NCERT Solutions for Class 9 Maths

NCERT Solutions for Class 9 Maths include stepwise solutions to all NCERT exercise questions from experts. These solutions are provided in a detailed manner so that every student can understand the concepts easily. They are self-explanatory so that students can revise Maths concepts on their own at any time. Students can download these solutions for free from the askIITians website and refer to them whenever they want. 

NCERT solutions can help students in a plethora of ways like:

• Preparing for end-term exams and unit tests
• Understanding Maths concepts 
• Preparing for competitive exams and olympiads
• Ensuring a solid foundation for Class 10 Maths 
• Increasing theoretical and practical knowledge 

Free NCERT Solutions for Class 9 Maths from askIITians

All these NCERT solutions for Class 9 Maths are prepared by askIITians faculty so that students can study for their Maths exams easily. Anyone can access these free solutions and download them for future reference. NCERT Class 9 Maths includes 15 Chapters on topics like number systems, coordinate geometry, linear equations in two variables, Euclid’s geometry, Heron’s formula, statistics, probability, etc. Given below is a chapter-wise list of NCERT question-answers for Class 9 NCERT Maths. 

Class 9 Maths NCERT Solutions | Chapter 1 to 15 

Download NCERT Class 9 Maths Solutions for Chapter 1 Number System

Chapter 1 Number Systems in NCERT Class 9 Maths book helps students understand important concepts like irrational numbers, real numbers and their decimal representation, representing real numbers on the number line, operations on real numbers, and laws of exponents for real numbers. There are 6 exercises in this chapter each of which are solved by our Maths experts for the students. Most of them are application-based questions which include formulae like:

1. √(a/b) = √a/√b
2. √ab = √a √b
3. (√a + √b) (√a – √b) = a – b
4. (a + √b) (a – √b) = a2 – b
5. (√a + √b) (√c + √d) = √ac + √ad + √bc + √bd
6. (√a + √b)2 = a + 2√ab + b

Class 9 Maths NCERT Chapter 1 Solutions

Chapter 1 Class 9 Maths Ex 1.1 - 4 Questions Chapter 1 Class 9 Maths Ex 1.2 - 4 Questions Chapter 1 Class 9 Maths Ex 1.3 - 9 Questions Chapter 1 Class 9 Maths Ex 1.4 - 2 Questions Chapter 1 Class 9 Maths Ex 1.5 - 5 Questions Chapter 1 Class 9 Maths Ex 1.6 - 3 Questions

Download NCERT Class 9 Maths Solutions for Chapter 2 Polynomials

NCERT Class 9 Maths Chapter 2 Polynomials introduces the concepts of polynomials in one variable, zeros of a polynomial, remainder theorem, and factorization of polynomials. It also includes important algebraic identities that will help students in further classes as well. Some important formulae used in solving the NCERT questions of this chapter include: 

• (x + y)2 = x2 + 2xy + y2
• x2 - y2 = (x + y) (x - y)
• (x + a) (x + b) = x2 + (a + b)x + ab
• (x - y)2 = x2 - 2xy + y2
• (x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx

There are a total of 5 exercises in this chapter with the majority of questions involving conceptual understanding of basic polynomials. We have provided step-by-step solutions to the chapter below:

Class 9 Maths NCERT Chapter 2 Solutions

Chapter 2 Class 9 Maths Ex 2.1 - 5 Questions Chapter 2 Class 9 Maths Ex 2.2 - 4 Questions Chapter 2 Class 9 Maths Ex 2.3 - 3 Questions Chapter 2 Class 9 Maths Ex 2.4 - 5 Questions Chapter 2 Class 9 Maths Ex 2.5 - 16 Questions

Download NCERT Class 9 Maths Solutions for Chapter 3 Coordinate Geometry

Chapter 3 of the Class 9 Maths NCERT textbook includes topics like the cartesian system and plotting a point in the plane if its coordinates are given. This chapter is quite interesting and it is easy to score full marks in this chapter if studied properly. Our NCERT solutions will help you understand every topic of this chapter clearly. There are three exercises in this that we have solved for your reference. Download them right away for free. 

Class 9 Maths NCERT Chapter 3 Solutions

Chapter 3 Class 9 Maths Ex 3.1 - 2 Questions Chapter 3 Class 9 Maths Ex 3.2 - 2 Questions Chapter 3 Class 9 Maths Ex 3.3 - 2 Questions

Download NCERT Class 9 Maths Solutions for Chapter 4 Linear Equations in Two Variables

Chapter 4 of NCERT Class 9 Maths solutions teaches what a linear equation is and how to find the solution of a linear equation. You will also study how to plot the graph of linear equations with two variables on the x-y plane. Then, you will study how to write the equations of lines parallel to the x-axis and y-axis. There are 4 exercises in this chapter that we have solved for you. 

