NCERT Solutions for Class 9 Maths (Updated for 2022-23) - GMS - Learning Simply
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# NCERT Solutions for Class 9 Maths (Updated for 2022-23)

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NCERT Solutions for Class 9 Maths includes solutions to all the questions given in the NCERT textbook for Class 9. The students can download PDF of chapter-wise solutions to these problems, from the links provided further below in this page. These Solutions of NCERT Class 9 Maths cover all the topics included in the textbook-like Number System, Coordinate Geometry, Polynomials, Euclid’s Geometry, Quadrilaterals, Triangles, Circles, Constructions, Surface Areas and Volumes, Statistics, Probability, etc.

With the help of these Solutions available for NCERT books for Class 9 Maths, students can practise all types of questions from the chapters. The CBSE Class 9 Maths Solutions have been designed by our experts in a well-structured format to provide several possible methods of answering the problems and ensure a proper understanding of concepts. The students are suggested to practise all these solutions thoroughly for their exams. It will also help them in building a foundation for higher-level classes.

Students are also provided with other online learning materials, question papers, worksheets etc. These materials are designed with respect to the CBSE syllabus and NCERT curriculum. Students are also advised to practise CBSE Class 9 Sample Papers to get an idea of the question pattern in the final exam.

## NCERT Solutions of Class 9th Maths Book Chapter brief:

Students having trouble in solving tough Math problems can refer to these CBSE Maths Class 9 Solutions of NCERT for better guidance and for quick review. Solving these exercises in each chapter will assure positive results.

### Chapter 1 Number System

This chapter discusses different topics, including rational numbers and irrational numbers. Students will also be learning the extended version of the number line and how to represent numbers (integers, rational and irrational) on it. A total of 6 exercises are present in this chapter that contains the problems based on all the topics asked in the chapter. This chapter also teaches students the representation of terminating/non-terminating recurring decimals (and successive magnification method) as well as the presentation of square roots of 2, 3 and other non-rational numbers on the number line. The chapter also deals with the laws of integral powers and rational exponents with positive real bases in Number Systems.

NCERT Solutions for Class 9 Maths Chapter 1 Exercises
☞ Exercise 1.1 – 4 Questions (4 short answers)

☞ Exercise 1.2 – 4 Questions (4 short answers)

☞ Exercise 1.3 – 9 Questions (8 short answers, 1 long answer)

☞ Exercise 1.4 – 2 Questions (2 long answers)

☞ Exercise 1.5 – 5 Questions (4 short answers, 1 long answer)

☞ Exercise 1.6 – 3 Questions (3 short answers)

### Chapter 3 Coordinate Geometry

The chapter Coordinate Geometry includes the concepts of the cartesian plane, coordinates of a point in xy – plane, terms, notations associated with the coordinate plane, including the x-axis, y-axis, x- coordinate, y-coordinate, origin, quadrants and more. Students, in this chapter, will also be studying the concepts of Abscissa and ordinates of a point as well as plotting and naming a point in xy – plane. There are 3 exercises in this chapter that contain questions revolving around the topics mentioned in the chapter, helping the students get thorough with the concepts.

NCERT Solutions for Class 9 Maths Chapter 3 Exercises
☞ Exercise 3.1 – 2 Questions (1 short answer, 1 long answer)

☞ Exercise 3.2 – 2 Questions (2 short answers)

☞ Exercise 3.3 – 2 Questions (1 short answer, 1 long answer)

### Chapter 4 Linear Equations in Two Variables

Along with recalling the knowledge of linear equations in one variable, this chapter will introduce the students to the linear equation in two variables, i.e., ax + by + c = 0. Students will also learn to plot the graph of a linear equation in two variables. There are 4 exercises in this chapter that consist of questions related to finding the solutions of a linear equation, plotting a linear equation on the graph and other topics discussed in the chapter.

