Class 12 Maths Chapter 6: Applications of Derivatives PYQs
Master Application of Derivatives through topic-wise previous year questions (2014-2026). These modules cover essential board exam topics including rate of change, monotonicity, optimization, and real-world case studies.
Practise derivatives as rates of change, use sign analysis to identify increasing and decreasing intervals, and apply first- or second-derivative tests to maxima and minima. The optimization and case-study questions connect these methods to geometry, measurement, and real-world decision problems.
Topic-wise PYQ Practice
- 1. Rate of Change of Quantities
- 2. Increasing & Decreasing Functions
- 3. Maxima & Minima (Local/Absolute)
- 4. Maxima & Minima (Optimization)
- 5. Case Study Questions
Step-wise marking is strictly enforced across all 2-mark, 3-mark, and 5-mark subjective questions. Always quote standard algebraic identities or theorem statements before carrying out algebraic substitutions. For matrix operations and vector cross-products, clearly tabulate intermediate matrix rows and components to guarantee full partial credit even if a minor arithmetic slip occurs in the final step.
CBSE Class 12 Chapter 6: Applications of Derivatives Blueprint & Exam Strategy
Marks Weightage: Unit III: Calculus (Contributes 6 to 8 Marks). Question blueprint: Features 1 MCQ on strictly increasing/decreasing intervals or rate of change, and a high-yield 4-Mark Case-Based Question (Section E) or 5-Mark optimization problem testing geometric maxima and minima (e.g. cylinder inscribed in a sphere, open cardboard box).
Examiner Advice: Always state the domain when finding intervals where a function is increasing or decreasing. In word optimization problems, express the quantity to be maximized or minimized in terms of a single variable, take the first derivative, set it to zero, and verify using the Second Derivative Test (d^2y/dx^2 < 0 for maximum, > 0 for minimum).