Chapter 5 Maths Class 12 PDF Download
Are you looking for a reliable and easy way to prepare for your CBSE Class 12 Maths exam? Do you want to access the best study material for Chapter 5 Continuity and Differentiability? If yes, then you have come to the right place. In this article, we will tell you how to download the PDF of Chapter 5 Maths Class 12 and why it is beneficial for your exam preparation. We will also provide you with the syllabus, important questions, and solutions for Chapter 5 Maths Class 12. So, read on and get ready to ace your exam.
Introduction
Chapter 5 Continuity and Differentiability is one of the most important chapters in CBSE Class 12 Maths syllabus. It deals with the concepts of continuity and differentiability of functions, their algebraic properties, derivatives of composite, implicit, inverse trigonometric, exponential, and logarithmic functions, logarithmic differentiation, derivatives of functions in parametric forms, second-order derivatives, mean value theorem, and Rolle's theorem. This chapter has a weightage of about 8 marks in the board exam and is also useful for competitive exams like JEE and NEET.
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To master this chapter, you need to understand the theory, practice the exercises, and solve the previous year questions. However, it can be difficult to carry all the books and notes everywhere you go. That's why downloading the PDF of Chapter 5 Maths Class 12 is a smart idea. It will help you to access the chapter anytime and anywhere on your device.
Why download Chapter 5 Maths Class 12 PDF?
There are many reasons why you should download the PDF of Chapter 5 Maths Class 12. Some of them are:
Benefits of Chapter 5 Maths Class 12 PDF
It is free of cost and easy to download from reliable sources like NCERT website or Vedantu.
It is compatible with any device like laptop, tablet, or smartphone.
It saves your time and money as you don't have to buy or carry heavy books.
It helps you to revise the chapter quickly and effectively.
It provides you with the latest and updated content as per the CBSE syllabus.
It enhances your learning experience with interactive features like diagrams, graphs, examples, and exercises.
How to download Chapter 5 Maths Class 12 PDF?
To download the PDF of Chapter 5 Maths Class 12, you can follow these simple steps:
Go to the NCERT website or Vedantu website.
Select the class, subject, and book name.
Click on the chapter name and open it in a new tab.
Click on the download button or save as option.
Choose the location where you want to save the file.
Open the file and start studying.
Chapter 5 Maths Class 12 Syllabus
Before you start studying Chapter 5 Continuity and Differentiability, you should know the syllabus of CBSE Class [assistant](#message) Some additional sentences are 12 Maths. The syllabus of CBSE Class 12 Maths is divided into six units, namely, Relations and Functions, Algebra, Calculus, Vectors and Three-Dimensional Geometry, Linear Programming, and Probability. The total marks of the board exam are 100, out of which 80 marks are for the theory paper and 20 marks are for the internal assessment. The duration of the theory paper is three hours.
Overview of Chapter 5 Maths Class 12 Syllabus
Chapter 5 Continuity and Differentiability belongs to the unit Calculus, which has a weightage of 35 marks in the board exam. The chapter has two main sections: Continuity and Differentiability. The section on Continuity covers the concepts of continuity of a function at a point and on an interval, algebra of continuous functions, and intermediate value theorem. The section on Differentiability covers the concepts of differentiability of a function at a point and on an interval, algebra of differentiable functions, derivatives of composite, implicit, inverse trigonometric, exponential, and logarithmic functions, logarithmic differentiation, derivatives of functions in parametric forms, second-order derivatives, mean value theorem, and Rolle's theorem.
Unit-wise marks distribution
The following table shows the unit-wise marks distribution for CBSE Class 12 Maths syllabus:
Unit
Marks
Relations and Functions
8
Algebra
10
Calculus
35
Vectors and Three-Dimensional Geometry
14
Linear Programming
5
Probability
8
Total
80
Topics and sub-topics covered
The following table shows the topics and sub-topics covered in Chapter 5 Continuity and Differentiability:
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Topic
Sub-topic
Continuity
Continuity at a point and on an interval.
Algebra of continuous functions.
Intermediate value theorem.
Differentiability
Differentiability at a point and on an interval.
Algebra of differentiable functions.
Derivatives of composite functions.
Derivatives of implicit functions.
Derivatives of inverse trigonometric functions.
Derivatives of exponential and logarithmic functions.
Logarithmic differentiation.
Derivatives of functions in parametric forms.
Second order derivatives.
Mean value theorems
Mean value theorem.
Rolle's theorem.
Chapter 5 Maths Class 12 Important Questions
One of the best ways to prepare for your CBSE Class 12 Maths exam is to practice the important questions for Chapter 5 Continuity and Differentiability. These are the questions that are most likely to be asked in the exam or are based on the important concepts of the chapter. Solving these questions will help you to revise the chapter, improve your problem-solving skills, and boost your confidence.
What are important questions for Chapter 5 Maths Class 12?
Important questions for Chapter 5 Maths Class 12 are the questions that test your understanding of the concepts, formulas, and methods of the chapter. They can be of different types, such as short answer, long answer, multiple choice, fill in the blanks, true or false, match the following, etc. They can also vary in difficulty level, from easy to moderate to hard.
Types of important questions for Chapter 5 Maths Class 12
Some of the types of important questions for Chapter 5 Maths Class 12 are:
Questions based on the definition and examples of continuity and differentiability of a function at a point and on an interval.
Questions based on the algebra of continuous and differentiable functions, such as finding the sum, difference, product, quotient, or composition of two or more functions.
Questions based on finding the derivatives of various types of functions, such as composite, implicit, inverse trigonometric, exponential, and logarithmic functions.
Questions based on applying logarithmic differentiation to find the derivatives of functions involving powers, products, or quotients.
