bab 1 eksponen dan logaritma

7/23/2019 Bab 1 Eksponen Dan Logaritma

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RENCANA PELAKSANAAN PEMBELAJARAN

Satuan Pendidikan : SMA Negeri 1 Maospati

Mata Pelajaran : Matematika (Peminatan)

Kelas/Semester : X/SatuMateri Pokok : Fungsi Eksponensial dan Logaritma

Alokasi Waktu : 21 × ! menit

A. Kompetensi nti

1 : Meng"argaidanmeng"a#atia$aran agama #ang dianutn#a%2 : Meng"argaidanmeng"a#atiperilaku$u$ur& disiplin&

tanggung$a'a& peduli (toleransi& gotongro#ong)& santun&

pera#adiri&

dalamerinteraksisearae*ekti*denganlingkungansoialdanal

amdalam$angkauanpergaulandankeeradaann#a%+ : Mema"amipengeta"uan (*aktual& konseptual& danprosedural)

erdasarkan rasa inginta"un#atentangilmupengeta"uan&

teknologi& seni&

uda#aterkait*enomenadanke$adiantampakmata% : Menoa& mengola"& danmen#a$idalamrana"konkret

(menggunakan& mengurai& merangkai& memodi,kasi&

danmemuat) danrana"astrak (menulis& memaa&

meng"itung& menggamar& danmengarang) sesuaidengan

#ang dipela$ari di sekola"dansumer lain #ang

samadalamsudutpandang/teori%

B. Kompetensi !asar dan ndikator Pen"apaian KompetensiN

o

Kompetensi !asar ndikator Pen"apaian

Kompetensi1

%

1%1 Meng"argai dan

meng"a#ati a$aran

agama #ang dianutn#a%

1%1%1

-erdoaseelumdansesuda"pela$

aran

2% 2%2 Memiliki rasa ingin

ta"u& pera#a diri& dan

ketertarikan pada

2%2%1 Memiliki rasa ingin ta"u

tentang *ungsi eksponen dan

logaritma

0



matematika serta

memiliki rasa pera#a

pada da#a dan

kegunaan matematika&

#ang terentuk melalui

pengalaman ela$ar%

2%+ Memilikisikapteruka&

santun& o$ekti*&

meng"argaipendapatda

nkar#atemandalaminter

aksikelompokmaupunakt

i.itasse"ari"ari%

2%2%2 Memiliki sikap meng"argai

pendapat teman dalam akti.itas

di kelas%

+% +%1% Mendeskripsikan dan

menganalisis

eragai konsep dan

prinsip *ungsi

eksponensial dan

logaritma serta

menggunakann#a

dalam men#elesaikan

masala"%

+%21%1 Mendeskripsikan konsep

*ungsieksponensial dan $enis 0

$enis eksponensial%

+%21%2 Menggunakan konsep

entuk akar dalam

men#elesaikan masala"

erkaitan dengan entuk akar%

+%21%+ Menggunakan konsep

pangkat pea"an dalam


erkaitan dengan pangkat

pea"an%

+%21% Men#elesaikan

permasala"an erkaitan

dengan persamaan eksponen%

+%21%! Mendeskripsikan

eragai konsep dan prinsip

*ungsi logaritma%

+%21% Menggunakan eragai

konsep dan prinsip *ungsi

logaritma dalam

1




logaritma%

+%21% Men#elesaikan

permasala"an erkaitan

dengan persamaan logaritma%%2% Menganalisisdata

si*at si*at gra,k

*ungsi eksponensial

dan logaritma dari

suatu

permasala"andan

menerapkann#a

pemea"an masala"%

+%2%1 Menganalisis data si*at si*at

gra,k *ungsi eksponensial dari

suatu

permasala"andanmenerapkann

#a pemea"an masala"

eksponensial%

+%2%2 Menganalisis data si*at si*at

gra,k *ungsi logaritma dari

suatu

permasala"andanmenerapkann

#a pemea"an masala"

logaritma%

%

%1 Men#a$ikan gra,k

*ungsi eksponensial

dan logaritma dalam

memea"kan masala"

n#ata

terkaitpertumu"an

dan peluru"an%

%1%1 Men#a$ikan gra,k *ungsi

eksponensial dalam

memea"kan masala" n#ata

terkaitpertumu"an dan

peluru"an%

%1%2 Men#a$ikan gra,k *ungsi

logaritma dalam memea"kan

masala" n#ata

terkaitpertumu"an dan

peluru"an%%2 Mengola" data dan

menganalisis

menggunakan .ariael

dan menemukan relasi

erupa *ungsi

eksponensial dan

logaritma darisituasimasala" n#ata

%2%1 Mengola" data dan

menganalisis menggunakan

.ariael dan menemukan relasi

erupa *ungsi eksponensial dari

situasimasala" n#ata terkait

eksponensial serta

men#elesaikann#a%%2%2 Mengola" data dan

2



serta

men#elesaikann#a%

menganalisis menggunakan

.ariael dan menemukan relasi

erupa *ungsi logaritma dari

situasimasala" n#ata terkait

logaritma serta

men#elesaikann#a%

C. MA#ER PEMBELAJARAN

1% 3onsep *ungsi eksponensial%

2% 4enis$enis eksponen

+% Pengertian entuk akar%

% Men#eder"anakan entuk akar%

!% 5perasi al$aar pada entuk akar%

% Merasionalkan pen#eut pea"an #ang memuat entuk akar%

% Pangkat pea"an%

6% Persamaan eksponen dengan ilangan pokok sama%

7% Persamaan eksponen dengan pangkat sama%

18% Persamaan eksponen erentuk persamaan kuadrat%

11% 3onsep *ungsi logaritma

12% Si*atsi*at logaritma

1+% Persamaan logaritma

!. KE$A#AN BELAJAR MEN$AJAR

Pertemuan Pertama(9ndikator +%1%1)

Penda%uluan( 18 menit)

1% ;uru men#iapkan sis'a untuk mengikuti proses pemela$aran%2% Melalui tan#a $a'a& sis'a diingatkan kemali mengenai *ungsi dan

eksponensial (apersepsi)%+% ;uru men#ampaikantu$uanpemela$aran#aitu& *ungsi eksponen dan

$enis $enisn#a%% ;uru

memoti.asisis'adenganmenun$ukkanman*aatmempela$ari*ungsi

3



eksponensial dalam ke"idupan%Misaln#a&per"itungan unga

taungan di ank%

Ke&iatan nti( 8 menit)

1% ;uru mengin*ormasikan mengenai pengertian *ungsi eksponensial%2% Sis'a mengamati gamar

