## NCERT Maths Class 9 Solutions

Maths can be the subject of a lot of nightmare for students! Some do enjoy it but others are quite reluctant to approach it. Students need to understand this subject in totality to appreciate it. Class 9^{th} mathematics aims to provide the student with a holistic and fundamental approach to topics that forms the base for concepts that they will learn in higher classes. The chapters covered in NCERT Maths Class 9 Solutions are:

- Number System
- Polynomial
- Coordinate Geometry
- Linear Equations in Two Variables
- Introduction to Euclid’s Geometry
- Lines and Angles
- Triangles
- Quadrilaterals
- Areas of Parallelograms
- Circles
- Constructions
- Heron’s Formula
- Surface Areas and Volumes
- Statistics
- Probability

The study material that is provided, aims to allow the student to judge the manner of solving the mathematics problems given subject wise. It also helps them to then be able to tackle similar maths problems and enables them to solve it in the easiest possible manner. Elaborate explanations are provided to clear any doubts.

The subheads of each chapter are mentioned below for easy understanding.

## Number System

The number system is a way of expressing numbers. The mathematical notations that are used to represent numbers of a given particular set with the help of digits or any other symbol in a more or less consistent manner. The different number systems are dealt with are –

- Decimal number system (Base- 10)
- Binary number system (Base- 2)
- Octal number system (Base-8)
- Hexadecimal number system (Base- 16)

## Polynomial

Polynomial means many terms. Therefore a polynomial can have many terms including constants, variables and exponents. The chapter deals with the different kinds of polynomials, non-polynomials, special kinds of polynomials such as monomial, binomial, trinomial. Degrees of a polynomial. The standard form of a polynomial. Operations with polynomials such as addition, multiplication, subtraction, division etc.

## Co-ordinate Geometry

This chapter deals with the link between algebra and geometry using graphs, curves, lines etc. The geometric aspect of algebra is explored in this chapter. It discusses what co-ordinate and coordinate planes are and how to read Cartesian planes.

## Linear Equations in Two Variables

Equations with two variables are known as a linear equation in two variables. This chapter will help the student differentiate between linear equation in one variable and linear equation in two variables. It also helps the student grasp the concept of solving equations in such a format.

Chapter-4-Linear-equations-in-two-variables

## Introduction to Euclid’s Geometry

Geometry deals with the shape, position, size and spatial relationship of figures. This chapter deals with the advent of geometry. The history of Euclidean geometry. Euclid’s postulates.

Chapter-5-Introduction-to-Euclids-Geometry

## Lines and Angles

Since geometry deals with shapes and sizes of figures and properties, one needs to learn more about the lines and angles. This chapter deals with the basics of lines and its definition. Angles, its various terms such as vertex, arm etc. Different angles such as right angle, acute angle, obtuse angle, straight angle, complementary angle, adjacent angle, reflex angle etc.

## Triangles

This chapter deals with the various types of triangles, the definition of triangle, Triangles classified on the basis of length, scalene triangle, isosceles triangle, equilateral triangle. Then Triangles on the basis of their angle. Acute angled triangle, right angle triangle, obtuse angle triangle. Properties of a triangle. Area of a triangle. Area using herons formula.

## Quadrilaterals

A polygon that has four sides or edges – four corners or vertices. They can be squares, kites, rectangles, trapezoids etc. Introduction to different kinds of quadrilaterals. Classification into concave, convex and intersecting. Properties of a quadrilateral.

## Area of Parallelogram

It is a type of quadrilateral where the opposite sides are parallel. Area is deduced using the properties of parallelogram and triangle. Topics discussed are area axiom, congruent axiom.

Chapter-9-Areas-of-Parallelograms-and-Triangles

## Circles

It is a shape that is closed with a set of points in a plane that are at a specific distance from the center. It deals with the concepts of radius, diameter, circumference and derivation of the area of a circle.

## Constructions

It discusses the construction of a geometric figure using tools such as rulers, protractors, compasses etc. How to construct different shapes such as circles, triangles, squares etc.

## Herons Formula

Heron, who was a mathematician, derived the formula for calculating the area of a triangle with the help of the measurement of the length of all three sides. The chapter discusses the derivation of Herons formula and how to use it.

## Surface Area and Volumes

This chapter discusses total surface area, curves surface area. How to determine volume. The surface area and volume formulae for various shapes such as square, rectangle, parallelogram, triangle, circle etc.

Chapter-13-Surface-Areas-and-Volumes

## Statistics

Provides with the definition of statistics. What are mathematical statistics and its scope? The various methods of deriving the same from data collection, data summarization and analysis. The various kinds of data, various graphs and depictions of statistics as well as formulas used.

## Probability

The chapter covers the line of probability. The general probability formula, terms related to probability, conditional probability

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