LKS AKUUH 2

S

LKS MAT MATEMAT EMATIKA IKA BERBASIS BERBASI S META M ETAKOGNITIF KOGNITIF LEMBA# KEIATAN SIS$A %

•

Standar Kompetensi

: 1. Memahami bentuk aljabar, relai, !un"i, #an $era maan

"ari luru. •

Kompetensi Dasar

•

Indikator Tujuan

: 1.% Membuat keta "ra!ik !un"i aljabar e#erhana $a#a item k&&r#inat 'arteiu. : 1.%.1. Men(uun tabel $aan"an nilai $eubah #en"an nilai !un"i : Si)a #a$at men(uun tabel $aan"an nilai $eubah #en"an nilai !un"i

A. MENYUSUN TABEL TABEL PASANAN PASANAN NILAI NILAI PEUBA! DENAN DENAN NILAI NILAI "UNSI

Kalian telah mempelajari bahwa suatu fungsi f ( x x ) mempunai !ariabel x !ariabel x "an untu# nilai !ariabel x !ariabel x tertentu$ #ita "apat menghitung nilai fungsina% &i#a nilai !ariabel suatu fungsi berubah ma#a a#an menebab#an perubahan pa"a nilai fungsina

Masi Masih h in ingat gat# #ah #amu amu tent tentang ang mengh menghit itun ung g nilai fungsi' &i#a f()  *+, $ ma#a pasangan nilai peubah "engan nilai fungsi ang mung#in a"alah sebagai beri#utf(.)  *(.) +, , $ f(,)  *(,) +,  $ f(0)  *(0) 1 ,  .2 $ "st

*ntuk me(uun tabel antara nilai $eubah #en"an nilai !un"i lakukan ke&iatan % berikut ini+

MATEMATIKA SMP/MTs KELAS VIII

1

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LKS MAT MATEMAT EMATIKA IKA BERBASIS BERBASI S META M ETAKOGNITIF KOGNITIF

Kegiatan Diskusikan soa' di (a)a* ini den&an teman se(an&kumu da'am )aktu +, menitPerkirakan'a* )aktu )aktu /an& di(erikan untuk men&erjakan tu&as tu&as den&an (aik a&ar (isa se'esai se'esai tepat pada )aktun/a0kemu#ian maukan nilai / terebut ke #alam $eramaan !/0 /23, #i#a$at+

!/0  /23 { x ∨0 ≤ x ≤ 8, x ∈ bilan"an bulat. !90  90 2 3  3 a. Tentu tuka kan n nil nilai x terebut4 terebut4 !10 ai x 10 23% b. Tentukan Tentukan nilai $erubahan !0  ...0 2 3  !un"i ..... !/0 #ari $eramaan terebut4 5. Tulikan nilai $erubahan !...0 ...0 2 3 !un"i ..... !/0 $a#a &al n&.1.b #iata #alam tabel. 6a)ab+ !...0  ...0 2 3  ..... maalah  Memahami !...0  ...0 2 3  ..... 10 A$a A$a (an" (an" #itan #itan( (akan7 akan7 !...0  ...0 2 3  ..... { x ∨0 ≤ x ≤ 8, x ∈ bilan"an bulat. a.!...0 Nilai x Nilai x #imana #imana  ...0 2 3  .....  ...0 2 3  ..... b.!...0 Nilai $erubahan !un"i !/0 #ari $eramaan !/0 /23. /23. 5. 5. Tulikan Tulikan $erub nilai nilai (an" (an" telah tela h !/0 #iketahui #ike tahui ke #alam tabel #alam beriku berikut+ Menulikan Menul$erubahan ikan ahan nilai nilai $erubah $e rubahan an !un"i !un "i ! /0 $a#a $a# a &al n&.1.b n&.1.b #iata tabel. tt+ abel. -iketahui !/0 /23, #en"an nilai x (aitu

0 A$a A$a (an" (an" #ik #iket etah ahui ui77

{ x ∨0 ≤ .x..≤.. 8, x ∈.... bilan"an /!/0 /23, #en"an 9 nilai x .... bulat. .... nilai 1 x (aitu  !/0 /2 3 3 % ..... ..... ..... ..... ..... 8 meren5anakan trate"i.  Men(uun 

.... .....

: .....

Ba"aimana 5ara untuk men(eleaikan &al terebut0 { x ∨0 ≤ x ≤ 8, x ∈ bilan"an bulat, nilain(a (aitu 9 am$ai #en"an : , hail ja)aban a
a. Nilai / terebut a#alah = ........................................... .................................................................. ............................................> .....................> b. Nilai $erubahan !un"i ∈ $a#a $eramaan /23 a#alah berarti a#a ; nilai / #an meru$akan meru$akan

bilan"an bulat.