+% ;uru mengin*ormasikan a"'a gamar terseut merupakan gra,k

*ungsi eksponensial%% Sis'a menan#akan ara menggamarkan gra,k *ungsi

eksponensial!% Sis'a ersama guru menggamar gra,k *ungsi eksponensial% ;uru mengeek gra,k #ang tela" diuat menggunakan maple% Meminta sis'a men#elesaikan soal lati"an teriming (Lampiran

&<alaman 16) seara mandiri% (Mengeksplorasi dan Mengasosiasi)

6% ;uru erkeliling untuk memiming sis'a menger$akan lati"an soalteriming%

7% Meminta eerapa sis'a ma$u ke depan untuk mendemonstrasikan

ara men#elesaikann#a% (Mengkomunikasikan)18% Sis'a #ang lain akti* memeri komentar ter"adap "asil temann#a

dengan sikap saling meng"argai pendapat teman lainn#a%11% ;urumengkon,rmasikan peker$aan #ang didemonstrasikan%12% Memeri kesempatan kepada sis'a untuk ertan#a1+% ;uru men$elaskan $enis 0 $enis eksponen& #aitu pangkat ulat positi*

dan pangkat ulat negati* dan nol1% ;uru memerikan onto" masing 0 masing $enis eksponen%1!% Memeri kesempatan kepada sis'a untuk ertan#a1% Meminta sis'a men#elesaikan soal lati"an teriming seara

mandiri% (Mengeksplorasi dan Mengasosiasi)1% ;uru erkeliling untuk memiming sis'a menger$akan lati"an soal

teriming%16% Meminta eerapa sis'a ma$u ke depan untuk mendemonstrasikan

ara men#elesaikann#a% (Mengkomunikasikan)

17% Sis'a #ang lain akti* memeri komentar ter"adap "asil temann#a

dengan sikap saling meng"argai pendapat teman lainn#a%

4



28% ;urumengkon,rmasikan peker$aan #ang didemonstrasikan%21% Memerikan lati"an lan$utan sekaligus seagai kuis%22% Sis'a mengumpulkan kuis

Penutup( 18 menit)

1% ;uru memimingsis'auntukmemuatrangkuman%2% ;uru melakukan re=eksi dengan meminta sis'a mengungkapkan

pesan dan kesan setela" mengikuti pemela$aran "ari ini%

+% ;uru meminta sis'a untuk mempela$ari materi selan$utn#a

mengenai entuk akar%

Pertemuan Kedua (9ndikator +%1%2)

Penda%uluan( ! menit)1% ;uru men#iapkan sis'a untuk mengikuti proses pemela$aran%2% Melalui tan#a $a'a& sis'a diingatkan kemali mengenai *ungsi

eksponensial (apersepsi)%+% ;uru men#ampaikantu$uanpemela$aran #aitu& entuk akar dan

ara men#eder"anakan entuk akar%% ;uru

memoti.asisis'adenganmenun$ukkanman*aatmempela$arientuk

akar%Ke&iatan nti( +! menit)

1% ;uru memerikan onto" dan

non onto" entuk akar%

2% Sis'a dieri kesempatan untuk

menan#akan mengapa keduan#a diseut onto" dan non onto"

entuk akar%+% Sis'a ersama guru

mendeskripsikan entuk akar

5



% Sis'a memerikan onto" dan

non onto" entuk akar%!% ;uru memerikan onto" ara men#eder"anakan entuk akar% Sis'a ersama guru mendeskripsikan ara men#eder"anakan

entuk akar

% Mementuk kelompok ela$ar "eterogen eranggotakan +! sis'a%6% Men$elaskan aturan pada pemela$aran #aitu eragi tugas&

meng"argai pendapat orang lain& mengemukakan pendapat& akan

ada peng"argaan& dan seagain#a%7% ;uru memagikan L3S kepada masingmasing sis'a pada tiap

kelompok untuk diker$akan seara erkelompok%18% Men$elaskan tugas #ang "arus diker$akan erdasarkan L3S #ang

diagikan%11% Sis'a men&amatioperasi pada entuk akar #ang ada pada L3S

kegiatan 112% Sis'a menan'akan ara men#elesaikan operasi pada entuk akar%1+% Sis'a erdiskusi dan eker$a erkelompok untuk menermati dan

menger$akan onto" soal #ang ada dalam kegiatan 1 L3S%

Men&eksplorasi1% ;uru erkeliling dan memiming kelompokkelompok ela$ar $ika

mengalami kesulitan%1!% -erdasar langka" langka" kegiatan pada L3S& sis'a dapat

men#impulkan mengenai operasi pada entuk akar% Men&asosiasi1% Meminta minimal sala" satu kelompok untuk mempresentasikan

"asil ela$ar kelompokn#a dan dengan pera#a diri%

Men&komunikasikan1% Meminta sis'a lain atau kelompok lain untuk menanggapi atau

menga$ukan pertan#aandengan sikap salin& men&%ormati%16% Mengkon,rmasi "asil ela$ar kelompok seara klasikal tentang

operasi al$aar pada entuk akar%

17% Memerikan peng"argaan kepada kelompok dengan nilai rata 0rata teraik%

28% Memerikan onto" soal operasi pada entuk akar%21% Memerikan lati"an soalsekaligus seagai kuis%22% Sis'a mengumpulkan kuis

Penutup( ! menit)

1% ;uru memimingsis'auntukmemuatrangkuman%

2% ;uru melakukan re=eksi dengan meminta sis'a mengungkapkan


6



+% ;uru meminta sis'a untuk mempela$ari materi selan$utn#a

mengenaimerasionalkan pen#eut pea"an #ang memuat entuk

akar

Pertemuan Keti&a (9ndikator +%1%+)(24P)Penda%uluan( 18 menit)

1 ;uru menguapkan salam dan meminta sis'a untuk erdo>a

ersama%2 ;uru mengkondisikan sis'a untuk mengikuti proses pemela$aran%+ Melalui tan#a $a'a& sis'a diingatkan kemali mengenai materi

pertemuan seelumn#a #aitu entuk akar dan ara

men#eder"anakann#a%(apersepsi)

;uru men#ampaikantu$uanpemela$aran #aitu& merasionalkan

pen#eut pea"an #ang memuat entuk akar% Sis'a akan dientuk

men$adi eerapa kelompok untuk menemukan konsep ara

merasionalkan pen#eut pea"an #ang memuat entuk akar%

Ke&iatan nti( ! menit)

