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## Algebra Concept

### Class 6

• Introduction to Algebra
• Matchstick Problems
• The idea of a variable
• Use of variables in common rules
• Expressions with variables
• Practical applications of expressions
• What is the equation
• A solution of an equation

### Class 7

• Integers Formulas
• The Triangle and its Properties Formulas
• Congruence of Triangles Formulas
• Comparing Quantities Formulas
• Perimeter and Area
• Algebraic Expressions Formulas
• Exponents and Powers Formulas

### Class 8

• Rational numbers
• Linear equations in one variable
• Data handling
• Squares and square roots
• Cubes and cube roots
• Comparing quantities
• Algebraic expressions and identities
• Mensuration
• Exponents and powers
• Factorisation
• Playing with numbers

### Class 9

• Number systems
• Polynomials
• Coordinate geometry
• Linear equations in two variables
• Lines and angles
• Triangles
• Areas of parallelograms and triangles
• Circles
• Surface areas and volumes
• Statistics
• Probability

### Class 10

• Arithmetic progression
• Polynomial
• Linear equation in two variable

### Class 11

• Progressions
• Linear inequalities
• Binomial theorem
• Permutations & combinations
• Mathematical induction

### Class 12

• Relations and Functions
• Reflexive
• Symmetric
• Transitive
• Equivalence relations
• Matrices
• Continuity and Differentiability
• Linear Programming

• Polynomials
• Factoring
• Functions and sequences
• Exponents and radicals
• Systems of equations
• Pythagorean theorem
• Equations, inequalities, and absolute value
• The number system
• Histograms
• Slope
• Finding the square
• Midpoint and distance formulas
• Probability
• Statistics and data analysis
• Square roots
• Rational expressions
• Problem solving

Algebra sounds like rocket science to many students, but this one chapter in Math holds a very pivotal role in our lives. The importance of Algebra in real life is play vital role too. However, before that, let us shed some light on what exactly Algebra is all about.

Maths, the least popular subject of the school. A subject by the name of which a student gets jitters and the topic algebra too. Every one of us at some point in time beseeched God to make the Maths paper as simple as he could.

The reason why Maths has always been a spine-tingling subject of our curriculum is its constant learning of formulas that made us indulge in a mental challenge all the time.

One such part of Maths that gave every student night terrors is ALGEBRA. Every student who enters into a high school or elementary school gets introduced to this chapter in Maths.

Algebra is an integral part of every student’s maths curriculum in high school. A chapter which was sufficient enough to give those exam jitters to us and everyone like us in the school. However, if it is not a part of our curriculum, many students might not get the heights in their careers they always aspired.

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## What is Algebra?

Algebra is a branch of mathematics that deals with symbols and following rules that helped in maneuvering those symbols. In elementary algebra, these symbols represent quantities without a fixed value more commonly known as variables.

Simply putting it, algebra is all about finding the undefined variables into equations and finally solving them. It is that branch of mathematics that substitutes letters for numbers, and it is an algebraic equation that represents a scale on both ends on what is done. Algebra constitutes complex numbers, real numbers, matrices, vectors, and various other forms of mathematical representations.

Now, let’s take a look at the history of Algebra.

## Evolution of Algebra

The roots of algebra are as deep as in the 539BC. It is said that people of Mesopotamia used the then called Babylonians mathematics which took a form of advanced arithmetical system, now commonly referred to as ALGEBRA

The Babylonians used algebra in those days, developed a course of formulas using Algebra to solve problems similar to today by using linear equations, quadratic equations, and many more similar formulas.

Eventually, with passing time, it was the Greeks who officially first raised the curtains to introduce Algebra in the third century following the footsteps of the Babylonians. Diophantus was eventually named as the FATHER OF ALGEBRA.

However, it was Rene Descartes who gifted us what we learn and use today in the form of Algebra through his book entitled La Geometry.

Now, that we gave a good dose of history and evolution of Algebra, let us talk about the importance of Algebra in real life. Yes, this is one such part of our mathematics curriculum which will and is helping many in their real lives.

But, first, how many of you remember mathematics the GENERAL EQUATION of Algebra? Here are some of the equations to give the much-required ‘Algebra nostalgia to all of you.

Self-study is a time saver, time being important as well as limited for students. A student can choose to do self-study from the confines of his home rather than getting tuitions from far off places. Another reason for its popularity is the advantage of it being cost effective.

