Algebra
Algebra in aptitude tests involves solving equations, simplifying expressions, and applying identities. It is widely used in banking, SSC, CMAT, and placement exams to test logical and mathematical reasoning.
Fundamental Principles
Algebraic Expression
A mathematical expression consisting of variables, constants, and operations like addition, subtraction, multiplication, and division.
Linear Equation
An equation of degree 1, such as ax + b = 0, where 'a' and 'b' are constants.
Quadratic Equation
An equation of degree 2 in the form ax² + bx + c = 0.
Algebraic Identities
Predefined formulas used to simplify expressions, such as (a+b)² = a² + 2ab + b².
Essential Formulation Tips
- Memorize key algebraic identities for faster calculations.
- Always simplify expressions step by step.
- Use substitution method to solve equations quickly.
- Check for common factors before solving equations.
Shortcut Execution Techniques
- Use identities like (a+b)² and (a-b)² to avoid long multiplication.
- For quadratic equations, try factorization before using formulas.
- Convert word problems into equations step-by-step.
Contextual Inquiries (FAQs)
Q: What are the most important topics in algebra for aptitude exams?
A:
Q: How to solve algebra questions quickly?
A:
Example Breakdown: Algebraic Identity Example
Very common exam question.Use identity: (a + b)² = a² + 2ab + b².
Substitute: (x + 5)² = x² + 2×x×5 + 25.
Simplify: x² + 10x + 25.
Final Answer: x² + 10x + 25.
Example Breakdown: Linear Equation Example
Basic algebra solving technique.Subtract 5 from both sides: 2x = 10.
Divide by 2: x = 5.
Final Answer: x = 5.
Example Breakdown: Quadratic Equation Example
Most repeated exam pattern.Factorize: x² - 5x + 6 = (x - 2)(x - 3).
Set each factor to zero.
x = 2 or x = 3.
Final Answer: x = 2, 3.
Algebra Aptitude Practice Questions
Practice algebra questions for banking, SSC, CMAT, and placement exams.
Q1. Simplify: (x - 3)²
Q2. Solve: 3x - 9 = 0
Q3. Solve: x² - 9 = 0