1 ;uru mengin*ormasikan tentang ilangan rasional dan irrasional

pada entuk akar%

2 ;uru mengin*ormasikan tentang pea"an dengan pen#eut #angmemuat ilangan irrasional (entuk akar)%

3 ;uru meminta sis'a mementuk kelompok ela$ar "eterogen

eranggotakan +! sis'a%

4 Sis'a dierikan kesempatan untuk erkumpul dengan

kelompokn#a%

5 ;uru men#ampaikan kepada sis'a& a"'a sis'a diperole"kan

untuk (ertan'a $ika dalam proses erkelompok menggalamikesulitan atau menemukan "al"al #ang tidak dimengerti%

6 Sis'a dieri L3S panduan #ang akan digunakan dalam kegiatan

erkelompok% (Lampiran 5)

7 ;uru men#ampaikan in*ormasi durasi erdiskusi selama 8 menit

dan memperole"kan sis'a memuka uku seagai sumer

in*ormasi%

6 ;uru men$elaskan tugas #ang "arus diker$akan erdasarkan L3S#ang diagikan%

7



7 Sis'a men&amatipea"an dengan pen#eut #ang memuat entuk

akar #ang ada pada L3S kegiatan 1+%

18 Sis'a dierikan kesempatan untuk ertan#a%

11 Sis'a erdiskusi dan eker$a erkelompok untuk menermati dan

menger$akan onto" soal #ang ada dalam kegiatan 1+ L3S%( Mengeksplorasi)

12 ;uru erkeliling dan memiming kelompokkelompok ela$ar $ika

mengalami kesulitan%

1+ -erdasarkan langka" langka" kegiatan pada L3S& sis'a di"arapkan

dapat menemukanaramerasionalkan pen#eut pea"an #ang

memuat entuk akar% (Mengasosiasi)

1 Sis'a diminta untuk mempresentasikan "asil ela$ar kelompokn#adan dengan pera#a diri% (Mengkomunikasikan)

1! ;uru meminta sis'a lain atau kelompok lain untuk menanggapi

atau menga$ukan pertan#aandengan sikap salin& men&%ormati%

1 ;uru mengkon,rmasi "asil ela$ar kelompok seara klasikal

tentang merasionalkan pen#eut pea"an #ang memuat entuk

akar%

1 ;uru memerikan onto" soal merasionalkan pen#eut pea"an

#ang memuat entuk akar%

16 ;uru memerikan lati"an soal untuk diker$akan di ruma"%

Penutup( ! menit)

1 ;uru memimingsis'auntukmemuatrangkuman%

2 ;uru melakukan re=eksi dengan meminta sis'a mengungkapkan


+ ;uru meminta sis'a untuk mempela$ari materi selan$utn#a

mengenai pangkat pea"an%

Pertemuan Keempat (9ndikator +%1%)


1% ;uru men#iapkan sis'a untuk mengikuti proses pemela$aran%

8



2% Melalui tan#a $a'a& sis'a diingatkan kemali mengenai materi

pada pertemuan seelumn#a (apersepsi)%+% ;uru men#ampaikan tu$uan pemela$aran #aitu& persamaan

eksponen%% ;uru memoti.asi sis'a dengan menun$ukkan man*aat mempela$ari

persamaan eksponen dalam ke"idupan%


1% ;uru mengin*ormasikan mengenai persamaan eksponensial dengan

ilangan pokok sama%

2% ;uru memerikan onto" ara men#elesaikan persamaan eksponensial

+% ;uru mengin*ormasikan mengenai persamaan eksponen dengan pangkat

sama%

% ;uru mengin*ormasikan mengenai persamaan eksponen erentuk

persamaan kuadrat

!% ;uru memerikan onto" ara men#elesaikan persamaan eksponensial

dengan ilangan pokok sama%

% ;uru memerikan onto" ara men#elesaikan persamaan eksponensial

dengan pangkat sama

% ;uru memerikan onto" ara men#elesaikan persamaan eksponen

erentuk persamaan kuadrat

6% Meminta sis'a men#elesaikan soal lati"an teriming% (Mengeksplorasi

dan Mengasosiasi)

7% ;uru erkeliling untuk memiming sis'a menger$akan lati"an soal

teriming%

18% Meminta eerapa sis'a ma$u ke depan untuk mendemonstrasikan

ara men#elesaikann#a% (Mengkomunikasikan)

11% Sis'a #ang lain akti* memeri komentar ter"adap "asil temann#a

dengan sikap saling meng"argai pendapat teman lainn#a%

12% ;uru mengkon,rmasikan peker$aan #ang didemonstrasikan%

1+% Memeri kesempatan kepada sis'a untuk ertan#a

Penutup( 18 menit)




+% ;uru meminta sis'a untuk mempela$ari materi selan$utn#a%

9



Pertemuan Kelima dan Keenam (9ndikator +%1%! dan +%1%)


1% ;uru menguapkan salam dan meminta sis'a untuk erdo>a

ersama%2% ;uru mengkondisikan sis'a untuk mengikuti proses pemela$aran%+% Melalui tan#a $a'a& sis'a diingatkan kemali mengenai materi

pertemuan seelumn#a #aitu entuk akar dan ara

men#eder"anakann#a%(apersepsi)% ;uru men#ampaikantu$uanpemela$aran #aitu& menemukan

konsep logaritma dan si*atsi*atn#a%


1% Sis'a melakukan pengamatan untuk menentukan konsep logaritmadan si*at 0 si*atn#a terdapat pada uku pegangan sis'a%

2% Sis'a diara"kan untuk mempela$ari konsep logaritma dan si*at 0

si*atn#a pada sumer lain #ang rele.an%+% ;uru meminta sis'a untuk menuliskan in*ormasi #ang terdapat dari

masala" terseut dengan menggunakan a"asa sendiri% Sis'a dieri kesempatan untuk menga$ukan pertan#aan #ang

terkait dengan materi menemukan konsep logaritma dan si*at 0

si*atn#a!% Sis'a diara"kan untuk menga$ukan pertan#aan tentang "al 0"al

#ang elum diketa"ui dari materi #ang dipela$ari%% ;uru memuka akra'ala mengenai ara menemukan konsep

logaritma dan si*at 0 si*atn#a% ;uru memagi sis'a ke dalam eerapa kelompok dengan tiap

kelompok terdiri dari sampai ! sis'a%6% ?iap kelompok mendapat tugas untuk men#elesaikan materi

menemukan ilangan logaritma dan si*at 0 si*atn#a serta

menerapkan untuk men#elesaikan masala" #ang erkaitan dengan

logaritma #ang ada pada lemar ker$a sis'a ( L3S ) #ang diagikan%7% ;uru meminta sis'a untuk mendiskusikan materi #ang tela"

dierikan18% Selama sis'a eker$a di dalam kelompok& guru

memper"atikan dan mendorong semua sis'a untuk terliat diskusi&

dan mengara"kan ila ada kelompok #ang meleneng $au"

peker$aann#a%

11% Sala" satu kelompok diskusi (tidak harus yang terbaik ) diminta

untuk mempresentasikan "asil diskusin#a ke depan kelas%

10



Sementara kelompok lain& menanggapi dan men#empurnakan apa

#ang dipresentasikan%12% ;uru mengumpulkan semua "asil diskusi tiap kelompok

*+. @engan tan#a $a'a& guru mengara"kan semua sis'a pada

kesimpulan mengenai "asil re.iu operasi pada ilangan logaritma

erdasarkan presentasi sala" satu kelompok%

Penutup( ! menit)