=..........................................>

b. Nilai $erubahan !un"i !/0 #ari $eramaan !/0 /23, berarti berarti nilai / (an" telah x → 2 x + 3 ⇔0→ 3 5. #iketahui #i maukan ke #alam $eramaan $era maan !/0 /23, ehin""a #i $er&leh nilai 1→ 5 5→ … $erubahan !un"in(a. 5. Menulikan nilai $erubahan 2 → … 6!un"i → … !/0 ke #alam tabel, berarti etelah men"etahui $erubahan nilai !un"in(a kemu#ian kemu#ian nilai terebut #imaukan ke #alam tabel. 3 →… 7 → …

 Menera$kan 8 men""unakan trate"i (an" telah #i ren5anakan. { x ∨0 ≤ x ≤ 8, x ∈ bilan"an bulat, nilain(a (aitu 9 am$ai a. Nilai x x #imana #imana 4 → … 8 → …  6ika #en"an kalian : ti#ak memahami . Nilai / terebut materi (an" #ibaha, ba5alah kembali &al #en"an 5ermat #an men"in"at k&ne$ erta trate"i (an" #i$erlukan #alam men(eleaiakan a#alah............................................... a#alah........................ .............................................. ............................................ ..................... b. !/0 /23 ,bia nilaimenja)ab / (an" telah #ari &al a &al a"ar kalian &al#iketahui (an" #iberikan. a#alah ...................................... ......................................




S


Kegiatan Diskusikan soa' di (a)a* ini den&an teman se(an&kumu da'am )aktu +, menitPerkirakan'a* )aktu )aktu /an& di(erikan untuk men&erjakan tu&as tu&as den&an (aik a&ar (isa se'esai se'esai tepat pada )aktun/a0kemu#ian maukan nilai / terebut ke #alam $eramaan !/0 /23, #i#a$at+

!/0  /23 { x ∨0 ≤ x ≤ 8, x ∈ bilan"an bulat. !90  90 2 3  3 a. Tentu tuka kan n nil nilai x terebut4 terebut4 !10 ai x 10 23% b. Tentukan Tentukan nilai $erubahan !0  ...0 2 3  !un"i ..... !/0 #ari $eramaan terebut4 5. Tulikan nilai $erubahan !...0 ...0 2 3 !un"i ..... !/0 $a#a &al n&.1.b #iata #alam tabel. 6a)ab+ !...0  ...0 2 3  ..... maalah  Memahami !...0  ...0 2 3  ..... 10 A$a A$a (an" (an" #itan #itan( (akan7 akan7 !...0  ...0 2 3  ..... { x ∨0 ≤ x ≤ 8, x ∈ bilan"an bulat. a.!...0 Nilai x Nilai x #imana #imana  ...0 2 3  .....  ...0 2 3  ..... b.!...0 Nilai $erubahan !un"i !/0 #ari $eramaan !/0 /23. /23. 5. 5. Tulikan Tulikan $erub nilai nilai (an" (an" telah tela h !/0 #iketahui #ike tahui ke #alam tabel #alam beriku berikut+ Menulikan Menul$erubahan ikan ahan nilai nilai $erubah $e rubahan an !un"i !un "i ! /0 $a#a $a# a &al n&.1.b n&.1.b #iata tabel. tt+ abel. -iketahui !/0 /23, #en"an nilai x (aitu

0 A$a A$a (an" (an" #ik #iket etah ahui ui77

{ x ∨0 ≤ .x..≤.. 8, x ∈.... bilan"an /!/0 /23, #en"an 9 nilai x .... bulat. .... nilai 1 x (aitu  !/0 /2 3 3 % ..... ..... ..... ..... ..... 8 meren5anakan trate"i.  Men(uun 

.... .....

: .....

Ba"aimana 5ara untuk men(eleaikan &al terebut0 { x ∨0 ≤ x ≤ 8, x ∈ bilan"an bulat, nilain(a (aitu 9 am$ai #en"an : , hail ja)aban a
a. Nilai / terebut a#alah = ........................................... .................................................................. ............................................> .....................> b. Nilai $erubahan !un"i ∈ $a#a $eramaan /23 a#alah berarti a#a ; nilai / #an meru$akan meru$akan

bilan"an bulat.

