Chapter 14 of 19
Revision Notes
Inequalities — Revision Notes
CAT · Quantitative Aptitude
Free Inequalities revision notes for CAT Quantitative Aptitude 2026 — key concepts, formulas, and definitions for quick revision.
Interactive on Super Tutor
Studying Inequalities? Get the full chapter — free.
Practice questions, revision notes, formula sheet and AI doubt-solver — built for CAT Quantitative Aptitude.
Super Tutor
This is just one of 16+ visuals inside Super Tutor's Inequalities chapter
Explore the full setRevision Notes — Inequalities
Key concepts, formulas, and definitions from Inequalities for CAT Quantitative Aptitude preparation.
Key Topics to Revise
1
Basic Concepts and Definitions
- Two real numbers or algebraic expressions related by >, <, ≥, or ≤ form an inequality
- Strict inequalities use > or < signs, while slack inequalities use ≥ or ≤ signs
- For any two real numbers a and b: either a = b, a > b, or a < b (only one can be true)
2
Properties and Transformations of Inequalities
- Addition and subtraction of the same constant preserves inequality direction
- Multiplication or division by positive constants preserves inequality direction
- Multiplication or division by negative constants reverses inequality direction
3
Important Standard Inequalities
- a² + b² ≥ 2ab (AM-GM for squares)
- |a + b| ≤ |a| + |b| (Triangle inequality)
- |a - b| ≥ ||a| - |b|| (Reverse triangle inequality)
4
Linear Inequalities
- Linear inequalities have the form ax + b ⋈ 0 where ⋈ represents any inequality symbol
- Solutions are ranges of values, not specific points
- Graph solutions on number lines using open/closed circles
Get complete revision notes with diagrams and examples — continue in Super Tutor
Key Concepts
Inequalities use symbols > (greater than)Key rules includeInequalities of the form ax+b>0 (orInequalities of form ax²+bx+c>0 where solutionKey inequalities include
Frequently Asked Questions
What topics are covered in Inequalities for CAT?
Inequalities is an important chapter in CAT Quantitative Aptitude. It covers key concepts and formulas that are frequently tested in the exam. Key topics include: Basic Concepts and Definitions, Properties and Transformations of Inequalities, Important Standard Inequalities, Linear Inequalities.
How important is Inequalities for CAT?
Inequalities is a frequently tested chapter in CAT Quantitative Aptitude. Questions from this chapter appear regularly in previous year papers. There are 53 practice questions available for this chapter.
How to prepare Inequalities for CAT?
Start by understanding the core concepts, then solve practice questions. Focus on formulas and their applications. Use revision notes for quick review before the exam.
More resources for Inequalities
For CAT aspirants
Get the full Inequalities chapter — for free.
Practice questions, revision notes, formula sheet and AI doubt-solver for CAT Quantitative Aptitude.