Class 9 is the transition from middle school to high school. This is the stage that provides a foundation for their upcoming classes and a base for their board examinations. It is the CBSE Class 9 Mathematics NCERT textbooks are updated and revised frequently. The students of class 9th always get a syllabus that is according to the current trends that are being followed across the world. The subject experts compile the NCERT books throughout the nation after extensive research. They go through the process of researching the best curriculum and compiling this textbook to provide pertinent and authentic information. The subject materials provided in the book are well-balanced with enough content to cater to the curious minds and nurture their educational growth. The materials have been designed to clear out all the fundamental concepts and basics on all topics.

Learning important concepts given in the syllabus is very important for every student to get better marks in examinations. Better understanding helps in faster learning. And Mathematics is a subject full of concepts and practice is key to score marks in this subject, and it is essential for Class 9 students to focus on understanding every concept thoroughly since the topics of upcoming classes are based on the topics provided to them now. Without NCERT Solutions, students may find it challenging to answer every question. After considering this, Aakash provides free solutions to NCERT Class 9 Mathematics. These solutions have been prepared after thorough research of the grade subject and about the current educational demands. The solution includes all essential topics in proper order to make sure that students systematically use them. This is one of the key features that make it stand out from the other NCERT Solutions available online.

The experienced faculty and the subject experts of Aakash together solve and compile to prepare the NCERT Solution. The solutions are prepared in a transparent manner to clear all the queries the students may have. It gives the students a clear understanding of complex concepts step by step and eventually the subject as a whole. These solutions undertake the responsibility to improve the knowledge and the marks obtained by the student in assessments. To ensure better understanding, the language that is used in explanations is elementary, which makes the students with slow comprehension skills understand as well. These solutions are divided into a Chapter-wise as well as Topic-wise fashion to ensure the students’ in-depth understanding. Aakash makes sure that no syllabus or topic is left uncovered.

Aakash’s NCERT Solutions for Class 9 Mathematics provides Solutions to all chapters to help reduce stress due to problems in understanding concepts and eases the tension. This is highly recommended for students who self-study. If the students still face a problem with the subject and have more doubts about being clarified, Aakash holds doubt sessions to aid students with their doubts.

We provide free PDF material for all NCERT Solutions for Class 9 Mathematics, and we highly recommend the students to download and go through the same after studying their NCERT subject textbook. Doing this can improve the students’ level of understanding and clarify concepts or topics they were not clear about before. They help in the in-depth knowledge and understanding of basics and immensely help students score better marks.

This is the first chapter of NCERT Class 9 Mathematics, and it deals with the number line, and types of Real Numbers, i.e., Rational number and its types such as Natural Numbers, Whole Numbers, Integers, Fractions, Decimals, and Irrational Numbers. It introduces students to the Laws of Exponent for real numbers such as Product Law, Quotient Law, Power Law and Power of Product and the Operation on real numbers. Students learn to spot Rational and Irrational Numbers, Decimal Expansions, Complex Numbers, and Imaginary Numbers.

The chapter will teach the students, the meaning, types and degree of Polynomials, Classification of Polynomials such as Monomials, Binomials and Trinomials, Classification of Polynomials based on degree such as Linear Polynomial, Quadratic Polynomial and Cubic Polynomial, Zeros of Polynomials, Remainder Theorem and Operations on Polynomials like Addition, Subtraction, Multiplication, Division and Factorisation of Polynomials.

This chapter introduces students to the meaning of Coordinate geometry and its systems which includes, Number Line, Cartesian Coordinate System, Plane and Three-Dimensional. It mainly focuses on the topic Coordinate Geometry in a Plane where students learn to plot a point in the plane if its coordinates are given.

This chapter explains the meaning of Linear Equations. It deals with the various methods of solving Linear Equations like Graphical Method where students learn to solve linear equations in two variables by plotting a graph and Substitution Method and Equations of lines parallel to the x-axis and y-axis.

This is a narrow chapter that mainly focuses on and introduces students to various definitions given by Euclid for plane geometry, Euclidean Geometry Axioms, and Euclid’s Five Postulates and Equivalent Versions of Euclid’s Fifth Postulate.

This chapter deals with basic applications of angles and their relationship with lines. Students learn how angles are formed and their properties a) when two lines intersect each other and b) when a line intersects two or more parallel lines at distinct points.

This chapter recalls the properties and Congruence of Triangles. It further states the Criteria for congruence of triangles (also called as rules of congruency) such as SSS (Side-Side-Side) Criterion, SAS (Side-Angle-Side) Criterion, ASA (Angle-side-Angle) Criterion and RHS (Right Angle-Hypotenuse-Side) Criterion and ASA (Angle-Side-Angle) Criterion with some axioms and theorems. It explains about Corresponding Parts of Congruent Triangles (CPCT).