NCERT Solutions for Class 9 Maths Chapter 4 Exercises
☞ Exercise 4.1 – 2 Questions (2 short answers)

☞ Exercise 4.2 – 4 Questions (3 short answers, 1 long answer )

☞ Exercise 4.3 – 8 Questions (4 short answers, 4 long answers)

☞ Exercise 4.4 – 2 Questions (2 long answers)

### Chapter 5 Introduction to Euclids Geometry

This chapter discusses Euclid’s approach to geometry and tries to link it with the present-day geometry. Introduction to Euclid’s Geometry provides the students with a method of defining common geometrical shapes and terms. Students will be taken deeper into the topic of axioms, postulates and theorems with the two exercises present in the chapter.

NCERT Solutions for Class 9 Maths Chapter 5 Exercises
☞ Exercise 5.1 – 7 Questions (4 short answers, 3 long answers)

☞ Exercise 5.2 – 2 Questions (1 short answer, 1 long answer)

### Chapter 6 Lines and Angles

This chapter revolves around the theorems present in the topics of Lines and Angles. Students might often be asked to prove the statements given in the questions. There are 3 exercises in the chapter, solving which students would be able to understand the concepts covered in the chapter thoroughly. There are four axioms and eight theorems covered in the chapter.

NCERT Solutions for Class 9 Maths Chapter 6 Exercises
☞ Exercise 6.1 – 6 Questions (5 short answers, 1 long answer)

☞ Exercise 6.2 – 6 Questions (3 short answers, 3 long answers)

☞ Exercise 6.3 – 6 Questions (5 short answers, 1 long answer)

### Chapter 7 Triangles

In this chapter, students will study in detail about the congruence of triangles, rules of congruence, some properties of triangles and the inequalities in triangles. The chapter has a total of 5 exercises, in which the students are asked “to-prove” as well as application-level problems. With this chapter, students will also learn to prove the properties that they learnt in earlier classes. The chapter also teaches the students to apply the various congruence rules while solving the problems. There are about eight theorems covered in this chapter.

NCERT Solutions for Class 9 Maths Chapter 7 Exercises
☞ Exercise 7.1 – 8 Questions (6 short answers, 2 long answers)

☞ Exercise 7.2 – 8 Questions (6 short answers, 2 long answers)

☞ Exercise 7.3 – 5 Questions (3 short answers, 2 long answers)

☞ Exercise 7.4 – 6 Questions (5 short answers, 1 long answer)

☞ Exercise 7.5 – 4 Questions (3 short answers, 1 long answer)

A figure obtained by joining four points in order is called a quadrilateral. This chapter takes the students to the depth of the topics of Quadrilaterals. The chapter contains 2 exercises that contain only one theorem to prove. However, there are a total of nine theorems that can be used to solve the application or conceptual level questions asked. Angle sum property of a Quadrilateral, types of quadrilaterals, properties of a parallelogram, and the mid-point theorem are taught explained in this chapter to help the students in learning the concepts thoroughly.

NCERT Solutions for Class 9 Maths Chapter 8 Exercises

### Chapter 9 Areas of Parallelograms and Triangles

In this chapter, an attempt has been made to consolidate the knowledge about the formulae to find the areas of different figures, by studying relationships between the areas of geometric figures, provided they lie on the same base and between the same parallels. This study will also be useful in the understanding of some results on ‘similarity of triangles’. The chapter contains 4 exercises of which, most of the questions ask the students to prove the statements given.

NCERT Solutions for Class 9 Maths Chapter 9 Exercises
☞ Exercise 9.1 – 1 Question (1 short answer)

☞ Exercise 9.2 – 6 Questions (5 short answers, 1 long answer)

☞ Exercise 9.3 – 16 Questions (12 short answers, 4 long answer)

### Chapter 10 Circles

A circle can be defined as a collection of all the points in a plane, at a fixed distance from a fixed point in the plane. Topics like Angle Subtended by a Chord at a Point, Equal Chords and their respective distances from the Centre, the Angle Subtended by an Arc of a Circle, Cyclic Quadrilaterals and other terms related to circles are covered in this chapter. A total of twelve theorems are present in this chapter, learning which the students will get a clearer idea of the concepts taught. There are 6 exercises in this chapter which consist of questions from all the concepts present in the chapter.

