Inequalities
Learning Time: 5-15 hours
Content: Inequalities involve mathematical expressions that determine the range of values a variable can take. The 2025 curriculum covers linear inequalities, absolute value inequalities, second-degree inequalities, and systems. The TYT focuses on basic solution methods, while the AYT focuses on advanced analysis and applications.
- Basic Concepts:
- Inequality Signs (, ≤, ≥)
- Linear Inequalities (ax + b < c)
- Solution Set and Interval Representation (a < x < b)
- Solution Techniques:
- Operations Rules (Change of Inequality Sign, Negative Multiplication)
- Absolute Valued Inequalities (|x – a| < b)
- Graphical Solution (Number Line and Coordinate Plane)
- Advanced Calculus (AYT):
- Quadratic Inequalities (ax² + bx + c > 0)
- Systems of Inequalities (Overlap and Intersection Regions)
- Mathematical Proofs and Complex Problems (Trigonometric Inequalities)
- Applications:
- Economic Frontier Analysis (Cost and Profit Bounds)
- Physical Constraints (Speed and Distance Range)
- Daily Life Examples (Budget Planning, Time Management)
- Affecting Factors:
- Number of Variables
- Inequality Type (Linear/Quadratic/Absolute Value)
- Complexity of the Solution Range
Course Features
- Lectures 0
- Quizzes 0
- Duration 5 hours
- Skill level Expert
- Language English
- Students 15
- Assessments Yes
