Class 12 Mathematics Case Study Questions
CBSE Board Exam Preparation – Chapter-wise Practice Questions with Solutions
Chapter 1: Relations and Functions
This chapter introduces different types of relations and functions, including empty, reflexive, symmetric, and transitive relations. You’ll learn about one-one, onto, and bijective functions, along with binary operations.
Chapter 2: Inverse Trigonometric Functions
Inverse trigonometric functions are fundamental in calculus and have wide applications. This chapter covers their principal value branches, properties, and graphs.
Chapter 3: Matrices
Matrices are powerful mathematical tools used in various fields. This chapter covers different types of matrices, operations on matrices, and finding inverses.
Chapter 4: Determinants
Determinants provide important information about matrices and linear systems. This chapter explores properties of determinants, their applications in finding areas, and solving systems of linear equations.
Chapter 5: Continuity and Differentiability
This fundamental calculus chapter explores the concepts of continuity and differentiability. You’ll learn various differentiation techniques including chain rule, implicit differentiation, and logarithmic differentiation.
Chapter 6: Applications of Derivatives
This chapter explores practical applications of derivatives in various fields. You’ll learn to determine rates of change, find tangents and normals to curves, approximate values, and solve optimization problems.
Chapter 7: Integrals
Integration is the inverse process of differentiation. This chapter covers various methods of integration including substitution, partial fractions, and integration by parts.
Chapter 7(a): Definite Integrals
Integration is the reverse of differentiation and is used to find areas under curves. In this section, we focus on definite integrals, which calculate the exact area between a curve and the x-axis over a specific interval.
Chapter 8: Applications of Integrals
This chapter demonstrates how integration can be used to calculate areas under curves and between curves. You’ll learn to find areas bounded by lines, parabolas, circles, and other common curves.
Chapter 9: Differential Equations
Differential equations model numerous real-world phenomena. This chapter introduces basic concepts of differential equations, their formation, and solution methods including variable separable and homogeneous techniques.
Chapter 10: Vector Algebra
Vectors are quantities having both magnitude and direction. This chapter covers vector operations, dot and cross products, and their geometric interpretations.
Chapter 11: Three Dimensional Geometry
This chapter extends coordinate geometry to three dimensions. You’ll learn about direction cosines and ratios, equations of lines and planes, and how to calculate angles and distances between geometric elements in 3D space.
Chapter 12: Linear Programming
Linear programming is a method to achieve the best outcome in mathematical models. This chapter covers problem formulation, graphical solution method, and identification of feasible and optimal solutions.
Chapter 13: Probability
Probability quantifies uncertainty. This chapter covers conditional probability, multiplication theorem, independent events, Bayes’ theorem, and probability distributions of random variables.
Case study questions in Class 12 Mathematics are application-based problems that present a real-life scenario, data set, or detailed passage. Instead of direct formulas, you must analyze the situation, extract relevant mathematical concepts (like Calculus, Algebra, or Vectors), and solve interconnected sub-questions to reach a conclusion.
Important chapters with available case studies include: Relations & Functions, Inverse Trigonometric Functions, Matrices & Determinants, Continuity & Differentiability, Application of Derivatives, Integration, Application of Integrals, Differential Equations, Vector Algebra, Three Dimensional Geometry, and Linear Programming.
You can download free PDFs of chapter-wise case study questions from educational resource websites. These PDFs typically contain sets of questions with detailed solutions and are compiled according to the latest CBSE/board exam patterns.
They help by:
- Enhancing conceptual understanding through real-world application.
- Improving analytical and problem-solving skills.
- Familiarizing you with the new, competency-based pattern in board exams.
- Teaching time management with complex, multi-step problems.
Yes, most curated case study resources provide step-by-step solutions or detailed answer keys. This allows you to verify your approach, understand the methodology, and learn from mistakes.
Aim to practice 15-20 varied case study questions per chapter. Focus on quality analysis over quantity. Ensure you cover different types of scenarios and difficulty levels within each topic.
The effective strategy is:
- Read Carefully: Understand the complete scenario and given data.
- Identify Concepts: Relate the situation to specific chapter concepts and formulas.
- Plan Sequentially: Solve sub-questions in order, as answers often build upon previous parts.
- Review: Check if your final answers logically fit the initial scenario.
Absolutely. Many educational platforms host interactive sections where you can practice case study questions online. These often provide instant feedback and are accessible on both mobile devices and desktops.
While JEE Main/Advanced focus more on deep theoretical problems, practicing case studies strengthens your applied mathematics skills, logical reasoning, and data interpretation—valuable assets for all competitive exams.
If stuck:
- Re-read the passage; key information is often embedded in the text.
- Break down the problem into smaller, familiar mathematical steps.
- Refer to the theoretical concepts from your textbook.
- Review similar solved examples from practice resources before attempting again.