2%;uru melakukan re=eksi dengan meminta sis'a mengungkapkan



Pertemuan Ketuju% (9ndikator +%1%)


1% ;uru men#iapkan sis'a untuk mengikuti proses

pemela$aran%2% Melalui tan#a $a'a& sis'a diingatkan kemali mengenai materi

pada pertemuan seelumn#a (apersepsi)%+% ;uru men#ampaikan tu$uan pemela$aran #aitu& persamaan

logaritma%% ;uru memoti.asi sis'a dengan menun$ukkan man*aat mempela$ari

persamaan logaritma dalam ke"idupan%


1% ;uru mengin*ormasikan

mengenai persamaan logaritma%2% ;uru memerikan onto" ara

men#elesaikan persamaan logaritma%

+% Meminta sis'a men#elesaikansoal lati"an teriming% (Mengeksplorasi dan Mengasosiasi)

% ;uru erkeliling untuk

memiming sis'a menger$akan lati"an soal teriming%!% Meminta eerapa sis'a ma$u

ke depan untuk mendemonstrasikan ara men#elesaikann#a%

(Mengkomunikasikan)% Sis'a #ang lain akti* memeri

komentar ter"adap "asil temann#a dengan sikap saling meng"argaipendapat teman lainn#a%

11



% ;uru mengkon,rmasikan

peker$aan #ang didemonstrasikan%6% Memeri kesempatan kepada

sis'a untuk ertan#a

Penutup( 18 menit)

1% ;uru memiming sis'a untuk memuat rangkuman%




,. PENLAAN

1% Sikap sosial

a% ?eknikPenilaian : 5ser.asi

% -entuk 9nstrumen: Lemar oser.asi

% 3isikisi:

No

%

Sikap/nilai Skor MaB

1 Casa ingin ta"u

2 Meng"argai pendapat orang lain

9nstrumen: li"at Lampiran 1

2% Pengeta"uan

a ?eknikPenilaian: ?es

-entuk 9nstrumen: Draian

3isikisi

No

%9ndikator

Skor MaB

1% Mendeskripsikan konsep *ungsi

eksponensial dan $enis 0 $enis

eksponensial%

18

2% Menggunakan konsep entuk akar dalam

men#elesaikan masala" erkaitan dengan

entuk akar%

18

+% Menggunakan konsep pangkat pea"an 18

12



dalam men#elesaikan masala" erkaitan

dengan pangkat pea"an%% Men#elesaikan permasala"an erkaitan

dengan persamaan eksponen

18

!% Mendeskripsikan eragai konsep dan

prinsip *ungsi logaritma%

18

% Menggunakan eragai konsep dan

prinsip *ungsi logaritma dalam

men#elesaikan masala" logaritma%

18

% Men#elesaikan permasala"an erkaitan

dengan persamaan logaritma%

18

6% Menganalisis data si*at si*at gra,k *ungsi

eksponensial dari suatu

permasala"andanmenerapkann#a

pemea"an masala" eksponensial%

1!

7% Menganalisis data si*at si*at gra,k *ungsi

logaritma dari suatu

permasala"andanmenerapkann#a

pemea"an masala" logaritma%

1!

9nstrumen: li"at Lampiran 2

+% 3eterampilan

a% ?eknikPenilaian: 5ser.asi

% -entuk 9nstrumen: Lemar 5ser.asi

% 3isikisi:

No

%9ndikator

Skor MaB

1% Men#a$ikan gra,k *ungsi eksponensial

dalam memea"kan masala" n#ata

terkaitpertumu"an dan peluru"an%

2% Men#a$ikan gra,k *ungsi logaritma dalam

memea"kan masala" n#ata

terkaitpertumu"an dan peluru"an%

+% Mengola" data dan menganalisis

menggunakan .ariael dan menemukan

relasi erupa *ungsi eksponensial dari

situasimasala" n#ata terkait eksponensial

13



serta men#elesaikann#a%% Mengola" data dan menganalisis

menggunakan .ariael dan menemukan

relasi erupa *ungsi logaritma dari

situasimasala" n#ata terkait logaritma

serta men#elesaikann#a%

9nstrumen: li"at Lampiran 3.

$. ME!A/ALA#- BAAN- !AN SMBER BELAJAR

Media/alat : 3omputer& L@%

-a"an :

Sumer -ela$ar :1. Po'erpoint

2. -uku (Masduki dan Sui#ati SN% 281+% Matematika untuk SMAMA

!e"as #. 4akarta : Masmedia)

Magetan& Agustus 281!

Mengeta"ui&3epala SMAN 1 Maospati& ;uru Matematika&

@ra% Siti Cupia"& M%Pd Nurdians#a"& S%Pd

N9P% 17812111768+2887 N9P%

17621828288781188

14



Lampiran * 0Lem(ar Penilaian Perilaku Berkarakter/A1ekti10LP*))

Lemar oser.asi entuk da*tar ek ($he$k "ist ) untuk sikap sosial%

Nmr

%

Aspek #ang diukur 1 2 +

1% Casa ingin ta"u ter"adap materi pemela$aran

2% 3emauan mendengarkan dan meng"argai

pendapat teman dalam akti.itas di kelas%

Pedoman Penilaian

Aspek ke2

Skor* 3 + 4

1 ?idak perna"

ertan#a atau

erpendapat

dalam

akti.itas

dan/atau

diskusi di

kelas%

-ertan#a atau

mengeluarkan

pendapat 1 kali

dalam akti.itas

dan/atau

diskusi di kelas%

-ertan#a atau

mengeluarkan

pendapat 2

kali dalam

akti.itas

dan/atau

diskusi di

kelas%

-ertan#a atau

mengeluarkan

lei" dari 2 kali

dalam akti.itas

dan/atau

diskusi di

kelas%

2% ?idak mau

mendengarka

n pendapat

teman%

Mendengarkan

tetapi tidak

mau

meng"argai

pendapat

teman%

Mau

mendengarkan

dan

meng"argai

pendapat

teman%

Mau

mendengarkan

serta

meng"argai

pendapat

teman dan

memeri

argumen

apaila tidak

sependapat%Kriteria

A 5 ?otal Skor 0 6

B 5 ?otal Skor ! 0 C 5 ?otal Skor+ 0

15



! 5 ?otal Skor 1 0 2

16



Lampiran 3 0Lem(ar Lati%an Lanjutan)

