What is periodic Table?

The periodic table contains the table of chemical elements arranged in a particular order. It shows the symbols of the element, it gives the full name of the element; it also gives their atomic and mass number.  The elements are arranged in columns and rows based on their structure and properties. This arrangement in columns and rows are called groups and periods.  Since the horizontal rows are named as periods it is called “the periodic-table”.

Periodic table for kids can be explained in a simple manner so that it can be easily understood. The periodic table basics are listed below.
It is nothing but it is like a usual table containing rows and columns.  These rows and Columns give us the information about the various elements.  This is of immense help to chemists to help them understand how and why elements react.  There are more than 100 elements arranged in the periodic-table. The table is read just like any other information from left to right and top to bottom.  The elements are arranged in order of their atomic number in ascending manner.  Rows are called as periods and columns are called as groups.

Periodic table names:   It contains the names of more than 100 elements.  The first one found on the extreme upper left corner of the table is hydrogen. The atomic number of Hydrogen is 1. The element that is located at the extreme right top corner is Helium, which has an atomic number of 2. Elements are listed in this pattern.  To find the next element one has to look down one row to the left side of the table to find the next element. Which will be lithium, then comes Beryllium, Carbon, Boron, Nitrogen and so on.  

Periodic table charges refer to the ionic charge of the corresponding element.    If the number of protons and   number electrons is not same then the atom gains or loses   the charge. The charge of an electron is negative and the charge of a proton is positive.  If the atom is not reacting then the charge will be zero since the number of electrons and protons are equal.    The charge of the atom becomes negative if it gains an electron since electron has negative charge, this leads to the atom become an anion.   The charge of the atom becomes positive if there is a lose in the electron.  This leads to the atom becoming cation.

Basics of Simple Interest

The term interest refers to the cost of borrowing money. The interest calculation varies from plan to plan and is also based on the lenders and the time period of lending/depositing the amount. This interest is calculated in different ways such as interest only on principal, interest on principal and interest so far earned/incurred, monthly interest, cumulative interest etc.  The amount for which the interest is calculated can be a loan (amount borrowed for need) or a deposit (amount deposited as savings).

Definition
The interest which is calculated only on the principal amount borrowed or deposited is termed to be Simple Interest that is denoted as SI in short.  This type of interest does not include the interest so far incurred or earned on the principal amount.

When an amount is borrowed, the amount borrowed is called the Principal. The duration which the borrower takes to return the Principal is termed as the time period and is calculated in number of days/months/year.  The next and most important part is the rate of interest which states the interest percentage for the given principal amount.  All the three put together explains what is Simple Interest. The interest percentage is directly proportional to the lender and the time duration to repay the amount.   Also it depends upon whether it is a loan or a deposit.

Formula for SI Calculation
Formula 1: “R as number”
The Simple Interest Formula is given by S.I = (P*N*R)/100.

Formula 2: “R as percentage”
The Simple-Interest Formula is given by S.I = P*N*R.

This shows how to calculate Simple Interest using the interest for the given principal amount P, with rate of interest R/period of a given period of time P.

Example of SI Calculation
If a principal amount of Rupees 1000 is borrowed/deposited by a person for a period of 2 years with 3% rate of interest, then the simple-interest is given by

By applying the values of P, N and R given, we get

Formula 1: R as number

We know that the rate of interest is 3%. We take R = 3

S. I.  = (P * N* R)/100
S. I.  = (1000 * 2 * 3)/100 = 6000/100 = 60

Formula 2: R as percentage

We know that R = 3% = 3/100 = .03

S.I. = P * N* R
S.I. = 1000*2*.03 = 60.00 = 60

Applications of SI
In post offices, schemes such as MIS pay simple interest for the amount deposited for five years as recurring deposit.

Credit cards charging simple-interest for the amount to be paid is more beneficial.

Markup

This topic is related to business, fundamentally buying and selling. The total expense that you incur on an item before selling is the actual cost of that item. The price at which you sell the same item is your revenue. The difference of (price – cost) is the profitor the income you get out of the sale. If, for any reason, the difference is negative, then it is no more a profit but a loss.  Let us continue our discussions with only the situations of profit.

The profit definitely has a bearing on the decision of fixing your price. If the market situation is favorable you can fix the price at your discretion as long as it is more than the cost you have incurred plus the income you desire to have. But in the competitive world the situation is not so.