This chapter deals with the Angle Sum Property of a Quadrilateral, Types of Quadrilaterals such as Trapezium, Parallelograms, Rectangle, Rhombus, Square, and Kite. It further elucidates the Properties of a Parallelogram and Conditions for a Quadrilateral to be a Parallelogram. This chapter also introduces students to the Mid-Point Theorem.

This chapter recalls the meaning of the area and explains the methods of calculating Areas of Parallelograms and Triangles. It deals with basic concepts of Areas of Parallelograms and Triangles, Figures on the Same Base and Between the Same Parallels, Triangle on the Same Base and Between the Same Parallels and Parallelograms on the Same Base and Between the Same Parallels.

This chapter lists out the Properties of Circle and terms relating to circles such as Diameter, Circumference, Radius, Arc, Chord, Sector, Secant and Tangent. It also elucidates the 5 important theorems of Circle. It deals with other related topics and such as Angle Subtended by a Chord at a Point, Angle Subtended by an Arc of a Circle, Perpendicular from the Centre to a Chord, Circle through Three Points, Equal Chords and Their Distances from the Centre and Cyclic Quadrilaterals.

This chapter has the target to provide a basic understanding of how shapes are formed and elucidates the steps to constructing a bisector, a perpendicular bisector and triangles. Students learn to bisect a given angle, construct a triangle given its perimeter and two base angles, construct a triangle given its base, the sum of the other two sides, and a base angle, construct an angle of 60 degrees, and to draw perpendicular bisector of a given line segment.

In this chapter, students are recalled the concepts learned in their previous classes in the introduction. It further depicts the properties of different shapes and figures and the application of Heron’s formula to find out the Area of Triangle and Areas of Quadrilaterals, and the derivations of the formula.

This chapter deals with calculating the Surface Area of various objects with different shapes like a Cuboid and a Cube, Right Circular Cylinder, Right Circular Cone and a Sphere. It further teaches students how to calculate the volumes of various objects with different shapes such as Cuboid, Cylinder, Right Circular Cone, and a Sphere.

This chapter gives the meaning of statistics and the implementation of statistics in our day-to-day lives. It deals with topics such as Collection of Data, i.e., gathering data by performing an activity, Presentation of Data, i.e., find out the ways to present the collected data, and Graphical Representation of Data, i.e., graphs where each item of the data is comparable. This chapter introduces the topic, Measures of Central Tendency.

In this narrow chapter, students are introduced to the basic concept and meaning of probability. It also depicts the rules and methods to find out the probability of a particular event and the outcome of events.

Maths is one of the most important subjects for students belonging to any class. It plays a vital role in increasing the students’ assessment score. Various students find it difficult to follow the steps. The syllabus leads to stress and confusion.

Aakash utilizing their solutions PDF tries to give a solution to every numerical. This ensures that every student can have a holistic approach in understanding the concept and practising the question on their taking the necessary help from the Aakash Solutions PDF.

The Aakash NCERT Solutions for Mathematics have the following highlights:

- Step-by-Step solution to ensure the understanding of the solving process by the student.
- Solutions to all the problems, whether numerical or proving for grade 9 in NCERT mathematics has been provided.
- The language used in communication has been kept very easy to make it understandable to all.
- Every step has the necessary reasons to ensure a clear understanding of the flow of steps.
- The NCERT Solutions are provided without any cost by the Aakash Institute.
- The Solutions are prepared and compiled by industry leaders and experts in teaching the subject with years of experience.

**Q**. Where to find and download NCERT Solutions for Class 9 Mathematics?

**A**. Aakash provides free NCERT Solutions in PDF format for NCERT Class 9 Mathematics which is available on the Aakash website. The solutions are arranged in a proper sequence topic-wise.

**Q**. What is remarkable in the Aakash NCERT Solutions for Class 9th Maths?

**A**. Every step to the solution in the PDF provided is clearly explained to help students. It is to aid them to gain a clear idea of the concept. Aakash ensures that a thorough study of the material will enable the students to obtain an insight into each concept and method. Furthermore, the students will be able to solve any numerical question or prove the question posed to them from any topic.

**Q**.Will just browsing through the NCERT solutions for class 9th mathematics be enough to score good marks?

**A**.To ensure good marks in mathematics, the student needs to practise solving the problems as well. It is only by practise that he/she would know about the method and solve the question in the assessment. Reading or browsing through the solutions PDF is not enough. A student can find NCERT solutions for class 9th mathematics on Aakash website.

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