Questions based on finding the derivatives of functions in parametric forms, such as curves or equations involving two or more variables.
Questions based on finding the second-order derivatives of functions and their applications.
Questions based on verifying or applying the mean value theorem or Rolle's theorem to a given function or equation.
Sources of important questions for Chapter 5 Maths Class 12
Some of the sources of important questions for Chapter 5 Maths Class 12 are:
The NCERT textbook and exemplar book for Class 12 Maths.
The previous year question papers and sample papers for CBSE Class 12 Maths board exam.
The mock tests and practice tests available online or offline from various sources like Vedantu, Toppr, etc.
The reference books and guides for CBSE Class 12 Maths like R.D. Sharma, R.S. Aggarwal, etc.
Chapter 5 Maths Class 12 Solutions
Another way to prepare well for your CBSE Class 12 Maths exam is to refer to the solutions for Chapter 5 Continuity and Differentiability. These are the step-by-step explanations and answers to the questions and exercises given in the NCERT textbook and other sources. Reading these solutions will help you to understand the concepts, methods, and formulas of the chapter better. They will also help you to check your answers, clear your doubts, and improve your accuracy.
What are solutions for Chapter 5 Maths Class 12?
Solutions for Chapter 5 Maths Class 12 are the detailed and accurate solutions to the questions and exercises given in the NCERT textbook and other sources for Chapter 5 Continuity and Differentiability. They are written by expert teachers and subject matter experts who have years of experience in teaching CBSE Class 12 Maths. They follow the latest CBSE syllabus and marking scheme and adhere to the CBSE guidelines.
Features of solutions for Chapter 5 Maths Class 12
Some of the features of solutions for Chapter 5 Maths Class 12 are:
They cover all the topics and sub-topics of the chapter in a systematic and logical manner.
They provide clear and concise explanations with relevant examples and diagrams wherever necessary.
They use simple and easy-to-understand language that is suitable for CBSE Class 12 students.
They show all the steps and calculations involved in solving a problem with proper reasoning and justification.
They highlight the important points, formulas, and tips to remember while solving a problem.
They also provide alternative methods or shortcuts to solve a problem whenever possible.
Sources of solutions for Chapter 5 Maths Class 12
The NCERT solutions for Class 12 Maths Chapter 5 Continuity and Differentiability available on the NCERT website or Vedantu website.
The RD Sharma solutions for Class 12 Maths Chapter 5 Continuity and Differentiability available on the Vedantu website or other online platforms.
The RS Aggarwal solutions for Class 12 Maths Chapter 5 Continuity and Differentiability available on the Vedantu website or other online platforms.
The video lectures and live classes by expert teachers and tutors on YouTube, Vedantu, Toppr, etc.
Conclusion
In this article, we have provided you with all the information you need to download the PDF of Chapter 5 Maths Class 12 and prepare for your CBSE Class 12 Maths exam. We have also given you the syllabus, important questions, and solutions for Chapter 5 Continuity and Differentiability. We hope that this article has helped you to understand the chapter better and boost your confidence. We wish you all the best for your exam.
FAQs
Here are some of the frequently asked questions about Chapter 5 Maths Class 12:
What is the difference between continuity and differentiability of a function?
A function is continuous at a point if the limit of the function at that point is equal to the value of the function at that point. A function is differentiable at a point if the derivative of the function at that point exists and is finite. A function can be continuous but not differentiable at a point, but if a function is differentiable at a point, then it is also continuous at that point.
What are the conditions for Rolle's theorem and mean value theorem to be applicable?
Rolle's theorem and mean value theorem are two important results in differential calculus that relate the values of a function and its derivative on an interval. Rolle's theorem states that if a function is continuous on a closed interval [a,b] and differentiable on an open interval (a,b) and f(a) = f(b), then there exists at least one point c in (a,b) such that f'(c) = 0. Mean value theorem states that if a function is continuous on a closed interval [a,b] and differentiable on an open interval (a,b), then there exists at least one point c in (a,b) such that f'(c) = (f(b) - f(a))/(b - a).
How to find the derivatives of inverse trigonometric functions?
The derivatives of inverse trigonometric functions can be found by using the implicit differentiation method. For example, to find the derivative of y = sin(x), we can write x = sin(y) and differentiate both sides with respect to x. We get 1 = cos(y) dy/dx, which implies dy/dx = 1/cos(y). Since cos(y) = (1 - x), we get dy/dx = 1/(1 - x). Similarly, we can find the derivatives of other inverse trigonometric functions.
How to use logarithmic differentiation to find the derivatives of functions involving powers, products, or quotients?
Logarithmic differentiation is a technique that uses the properties of logarithms to simplify the differentiation of functions involving powers, products, or quotients. For example, to find the derivative of y = x, we can take the natural logarithm of both sides and get ln(y) = x ln(x). Then we can differentiate both sides with respect to x and get (1/y) dy/dx = ln(x) + 1. Multiplying both sides by y, we get dy/dx = y (ln(x) + 1). Since y = x, we get dy/dx = x (ln(x) + 1). Similarly, we can use logarithmic differentiation to find the derivatives of other functions involving powers, products, or quotients.
How to find the derivatives of functions in parametric forms?
A function in parametric form is a function that is expressed in terms of one or more parameters. For example, a curve can be represented by x = f(t) and y = g(t), where t is a parameter. To find the derivative of y with respect to x, we can use the chain rule and get dy/dx = (dy/dt)/(dx/dt). To find the second derivative of y with respect to x, we can use the quotient rule and get d 2y/dx = (dy/dt)(dx/dt) - (dy/dt)(dx/dt)/(dx/dt). Similarly, we can find the derivatives of other functions in parametric forms. 44f88ac181
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