CBSE Class 12 Mathematics Part 2 Limits Derivatives and Integrals

CBSE Class 12 Mathematics – Part 2 is a structured Mathematics course designed primarily for Class 12 CBSE Board students preparing for their Mathematics examination. Students from other school boards may also join the course to strengthen their understanding of Class 12 Calculus and improve their mathematical problem-solving skills.
This is Part 2 of a structured four-part Class 12 Mathematics series designed to cover the complete syllabus progressively. This part focuses on Limits and Derivatives, Continuity and Differentiability, and Applications of Derivatives, with emphasis on conceptual clarity, systematic problem-solving, numerical practice and Board examination preparation.
The course is available in both English and Hindi medium. Teachers are requested to mention the teaching medium while creating a batch so that students can select the appropriate course according to their preference.

Topics Covered
1. Limits and Derivatives (सीमा और अवकलज)
Students develop an intuitive understanding of limits and learn to evaluate limits of polynomials, rational functions, trigonometric functions, exponential functions and logarithmic functions. The chapter establishes the fundamental concepts required for understanding differential calculus and solving Class 12 Mathematics problems.

2. Continuity and Differentiability (सांतत्य तथा अवकलनीयता)
Students learn the concepts of continuity and differentiability and develop systematic methods for finding derivatives. The chapter covers derivatives of composite functions, the chain rule, derivatives of inverse trigonometric functions, implicit differentiation, exponential and logarithmic functions, logarithmic differentiation, derivatives of functions expressed in parametric form and second-order derivatives.

3. Applications of Derivatives (अवकलज के अनुप्रयोग)
Students learn important applications of derivatives, including increasing and decreasing functions, tangents and normals, and maxima and minima. The course uses graphical and geometrical interpretation to develop conceptual understanding of the first derivative test and introduces the second derivative test as a systematic tool for solving problems. Students also practise simple application-based and real-life problems involving derivatives.

Practice, Tests and Study Material
The course includes structured practice and assessment to strengthen conceptual understanding and examination readiness.
• R.D. Sharma Mathematics for Class 12 is recommended as a basic reference and practice book.
• Two tests are included: one objective test and one subjective test.
• Selected questions from the previous 10 years of relevant Board examination papers are practised in class.
• Teachers may provide additional worksheets, practice questions, revision exercises and other study material according to students' academic requirements.

Learning Outcomes
By completing this part of the course, students can develop:
• Strong conceptual understanding of Class 12 Calculus
• Better understanding of limits, continuity and differentiation
• Systematic techniques for solving derivative-based problems
• Ability to apply derivatives to mathematical and real-life situations
• Improved numerical accuracy and problem-solving skills
• Better preparation for the CBSE Class 12 Mathematics Board Examination
• A strong foundation for JEE and other competitive Mathematics preparation