NCERT Solutions for Class 9 Maths: In this article, we bring you the detailed NCERT Solution for Class 9 Maths. The NCERT Class 9 Maths solutions provided here are prepared by the top academic experts at Embibe which are in accordance with the NCERT textbook. Besides that, we are also providing you with PDF Download of NCERT Solutions for Class 9 Maths which will help you to study offline.
The NCERT Class 9 maths solutions provided here are precise and elaborate in nature. The step by step simplified methods of problem-solving will help you a lot to follow and learn the concepts. This, in turn, will help you to have a better understanding of the concept which is directly linked with the speed and accuracy of the solutions. Apart from this, it will also act as a very good reference material to complete your assignments on time. Thus, read on to get the NCERT Solutions for Class 9 Maths PDF for all 15 chapters.
NCERT Solutions For Class 9 Maths
Mathematics is a very challenging subject for many students and if students continue with the same belief then this may turn up to greater struggle later. In reality, maths is not very tough in nature. The difference lies in the approach deal with the problems. All you need is a proper understanding of the subjects and regular practice. The most important part is to solve the problems on your own than to just glance through the process. Negligence at the initial stage may turn into fear to face the subject. If you practice and follow the right approach you will love dealing with maths. This habit will not only help you ace Class 9 final exams but also help you to face the Class 10 Maths with confidence.
In this process of understanding the concepts and problem-solving process, the NCERT Class 9 Maths solutions will help you a lot. Get the NCERT Class 10 Maths Solutions For all chapters by clicking on the link below:
NCERT Solutions For Class 9 Maths: Chapter-Wise NCERT Solutions PDF Links
The NCERT Solutions For Class 9 Maths PDF is provided below:
- • Chapter 1: Number Systems
- • Chapter 2: Polynomials
- • Chapter 3: Coordinate Geometry
- • Chapter 4: Linear Equations in Two Variables
- • Chapter 5: Introduction to Euclid’s Geometry
- • Chapter 6: Lines and Angles
- • Chapter 7: Triangles
- • Chapter 8: Quadrilaterals
- • Chapter 9: Areas of Parallelograms and Triangles
- • Chapter 10: Circles
- • Chapter 11: Constructions
- • Chapter 12: Heron’s Formula
- • Chapter 13: Surface Areas and Volumes
- • Chapter 14: Statistics
- • Chapter 15: Probability
Advantages Of NCERT Solutions For Class 9 Maths
Go through the advantages of referring to the NCERT Solutions For Class 10 Maths are as follows:
- Reference Material to solve Exercise Problems: The NCERT Class 9 Science Solutions provided here are will guide you in solving the exercise problems. The simple and step by step approach of the NCERT solutions will help you to easily follow the problem-solving procedures.
- For Practice and Revision: The NCERT Solutions provided will help students to do exam focussed practice covering all the important topics. Besides that, the NCERT solutions will also act as a great material for quick revision during exams.
- Better Understanding: The simplified, precise approach followed will help the students to understand the problem-solving technique and the concept related to it. This in-depth and hands-on experience in solving the exercise problems will help you with better understanding, in turn, boosting your confidence.
- To Complete Assignments: After the completion of the lessons students head towards solving the exercise problems which may also be as an assignment. At times students may be stuck with some questions wanting for a clue
- To Ace competitive exams: The proper understanding of the concepts and fundamentals will not only be helpful in acing the upcoming exams but also lay a good foundation for your future academic journey. Besides that, the NCERT textbooks will also act as a basic reference to crack various competitive exams. Be it cracking Government job exams, JEE, NEET, UPSC, and any other exam, NCERT books will be the basic reference.
CBSE NCERT Solutions For Class 9 Maths: Chapter Descriptions
Let’s look at what each of these chapters is about. Read the description of the Class 9 Maths to have a glimpse about each chapter.
NCERT Solutions for Class 9 Chapter 1 Number Systems
Imagine you are standing at position A and you decide to start walking on the line ahead. Say you take a walk of 1 m distance ahead. Now imagine if you are walking in a straight line. How much you can cover 2m, 3m, 5m, 10m, 100m, 1km, 100 km…? Will it end somewhere? The answer is, No, you can cover as much distance as you want to. There is no end. That’s why there is something called infinity represented by the symbol ‘∞’. So in a number system, it starts from 0 (your current position), 1, 2, 3, 4, 5, goes on up to ∞.
NCERT Solutions for Class 9 Chapter 2 Polynomials
In order to understand polynomial, let’s take an example 2x – 3y + a. Now in this expression, the x is something which we don’t know that’s why we have represented as some symbol. y is also a symbol to represent as an unknown quantity. Now there are two kinds of unknown quantities, one is varying (called as a variable) while other is constant. We usually represent variables like x, y, z while constant as a,b,c. Now anything like 2x – 3y + a which changes based on the variables like x and y can be called as Polynomials. We can represent this polynomial as f(x). Hence f(x) = 2x – 3y + a.
NCERT Solutions for Class 9 Chapter 3 Coordinate Geometry
In this chapter, you will learn about how a point can be identified in a plane or space. When we talk about the point in space, we call it 3D geometry. While when we talk about a pint in a plane, we call it as coordinate geometry. But why do need to study this chapter? In order to understand the importance of this chapter, look at this example. If there is a girl standing on the streets, then how you will define her location? We will imagine a map having a north-south direction where the streets will be drawn. After having the reference you can easily point the location of the girl. Coordinate Geometry has many applications. One famous application is Maps.
