What is NCERT?
After listening to the title of the article, “NCERT maths class 9 solutions” the first topic is, what is NCERT? The full form of NCERT is the National Council of Educational Research and Training. This organization comes under the Government of India and they established this organization on 1 September 1961.
The picture above is the logo of NCERT. NCERT sets a curriculum for the classes and the CBSE board uses these NCERT books as a syllabus of a particular subject. Most of the schools in India that are under the CBSE board use NCERT textbooks as their main textbook. They conduct exams based on the chapters and lessons in these books. Students refer to them to prepare for their exams, and NCERT books are of good quality.
NCERT usually provides books for classes 1-12 and these books are the best options to refer to while preparing for board exams. Students need not be confused as NCERT books cover the entire syllabus and there is not much need for other reference books.
Advantages of using NCERT books
Here are a few advantages of using the NCERT books-
We have heard many students complaining about their boring black and white textbooks. As silly as it may sound, colors are important and they grab the attention of students. If the textbook has colors, students are more drawn towards reading them. And NCERT books are not like those boring black and white textbooks. They have a bit of color in them, even in the diagrams which encourages the students to read it.
The language followed in the NCERT books is fairly easy. They explain every concept in a simple way. Students do not need a dictionary to understand the meaning of the terms and neither do they need to have a very rich vocabulary to understand the language used. NCERT books are for every student, no matter how intelligent they are or how developed their English is.
The NCERT books are enough to clear every little doubt regarding a topic. They explained every concept thoroughly in detail. Students will not need to mug up anything. They explained the theories clear enough to make them understand. Students can just revise the formulas and how they can execute the sums before the exams.
There is enough number of solved examples that can help to solve the exercises. They plan the exercises in such a good way, that it will help a student complete a chapter thoroughly. It will help them to learn to apply the concepts when they face different numerical in the exam. In fact, the questions are usually the same type in the exam as they are in the NCERT books. The numbers or data might be different but if a student is thorough in his/her NCERT textbook, they will not face much difficulty in solving the problems during the examination.
NCERT Class 9 textbooks
Here is the list of the textbooks issued for class 9 by NCERT-
Kshitij- It is a collection of Hindi literature and its price is Rs55.
Kritika- It is a collection of Hindi stories to improve the reading and writing skills of our National language. Its price is Rs25.
Sparsh- It is a textbook for the students who have Hindi as their second language. This book includes six prose’s and seven poems. Its price is Rs50.
Sanchayan- It is a supplementary book for students having Hindi as the second language and its price is Rs25.
Beehive- This is the English textbook and is a compilation of different prose and poetry. Its price is Rs65.
Moments- This is the supplementary reader that contains many stories for the students to read. Its price is Rs35.
Shemusi- This is a Sanskrit book and contains short questions, solved questions, MCQ, fill in the blanks, etc based on certain concepts. Its price is Rs50.
Mathematics- This is the textbook for the mathematics subject and its price is Rs135.
Science- This book is the Science textbook its price is Rs135.
Vigyan- This book contains short questions, solved examples, and MCQ questions about the Science subject.
India and contemporary world-History- The price of this book is Rs115.
Contemporary India- Geography- The price of this book is Rs50.
Economics- The cost of this book is Rs35.
Democratic politics- The price of this book is Rs80.
Apart from NCERT maths class 9 solutions, we can also find the solutions of the other subjects online. Every book has good quality content to educate a student about various subjects like English, Hindi, Sanskrit, Maths, Science, Economics, History and Geography. The students will gain a lot of knowledge from reading these books and will help them as well.
|Book Name||Price||Buy Now|
|Oswaal NCERT Exemplar (Problems - solutions) Class 9 Mathematics Book (For March 2020 Exam)||Rs.178||Click here|
|NCERT Solutions - Mathematics for Class IX||Rs.132||Click Here|
|NCERT Exemplar Problems-Solutions MATHEMATICS class 9th||Rs.90||Click Here|
|CBSE NCERT Solutions Mathematics for Class 9 (2019-20)||Rs.130||Click Here|
|Oswaal NCERT Problems - Solutions (Textbook + Exemplar) Class 9 Mathematics Book (For March 2020 Exam)||Rs.203||Click Here|
|Solution to NCERT Mathematics||Rs.140||Click Here|
|Mathematics Textbook for Class - 9 - 962||Rs.155||Click Here|
|Golden Mathematics: (With Sample Papers) A book with a Difference Class-9 (For 2019 Final Exams)||Rs.330||Click Here|
NCERT maths class 9 solutions for Chapter 1
The first chapter in the NCERT maths book is Number Systems. This chapter will be very interesting for the students who have a keen interest in numbers and problems related to numbers. This chapter deals with various topics like natural numbers, whole numbers, integers, rational numbers, irrational numbers, real numbers, exponents, laws of exponents, number lines, etc.