=..........................................>

b. Nilai $erubahan !un"i !/0 #ari $eramaan !/0 /23, berarti berarti nilai / (an" telah x → 2 x + 3 ⇔0→ 3 5. #iketahui #i maukan ke #alam $eramaan $era maan !/0 /23, ehin""a #i $er&leh nilai 1→ 5 5→ … $erubahan !un"in(a. 5. Menulikan nilai $erubahan 2 → … 6!un"i → … !/0 ke #alam tabel, berarti etelah men"etahui $erubahan nilai !un"in(a kemu#ian kemu#ian nilai terebut #imaukan ke #alam tabel. 3 →… 7 → …

 Menera$kan 8 men""unakan trate"i (an" telah #i ren5anakan. { x ∨0 ≤ x ≤ 8, x ∈ bilan"an bulat, nilain(a (aitu 9 am$ai a. Nilai x x #imana #imana 4 → … 8 → …  6ika #en"an kalian : ti#ak memahami . Nilai / terebut materi (an" #ibaha, ba5alah kembali &al #en"an 5ermat #an men"in"at k&ne$ erta trate"i (an" #i$erlukan #alam men(eleaiakan a#alah............................................... a#alah........................ .............................................. ............................................ ..................... b. !/0 /23 ,bia nilaimenja)ab / (an" telah #ari &al a &al a"ar kalian &al#iketahui (an" #iberikan. a#alah ...................................... ......................................




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 Keim$ulan + -ari &al $a#a ke"itan 1 #iata, a$a (an" kalian im$ulkan tentan" men(uun tabel $aan"an nilai $eubah #en"an nilai nilai !un"i7 Lan"kah ?lan"kah a$a aja (an" (an" haru #i kerjakan7 6a)ab+ .......................................................... ........................................................................................ ............................................................ ........................................ .......... .......................................................... ........................................................................................ ............................................................ .................................................... ...................... .......................................................... ........................................................................................ ............................................................ .................................................... ...................... .......................................................... ........................................................................................ ............................................................ .................................................... ...................... ........................


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


6a)ab+ Memahami maalah Selamat 10 A$a A$a (an" (an" #ita #itan( n(ak akan an77 Berdiskusi............. a. ............................................................ .......................................................................................... ............................................................ ................................ b. ............................................................ .......................................................................................... ............................................................ ................................ .. 5. ............................................................ .......................................................................................... ............................................................ ................................ 0 A$a A$a (an (an" " #ik #iket etah ahui ui77 ............................................................ ............................................................................................ .............................................................. ................................................ ..................

Apapun yang yang kamu bisa lakukan, lakukan, ............................................................ .............................. .............................................................. ................................................ .................. Atau A tau kamu mimpi mimpi bisa lakukan, lakukan,.............................................................. Mulailah.............................................................. itu; ............................................................ .............................. .............................................................. ............................................ .............. Di dalam keberanian terdapat  Men(uun 8 meren5anakan trate"i. Ba"aimana kejeniusan, 5ara untuk men(eleaikan &al terebut0 Kekuatan, dan keajaiban; { x ∨−1 ≤ x ≤ 3, x ∈ bilanganbulat } berarti, nilain(a Nilai x x #imana #imana sekarang. (aitu a. Nilai Mulailah “ ” (aitu ..... am$ai #en"an ..... , berarti berarti a#a ..... nilai / #an meru$akan

∈

bilan"an

bulat. (. Nilai $erubahan !un"i !/0 #ari $eramaan !/0 %/23, berarti ...................................................... .................................................................................... ............................................................ ........................................... ............. ........................................................... ......................................................................................... ............................................................ .................................................. .................... ........................................................... ............................. ............................................................ ............................................................ .................................................. .................... Kerjakan'a* se1ara mandiri da'am )aktu 2, menit................. Perkirakan'a* )aktu /an& di(erikan a&ar (isa men&erjakan se'esai pada )aktun/a01. Menulikan nilai $erubahan !un"i !/0 ke #alam tabel, → %. -ik ikeeta tahu huii !un un" "i f(x) + x % x 2 3 #en"an nilai x (aitu berarti ...................................................... .................................................................................... ............................................................ ........................................... ............. ........................................................... ............................. ............................................................ .................................................. .................... { x ∨− } } . ............................................................ 1 ≤ x ≤ 3, x ∈ bilanganbulat

........................................................... ......................................................................................... ............................................................ .................................................. .................... a. Te Tentukan ntukan nilai / terebut4 b. Tentukan Te................. ntukan nilai $erubahan !un"i !un"i !/0 #ari $eramaan terebut4 8 men""unakan trate"i (an" telah ren5anakan.  5.Menera$kan Tulikan nilai $erubahan !un"i !/0 $a#a &al#in&.1.b #iata #alam tabel4 { x ∨−1 ≤ x ≤ 3, x ∈ bilan"an bulat, ja#i nilai / a. Nilai x x #i #imana a#alah ........................... ........................................................... .............................................................. ............................................................ ...................................... ........ ... b. !/0  /23, nilai / (an" telah #iketahui #ari &al a a#alah .................................. kemu#ian maukan nilai / terebut ke #alam $eramaan !/0 %/23 (aitu+ ........................................................... ......................................................................................... ............................................................ .................................................. .................... ........................................................... ......................................................................................... ............................................................ .................................................. .................... ........................................................... ......................................................................................... ............................................................ .................................................. ....................

