lesson plan integer exponent (wantini)

7/23/2019 LESSON PLAN Integer Exponent (Wantini)

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LESSON PLAN

Name of School : SMA BANUA KALSEL

Class / Semester : X / 1

Subject : Mathematcs

Aca!emc "ear : #$1#/#$1%

U&t : E'(o&e&t

)ate : No*ember +th #$1#

,me Allocato& : - ' -. m&utes

rst a&! Seco&! Meet&0

TOPIC : INTEGER EXPONENT

Media:RESOURCES and REFERENCES: MATHEMATICS SERIES and MATHEMATICS FOR SENIOR

HIGH SCHOOL YEAR X

OBJECTIVES:

• Students ae a!"e t# si$%"i&' e(%#nenti#na" e(%essi#n usin) e(%#nent %#%eties

TEACHING PROCESS:

P#)a$ and A*ti+ities Ti$e Met,#d

Int#du*in):

-. O%enin) t,e *"ass

Tea*,e sa'in) )eetin) t# students/ 0assa"a$ua"ai1u$2 # 0 G##d

$#nin) *"ass2.

3. C,e*1in) t,e student %esen*e.

4. Re+ie5s %e+i#us "ess#n/ e$ind a "ess#n a!#ut e(%#nent in 6uni#

,i), s*,##"/ e(a$%"e: ,#5 &#$ #& e(%#nent/ 5,at *a""ed an' n#tati#n

in t,at e(%essi#n/ e(a$%"e: student $ust !e $enti#n t,at &#$ #&

e(%#nent is an 7# in an#t,e +aia!"es8/ t,en as1 t# student 5,at a

$eanin) a and 5,at a $eanin) n 7a is *a""ed t,e !ase and n is *a""ed

t,e e(%#nent8

-9

$inutes

E(%"anati#n

T,e Main A*ti+ities :

-. E(%"ain a!#ut e(%#nenti#na" e(%essi#n/ e(%#nent %#%eties and ,#5

t# si$%"i&' e(%#nenti#na" e(%essi#n usin) e(%#nent %#%eties.

T# &ind a de&initi#n #& e(%#nent !' e(a$%"e:

a2= a . a

a3= a . a . a

a4= a . a . a . a

.

.

9

$inutes

E(%"anati#n



.

an = a . a . a . .... a/ 5,ee a ; R.

n &a*t#s #& a

S# t,at e(%#nent is %#du*t #& a nu$!e !' itse"& 5,ee a <9 and a ;R

F# an' ea" nu$!e a and an' %#siti+e inte)e n/a. an = a . a . a . .... a

n &a*t#s #& a

!. a9 = -

*. a-n =

1

an

&# e(a$%"e:

9/>- = 9/>

3? = 3 . 3 . 3 . 3 = -

7@48@3 =

1

(−3)2 =1

(−3) . 1

(−3)=

1

9

T,e %#%eties #& inte)e e(%#nent

-8 T,e %#du*t u"e

a$ . an = am+n/ 7a ;R and m, n ; 8

%##&: "et >4.>3 = 7> . > . >8 . 7> . >8 = > . > . > . > . > = > >

a4.a3 = 7a . a . a8 . 7a . a8 = a . a . a . a . a = a>

a$

. an

= 7a . a . a.... a8 . 7a . a . a....a8 = 7a . a . a.... a8 $ ti$es n ti$es 7$ n8 ti$es

= am+n

Gi+in) s#$e e(a$%"es.

38 T,e u#tient u"e

am

an = am-n / 7a ;R and m, n ; 8

P##&: *#nside t,e u#tientam

a

n = a$ .1

a

n = a$ . a@n =

am-n

Gi+in) s#$e e(a$%"es

48 P#5e u"e

• (am)n

= am.n

• (a . b )m

=am

bm

7a/ ! ; R/ ! < 9 and m, n ; 8



• ( ab )m

=am

am

P##&:

(am )n=am am am … am=am+m+m+…+m=am .n

n ti$es

(a . b )m=(a .b ) . (a . b ) . (a . b ) … (a .b )=(a . a . a …) . (b . b . b … b )=am

bm

( ab )m

=a

b. a

b. a

b …

a

b=a .a .a…a

b .b .b…b=am

am

Gi+in) s#$e e(a$%"es

3. Gi+in) e(a$%"e #& %#!"e$ t# t,e studentSi$%"i&' ea*, e(%essi#n/ e$#+in) an' ne)ati+e e(%#nent as needed:

a. (2 x

5 y−2 )−3

=2 x−15

y6=

2 y6

x15

!.15a

−3b−2

3a−4b5 =5

a

b7

4. Gi+in) s#$e %#!"e$s t# t,e student &# e(e*ise

Si$%"i&' ea*, e(%essi#n/ e$#+in) an' ne)ati+e e(%#nent as needed:

a. ( x2

x3

y2 )

