This Class 12 Mathematics worksheet on Continuity and Differentiability is designed mainly for CBSE board exam preparation and objective-based practice. The worksheet contains a large set of 75 MCQ-type questions, all framed directly from NCERT concepts. It covers limits, continuity at a point, left-hand and right-hand limits, differentiability, standard derivatives, piecewise functions, greatest integer function, modulus functions, inverse trigonometric functions, exponential and logarithmic differentiation, and points of discontinuity. Overall, the worksheet reflects the exact pattern and difficulty level of one-mark questions commonly asked in board exams Continuity and Differentiabilit….
I am writing about this worksheet because Continuity and Differentiability is a chapter where students often feel confident with formulas but lose marks due to conceptual gaps. Small errors in evaluating limits, handling piecewise definitions, or confusing continuity with differentiability can easily lead to wrong answers. A structured worksheet like this helps convert NCERT theory into exam-ready understanding. By analysing these questions carefully, students can clearly see how concepts are tested and where common mistakes usually happen.
Structure of the Continuity and Differentiability Worksheet
The worksheet consists of 75 multiple-choice questions, each carrying one mark. The questions range from direct concept-based MCQs to logic-oriented and application-based problems. Many questions appear simple but are designed to test depth of understanding rather than lengthy calculations.
The overall difficulty level ranges from moderate to high, making this worksheet suitable for revision after completing the chapter.
Limits and Continuity at a Point
A large number of questions focus on limits and continuity. Students are tested on:
- Evaluation of limits using standard formulas
- Left-hand limit and right-hand limit
- Continuity of piecewise functions at a given point
- Finding constant values to make a function continuous
These questions form the foundation of the chapter and are frequently asked in exams.
Differentiability and Its Conditions
The worksheet clearly distinguishes between continuity and differentiability. Questions test understanding of:
- Conditions for differentiability at a point
- Functions that are continuous but not differentiable
- Behaviour of functions like |x|, |sin x|, and greatest integer function
- Points where derivative does not exist
These MCQs help students avoid the common mistake of assuming continuity implies differentiability.
Modulus and Greatest Integer Functions
Several MCQs are based on special functions, including:
- Modulus functions and corner points
- Greatest integer function and step behaviour
- Identifying points of discontinuity
- Continuity intervals of piecewise-defined functions
Such questions are concept-heavy and require careful graphical and logical understanding.
Inverse Trigonometric Functions
The worksheet includes many questions on inverse trigonometric functions, such as:
- Derivatives of inverse trigonometric expressions
- Continuity of inverse trigonometric functions
- Domain-related reasoning
- Composite inverse trigonometric functions
These questions are direct scoring areas if NCERT formulas are revised properly.
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Exponential and Logarithmic Differentiation
Several MCQs test differentiation of exponential and logarithmic expressions. Topics include:
- Differentiation of log-based functions
- Exponential functions involving variables in power
- Implicit differentiation
- Logarithmic differentiation techniques
These questions test both formula knowledge and algebraic simplification.
Piecewise and Special Functions
The worksheet strongly focuses on piecewise-defined functions. Students are tested on:
- Finding continuity at junction points
- Selecting constants to ensure continuity
- Behaviour of functions defined differently in different intervals
Such questions are very common in board exams and require careful step-by-step evaluation.
Trigonometric and Composite Functions
Many questions involve trigonometric expressions and their derivatives, including:
- Composite trigonometric functions
- Functions involving sin, cos, tan, sec, and their inverses
- Differentiation with respect to another function
These MCQs test fluency with standard differentiation rules.
What Students Can Learn from This Worksheet
From analysing this worksheet, a few key points become clear:
- Continuity must be checked using limits, not assumptions
- Differentiability requires equal left and right derivatives
- Modulus and GIF questions are frequent exam favourites
- Piecewise functions demand careful evaluation at junctions
- Regular MCQ practice reduces conceptual and calculation errors
Overall, this Class 12 Continuity and Differentiability worksheet is a strong revision and practice resource. It helps students strengthen conceptual clarity, improve logical reasoning, and gain confidence in handling one-mark calculus questions in board examinations.