@ MATEMATIKA SMP/MTs KELAS VIII .................................................. ........................................................... ............................. ............................................................ ............................................................ .................... ........................................................... ......................................................................................... ............................................................ ............................................... .................

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LKS MATEMATIKA BERBASIS METAKOGNITIF

5.

Tulikan $erubahan nilai (an" telah #iketahui ke #alam tabel berikut+

/ !/0 

..... .....

..... .....

..... .....

..... .....

.... .....

%/23


…→… …→…

…→… …→…

 6ika kalian ti#ak memahami materi (an" #ibaha, ba5alah kembali &al #en"an 5ermat #an men"in"at k&ne$ erta trate"i (an" #i$erlukan #alam men(eleaiakan &al a"ar kalian bia menja)ab &al (an" #iberikan.

. -iketahui

2 f ( x ) : x → x + 2 , #en"an x ={− 4,−3,−2, −1,0,1,2 } . Tentukan nilai

$eubah #ari !un"i terebut #an tulikan #alam tabel4 6a)ab+  Memahami maalah 10 A$a (an" #itan(akan7 .................................................................................................................................. .................................................................................................................................. .... 0 A$a (an" #iketahui7 .................................................................................................................................. .................................................................................................................................. ...

 Men(uun 8 meren5anakan trate"i. Nilai / (an" #iketahui (aitu $eramaan x

2

+2

{−4, − 3,−2, −1,0,1,2 }

.

$erubahan !un"i !/0

#ari

, berarti

...................................................................................................................................................... % MATEMATIKA SMP/MTs KELAS VIII ...................................................................................................................................................... ................................................................................................................................................

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


Kemu#ian tuli ke#alam tabel. Menera$kan 8 men""unakan trate"i (an" telah #i ren5anakan. {−4, − 3,−2, −1,0,1,2 } . $erubahan !un"i !/0 #ari Nilai / (an" #iketahui (aitu $eramaan x

2

+2

(aitu+

............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... Kemu#ian tuli $erubahan nilai terebut ke#alam tabel+

/ !/0

.....  .....

..... .....

..... .....

..... .....

...... .....

..... .....

..... ......

2

x + 2


Nilai $erubahan !un"i $a#a $eramaan

x + 2 a#alah =........................................>

nilai x → nilai perubahan x …→… …→…

…→… …→…

…→… …→…

…→… 1

3. -iketahui

Suatu

!un"i f

#irumukan

&leh f(x):

x

 2

( x + 3 )

x ∨10 ≤ x ≤ 15


a. Tentukan nilai / #imana

,

#imana



x ∨10 ≤ x ≤ 15 4

1

( x +3 )

S


0 A$a (an" #iketahui7 ......................................................................................................................................... .........................................................................................................................................



...................................................................................................................................... Men(uun8 meren5anakan trate"i+ Ba"aimana 5ara untuk men(eleaikan &al terebut0 ................................................................................................................................................ ........................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................



... Menera$kan 8 men""unakan trate"i+ ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................



................
 6ika kalian ti#ak memahami materi (an" #ibaha, ba5alah kembali &al #en"an 5ermat #an in"atlah k&ne$ erta trate"i (an" #i$erlukan #alam men(eleaiakan &al a"ar kalian bia menja)ab &al (an" #iberikan.


C

S


 Keim$ulan + -ari &al n& 1,  , #an 3 #iata, a$a (an" kalian im$ulkan tentan" men(uun tabel $aan"an nilai $eubah #en"an nilai !un"i7 Lan"kah ?lan"kah a$a aja (an" haru #i kerjakan7 6a)ab+ .......................................................... ........................................................................................ .............................................................. ............................................. ............. ......................................................... ....................................................................................... ............................................................ ........................................................... ............................. ......................................................... ....................................................................................... ............................................................ ........................................................... ............................. ......


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#E"LEKSI: 1. Tulikan Tulikan k&ne$ k&ne$ a$a aja (an" $entin $entin" " ketika men(uun men(uun tabel tabel $aan"an $aan"an nilai $eubah $eubah #en"an nilai !un"i4 .............................................. ..................................................................... .............................................. .............................................. .............................................. .................................. ........... .............................................. ..................................................................... .............................................. .............................................. .............................................. .................................. ........... .............................................. ................................................................. ................... . A$akah kalian kalian u#ah u#ah $aham untuk untuk men(uu men(uun n tabel $aan"an $aan"an nilai $eubah $eubah #en"an #en"an nilai nilai !un"i7 6ika belum, ba"ian mana (an" menurut kalian uah #i$ahami7 .............................................. ..................................................................... .............................................. .............................................. .............................................. .................................. ........... .............................................. ..................................................................... .............................................. .............................................. .............................................. .................................. ........... .............................................. ................................................................ .................. 3. Tulikan Tulikan man!aat man!aat (an" (an" kalian $er&leh $er&leh etelah etelah mem$elajari mem$elajari men(uun men(uun tabel tabel $aan"an $aan"an nilai $eubah #en"an nilai !un"i4 .............................................. ..................................................................... .............................................. .............................................. .............................................. .................................. ........... .............................................. ..................................................................... .............................................. .............................................. .............................................. .................................. ........... .............................................. ................................................................. ...................


