function and relation

 In the previous post we have discussed about Define one to one correspondence and In today's session we are going to discuss about function and relation.
Function and relation are two different concepts of mathematics. A relation is resembles a function only if it is one – one & onto. Therefore, we can say that all functions are relations but not all relations can be functions. In the Cartesian system we represent the 1^st value of ordered pairs as the x – coordinate and the 2^nd value as the y – coordinate. So, we can define a relation a usual set of orderly pairs and the mapping is not necessarily be one – one & onto.
Suppose we have two sets A = 2, 4, 5, 6, 8, 10 and B = 4, 16, 8, 10, 12. The mapping is done from set A to set B such that the elements in set B consist of multiples in set A. Element 4 of set B has multiples as 2 & 4 in set A. Similarly, for 16 we have 2, 4 & 8, for 8 we have 2, 4 & 8, for 10 we have 2, 5 & 10 and for 12 we have 2, 4 and 6. Thus this mapping is one to many mapping and thus this relation does not represent a function. Thus the ordered pairs we form are: (2, 4), (4, 4), (2, 16), (4, 16), (8, 16), (2, 8), (4, 8), (8, 8), (2, 10), (5, 10), (10, 10), (2, 12), (6, 12) and (4, 14).
To define a functionhttp://en.wikipedia.org/wiki/Function_(mathematics) we must have unique output for every input i.e. one value in range for every value in domain and also all the values of domain and range must be covered. For instance, we have pairs like: (1, 2), (4, 8), (2, 4), (3, 6) and (5, 10).
Next we study about how to find the surface area of a cylinder. For this we have a general formula that is given as follows: 2 pi a² + 2 pi a l. Where, a and l are the radius and height of the cylinder. These concepts are detailed in the  icse syllabus 2013.

Define one to one correspondence

 In the previous post we have discussed about What is Mathematical Induction and In today's session we are going to discuss about Define one to one correspondence.


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One to one correspondence can be defined as property of a set according to which every member of set is related exactly one member of another set. This concept is applied on sets. Set is just a way to store similar kind of values into it and describe the relationship between these values or objects. If we want to describe this concept in the form of simple definition then we can say that it is a situation which occurs only when members of one set are evenly matched with members of another set. According to this one to one correspondence; we need to remember one thing that any member of first set can make a pair with any one member of another set.

Suppose we have two sets which are named as A and B respectively. Set A and B has some members that are shown below:

A = a, b, c, d, e,

B = I, j, k, l, m,

If we follow one to one correspondence concept on above given sets then each and every member of set 'A' can make a pair with one member of Set 'B'.

A → B = a, i, b, j, c, k, d, l, e, m

Above each member of set A makes pair with only one member of Set B. Any member of Set A can make pair with any member of Set B, there is no restrictions to make a pair. One more thing we need to remember is that none of the member should be left as unpaired. It means each and every member must carry a pair value with another set.

In mathematics, concept of Molality Formula can be denoted by numbers of moles of any given substance per liter of solution.

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What is Mathematical Induction

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Mathematical Induction is basically a technique which is used to establish the proof that a given statement is true for all positive integers or natural numbers. We need to prove two statements which are: First statement in the infinite sequence of statements should be true and if anyone statement in infinite sequence of statements is true then next statement will also be true.

Suppose, we have 'n' natural numbers then P(n) holds all natural numbers so:

0 + 1 + 2 + 3 + 4 + 5 +.........+ n = n (n + 1) / 2,

Where P(n) provides a formula to calculate the sum of natural numbers.

Now we use inductive step to prove the above statement. Where P(k) holds natural number then according to statement P (k + 1) also holds then

(0 + 1+ 2+...................+ k) + (k + 1) = [(k+ 1) ((k+ 1) + 1)] / 2,

After using the induction hypothesis:

k (k + 1)/ 2 + (k + 1),

k (k + 1)/ 2 + (k + 1) = [k(k + 1) + 2(k + 1)] / 2,

= (k² + k + 2k + 2) / 2,

= (k + 1) ( k + 2) / 2,

= [(k + 1) ((k + 1) + 1)] / 2.

So the resulting equation shows that P (k+ 1) also holds.

To understand it, we will take an example: We have an equation 23ⁿ – 1 and we have to prove that it is divisible by 11 for all positive integers 'n'.

So, to prove that we put the value of n = 1 then

23¹ – 1 = 22 which is divisible by 11.

Now, according to induction theorem if P (k) holds then P (k + 1) also holds so

23^{k + 1} – 1= 23. 23^k - 1

= 11. 2. 23^k + (23^k – 1),

Here we can see that resulting equation is divisible by 11.

Multiplying and Dividing Fractions is a concept of algebra.

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word problem help

In the previous post we have discussed about Relations and Functions and In today's session we are going to discuss about word problem help. The study of mathematics is basically aimed with relating it with the real life so that the objective of studying math is fulfilled.  Our life basically related to math at every angle of life.
By word problems we mean that the statements of the problems are given from the real life and we need to get the solution to the problem by understanding the mathematical operation to be performed.  To get word problem help, we can visit online math tutors which can support us to learn the logics to be used in solving the word problems.
We need to master the concept of analyzing the type of the problem and then check which mathematical operation will be performed on the given problem in order to get the solution. We are given certain tips to find the key words which help us to check the operation to be performed. Suppose we have the key words like add, sum, join, combined, greater, in all etc. we simply conclude that the sum of the digits will  help us to get the solution of the problem. In the same way if we have the words like less, reduce, decreased by etc help us to get the solution  for the given problem.