There are six exercises in the chapter number system, namely 1.1, 1.2, 1.3, 1.4, 1.5 and 1.6. Each exercise contains several problems that can help a student clear all their doubts related to the number system. There are 4 questions in the first exercise, 4 in the second, 9 in the third, 2 in the fourth, 5 in the fifth and 3 in the third.
deals with questions where the students can identify which numbers are integers, natural numbers, rational numbers, etc and the students can learn how to identify them.
deals with how students can represent different numbers on the number line correctly.
deals with decimal numbers and their expansion using the long division method.
It helps the students to represent decimal numbers on the number line.
Deals with laws related to solving rational and irrational numbers.
The last exercise deals with exponents and laws that we can use to solve sums related to exponents.
Here are two links that have detailed solutions to all the sums of the exercises in the first chapter- Number system.
NCERT maths class 9 solutions for chapter 2
The second chapter of NCERT class 9 mathematics is Polynomials. A polynomial is an expression that contains variables and coefficients. A polynomial may include operations like addition, subtraction, multiplication, and exponents. The NCERT maths class 9 solutions in chapter 2 include the basics of polynomials, polynomials in one variable, zeroes of a polynomial, remainder theorem, factorization of polynomials and algebraic identities.
There are five exercises related to the different concepts of polynomials in chapter 2. The names of the exercises are 2.1, 2.2, 2.3, 2.4 and 2.5. Each of these exercises contains problem sums to help a student clear their fundamental concepts about polynomials to prepare them for facing questions during the exam. There are many students who find polynomials complicated and tough. But the NCERT books have explanations about all the required concepts in a very simple and organized manner which will help students understand, but only through proper practice.
There are five questions in exercise 2.1 which help a student recognize which polynomials are in one variable and which are not.
Exercise 2.2 has 4 questions with multiple sub-questions where a student needs to find out the answer of expression by replacing the value of the variable with a, particularly given number. This exercise helps a student to understand the roots of an equation or zeroes of a polynomial.
2.3 has three questions that deal with the division of polynomials with another expression.
2.4 has 5 questions dealing with factor theorem and factorization of polynomials.
2.5 has 16 questions that deal with evaluation, factorization, and expansion of identities.
Here are two links that have NCERT maths class 9 solutions for chapter 2 polynomials.
NCERT maths class 9 solutions for chapter 3
The next chapter in the Mathematics textbook is Coordinate Geometry. We can also call coordinate geometry as Cartesian geometry because this branch of geometry uses a coordinate system on a Cartesian plane. Coordinate geometry makes use of algebra, curves, and lines to find a distance between two points, dividing lines in particular ratios, finding midpoints, etc.
Students find this chapter interesting because this chapter is not that tough if they get the basics right. It has a few formulas and most of them can solve most of the problem sums by remembering the basic concept and using the formulas. There are three exercises in this chapter- 3.1, 3.2 and 3.3.
It has two problem sums which deal with basic plotting of points in a Cartesian plane using coordinates.
It contains 2 questions as well that deal with plotting, ordinates, and abscissa.
shows about quadrants and how a set of coordinates can determine whether they are in the positive quadrant or the negative quadrant.
These two links have solutions of all the three exercises in coordinate geometry-
NCERT maths class 9 solutions for chapter 4
The name of chapter 4 is linear equations in 2 variables. A linear equation in two variables usually has two sets of equations having two unknown variables. We can find the value of these variables by solving the two equations. This concept uses a lot of algebra, but it is fairly easy. There are different methods to solve two sets of equations having two variables. This chapter has 4 exercises- 4.1, 4.2, 4.3 and 4.4.
It has 2 questions with many sub-questions and deals with the basics of linear equations and how to represent them in terms of one variable.