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Penilaian Tu&as

No soa'

Skor

Ke'ompo

a

%3

k

(

%3

1

%3

%

%3

+

+,

2

+,

4um'a* skor

%,,

Mandiri

Ni'ai 5 jum'a*

Catatan Guru:

Nilai:

Paraf :

LEMBA# KEIATAN SIS$A +

•

Standar Kompetensi

: 1. Memahami bentuk aljabar, relai, !un"i, #an $eramaan

"ari luru. : 1.% Membuat keta "ra!ik !un"i aljabar e#erhana $a#a item k&&r#inat 'arteiu. : 1.%.. Men""ambar "ra!ik !un"i $a#a k&&r#inat 'areiu. : Si)a #a$at men""ambar men""ambar "ra!ik !un"i $a#a k&&r#inat 'arteiu.

•

Kompetensi Dasar

•

Indikator Tujuan


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B. MENAMBA# #A"IK "UNSI "UNSI PADA PADA K66#DINAT K66#DINAT 7A#TESIUS. 7A#TESIUS.

Suatu pemetaan atau fungsi "ari himpunan A #e

himpunan

4

"apat

"ibuat

gra5#

Gambar "ra!ik "ra!ik terebut terebut meru$akan meru$akan "ambar "ra!ik 'arteiu !un"i

pemetaanna%

6ra5 a5# #

suatu

pemetaan

f : x → x + 1 .

Aturan (an" memetakan him$unan A kehim$unan kehim$unan B B $a#a $a#a "ambar terebut a#alah untuk etia$

(fun (f ungs gsi) i) a" a"ala alah h be bent ntu# u# "i "iag agra ram m 7a 7art rtes esiu ius s

x an" an""&t "&taa A #i$etakan ke  x 2 10 an""& an""&ta ta B B.. Suatu !un"i #in&taikan #en"an huru! ke5il,

"ari suatu pemetaan (fungsi)%

: : 1 e$e e $ert rtii f, g, atau h. 6ika !un !un"i "i $a# $a#aa "am "ambar bar ter tereb ebut ut #in #in&ta &taik ikan an #en #en"an "an f x → x + Perhati#an

gambar "i samping

#iba5a+ !un"i f !un"i f memetakan memetakan x x ke ke x x 2 10.

f : : x → x + 1

-en"an #emikian, #emikian, $a#a $emetaan $emetaan

#arii him$unan #ar him$unan A ke him$una him$unan n B

#i$er&leh+ *ntuk /  1,

f : : 1

 1 2 1 atau

f : 1

*ntuk /  ,

f : 2

 ... 2 1 atau

f : : 2

 ... ehin""a , ...0

*ntuk /  3,

f : 3

 ... 2 1 atau

f : 3

 ... ehin""a 3, ...0

  ehin""a 1, 0

∈

∈ ∈

f, f, f .

*ntuk memu#ahkan 5ara menuli atau memba5a, uatu $emetaan #a$at -itulikan #alam bentuk tabel atau #a!tar. *ntuk !un"i f + x  x 2 1, tabeln(a a#alah eba"ai berikut+

/ !/0  / 2 1
1  1,0

 ... ,...0

3 ... 3,...0

berurutan
#inama #in amakan kan

koordinat titik .

-en"an men""unakan $aan"anD$aan"an berurutan (an" #i$er&leh $a#a Tabel #i ata #a$at #i"ambar "ra!ik 'arteiu untuk !un"i f !un"i f + x  x 2 1 e$erti tam$ak $a#a "ambar #i ba)ah ini+


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Gambar terebut meru$akan "ra!ik 'arteiu !un"i f + x  x 2 1 #en"an #&main D!  A  =1, , 3,>, k&#&main B  =1, , 3, @> #an Ran"e R!  =, 3, @> (an" #i"ambarkan #en"an n&ktahD n&ktah. 6ika #&main #an k&#&mainn(a #i$erlua $a#a him$unan bilan"an r iil, ran"en(a #itunjukkan #en"an "ari (an" melalui n&ktahDn&ktah e$erti $a#a "ambar . 'atatan+ n&ktah  titik .

