Friday 28 September 2012

7th Grade Math

 In the previous post we have discussed about Free word problem solver and In today's session we are going to discuss about 7th Grade Math.

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7th grade math consists of many vital concepts that would be needed to solve higher grade math problems. Let us discuss the 7th grade math as follows:
1. Starting is done with a very basic conceptual understanding of numbers and mathematical operations. Numbers like rational numbers, the roots of perfect square, ratios and proportions, problems on percentages like profit – loss & discounts etc.
2. Learning the decimal numbers, conversion from fractions to decimals and vice – versa, comparison between different types of numbers etc.
3. Understanding scientific representation of numbers, problems involving surds & radicals, functions like absolute value, and also the idea of real numbers.
4. Operations that we learn are like addition, subtraction, multiplication and division of integers, fractions, decimals etc. Solving exponents, logarithms and properties related to them.
5. Learning the characteristics of numbers and using them in solving the maths problems related to algebra.
6. Next comes the geometrical maths which involves the understanding of the characteristics of angles and different shapes. Angles can be categorized as: Adjacent, Vertical, Linear, Complementary, Supplementary or Corresponding angles. Shapes or figures we learn like circles, lines, planes, polygons etc.
7. We learn to sketch the graphs of different figures on basis of their equations. Solving their equations and finding various parameters related to them. Understanding the behaviour of various functions (whether increasing, decreasing, inflection point, critical points etc.)
8. Learning the congruencies of triangles and solving the problems using different corollaries and well – defined theorems.
Let's see how to convert a decimal to a fraction?
A decimal has place values starting from tens place value. We remove the decimal and put number of zeros in front of one in the denominator according to the place values and then solve for the fraction. These concepts are detailed in iit sample papers.

Thursday 27 September 2012

Free word problem solver

In the previous post we have discussed about Seventh Grade Math and In today's session we are going to discuss about Free word problem solver. Mathematical word problem can be defined as a problem that are described in the form of narrative which are answered by converting them into corresponding computational form or in the form of equations. In simple terms we can say that a word problem is a problem which is written in word form and they are solved using mathematical properties. In mathematics, word problem basically deals with real world problems. There are two ways to defined to solve a math word problem that are given below:
A) First we need to convert the words in form of numerical equation or expression.
B) After that we can solve that problem very easily by applying mathematical rules.
Word problem solver free can be used for solving word problems. In school, most of students face difficulties while solving math word problem. To make student capable to successfully deal with these problems there are word problem solver available on Internet. These kinds of word problem solver provide their facility without charging any fees. Word problem solver free can be considered as sophisticated tool which is capable of solving any word problem by accepting problem from user and shows the answer in few seconds.
This kind of problem solver is very useful for those students who are beginners for solving math word problems. First describe the concept very clearly and carefully. After that solve the problem by generating the answer in step by step manner.
Math problem solver helps students to understand basic concepts and operations involved in word problem. In number system, irrational Number Examples include those examples that belong to concept of irrational numbers.
Next we will study Irrational Numbers Examples.
ICSE syllabus 2013 is available online, which can be downloaded for free.

Friday 14 September 2012

Seventh Grade Math



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When we study Seventh Grade Math, we come across number system. In this chapter we will get the detailed knowledge about the types of numbers and their properties.
We start the concept with the study of the natural numbers. All the numbers which start from 1, 2, 3, 4, . . . . . . . . . upto infinite are called natural numbers. We say that the natural numbers are the counting numbers. We observe that each natural number has the successor , which we get by adding 1 to the given number. In the same way each natural number except 1 has a predecessor, which we get be subtracting 1 from the given number.
Now we come to the whole numbers. These numbers are used for measurement of the units. Thus we start whole numbers from 0. All the whole numbers have successors as natural numbers and leaving 0, each number has the predecessor too. Now we look at the Integers. Integers are the series of numbers which start from minus infinite and goes upto + infinite. All the numbers of the series can be expressed on the number line and we observe that the middle most number of the  series of integers in 0. Thus we say that the digits that exist on the right side of the  number 0 are positive numbers and the numbers which exist at the left side of the  number line are all negative numbers. Further we also observe that in the series of integers, all the numbers have their successor and the predecessors.
To learn about the  Measure Of Central Tendency, which is the topic of statistics, we can take help of math online tutors. It is the part of the curriculum of grade 8 of the Icse Syllabus 2013. 

