2ND SPELL - X-CLASS- Maths - Dec,1 to 4 Periods - Computers (1)

7/30/2019 2ND SPELL - X-CLASS- Maths - Dec,1 to 4 Periods - Computers (1)

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PROGRESSIONS APSWREISOCIETY J.TIRUPATI RAOLESSON PLAN FORMAT PGT MATHS

PERIOD: 1 APSWRSCHOOL/JC, PVP

Date and Time: class: X Subject: Maths Medium: English


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Content analysis/concepts/subconcepts Activities indicating behavioral/learning out comes

Aids/experimentsto be done

/demonstrations

etc. method Evaluation

By teacher By Pupil

Problem: ,......3,2,1 nnnAre in A.P. find ., .138 nandttt

112 =+= nnd)1(8178 +=+= ndat

What do you call this

sequence?

What is A.P?

What do you call the fixed

number?

By which, common difference

is denoted?In the A.P, 3, 7, 11, 15..

what is a and d.

What is formula for general

term in A.P?

If3

4=a and d=2 find 7t

and nt ?

Find 7t .

Find .nt

What is given A.P?

What is first term?

Find common difference d?

Find .8t

A.P

Arithmetic Progression is a sequence in which

each term, except the first is obtained by adding a

fixed number to the term immediately preceedingit

Common difference

d

a=3; d=2

dna )1( +

3

4=a and d=2

3

3212

3

426

3

4

)17(

7

7

=+

=+

=

+=

t

dat

3106

3102

3

4222)1(

3

4

==

=+=

nn

nntn

,......3,2,1 nnn1n

112 =+= nnd981)1(8178 ==+=+= nnndat

13

121)1(1211213

=

=+=+=

n

nndat

0)1)(1()1()1( =+=+= nndnatn

Analyti

cal

method

What is

nth term


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Recapitulation: 1.What is the general form of nth term in AP?

2. Find 100t

Behavioral changes: Students find the required terms in A.P.

Assignment: exercise (1) problems 1 to 22.


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PERIOD: 3. APSWRSCHOOL/JC, PVP


C l i / / b Aid / i


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/demonstrations


By teacher By Pupil

Problem: The 8th term of an A.P is

17 and the 19th term is 39. Find 25th

term.

178 =t and 3919 =t

?25 =t

dat 78 += =17..(1)

39189 =+= dat (2)

211

22

2211)1()2(

==

=

d

d

31417

17)2(7

==

=+

a

a

51483)2(243

2425

=+=+=

+= dat

Problem:2: If 7 times of the 7thterm of AP is equal to 11times of

the 11th term. Show that 18th term is

zero.

dat 67 +=

............427)6(77 7 dadat +=+=

What is the nth term in A.P?

Find the common difference

in the A.P ,........3

5,

3

4,

xxx

What is the next term in this?

What is given?

What is required?

Write 8th term in A.P?


Solve (1) and (2) and find a, d

Find .25t

What is to be proved?

Write PinAt .7 ?

Find 7 times of 7th term.


dnatn )1( +=

Find33

34

3

4 xxxx

xd =

==

36

335 xxx =+

178 =t and 3919 =t

?25 =t

dat 78 += =17..(1)

39189 =+= dat (2)

211

222211)1()2(

==

=

d

d

31417

17)2(7

==

=+

a

a

51483)2(243

2425

=+=+=+= dat

18th term is zero

dat 67 +=

)1......(..........427)6(77 7 dadat +=+=

dat 1011 +=

)2........(11011)10(111111

dadat +=+=

Analyti

cal

method


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Recapitulation: 1.If ba btat = ,then what is bat + ?

Behavioral changes: students find required term in A.P.

Studnets understands that m times of mth tem is equal to ntimes of nth term the (m+n)th term is zero.

Assignment: exercise 1 problems No.25 to 30.


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Recapitulation: 1. what is the sum of n terms in A.P?2. If first term is a and last term is l then what is the sum of n terms in A.P?

Behavioral changes: 1.Students understanding the gauss method of summation of A.P?

2. Students recall the formula for nth term in A.P?

3. Students find the sum of terms (number of terms given) in A.P.

Assignment: Exercise problems 1 to 15.


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Content analysis/concepts/sub Aids/expe


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Aids/experiments to

be done

/demonstr

ations etc.

method Evaluation

By teacher By Pupil

Problem1: Find the sum of 16, 11,

6 ,.. to 23 terms.

Problem: if 20,10;3

2=== nld

Find sum of 20 terms

What is the n th term in an A.P?

What is the formula for sum of n

terms in A.P?

If an AP has n terms and the first and

last terms are a and l then what is?nS

The terms are in which progression?

