SUGGESTED METHODOLOGY FOR INTRODUCTION AND REVISION IN CLASS XI MATHEMATICS
S.No
Unit
Topic
SETS
1
SETS AND
FUNCTIONS
RELATIONS
AND
FUNCTIONS
Objectives/Area to be covered
 KNOWLEDGE OF SETS AS A
COLLECTION OF WELL
DEFINED OBJECTS
 OPERATION ON SETS
 DIAGRAMATIC
REPRESENTATION OF SETS
 IDEA OF SUBSETS
 CARTESIAN PRODUCT TO BE
EXPLAINED AS THE SET OF
ALL ORDERED PAIRS
 UNDERSTANDING RELATION
AS A SUB SET OF CARTESIAN
PRODUCT UNDER CERTAIN
PREFIXED CONDITIONS
 FUNCTIONS AS A RELATION
WITH SOME MORE
CONDITIONS
 TYPES OF FUNCITONS WITH
EXAMPLES
Suggested Methodology
 GIVING THE CHILDREN THE
ACTIVITY OF MAKING A
COLLECTION OF OBJECTS AND
CHEKING WHETHER IT IS A SET OF
NOT
 EXPLAINING THE STUDETNS THAT
THE NUMBERS THEY HAVE
LEARNT IN LOWER CLASSES ARE
NOW SET OF NUMBERS
 GIVING ACTIVITIES TO FIND THE
UNION AND INTERSECTION OF
SETS
 MORE PRACTICE ON OPERATION
ON SETS BY VENN DIAGRAM
 ASKING THE STUDENTS TO FORM
THE SET A  B & B  A
 GIVING ACTIVITY FOR THE
STUDENTS FORM ALL THE
SUBSETS OF A  B &
IDENFITIFYING THE RELATION SET
FROM IT
 GIVING THE IDEA TO GET THE
DOMAIN FROM THE FIRST
ELEMENTS AND RANGE FROM THE
SECOND ELEMENT.
 GIVING THE PRACTICE TO
IDENTIFY THE FUNCTION BY
ARROW DIAGRAM
Suggested teaching
aids
 POWER POINT
PRESENTATION
 CHARTS WITH
OPERATION ON
SETS BY VENN
DIAGARAM
Duration
Remarks
1 HOUR
COLLECTION
OF
NUMBERS AS
SET OF
NUMBERS
TO BE
STRESSED
THE SETS
AND
SUBSETS ON
NUMBERS
TO BE
EXPLAINED
 POWER POINT
PRESENTATION
 CHARTS WITH
EXAMPLES
WHERE A
RELATION IS A
FUNCTION AND
A RELATION
WHICH IS NOT A
FUNCTION.
1 HOUR
FUNCTIONS
TO BE USED
IN CLASS XI &
XII TO BE
EXPLAINED
IN DETAIL
S.No
1
2
Unit
SETS AND
FUNCTIONS
ALGEBRA
Topic
Objectives/Area to be
covered
 INTRODUCTION OF
VARIOUS MEASURE OF
ANGLES AND THEIR
CONVERSIONS
 THE NECESSITY TO USE
RADIAN AS AN ANGLE
MEASURE
 SIGNS OF
TRIGONOMETRIC
ANGLES
TRIGONOMETRIC
 SUM & DIFFERENCE
FUNCTIONS
FORMULAE
 IDEA OF SOLUTIONS OF
A TRIGONOMETRIC
EQUATIONS
MATHEMATICAL
INDUCTION
 CONCEPT OF
INDUCTION AS A
METHOD OF PROVING
RESULTS
 STEPS INVOLVED IN THE
INDUCTION PROCESS
Suggested Methodology
 EXPLAINING THE RADIAN AS
ANOTHER DEGREE MEASURE
AND ITS VALUE FOR 0, 30,
45, 60, 90, etc FOR EASY
REFERENCE
 EASY METHOD TO
REMEMBER THE SIGN OF
TRIGONOMETRIC
FUNCTIONS AND THE
NATURE OF FUNCTIONS IN
DIFFERENT QUADRANTS.
 PROBLEMS USING MORE
THAN ONE SET OF
FORMULAE TO BE SOLVED