Pertemuan pertama

Petunjuk

1% -erdoala" seelum menger$akan soal2% Selesaikan soal erikut dengan singkat dan $elas

Soal

1% ;amarkan gra,k *ungsi eksponensial f ( x )=1

2

2 x

& x∈ R

2% Seder"anakan entuk 0 entuk di a'a" ini

a%(3a

3)2

9b2 :

8a5

2(b2)2

% (3b2×3c3

c2 )

2

Pedoman Penilaian nstrumen Pen&eta%uan

Nm

r

Soal Alternati* 4a'aan Sko

r

1% ;amarkan gra,k *ungsi

eksponensial f ( x )=1

2

2 x

&

x∈ R

2% Seder"anakan entuk 0

entuk di a'a" ini

a%(3a

3 )2

9b

2 :

8a5

2 ( b2

)2

% (3b

2×3c

3

c2 )

2

a%(3a

3 )2

9b2 :

8a5

2 ( b2 )2=

9a6

9b2

× 2b

4

8a5

¿ a6−5

b

4−2

4

¿ ab

2

4

% (3b

2×3 c

3

c2 )

2

=(9b2

c3−2)2

¿18b2×2

c2

+

!

2

+

!

2

17



¿18b4

c2

Skor Maksimal 46

Per"itungan nilai ak"ir dalam skala 8 0 188& seagai erikut:

Nilai Akhir= Perolehan Skor

Total Skor Max ×100

Pertemuan Keti&a

Petunjuk


Soal

1% Seder"anakan entuk akar (√ 12−√ 2 )(√ 5+√ 3)

2% N#atakan dalam entuk √ a+√ b atau √ a−√ b

a% √ 0,05−√ 0,0024

% √ 13+√ 168

1% Casionalkan pen#eut pea"an di a'a" ini

a%√ 5+√ 2

√ 18+√ 6

%√ 28

√ 8−√ 3

Pedoman Penilaian nstrumen Pen&eta%uan

Nmr Soal Alternati* 4a'aan Sko

r

1% Seder"anakan entuk

akar (√ 12−√ 2 )(√ 5+√ 3)

(√ 12−√ 2 ) (√ 5+√ 3 )

¿√ 60+√ 36−√ 10−√ 6

¿2√ 15+6−√ 10−√ 6

+

2

18



2% N#atakan dalam entuk

√ a+√ b atau √ a−√ b

a% √ 0,05−√ 0,0024

% √ 13+√ 168

a% √ 0,05−√ 0,0024=√ 0,05−2√ 0,0006

¿√ (0,03+0,02 )−2√ (0,03 )(0,02)

0,02

√ 0,03−√ (¿)2

¿¿

¿√ ¿

¿√ 0,03−√ 0,02

% √ 13+√ 168=√ 13−2√ 42

¿√

(7

+6

)−2√

(7

)(6

)

¿√ (√ 7−√ 6)2

¿√ 7−√ 6

+

+

2

2

+

+

2

2

+% Casionalkan pen#eut

pea"an di a'a" ini

a%

√ 5+√ 2

√ 18+√ 6

%√ 28

√ 8−√ 3

a%√ 5+√ 2

√ 18+√ 6= √ 5+√ 2

3√ 2+√ 6× 3√ 2−√ 6

3√ 2−√ 6

¿3√ 10−√ 30+6−√ 12

18−6

¿3√ 10−√ 30+6−2√ 3

12

%√ 28

√ 8−√ 3=

2√ 7

2√ 2+√ 3×

2√ 2−√ 3

2√ 2−√ 3

¿

4√ 14−2√ 21

8−3

¿ 4√ 14−2√ 21

5

!

+

2

!

+

2

Skor Maksimal 46

Per"itungan nilai ak"ir dalam skala 8 0 188& seagai erikut:

19



Nilai Akhir= Perolehan Skor

Total Skor Max ×100

20



Lampiran + 0Lem(ar Penilaian Keterampilan 0LP+))

*. arila" suatu data tunggal dan kelompok kemudian sa$ikan ke dalam

entuk tael dan diagram #ang sesuai dengan data #ang kamu

perole"G ?uliskan langka"langka" #ang kamu lakukan untuk

men#a$ikan data terseut dan eri keterangan%

Pedoman Penilaian Keterampilan

N

o

Na

ma

Men#a$ikan

gra,k *ungsi

eksponensial

dalam

memea"kanmasala"

n#ata

terkaitpertum

u"an dan

peluru"an%

Men#a$ikan

gra,k *ungsi

logaritma

dalam

memea"kanmasala"

n#ata

terkaitpertum

u"an dan

peluru"an%

Mengola"

data dan

menganalisis

menggunaka

n .ariaeldan

menemukan

relasi erupa

*ungsi

eksponensial

dari

situasimasala" n#ata

terkait

eksponensial

serta

men#elesaik

ann#a%

Mengola"

data dan

menganal

isis

menggunakan

.ariael

dan

menemuk

an relasi

erupa

*ungsilogaritma

dari

situasima

sala"

n#ata

terkait

logaritmaserta

#ot

al

Sk

or

+ 2 1 + 2 1 + 2 1 + 2 1

12+

21



Lampiran 4 0Lem(ar Lati%an #er(im(in&)

Petunjuk


Soal

1% ;amarkan gra,k *ungsi eksponensial f ( x )=3 x

& x∈ R

2% Seder"anakan entuk 0 entuk di a'a" ini

a%2a

3×4a

4

a2

% (5b

42 c

3

b3 )

2

Ja7a(an

1% F(B)

2% a%2a

3×4a

4

a2

=8a3+4−2=8a

5

%

10b4−3

c3

¿¿

(5b

42c

3

b3 )