What do you find?

What is the first term?

Find common differenced?

What is n?

Find ?23S

What is given required in this

problem?

What is the formula for finding sum of

dnatn )1( +=

( )dnan

Sn )1(22

+=

)(2

lan

Sn +=

A.P

23S

16=a

51611 ==d

n=23

( ) )1(22

dnan

Sn +=

( ))5)(123(1622

2323 +=S

=

( ) 392378223)11032(

223 ==

=-897

20,10;3

2=== nld

)(2

lan

Sn +=

dnal )1( +=

Deductive

method

?23S


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Content analysis/concepts/sub Aids/experiments


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/demonstrations


By teacher By Pupil

Arithmetic mean: when three

quantities are in A.P, the middle

term is called arithmetic mean ofthe other two.

Arithmetic means:

Problem: Insert 5 arithmetic means

between 4 and 22.

Give an example for A.P?

Take any three terms which

are in A.P?

What is the average of 7 and15?

What do you call 11?

If a, b c are in A.P, what do

you call b?

If a, b, c are in AP, then their

common difference

Find the A.M of a, b.

Observe this A.P. how many

numbers lies between 2 and17? What are they?

What do you call 5,8,11,14,17

between 2 and 17.

Let take any 5 arithmetic

means between 4 , 22.

22,,,,,4 ,54321 aaaaa Are in

which progression?

How many terms are there?

Wh t i 7th

t ?

3, 7, 11, 15..

7,11,15

112157 =+

-------

Arithmetic mean of a and c

2

2

ca

b

acb

bcabd

+=

+=

==

2

.,,

baA

PAbAa

+=

4.

5,8,11,14,17

Arithmetic means

22,,,,,4 ,54321 aaaaa

A.P

7

22

67 += dat

2,5,8,11,14,17

Analyti

cal

method

What is

A.M of x

and y?


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Recapitulation: 1.what is arithmetic mean?2. What is the A.M of a and b?

3. If a, b, c are in A.P, is b?

Behavioral changes: 1.students understands concept of A.M.

2. Students find the A.M of given two numbers.

3. Students insert the Arithmetic means between two given numbers.

Assignment: 1.Exercise -2; Problems 19 & 20.

2. What is the A.M of a + b and a-b?3. If n A.Ms are in between a and b. then find common differenced.


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y pconcepts Activities indicating behavioral/learning out comes

pto be done

/demonstrations


By teacher By Pupil

Arithmetic mean: when three

quantities are in A.P, the middle

term is called arithmetic mean ofthe other two.

Arithmetic means:

Problem: Insert 5 arithmetic means

between 4 and 22.

Give an example for A.P?

Take any three terms which

are in A.P?

What is the average of 7 and15?

What do you call 11?

If a, b c are in A.P, what do

you call b?

If a, b, c are in AP, then their

common difference

Find the A.M of a, b.

Observe this A.P. how many

numbers lies between 2 and17? What are they?

What do you call 5,8,11,14,17

between 2 and 17.

Let take any 5 arithmetic

means between 4 , 22.

22,,,,,4 ,54321 aaaaa Are in

which progression?

How many terms are there?

Wh i 7th

?

3, 7, 11, 15..

7,11,15

112157 =+

-------

Arithmetic mean of a and c

2

2

ca

b

acb

bcabd

+=

+=

==

2

.,,

baA

PAbAa

+=

4.

5,8,11,14,17

Arithmetic means

22,,,,,4 ,54321 aaaaa

A.P

7

22

67 += dat

2,5,8,11,14,17

Analyti

cal

method

What is

A.M of x

and y?


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Recapitulation: 1.what is arithmetic mean?2. What is the A.M of a and b?

3. If a, b, c are in A.P, is b?

Behavioral changes: 1.students understands concept of A.M.

2. Students find the A.M of given two numbers.

3. Students insert the Arithmetic means between two given numbers.

Assignment: 1.Exercise -2; Problems 19 & 20.

2. What is the A.M of a + b and a-b?3. If n A.Ms are in between a and b. then find common differenced.


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Content analysis/concepts/sub concepts Aids/experiments


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y p pActivities indicating behavioral/learning out comes

pto be done

/demonstrations


By teacher By Pupil

Now we find sum of squares of first

n natural numbers:

Sum of squares of first n natural

numbers ++=6

)12)(1(2 nnnn

26

)12)()(1()12)(1(

x

xxxxxx

=

++

2

2

2

)32)(1)(2()12()1(

1

.......................................

3.65.3.27.4.33

2.63.2.15.3.22

1.61.1.03.2.11

nx

nnnnnn

nx

x

x

x

=

=

==

==

==

What is the general term in

A.P?