NCERT Solutions for Class 9 Chapter 4 Linear Equations In Two Variables
Linear Equation is the equation that has a degree of one. The degree one means the equation like x + y = 3 or x + 2y – z =7 are linear equations. But here we are talking only about the linear equation in two variables. Hence we will not call the x + 2y – z = 7 as a linear equation in two variables since it has three variables. After understanding which kind of equations fall under linear equations in two variables, you can now proceed with how we will form the equations from a problem.
So assume that there are two kinds of fruits apple and orange. The total number of apples and oranges is 20. But the number of apple and orange is unknown. Hence, we can form an equation: x + y = 20. Where x is the number of apple and y is the number of oranges. NO win order to find the number of apple and oranges, you need to have one more equation that has the relationship between apple and orange (in other words contains x and y). For example, if we know that the number of apples is twice that oF the oranges then we can form an equation as x = 2y. And solve the above equations and thus calculate the number of apples and oranges.
NCERT Solutions for Class 9 Chapter 5 Introduction to Euclid’s Geometry
Throughout history, humans have used the knowledge of geometry to construct the pyramids, houses, statues and drainage systems. Euclid was a Greek mathematician, who has done studies on the geometry. He has defined point, line, straight line, surface, plane surface. In this chapter, you will also learn about Axioms and Postulates. Postulates are the assumptions that are specific to geometry. While the Axioms are the assumptions not specific to the geometry.
NCERT Solutions for Class 9 Chapter 6 Line and Angles
A line can only be formed by two or more points. The line segment can be defined as a line that has two endpoints. While the ray is the line with only one endpoint while the other point is free. If three or more lines are on the same line then they called collinear points. An angle is also formed when two rays are originated from the same source but they are going in different directions.
NCERT Solutions for Class 9 Chapter 7 Triangles
A triangle is formed when three intersecting lines are crossing each other. In this chapter, you will learn about the congruence of the triangle. Congruence means two objects having the same figure. The congruence of triangles means that there is more than 1 triangle that is similar in size and shape. One easy way to find out whether the two triangles are congruent or not is by finding the angle and the sides. If both are the same then they are called congruent triangles.
NCERT Solutions for Class 9 Chapter 8 Quadrilaterals
A quadrilateral is a figure having four different sides, four angles and four different sides. The sum of all the angles of the quadrilateral are 360 degrees. There are different types of quadrilateral: trapezium, parallelogram, square, rectangle, rhombus and a kite. In this chapter, you will learn about various theorems on the quadrilateral. On the basis of these theorems, you will be able to solve various questions in this chapter.
NCERT Solutions for Class 9 Chapter 9 Areas of Parallelograms and Triangles
In this chapter, you will be learning about different figures lying on the same base or between the same parallels. There will be some activities that you need to perform. You will learn that parallelograms, as well as triangles on the same base and between the same parallels, are equal in area. This chapter is filled with theorems where you need to understand each of the theorems in order to solve the exercises.
NCERT Solutions for Class 9 Chapter 10 Circles
The collections of all the points on a plane having a fixed distance from a certain point will lead to the formation of a circle. The fixed point is called a center while the fixed distance is called a radius. The circle divides the plane into three parts: inside the circle, on the circle, and the area outside the circle. If you take any two-point on the circle then the line formed by joining these two lines will be called chords. If the line is passing through the center of the circle then the chord will be called as diameter.
NCERT Solutions for Class 9 Chapter 11 Constructions
This chapter is more practical. Here the students will be taking the geometry box, and with the help of a compass and various tolls will be learning how to draw two lines at a different angle. Moving forward, you will also be drawing triangles, on the given its base length, side length, and base angles. In the end, you will be able to draw the perpendicular bisector of a given line segment, construct an angle of 60°, construct a triangle given its base, a base angle and the sum of the other two sides, construct a triangle given its base, a base angle and the difference of the other two sides, construct a triangle given its perimeter and its two base angles
NCERT Solutions for Class 9 Chapter 12 Heron’s Formula
Heron’s formula is used to find the area of the triangle. In this chapter, you will learn how this formula came into the picture. You will also learn how to calculate the area of the quadrilateral whose sides and one diagonal are given using Heron’s formula. The application of Heron’s formula can be used in various outdoor geometries.
NCERT Solutions for Class 9 Chapter 13 Surface Areas and Volumes
A cuboid is formed by six different rectangles. So if you want to find the surface area of the cuboid then you need to find the area of all the rectangles. After finding the areas of all the surfaces, you need to add then which will give you the Surface area of the cuboid. Similarly, you will also discover the surface area of the cylinder. A cylinder is formed by many circles. So if you take the area of one circle and multiply with the length and height of the rectangle that is formed when you unfold the cylinder, it will give you the surface area of the cylinder.
NCERT Solutions for Class 9 Chapter 14 Statistics
Statistics are representation of data. A data can be facts or figures which can be numerical. In this chapter, you will be performing various exercises on the given data. You will learn tally, graphical representation of data like bar graphs, histogram, frequency polygons. Going forward you will learn Measures of Central tendency of Ungrouped data which are nothing but Mean, Median, and Mode.
NCERT Solutions for Class 9 Chapter 15 Probability
In this chapter, you will be learning about the event. An event for an experiment is the collection of some outcomes of the experiment. You will also learn how and when to use the empirical formula. In this chapter, you will be given various scenarios where you will be asked to calculate the probability of the occurrence. This chapter is very much important as it will help you in higher studies.
We have now provided you with NCERT Solutions For Class 9 Maths. This will help you to solve the problems with proper understanding. It is advisable that you use this as reference material and learn the problem-solving process in case if you are unable to solve it. Besides that, you can also solve the NCERT Class 8 Maths questions at Embibe to learn more and strengthen your basics.
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