CLASS 10 MATHS

INTRODUCTION –

Class 10 math contains chapters which are sequence like real numbers, polynomials, Pair of Linear Equation in Two variables, Quadratic equations, Arithmetic Progression, Triangles, Coordinate Geometry, Introduction to Trigonometry, Some applications of Trigonometry, Circles, Construction, Area Related to Circles, Surface area and Volumes, statistics, and Probability. These chapters tell us the constructivist approach to the learning of mathematics. It will help to develop the ability to particularize and generalize, to solve and pose meaningful problems, to look for patterns and relationships, and to apply the logical thinking behind the mathematical proof. 

CLASS 10 MATHS-

As we know there are a total of 15 chapters in class 10 maths, which are listed in the sequence above. There are a lot of proofs and solutions that are explained in a systematic manner to help the learner develop a clear and logical way to express the arguments. All the geometric constructions are accompanied by an analysis of the construction and the proof for the steps taken to do the required construction. Below we will talk about the class 10 maths notes in a nutshell for each chapter

CLASS 10 MATHS NOTES-

Let’s discuss each chapter in brief –

  1.REAL NUMBERS-

In chapter I, Real numbers talks about two important properties of positive integers called Euclid’s division algorithm and the Fundamental Theorem of arithmetic. Euclid division algorithm has to do with the divisibility of integers. The Fundamental Theorem of arithmetic on the other hand involves the multiplication of positive integers.    

  2.POLYNOMIALS-

In chapter 2, Polynomials, We already know about polynomials. If p(x) is a polynomial in x, the highest power of x in p(x) is called the degree of polynomial p(x). This chapter tells about linear polynomials, quadratic polynomials, and many more.

  3..PAIR OF LINEAR EQUATIONS IN TWO VARIABLES-

IN Chapter- 3, Linear equations in two variables – chapter tells about how to find the solution through the graphical method, how to solve the pair of equations by the algebraic method, and many more.

 4.QUADRATIC EQUATIONS-

In chapter -4, Quadratic Equations, The standard form of a quadratic equation is given, how to check whether the quadratic equation is a quadratic equation or not. Different methods to find the solution of a quadratic equation like by completing squares, etc.

 5.ARITHMETIC PROGRESSIONS-

Chapter 5, Arithmetic Progressions –  It talks about the meaning of arithmetic Progression, Sum of first n terms of an AP, nth term of AP. 

 6.TRIANGLES-

In chapter-6, Triangles- this chapter talks about what is a triangle, the similarity of triangles, the criteria of similarity of triangles, and many more. 

 7.COORDINATE GEOMETRY-

In Chapter-7, Coordinate Geometry, this chapter tells about the x-axis, y-axis, distance formula, section formula, etc. 

 8.INTRODUCTION TO TRIGONOMETRY-

Chapter- 8 Introductions to trigonometry, the chapter explains the trigonometric ratios, Trigonometric ratios of some specific angles, trigonometric ratios of complementary angles etc. 

 9.SOME APPLICATIONS OF TRIGONOMETRY-

This chapter-9, tells about the ways in which trigonometry is used in the life around you. The knowledge of trigonometry is used to construct maps, determine the position of an island in relation to the longitude and latitude. 

 10.CIRCLES-

The chapter-10 of circles, tells about the definition of a circle, tangent to the circle, number of tangents from a point on a circle. 

 11.CONSTRUCTIONS-

Chapter-11, construction talks about some constructions by using the knowledge of the earlier constructions and the mathematical reasoning behind why such construction work.

 12.AREA RELATED TO THE CIRCLES-

Chapter -12, area related to the circles, explains about perimeter and area of the circle. It even tells about the area of sector and segment of a circle and many more concepts related to the circle. 

 13.SURFACE AREAS AND VOLUMES-

Chapter- 13, we will talk about the surface areas and volumes of solids like cuboids, cones, cylinders, and spheres. 

 14.STATISTICS-

Chapter- 14, statistics discuss the concept of cumulative frequency, the cumulative frequency distribution, and how to draw cumulative frequency curves, called ogives. 

 15.PROBABILITY –

Chapter- 15, Probability provides an introduction to the theoretical also called classical probability of an event and discusses simple problems based on this concept. 

 CLASS 10 MATHS LINEAR EQUATION-

  As we have discussed above what chapter of linear equations covered.  An equation in the form of ax+by+c=0, where a, b, and c are real numbers, and a and b are not both zero, is called a linear equation in two variables x and y. 

This is true for any linear equation, that is, each solution (x, y) of a linear equation in two variables,

ax+by+c=0  corresponds to a point on the line representing the equation, and vice versa. 

GRAPHICAL METHOD-

The graph of a pair of linear equations in two variables is represented by two lines-

• A pair of linear equations that has no solution is called an inconsistent pair of linear equations.
• A pair of linear equations in two variables, which has a solution, is called consistent pair of linear equations.
• The lines may be coincident. In this case, the equation has infinitely many solutions- each point on the line being a solution. The pair of equations is dependent( consistent).  

ALGEBRAIC METHOD-

There are the following methods discussed below to find the solutions of a pair of linear equations-

1. Substitution Method
2. Elimination Method
3. Cross- multiplication Method

CONCLUSION-

The class 10 maths covers the chapters which we have already discussed in brief. The class 10 maths linear equation defines the general form of a pair of linear equations. Two linear equations in the same two variables are called a pair of linear equations in two variables. A pair of linear equations in two variables can be represented and solved by the graphical method and algebraic method. There are several situations that can be mathematically represented by two equations that are not linear to start with. But we alter them so that they are reduced to a pair of linear equations.