# NCERT Solutions for Class 9 Maths

Trying to find a solution that can make your learning easier than before? We understand how tough it gets when you get stuck on math problems and even after applying** **formulas, you are not able to get it right can make you more frustrated than you already are. This is where GeeksforGeeks make sure you’re taken care of. Our NCERT Solutions for Class 9 Maths, CBSE Class 9 Maths Notes, and RD Sharma Solutions for Class 9 have all the solutions you need.

NCERT Solutions for Class 9 Maths provides chapter-wise solutions to problems given in the respective NCERT textbook. The questions solved here in the solutions provided by GeeksforGeeks, give an approach to understanding the concepts in a better way. This CBSE Class 9 NCERT solution covers all the chapters in the NCERT book like Number System, Coordinate Geometry, Triangles, Circles, Mensuration, and many more with solutions for all the relevant exercises.

Go through our website and check the NCERT Solutions for Class 9 Maths, curated by subject matter experts who follow the structure that is given in the NCERT textbooks. This can also help you to precede onto Class 10 and appear for the boards. Our CBSE NCERT solution for class 9 Maths can help you face the questions that you’ll learn in class 10 and can increase your theoretical and practical knowledge.

To improve the basic knowledge of students, we have also covered 1500+ Most asked Questions of Mathematics, Chapterwise Important Formulas, and many more based on the new Class 9th CBSE curriculum.

## Chapter 1: Number Systems

Here we have covered **NCERT Solutions for Class 9 Maths Chapter 1**– Number systems. It briefly covers the concept of rational and irrational numbers, real numbers, and their representation on the number line. Along with the laws of rational exponents and integral powers.

This chapter in total consists of six exercises, including a total of 27 questions, out of which 5 are easy, 7 are mid-level and 10 are difficult questions. Exercise 1.1 helps to learn the basics of rational and irrational numbers, and Exercise 1.2 explains the concept of real numbers and their expansion. Further, Exercise 1.3 helps to learn ‘How to represent real numbers on the number line’. Later, in exercises 1.4, 1.5, and 1.6 mathematical operations, rationalizing, and laws of rational exponents and integral powers for real numbers are discussed.

**NCERT Solutions for Class 9 Maths of Chapter 1 are here: **

- NCERT Maths Solutions Class 9 Exercise 1.1 – 4 Questions & Solutions (4 short Answers)
- NCERT Maths Solutions Class 9 Exercise 1.2 – 4 Questions & Solutions (4 short Answers)
- NCERT Maths Solutions Class 9 Exercise 1.3 – 9 Questions & Solutions (8 short Answers, 1 long Answer)
- NCERT Maths Solutions Class 9 Exercise 1.4 – 2 Questions & Solutions (2 long Answers)
- NCERT Maths Solutions Class 9 Exercise 1.5 – 5 Questions & Solutions (4 short Answers, 1 long Answer)
- NCERT Maths Solutions Class 9 Exercise 1.6 – 3 Questions & Solutions (3 short Answers)

**At GeeksforGeeks, you may also find the following resources for Class 9 Chapter 1 Number System:**

- Class 9 Maths Notes Chapter 1
- Class 9 RD Sharma Solutions Number Systems Chapter 1, Chapter 2 and Chapter 3
- All important formulas for Chapter 1

## Chapter 2: Polynomials

The chapter **Polynomials **guides to learning polynomials of degree 1 (Linear polynomials), 2 (quadratic polynomials), and 3 (cubic polynomials), etc, and terminology related to it. This chapter also covers the concept of **factor theorem**, **algebraic identities of quadratic polynomials**, **split the middle theorem**, **algebraic identities for cubic polynomials**, etc.

In this chapter five exercises are there, that consist of a total of 33 questions. 10 are mid-level, 14 are basic and 9 are tough-level problems. Exercises 2.1, and 2.2 cover topics like polynomials in one variable, zeroes of a polynomial, types of polynomials, and their degree. Exercises 2.3 and 2.4 are based on the concept of the factor theorem. Further, Exercise 2.5 helps to learn the algebraic identities of quadratic and cubic polynomials and split the middle theorem.