Important points included in NCERT Class 9 Maths Chapter 4 are: 

1. A linear equation with two variables may have infinitely many solutions. 
2. The graph of a linear equation is always a straight-line graph. 
3. The equation of the y-axis is x = 0.
4. The equation of the x-axis is y = 0.
5. The equation of a line passing through origin is y=mx. 

Class 9 Maths NCERT Chapter 4 Solutions

Chapter 4 Class 9 Maths Ex 4.1 - 2 Questions Chapter 4 Class 9 Maths Ex 4.2 - 4 Questions Chapter 4 Class 9 Maths Ex 4.3 - 8 Questions Chapter 4 Class 9 Maths Ex 4.4 - 2 Questions

Download NCERT Class 9 Maths Solutions for Chapter 5 Introduction to Euclid’s Geometry

Chapter 5 of the Class 9 Maths NCERT textbook is about Euclid’s geometry. It includes some important Axioms and Postulates by Euclid. There are just two exercises in this chapter. So you must complete this chapter quickly and score full marks in it. Most of the questions test your analytical skills in this chapter. Read our solutions carefully and understand the concepts for better learning. 

The five Postulates by Euclid are:

Postulate 1 – A straight line may be drawn from anyone point to any other point.

Postulate 2 – A terminated line can be produced indefinitely.

Postulate 3 – A circle can be drawn with any centre and any radius.

Postulate 4 – All right angles are equal to one another.

Postulate 5 – If a straight line falling on two straight lines makes the interior angles on the same side of it taken together less than two right angles, then the two straight lines, if produced indefinitely, meet on that side on which the sum of angles is less than two right angles.

Class 9 Maths NCERT Solutions Chapter 5 Exercises

Chapter 5 Class 9 Maths Ex 5.1 - 7 Questions Chapter 5 Class 9 Maths Ex 5.2 - 2 Questions

Download NCERT Class 9 Maths Solutions for Chapter 6 Lines and Angles

NCERT Class 9 Maths Solutions for Chapter 6 include topics like intersecting and non-intersecting lines, pairs of angles, parallel lines, transversal, and angle sum property of a triangle. You must understand the concepts of this chapter thoroughly as the topics you learn here will help you in forming a strong foundation for higher classes. There are just 2 exercises in this chapter so make sure you solve all the questions carefully and practice well. Our online NCERT solutions will help you understand this chapter thoroughly.

Class 9 Maths NCERT Chapter 6 Solutions

Chapter 6 Class 9 Maths Ex 6.1 - 6 Questions Chapter 6 Class 9 Maths Ex 6.2 - 6 Questions Chapter 6 Class 9 Maths Ex 6.3 - 6 Questions

Download NCERT Class 9 Maths Solutions for Chapter 7 Triangles

askIITians’ online NCERT Solutions for Chapter 7 include important topics related to triangles and their properties. These solutions will help you understand how to find if two or more triangles are congruent with each other and how to find the equality of two triangles. 

Some important theorems included in the Triangles chapter are:

1. SAS congruence rule – Two triangles are congruent if two sides and the included angle of one triangle are equal to the two sides and the included angle of the other triangle.
2. ASA congruence rule – Two triangles are congruent if two angles and the included side of one triangle are equal to two angles and the included side of the other triangle.
3. Angles opposite to equal sides of an isosceles triangle are equal.
4. The sides opposite to equal angles of a triangle are equal.
5. SSS congruence rule – If three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent.
6. RHS congruence rule – If in two right triangles the hypotenuse and one side of one triangle are equal to the hypotenuse and one side of the other triangle, then the two triangles are congruent.
7. If two sides of a triangle are unequal, the angle opposite to the longer side is larger (or greater).
8. In any triangle, the side opposite to the larger (greater) angle is longer. 
9. The sum of any two sides of a triangle is greater than the third side.