Tuesday 28 August 2012

Unit Circle

In the previous post we have discussed about one to one correspondence and In today's session we are going to discuss about Unit Circle. Unit Circle is defined as a circle that is having radius value is equal to 1. Let's us see the steps of making a this circle. Steps of making a circle is given as:
Step 1: To construct a circle it is very essential to have a radius value is equal to one always. If it is not so then it is not a unit circle.
Step 2: Now draw a tangent and solve equation with the help of Pythagoras theorem.
In mathematical geometry, Equation of circle (unit) is given by: i2 + j2 = 1, here ‘i’ plot the coordinate value along to x – axis and ‘j’ plot the coordinate value along to y – axis.
Now we will discuss the table based on circle. The table is shown below:


s.no
Ó¨ (rad)
Ó¨0
Sin Ó¨
Cos Ó¨
tanÓ¨ = sinÓ¨ / cos Ó¨
1
0
Л / 6
0
30
√0 / 2 = 0
√1 / 2 = 1 / 2
√4 / 2 = 1
√3 / 2
√0 / √4 = 0
√1 / √3 = √3 / 3
2
Л / 3
60
√3 / 2
√1 / 2 = 1 / 2
√3 / √1 = √3
3
Л / 2
90
√4 / 2 = 1
√0 / 2 = 0
----

Using these value we can solve any problem related to unit circle.
Some properties are also based on circle which are given as:
Distance assess from center of circle to any point on a circle is radius of circle. Radius is always half of diameter.
Line that is passing passes through center of circle is diameter of circle. Diameter of circle is always twice the radius value of circle.
Circumference – Formula to calculate circumference of circle is given by: Circumference of circle = 2 лR.
By using Properties of Multiplication we can easily solve the mathematical problems. cbse syllabus for class 9th 2013 is useful for class 9th student.

Saturday 25 August 2012

one to one correspondence


In the previous post we have discussed about algebra quadratic equations and In today's session we are going to discuss about one to one correspondence. In this blog we will see discuss one to one correspondence. One – to – one correspondence is a process in which a condition in which elements of one set (Let a set A) can be properly (or evenly) matched with elements of second set (other set B). Here the meaning of this word evenly is each element of set 'A' relates to one and only one member of set 'B' and each element of set 'B' relates to one and only one member of set 'A'. It means each element of set 'A' is connect with exactly one element of set 'B' and vice versa. Now we will understand the detail of one to one correspondence. If we understand the terms of order pair (x, y) where 'x' is a element of set 'A' and 'y' is an element of set 'B'. Here two orders are not possible for this condition that has first element same and two order is not correct for same element. If this type of condition stable in a set than it shows one – to – one correspondence between sets A and B.

In other words, if two sets have same cardinality than one – to – one correspondence stable among two sets. Let’s have small introduction about one - to - one function. Basically one - to – one function is taken to check whether one – to – one correspondence stable among infinite sets.

Let's we have given a function and if function is one – to – one then one – to – one correspondence lie among the set of positive integers and set of odd positive integer. We can also calculate one – to – one correspondence between rational numbers and integer numbers, (any number represented as ratio of two whole numbers is called as rational number) but we can not calculate one – to – one correspondence among real numbers and integers.

Pythagorean Triples List contains with three positive integers p, q, and r, such that p2 + q2 = r2. Before attempting the 12th board exam please solve cbse sample papers 12.

Saturday 18 August 2012

algebra quadratic equations

In the previous post we have discussed about Factoring Polynomials and In today's session we are going to discuss about algebra quadratic equations. In mathematics, algebra quadratic equations can be defined as an equation that has highest degree equals to 2. In other words it can be defined as an equation that has highest power is a square not more than two. If any expression has highest power more than 2 then it is not quadratic equation. Quadratic equation can be written as: pt2 + qt + r = 0. Formula to solve algebra quadratic expression is given as:

⇨ t = - b + √ (b2 – 4ac) / 2a.
Let’s talk about how to write a quadratic equation if roots value are known. Here we will follow some steps to write a quadratic equation.
Step 1: First of all we take two roots of an equation to write quadratic equation. Let we have two roots of an equation that is 5 and -7.
Step 2: Then we have to put roots in given form of q = (p - a) (p – b), here we put one root for variable ‘a’ and other root for next variable ‘b’. Put both roots in given form:
q = (p - a) (p – b), put a = 5 and b = -7,
So, it can be written as:
q = (p - 5) (p + 7),
Step 3: Multiply variable ‘p’ with all value of next pair and apply same procedure for second value. So it can be written as:
On multiplying we get:
q = (p - 5) (p + 7),
q = p2 + 7p – 5p – 35.
Step 4: Now we have to combine the same terms if present in equation otherwise this is required solution. So in above expression we have two like terms. On combining the equation we get:
q = p2 + 2p – 35. This is required quadratic form. (know more about Quadratic equation, here)

Rotational Kinetic Energy of a rigid body is found by first dividing kintic energy up into a collection of smaller masses. Before entering in 10 th board example please solve all cbse sample papers for class 10.

Factoring Polynomials

In mathematics, any expressions which is join with constants, variables and exponent values is said to be polynomial expression. And also polynomial expression is join with together by mathematical operators like (+, -, *, /). Infinite values are not taken in case of polynomials expression. For example: 12xy2 – 4x + 7y3 – 20, this given equation is polynomial equation, in this equation exponents values are 0, 1, 2 and 3. Negative and fraction values are also taken in case of polynomial expression. It is not joined with together by division operator.
Let’s discuss that how to solve Factoring Polynomials. Here we will understand the quadratic to calculate polynomial expressions.
Let we have a polynomial expression 2p2 + 4p – 10, we can factorize this polynomial as shown below:
We will find its factor by quadratic formula. Formula to find factors is given by:
P = -b + √ (b2 - 4ac) / 2a, here value of 'a' is 2, value of 'b' is 4 and value of 'c' is -10. So put these values in formula. On putting these values we get:
P = - 4 + √ [(4)2 - 4(2) (-10)] / 2(2); on moving ahead we get,
P = - 4 + √ (16 + 80) / 4, we can also write it as,
P = - 4 + √ (96) / 4. So, here we get two factor of this expression, one positive and other negative.
P = -4 + √ 24 and P = -4 - √ 24.
These two are factors of above expression. With the help of quadratic formula formula we can find factors of any polynomial expression. (know more about Factoring Polynomials, here)
Rotational Inertia can be defined as the moment of inertia that must be specified with respect to a selected axis of rotation. It is also said to be moment of inertia. icse board papers 2013 is useful for 2013 exam point of view.

Monday 30 July 2012

list of irrational numbers

In the previous post we have discussed about is pi a rational number and In today's session we are going to discuss about list of irrational numbers. Real numbers which are not rational are defined as irrational numbers. We can't write irrational number in an simple fractional form as p/q.It is cannot be written in form of p/q, where p and q are integer and q≠0. The decimal point goes on endlessly without any specific pattern called irrational number.
Example:             1.5 = 3/2 (Rational Number)
                                ∏ = 3.1415926535897….. =  ?/? (No ratio, Irrational Number)
The List Of Irrational Numbers consists of number that cannot express in the form of ratio:
List Of Irrational Numbers

Present Form
∏ (pi)
3.14159625358…
e (Euler Number)
2.71828182459…
Ñ°
1.61803398874…
√2
1.41421356237…
√3
1.73205080756...
√5
2.23606797749…
√7
2.64575131106…
√11
3.31662479035…
√13
3.60555127546…
√17
4.12310562562…
√19
4.35889894354…
√23
4.79583152331..
√29
5.38516480713…
√31
5.56776436283…
√37
6.08276253029…
√41
6.40312423743…
√43
6.55743852430…
√47
6.85565460040…

Listed below are a few facts related to Irrational Numbers:
·         If r is Irrational Numbers then –r also Irrational Numbers.
·         Irrational Numbers + Rational Numbers = Irrational Numbers
·         √2 + 6 = 7.618033988… (Irrational Numbers)
·         Irrational Numbers  x  Rational Numbers= Irrational Numbers
·          3 x √7 =  Irrational Numbers
·         ∏ x ∏ = Irrational Numbers
·         √2 x √2 = Rational Numbers
·         √2 + √2 = Irrational Numbers
·         √2 - √2 = Rational Numbers
·         √2 / √2 = Rational Numbers
 The other example of Irrational Number is Uniform Circular Motion. Uniform Circular Motion defines, an object traveling in a circular path at a constant speed. In Uniform Circular Motion a equation related the magnitude of the acceleration of the speed:
Y= 2∏r/T                    a = 2∏Y/T
Where r is the radius of the path and T is the time taken to make a circle.
So final equation is:
a = Y*Y/r (centripetal equation)
So result from the Uniform Circular Motion is always Irrational.
In Iit Jee Papers some questions also based directly and indirectly on Irrational numbers and Last List Of Irrational Numbers. (know more about list of irrational numbers, here)

