download these NCERT solutions by clicking on the link.
NCERT solutions for class 9 contains chapters from algebra, geometry, statistics, and probability. NCERT solutions will cover every single chapter in great detail and give the answers to every problem mentioned in the chapter. Prepare these chapters very well in order to score high marks in the examination.
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NCERT solutions for class 9 maths chapter 1 Number Systems: The first chapter of class 9 maths NCERT discusses the number of systems with their applications. In this chapter, we are going to learn the extended form of the number line and learn how to represent various types of the number on it. The main sub-topics of this chapter are rational numbers, irrational numbers, how to represent real numbers on the number line, finding rational numbers between two numbers, conversion from decimal to fraction and vice versa. In NCERT solutions class 9 maths chapter 1 number systems we are proving the step by step solution to all the 61 questions. NCERT class 9 maths chapter 1 number systems have a weightage of 8 marks in the final examination.
Solutions of NCERT class 9 maths chapter 2 Polynomial: In earlier classes, we have learned the addition, subtraction, multiplication, division, factorization of algebraic equations. This chapter teaches you all about algebraic expressions and polynomials. Particularly, we will learn about the remainder theorem, factor theorem for factorizing the polynomials. The main sub-topics of this chapter are the degree of a polynomial, coefficient of variable, zeroes of a polynomial, finding the value of k, usage of algebraic identities and many more. In NCERT solutions class 9 maths chapter 2 polynomial, we are proving the step by step solution to all the 114 questions.
CBSE NCERT solutions for class 9 maths chapter 3 Coordinate Geometry: Here you get introduced to some basic concepts of coordinate geometry. There are a total of 3 exercises consisting of 9 questions each. NCERT solutions for class 9 maths chapter 3 coordinate geometry have been provided for all the questions available in the topic. In this chapter, we will study important concepts like the cartesian system, coordinates of the point in the XY-plane, abscissa, and ordinates of the points and many more.
NCERT solutions for class 9 maths chapter 4 Linear Equation in Two Variables: This chapter is part of algebra. In this particular chapter, we will discuss linear equations in two variables of the form where a, b and c are the real numbers, and a and b are not equal to zero. In this chapter, we will study important concepts like linear equations, solution of a linear equation, the graph of a linear equation in two variables, equations of lines parallel to x-axis and y-axis. There is a total of 4 exercises with 16 questions in this chapter. We are providing step by step solutions to all the 16 questions available in NCERT solutions class 9 maths chapter 4 linear equation in two variables.
Solutions of NCERT class 9 maths chapter 5 Introduction to Euclid's Geometry: We discuss Euclid’s approach to geometry in this lesson. We discuss various observations related to geometrical figures like- curves, lines, points and many more. Euclidean geometry was introduced by a greek mathematician Euclid. In this chapter, there are 2 exercises with 9 questions. In the NCERT class 9 maths chapter 5 introduction to Euclid’s geometry, we will learn Euclid’s definitions like a point, a plane, and a line and also study his axioms and theorems, Euclid’s five postulates and also study two equivalent versions of Euclid’s fifth postulate.
CBSE NCERT solutions for class 9 maths chapter 6 Lines and Angles: Lines and angles are everywhere around us. Whenever we join two points then the shape formed is called line. To find the height of a building or a tower, then we need to know angles and to design the structure of a building the architecture uses both lines and angles. In this chapter, we will study important topics such as basic terms like opposite angles, supplementary angles, complementary angles, intersecting lines, and non-intersecting lines, parallel lines and a transversal and discuss angle sum property of a triangle. Through NCERT solutions for class 9 maths chapter 6 lines and angles, we are providing you step by step solution to all the 2 exercises consisting of 13 questions.
NCERT solutions for class 9 maths chapter 7 Triangles: A shape made up of three straight lines is called triangle. In previous classes, we have studied the types of triangles, formulae to calculate the areas of all types of triangles. Here in NCERT class 9 maths chapter 7, you will learn congruency of triangles, thels theorem, angle bisector theorem and many more. The chapter is very important for class 9th as well as class 10th examination. In the 10th class, the concepts of this chapter are used very often. In class 9th final examinations most numbers of questions appear from this chapter only. There is a total of 4 exercises and 1 optional exercise which consists of overall 44 questions. through NCERT solutions class 9 maths chapter 7 triangles.
Solutions of NCERT class 9 maths chapter 8 Quadrilaterals: A shape which is made up of 4 sides or in other words, any 4 sided shape having a sum of all four angles 360 degrees is called quadrilaterals. The chapter starts with introductions to different types of quadrilaterals like rectangle, square, rhombus, parallelogram, kites, etc. In the NCERT Solutions for class 9 maths chapter Quadrilateral, we will study mainly about the parallelogram and its properties. There is a possibility of a bit higher difficulty level question can come related to this chapter. So a strong memory of all the properties and practicing all the problems available in the chapter is the only key to master this chapter. Through NCERT solutions for the class 9 maths chapter, we provide you solutions to all the 37 questions given in the whole chapter.