2

=¿

Petunjuk


Soal

1% Seua" persegi pan$ang A-@ mempun#ai pan$ang A- m dan

pan$ang- + m% ?entukan pan$ang diagonal persegi pan$ang

terseut%

2% Seder"anakan entuk akar √ 27 x6

y7 z

3

Ja7a(an

1% @iketa"ui A- H m& - H + m

Pan$ang diagonal H √ AB2

+BC 2

=√ 62

+32

=√ 36+9=√ 45=√ 9.5=3√ 5

22



4adi& pan$ang diagonal persegi pan$ang A-@ adala" 3√ 5

2% √ 27 x6

y7 z

3=√ 9.3. x6

. y6

. y . z2

. z=3 x3 y

3 z√ 3 yz

Petunjuk


Soal

1% N#atakan dalam entuk √ a+√ b atau √ a−√ b

a% √ 0,3−√ 0,08

2% Casionalkan pen#eut pea"an di a'a" ini

a%3

√ 8+√ 12

%5

3−√ 6

4a'aan

1% √ 0,3−√ 0,08=√ 0,3−2√ 0,02

¿√ (0,2+0,1)−2√ (0,2)(0,1)

0,1

√ 0,2−√ (¿¿)2

¿¿

¿√ ¿

¿√ 0,2−√ 0,1

2% a%3

√ 8+√ 12=

3

2√ 2+2√ 3× 2√ 2−2√ 3

2√ 2−2√ 3=

6√ 2−6√ 3

8−12=

6√ 2−6√ 3

(−4) =

−3√ 2+3√ 3

2

%5

3−√ 6=

5

3−√ 6× 3+√ 6

3+√ 6=

15+5√ 6

9−6=

15+5√ 6

3=5+

5√ 6

3

Petunjuk 1% -erdoala" seelum menger$akan soal

23



2% Selesaikan soal erikut dengan singkat dan $elas

Soal

a.

( x

2

3 y

−4

3

y

2

3 x2

)(. (27)

2

3 (32 )−4

5

".7 x

−3

2 y5

6

( x−6 y

−1

3 ) x−2

d. ( x

2

3 y

3

4

y

1

3 x

1

2 )−1

2

Ja7a(an8

24



Petunjuk


Soal

1% Supa#a !log B H 8&!& maka tentukan nilai B%

2% ?entukan nilai dari 2log 6 I +log 2 I log 8&1%

+% 4ika +log 2 H a& maka tentukan nilai dari 6log 7%

% Jusu* adala" seorang pela$ar kelas X di kota 3upang% 9a senang

er"emat dan menaung uang% Selama ini dia er"asil menaung

uangn#a se$umla" Cp1%888%888&88 di dalam seua" elengan #ang

25

a. ( x

2

3 y

−4

3

y

2

3 x2 )=( x

2

3−2

y

−4

3− 2

3 )=( x−4

3 y−2)=( 1

x

4

3 y2 )

b. (27)2

3 (32 )−4

5 =(33 )2

3 (25 )−4

5

¿ 3

2

24

c.

7 x

−3

2 y

5

6

( x−6 y−1

3 ) x−2

= 7 (4 )

−3

2 (27 )5

6

(4−6 (27)−1

3 ) (4 )−2

K ¿

7 (22 )−3

2 (33 )5

6

(4−6 (33 )−1

3 )(22 )−2

= 7 (2 )−3 (3 )

5

2

(4−6 (3 )−1) (2 )−4 =

7 (2 )−3 (3 )5

2 (2 )4

(4−6 1

3 ) =

7(2) (3 )5

2

(4−2 ) =

7 (2) (3 )5

2

2=7 (3 )

5

2

d.

( x

2

3 y

3

4

y

1

3 x

1

2

)

−1

2

=

( x

1

2 y

1

3

y

3

4 x

2

3

)

1

2

=

( x

1

4 y

1

6

y

3

8 x

2

6

)=( x

1

4−1

3 y

1

6−3

8 )=( x−1

12 . y

−5

24 )=

( 1

x

1

12 . y

5

24

)



teruat dari tana" liat% Agar uangn#a lei" aman& ia menaung

uangn#a di seua" ank dengan unga 18 per ta"un% -erapa lama

Jusu* men#impan uang terseut agar men$adi Cp1%%188&88%

4a'aan:

1% Supa#a !log B H 8&!& maka B H5

2% Nilai dari 2log 6 I +log 2 I log 8&1H !

+% 4ika +log 2 H a& maka 6log 7 Ha3

2

% Pola pertama"an $umla" uang Jusu* setiap ak"ir ta"un:

Per%itun&an (esar suku (un&a pada setiap ak%ir ta%un t

@ari

tael diatas&

$elas kita li"at a"'a Jusu* "arus

menaung selama ta"un agar uangn#a men$adi Cp1%%188&88

!%

26



Lampiran 6

Pertemuan Kedua8

Lem(ar Ke&iatan Sis7a 0LKS)

Pokok Ba%asan : 5perasi pada -entuk Akar

ari/#an&&al : %%%%%%%%%%%%%%%%%%%%%%%%%%%%/%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%Alokasi Waktu : 36 menitKelas : X %%%%%Nama Kelompok/Nama : %%%%%%%%%/%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

!er%akan dengan berke"&mp&k'

Petunjuk8

Ba"ala% do9a seelum mulai menger$akann#aG

Ba"a den&an "ermat setiap perinta" #ang adaG

4ika masi" ada #ang elum dipa"ami& (ertan'ala"G

Beranila% men"o(a dan jan&an takut sala%:

Ke&iatan *

1% a% -erapaka" "asil dari 2a+3a

% Misal a=√ 2 & erapaka" "asil dari 2a+3a

4a'a :

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%

2% a% -erapaka" "asil dari 4 b+2b+b

% Misal b=3√ 5 & erapaka" "asil dari 4 b+2b+b

4a'a :

27



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%

+% a% -erapaka" "asil dari b+3b+7b

% Misal b=4√ 7 & erapaka" "asil dari b+3b+7b

4a'a :

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%

% @ari ketiga onto" diatas& dapat disimpulkan a"'a

Ke&iatan 3

1% a% -erapaka" "asil dari 4 a−2a

% Misal a=√ 3 & erapaka" "asil dari 4 a−2a

4a'a :

28

pn√ r+q

n√ r=¿ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%

2% a% -erapaka" "asil dari 8b−4b−2b

% Misal b=3√ 3 & erapaka" "asil dari 8b−4b−2b

4a'a :

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%

+% a% -erapaka" "asil dari 5b−2b−b

% Misal b=5√ 2 & erapaka" "asil dari 5b−2b−b

4a'a :

