# NCERT Solutions for Class 9 Maths

NCERT Solutions for Class 9 Maths: Class 9 Maths contains 15 Chapters. All the chapters are prerequisite for NCERT Solutions of class 10. There are solved examples and exercise for practice in each chapter of the NCERT Solutions for Class 9 Maths. Understanding all the solved examples and practising all the exercise questions mentioned in the NCERT book will help you to improve your knowledge in the subject and also will help in your daily life calculations and also to score good marks in exams. Many of the chapters are basics for many competitive exams like Olympiad, CAT and many other government exams.

NCERT Solutions for class 9 contains chapters from algebra, geometry, statistics and probability. All the chapters are very important for higher studies and also for daily life calculations. The last two chapters of NCERT Solutions for Class 9 Maths Statistics and Probability are very important in Engineering, Science, Maths, Economics and Business etc. Prepare these chapters very well. All the chapters are equally important.

Here we will cover NCERT Solutions for Class 9 Maths in detail. In these mathematics, the following are the chapters:-

Chapter 1 Number systems

Chapter 2 Polynomial

Chapter 3 Coordinate Geometry

Chapter 4 Linear Equation in Two Variables

Chapter 5 Introduction to Euclid's Geometry

Chapter 6 Lines and Angles

Chapter 7 Triangles

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

CBSE Class 9 Weightage Distribution Of Mathematics-

 CBSE Class 9 Maths: Unit-wise Marks Distribution Units Marks Unit 1: Number Systems 08 Unit 2: Algebra 17 Unit 3: Coordinate Geometry 04 Unit 4: Geometry 28 Unit 5: Mensuration 13 Unit 6: Statistics & Probability 10 Total 80

The main chapters with a brief outline of the topics are given below-

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. Main topics of this chapter are rational numbers, irrational numbers, how to represent real numbers on the number line and many more. NCERT Class 9 Maths Chapter 1 Number Systems has a weightage of 8 marks in the CBSE final examination.

In this chapter, students get to know about a particular type of algebraic expression, called polynomial, and discuss its detailed terminologies. This chapter contains 5 exercises with 33 questions. In this chapter, we will study important concepts like polynomials in one variable, zeroes of a polynomial, remainder theorem, factorisation of polynomials and algebraic identities.

this chapter, students get to introduced by some basic concepts of coordinate geometry. There is a total of 3 exercises with 6 questions in NCERT Class 9 Maths Chapter 3 Coordinate Geometry. In this chapter, we will study important concepts like cartesian system, coordinates of the point in the XY-plane, abscissa and ordinates of the points.

In this chapter, we will discuss linear equations in two variables of the form $\dpi{100} ax+by+c=0$ where a, b and c are the real numbers, and a and b are not equal to zero. There is a total of 4 exercises with 16 questions in this chapter. 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.

This chapter, discusses Euclid’s approach to geometry. Euclidean Geometry was introduced by a Greek Mathematician Euclid In this chapter, there are 2 exercises with 9 questions. In 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.

Chapter 6 - Lines and Angles: Lines and angles are everywhere around us. 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, and complementary angles, intersecting lines and non-intersecting lines, parallel lines and a transversal and discuss angle sum property of a triangle.

We already study in brief about triangles and their properties in earlier classes. In this chapter, we are going to discuss triangles and its properties like congruence of triangles, isosceles triangle, etc in detail. It is one of the important chapters for a maths student. There is a total of 5 exercises with 31 questions in this chapter.

Chapter 8 - 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 parallelogram and its properties.

Chapter 9 - Areas of Parallelograms and Triangles: 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 different properties of areas of parallelogram and areas of triangles. The area of triangles can be used to calculate the area of lands by dividing it into triangular parts.

Chapter 10 - Circles: 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.

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 other two sides are given etc.

Chapter 12 - Heron's Formula: This chapter talks about how to find the area of a triangle if the side length of the triangle is given. 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.

Chapter 13 - Surface Areas and Volumes: 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. In this chapter of NCERT Maths, we will study about volumes and surface areas. If a square tank has to occupy 1000 l 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.

Chapter 14 - Statistics: We used to see many data 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. In the NCERT Solutions of statistics, we will study about the collection of data, representing it in order and analyzing results based on that. For example, we have collected data of marks in Maths obtained in our class. From this data, we 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. In this NCERT class 9 Maths chapter, we will study how to arrange data and how to obtain certain results from them.

Chapter 15 - Probability: 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 we are throwing a die. Then we 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, we will study how these probabilities are calculated.

Here we are going to provide step by step solutions for Class 9 Maths which will help students in the preparation of class 9 CBSE final exam. The NCERT Solutions for Class 9 prepared by our subject experts to facilitate easy understanding of concepts.