Contents

- 1 NCERT Solutions for Class 9 Maths
- 1.1 Chapter 1 Number Systems
- 1.2 Chapter 2 Polynomials
- 1.3 Chapter 3 Coordinate Geometry
- 1.4 Chapter 4 Linear Equations in Two Variables
- 1.5 Chapter 5 Introduction to Euclid’s Geometry
- 1.6 Chapter 6 Lines and Angles
- 1.7 Chapter 7 Triangles
- 1.8 Chapter 8 Quadrilaterals
- 1.9 Chapter 9 Areas of Parallelograms and Triangles
- 1.10 Chapter 10 Circles
- 1.11 Chapter 11 Constructions
- 1.12 Chapter 12 Heron’s Formula
- 1.13 Chapter 13 Surface Areas and Volumes
- 1.14 Chapter 14 Statistics
- 1.15 Chapter 15 Probability

NCERT Solutions for Class 9 Maths are a set of solutions in the form of chapter-wise solutions made specifically for Class 9th students.

## NCERT Solutions for Class 9 Maths

### Chapter 1 Number Systems

- Number Systems Class 9 Ex 1.1
- Number Systems Class 9 Ex 1.2
- Number Systems Class 9 Ex 1.3
- Number Systems Class 9 Ex 1.4
- Number Systems Class 9 Ex 1.5
- Number Systems Class 9 Ex 1.6

### Chapter 2 Polynomials

- Polynomials Class 9 Ex 2.1
- Polynomials Class 9 Ex 2.2
- Polynomials Class 9 Ex 2.3
- Polynomials Class 9 Ex 2.4
- Polynomials Class 9 Ex 2.5

### Chapter 3 Coordinate Geometry

- Coordinate Geometry Class 9 Ex 3.1
- Coordinate Geometry Class 9 Ex 3.2
- Coordinate Geometry Class 9 Ex 3.3

### Chapter 4 Linear Equations in Two Variables

- Linear Equations in Two Variables Class 9 Ex 4.1
- Linear Equations in Two Variables Class 9 Ex 4.2
- Linear Equations in Two Variables Class 9 Ex 4.3
- Linear Equations in Two Variables Class 9 Ex 4.4

### Chapter 5 Introduction to Euclid’s Geometry

### Chapter 6 Lines and Angles

### Chapter 7 Triangles

- Triangles Class 9 Ex 7.1
- Triangles Class 9 Ex 7.2
- Triangles Class 9 Ex 7.3
- Triangles Class 9 Ex 7.4
- Triangles Class 9 Ex 7.5

### Chapter 8 Quadrilaterals

### Chapter 9 Areas of Parallelograms and Triangles

- Areas of Parallelograms and Triangles Class 9 Ex 9.1
- Areas of Parallelograms and Triangles Class 9 Ex 9.2
- Areas of Parallelograms and Triangles Class 9 Ex 9.3
- Areas of Parallelograms and Triangles Class 9 Ex 9.4

### Chapter 10 Circles

- Circles Class 9 Ex 10.1
- Circles Class 9 Ex 10.2
- Circles Class 9 Ex 10.3
- Circles Class 9 Ex 10.4
- Circles Class 9 Ex 10.5
- Circles Class 9 Ex 10.6

### Chapter 11 Constructions

### Chapter 12 Heron’s Formula

### Chapter 13 Surface Areas and Volumes

- Surface Areas and Volumes Class 9 Ex 13.1
- Surface Areas and Volumes Class 9 Ex 13.2
- Surface Areas and Volumes Class 9 Ex 13.3
- Surface Areas and Volumes Class 9 Ex 13.4
- Surface Areas and Volumes Class 9 Ex 13.5
- Surface Areas and Volumes Class 9 Ex 13.6
- Surface Areas and Volumes Class 9 Ex 13.7
- Surface Areas and Volumes Class 9 Ex 13.8
- Surface Areas and Volumes Class 9 Ex 13.9

### Chapter 14 Statistics

- Statistics Class 9 Ex 14.1
- Statistics Class 9 Ex 14.2
- Statistics Class 9 Ex 14.3
- Statistics Class 9 Ex 14.4

### Chapter 15 Probability

**Chapter 1: Number System**

In this chapter, students will learn about the concept of an irrational number, real numbers, and their decimal expansions, they will also learn the techniques of real numbers on the number line, different kind of operations on real numbers, and about the laws of exponents for real numbers. Overall there are 7 exercises, solve the questions and in case of any doubt refer our book. As we provide a step-by-step description of each question for making you perfect in the number system.

**Chapter 2: Polynomial**

Polynomial is a type of algebraic expression. In previous classes, you understood factorization of algebraic expression, so apply those concepts and learn some new concepts while solving polynomials. Here students will familiarize themselves with the concept of polynomials in one variable, zeroes of a polynomial, remainder theorem, factorization of polynomials, and algebraic identities. There are 7 exercises in this chapter. Solve them and take our book help in case you are unable to get the desired answer or if you find it difficult to solve any question.

