Master Your Maths with NCERT Solutions

NCERT Solutions

Several new concepts are introduced in the curriculum of class 9. With the introduction of new concepts, students find some of the subjects more interesting whereas some subjects seem to be even more difficult. Of all the subjects in the curriculum of class 9, Maths is one of the most scoring subjects. While students struggle with a few subjects, Maths helps students to improve their aggregate percentages. The overview of some of the interesting chapters that will be introduced in class 9, is discussed below.

Number System:

This chapter of Maths introduces the concepts of rational, irrational and real numbers. Inserting one or more rational numbers between two given rational numbers will be taught in this chapter. Sums on identifying the rational and irrational numbers and converting rational numbers into decimals are also included in this chapter. In this chapter, there are sums for identifying the recurring and non-recurring decimals. The most scoring part of this chapter is the representation of numbers on the number line. Both the rational and irrational numbers, (the numbers having square root values) will be represented on the number line. Once students become familiar with the concepts of rational and irrational numbers, they will be able to learn the method of rationalization. In this method, the numbers that have irrational denominator can be rationalized. Both the numerator and denominator of the irrational number are multiplied by an appropriate number to rationalize the denominator. 


The concept of polynomials and their operations are required for understanding linear algebra and other related chapters. When more than two terms are there in an algebraic expression, then it is termed as a polynomial. Those algebraic expressions that have only one term, are called monomials. Those algebraic expressions that have two terms are called binomials. Those algebraic expressions that have more than two terms are called polynomials. In this chapter, there are sums for determining the coefficients of the terms in the polynomials. Also, there are sums for finding the degrees of polynomials. The remainder theorem and the process of determining the number of zeroes will be explained in this chapter as well. 

Coordinate Geometry:

In this chapter, the concept of coordinate axes and coordinate planes are introduced. Two axes, namely the x-axis and y-axis, and the corresponding quadrants are introduced in this chapter. The x-axis is the horizontal line and the y-axis is the vertical line. These two axes are mutually perpendicular to each other. These two axes make four quadrants. Once students become familiar with the axes and quadrants, they are able to solve the sums of the cartesian system. The x-axis and in one plane, known as the xy plane or the cartesian plane. Locating a given point on the coordinate plane, finding its ordinate and abscissa are some of the basic sums of this chapter. The abscissa of the point is its x-ordinate while the ordinate is its y coordinate.      

Linear Equations in two variables

This concept of linear equations in two variables will help students to solve the sums of several other chapters. This chapter is also referred to as ‘Simultaneous Equations’ in some books. The questions of this chapter will have two or more unknown quantities that have to be determined. The questions will have some information about the unknown quantities using which two equations can be framed. The concept of linear equations will help students to solve sums of various other chapters such as compound interest, percentage, quadrilaterals, polygons, profit loss, and discount, etc.

Lines and Angles:

In this chapter, students will learn about the various types of angles and their applications. The common types of angles include vertically opposite angles, corresponding angles, alternate angles, co-interior angles, complementary angles, supplementary angles, etc. The sums of this chapter require finding unknown angles in parallel lines, triangles. 


After learning about the various angles, the theorems of triangles are apparently easy to learn. In this chapter, the axioms of congruency of triangles are explained. The sums of this chapter are mostly related to the proofs of the congruency of triangles. Some sums require solving for the proof of congruency itself while some sums require related proofs of congruent triangles. The axioms of congruency include:

  • Angle Side Angle (ASA)
  • Side Side Side (SSS)
  • Side Angle Side (SAS)
  • Angle Angle Side (AAS)
  • Right angle, Hypotenuse, and Side (RHS)


In this chapter, quadrilaterals like rhombus, rectangle, square, parallelogram, etc are discussed. The properties of these quadrilaterals are explained with examples and diagrams. There are properties for diagonals, centroids, medians, altitudes, etc. Solving the sums of this chapter requires proper knowledge of the properties of all the quadrilaterals, thoroughly.

The above-mentioned chapters cover some of the most important concepts of Maths, that will be useful in the higher classes. Since some of the chapters are new, students may refer to the maths NCERT solutions class 9 by Vedantu, available on various online study portals. These step by step solutions are helpful for self-assessment of students, especially for revisions.

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