Students can take online help to  learn how to perform the operations of maths and solve the word problems. Different practice worksheets are also available online which help to develop the confidence. They help us to practice variety of word problems and get the real exposure to a variety of problems.
We also have the topic  Polar Moment of Inertia, which can be learned online. It is one of the topic in class 9^th. We can find  ntse sample papers online, which can be used for the preparation of the ntse exam conducted for the students of class X.

Relations and Functions

In the previous post we have discussed about Rotation Matrix and In today's session we are going to discuss about Relations and Functions. In mathematics, there are various ways are described that can maintain data in records in quick and accessible manner. Regarding to these technology relation and function are one of them. A Relations and Functions are two different things but they together to perform any particular task. A relation can be describing as a relationship between sets of data or values. Suppose there is a class in school. There are thirty students in class and each student has their own marks in particular subject. Now make a pair between names of students and their marks are known as relation.
On other hand arrange a pair of data in particular order can be considering as function. In the simple mean we can define the concept of Relations and Functions by using the concept of ordered pair which carries two values into it. Now on the basis of ordered pair a relation can simply be define as set of ordered pairs of values Like ( a0, b). Here ( a, b) can be consider as a ordered pair where value of ‘a’ can be considered as a value of domain and the second value of ordered pair are known as range. Here two new concepts arise during discussion that is domain and other is range. Here domain is known as collection of all first value of pair and range can be defined as collection of second value of ordered pair.
By using the definition of range and domain we can say that function is a process where the domain value makes a pair with only one value of their range. In mathematics, the values of ordered pair can either be negative or positive.
According to Radioactive Dating, it can be consider as a technique which is popular for date material like rocks. In India, those school’s who are affiliated from cbse Board, board provide cbse syllabus for class 9 to guiding school for better education.  

Rotation Matrix

Hi friends, in mathematics, today we will discuss about Rotation Matrix. And also we will study different method to solve the rotation matrix. Generally a rotation matrix is used to show a rotation in linear algebra. For example:

p = [ cos Ф - sin Ф]

      [ sin Ф cos Ф]

In the matrix mention above matrix points are rotated in xy – Cartesian plane ( here x is along to horizontal axis and y is along to vertical axis) through an angle Ф about the origin of coordinate system. Using the matrix multiplication we also found a rotated vector. So there is no effect of multiplication on zero vector or in other word it can be a coordinates of the origin. Commonly rotation matrix is used to calculate rotations about the origin of coordinate system. It can also be used to assist a simple algebraic description of such types of rotations and it can also be used for computation in physics, geometric, etc. If we talk about the case of three dimensional space then the rotation can be stop by given angle along a single axis of rotation. So, it can be simply calculated by an angle and vector by three entries. In case of 3x3 Rotation Matrix. It can be solved by nine entries of a rotation matrix that has three rows and three columns. It can not be used in higher dimensions. (know more about Rotation Matrix, here)

It is also said to be orthogonal matrices that has determinant value is equal to 1. It can be denoted as:

= Pa = P-1, det P = 1. this type of matrices are called as special orthogonal group. It can be denoted as 'SO (n). Entire rotational matrices are found using these matrix multiplication. For example:

= Pp (γ) Pq (β) Pr (α); it can be denoted as a rotation whose angles are α, β, γ. This is all about rotation Matrix.

Stem and leaf Plots can be defined as a method of organizing numerical data in order of place value. For the preparation of 8 class board example please prefer 8th class question papers.

Binary Numbers

In the previous post we have discussed about domain math and In today's session we are going to discuss about Binary Numbers. Before discussion about the Binary Numbers first we have to know about the number system that is a basic need for presenting a number. When we talk about any number it consist some of the digits in it and these digits is decided by the number system which is used to express the number. So there are basically four types of number system as decimal , binary , octal and hexadecimal number system . When we talk about the binary number system in which binary means two , so there are only two digits for expressing a number that are zero (0) and one (1). (know more about Binary Numbers, here)
In binary number system, all the values having two digits. When we talk about any number probably it is define into the decimal number system in which number having the value from 0 to 9 and all these 10 digits are used  to make different types of number and when we want to change any decimal number into the binary number that means every single digits of the given number will be multiplied with the  exponent of two that means if there is a number xyz and we want to change it in the binary number then in x y z ,digit x has a hundred position , y has a tens position and z has a ones position and then z is multiplied with the  2 >0 and y multiplied with the 2 > 1 and x is multiplied with the 2 > 2.
 Temperature Conversion Chart is used for define the temperature in different units and also describe the relation between these units that is used for changing the temperature in one unit to another.
Cbse board that stands for central board of secondry education provides Cbse Syllabus For Class 10 students that describe all the topics that will covered in the respective session.