**NCERT Solutions for Class 9 Maths of Chapter 2 are here:**

- NCERT Maths Solutions Class 9 Exercise 2.1 – 5 Questions & Solutions (5 Short Answers)
- NCERT Maths Solutions Class 9 Exercise 2.2 – 4 Questions & Solutions (4 Short Answers)
- NCERT Maths Solutions Class 9 Exercise 2.3 – 3 Questions & Solutions (3 Short Answers)
- NCERT Maths Solutions Class 9 Exercise 2.4 – 5 Questions & Solutions (4 Short Answers, 1 Long Answer)
- NCERT Maths Solutions Class 9 Exercise 2.5 Set 1, Set 2 – 16 Questions & Solutions (9 Short Answers, 5 Long Answers, 2 Very Long Answers)

**At GeeksforGeeks, you may also find the following resources for Class 9 Chapter 2 Polynomials:**

- Class 9 Maths Notes Chapter 2
- Class 9 RD Sharma Solutions Polynomials Chapter 1, Chapter 2, and Chapter 3
- All important formulas for Chapter 2

## Chapter 3: Coordinate Geometry

This chapter helps to learn the concepts of the Cartesian plane and various terminology related to it in detail. The chapter deals with problems on various subtopics like determining the x and y coordinates of a point in a cartesian plane, identifying quadrants, locating an object, and expressing it in the form of coordinates.

There are three exercises in this chapter, that consist of a total of 6 problems in class 9 maths chapter 3 coordinate geometry. Out of which 1 is easy, 2 are moderate and 3 are challenging problems. Exercise 3.1 explained How to locate a point on the coordinate plane?. While Exercises 3.2 and 3.3 discussed the topic of Plotting a point in the plane if its coordinates are given.

**NCERT Solutions for Class 9 Maths of Chapter 3 are here:**

- NCERT Maths Solutions Class 9 Exercise 3.1 – 2 Questions & Solutions (1 Short Answer, 1 Long Answer)
- NCERT Maths Solutions Class 9 Exercise 3.2 – 2 Questions & Solutions (2 Short Answers)
- NCERT Maths Solutions Class 9 Exercise 3.3 – 2 Questions & Solutions (1 Short Answer, 1 Long Answer)

**At GeeksforGeeks, you may also find the following resources for Class 9 Chapter 3 Coordinate Geometry:**

## Chapter 4: Linear Equations in Two Variables

Linear equations in one variable have been already discussed in earlier classes which deal with unique solutions. Now, in this chapter** ****linear equation comes with two variables** like ax + by + c = 0. Thus, this chapter introduces the concepts like the solutions including solving linear equations, graphical representation methods, and the depiction of parallel lines.

Exercises 4.1 and 4.3 are designed to learn about the formation and determination of the solution of a linear equation in two variables. However, Exercises 4.3 and 4.4 gave detailed learning of the topic of the graph of a linear equation in two variables.

**NCERT Solutions for Class 9 Maths of Chapter 4 are here:**

- NCERT Maths Solutions Class 9 Exercise 4.1 – 2 Questions & Solutions (2 Short Answers)
- NCERT Maths Solutions Class 9 Exercise 4.2 – 4 Questions & Solutions (3 Short Answers, 1 Long Answer)
- NCERT Maths Solutions Class 9 Exercise 4.3 – 8 Questions & Solutions (4 Short Answers, 4 Long Answers)
- NCERT Maths Solutions Class 9 Exercise 4.4 – 2 Questions & Solutions (2 Long Answers)

**At GeeksforGeeks, you may also find the following resources for Class 9 Chapter 4 Linear Equations in Two Variables :**

## Chapter 5: Introduction to Euclid’s Geometry

The chapter Introduction to** Euclid’s Geometry** explains **Euclid’s method of geometry** and linked it with modern-day geometry. Euclid’s five postulates deal with line segments, radii, perpendicular lines, and the variation of the fifth postulate. Euclid approached geometry by defining different axioms and postulates.

This chapter contains two exercises, that have a total of 9 questions, 4 are easy, 3 are moderate and 2 are difficult questions. Both Exercises 5.1 and 5.2 are based on the terms defined in the provided axioms and postulates.

**NCERT Solutions for Class 9 Maths of Chapter 5 are here:**

- NCERT Maths Solutions Class 9 Exercise 5.1 – 7 Questions & Solutions (4 Short Answers, 3 Long Answers)
- NCERT Maths Solutions Class 9 Exercise 5.2 – 2 Questions & Solutions (1 Short Answer, 1 Long Answer)

**At GeeksforGeeks, you may also find the following resources for Class 9 Chapter 5 Introduction to Euclid’s Geometry:**

## Chapter 6: Lines and Angles

As the name of the chapter says, this chapter deals with the properties of the angle formed when two or more lines intersect each other and the properties of these angles formed. Also, provides an understanding of the basic definitions of various terms that are used in geometry. Students learn about the different types of angles, pairs of angles, transversals, parallel lines, angle sum property of triangles, and axioms associated with these concepts.

