[Maths Class Notes] on Algebra Pdf for Exam

Algebra is one of the various branches of Mathematics. It deals with symbols and variables. Various arithmetical statements and operations such as equations, terms, expressions to draw a relationship between objects which are not constant, and do change over time. These objects in basic algebra are also termed ‘variables’.

Algebra includes several forms of mathematical representations, such as real numbers, complex numbers, vectors, matrices, and so on. Equations form a crucial part of algebraic applications. Different algebraic rules are used to solve elementary equations to study variables.

Introduction to Algebra

Talking about variables, algebra is used to determine unknown values like proportions, bank interest, percentage, distance, price, etc. It also uses symbols and letters to represent mathematical equations. The equations consist of some constants and some variables. With the help of the constants provided in the equation, we find out the value of the unknown/variable in algebra math.

Students of secondary as well as higher-secondary level must understand how this branch of mathematics works and how the rules are implemented. They must learn algebra with thorough attention as it holds sufficient weightage in the final exams. One of the most helpful platforms to understand this is . The App can be downloaded for free to understand algebra for beginners, practice sums, and score well in the exams.

Different Branches in Algebra

Here is a list of the branches and sub-branches of Algebra. These branches are applied accordingly to find the values of two or more variables. These algebraic branches are as follows:

1. Elementary Algebra

This branch deals with the basic properties of numbers, variables, constants, and relations between them. The topics which form a part of elementary algebra include equations, formation, manipulation, evaluation of expressions, equalities, inequalities, equation solving (algebraic as well as linear), and so on.

2. Advanced Algebra

This is a more detailed and intermediate step in algebra. The equations included in this branch helps study the following:

• Equalities

• Inequalities

• Matrices

• Conic sections

• Sequences

• Series

• Trigonometry

• Polynomial equation

• Graphic functions

• Rational expression

• Probability

3. Abstract Algebra

It deals with truth related to algebraic applications independent of its specific nature. The components included in this branch of algebra are:

• Sets

• Binary Operations

• Identity Element

• Inverse Element

• Associativity

4. Communicative Algebra

This is a branch of algebra that deals with communicative rings, including algebraic integer rings, polynomial rings, etc. It can also be said to be a branch of abstract algebra. It includes a study on ring theory, Banach algebra, representation theory, and so on.

5. Linear Algebra

This is a branch of mathematics that deals with linear equations and their representations through vectors and matrices. Linear algebra forms a fundamental aspect in every sector of mathematics.

The topics included in this branch of algebra are as follows:

Students can learn various concepts of algebra online through the App. The algebraic topics you can read on this App are:

1. Basics of algebra.

2. Adding, subtracting, and multiplying algebraic expressions.

3. Simplification of algebraic equations, using the BODMAS rule.

4. Substitution.

5. Solving inequalities of equations.

6. Exponents.

7. Surds.

8. Square roots.

9. Cube roots.

10. Laws of exponents.

11. Simplifying equations.

12. Algebraic properties (associative properties, distributive laws, communicative laws).

13. Cross multiplication.

14. Polynomials.

15. Adding, subtracting, multiplying, and dividing polynomials.

16. Rational expressions.

17. Long division of polynomials.

18. Conjugate.

19. Rationalizing denominator.

20. Quadratic equations.

The App covers all the mentioned topics in a detailed manner.