How to learn Algebra easily for scoring better in examinations! Some key points to consider!

What's Algebra: A brief definition 

Algebra is the branch of mathematics that helps in the representation of problems or situations in the form of mathematical expressions. It involves variables like x, y, z, and mathematical operations like addition, subtraction, multiplication, and division to form a meaningful mathematical expression.

Why Algebra is so important?

Algebra is necessary 

+ To help you understand what is important in a sequence of events. 

+Build Problem-Solving Skills

+Reasoning Skills - +Understanding how to move factors from one side of the equation.

+ To understand the balance of nature ll

+how it is all interrelated.

+To inculcate logical thinking in you

+ Boosting career opportunities

Scoring in Algebra

Many students can score full marks in Maths, while it is tougher to get 90+ in other subjects. However, it needs proper practice and a clear understanding of formulas.

CBSE syllabus for Class 10 Maths for the academic year 2020-2021 incorporates number frameworks, polynomial math, facilitating calculation, etc. Every one of the units referenced in the CBSE tenth Maths syllabus is significant because the last inquiry paper is set up according to the syllabus. It additionally gives data about marks weightage, practicals, tasks, projects, and so forth.

The Mathematics syllabus Chapter wise includes:

Unit-I: NUMBER SYSTEMS

CHAPTER 01Real Numbers

Unit-II: ALGEBRA

CHAPTER 01 Polynomials

CHAPTER 02 Pair of Linear Equations in Two Variables

CHAPTER 03

Quadratic Equations

CHAPTER 04

Arithmetic Progressions

UNIT III: COORDINATE GEOMETRY

CHAPTER 01

Lines (In two measurements)

UNIT IV: GEOMETRY

CHAPTER 01

Triangles

CHAPTER 02

Circles

UNIT V: TRIGONOMETRY

CHAPTER 01

Prologue to Trigonometry

CHAPTER 02

Geometrical Identities

CHAPTER 03

Statures and Distances: Angle of rising, Angle of Depression

UNIT VI: MENSURATION

CHAPTER 01

Regions Related to Circles

CHAPTER 02

Surface Areas and Volumes

UNIT VII: STATISTICS AND PROBABILITY

CHAPTER 01

Statistics

CHAPTER 02

Probability

Types of Algebra or Levels of Algebra 

Algebra 1 or Elementary Algebra

Elementary Algebra covers the traditional topics studied in a modern elementary algebra course. Arithmetic includes numbers along with mathematical operations like +, -, x, ÷. But in algebra, the numbers are often represented by the symbols and are called variables such as x, a, n, y. It also allows the common formulation of the laws of arithmetic such as, a + b = b + a and it is the first step that shows the systematic exploration of all the properties of a system of real numbers.

The concepts coming under elementary algebra include variables, evaluating expressions and equations, properties of equalities and inequalities, solving the algebraic equations and linear equations having one or two variables, etc.

Algebra 2 or Advanced Algebra

This is the intermediate level of Algebra. This algebra has a high level of equations to solve as compared to pre-algebra. Advanced algebra will help you to go through the other parts of algebra such as:

Equations with inequalities

Matrices

Solving system of linear equations

Graphing of functions and linear equations

Conic sections

Polynomial Equation

Quadratic Functions with inequalities

Polynomials and expressions with radicals

Sequences and series

Rational expressions

Trigonometry

Discrete mathematics and probability

Abstract Algebra

Abstract algebra is one of the divisions in algebra which discovers the truths relating to algebraic systems independent of the specific nature of some operations. These operations, in specific cases, have certain properties. Thus we can conclude some consequences of such properties. Hence this branch of mathematics called abstract algebra.

Abstract algebra deals with algebraic structures like the fields, groups, modules, rings, lattices, vector spaces, etc.

The concepts of the abstract algebra are below-

Sets – Sets is defined as the collection of the objects that are determined by some specific property for a set. For example – A set of all the 2×2 matrices, the set of two-dimensional vectors present in the plane and different forms of finite groups.

Binary Operations – When the concept of addition is conceptualized, it gives the binary operations. The concept of all the binary operations will be meaningless without a set.

Identity Element – The numbers 0 and 1 are conceptualized to give the idea of an identity element for a specific operation. Here, 0 is called the identity element for the addition operation, whereas 1 is called the identity element for the multiplication operation.

Inverse Elements – The idea of Inverse elements comes up with a negative number. For addition, we write “-a” as the inverse of “a” and for the multiplication, the inverse form is written as “a-1″.

Associativity – When integers are added, there is a property known as associativity in which the grouping up of numbers added does not affect the sum. Consider an example, (3 + 2) + 4 = 3 + (2 + 4)

Linear Algebra

Linear algebra is a branch of algebra that applies to both applied as well as pure mathematics. It deals with the linear mappings between the vector spaces. It also deals with the study of planes and lines. It is the study of linear sets of equations with transformation properties. It is almost used in all areas of Mathematics. It concerns the linear equations for the linear functions with their representation in vector spaces and matrices. The important topics covered in linear algebra are as follows:

Linear equations

Vector Spaces

Relations

Matrices and matrix decomposition

Relations and Computations

Commutative algebra

Commutative algebra is one of the branches of algebra that studies the commutative rings and their ideals. The algebraic number theory, as well as the algebraic geometry, depends on commutative algebra. It includes rings of algebraic integers, polynomial rings, and so on. Many other mathematics areas draw upon commutative algebra in different ways, such as differential topology, invariant theory, order theory, and general topology. It has occupied a remarkable role in modern pure mathematics.

How to master in Algebra

These are few points for you to consider to become a knowledgeable person about Algebra.

Below are 14 study tips and common pitfalls to avoid to help you succeed in algebra.

1. Know Your Arithmetic. ...
2. Remember PEMDAS . ..Parentheses, Exponents, Multiplication, Division, Addition, Subtraction
3. Get Positively Comfortable with Negative Numbers. ...
4. Show Your Work. ...
5. Don't Let the Letters Scare You. ...
6. Formulas Are Your Friends. ...
7. Be Sure to Answer the Right Question. ...
8. Work Practice Problems.

9. Learn from Your Mistakes

10. Don’t Divide By Zero

11. Mind the Parentheses

12. Watch Your Distribution

13. Only Cancel Factors

14. Don’t Forget to Distribute

Conclusions 

1. Students often wonder when they are studying algebra if it will actually be useful for them in life beyond the classroom. There is great news for those students: 

2. Algebra can absolutely be beneficial in life if they choose to understand it! Memorising how to solve algebraic equations may get a course completed, but truly understanding algebra helps us to notice how to use it in everyday problem-solving. 

3. Need further convincing? Contact the author with comments in the comments box. 

4. Your queries wil be acknowledged and proper reply will be given in appropriate time.