3ntu# lebih memahami menggambar gra5# fungsi pa"a #8

Kegiatan 2 MATEMATIKA SMP/MTs KELAS VIII

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Diskusikan soa' di (a)a* ini den&an teman se(an&kumu da'am )aktu +, menitPerkirakan'a* )aktu /an& di(erikan untuk men&erjakan tu&as den&an (aik a&ar (isa se'esai tepat pada )aktun/a0-

Gambarlah "ra!ik !un"i

f ( x ) : x → x + 3 #en"an #&main

Menera$kan 8 men""unakan trate"i+  bulat>

{ x ∨0 ≤ x ≤ 5, x ∈ bilan"an bulat>, maka x  6a)ab+ -&main  Memahami maalah+ f ( x )= x + 3, dimanax ={0, … , … , … , … , 5 } 10 A$a (an" #itan(akan7 =3 !un"i f ( x ) : x → x + 3 0 )=0 + 3"ra!ik f (Gambar



{ x ∨0 ≤ x ≤ 5, x ∈

bilan"an

{0, … , … , … , … , 5 }

0 A$a (an" #iketahui7 f ( … )=… + 3 =… { x ∨0 ≤ x ≤ 5, x ∈ bilan"an bulat> + Fun"i f ( x ) : x → x 3 #en"an #&main f ( … )=… + 3 =… Men(uun 8 meren5anakan trate"i+ A#a bebera$a =… untuk men""ambar "ra!ik !un"i+ f ( … )=… + 3lan"kah 10 Tentukan #&mainn(a. : 3 … )=… +nilai 3 =… 0 f (Tulikan $eubah !un"i ! x0 #ari $eramaan f ( x ) x → x + 30 f (Buat berurutan #ari !un"i terebut. 5 ) =5tabel 8 +3=$aan"an @0 Gambarkan n&ktahDn&ktah $aan"an berurutan terebut $a#a bi#an" 'arteiu. Tabel $aan"anhubun"kan berurutan #ari !un"i #iataitu(aitu+ Kemu#ian, n&ktahDn&ktah #en"an "ari.

/ y = f ( x ) = x + 3

1 3

 .....

3 .....

@ .....

% :

1,30

.....

.....

.....

%,:0

/,(0 Gambar "ra!ik #ari !un"i terebut (aitu +

Berbentuk

a$a

"ra!ik

terebut7 .................................................................................


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
{0, … , … , … , … ,5 }

Nilai $eubah !un"i ! x0 #ari $eramaan

f ( x ) : x → x + 3 

{3, … , … , … , … , 8 }



Bentuk "ra!ik terebut a#alah .................................................................................... 6ika kalian ti#ak memahami materi (an" #ibaha, ba5alah kembali &al #en"an 5ermat #an in"atlah k&ne$ erta trate"i (an" #i$erlukan #alam men(eleaiakan &al a"ar



kalian bia menja)ab &al (an" #iberikan. Keim$ulan + -ari &al $a#a ke"itan  #iata, lan"kah ?lan"kah (an" haru #ikerjakan untuk men""ambar "ra!ik !un"i $a#a k&&r#inat 'arteiu a#alah .............................................................................................................................................. .............................................................................................................................................. ...........................................................................................................................................


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Kerjakan'a* se1ara mandiri da'am )aktu 2, menitPerkirakan'a* )aktu /an& di(erikan a&ar (isa men&erjakan se'esai pada )aktun/a0-

1. Gambarlah "ra!ik !un"i f  x0 #i#e!iniikan eba"ai f  x0   x

{ x|1 ≤ x ≤ 10 }

, #imana

2

? 1, #en"an #&main

x ∈ bilangan cacah.

6a)ab+  Memahami maalah+ 10 A$a (an" #itan(akan7 ......................................................................................................................................... ................................................................................................................................. 0 A$a (an" #iketahui7 ......................................................................................................................................... .................................................................................................................................  Men(uun 8 meren5anakan trate"i+ Ba"aimana 5ara untuk men(eleaikan &al terebut0. ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ...  Menera$kan 8 men""unakan trate"i+ ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ ........................


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Gambar "ra!ik $eramaan terebut+

Gambar terebut berbentuk +................................................................................. ......




............................................................................................................................................. ............................................................................................................................................. ............................................................................................................................................. ............................................................................................................................................. ........................................................................................................................................... 6ika kalian ti#ak memahami materi (an" #ibaha, ba5alah kembali &al #en"an 5ermat #an in"atlah k&ne$ erta trate"i (an" #i$erlukan #alam men(eleaiakan &al a"ar kalian

bia menja)ab &al (an" #iberikan. . Gambarlah "ra!ik !un"i f + x   x $a#a bi#an" 'arteiu #en"an x ={−2,− 1,0,1, 2, } 6a)ab+  Memahami maalah+ 10 A$a (an" #itan(akan ...............................................................................................................................................

1 MATEMATIKA SMP/MTs KELAS VIII ..........................................................................................................................................