What is the sum of n terms in

A.P?

Write first n natural numbers

Are these terms are in A.P?

What is a and d?

Find sum of n naturalnumbers?

Sum of first natural numbers

are denoted byn .

Give any algebraic identity?

Why do you call this is an

identity?

What are the squares of first

n natural numbers?

What is their sum?

Substitute for x=1, 2, 3n ,

add and observe then

Add all terms and simplify.

dna )1( +

)(

2

lan

+

1,2,3,4,5,6..n

yes

a=1 d=1

)1(2

nn

Sn +=

= n )1(2

nn+ =

2

)1( +nn

222 2)( bababa ++=+

For all possible values of a and b the above

statement is true.

2222,........,3,2,1 n

-----

2

2

2

2

.6)12()1()12)(1(

)32)(1)(2()12()1(

1

.......................................

3.65.3.27.4.33

2.63.2.15.3.22

1.61.1.03.2.11

nnnnnnn

nx

nnnnnn

nx

x

x

x

=++

=

=

==

==

==

)...321(6)12)(1( 2222 nnnn ++++=++

2

Analyti

cal

method

10 ?

Give an

example

of

identity?


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Recapitulation: 1) =?n

2) =?2

n

3) =?3

n

Behavioral changes: Students understanding to find the formulas of ,n ,2n 3n .

Students observe ( )23 = nn


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concepts Activities indicating behavioral/learning out comes to be done

/demonstrations


By teacher By Pupil

Problem: Find the sum of n terms

of the series 1.3+3.5+5.7+.+nterms

What is the sum of 1+1+1+.

+1(20terms)

What is 1+1+1+.+1

(n times)

What isn ?

what is ?2

n

what is ?3

n

What is required to find?

If nth term in the series is nt

Then what is sum of n terms?

For finding the sum of n terms

in the series what do you find?

What is the given series?

How is every term in the

series?

What are the first factors inthe series?

Take in the same order; the

terms are in which

progression?

Find n the term?

What are the second factors in

20

nn =1

n =2

)1( +nn

++=6

)12)(1(2 nnnn

+=4

)1( 223 nnn

Sum of n terms

nt

n the term in the series

1.3+3.5+5.7+.

Every term has factors

1, 3, 5

A.P

a=1,d=3-1=2

12

2)1(1)1(

=

+=+=

n

ndnatn

3, 5, 7,

Analyti

cal

method


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Recapitulation: How do you find the sum of n terms in the given series?

Behavioral changes: Students find the sum of n terms in given series.

Student can solve various applicative problems.

Assignment: exercise 3.


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Recapitulation: 1.what is relation between ?, 23 nandnn

Behavioral changes: Students understand the relation between ?, 23 nandnn

Assignment: find the sum of n terms of nterms+++++++ .......)321()21(1


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PROGRESSIONS APSWREISOCIETY J.VISWESWARA RAOLESSON PLAN FORMAT PGT MATHS

PERIOD: 10 APSWRSCHOOL/JC, KOPPERLA





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/demonstrations


By teacher By Pupil

We observe that each term, exceptthe first, is obtained by multiplying

the term immediately preceding it

by a fixed number, of course non-

zero. Such sequences are called

geometric Progressions or briefly

G.P.

Geometric progression:

G.P is series in which the ratio of

each term except first term to the

preceding term is a constant; this

constant is called common ratio (r).

If the first term is a and the

common ratio (r), then the series

takes the form

..........,,, 32 ararara

The thn term or General Term of

a G.P:

Observe the following series?

In each of this sequence, wenote that each term, except the

first, Progresses in a definite

manner.

In the second example first

term ?1t

In the second example second

term ?2t

In the second example 3rd term?3t

Do you know name of the

series?

In G.P what is the ratio of

each term to the preceding

term?

What is called the constant?

Write general terms in the

G.P?

What is the ratio of first twoterms?

What is the general ratio?

Write a series of G.P?

In the series what is the first

term?

n2...,.........32,16,8,4,2

,3,3,3,3 432

n)01.0(000001.0,0001.0,01.0

23121 2,2,2 ttttt === and so on.

3

2333 =

32 333 =

-

Is constant. rt

t=

2

1

Common ratio

..........,,,32

ararara

a

arr

t

t==

2

1

r

t

t

r

r =

1

..........,,,32

ararara

a

ar

111

== arat

122

== arart

1323

== arart

Analyti

cal

method


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Recapitulation: Define G.P?Given an example of G.P?

What is the thn term of G.P?

Behavioral changes: Student understands the definition G.P

Student gives the examples of G.P. students identifying the G.P.