−2

. x3 : x2

y

!. ( a2

b

23

b−1

c )−2

+(−2a2

b c−3 )4

?. As1in) t# t,e student t# *#$e &#5ad in t,e *"ass ##$

>. C,e*1in) t,e student 6#! t#)et,e

C"#sin):

-. Gi+in) #%%#tunit' t# t,e student t# as1 a!#ut a "ess#n3. T,e tea*,e and t,e students su$$aiDe t,e su!6e*t $attes t,at 5ee

39

$inutes

n times

m times m timesm times

m times

m timesm



dis*used

4. Gi+in) %#st test

P#st Test:

Si$%"i&' ea*, #& t,e &#""#5in) e(%essi#n in t,ei %#siti+e inte)e e(%#nent.

-. (5−2m

2n−5 )−4

3. (a−7b5

c−9 ) : (10−10

c7

d−6 )

4. (2 pq

p2

q ).( p q5

p q2 )

2

?. x

−1 y− x y

−1

x−1− y

−1

HOMEOR:

S#"+e t,e %#!"e$ #n %a)e -33 in Mat,e$ati*s seies !##1

A%%#+ed !' Ban6a$asin/ - O1t#!e 39-3

Head$aste Tea*,e

s. H. ainuddin/ M.Pd Si antini/ M.Pd

NIP. -39- -9 - 99- NIP. -9- 3994-3 3 9--

LESSON PLAN




Aca!emc "ear : #$1#/#$1%

U&t : a!ca&

)ate : No*ember +th

#$1#,me Allocato& : + ' -. m&utes

%r! to .th Meet&0

TOPIC : Radi*an E(%essi#n

Media:

RESOURCES and REFERENCES: MATHEMATICS SERIES and MATHEMATICS FOR SENIOR

HIGH SCHOOL YEAR X

OBJECTIVES:• Students ae a!"e t# si$%"i&' adi*a" e(%essi#n usin) t,e adi*a" %#%eties



• Students ae a!"e t# addin) #& adi*a" e(%essi#n

• Student ae a!"e t# su!ta*ti#n #& adi*a" e(%essi#n

• Students ae a!"e t# ati#na"iDin) a den#$inat#

TEACHING PROCESS:P#)a$ and A*ti+ities Ti$e Met,#d

Int#du*in):



$#nin) *"ass2.


4. is*ussin) a!#ut ,#$e5#1 "ast $eetin)

?. Re+ie5s %e+i#us "ess#n/ e*a"" t,at a2 is suae #& a/ t,e ese+e #&

suae #%eati#n *a""ed ta1in) t,e suae ##t #& t,e nu$!e.>. As1 t# students t# $enti#n s#$e nu$!es 5,i*, is suae/ &#

e(a$%"e ?3 = - and 7@?83 = -/ s# t,at suae ##ts #& - is ± ?

-9 $in

T,e Main a*ti+ities:

-. E(%"ain a!#ut *#n*e%t #& ##ts !' stud'in) t,e ati#na" and iati#na"

nu$!es. e&initi#n #& ati#na" nu$!es ae nu$!es t,at *an !e

e(%essed as &a*ti#n

a

b / 5,ee a and b ae inte)e and b ≠ 0. F#

e(a$%"e:0=

0

1=

0

2 …

0,5=1

2=

5

10…

et*

Iati#na" nu$!es ae nu$!es t,at *ann#t !e e(%essed as &a*ti#n

a

b / 5,ee a and b ae inte)e and b ≠ 0. F# e(a$%"e:

√ 2,√ 3,√ 5 , e , π ,..

3. e&initi#n #& suae ##ts ae nu$!es in t,e adi*a" si)n 5,i*, a n#n

ne)ati+e ea" nu$!e.

4. P#%eties #& suae ##t

F# an' a ≥ 0, b ≥ 0 and n∈ Z /

a. √ a . b=√ a .√ b

9 $in



!. √a

b=

√ a

√ b,(b ≠0)

*. (√ a )n=√ an

Gi+in) e(a$%"e and %##&

?. Si$%"i&' #& suae ##ts

a. √ a2b=a√ b ,(a0,b0)

!. √ ( p+q )+2√ pq=√ p+√ q ,( p>q)

*. √ ( p+q )−2√ pq=√ p−√ q ,( p>q)

Gi+in) e(a$%"e and e(e*ise

>. Additi#n and su!ta*ti#n #& suae ##tsT,e suae ##ts *an !e addin) # su!ta*tin) 5,en ,a+e sa$e

adi*and.

a√ b ± c√ b=(a ± c )√ b


. Mu"ti%"i*ati#n and di+isi#n #& suae ##ts

C#nside !' %#%eties #& suae ##ts/ 5e *an $u"ti%"' and di+ide #&

suae ##ts.