TO GET USED TO THE
FORMULAE
 MORE PRACTICE WITH
POSITIVE VALUE AND
NEGATIVE VALUE IN
SOLVING TRIGONMETRIC
EQUATIONS TO BE GIVEN
 GIVING ACTIVITY FOR THE
STUDENTS TO CHECK THE
RESULT FOR A PARTICULAR
VALUE OF n  N.
 CATEGORIZING THE
PROBLEMS AS
a. PROBLEMS ON FORMULA
b. PROBLEMS ON
STATEMENTS
c. PROBLEMS WITH
INEQULAITIES
Suggested teaching
aids
Duration
Remarks
 POWER POINT 1 HOUR
PRESENTATIO
N
 CHARTS WITH
SETS OF
FORMULAE
INCLUSION
OF OBTUSE
ANGLES AND
NEGATIVE
ANGLES IN
CLASS XI &
XII TO BE
EXPLAINED
TO THE
STUDENTS
 POWER PONT
PRESENTATIO
N
 CHARTS WITH
STEPS IN THE
PROCESS OF
INDUCTION.
THE
CONCEPT OF
VALIDITY OF
STATEMENT
FROM n = K
TO n = k + 1
AND SO ON
TO BE
EXPLAINED
1 HOUR
S.No
Unit
Topic
COMPLEX
NUMBERS
2
ALGEBRA
LINEAR
INEQUALITIES
Objectives/Area to be covered
Suggested Methodology
 IMAGINING THE VALUE OF
AS .
 IDENTIFYING THE
IMAGINARY PART AS THE
COEFFCIENT OF
 CONJUAGTE OF A
COMPLEX NUMBER AND
ITS SIGNIFICANCE IN
ARGAND DIAGRAM
 THE POLAR COORDINATES
IN THE POLAR
REPRESTATION.
 SOLUTION OF QUADRATIC
EQUATION WITH COMPLEX
ROOTS.
 RECOLLECTION OF THE
QUADRATIC EQUATIONS OF
CLASS X WHERE THERE WAS ‘NO
SOLUTION’ OR ‘NO REAL ROOTS’
 EASY METHOD TO SIMPLIFY A
COMPLEX NUMBER AND
EXPRESS IN THE FORM
 EASY METHOD TO EXPRESS A
COMPLEX NUMBER IN POLAR
FORM.
 SOLUTION OF LINEAR
INEQUALITIES IN ONE
VARIABLE
 GRAPHICAL SOLUTION OF
SYSTEM OF LINEAR
INEQULITIES IN TWO
VARIABLES
 DIFFERENCE BETWEEN THE
SOLUTION OF LINEAR
EQUATION AND LINEAR
INEQUATION IN ONE VARIABLE
TO BE EXPLAINED
 DIFFERENCE BETWEEN THE
SOLUTION OF LINEAR
EQUATION AND LINEAR
INEQUATION IN TWO VARIABLE
TO BE EXPLAINED
 IDENTIFICATION OF THE
SOLUTION REGION BY
CHECKING THE INCLUSION OF
EXCULSION OF THE ORIGIN TO
BE EXPLAINED
 GIVING A PROJECT WORK TO
THE STUDENTS ON SOLVING
THE SYSTEM ON GRAPH SHEETS
Suggested teaching
aids
 POWER POINT
PRESENTATION
 CHARTS ON THE
ALGEBRA OF
COMPLEX
NUMBERS
 CHART ON
ARGAND
DIGARAM
 CHART
EXPLAINING THE
POLAR
Duration
Remarks
1 HOUR
COMPLEX
NUMBERS
AS A
SUPERSET
OF ALL
NUMBERS
CAN BE
EXPLAINED
THE IDEA OF
NEGATIVE
ANGLES
TAKEN IN
POLAR
REPRESENTATION
REPRESETNATIONS
 USE OF
SOFTWARE
‘GEOGEBRA’ TO
EXPLAIN THE
SOLUTION SET
1 HOUR
TO BE
EXPLAINED
THE
CONCEPT OF
INFINITE
SOLUTION
TO BE
EXPLAINED
THE
SOLUTION
SET FOR
PROBLEMS
WITH x  0
& y  0 TO
BE
EXPLAINED
S.No
Unit
Topic
Objectives/Area to be covered