#### General Equations of Algebra

a2 – b2 = (a-b)*(a+b)
(a+b) 2 = a2+2ab + b2
a 2+b2 = (a-b)2 +2ab

Now, we are sure a few of these general equations rings a bell for many of you.

## The importance of algebra in real life

whether you believe it or not, algebra is needed in many spheres of life. The numbers and equations gifted by Algebra are frequently used in almost everywhere in this world(shocking, No?). Take, for example; you are out for grocery shopping. Now, the addition and subtraction are the only sources to help you keep yourself budgeted with the items in the cart. However, for those who are not convinced of what to leave and what to take a cashier can help them using some formulation of algebra.

Not many of you are aware, even the economists of every country takes the help of Algebra to understand the economy better. Money is always a part that lands a person or an economy in a dilemma. In that case, algebra is the only source of help on can get through to solve the problems with how to subtract debts or loans that one has gained throughout the years.

Algebra is also considered as a ‘trump card’ for success in any business. Let us take an example; a person runs an online toy store, algebra is what will come in handy for him to calculate his profit margin on any given item and make up his mind whether that item is worth stocking. Algebra would also help him in calculating the lowest price he can sell an item and still make a glaring profit from it.

Also, for every student who wishes to master the statistics and calculus, algebra is a must-have thing for them. The concepts of algebra when combined with statistics and calculus are well-used in solving complex problems in one’s job.

Here are some of the many instances where algebra comes in handy in real life. There are various types of algebra that one should know before applying any one of it in their real life, solving problems. Therefore, to help all the quick-witted brains to make their life decisions more accessible, we’ll describe the types of algebra.

## Types of Algebra

There are THREE main types of algebraic expressions, by the position of variables, the types of functions and operations, and the behavior of their graphs. The types are:

• ### Monomial Expression

• The algebraic expression consisting of just ONE term is known as Monomial expressions. An example of a monomial expression is 3x4, 3xy.

• ### Binomial Expression

• The algebraic equation consisting of two unlikely terms are considered as Binomial expression. Examples of Binomial expressions are 5xy+8, xyz+x3, and many more such kinds.

• ### Polynomial Expression

• A polynomial expression is considered the ones which consist of more than one term with non-negative integral exponents of a variable. Examples of polynomial expressions are ab+bc+ca, etc.

Why Should School Students Learn Algebra?

Learning algebra at school and mastering this broad-spectrum, versatile and resourceful branch of mathematics can be a fulfilling experience for students. If students spend just a couple of hours on a regular basis, they’ll pick up the basics of solving a wide range of algebraic problems. Once they imbibe the fundamentals, they can regularly practice solving elementary, advanced, abstract, commutative, and linear algebraic sums.

Understanding the essentials of algebra not only enable you to complete an academic program or course effectively but equip you with wisdom and skills that you can use a lifetime.

The versatility of algebra comes in handy in every sphere of life

It is not only mathematicians but even most academicians, educationists, scholars, and professionals from all other walks of life unanimously agree on the versatility of algebra. You can liken algebra to an all-purpose tool or a magic wand that can help deal with everyday problems of life.

Algebra can help you to measure your living room dimensions and determine the size of an electronic item like TV or refrigerator that’ll fit comfortably in the space. Algebraic notations and symbols are crucial for deciphering and understanding musical notes, forces of gravity, behavior of solids, liquids, and gases. The myriad branches of science that have helped us comprehend and appreciate everyday natural phenomenon, use algebra extensively.

While you visit the market for buying essentials, reining in your expenses is your topmost priority. And this is where algebra can come to your aid; you assign an alphabetical or numeric symbol to each expense head (item), and quickly calculate the distinct value of each, given your total expenditure. If you’ve chosen to pursue a study program in high school, college, and university where mathematics is a compulsory subject, you’ll indispensably need algebra.

You’ll find algebra incredibly handy when you prepare for competitive exams that’ll be your passport to a job you may want to do to finance your studies. Simply put, you should maintain a flexible approach when it comes to learning algebra, and ensure that you develop and perfect effective methods for the same.

Algebra can boost and bolster logical reasoning

You can bet that you’ll be able to think more logically and with greater clarity if and when you practice doing algebraic sums habitually. To be specific, try to solve at least 5-10 problems relating to different sub-branches of algebra such as elementary algebra, linear algebra, abstract algebra, and Boolean algebra, regularly. You’ll discover to your amazement that you’re able to solve problems pertaining to other branches of mathematics with remarkable ease.