Students solve the problems.

Assignment: solve exercise 4 problems on page No.139.


PERIOD: 11 APSWRSCHOOL/JC, KOPPERLADate and Time: class: X Subject: Maths Medium: English




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/demonstrations


By teacher By Pupil

If a, b, c are in G.P. b is said to be the

geometric mean between a and c.

a ,b ,c are in G.P b

c

a

b

=acbacb ==

2 (a

and c are +ve)

The geometric mean of p and q ispq

Problem:

Inset 5 geometric mean between

.2433

1and

3

1, 543,21

,,, ggggg ,243 PG.

5 + 2 = 7

3

1=a

24367 == art

3

37292433

1 666

=

===

r

rr

3

11 == at

Define arithmetic mean?

If a, b, c is in G.P. then what is

called b?

If a, b, c is in G.P. Find the

common ratios?

If and c are positive find b?

What is the geometric mean of

6 and 24?

Let take any 5 geometric

means?

If insert between .2433

1and

all the numbers are in which

progression?

How many numbers are there?


What is the last (7th) term?

Replace3

1=a , we have

Find the eometric means?

If a, b, c are in A.P then b is called arithmetic

mean of a and c.

Geometric mean

=rb

c

a

b =

acbacb ==2

12144246 ==

543,21,,, ggggg

3

1, 543,21 ,,, ggggg ,243 PG.

5 + 2 = 7

3

1=a

2436

7 == art

3

37292433

1 666

=

===

r

rr

133

1

3

1

12

1

====

==

argt

at

Analyti

cal

method


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Recapitulation: Define geometric mean of three numbers?

What is the geometric mean of a and b?

What is the value of ( ) ?)( 22 yxyx ++

Behavioral changes: Students understanding the concept of geometrical mean.

Student finds the geometric means between any two numbers.

Students find the numbers when A.M and G.M is given?

Assignment: solve the exercise problems page No.145

PROGRESSIONS APSWREISOCIETY J.VISWESWARA RAO

LESSON PLAN FORMAT PGT MATHS




Aids/experiments to be


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concepts Activities indicating behavioral/learning out comes ments to be

done

/demonstrat

ions etc.

method Evaluation

By teacher By Pupil

The sum of the first n terms

of a G.P.:

32 ++++=n arararaS

n

arararrS +++=32

)1( n

n

ra

ara

=

=

r

raS

n

n

=1

)1((r

= rr

raS

n

n

Problem:Find sum of 8 terms in the

geometric progression 3, 6, 12,

24..?

What is the sum of n terms?

What is thn term in G.P?

What is the sum of n terms in

G.P?

Let us take first term of a G.P.

as

What is common ratio?

Let us we write sum of n

terms

Find nrS =

Find nn rSS ?

)1( rSn

Find nS ?

What is the last term in G.P?

Using l rewrite the nS ?

Write given geometricprogression?

( )dnan

Sn )1(22

+=

1=

nn art

-----

a

r

132 +++++=

n

n ararararaS

nn ararararrS ++++=

32

)1( n

n

ra

ara

==

r

raS

n

n

=1

)1((r

= r

r

raS

n

n

1=

narl

1

=r

alrSn

3, 6, 12, 24..?

Analyti

cal

method

What is

the sum

o0f nterms in

G.P?

i l i h i h f l f f i G ?


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Recapitulation: What is the formula of sum of n terms in G.P?

Behavioral changes: Students understanding the deduction of the formula of sum of n terms in G.P.

Students solve the problems related to above formula.

Assignment: solve exercise problems page No.170.

PROGRESSIONS APSWREISOCIETY J Vi


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PROGRESSIONS APSWREISOCIETY J.Visweswara raoLESSON PLAN FORMAT PGT MATHS

PERIOD: 13 APSWRSCHOOL/JC, kopperla





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p g g

/demonstrations


By teacher By Pupil

Problem:

Calculate ( )=

+11

1

32k

k?

Problem:2

What is the formula of sum of

n terms in G.P?

What is given?

Expand?

Find the value

=11

1

2k

?

Find the Value=

11

1

3k

k?

The terms are in which

progression?

Find 11S ?

( )=

+11

1

32k

k

r

raS

n

n

=1

)1((r

= rr

raS

n

n

( )=

+11

1

32k

k

==

+11

1

11

1

32k

k

k

=2+2+2+----+2=22

113213333 +++=

Geometric progression

13

)13(3

1

)1(

133

3,3

11

2

=

=

>===

r

raS

ra

n

n

2

)13(3 1111

=S

=22+2

)13(3 11

3,21, ggg

,m 3,21, ggg ,n

Analyti

cal

method

n


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Recapitulation: what is the value of ?11

=

n

n

If 3,21, ggg are three geometric means between m and n. what is the relation between them?

