Introduction
Algebra is the branch of mathematics where we use letters (called variables) to stand for unknown or general numbers, so that we can describe relationships and solve problems that plain arithmetic cannot. In government job exams (BCS, Bank, IT-officer, NTRCA), algebra is one of the highest-scoring and most predictable areas: questions on equations, the laws of indices (exponents), and the standard algebraic formulas (identities) appear in almost every paper, and they can be solved quickly once you master a small set of rules.
This lesson builds the topic from first principles. You will learn what an equation really means, how to solve linear and quadratic equations, the complete laws of indices, the key algebraic identities used again and again in exams, and the fast shortcuts that examiners love to test.
Learning Objectives
- Understand variables, constants, coefficients, terms and expressions.
- Solve linear equations in one and two variables (including simultaneous equations).
- Solve quadratic equations by factorisation, formula and the discriminant.
- Master all the laws of indices and simplify expressions with powers and roots.
- Memorise and apply the standard algebraic identities (formulas).
- Use the special results for a + b, a − b, ab, a² + b², a³ + b³, a + 1/a etc. as exam shortcuts.
- Avoid the classic sign and index mistakes that cost marks.