Algebra could go a long way in enabling you to fine-tune and sharpen your cognitive skills and reasoning capability, eventually letting you complete your study program successfully.

Algebra can help you in making significant decisions

When you graduate from the academic phase to the professional phase, you’ll need to make important decisions frequently about your career as well as your family life. For instance, when you start working, you’ll have to take out an employee health insurance plan.

Then again, when you marry and raise a family, you’ll need to set a monthly budget, buy a home, choose a family insurance policy, and take care of many other vital aspects. Needless to say, you’ll have to bank on algebra for taking a stand on important matters. Most significantly, if you’re well-versed in algebra, you can also help other members of your family in taking crucial decisions.

Algebra can help students in deciding on career goals

Some high-profile career options such as an electrical engineer, software engineer, actuary, investment banking analyst and business analyst requires the students to be good with numbers. Thankfully, there are umpteen career paths that students can choose from without requiring to excel in mathematics. Nevertheless, having a sound knowledge of algebra makes it easier for the pupils to choose a career path and pursue the same with missionary zeal.

Students can use algebra for understanding other mathematical branches

Students looking to make a career in the media, social science, actuarial science, health and wellness, engineering, medicine, or R& D will need to master other branches of mathematics, especially calculus and statistics. Having a robust understanding of algebra enables students to pick up the basics of statistics, calculus, and other mathematical branches.

High School Algebra: Everyday Applications

It is an open secret that the majority of school students dread mathematics chiefly because solving mathematical problems poses a near insurmountable challenge. Most of the students are unwilling or do not have the tenacity to exercise their intellect for working out the problems. However, algebra is one broad part or discipline of mathematics that many students find relatively easier than other mathematical branches like calculus, trigonometry or logarithms.

No wonder, a good number of secondary and high school students find algebra remarkably stimulating. The parents and guardians of school students might recollect taking a more than usual interest in grappling with algebraic basics like quadratic equations, linear equations, and so on. Students will surely agree that the excitement associated with studying mathematical notations and symbols and maneuvering these representations to solve algebraic problems is incomparable.

To put things in perspective, algebra not only plays a key role in a student’s academic life but also finds across-the-board applications in all other spheres of life. You’d invariably need algebra for studying specific subjects in high school and college as well as during your undergraduate and postgraduate years. Additionally, you’ll have to excel in this branch of mathematics for doing well in competitive exams which in turn will enable you to register for a professional program.

Moreover, you’ll need to solve algebraic sums, problems, and equations ingeniously and quickly for qualifying in job-oriented competitive and entrance exams. Then again, you’ll find algebra indispensable for estimating the price of various essential goods and services and keeping track of your expenses. In short, algebra as an integral part of mathematics touches almost every aspect of our life.

Indispensable for pursuing higher education

It does not bear emphasis algebra will be with you all the way throughout your academic period, especially if you opt for science or commerce stream. For instance, if you choose to study pure science subjects like physics, chemistry, and mathematics in high school, college, and university, you should be prepared to tackle advanced algebra. You’ll also have to deal with algebra if economics, statistics, music, psychology, and numerous other subjects are included in your study programs.

So, you see how algebra is inextricably interwoven with your academic career?

Could go a long way in helping you land your first job

Are you planning to work after clearing 10+2 in order to fund your undergraduate and/or postgraduate studies? Yes, you’ll find enough jobs that will easily enable you to finance your higher education as well as leave you with a substantial amount for building a nest egg. Though you may not need to be a graduate or postgraduate for applying to these job positions, you’ll need to have a high school certificate and be well-versed in algebra.

Essential for staying in business

While the majority of students go on to choose a profession of their liking, a good number of students opt to set up a startup. Regardless of the nature of your business, you’ll have to maintain a daily record of your earnings and expenditures so as to determine if you’re making a profit or incurring losses. Here again, algebra will help you work out the profit margin or extent of losses, and let you keep track of your revenues.

Applications in everyday life

Learning algebra in the early years, especially when you’re in secondary or high school serves you well throughout your life. Apart from helping you to pass specific subjects during your academic life, algebra plays a vital role in letting you breeze through competitive exams, written tests and interviews for a wide range of job positions. Algebra comes to your aid when you decide to settle down; helps you to choose a home as per your means, aids in preparing a monthly expenditure budget, facilitates choosing the best family insurance plan, and so on.

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