Lesson Plan, Class XI (Ch-12) | Limits & Derivatives

LESSON PLAN   SUBJECT MATHEMATICS    CLASS 10+1

Lesson plan for maths class XI  Limits & Derivatives cbse lesson plans for mathematics teachers,   lesson plan for maths class XI,  lesson plan for maths teacher in B.Ed.

RMB DAV CENTENARY PUBLIC SCHOOL NAWANSHAHR
NAME OF THE TEACHER				DINESH KUMAR
CLASS	XI	CHAPTER	12	SUBJECT	MATHEMATICS
TOPIC	Limits & Derivatives			DURATION : 20 Class Meetings

PRE- REQUISITE KNOWLEDGE:

• Knowledge of simple calculations of algebra
• Knowledge of trigonometry class 10^th and 11^th

TEACHING AIDS:

Green Board, Chalk,  Duster, Charts, smart board, projector, laptop etc.

METHODOLOGY:

Lecture method, Demonstration and scaffolding method of teaching.

LEARNING OBJECTIVES:-

• Introduction of derivatives as it is the rate of change of distance functions.

• Introduction of the derivatives geometrically.

• Intuitive idea of limits.

• Limits of polynomial, rational, trigonometric, logarithmic and exponential functions.

• Definition of derivatives relate it to scope of tangent of the curve.

• Derivative of sum, difference, product and quotient of functions.

• Derivatives of polynomial and trigonometric functions.

LEARNING OUTCOMES

• After studying this lesson student should know 

• The term limits and derivatives. 

• Students should know the different method of finding the limits, left hand limit , right hand limit, 

• Method of finding the derivative by first principal, 

• Product rule and quotient rule of the derivatives and different methods of finding the derivatives.

RESOURCES

NCERT Text Book, 

NCERT Exemplar Book of mathematics, 

Resource Material : Worksheets , E-content, Basics and formulas from cbsemathematics.com)

KEY WORDS

Limit, Left-Hand Limit (LHL) , Right-Hand Limit (RHL), Finite Limit, Infinite Limit, Limit at a Point, Continuity (Basic Idea), Standard Limit, Rationalization, Factorization, Substitution Method, Derivative, Differentiation, Independent Variable, Dependent Variable, Function, First Principle of Derivative.

CONTENT OF THE TOPIC

• Interoduction

• Algebra of Limits

• Derivatives

• Derivative by First Principal

• Definition of Limit

• Undefined terms:

• Left Hand Limit and Right Hand Limit

• Different methods and formulas of derivatives

PROCEDURE :

Start the session by asking the question related to the algebraic identities, simple algebraic calculations and some formulas of trigonometry. Now give some introduction of limits and derivatives and introduce the topic limits and derivatives step by step as follows.

[Explanation of limits]

[Explanation of Derivatives]

Introduction

Today, we begin one of the most important topics in Mathematics—Limits and Derivatives. This chapter forms the foundation of Calculus, a branch of mathematics developed to study change and motion. Calculus has wide applications in science, engineering, economics, medicine, and many other fields.

The concept of a limit helps us understand the value that a function approaches as the input gets closer and closer to a particular point. It enables us to analyze the behaviour of functions even when the function value at that point is not directly known.

Definition of Limit

Suppose f is a real function on a subset of the real numbers and let c be a point in the domain of f. Then f is continuous at c if 

Algebra of Limits

Let f(x) and g(x) are two functions such that    and    exist.

1)   

2)  

3)  

4)   

Limit of constant function remain constant

Undefined terms: 

  all these terms are called undefined terms

Left Hand Limit and Right Hand Limit

If at any point c given function have two different values then at that point (c) we calculate LHL and RHL. and the limit exist if

Left Hand Limit = Right Hand Limit = f(c)

LHL is denoted by    

RHL is denoted by  

 When limit exist then 

For a function f(x) the limits    and    may or may not exist

If both limits    and    exist, they may not be equal.

If    then    does not exist

If  , then  exist and is equal to the common limit.

A function is said to be continuous if its limit exist or if     or if 

Left Hand Limit = Right Hand Limit = f(c)

Derivatives

Building on the concept of limits, we define the derivative of a function. A derivative measures the instantaneous rate of change of one quantity with respect to another. Geometrically, it represents the slope of the tangent to a curve at a given point, while in real life it helps us calculate quantities such as velocity, acceleration, growth, and decay.

Derivative by First Principal

  

  

Different methods and formulas of derivatives

Now explain Algebra (sum and difference ) of derivatives of functions, derivative of polynomial and trigonometric functions. Product rule and quotient rule of polynomials.

Derivative of logarithmic and exponential functions with all formulas of derivatives and their use in different problems.

STUDENTS DELIVERABLES:-

• Review questions given by the teacher. 

• Students should prepare the presentation individually or in groups on the formulas of limits and derivatives.  

• Solve NCERT problems with examples.

EXTENDED LEARNING:

Students can extend their learning in   through the Resource Centre Mathematics . Students can also find many interesting topics on mathematics at the site:   cbsemathematics.com

DIFFERENTIAL LEARNING

For Below Average Students

• Mind/ Concept maps

• Charts , Models and activity

• Simple questions

For Average Students

• Learning situations through watching video, creating collage, completing puzzles, assignment.

For Above Average Students:

• Group Discussion

• Higher Order Thinking  Skill questions

SKILLS ENHANCED

Observation  skill,  analytical skill,  critical thinking, team work, constructive approach, interpersonal skill,  engagement  in learning process etc.

ASSESSMENT TECHNIQUES:

• Assignment sheet (Home Assignment) will be given as home work at the end of the topic. 
• Separate sheets which will include questions of logical thinking and Higher order thinking skills will be given to the above average students.
• Class Test , Oral Test , worksheet and Assignments. can be made the part of assessment.
• Re-test(s) will be conducted on the basis of the performance of the students in the test.

Competency based assessment can be taken so as to ensure if the learning outcomes have been achieved or not. e.g.

• Puzzle

• Quiz

• Misconception check

• Peer check

• Students discussion

• Competency Based Assessment link: M C Q

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