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0 A$a (an" #ketahui7 ................................................................................................................................... .............................................................................................................................  Men(uun 8 meren5anakan trate"i+ Ba"aimana 5ara untuk men(eleaikan &al terebut0. ............................................................................................................................................ ............................................................................................................................................ ............................................................................................................................................ ............................................................................................................................................ ...........................................................................................................................................  Menera$kan 8 men""unakan trate"i+ ............................................................................................................................................ ............................................................................................................................................ ............................................................................................................................................ ............................................................................................................................................ ............................................................................................................................................ ............................................................................................................................................ ............................................................................................................................................ ............................................................................................................................................ .....

Gambar "ra!ik !un"i terebut4

Gambar !un"i terebut berbentuk + .............................................................................................................................. 1C MATEMATIKA SMP/MTs KELAS VIII ..

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


......................................................................................................................................... ......................................................................................................................................... ......................................................................................................................................... ......................................................................................................................................... ......................................................................................................................................... ... 6ika kalian ti#ak memahami materi (an" #ibaha, ba5alah kembali &al #en"an 5ermat #an in"atlah k&ne$ erta trate"i (an" #i$erlukan #alam men(eleaiakan &al a"ar kalian bia menja)ab &al (an" #iberikan.

3. Suatu !un"i #itentukan &leh aturan g + x 

x

2

2 1. Gambarkan "ra!ik !un"i g jika

#&main #an k&#&mainn(a meru$akan him$unan bilan"an riil. 6a)ab+  Memahami maalah + 10 A$a (an" #itan(akan7 ..................................................................................................................................... ............................................................................................................................... 0 A$a (an" #iketahui7 ..................................................................................................................................... ...............................................................................................................................  Men(uun 8 meren5anakan trate"i+  Ba"aimana 5ara untuk men(eleaikan &al terebut0 ......................................................................................................................................... ......................................................................................................................................... ......................................................................................................................................... ........................................................................................................................................  Menera$kan 8 men""unakan trate"i+ ............................................................................................................................................ ............................................................................................................................................ ............................................................................................................................................ ............................................................................................................................................ .......................................................................................................................................... ............................................................................................................................................ ............................................................................................................................................ ......................................................................................................................................


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Gambar "ra!ik terebut a#alah+

Gra!ik !un"i terebut berbentuk+ .............................................................................................................. ................... 


kalian bia menja)ab &al (an" #iberikan. Keim$ulan+ ............................................................................................................................................ ............................................................................................................................................ ........................................................................................................................................


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RE!EKS" 1. Tulikan a$a 5ara 8 lan"kah a$a aja untuk men""ambar "ra!ik !un"i $a#a k&&r#inat 'arteiu4 ................................................................................................................ ................................................................................................................ ................................................................................................................ ........................................................... . A$akah kalian u#ah $aham untuk men""ambar "ra!ik !un"i $a#a k&&r#inat 'arteiu7 6ika belum, ba"ian mana (an" belum #i$ahami7 ................................................................................................................ ......................................................................................

Penilaian

Tu&as

No soa'

Skor

Ke'ompo

%

+3 Ni'ai 5 jum'a*


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LKS MATEMATIKA BERBASIS METAKOGNITIF k Mandiri

%

+3

+

+3

2

+3

4um'a* skor

%,,

Catatan Guru:

Nilai:

Paraf :

LEMBA# KEIATAN SIS$A 2

•

Standar Kompetensi

: 1. Memahami bentuk aljabar, relai, !un"i, #an $eramaan

"ari luru. • •

•

Kompetensi Dasar : 1.. Menentukan "ra#ien, $eramaan #an "ra!ik "ari luru. Indikator : 1..1. Menjelakan $en"ertian "ra#ien "ari luru. 1... Menentukan "ra#ien "ari luru #alam berba"ai bentuk Tujuan : 1. Si)a #a$at menjelakan $en"ertian "ra#ien "ari luru. Sebelum memahami persamaan lurus$ a"a . Si)apengertian #a$at menentukan "ra#ien "arigaris luru #alam berba"ai bentuk.

bai#na #amu mengingat #embali materi tentang #88r"inat 7artesius% Persamaan garis lurus selalu "igambar#an "alam #88r"inat 7artesius% K88r"inat

PE9SAMAA: L393S ;artesius ini a#an 6A9IS "iguna#an untu#

persaamaan garis lurus% K88r"inat ;artesius A. Pen&ertian Persamaan aris 'urus

mempelajari

"iguna#an

untu#

menata#an suatu titi# ($) ang "igambar#an pa"a sebuah bi"ang ;artesius ter"iri "ari sumbu < "an sumbu =% Sumbu < merupa#an sumbu men"atar untu# menata#an nilai  (absis) "an sumbu = merupa#an sumbu !erti#al untu# menata#an nilai  (8r"inat)%


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Perhati#an gambar beri#ut>

•

Tulikan k&&r#inat titik A4 6a)ab+ ....,...0 A$akah #a$at #ibentuk uatu "ari

•

luru (an" melalui titik A7 6ika (a "ambarlah titik A4 6a)ab+ ....................................... Bera$a ban(ak "ari luru (an"

•

#a$at #ibentuk melalui titik A7 6a)ab+ .......................................