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%

29




Ke&iatan +

1% -erapaka" "asil dari 3a ×2b

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%

2% -erapaka" "asil dari 3a1

3 ×3b1

3 (9ngat si*at

b

a ×¿¿¿

)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

+% Misal a1

3= 3√ a dan b

1

3= 3√ b & erapaka" "asil dari 3

3√ a×3

3√ b

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%

% -erapaka" "asil dari 3(2)1

3 ×3(3)1

3 (9ngat si*at

b

a ×¿¿¿

)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%

30

pn√ r−q

n√ r=¿ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



!% Misal (2)1

3=3√ 2 dan (3)

1

3=3√ 3 & erapaka" "asil dari 3

3√ 2×3

3√ 3

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%

% @ari kedua onto" diatas& dapat disimpulkan a"'a

Ke&iatan 4

1% -erapaka" "asil dari6 a

2b

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%

2% -erapaka" "asil dari3a

1

3

3b

1

3

(9ngat si*at

a

b¿1

n=a

1

n

b

1

n

¿

)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%

+% Misal a1

3= 3√ a dan b

1

3= 3√ b & erapaka" "asil dari

33√ a

33√ b

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%

31

an√ c × b

n√ d=¿ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%

% -erapaka" "asil dari3(2)

1

3

3 (3)

1

3 (9ngat si*at

a

b¿1

n=a

1

n

b

1

n

¿

)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%

!% Misal (2)1

3=3√ 2 dan (3)

1

3=3√ 3 & erapaka" "asil dari

3 3√ 2

3

3

√ 3

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%


Kun"i Ja7a(an LKS

Ke&iatan *

1% a% -erapaka" "asil dari 2a+3a

% Misal a=√ 2 & erapaka" "asil dari 2a+3a

4a'a :

a% 2a+3a=5a

% 2a+3a=2√ 2+3√ 2=5√ 2

2% a% -erapaka" "asil dari4 b

+2b

+b

32

an√ c

bn√ d

=¿%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



% Misal b=3√ 5 & erapaka" "asil dari 4 b+2b+b

4a'a :

a% 4 b+2b+b=7b

% 4

b+2

b+b=4

3√ 5

+2

3√ 5

+

3√ 5

=7

3√ 5

+% a% -erapaka" "asil dari b+3b+7b

% Misal b=4√ 7 & erapaka" "asil dari b+3b+7b

4a'a :

a% b+3b+7b=11b

% b+3b+7b=4√ 7+3

4√ 7+7

4√ 7=11

4√ 7


Ke&iatan 3

1% a% -erapaka" "asil dari 4 a−2a

% Misal a=√ 3 & erapaka" "asil dari 4 a−2a

4a'a :

a% 4 a−2a=2a

% 4 a−2a=4 √ 3−2√ 3=2√ 3

2% a% -erapaka" "asil dari

8b−4b−2b

% Misal b=3√ 3 & erapaka" "asil dari 8b−4b−2b

4a'a :

a% 8b−4b−2b=2b

% 8b−4b−2b=83√ 3−4

3√ 3−2

3√ 3=2

3√ 3

+% a% -erapaka" "asil dari 5b−2b−b

33

pn√ r+q

n√ r=( p+q) n

√ r



% Misal b=5√ 2 & erapaka" "asil dari 5b−2b−b

4a'a :

a% 5b−2b−b=2b

% 5

b−2

b−b=5

5√ 2

−2

5√ 2

−

5√ 2

=2

5√ 2


Ke&iatan +

1% -erapaka" "asil dari 3a×2b

3a ×2b=6ab

2% -erapaka" "asil dari 3a

1

3

×3b

1

3

(9ngat si*at

b

a ×¿

¿¿ )

3a1

3 ×3b1

3=9(ab)1

3

+% Misal a1

3= 3√ a dan b

1

3= 3√ b & erapaka" "asil dari 3

3√ a×3

3√ b

33√ a×3

3√ b

=9

3√ ab

% -erapaka" "asil dari 3(2)1

3 ×3(3)1

3 (9ngat si*at

b

a ×¿¿¿

)

3(2)1

3 ×3(3)1

3=9(2×3)1

3=9(6)1

3

!% Misal (2)

1

3=3

√ 2 dan (3)

1

3=3

√ 3 & erapaka" "asil dari 3

3

√ 2×3

3

√ 3

34

pn√ r−q

n√ r=( p−q) n

√ r



33√ 2×3

3√ 3=9

3√ 2×3=9

3√ 6


Ke&iatan 4

1% -erapaka" "asil dari6 a

2b

6 a

2b=3

a

b

2% -erapaka" "asil dari3a

1

3

3b

1

3 (9ngat si*at

a

b¿1

n=a

1

n

b

1

n

¿

)

3a1

3

3b

1

3

=(a

b)1

3

+% Misal a1

3= 3√ a dan b

1

3= 3√ b & erapaka" "asil dari

33√ a

33√ b

33√ a

33√ b

=3

√a

b

% -erapaka" "asil dari3(2)

1

3

3 (3)1

3 (9ngat si*at

a

b¿1

n=a

1

n

b

1

n

¿

)

35

an

√ c × bn

√ d=abn

√ cd



3(2)1

3

3 (3)1

3

=(2

3)1

3

!% Misal (2)

1

3

=

3

√ 2 dan (3)

1

3

=

3

√ 3 & erapaka" "asil dari

3 3√ 2

33

√ 3

3 3√ 2

33√ 3

=3

√ 2

3


Pertemuan Keti&a8

Lem(ar Ke&iatan Sis7a 0LKS)

Pokok Ba%asan : Merasionalkan Pen#eut Pea"an #ang memuat

entuk akar

ari/#an&&al : %%%%%%%%%%%%%%%%%%%%%%%%%%%%/%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Alokasi Waktu : +; menit

Kelas : X %%%%%

Kelompok/Nama : %%%%%%%%%/%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

!er%akan dengan berke"&mp&k'

Petunjuk8

Ba"ala% do9a seelum mulai menger$akann#a%

Ba"a den&an "ermat setiap perinta" #ang ada%

4ika masi" ada #ang elum dipa"ami& (ertan'ala"%

Beranila% men"o(a dan jan&an takut sala%.