. Rati#na"iDin) a den#$inat#

a. Fa*ti#n in &#$ #&a

√ b

A &a*ti#n in &#$ #&a

√ b *an !e asi#na"iDed !' $u"ti%"'in)

t,e &a*ti#n nu$!e 5it,√ b

√ b .

a

√ b (√ b

√ b .=a√ b

b .

!. Fa*ti#n in &#$ #&a

b+√ c

A &a*ti#n in &#$ #&a

b+√ c *an !e asi#na"iDed !' $u"ti%"'in)



t,e &a*ti#n nu$!e 5it,b−√ c

b−√ c

ab+√ c (

b−√ cb−√ c =

c

b−√ ¿¿a¿¿


K. Suae ##t #& an iati#na" su$

√ a±√ b=√ a+√ a2−b

2±√

a−√ a2−b

2

Gi+in) e(a$%"e and e(e*ise.

RAICAL EXPRESSION

-. e&initi#n #& adi*a" e(%essi#n is an e(%essi#n #& t,e &#$n√ a / a

*a""ed adi*and and n *a""ed t,e inde(/ 5,ee a ≥ 9 and n ∈ R

a.n√ xn=| x| / i& n is e+en

!.

n√ xn

=

x

/ i& n is #dd


3. P#%eties #& adi*a" e(%essi#n

Let a ≥ 9/ b ≥ 9 and k, m, n ∈ N 5,ee m <9 and n < 9 t,en

a.n√ a .b=

n√ a .

n√ b

!.n

√a

b=

n√ an√ b

, b ≠0

*. ( n√ a)m

=n

√ am

d.m

√ n√ a=

mn√ a

e.n√ am=

kn√ akm


4. Si$%"i&'in) adi*a" e(%essi#n

n ∈ N, n ≠1, for any real



a.n√ an

b=an√ b

?. Rasi#na"iDe t,e den#$inat# #& &a*ti#n

a. Fa*ti#n in &#$

an√ b

an

√ bm.

n√ bn−m

n

√ bn−m=

a n√ bn−m

b

!. Fa*ti#n &#$ #&3√ a+

3√ b

Mu"ti%"' t,e nu$eat# and den#$eat# !'3√ a2− 3

√ ab+3√ b2

*. Fa*ti#n &#$ #&3√ a−

3√ b

Mu"ti%"' t,e nu$eat# and den#$eat# !'3√ a2+ 3

√ ab+3√ b2

Gi+in) e(a$%"e and e(e*ise.

>. As1in) t# t,e student t# *#$e &#5ad in t,e *"ass ##$

. C,e*1in) t,e student 6#! t#)et,e

C"#sin):

-. Gi+in) #%%#tunit' t# t,e student t# as1 a!#ut a "ess#n

3. T,e tea*,e and t,e students su$$aiDe t,e su!6e*t $attes t,at

5ee dis*used

4. Gi+in) %#st test

39

$inutes

P#st Test:

-. Si$%"i&' t,e adi*a" e(%essi#n !e"#5:

a.√ a4 3√ a√ a

3

√ a√ a

!.3√ 0.125+

15√ 32

+√ 0.5

*.4√ 32+

4√ 162−

4√ 512

3. Rasi#na"iDe t,e den#$inat# #& ea*, &a*ti#n

a.4√ 2−√ 3

√ 2+√ 3

!.

13√ 3−

3√ 2

*.

13√ 16−

3√ 12+

3√ 9



HOMEOR:

S#"+e t,e %#!"e$ #n %a)e - in Mat,e$ati*s seies !##1

A%%#+ed !' Ban6a$asin/ - O1t#!e 39-3

Head$aste Tea*,e


NIP. -39- -9 - 99- NIP. -9- 3994-3 3 9--

LESSON PLAN




Aca!emc "ear : #$1#/#$1%

U&t : A,2ONAL EXPONEN,)ate : No*ember +th #$1#

,me Allocato& : # ' -. m&utes

+th meet&0

TOPIC : Rati#na" E(%#nent

Media:


HIGH SCHOOL YEAR XOBJECTIVES:



• Students ae a!"e t# si$%"i&' ati#na" e(%#nent usin) "a5s #& e(%#nent

TEACHING PROCESS:


Int#du*in):



$#nin) *"ass2.



?. Re+ie5s %e+i#us "ess#n/ e*a"" "a5s #& e(%#nent and inte)e

e(%#nent.

-9 $in

T,e Main A*ti+ities:

-. Undestandin) ati#na" e(%#nent t# t,e students/ !' t,e "a5s &#

e(%#nents (a x ) y=a xy

s# t,at/ "et $ and n !e inte)es su*, t,at n 9.

T,en an

m=m√ an

/ i& n is e+en/ a $ust !e n#n@ne)ati+e.