The second exercise has 4 questions that deal with solutions of an equation and how to find the value of a variable if they give the value of the second variable.
It has 8 questions that deal with plotting the equations on a graph using the coordinate system, finding out values of the equations from the graph, etc. It also has a few data-based questions that help a student form equations and solves them by comparison.
The last exercise has sums relating to representing an equation in one variable or two variables.
Here are two links that contain the solutions for this chapter-
NCERT maths class 9 solutions for chapter 5
The name of chapter 5 in mathematics is Introduction to Euclid’s geometry. In this method, we can assume a small set of intuitively appealing axioms, and we can deduce many prepositions from them.
We can use Euclid’s geometry in various applications and this concept is new, so it requires practice. Two exercises in this chapter of Euclid’s geometry called 5.1 and 5.2. There are four to five postulates that we need to understand about this chapter and we can solve most of the problems after that.
Seven questions in the first exercise and it deals with true and false statements based on the basic postulates and some definitions about geometrical shapes like parallel lines, line segments, a radius of a circle, square, etc.
The second exercise contains some basic proofs regarding the postulates and the methods to verify them.
These two links contain the NCERT maths class 9 solutions for chapter 5 –
NCERT maths class 9 solutions for chapter 6
Lines and angles are two basic parts of geometry. There are some standard properties and definitions in this chapter, and the properties help a lot in solving the problems. There are different types of angles like the right angle, obtuse angle, acute angle and different pairs of lines. And each has its distinct properties. This chapter has three exercises- 6.1, 6.2 and 6.3.
It has 6 questions where there are diagrams about various angles and the students need to find the value of the unknown angle using different properties of angles.
Again it has 6 questions that deal with more complex sums related to line segments and angles. The student has to remember the properties to apply them.
It has six questions, which deal with more sums related to intersecting lines, perpendicular lines, angles, etc.
These are two links which contain solutions for the above chapter-
NCERT maths class 9 solutions for chapter 7
A polygon that has three sides and three vertices are called a triangle. The value of every angle of the triangle adds up to 180 degrees. This shape is basic and two-dimensional. There are different triangles like an equilateral, isosceles, right angle, etc. Each triangle has its own properties. Equilateral triangles have all 3 equal sides, isosceles has two equal sides and two equal angles while the right-angle triangle has one angle equal to 90 degrees. This chapter has 5 exercises.
7.1 has 8 questions that deal with proofs and verification related to the different properties of the triangle.
7.2 has 8 questions that deal with proofs related to triangles and line segments and their properties.
7.3 has 8 questions dealing with more complex proofs.
7.4 has 6 questions where they combined the proofs with quadrilaterals.
7.5 has 4 questions that deal with construction based on instructions.
Students can refer to these links below-
NCERT maths class 9 solutions for chapter 8
Chapter 8 is Quadrilaterals. A quadrilateral has 4 edges and 4 vertices. But then, there are different quadrilaterals like the square, rectangle, trapezoid, etc. This chapter has 2 exercises. Quadrilaterals are two dimensional and have their own set of properties.
8.1 has 12 questions that deal with verification and proofs based on the properties of quadrilaterals and line segments. Bisecting the quadrilateral into different shapes can help to solve them better.
8.2 has 7 questions that deal with more complex proofs regarding quadrilaterals and their properties.
Students can refer to these links below-
NCERT maths class 9 solutions for chapter 9
The name of chapter 9 in the areas of parallelograms and triangles. For geometrical shapes, they have their own perimeters and areas. There are different formulas for calculating the perimeter or area of a parallelogram and triangle. These formulas are very important to solve problems related to this chapter. There are three exercises-
9.1 deals with figures that lie on the same base and between the same parallels.
9.2 deals with proofs related to parallelograms and triangles and their properties.
9.3 deals with verifications, bisecting lines, diagrams, etc.
These two links contain the NCERT maths class 9 solutions for chapter 9 –
NCERT maths class 9 solutions for chapter 10
The name of chapter 10 is Circles. A circle is a two-dimensional shape that has no edges or vertices. It is round and has a radius. The radius is half of the diameter and the diameter is twice that of the radius. A circle has many related terms like circumference, area, arc, chord, etc. There is a method to calculate each of the terms. The angle made by an entire circle is 360 degrees. There are 6 exercises in this chapter.