Behavioral changes: student solves different type of applicative problems using geometric progression concepts.

Assignment: solve exercise 5 problems page No.145.








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p g g

/demonstrations


By teacher By Pupil

Infinite Geometric progressions:

Let us consider the G.P

,......9

4,

3

2,1 find the sum of

n terms of this G.P is?

What happens if the number

of terms n becomes larger and

larger.

If n=1 find the valuen

3

2

If n=5 find the value

n

3

2


3

2


3

2

We see that as n becomes

Larger and largern

3

2

becomes smaller and smaller.

It approaches zero.

How to write?

What is formula of sum of nterms is r


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Recapitulation: What is the sum of infinite terms in G.P?

Behavioral changes: students understanding infinite geometric progression.

Students converting a recurring decimal number into rational number with the help of sum of infinite series.

Assignment: solve exercise problems page No.148.



PERIOD: 15 APSWRSCHOOL/JC, KOPPERLADate and Time: class: X Subject: Maths Medium: English

Content analysis/concepts/sub conceptsActivities indicating behavioral/learning out comes



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done

/demonstratio

ns etc.

method Evaluation

By teacher By Pupil

HORMONIC PROGRESSION(H.P):

A progression is said to be Harmonic

Progression, if the reciprocals of these

terms form an arithmetic progression.

The nth term of H.P:

dnatn

)1(

1

+=

There is no concise general formula for

the sum of n terms in H.P.

PROBLEM: in a harmonic progression

the 4th term is9

1and 13th term is

27

1.

Write the harmonic progression.

Consider the sequence

,......12

1,

9

1,

6

1,

3

1what are the

reciprocals of these terms?

3, 6,9,12 these term are belongs to

which progression?

What do you call the progression?

,......12

1,

9

1,

6

1,

3

1is a harmonic

progression why?

Take general terms in A.P?

What is the nth term in A.P?

What is its reciprocal?

nth term in harmonic progression

Let us take a harmonic progression

What is the 4th term?

They are 3,6,9,12 respectively

They are in A.P

------

Their reciprocals are in A.P

3, 6,9,12 PA.

PareinAdadaa .,.........2,, ++dna )1( +

dna )1(

1

+

=dna )1(

1

+

,......3

1,

2

1,

1,

1

dadadaa +++

)1(93

9

1

3

1

=+

=+

da

da

Analyti

cal

method

What is

the nth

term in

H.P.?


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Recapitulation: Define harmonic progression?

What is the nth term in H.P?

If x, y are in H.P. what is the harmonic mean between x and y?

What is the relation between A, G, H?

Behavioral changes: Students recall A.P and understanding harmonic progression.

Students find the required term in H.P.

Students solve problems.

Assignment: Solve exercise problems page No.151

PROGRESSIONS APSWREISOCIETY J VISWESWARA RAO


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d


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done

/demonstrat

ions etc.

method Evaluation

By teacher By Pupil

Insert 4 harmonic means between

42

1

12

1and

Problem:

If )(),(),( baandaccb +++ are

in H.P.show that 2221

,1

,1

cba

will also be in H.P.

What is the harmonic mean of

a and b?

Let take 4 harmonic means

Insert these harmonic means

How many terms are there inH.P?

What is the 6th term?


Find d?

Find harmonic means.

What is given?

What is the harmonic mean of

a and b?

Find harmonic mean of given

ba

abH

+=

2

4321

1

,

1

,

1

,

1

hhhh

12

1,

4321

1,

1,

1,

1

hhhh,42

1

6 terms

)1(425

42

1

5

1

=+

=+

da

da

1212

11== a

a

65

30

3012425

42512

425

==

==

=+

=+

d

d

d

da

36

11,

30

11,

24

11,

18

11

4321

====hhhh

PHbaandaccb .)(),(),( +++

ba

abH

+=

2

2)(2)2)((

))((2

bbccabaacbac

bacb

bacbac

+++=+++

+++

++=+

Analyti

cal

method

Recapitulation: What is the relation between A.M, G.M, and H.M of two given numbers?


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Recapitulation: What is the relation between A.M, G.M, and H.M of two given numbers?

If 2222 cab += then 222 ,, cba are in which progression?

Behavioral changes: Students understanding the relationship between A.M, G.M and H.M

Students solve application of harmonic progression problems.

Assignment: solve exercise 7 page No.151.


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2ND SPELL - X-CLASS- Maths - Dec,1 to 4 Periods - Computers (1)

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