CBSE NCERT solutions for class 9 maths chapter 9 Areas of Parallelograms and Triangles: Parallelogram is a four-sided quadrilateral in which opposite sides, as well as opposite angles, are always equal. Many shapes in our daily life are in the form of triangles and parallelograms such as a rooftop, walls, top of a table, etc. In this chapter, we will study the different properties of areas of parallelograms and areas of triangles. The area of triangles can be used to calculate the area of land by dividing it into triangular parts. The topic will help you in creating a strong foundation for higher-level questions based on parallelograms and triangles. In NCERT solutions for class 9 maths chapter 9 areas of parallelograms and triangles, there are a total of 14 questions in and we have given the best possible solution to each and every question.
NCERT solutions for class 9 maths chapter 10 Circles: You all have come across different shapes in daily life such as- coin, wheel, keyring, button, bangles, etc. All these things are circular shapes. The chapter starts with basic terminologies related to circles such as chords, diameter, arc sector and segment. The NCERT Class 9 Maths Chapter 10 Circles also talks about the properties of circles and cyclic quadrilaterals. Most of the students struggle with this chapter as it has lots of theorems and properties to remember but if you go through the formation or proof of that particular theorem then everything would be easy. It is one of the most property-based topics in class 9 mathematics and you can check solutions to all the 46 questions in great detail.
Solutions of NCERT class 9 maths chapter 11 Constructions: The chapter constructions include the construction of certain angles, and angle bisectors, construction of triangles using certain given conditions. For example how to construct a triangle if the base angle and sum of the other two sides are given etc. Construction helps in the geometrical part of mathematics. The more you are comfortable in construction the much better you will understand the geometry. In NCERT solutions for class 9 maths chapter 11 constructions, there are total 14 questions in and we have given the best possible solution to each and every question.
CBSE NCERT solutions for class 9 maths chapter 12 Heron's Formula: We have learnt many formulae to find the area of a specific kind of triangle. There are separate formulae for finding the area of the right-angle triangle, equilateral triangle, etc. This chapter talks about how to find the area of a triangle if the side length of the triangle is given. This formula is applicable to all kinds of triangles. The application of Heron's Formula includes measuring the area of land of irregular shape. The land will be divided into different triangles and areas will be measured using Heron's Formula. The formula was introduced by a mathematician called Heron, that's why this is called Heron's Formula. In the NCERT class 9 solution, you will find a great explanation for each and every question.
NCERT solutions for class 9 maths chapter 13 Surface Areas and Volumes: In this particular chapter, we will learn about the surface areas and volumes of a cube, cuboid, cone, cylinder, sphere, hemisphere, etc. The area of the material used to make that particular shape is called the area of the particular shape. We used to see water tanks of capacity 1000 liters, 750 liters, etc. Which means that the tank can occupy a volume of 1000 liters. We will study about volumes and surface areas in this chapter of NCERT Maths,. If a square tank has to occupy 1000 lts what should be the height, length, and breadth of the tank? What should be the area of the sheet required to cover a gift in the shape of a cylinder? Such questions can be answered after studying this chapter.
Solutions of NCERT class 9 maths chapter 14 Statistics: We see data in various forms like a weather report for a day, number of seats in elections and how many seats are won by a particular party, number of people affected by a particular disease in an area, number of people consuming alcohol during new year day and comparing it with previous year, etc. Here, you will study about the collection of data, representing it in order and analyzing results based on that. For example, you have collected data on marks in maths obtained in the class. From this data, you will understand how many students have passed, how many students got a full mark, what is the most repeated mark, what is the average of the mark, etc. You will study how to arrange data and how to obtain certain results from them in this chapter.
CBSE NCERT solutions for class 9 maths chapter 15 Probability: Probability means chances of happening something. It is one of the best chapters you will learn in class 9 maths. We used to tell there is a chance for rain today, there is a chance for India to win the match, etc. All our predictions are based on certain previous observations. Consider that you are throwing a die. Then you may get 1,2,3,4,5 or 6. That is there are six outcomes in the experiment of throwing a die. We will say the probability or chance of getting a 3 on die is 1/6. In this chapter of the NCERT solutions of class 9 maths, you are going to study how these probabilities are calculated.
You can use NCERT solutions for class 9 maths as an assistant while doing homework.
You can observe some easy methods to solve every problem related to the chapter as well as the important formulae.
NCERT solutions for class 9 maths are written step by step so that you understand how to solve the problems easily and thus score full marks in the examination.
We all know class 10th examination is a board exam. So in order to score high marks in board exams, we have to be good with the subjects of class 9th which form the foundation for class 10.
This curriculum is a combination of crucial mathematical chapters that are prerequisites for class 10 maths. If you learn NCERT solutions for class 9 science, you will find the difference while answering in the exam.
Q2 Does Euclid’s fifth postulate imply the existence of parallel lines? Explain.
Q : 3 If two equal chords of a circle intersect within the circle, prove that the line joining the point of intersection to the centre makes equal angles with the chords.
8.(iv) In countries like USA and Canada, temperature is measured in Fahrenheit, whereas in countries like India, it is measured in Celsius. Here is a linear equation that converts Fahrenheit to Celsius:
(iv) If the temperature is 0°C, what is the temperature in Fahrenheit and if the temperature is 0°F, what is the temperature in Celsius?