There are 5 exercises in this chapter that will help you understand all these theorems. We have provided step-by-step solutions for every question. Download them from the links given below:

Class 9 Maths NCERT Chapter 7 Solutions

Chapter 7 Class 9 Maths Ex 7.1 - 8 Questions Chapter 7 Class 9 Maths Ex 7.2 - 8 Questions Chapter 7 Class 9 Maths Ex 7.3 - 5 Questions Chapter 7 Class 9 Maths Ex 7.4 - 6 Questions Chapter 7 Class 9 Maths Ex 7.5 - 4 Questions

Download NCERT Class 9 Maths Solutions for Chapter 8 Quadrilaterals

NCERT Class 9 Maths Solutions for Chapter 8 are available on our website for free. These solutions will help you understand all the important topics of this chapter like angle sum property, types of quadrilaterals, properties of a parallelogram, and the mid-point theorem. Important theorems of this chapter include: 

1. A diagonal of a parallelogram divides it into two congruent triangles
2. In a parallelogram, opposite sides are equal.
3. If each pair of opposite sides of a quadrilateral is equal, then it is a parallelogram.
4. In a parallelogram, opposite angles are equal.
5. If in a quadrilateral, each pair of opposite angles is equal, then it is a parallelogram.
6. The diagonals of a parallelogram bisect each other. 
7. If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.
8. A quadrilateral is a parallelogram if a pair of opposite sides are equal and parallel.
9. The line segment joining the mid-points of two sides of a triangle is parallel to the third side.
10. The line drawn through the midpoint of one side of a triangle, parallel to another side bisects the third side.

Class 9 Maths NCERT Chapter 8 Solutions

Chapter 8 Class 9 Maths Ex 8.1 - 12 Questions Chapter 8 Class 9 Maths Ex 8.2 - 7 Questions

Download NCERT Class 9 Maths Solutions for Chapter 9 Areas of Parallelograms and Triangles

Class 9 Maths NCERT Chapter 9 solutions are about finding areas of parallelograms and triangles. You will also learn how to find areas of geometric figures provided they lie on the same base and between the same parallels. You must revise the following three theorems before you solve the NCERT questions: 

1. Parallelograms on the same base and between the same parallels are equal in area.
2. Two triangles on the same base (or equal bases) and between the same parallels are equal in area.
3. Two triangles having the same base (or equal bases) and equal areas lie between the same parallels.

There are 4 exercises in this chapter. Download the NCERT solutions for free from our website and start solving the exercise questions immediately. 

Class 9 Maths NCERT Chapter 9 Solutions

Chapter 9 Class 9 Maths Ex 9.1 - 1 Question Chapter 9 Class 9 Maths Ex 9.2 - 6 Questions Chapter 9 Class 9 Maths Ex 9.3 - 16 Questions Chapter 9 Class 9 Maths Ex 9.4 - 8 Questions

Download NCERT Class 9 Maths Solutions for Chapter 10 Circles

Chapter 10 of NCERT Class 9 Maths is about circles. You will study topics like angle subtended by a chord at a point, perpendicular from the centre to a chord, circle through three points, the angle subtended by an area of a circle, etc. We have solved every question stepwise so that every student can understand them on their own. There are more than 10 theorems in this chapter. Here are a few important ones:

1. Angles in the same segment of a circle are equal.
2. The line is drawn through the centre of a circle to bisect a chord that is perpendicular to the chord.
3. If the sum of a pair of opposite angles of a quadrilateral is 180º, the quadrilateral is cyclic.
4. Equal chords of a circle (or of congruent circles) are equidistant from the centre (or centres).
5. Chords equidistant from the centre of a circle are equal in length.
6. The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.
7. The sum of either pair of opposite angles of a cyclic quadrilateral is 180º.

There are 6 exercises in this chapter that test your numerical, analytical, and problem-solving skills. Our online NCERT solutions will help you in solving every question easily. Download them from the links given below. 

Class 9 Maths NCERT Chapter 10 Solutions

Chapter 10 Class 9 Maths Ex 10.1 - 2 Questions Chapter 10 Class 9 Maths Ex 10.2 - 2 Questions Chapter 10 Class 9 Maths Ex 10.3 - 3 Questions Chapter 10 Class 9 Maths Ex 10.4 - 6 Questions Chapter 10 Class 9 Maths Ex 10.5 - 12 Questions Chapter 10 Class 9 Maths Ex 10.6 - 10 Questions

Download NCERT Class 9 Maths Solutions for Chapter 11 Constructions

NCERT Solutions for Class 9 Maths Chapter 11 help you understand topics like how to construct triangles, perpendicular bisectors, and various angles. This is a scoring chapter and one of the easiest chapters of Class 9 Maths. So, you must solve its exercises and make sure all the concepts are clear to you. There are just 2 exercises in this chapter. So download the NCERT solutions right away and start practising.