**Chapter 3: Coordinate geometry**

In earlier classes, you studied the location of a point on a particular line. And now in this chapter, you will learn how to locate point which is not present on that line, but at some other place. In this chapter students will be introduced to the concept of Cartesian system, plotting a point in the plane if its coordinates are given. Make yourself aware of X and Y axis and plot a point using a graph. There are 5 exercises in this chapter including the summary.

**Chapter 4: Linear Equations and Two variables**

In previous classes, you understood linear equations in one variable and now it’s the time to add one more variable. In this chapter, students will understand what is a linear equation, solving linear equations, graphical representation of linear equation in two variables, equations of lines parallel to the x-axis, and y-axis. Like other chapters there are 5 exercises including the summary exercise. Attempt all the questions for knowing your practice, and consult our book in case you need any help.

**Chapter 5: Introduction To Euclid’s Geometry**

Here students will learn about Euclid’s definition, axioms, and postulates, equivalent versions’ of Euclid’s fifth postulate. There is a theorem in this chapter which states that two distinct lines can’t have more than one common point. Solve the exercises, know about the postulates of Euclid for grasping the chapter in a better way. And yes for any kind of difficulty refer our book containing solutions of all exercises.

**Chapter 6: Lines and Angles**

In chapter 5 students understood that the minimum two points are needed to draw a line, they also became aware of some axioms. Now, this chapter introduces students to the basic terms and definition of line and angles. Students will learn about intersecting and non-intersecting lines, pair of angles, transversal and parallel lines, lines parallel to the same line, and finally the angle sum property of a triangle. And like previous chapters, this chapter also ends up with exercises.

**Chapter 7: Triangles**

In your previous classes, you learned about triangles and their properties and in chapter 6 you understood some triangle properties. Students will learn about the congruence of triangles, criteria for congruence of triangles, properties of a triangle, and inequalities in a triangle in this chapter. Congruent triangles are those triangles who are equal in size or you can say a replica of each other. Learn more about congruent triangles and solve the exercises at the end.

**Chapter 8: Quadrilaterals**

In previous chapters, students learned about triangles which have three angles. Now add one more angle in the figure and see what comes up. A quadrilateral has 4 angles. Here, students will learn about the angle sum property of quadrilaterals, different type of quadrilaterals, properties of a parallelogram, conditions that make a quadrilateral parallelogram. Finally, students will be introduced to the concept of the mid-point theorem. So learn the new concepts and take our help in case you stuck somewhere.

**Chapter 9: Areas of parallelogram and triangles**

In this chapter, students will learn about figures having the same base and between the same parallels, parallelograms on the same base and between the same parallels, triangles on the same base and between the same parallels. Also, learn about trapezium. There are 4 exercises in this chapter. Solve each of them, initially, you may find them difficult, but try to attempt them by yourself and take the guidance of our book in case of any doubt.

**Chapter 10: Circles**

Here students will learn what is a circle and its related terms, the angle of a chord at a point, perpendicular from the center to a chord, circle through three points, equal chords and their distance from the center, the angle subtended by the arc of a circle, and cyclic quadrilaterals. There are 2 theorems in this chapter related to chords. Go through these theorems and learn how to prove them. Refer our solved book in case you face any difficulty.

**Chapter 11: Construction**

In previous chapters, you came across triangles. But those triangles were not made with precision. As those were for your understanding purpose only. Now in this chapter, students will learn about the basics of construction, and work with some construction on triangles. Know how to measure the angle with protector, how to draw perpendicular and how to use the compass. You may find this chapter interesting if you get the correct knowledge of construction. Solve the exercises at the end.

**Chapter 12: Heron’s formula**

From previous chapters, you have an understanding of squares, triangles, rectangles, and quadrilaterals. You know how to calculate perimeters and area. Now in this chapter calculate the area with a different formula. Here, students will learn about the area of a triangle as per Heron’s formula, application of heron’s formula while finding the area of a quadrilateral. Solve the exercise and take a grasp on this new formula.

**Chapter 13: Surface Area and Volumes**

Through previous chapters, you became aware of the area and perimeter of figures. Now learn about new shapes and sizes in this chapter and how to calculate their volume and surface area. Here students will learn about calculating the surface area of cuboid, and cube, right circular cylinder, right circular cone, the surface area of a sphere, Volume of a cuboid, the volume of a cylinder. Moreover, students will come to know about the volume of right circular cone, and volume of a sphere.

**Chapter 14: Statistics**

In your day-to-day life, you may come across various data in newspaper or magazines. You can also take an example of polling results. All these data, when kept in a meaningful manner is called statistics. Here, in this chapter students will learn about data collection, data presentation, representing data graphically, measurement of central tendency. Solve exercises and learn about the calculation of mean, median and mode. As these three are important from a statistics point of view.

**Chapter 15: Probability**

In this chapter, students will become familiar with the concept of probability and its experimental approach. Probability is nothing but the uncertainty of any circumstances. And in mathematics, it is possible to calculate probability. The chapter contains activities which you need to do by yourself. It also contains examples along with the exercises. Understand examples and solve exercises for achieving mastery in probability.