PERMUTATION &
COMBINATION


2
ALGEBRA

BINOMIAL THEOREM FOR
POSITIVE INTEGRAL VALUES
SIMPLE EXPANSIONS USING
BINOMIAL THEOREM
APPLICATIONS





ARITHMETIC PROGRESSION
ARITHMETIC MEAN
GEOMETRIC PROGRESSION
GEOMETRIC MEAN
SUM OF SPECIAL SERIES

BINOMIAL
THEOREM
SEQUENCES AND
SERIES
FUNDEMENTAL PRINCIPLE
OF COUNTING
MEANING OF n!
METHODS TO FIND
PERMUTATION OF
REPEATED AND NON
REPEATED ITMS
METHODS TO FIND THE
NUMBER OF
COMBINATIONS
Suggested Methodology
 RECOLLECTION OF THE CONCEPT
‘MULTIPLICATION IS REPEATED
ADDITION’ WHILE INTRODUCING
PRINCIPLE OF COUNTING.
 SIGNIFICANCE OF TAKING 0! = 1
 DOING PROBLEMS WITH THE
SUBDIVISIONS ADDED IN A
GRADUAL MANNER
 MORE PROBLEMS ON REPEATED
ITEMS ON PERMUTTIONS
 MULTIPLIYING THE ANSWER
WHEN ‘AND’ COMES BETWEEN
EVENTS AND ADDING WHEN ‘OR’
COMES BETWEEN EVENTS
 RECOLLECTING THE EXPANSIONS
(a + b)2 & (a +b)3 AND CHECKING
THEM THROUGH BINOMIAL
THEOREM
 THE PATTERN OF SIGNS IN THE
EXPANSIONS TO BE EXPLAINED
 CONNECTING THE IDEA OF
MIDDLE TERMS WITH THAT OF
MEDIAN THEY STUDIED IN CLASS
X
 FORMULA ALREADY LEARNT TO
BE RECOLLECTED
 RELATION BETWEEN THE TERMS
OF A.P AND G.P TO BE
EXPLAINED
 METHOD TO GET THE GENERAL
TERMS OF SPECIAL SEQUENCES
TO BE TAUGHT
Suggested teaching
aids
 CHARTS ON
FORMULAE OF
PERMUTATION
AND
COMBINATON






Duration
Remarks
1 HOUR
PERMUTATION
WITHOUT
CONDITION AND
WITH
CONDITION
MAY BE
EXPLAINED TO
THE STUDENTS
POWER POINT
PRESENTATION
CHART ON PASCAL
TRIANGLE
CHART ON SOME
IMPORTANT
EXPANSIONS
1 HOUR
EXPANSIONS
WITH THREE
TERMS MAY BE
TAUGHT
POWER POINT
PRESENTATION
CHARTS ON
FORMULAE
CHARTS ON
SUMMATION OF
SPECIAL SERIES
1 HOUR
PROBLEMS ON
COMBINATION
OF A.P AND G.P
MAY BE DONE
IN THE CLASS
S.No
Unit
Topic
STRAIGHT
LINES
Objectives/Area to be
covered
Suggested Methodology
 SLOPE OF A LINE
 VARIOUS FORMS OF
EQUATIONS OF A LINE
 GENERAL EQUATIONS
OF A LINE
 DISTANCE OF A POINT
FROM A LINE
 RECOLLECTION OF LINEAR
EQUAITON OF TWO
VARIABLES FROM CLASS X
 SIGNIFICANCE OF VARIOUS
FORMS OF LINES AND
THEIR USE
 EASY METHOD TO GET THE
SLOPE OF THE LINE FROM
SLOPE INTERCEPT FORM
 EASY METHOD TO FIND
THE POLAR FORM OF A
LINE
 IDEA OF GETTING
FRUSTAM OF A CONE AND
SECTIONS OF A CONE MAY
BE EXPLAINED
 VARIOUS TYPES OF CONCIC
SECTIONS AND MTHODS
TO REMEMBER THEIR
TYPES MAY BE EXPLAINED
IN DETAIL.
 A PROJECT MAY BE GIVEN
ASKING THE STUDENTS TO
REPRESENT THE CONCIC
SECTIONS ON GRAPH
SHEETS
 THE APPLICATINS OF THE
CONCIC SECTIONS IN DAY
TO DAY LIFE MAY BE
EXPLAINED WITH
EXAMPLES.
 THE SIGNIFICANCE OF
 SECTIONS OF A CONE
 CIRCLES, PARABOLA,
HYPERBOLA, ELLIPSE
3
COORDINATE
GEOMETRY
CONIC
SECTIONS
Suggested teaching
aids
Duration
Remarks
 USE OF
SOFTWARE
‘GEOGEBRA’
TO EXPLAIN
THE NATURE
OF LINES
 CHARTS WITH
VARIOUS
FORMS OF
LINES
1 HOUR
SIGNIFICANCE
OF SLOPEOF
A LINE MAY
BE
EXPLAINED IN
DETAIL AS IT
IS USED IN
CLASS XII
 POWER POINT
PRESENTATION
 CHARTS WITH
VARIOUS
TYPES OF
CONCE
SECTONS
EXPLANING
THEIR PARTS
1 HOUR
GENERAL
FORM OF
EQAUTION OF
A CIRCLE MAY
BE
INTRODUCED
S.No
4
Unit
CALCULUS
Topic
LIMITS AND
DERIVATIVES
Objectives/Area to be
covered
 MEANING OF LIMTS
 STANDARD LIMITS
 MEANING OF
DERIVATIVE
 DERIVATIVE THROUGH
FIRST PRINCIPLE
 FORMULA ON
DERIVATIES
FOCUS MAY BE EXPLAINED
IN DETAIL
Suggested Methodology