So you have to very prudently decide the amount to be added by which you are neither priced out nor suffer a loss. The amount such added is called as markup. So basically it is also refers to the profit but decided purely on the cost and not on the favorable market conditions. Hence, mark up is the minimal profit in business.

Now let us go to the mathematical part like markup percentage, calculating mark up or mark up calculation.  Suppose ‘x’ is the cost of purchase of an item plus the other incidental expenses you incurred. Let ‘y’ be the minimum amount that you feel the transaction is worth.

All said and done that is the amount of income for your survival which cannot be considered as a part of the actual cost. So the percentage of markup is [(y/x)*100]%. Generally a merchant uses this percentage as a key for similar items and for a brief period.

Now let us do an actual mark-up pricing example. Suppose you buy an item for $95 and incurred $5 subsequently to cover up all the incidentals and overheads. so the actual cost of the item is $100. Your experience prompts you that only with 20% mark-up on each sale you can sustain in business. So the sale you could decide is $120. But the merchant will not immediately decide on this.

If he senses that the particular item is in great demand or others are selling at higher price, he will sell only at the market price and hence in such case the actual markup is much higher than he envisaged. On the other hand, even with the minimal adding of 20% if he is priced out in the market he will decide to stop selling that particular item.

Using Elimination to Solve Linear Equations

There are different types of equations in mathematics. There can be different methods to solve these equations. One can use solve by elimination method to solve the equations. The equations can be linear and also quadratic in nature. Sometimes they are cubic in nature. This method is used to solve a set of linear equations. If the numbers of variables to be found out are ‘2’, then a set of equations must be given to find them.

A set of equations means two equations must be given. The number of equations can be deciding factor in finding the solution. In this method an unknown variable is eliminated first. Then the value of the second variable can be easily found out. Once the value of the first variable is found out then this value can be substituted in any one of the given equations and the second variable can be easily found out. This is one of the easiest techniques that can be used to find the unknowns in linear equations. For solving equations having three unknowns three equations must be given, otherwise it is not possible to find the unknowns. This is a prerequisite to find the unknowns.

The ‘solve by elimination technique is used when a set of linear equations are to be solved. This technique can be very useful and simple to use. There are various techniques available to solve linear equations. This is one of the simplest methods and can easily understood and used.

This is why it is most commonly used by the students. It is also easy to cross-check the answers. The solution obtained must satisfy the given equations. The process of solving by elimination can make the task of solving of linear equations very easy.

Once solve by the elimination method is learnt, the other methods to solve the linear equations can also be learnt. This is the basis for the other methods. So, one must thoroughly understand this method. Here elimination refers to the fact that a variable is first eliminated in this method. Once a variable is eliminated the second variable can be easily found out. Then this value helps in finding the other variable.

This can be done by using the principle of substitution. The value found out is substituted back into the equation and the value of the other variable is easily found out.

Diagonal Matrix Properties

A (mxm) matrix is a square array of numbers which has equal number of rows and columns here denoted by ‘m’. The elements of a square matrix that start from the left corner towards the right corner like a diagonal is called the Main Diagonal of a Matrix. For example, a 3x3 matrix given by
A=[-1  3  4]
 [2   1  0]
 [7  0   5]
The elements [ -1,1,5] form the elements of the main diagonal. Now consider A=(aij) to be a square matrix then the elements in aii is the diagonal of a matrix.  A square matrix in which all elements except the elements of the leading diagonal are zero is called a Matrix Diagonal. In this all the non diagonal elements are zero. For instance, a square matrix given by A=[aij]nxn to be a diagonal-matrix , aij is equal to zero wherever ‘i’ is not equal to ‘j’. Example of a diagonal-matrix can be given as follows, a 3x3 matrix given by
A=[2    0    0]
     [0   -1    0]
     [0    0    5]

Let us now take a look at the Diagonal Matrix Properties:
• If A and B are two diagonal matrices of the same order then, A+B and AB are also diagonal matrices.  Also AB=BA, that is they commute
• A square matrix is diagonal only if it is triangular and normal
• If A is a diagonal-matrix then the adjugate of A is also a diagonal matrix
• Any diagonal matrix is symmetric
• It is a scalar matrix when all the entries of the diagonal are equal
Determinant Diagonal Matrix
The determinant of a 2x2 square matrix A=[a    b] can be defined as |A|=ad-bc. It is denoted by det(A)
    [c    d]
Let A=[aij] be a nxn matrix where n is greater than or equal to two. We can define determinant,
|A|= a11C11 + a12C12+……..+a1nC1n which is equal to summation(i= 1 to n)[a1iC1i]. If A is a nxn diagonal matrix then |A| is the product of the elements in its main diagonal.
Let A = [a11       0       0……     0]
             [0         a22     0 ……   0]
     [0          0      a33……    0]
     [..         ..      ..     ..]
     [..         ..      ..     ..]
     [0          0        0…. .ann]

