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NCERT solutions for class 9 maths are provided here. Do you spend more time than the expected while doing homework and preparing for exams? if yes, then detailed solutions created by experts are very helpful. These NCERT solutions are prepared based on latest syllabus of CBSE 2023-24, covering comprehensive, step by step solutions of each and every problem. NCERT class 9 maths syllabus contains 15 chapters which make a strong base for the class 10 NCERT maths. Students can download all the ncert maths class 9 chapter pdf solutions using the link provided below. NCERT solutions for class 9 contains chapters Number System, Coordinate Geometry, Polynomials, Euclidean Geometry, Quadrilaterals, Triangles, Circles, Constructions, Surface Areas and Volumes, Statistics, and Probability.
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. Class 9th Maths NCERT Solutions, 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. Class 9 maths NCERT solutions will be easily available here with a detailed explanation and you can download these class 9 maths solutions pdfs by clicking on the link.
Chapter No. | Chapter Name |
Chapter 1 | |
Chapter 2 | |
Chapter 3 | |
Chapter 4 | |
Chapter 5 | |
Chapter 6 | |
Chapter 7 | |
Chapter 8 | |
Chapter 9 | |
Chapter 10 | |
Chapter 11 | |
Chapter 12 | |
Chapter 13 | |
Chapter 14 | |
Chapter 15 |
Number Systems Class 9 Solutions: 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 first chapter has a weightage of 8 marks in the final examination.
Polynomial Class 9 Solutions: 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 Class 9 maths NCERT solutions , we are proving the step by step solution to all the 114 questions.
Coordinate Geometry Class 9 Solutions: 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.
Linear Equation in Two Variables Class 9 Solutions: 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 Class 9 maths NCERT solutions chapter 4.
Introduction to Euclid's Geometry Class 9 Solutions: 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.
Lines and Angles Class 9 Solutions: 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.
Triangles Class 9 Solutions: A shape made up of three straight lines is called a 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, 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.
Quadrilaterals Class 9 Solutions: 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 practising all the problems available in the chapter is the only key to master this chapter. Through Class 9 maths NCERT solutions , we provide you with solutions to all the 37 questions given in the whole chapter.
Areas of Parallelograms and Triangles Class 9 Solutions: 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.
Circles Class 9 Solutions: 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.
Constructions Class 9 Solutions: 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.
Heron's Formula Class 9 Solutions: 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 Class 9th Maths NCERT solutions , you will find a great explanation for each and every question.
Surface Areas and Volumes Class 9 Solutions: 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 litres, 750 litres, etc. Which means that the tank can occupy a volume of 1000 litres. We will study about volumes and surface areas in this chapter of Class 9 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.
Statistics Class 9 Solutions: 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 the 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.
Probability Class 9 Solutions: 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, you are going to study how these probabilities are calculated.
Unit | Unit Name | Marks |
I | Number Systems | 10 |
II | Algebra | 20 |
III | Coordinate Geometry | 04 |
IV | Geometry | 27 |
V | Mensuration | 13 |
VI | Statistics and Probability | 06 |
Total | 80 | |
Internal Assessment | 20 | |
Total | 100 |
Internal Assessment | Marks |
Pen Paper Test and Multiple Assessment (5+5) | 10 Marks |
Portfolio | 05 Marks |
Lab Practical (Lab activities) | 05 Marks |
Total Marks | 20 Marks |
When preparing for exams, it is recommended that students begin by completing the units that carry more weightage and then move on to the units with lower weightage. This approach enables students to cover the essential concepts first and increases their confidence to perform well in the final exams.
To prepare for NCERT maths class 9, students are advised to analyze all the concepts covered in the syllabus and create a comprehensive study plan. It is not sufficient to simply memorize the concepts for scoring well in Maths exams. Instead, students should strive to understand the logic and concepts presented in each topic. Regular practice of the NCERT Solutions for 9th class. is essential to develop a strong grasp of fundamental mathematical concepts.
A highly effective method for learning the Class 9 Maths chapters is to work through the NCERT Textbook, which includes a multitude of questions that are critical from an exam standpoint. Before the exercise questions, solved examples are provided to aid students in comprehending the process for solving difficult problems. This approach also enhances analytical and logical thinking abilities, which are crucial for achieving good scores in exams.
Absolutely! Solved solutions for the questions in the NCERT Class 9 Maths chapters are available. Careers360 has a team of skilled instructors who design the solutions with great care while taking into account the IQ levels of Class 9 students. Both chapter-wise and exercise-wise solutions can be found online and offline, completely free of charge. The solutions conform to the CBSE guidelines and exam format, with the goal of assisting students in achieving high grades on their exams.
Since Mathematics is a subject that necessitates frequent practice, it is highly recommended that students solve questions from the 9th class maths on a daily basis. This will instill confidence in students, making it easier for them to tackle difficult exam questions. Additionally, it strengthens a student's grasp of the fundamental concepts that will be built upon in higher levels of education.
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