Saturday 21 July 2012

is pi a rational number

In the previous post we have discussed about Types of Angles and In today's session we are going to discuss about is pi a rational number. Before studying is pi a rational number, it is necessary to discuss about the rational and irrational. In mathematics, a number can be written in the fraction form or written in x/y (in ratio) are known as rational number. For example: 0.8 the number is rational because it is also written in the fraction form. So we can write it as 4/5. A real numbers which cannot be written in the fraction form or cannot be written in x/y form are known as irrational number. For example:  ’√2’ is not written in the ratios. So √2 is included in the categories of irrational number. In other word we can say that the numbers are not rational are included in irrational numbers categories.

Now we will see is pi a rational number? Using the definition of rational number and irrational number we can easily find that ‘pi’ is irrational number because it cannot be written in the form of x/y or in form of fraction.  We can easily compare any number by the definition of rational number and irrational number.  Suppose we have given some number 2.66, 5, 1.87, √2, 0.111, √3, √99, now find which number is rational number and which one is irrational number.
Using the definition of rational number and irrational number we can easily compare the given number. (know more about Rational number, here)
2.66 can be written as 8/3, so it is rational number. 1.87 can be written as 15/8 so it is also rational number. √2, √3 and √99 cannot be written in the fraction form so these numbers are irrational number. And 0.111 can be written as 1/9 so it is also a rational number. This is how we can find the number should be rational or irrational.
Now we will see the Unbalanced ForceUnbalanced forces are forces which produce a non-zero net force. Before entering in the iit examination hall please focus on iit question paper 2013. It is very beneficial for exam point of view.

Friday 13 July 2012

Types of Angles


In the previous post we have discussed about Point and In today's session we are going to discuss about Types of Angles. By the term angle, we mean the distance in degrees between the two rays, which have the same vertex. There are different Types Of Angles.

Let us take them one by one. The angles are classified based on the measure of the angles.
1.  Acute Angle : We say that the angle is an acute angle if we have  the measure of the angle less than 90 degrees.
2.  Right Angle : If we have the measure of the angle equal to 90 degrees, then we say that the angle measure is a right angle.
3.  Obtuse Angle : If the angle measure of the angle is greater than 90 degrees and the measure ls less than 180 degrees, then we say that the angle is obtuse angle.
4.  Straight Angle : If the measure of the angle is 180 degrees, then we say that the angle is a straight angle. It simply forms a straight line by  the two arms of the angle.
5.  Reflex angle: All the angles with the measure  of greater than 180 degrees and less than 360 degrees, then we say that the angle is a reflex angle.
6.  Complete Angle: Any angle measure of 360 degrees is called the  complete angle. (know more about Angle, here)
We come across the terms complementary angles and the supplementary angles : If the sum of the two angles is equal to 90 degrees, then we say that the two angles are complementary. On the another hand we say that if the measure of the two angles sum up to 180 degrees, then it is the pair of complementary angles.
To learn about the  Average Speed Formula, we can take the help of online tutor for math which can help us to clear the concepts. Icse 2013 Solved Papers are also available online, which the students can download and understand the concepts.


