Algebra: Complete Guide for Aptitude Preparation (2025)

Algebra is one of the most important sections in aptitude tests, competitive exams, and job assessments. A strong foundation in Algebra helps you solve complex quantitative problems with ease. In this guide, we’ll cover the concepts, formulas, solved examples, and practice questions you need to master Algebra for exams like SSC, Banking, UPSC, CAT, GRE, and more.

What is Algebra?

Algebra is the branch of mathematics that deals with symbols, variables, and numbers to solve equations and represent real-life problems.

Instead of working only with numbers, Algebra introduces letters (like x, y, z) that represent unknown values.

Example:

• Solve for x: 2x + 3 = 7
  2x = 4 → x = 2

Key Topics in Algebra

1. Basic Algebraic Expressions

• Constants, Variables, Coefficients
• Like & Unlike terms

2. Laws of Algebra (BODMAS)

• • Addition, Subtraction, Multiplication, Division rules

3. Polynomials

• • Degree, Coefficients, Types

4. Factorization

• (a² – b²) = (a – b)(a + b)
• (x² + 2xy + y²) = (x + y)²

5. Linear Equations in One Variable

• • ax + b = 0

6. Linear Equations in Two Variables

• • ax + by + c = 0

7. Quadratic Equations

• ax² + bx + c = 0
• Roots formula: x = (-b ± √(b² – 4ac)) / 2a

8. Inequalities

, <, ≥, ≤

Algebra Formulas You Must Know

• (a + b)² = a² + 2ab + b²
• (a – b)² = a² – 2ab + b²
• (a + b)(a – b) = a² – b²
• (x + a)(x + b) = x² + (a + b)x + ab
• Quadratic Formula: x = (-b ± √(b² – 4ac)) / 2a

Solved Examples

Example 1:

If 2x + 5 = 15, find x.
2x = 10 → x = 5

Example 2:

Factorize: x² – 9
(x – 3)(x + 3)

Example 3:

Solve: x² – 5x + 6 = 0
Roots: (x – 2)(x – 3) = 0 → x = 2, 3

Practice Questions

• If 5x + 7 = 32, find x.
• Factorize: x² + 7x + 10
• Solve: 2x² – 3x – 2 = 0
• If (a + b)² = 81 and a = 5, find b.
• Solve for y: 3y + 4 = 19

Tips to Master Algebra for Aptitude Exams

• Memorize important formulas & identities.
• Practice factorization problems daily.
• Strengthen basics before moving to quadratic equations.
• Solve previous years’ aptitude papers.
• Use shortcuts only after understanding concepts.

Algebra is a scoring topic in aptitude exams if practiced well. By learning formulas, solving practice questions, and applying shortcuts, you can improve speed and accuracy. Keep practicing regularly, and you’ll master Algebra in no time.

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