F# e(a$%"e: 3

2

5=5

√ 32

3. Si$%"i&' t,e ati#na" e(%#nent usin) "a5s #& e(%#nent.

F# e(a$%"e: si$%"i&' t,e e(%essi#n√ x3

y2+√ x2

y3

√ x2 y+√ x y

2

√ x3 y

2+√ x2 y

3

√ x2 y+√ x y

2 =

( x3 y

2 )1 /2+ ( x2 y

3 )1 /2

( x2 y )1/2+( x y

2 )1/2

x3 /2

y+ x y3 /2

x y

1/2

+ x

1 /2

y

= xy ( x

1

2+ y1

2 )

x

1

2 y

1

2( x1

2+ y

1

2)

= x

1

2 y

1

2=√ xy

Gi+in) $#e e(a$%"e and e(e*ise

. As1in) t# t,e student t# *#$e &#5ad in t,e *"ass ##$

K. C,e*1in) t,e student 6#! t#)et,e

9 $in

C"#sin):



5ee dis*used

4. Gi+in) %#st test

39

$inutes

P#st Test:



-. Si$%"i&' e(%essi#n and 5ite t# t,e e(%#nent !e"#5:

a.3

√ √ x3√ x4:√ x

!.

4√ 2 x .

4√ x

3.4√ 4 x

2

√ 2 xy .√ 2 x .√ 2 y

3. E+a"uate √ 56+√ 56+√ 56+…

HOMEOR:

S#"+e t,e %#!"e$ #n %a)e -> in Mat,e$ati*s seies !##1

A%%#+ed !' Ban6a$asin/ - O1t#!e 39-3

Head$aste Tea*,e


NIP. -39- -9 - 99- NIP. -9- 3994-3 3 9--

LESSON PLAN

Name of School : SMA BANUA KALSELClass / Semester : X / 1


Aca!emc "ear : #$1#/#$1%

U&t : EXPONEN, E3UA,2ONS


,me Allocato& : # ' -. m&utes

4th meet&0

TOPIC : E(%#nent Euati#nsMedia:


HIGH SCHOOL YEAR X

OBJECTIVES:

• Students ae a!"e t# s#"+e e(%#nent euati#ns usin) "a5s #& e(%#nent

TEACHING PROCESS:


Int#du*in):-. O%enin) t,e *"ass

-9 $in




$#nin) *"ass2.




e(%#nent.

T,e Main A*ti+ities:

-. E(%"ain ,#5 t# s#"+e e(%#nent euati#ns !' )i+in) e(a$%"e

a. 3( = K/ t' t# )et t,e sa$e !ase #n ea*, side #& t,e euati#n

3( = 34

S# t,at ( = 4

!. 42 x+1=64

4

2 x+1

=4

3

2 x+1=3

2 x=2

x=1

*. (19 ) x−1

=3

√ 33 x+1

( 1

32

)

x−1

=(33 x+1 )1 /3

3−2( x−1)=3

1 /3(3 x+1)

−2 x+2= x+1

3

3 x=5

3

x=5

9

3. Gi+in) $#e e(a$%"e and e(e*ise t# t,e students

4. As1in) t# t,e student t# *#$e &#5ad in t,e *"ass ##$

?. C,e*1in) t,e student 6#! t#)et,e

9 $in

C"#sin):



5ee dis*used

4. Gi+in) %#st test

39

$inutes

P#st Test: Find t,e +a"ues #& ( t,at satis&' t,e &#"#5in) euati#ns:



-. √ 162 x+4=(0.25 )−3 x−3

3. x√ 2.2

x=4

4. 2 x +1+4

x=80

HOMEOR:

S#"+e t,e %#!"e$ #n %a)e -> in Mat,e$ati*s seies !##1

A%%#+ed !' Ban6a$asin/ - O1t#!e 39-3

Head$aste Tea*,e


NIP. -39- -9 - 99- NIP. -9- 3994-3 3 9--



LESSON PLAN




Aca!emc "ear : #$1#/#$1%

U&t : LO5A2,6M


,me Allocato& : + ' -. m&utes

7th to 1$th meet&0

TOPIC : L#)ait,$

Media:


HIGH SCHOOL YEAR X

OBJECTIVES:

TEACHING PROCESS:


Int#du*in):



$#nin) *"ass2.




e(%#nent.

-9 $in

T,e Main A*ti+ities

-. Gi+en t,e de&initi#n #& "#)ait,$/ loga x= y ↔a y= x / &# a 9/ a

< 9 and x>0,∧ y∈ R

F# e(a$%"e:

ite t,e eua"ities in "#)ait,$i* &#$ and in e(%#nent &#$.

a. 34 = K

34 = K ↔ log28=3

!. log3

1

27=−3

log3

1

27=−3 ↔ 3−3

= 1

27

9 $in

lesson plan integer exponent (wantini)

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