Thursday 12 July 2012

Point

Point indicates the location on the plane. When we talk about a point on the plane, it can be indicated by a small decimal, which can not be further broken.  We us a point to locate the position on the plane, so we say that a point is used to mark the position which is marked with the respect to x and y axis. In case we have many collinear points on the plane, then we say that the line is formed by joining these points.
In order to find the location of a point on the plane, we will relate it with the coordinates of x axis and y- axis. Thus we say that  the coordinates of x , y axis of the point can be written which shows that the point exist at a particular place which has a particular location.  We always represent the point on the plane by the capital letters say Point A, B, C etc.
 If  we say that the point on the plane exist at the position ( 3 , 2), it simply means that the point  is at the distance of 2 units from the origin towards the x axis and it is at the distance of 3 units towards y axis. (know more about Point, here)
An interesting fact about the point is that  if a point is drawn on the plane then infinite number of lines can be drawn from that given point.  Also if we have two given points, then we can only draw one and only one line which can pass through the two given points. In case we have 3 points and one line is drawn passing through the tree given points, it simply indicates that the three lines are collinear, otherwise  3 line segments will be drawn passing through the given  lines and the closed figure so formed will be  called as a triangle. 
To learn about  Instantaneous Speed, we can visit online tutor. cbse paper for class 9 is also available online and In the next session we will discuss about Types of Angles


Tuesday 10 July 2012

parts of a circle

By the term circle, we mean that the circular closed curve which is formed by joining the points which are plotted with the  compass around the fixed point and at the equal distance around it. This fixed distance is called the radius of the circle.  
There are different parts of a circle, some of them are as follows :
The point in between the circle is called the center of the circle. It is normally represented  by the alphabet O.
The boundary of the circle is called the circumference of the circle. It is also termed as the perimeter of the circle.
The distance from the center of the circle to the boundary of the circle is called the radius of the circle. 
If we draw any line segment in the interior of the circle, such that the end point of the line segment touches the boundary of the circle at both the ends, then we say that it is the chord of the circle.
There can be any number of chords which can be drawn inside the circle.  The chord of the circle which  passes from the center of the circle is the longest chord of the circle. We also call it as the diameter of the circle.  When a diameter is drawn inside the circle, we observe that the  diameter of the circle is equal to the two times of the radius of the circle. Thus it can be written as follows :
 Diameter = 2 * Radius
Or Radius of the circle = diameter / 2
 The line which we draw outside the circle and it touches only at one point  on the circle is called the tangent to the circle.  Also we must remember that the tangent to the circle is always perpendicular to the  radius of the circle at that particular point.
To learn about the Sampling Methods, we can take the help of maths online tutorials. We also come across the questions based on the sampling methods in the  icse board papers and In the next session we will discuss about area of circle


area of circle

In today session we are going to discuss how to find the area of circle. The area of circle can be obtain by the following ways.
1: If we know the radius of the circle then the area of circle can be calculated by the using the method
   Area of circle = pi * r2
Where r is the radius of the circle and  (pi) is the constant having fixed value 3.142 or 22/7
2: We can also understand how to make a pie chart by using circle. If we know the diameter d of the circle. If diameter d is given then the area of circle can be calculated by the using the method
Area of the circle = pi * d2/4 .Where d is the diameter of the circle and  (pi) is the constant having fixed value 3.142 or 22/7
3: Now the circumference of the circle, if circumference c is given then the area of circle can be calculated by the using the method
 Area of the circle = c2/4*pi.Where c is the circumference of the circle and  (pi) is the constant having value 3.142 or 22/7.At the end of the above method we determine the area of the circle .There is an another way to find the area of the circle. By using the method of area of sector of the circle = (pi*R2*angle) / 360
Where r is the radius of the circle and (pi) is the constant having fixed value 3.142 or 22/7.For the area of whole circle angle must be equal to 360 degree. Therefore the area of the circle will be = (pi*R2*360) / 360 it implies that Area of the circle = pi*R2  

The questions on how to make pie chart and area of circle can be asked in icse question papers 2013 and In the next session we will discuss about parts of a circle.(want to Learn more about area of circle, click here),