This chapter consists of three exercises in which Exercises 6.1 and 6.2 give the knowledge about the different types of angles linear, reflex, right, obtuse, acute, complementary, and supplementary angles and their measures. Moreover, Exercise 6.3 covers the topic of angle sum property.

- NCERT Maths Solutions Class 9 Exercise 6.1 – 6 Questions & Solutions (5 Short Answers, 1 Long Answer)
- NCERT Maths Solutions Class 9 Exercise 6.2 – 3 Questions & Solutions (3 Short Answers, 3 Long Answers)
- NCERT Maths Solutions Class 9 Exercise 6.3 – 6 Questions & Solutions (5 Short Answers, 1 Long Answer)

**At GeeksforGeeks, you may also find the following resources for Class 9 Chapter 6 Lines and Angles:**

## Chapter 7: Triangles

This chapter gives a detailed description of the congruence of triangles, their rules, properties, and the inequalities in triangles.

In total five exercises, the latter topics are covered. Exercises 7.1, 7.2, and 7.3 lay emphasis on the topic of congruence of triangles and properties of triangles. Further, Exercises 7.4 and 7.5 are based on the triangle inequalities.

**NCERT Solutions for Class 9 Maths of Chapter 7 are here:**

- NCERT Maths Solutions Class 9 Exercise 7.1 – 8 Questions & Solutions (6 Short Answers, 2 Long Answers)
- NCERT Maths Solutions Class 9 Exercise 7.2 – 8 Questions & Solutions (6 Short Answers, 2 Long Answers)
- NCERT Maths Solutions Class 9 Exercise 7.3 – 5 Questions & Solutions (3 Short Answers, 2 Long Answers)
- NCERT Maths Solutions Class 9 Exercise 7.4 – 6 Questions & Solutions (5 Short Answers, 1 Long Answer)
- NCERT Maths Solutions Class 9 Exercise 7.5 – 4 Questions & Solutions (3 Short Answers, 1 Long Answer)

**At GeeksforGeeks, you may also find the following resources for Class 9 Chapter 7 Triangles:**

- Class 9 Maths Notes Chapter 7
- Class 9 RD Sharma Solutions Triangles Chapter 1 and Chapter 2
- All important formulas for Chapter 7

## Chapter 8: Quadrilateral

The chapter **Quadrilateral **is all about the different types of quadrilaterals (rectangle, square, parallelogram, trapezium, etc) and their different properties like the angle sum property of a quadrilateral. Further, the last section of the chapter provides a brief introduction to the midpoint theorem and its converse.

This chapter consists of two exercises, in which exercise 8.1 helps to learn about the different properties of different quadrilaterals while exercise 8.2 explains the application of the mid-point theorem and its converse.

**NCERT Solutions for Class 9 Maths of Chapter 8 are here:**

- NCERT Maths Solutions Class 9 Exercise 8.1 – 12 Questions & Solutions (2 Short Answers, 6 Long Answers, 4 Very Long Answers)
- NCERT Maths Solutions Class 9 Exercise 8.2 – 7 Questions & Solutions (2 Short Answers, 3 Long Answers, 3 Very Long Answers)

**At GeeksforGeeks, you may also find the following resources for Class 9 Chapter 8 Quadrilateral:**

## Chapter 9: Areas of Parallelograms and Triangles

As the name suggests **Areas of parallelogram and triangles**, this chapter gives the understanding of the formula to determine the areas of different closed shapes using the relation between the areas of different geometric shapes.

A total of four exercises are present in the chapter in which Exercise 9.1 is based on the topic Figures on the Same Base and Between the same parallels. While Exercise 9.2 is based on the problems on the theorem for the parallelograms that have the same area and Exercises 9.3 and 9.4 cover the problems from the topic, triangles on the same base and between the same Parallels.

**NCERT Solutions for Class 9 Maths of Chapter 9 are here:**

- NCERT Maths Solutions Class 9 Exercise 9.1 – 1 Questions & Solutions (1 Short Answer)
- NCERT Maths Solutions Class 9 Exercise 9.2 – 6 Questions & Solutions (5 Short Answers, 1 Long Answer)
- NCERT Maths Solutions Class 9 Exercise 9.3 Set 1, Set 2 – 16 Questions & Solutions (12 Short Answers, 4 Long Answers)
- NCERT Maths Solutions Class 9 Exercise 9.4 – 8 Questions & Solutions (4 Short Answers, 1 Long Answer, 3 Very Long Answers)

**At GeeksforGeeks, you may also find the following resources for Class 9 Chapter 9 Areas of Parallelograms and Triangles:**

## Chapter 10: Circles

This chapter is related to the different properties and the terminology of the circles. The chapter **Circles **included various topics such as angles subtended by a chord at a point, perpendiculars dropped from the center to a chord, and how to calculate the distance of equal chords from the center. Other discussions include angles subtended by an arc of the circle, cyclic quadrilaterals, and their attributes.