10.1 deals with true or false and fill in the blanks questions related to the basic properties of the circle.
10.2 deals with proofs related to the properties of circles.
10.3 deals with the construction of circles.
10.4 deals with data-based questions on finding out different parts of a circle.
10.5 has questions related to complex shapes involving circles and finding out different angles.
10.6 has questions on proofs related to circles.
These two links contain the NCERT maths class 9 solutions for chapter 10 –
NCERT maths class 9 solutions for chapter 11
Constructions need a few instruments like a pencil, compass, ruler, and protractor. They give the questions and we have to construct the shape and mention the steps involved in the construction. We can construct several shapes with precise lengths of the sides and angles. There are two exercises-
11.1 deals with the construction of different angles and triangles by using a protractor and they mention the shapes how to construct them.
11.2 has questions where they have given some sides and angles and students have to construct according to that.
These two links contain the NCERT maths class 9 solutions for chapter 11 –
NCERT maths class 9 solutions for chapter 12
Chapter 12 is Heron’s formula. This formula got its name from Hero of Alexandria. This formula allows us to calculate the area of the triangle when they mention all three sides. We do not have to calculate any angle or the height of the triangle, so Heron’s formula makes it an easy process.
There are two exercises in this chapter.
12.1 deals with questions on triangular-shaped traffic lights, slides, flyovers, etc where they mention some data and the students need to find out the required data.
12.2 has questions on parallelograms, quadrilaterals, trapezoids, etc where students need to calculate the required data using properties.
These two links contain the NCERT maths class 9 solutions for chapter 12 in detail-
NCERT maths class 9 solutions for chapter 13
The name of chapter 13 is Surface areas and volumes. We calculate surface areas and volumes for three-dimensional shapes like cubes, cuboids, cones, spheres, etc. The formulas for surface area and volume for each individual shape is different, and it is very essential to remember the formulas to solve questions related to this topic. This chapter has 9 exercises.
13.1 deals with questions based on rooms and costs where they mention the data and the student need to calculate the value using the formulas.
13.2 deals with questions related to surface area and lateral surface areas of cylinders.
13.3 deals with questions related to surface area and lateral surface areas of cones.
13.4 has questions related to the surface area of spheres, hemispheres, and other shapes based on these.
13.5 deals with volumes of cubes and cuboids.
13.6 deals with volumes of cylinders and cylindrical objects.
13.7 deals with volumes of cones and conical objects.
13.8 deals with volumes of spheres and spherical objects.
13.9 has mixed questions based on this chapter.
These two links contain the NCERT maths class 9 solutions for chapter 13 in detail-
NCERT maths class 9 solutions for chapter 14
The name of chapter 14 in Statistics. Statistics is a branch of maths where they provide the analyzed data and we can represent that data in the form of bar charts, line charts, pie charts, graphs, flowcharts, etc. These are great for presentations and displaying data in a presentable format. We can use them especially to interpret a large quantity of data. This chapter has 4 exercises.
14.1 has questions about simple statistical data and the determination of whether that data is primary or secondary.
14.2 has tabular data and students need to prepare frequency distribution tables and find required values.
14.3 has more complex data and students need to plot the data on graphs.
14.4 focuses on the mean, median, and mode of the data.
These two links contain the NCERT maths class 9 solutions for chapter 14 in detail-
NCERT maths class 9 solutions for chapter 15
Probability defines the chances of occurrence of any event. It helps us to calculate the probability of success or failure of any event or the chances of receiving a particular result. We can use it in the event of rolling a dice, tossing a coin, picking up a particular colored ball from a bag of multicolored balls, picking up a particular card from a deck, etc. Probability is an important chapter as it has many applications like an aptitude test for a job interview. There is only one exercise in this chapter.
15.1 has different sums where they give the data and the student to identify the event and find out the probability of the event occurring. There are many questions in this chapter that will surely clear the concept of probability and help the students to attempt different questions related to this chapter.
These two links contain the NCERT maths class 9 solutions for chapter 15 in detail-
NCERT set the above chapters to help in the overall development of a 9th-grade student. The topics are such that they will be helpful in the coming years too. NCERT maths class 9 solutions are a great option for students to refer to in case they find any difficulty in solving a particular sum. But mathematics needs practice and the solutions should be a mere reference. It will help if the students attempt the sums on their own and see what improvement their approach needs.