NCERT Solutions for Class 9 Maths Chapter 10 Exercises
☞ Exercise 10.1 – 2 Questions (2 short answers)

☞ Exercise 10.2 – 2 Questions (2 long answers)

☞ Exercise 10.3 – 3 Questions (3 long answers)

☞ Exercise 10.4 – 6 Questions (6 long answers)

☞ Exercise 10.5 – 12 Questions (12 long answers)

☞ Exercise 10.6 – 10 Questions (10 long answers)

### Chapter 11 Constructions

In this chapter, students will learn some basic constructions. The method learnt will then be used to construct certain kinds of triangles. There are 2 exercises present in this chapter, of which the first exercise deals with the construction of a certain angle or the bisector of a given angle. On the other hand, the second exercise deals with the constructions of triangles, when different parameters are given.

NCERT Solutions for Class 9 Maths Chapter 11 Exercises

☞ Exercise 11.2 – 5 Questions (5 very long answer)

### Chapter 12 Heron’s Formula

The chapter discusses Heron’s formula, which can be used to calculate the area of a triangle when the length of all three sides is given. In this method, there is no need to calculate the angles or other distances in the triangle. This formula can be used not only to find the area of triangles but also to find the areas of quadrilaterals and other polygons by dividing them into triangles. There are 2 exercises in this chapter which help the student in understanding the method of solving the problems based on Heron’s formula.

NCERT Solutions for Class 9 Maths Chapter 12 Exercises

☞ Exercise 12.2 – 9 Questions (4 long answers, 5 very long answers)

### Chapter 13 Surface Areas and Volumes

In this chapter, students shall learn to find the surface areas and volumes of cuboids and cylinders in detail and broaden the study to some other solids, such as cones and spheres. This chapter is just an extended version of the chapter mensuration, in which the students learnt about the surface areas and volumes in earlier classes. There are 8 exercises in this chapter, and these exercises contain problems that are based on surface areas and volumes of different solids such as cubes, cuboids, spheres, cylinders, cones, and hemispheres.

NCERT Solutions for Class 9 Maths Chapter 13 Exercises
☞ Exercise 13.1 – 8 questions

☞ Exercise 13.2 – 11 questions

☞ Exercise 13.3 – 8 questions

☞ Exercise 13.4 – 9 questions

☞ Exercise 13.5 – 9 questions

☞ Exercise 13.6 – 8 questions

☞ Exercise 13.7 – 9 questions

☞ Exercise 13.8 – 10 questions

☞ Exercise 13.9 – 3 questions

### Chapter 14 Statistics

The branch of Mathematics in which the extraction of meaningful information is studied is known as Statistics. It can also be defined as the collection of data on different aspects of the life of people, useful to the State. The chapter teaches about the different presentation of the data, including the frequency distribution as well. The chapter also helps the students learn the graphical representation of data, using different graphs such as Bar graphs, Histograms, Frequency polygons, etc. The chapter also lets the students learn the measure of central tendency mean, median and mode of the raw data. A total of 4 exercises are present in the chapter that includes problems related to all these concepts.

NCERT Solutions for Class 9 Maths Chapter 14 Exercises
☞ Exercise 14.1 – 2 questions (2 short answers)

☞ Exercise 14.2 – 9 questions (9 long answers)

☞ Exercise 14.3 – 9 questions (6 short answers, 3 long answers)

☞ Exercise 14.4 – 6 questions (2 short answers, 4 long answers)

### Chapter 15 Probability

The collection of some outcomes of an experiment is known as an event of an experiment. The chances of occurrence of an event are known as probability. In this chapter, students will learn to measure the chance of occurrence of a particular outcome in an experiment. This chapter contains only 1 exercise. The problems covered in this exercise are based on real-life incidents, enhancing the interest of the students in solving the questions.

NCERT Solutions for Class 9 Maths Chapter 15 Exercises
☞ Exercise 15.1 – 10 Question ( 4 short answers, 3 long answers, 3 very long answers)

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