A total of 6 exercises are there in the chapter, Exercise 10.1 and 10.2 are related to the terminologies and the basic properties of the circles. However, Exercise 10.3 is based on the two theorems of the circles. Exercise 10.4 works upon the problem related to equal chords and their distances from the center. Moreover, exercises 10.5 and 10.6 are based on the topics and theorems related to the angle subtended by an arc of a circle.

**NCERT Solutions for Class 9 Maths of Chapter 10 are here:**

- NCERT Maths Solutions Class 9 Exercise 10.1 – 2 Questions & Solutions (2 Short Answers)
- NCERT Maths Solutions Class 9 Exercise 10.2 – 2 Questions & Solutions (2 Long Answers)
- NCERT Maths Solutions Class 9 Exercise 10.3 – 3 Questions & Solutions (3 Long Answers)
- NCERT Maths Solutions Class 9 Exercise 10.4 – 6 Questions & Solutions (6 Long Answers)
- NCERT Maths Solutions Class 9 Exercise 10.5 – 12 Questions & Solutions (12 Long Answers)
- NCERT Maths Solutions Class 9 Exercise 10.6 – 10 Questions & Solutions (10 Long Answers)

**At GeeksforGeeks, you may also find the following resources for Class 9 Chapter 10 Circles:**

## Chapter 11: Constructions

The chapter **Constructions **in this class helps to understand the approach to constructing different types of triangles for different given conditions.

This chapter comprises two exercises in which the problems in Exercise 11.1 deal with the construction of a different angle or the bisector of a given angle, Exercise 11.2 are related to constructions of triangles, in the case when different parameters are given.

**NCERT Solutions for Class 9 Maths of Chapter 11 are here:**

- NCERT Maths Solutions Class 9 Exercise 11.1 – 5 Questions & Solutions (2 Short Answers, 2 Long Answer, 1 Very Long Answer)
- NCERT Maths Solutions Class 9 Exercise 11.2 – 5 Questions & Solutions (5 Very Long Answers)

**At GeeksforGeeks, you may also find the following resources for Class 9 Chapter 11 Constructions:**

## Chapter 12: Heron’s Formula

This chapter discusses only **Heron’s formula** and its applications which are used to determine the area of a triangle when all the three sides of the triangle are provided.

The chapter comprises only two exercises, both Exercises 12.1 and 12.2 consist of problems related to the application of Heron’s formula.

**NCERT Solutions for Class 9 Maths of Chapter 12 are here:**

- NCERT Maths Solutions Class 9 Exercise 12.1 – 6 Questions & Solutions (2 Short Answers, 2 Long Answers, 2 Very Long Answers)
- NCERT Maths Solutions Class 9 Exercise 12.2 – 9 Questions & Solutions (4 Long Answers, 5 Very Long Answers)

**At GeeksforGeeks, you may also find the following resources for Class 9 Chapter 12 Heron’s Formula:**

## Chapter 13: Surface Areas and Volumes

The chapter **Surface areas and volumes **mainly deal with the formula, to determine the surface areas and volumes of different shapes like cube, cuboid, and cylinder and their applications. The problems related to each topic of this chapter are discussed in nine different exercises.

Exercises 13.1, 13.2, and 13.3 concepts like the surface areas and volume of the various geometrical shapes like cubes, cuboids, and more. However, Exercises 13.4, 13.5, 13.6, 13.7, 13.8, and 13.9 are focused on the problems based on the applications of the mentioned formulae.

**NCERT Solutions for Class 9 Maths of Chapter 13 are here:**

- NCERT Maths Solutions Class 9 Exercise 13.1 – 8 Questions & Solutions (4 Short Answers, 4 Long Answers)
- NCERT Maths Solutions Class 9 Exercise 13.2 – 11 Questions & Solutions (5 Short Answers, 6 Long Answers)
- NCERT Maths Solutions Class 9 Exercise 13.3 – 8 Questions & Solutions (6 Short Answers, 2 Long Answers)
- NCERT Maths Solutions Class 9 Exercise 13.4 – 9 Questions & Solutions (4 Short Answers, 5 Long Answers)
- NCERT Maths Solutions Class 9 Exercise 13.5 – 9 Questions & Solutions (4 Short Answers, 5 Long Answers)
- NCERT Maths Solutions Class 9 Exercise 13.6 – 8 Questions & Solutions (8 Short Answers)
- NCERT Maths Solutions Class 9 Exercise 13.7 – 9 Questions & Solutions (9 Long Answers)
- NCERT Maths Solutions Class 9 Exercise 13.8 – 10 Questions & Solutions (5 Short Answers, 5 Long Answers)
- NCERT Maths Solutions Class 9 Exercise 13.9 – 3 Questions & Solutions (3 Long Answers)