5
 STATEMENTS

 COMPONENTS OF A
STATEMENT
 CONNECTIONS USED IN
A STATEMENT

 VALIDATING A
MATHEMATICAL MATHEMATICAL
STATEMENT
REASONING
REASONING

Suggested
teaching aids
RECOLLECTING THE ‘NOT
 CHARTS ON
DEFINED’ VALUE OF A
STANDARD
FUNCTION AT A POINT AND
LIMITS
THEN INTRODUCING THE
 CHARTS ON
CONCEPT OF LIMITS
FORMULAE OF
METHOS TO CONVERT A
DERIVATIVES
LIMIT PROBLEM INTO
PRODUCT OF STANDARD
LIMITS
PROBLEMS WITH
COMBINATION OF
POLYNOMIAL AND
TRIGONOMETRIC
FUNCTIONS
MATHEMATICAL
 CHART PAPER
STATEMENTS ALREADY
ON
LEARNT IN LOWER CLASSES
COMPONENTS
ARE TO BE RECOLLECTED
OF A
THE METHODS USED IN
STATEMENT
PROVING SOME THEOREMS  CHART ON
IN LOWER CLASSES TO BE
EXPLAINING
RECOLELCTED
THE METHODS
AN ASSIGNMENT MAY BE
TO REWRITE A
GIVEN TO THE STUDNETS
STATEMENT
TO IDENTITY THE METHOD
USED IN VALIDATING A
MATHEMATICAL
STATEMENT
Duration
Remarks
1 HOUR
MEANING
OF
DERIVATIV
E TO BE
EXPLAINED
AS IT IS
USED N
CLASS XII
1 HOUR
PRACTICE
ON
PROVING
THE SAME
RESULT BY
VARIOUS
METHODS
MAY BE
GIVEN.
S.No
Unit
Topic
Objectives/Area to be
covered
 MEASURE OF
DISPERSION
 MEAN DEVIATION
 VARIANACE AND
STANDARD
DEVIATION
 COEFFICIENT OF
VARIATION
STATISTICS
6
STATISTICS
&
PROBABILITY
PROBABILITY
 RANDOM
EXPERIMENT
 SAMPLE SPACE
 EVENT SPACE
 PROBABILITY OF AN
EVENT
 PROBABILITY OF
‘NOT’, ‘AND’ & ‘OR’
EVENTS
Suggested Methodology
 MERITS AND DEMERITS
OF MEAN TO BE
EXPLAINED
 SIGNIFICANCE OF
MEASURE OF DISPERSION
TO BE EXPLAINED WITH
EXAMPLES
 PROBLEMS TO COMPARE
THE VARIANCE AND
COEFFICIENT OF
VAIRATION OF TWO SETS
OF DATA TO BE GIVEN.
 STUDENTS TO BE
ENCOURAGED TO USE
THE STEP DEIVATION
METHOD TO DO
PROBLEMS ON GROUPED
DATA
 IDEA OF SET THEORY TO
BE RECOLLECTED
 SOLVING PROBLEMS OF
PROBABILITY USING
PROPERTIES OF SETS
Suggested teaching
aids
 CHARTS ON
FORMULAE
Duration
Remarks
1 HOUR
THE
APPLICATION
OF
COEFFICIENT
OF
VARIATION
IN
CHECKING
THE
CONSISTANACY
TO BE
EXPLAINED
 POWER POINT
PRESENTATION
 CHARTS ON
THEOREMS
ON
PROBABILITY
1
HOURS
RELATION
BETWEEN
THE
EVENTS
MAY BE
DISCUSSED