Ke&iatan *

36

an√ c

bn

√ d

=a

b

n

√

c

d



1 Seder"anakan men$adi entuk paling seder"ana dengan mengisi

titiktitik di a'a" ini:

a1

√ 4=…

1

4 √ 4=…

4adi& …=…

2 Seder"anakan men$adi entuk paling seder"ana dengan mengisititiktitik di a'a" ini:

a1

√ 9=…

1

9√ 9=…

4adi& …=…

+ 4ika meli"at kesimpulan pada nomor 1 dan 2& makaseder"anakan

pea"an erikut:

a2

√ 3=…

1

√ 5=…

4ika pada nomor 1& 2& dan + diseut merasionalkan pea"an #ang

memuat entuk akar& maka entuk rasional daria

√ b adala" %

37



! ?emukan ara untuk merasionalkan pea"an #ang memuat entuk

akar dengan entuka

√ b menggunakan si*at: √ a ×√ a=a &a

b B 1

Ha

b & dana

a H 1%

4a'a:

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Ke&iatan 3

1 Seder"anakan men$adi entuk paling seder"ana dengan mengisititiktitik di a'a" ini:

a%1

4−√ 4=…

%1(4+√ 4)

42−(√ 4 )

2=…

4adi& …=…



a1

5−√ 9=…

1(5+√ 9)

52−(√ 9)2

=…

38



4adi& …=…

+ @engan meli"at entuk pada nomor 1 dan 2% Seder"anakan pea"an

erikut:

a1

3−√ 2=…

2

4−√ 5=…


memuat entuk akar& maka entuk rasional daric

a−√ b adala"

%


akar dengan entuk

c

a−√ b menggunakan si*at:√ a ×√ a=a

&

a

b

B 1 Ha

b & dana

a H 1%

(9ngat: (a−b ) (a+b )=a2−b

2

)

4a'a:

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

39



Lalu& agaimana untuk entuk rasional daric

a+√ b 4elaskan%

4a'a:

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Ke&iatan +



a1

√ 9−√ 4=…

√ 4¿¿¿2

(√ 9)2−¿

1(√ 9+√ 4)¿

4adi& …=…



a1

√ 16−√ 4=…

40



√ 4¿¿¿2

(√ 16)2−¿

1(√ 16+√ 4)

¿

4adi& …=…

+ @engan meli"at entuk pada nomor 1 dan 2% Seder"anakan pea"an

erikut:

a1

√ 5−√ 3=…

2

√ 6−√ 2=…



√ a−√ b adala"

%


akar dengan entukc

√ a−√ b menggunakan si*at: √ a ×√ a=a &a

b

B 1 Ha

b & dana

a H 1%

(9ngat: (a−b ) (a+b )=a2−b

2

)

4a'a:

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

41



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%

Lalu& agaimana untuk entuk rasional daric

√ a+

√ b

4elaskan%

4a'a:

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%

42



Kun"i LKS

Ke&iatan *

1% Seder"anakan men$adi entuk paling seder"ana dengan mengisi


a%1

√ 4=

1

2

%1

4 √ 4=

1

4×2=

1

2

4adi&

1

√ 4=

1

4

√ 4



a%1

√ 9=

1

3

%1

9√ 9=

1

9×3=

1

3

4adi&1

√ 9=

1

9 √ 9

+% 4ika meli"at kesimpulan pada nomor 1 dan 2& makaseder"anakan

pea"an erikut:

a%

2

√ 3 H

2

3 √ 3

%1

√ 5=

1

5 √ 5

% 4ika pada nomor 1& 2& dan + diseut merasionalkan pea"an #ang

memuat entuk akar& maka entuk rasional daria

√ b adala"a

b√ b

43



!% ?emukan ara untuk merasionalkan pea"an #ang memuat entuk

akar dengan entuka

√ b (9ngat: si*at: √ a ×√ a=a &a

b B 1 Ha

b &

dana

a H 1)

4a'a:

a

√ b×

√ b

√ b Ha

b√ b

Ke&iatan 3



a%1

4−√ 4= 1

4−2=1

2

%1(4+√ 4)

42−(√ 4 )

2=

4+√ 4

16−4=

6

12=

1

2

4adi&1

4−√ 4=

1(4+√ 4)

42−(√ 4)

2



a%1

5−√ 9=

1

2

%1(5+√ 9)

52−(√ 9)

2=

5+325−9

= 8

16=

1

2

44



4adi&1

5−√ 9= 1(5+√ 9)

52−(√ 9)

2

+% @engan meli"at entuk pada nomor 1 dan 2% Seder"anakan pea"an

erikut:

a%

√ 2¿¿¿2

32−¿

1

3−√ 2=

1(3+√ 2)¿

%

√ 5¿¿¿2

42−¿

2

4−√ 5=

2(4+√ 5)¿



a−√ b adala"

√ b¿¿

a2+¿

c(a+√ b)¿

45




akar dengan entukc

a−√ b menggunakan si*at: √ a ×√ a=a &a

b

B 1 Ha

b & dana

a H 1%

(9ngat: (a−b ) (a+b )=a2−b

2

)

4a'a:

c

a−√ b=

c

a−√ b ×

a+√ b

a+√ b

% Lalu& agaimana untuk entuk rasional daric

a+√ b 4elaskan%

4a'a:

c

a+√ b=

c

a+√ b

× a−√ b

a−√ b

Ke&iatan +



a%1

√ 9−

√ 4

= 1

3−2=1

%

√ 4¿¿¿2

(√ 9)2

−¿1(√ 9+√ 4)

¿

46



4adi&

√ 4¿¿

(√ 9)2

−¿1

√ 9−√ 4=

1(√ 9+√ 4)¿



a%1

√ 16−√ 4=

1

4−2=

1

2

%

√ 4¿¿

¿2(√ 16)

2

−¿1(√ 16+√ 4)

¿

4adi&

√ 4¿¿

(√ 16)2−¿

1

√ 16−√ 4=

1(√ 16+√ 4)

¿

+% @engan meli"at entuk pada nomor 1 dan 2% Seder"anakan pea"an

erikut:

a%1

√ 5−√ 3=

1(√ 5+√ 3)

(√ 5)2

−(√ 3)2=√ 5+√ 3

5−3=√ 5+√ 3

2

%

6

√ ¿¿¿2−(√ 2)

2

¿¿

2

√ 6−√ 2=2(√ 6+√ 2)

¿

47





√ a−√ b adala"

√ a¿¿√ b¿¿¿c¿


akar dengan entukc

√ a−√ b menggunakan si*at: √ a ×√ a=a &a

b

B 1 Ha

b & dana

a H 1%

(9ngat: (a−b ) (a+b )=a2−b

2

)

4a'a:

c

√ a−√ b=

c

√ a−√ b×

√ a+√ b

√ a+√ b

% Lalu& agaimana untuk entuk rasional daric

√ a+√ b 4elaskan%

4a'a:

c

√ a+√ b=

c

√ a+√ b×

√ a−√ b

√ a−√ b

bab 1 eksponen dan logaritma

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