**At GeeksforGeeks, you may also find the following resources for Class 9 Chapter 13 Surface Areas and Volumes:**

- Class 9 Maths Notes Chapter 13
- Class 9 RD Sharma Solutions Surface Areas and Volumes Chapter 1, Chapter 2, Chapter 3, and Chapter 4
- All important formulas for Chapter 13

## Chapter 14: Statistics

The chapter **Statistics **helps to learn the representation of data differently along with the frequency distribution. With the help of a total of four exercises the concept of graphical representation of data, using various graphs like Frequency polygons, Histograms, Bar graphs, etc.

Exercise 14.1 comprises the descriptive problems to understand the basics of statistics and Exercise 14.2 helps to learn to plot the frequency distribution table for the given data. While, Exercise 14.3 include problems with frequency polygons and histogram, and Exercise 14.4 is based on the concept of mean, mode, and median.

**NCERT Solutions for Class 9 Maths of Chapter 14 are here:**

- NCERT Maths Solutions Class 9 Exercise 14.1 – 2 Questions & Solutions (2 Short Answers)
- NCERT Maths Solutions Class 9 Exercise 14.2 – 9 Questions & Solutions (9 Long Answers)
- NCERT Maths Solutions Class 9 Exercise 14.3 – 9 Questions & Solutions (6 Short Answers, 3 Long Answers)
- NCERT Maths Solutions Class 9 Exercise 14.4 – 6 Questions & Solutions (2 Short Answers, 4 Long Answers)

**At GeeksforGeeks, you may also find the following resources for Class 9 Chapter 14 Statistics:**

- Class 9 Maths Notes Chapter 14
- Class 9 RD Sharma Solutions Statistics Chapter 1, Chapter 2 and Chapter 3
- All important formulas for Chapter 14

## Chapter 15: Probability

The last chapter covered in CBSE NCERT Solutions for class 9 maths is chapter 15 **Probability**. Probability discusses the concept of the Chances of occurrence of a specific outcome in an experiment. This chapter consists of only one exercise which is based on the problems from everyday life examples to understand the experimental approach to probability.

**NCERT Solutions for Class 9 Maths of Chapter 15 are here:**

- NCERT Maths Solutions Class 9 Exercise 15.1 – 10 Questions & Solutions (4 Short Answers, 3 Long Answers, 3 Very Long Answers)

**At GeeksforGeeks, you may also find the following resources for Class 9 Chapter 15- Probability:**

**Important Resources for CBSE Class 9th provided by GeeksforGeeks**

**CBSE Class 9 Maths Notes****RD Sharma Solutions Maths Class 9****CBSE Class 9 Maths Formulas****CBSE Class 9 Physics Notes****CBSE Class 9 Chemistry Notes**

**Frequently Asked Questions (FAQs)**

**Question 1: What are some important tips for Class 9 Maths Chapter 6 Lines and Angles?**

**Answer:**

This chapter teaches a number of properties that students must learn. The following tips can help you in optimizing this process.

- Answer a series of questions about the properties of angles created when a transversal intersects two or three parallel lines.
- Understand the logic underlying theorems like the triangle’s angle sum property.
- Make a mental note of how the angles relate to one another.

**Question 2: List out some important formulas from Class 9 Maths.**

**Answer:**

Polynomials, number systems, geometry, probability, and other topics are covered in class 9 math. Higher-grade mathematics requires an understanding of the formulas and concepts behind these topics. To reduce the time it takes to give answers and ensure efficiency, formulas are required. An outline of the important maths formulas covered in the NCERT solutions for class 9 maths is provided here.

Important formulas from Geometry:

- Area of a triangle = ½ × b × h
- Perimeter of a triangle = a + b + c
- Area of parallelogram = b × h
- Perimeter of a parallelogram = 2(a + b)

Important formulas from Surface Area and volume:

- TSA of a cuboid = 2(lb + bh +lh)
- Volume of a cuboid = l×b×h
- TSA of a cube = 6a
^{2}- Volume of a cube = a
^{3}

Important Algebraic Equations:

- (a + b)
^{2}= a^{2}+ b^{2}+ 2ab- (a – b)
^{2}= a^{2}+ b^{2}– 2ab- (a + b) (a – b) = a
^{2}– b^{2}