be a nxn diagonal matrix, then the determinant of this matrix can be given by a simple formula, det (A)=|A|= pi(i= 1 to n)[aii]
Consider the following example,
A=[2   0    0]
      [0   5    0]
      [0   0    1]

then det(A)=|A|= (2)(5)(1)=10
Note that if any of the elements of the main diagonal is zero then determinant would also be zero.

Process of Solving Inequalities

In mathematics both equalities and inequalities are present. The equalities give rise to equations. In equations the ‘equal to’ sign is used. There are various methods to solve the equations. The best and the easiest method must be used in order to arrive at the answer quickly and efficiently.

The concept of solving inequalities by addition and subtraction is very easy to understand and use. The concept can be very easy to understand if one is thorough with the concept of basic arithmetic operations like addition and subtraction.

The concept of inequality can be easily understood with the help of examples. The examples can help in explaining the concept very clearly.

In solving inequalities using addition or subtraction, the basic arithmetic operations of addition and subtraction are used. The inequality is called an inequality because the terms on the left side will not be equal to the terms on the right hand side. This is the basic reason for the term being called an inequality. This is the basic difference between the equality and inequality. In equality the terms on the left side will be equal to the terms on the right hand side.

The process of transposing will be used to solve the equations. Even in the case of inequalities the same process or principle is used. This is very simple principle. The terms on one side of the equation are moved to the others side; while doing so the sign of the term changes.

The positive term becomes the negative term and the negative term becomes the positive term. The multiplication becomes division and division becomes multiplication. So, one must be very careful while transposing the terms.

An inequality is formed when a term may be less on side or the other side. This is nothing but a side is surplus and the other side contains slack variable. So, the surplus has to be reduced to convert the inequality into equality.

But the same method can be used to solve both types of problems. Once the solutions are obtained for these types of problems it is necessary to check the feasibility of the solutions. All the solutions obtained might not satisfy the given equations. So, one has to be careful in selecting the final solutions. These solutions which are selected must satisfy the given equations. In case of inequality the solution must satisfy the inequality.

Plan your study schedule with your private tutor

It is proved that private tutoring helps students in excelling in exams. It nurtures students’ understanding skill and brush up their knowledge. Students can schedule their learning sessions with preferred private tutor and experience a better session.

Private tutors help students to perform well
Private tutoring has achieved a noticeable popularity among students of any grade. Class timings of school are limited and sometimes it is not adequate to learn a subject thoroughly. To handle this problem, private tutoring is taken as a useful solution by many students. This facility allow students to understand any topic at their pace. Most importantly, with this service, students get extra time to clear their doubts and understand each concept precisely. Private learning helps student in enhancing their performance in exam. Apart from assisting to complete the prescribed curricula, private tutors also help students in solving different worksheets that builds a good learning skill.

Flexibility makes private tutoring a one stop solution for students

Several positive features have made private learning service a useful learning option to students. It is flexible and beneficial as it provides extra time to students to get better understanding on each topic. Numbers of learning centres are available and students can choose any centre that comes near to their residence. They can choose online learning service as well. With this service, they can schedule their learning sessions from home. Moreover, experienced and well-trained tutors are the asset of this learning platform. They sincerely guide students and nurture their talent in a better way.

Different modes of tutoring
Online tutoring and live tutoring at centres are two types of private tutoring service where students can take additional learning help to complete their topic thoroughly. There are some differences between these two methods.
* Live tutors assist students in a group whereas online tutors provide one-on-one session to students. Hence, online assistance is more beneficial to students who feel hesitate to ask questions in class.
* Live tutors are only available in learning centres and students need to visit the centres to attend allotted classes whereas in online platform, students can schedule their own sessions from home at their convenient time. Hence, online learning help saves students time.

Online private tutors are more popular than live tutors
Several positive aspects have made online tutoring more popular than live private tutoring. Online learning mode is flexible, safe and fun-to-use. The expert tutors are available 24 hours and they not only help in understanding different topics but also assist in completing homework and assignments on time. Additionally, the usage of advanced and user-friendly tools like virtual whiteboard and attached chat option make each session interactive and productive. So students can take assistance from tutors to perform better in exams.