Class 9 Maths NCERT Chapter 11 Solutions

Chapter 11 Class 9 Maths Ex 11.1 - 5 Questions Chapter 11 Class 9 Maths Ex 11.2 - 5 Questions

Download NCERT Class 9 Maths Solutions for Chapter 12 Heron’s Formula

Heron’s formula is an important formula that will help you solve many questions in olympiads and competitive tests. Class 9 Maths Chapter 12 is based on Heron's formula. This formula is used to find the area of a triangle when the length of all its sides is given. With this formula, you can find areas of different types of triangles like equilateral, isosceles, or scalene triangles. The following formulae will help you solve the NCERT exercise questions of this chapter.

• Semi Perimeter s = (a + b + c)/2
• Area of a Triangle = √[s (s - a) (s - b) (s - c)]

You can easily score full marks in this chapter if you solve all the exercise questions. There are two exercises in this chapter, the solutions of which are given below. Just click on the links and download exercise-wise online NCERT solutions. 

Class 9 Maths NCERT Chapter 12 Solutions

Chapter 12 Class 9 Maths Ex 12.1 - 6 Questions Chapter 12 Class 9 Maths Ex 12.2 - 9 Questions

Download NCERT Class 9 Maths Solutions for Chapter 13 Surface Areas and Volumes

NCERT Solutions for Class 9 Maths Chapter 13 include topics like the surface area of a cube, cuboid, right circular cylinder, right circular cone, and sphere. These solutions also include finding the volume of a cuboid, cylinder, right circular cone, and sphere. Important formulae used in this chapter include: 

• TSA of a Cuboid = 2(lb + bh + hl)
• TSA of a Cube = 6a2
• TSA of a Cylinder = 2πr(r + h)
• TSA of a Cone = πr(l + r)
• TSA of a Sphere = 4πr2
• TSA of a Hemisphere = 3πr2

There are 9 exercises in this chapter. It might take time but you must solve all the exercise questions to score full marks in this chapter. We have provided stepwise solutions for all exercise questions so that you can have a complete understanding of all the topics of this chapter. 

Class 9 Maths NCERT Chapter 13 Solutions

Chapter 13 Class 9 Maths Ex 13.1 - 8 Questions Chapter 13 Class 9 Maths Ex 13.2 - 11 Questions Chapter 13 Class 9 Maths Ex 13.3 - 8 Questions Chapter 13 Class 9 Maths Ex 13.4 - 9 Questions Chapter 13 Class 9 Maths Ex 13.5 - 9 Questions Chapter 13 Class 9 Maths Ex 13.6 - 8 Questions Chapter 13 Class 9 Maths Ex 13.7 - 9 Questions Chapter 13 Class 9 Maths Ex 13.8 - 10 Questions Chapter 13 Class 9 Maths Ex 13.9 - 3 Questions

Download NCERT Class 9 Maths Solutions for Chapter 14 Statistics

Online NCERT Solutions for Class 9 Maths Chapter 14 include topics like the collection of data, the grouping of data, representation of data, and measures of central tendency. Statistics is an important chapter that will help you in Class 10. It is also included in the olympiads and competitive tests. So, you must study this chapter with full attention. There are 4 exercises in this chapter. Download their solutions for free from the links given below. 

Class 9 Maths NCERT Chapter 14 Solutions

Chapter 7 Class 9 Maths Ex 14.1 - 2 Questions Chapter 7 Class 9 Maths Ex 14.2 - 9 Questions Chapter 7 Class 9 Maths Ex 14.3 - 9 Questions Chapter 7 Class 9 Maths Ex 14.4 - 6 Questions

Download NCERT Class 9 Maths Solutions for Chapter 15 Probability

NCERT Solutions for Class 9 Maths Chapter 15 include finding the probability of an event. This is a small chapter with only one exercise. So why waste any time? Just solve the NCERT questions and complete the chapter. You can easily score full marks in this chapter. 

Class 9 Maths NCERT Chapter 15 Solutions

Chapter 15 Class 9 Maths Ex 15.1 - 13 Questions

Download NCERT Solutions for Class 9 Maths Today! 

The NCERT book is recommended by every teacher as the concepts taught in NCERT helps students form a solid foundation of Maths concepts. Online NCERT solutions make it easier for students to understand the concepts of every chapter in-depth. They can refer to these solutions at any time based on their convenience. Our Maths experts have provided step by step solutions to the exercise questions of the Class 9 Maths NCERT textbook. Download the solutions for free right away and start learning.