Wednesday 4 July 2012

proportion

Ratio and proportion are the mathematical concept that basically deals with expressing the relationship between similar kinds of values. The concept of ratio can be define as a way to perform the task of comparing the two values to each other and represent their relationship between them. On the other hand, the concept of proportion can be described as tools that perform the task of equalizing the two ratios to each other. (Know more about proportion in broad manner, here,)
In a simple mean we can say that proportion is a way to set two ratios as equal. It means proportion is a special term of an algebra equation to compare two ratios or make them as equivalent fractions. In ratio, we just focus on what is the impact on another number when we make any changes in first number. But in proportion we need to focus to equalize the one ration to another ratio. Generally the concept of ration can be represented by using four variables u, v, w and x as:
 u : v = w : x,
 or
u / v = w / x.
Normally in the case of proportion, mostly we need to calculate the unknown value of the ratio. To perform the task of getting the unknown value of proportion we need to follow some of the task that are given below:
Suppose there is a statement in which we need to calculate the value of n in below given proportion.
6 / 15 = n / 10
Here first we need to perform the task of cross multiplication of proportional values:
   6 * 10 = n * 15,
    60 = n * 15,
    n * 15 = 60,
      n = 60 / 15,
     n = 4.
Now using the value of n we can represent the proportion as;
6 / 15 = 4 / 10
In mathematics,  Discrete Variable can be define as  a variables that can't be take all values through out the limits of the variable. In examination, cbse previous year question paper describe possibility of what type of questions have higher possibility to come in exam.

Saturday 16 June 2012

Multiplying Polynomials

In the previous post we have discussed about Use Greatest Common Factor Calculator and In today's session we are going to discuss about Multiplying Polynomials. We will learn about Multiplying Polynomials in this unit. To understand the concept of multiplying polynomial we come across different types of polynomials. In case we have to multiply a monomial with the monomial, we will simply multiply the coefficient of both the terms and then the powers of the variables are added up. Suppose we are multiplying 3x with 5xy>2, here we have the coefficient of the terms as 3 and 5, so we write
3x   * 5xy>2 = 15 * x>2 * y>2
Thus we say that constants are multiplied separately and then the variables are multiplied separately to get the product of two monomials. (know more about Polynomial, here)
Now proceeding further, let us consider the two   polynomials, where one of them is a monomial and the other one is a binomial, (it means a single term is to be multiplied with the two terms) In such a situation, we will multiply the single term of the monomial with both the terms of the binomial separately and thus the result we will get will be the binomial.
Let us consider the following example: Multiply 2x>2 with ( 3x + 5y)
 Here 2x>2 is a monomial and the expression 3x + 5y is the binomial. So we will first multiply the term 2x>2 with 3x and then the same term is multiplied with the term 5y. Thus we get the product as follows:
 ( 2x>2 * 3x) + ( 2x>2 * 5y)
= 6 x>3 + 10x>2 Y Ans
 Thus we observe that the resultant polynomial is the binomial. In the same way if a trinomial is multiplied with the monomial, we get the polynomial as the trinomial only.

  To learn about the Positive Correlation, we can make use of math online tutors. cbse board books are also available online which the students can use to consult the specific topics.

Friday 15 June 2012

Use Greatest Common Factor Calculator

In the previous post we have discussed about How to use Matrix Multiplication Calculator and In today's session we are going to discuss about Use Greatest Common Factor Calculator. In mathematics, GCF stands for greatest common factor which is used for solve the various kind of problem. The greatest common factor is the numbers which can be define as a common factor for two or more numbers. The GCF is most popularly known as a highest common factor which is able to divide the two or more positive integer without any remainder. In mathematics, Greatest common factor calculator mostly deals with the integer values and fractional values to reduce the complexity for performing the various tasks.
In the term Greatest common factor calculator we generally deal with the three words, (a) Greatest (b) common (c) factor. Here factor can be defined as a number which are used for performing the multiplication of two or more numbers. In the same aspect ‘common factor’ refers to the number which works as a common number for groups of numbers. Now the question arises in our mind that how to we calculate the greatest common factor for positive integer value. Lets we show you below:
Suppose we want to get the greatest common factor of two or more numbers then we need to follow the following given steps of greatest common factor calculator.
A)      First of all perform the prime factorization of each number that is given.
Suppose we have a number 15 then there prime factor will:
      15 = 3 * 5
B) After performing the prime factorization we can easily perform the multiplication of those factors that are common factors in all given numbers. If in any case there is no prime factor exists in between the prime factors of numbers then GCF can be consider as 1 for all positive number values. (know more about Factorization, here)
From the process of prime factorization we can get either single common factor or multiple numbers of common factors. During the processing of Greatest common factor calculator, prime factorization plays an important role in solving various kinds of problem that are related to mathematics.  Volume of a Sphere Formula can be described as a calculation of three dimensional spaces that are occupied by the sphere. Sphere is a three dimensional rounded shaped figure which are enclosed by some boundary. Education board in any state works as a board for secondary and senior secondary education. They manage the flow of education and their examination every year.