•

Tulikan k&&r#inat titik A #an B4 6a)ab + Titik A ....,....0 Titik B ....,....0 A$akah #a$at #ibentuk ebuah "ari

•

luru (an" melalui titik A #an B7 6ika (a "ambarlah "ari terebut $a#a k&&r#inat 5arteiu #iam$in"4 6a)ab+....................................... Bera$a "ari luru (an" #a$at

•

#ibentuk melalui titik A #an B7 6a)ab+ ....................................... Keim$ulan+ Sebuah "ari luru #a$at terbentuk #en"an (arat e#ikitn(a a#a . . . . titik $a#a bi#an" 5arteiu Sumbu men#atar #iebut umbu x #an umbu te"ak #iebut umbu f  x0. A$abila !un"i #i ata #ntuk le$i% mema%ami tentang #itulikan #alam bentuk &ersamaan garis lurus &er%atikan y   x+1, maka umbu te"ak $a#a "ra!ik #iebut umbu y. -en"an #emikian y  ..... Karena "ra!ik #ari !un"i f  x0   x+1 atau y=  x+1 beru$a "ari luru, maka bentuk MATEMATIKA SMP/MTs KELAS VIII y= x+1 #iebut ..........................................

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a. Tulikan relai atau hubun"an jarak (an" #item$uh #an tari! taki #in(atakan #alam #ia"ram $anah4 b. Mialkan x men(atakan jarak (an" #item$uh #an y men(atakan tari! taki. Bera$akah tari! taki  y0 bila jarak (an" #item$uh a#alah x  t km7 5. Tulikan hubun"an jarak (an" #item$uh #an tari! taki $a#a tabel4 Pernahkah kamu belajar tentang persamaan #. Gambarkan hubun"an terebut $a#a k&&r#inat 'arteu4garis lurus dan 6a)ab+ graknya?  Memahami Bagaimana cara maalah+ kamu belajar menerapkan konsep tersebut agar 10 A$a (an" #itan(akan7 kamu terlibat Relai atau hubun"an jarakdan (an" dapat #item$uh. secara aktifa. dalam pembelajaran mengkonstruksi

sendiri pengetahuanmu tentang persamaan garis lurus? Untuk b. Tari! taki (0 bila jarak (an" #item$uh a#alah /  t km. kegiatan 3 berikut lebih jelasnya lakukanlah ini. 5.

Menulikan hubun"an jarak (an" #item$uh #an tari! taki $a#a tabel.

Kegiatan #. Gambar hubun"an terebut $a#a k&&r#inat 'arteiu. 0 A$a (an" #iketahui7 Kerjakan dan diskusikan den&an teman se(an&kumu da'am )aktu %, menit#iketahui + -&ra $er"i kerumah nenekn(a ejauh km, Su$ir Perkirakan'a*an" )aktu /an& di(erikan untuk men&erjakan tu&as %den&an (aik taki a&ar memberikan tari! a)al ebear R$ %999,99 #an etia$ atu kil&meter tari! (isa se'esai tepat pada )aktun/a0 bertambah R$ 1.%99,99.  Men(uun 8 meren5anakan trate"i. Ba"aimana untuk&leh men(eleaiakan &al terebut0. Karena ti#ak #itemani5ara&leh ke#ua &ran" tuan(a -&ra $er"i en#iri #en"an a. Membuat relai atau hubun"an jarak (an" #item$uh, berarti a#a  relai (an"

men""unakan taki. Su$ir taki memberikan tari! a)al ebear R$ %999,99 #an etia$ atu akan #ibuat, #ari 9 am$ai #en"an % karena #ari tem$at -&ra kerumah Nenek

kil&meter tari! bertambah R$ 1.%99,99.



ejauh % km. b. Memialkan / #en"an jarak tem$uh #an ( #en"an tari! taki. 5. Membuat tabel hubun"an jarak (an" #item$uh #an tari! taki #. Membuat "ambar $a#a k&&r#inat 'arteiu. Menera$kan 8 men""unakan trate"i a. Relai atau hubun"an jarak (an" #item$uh a#alah+ 0 → 5000 1 → 1500 ( 1 )+ 5000 =6500 2 → 1500 ( … ) + … =… 3 → 1500 ( … ) + … =… 4 → 1500 ( … ) + … =… 5 → 1500 ( … ) + … =…


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b. Mialkan x men(atakan jarak (an" #item$uh #an y men(atakan tari! taki. bila jarak (an" #item$uh a#alah x  t km maka tari! taki (0 a#alah y =… x + 5000 5.

Tabel hubun"an jarak (an" #item$uh #an tari! taki a#alah+

4arak /an& ditempu* km0

Tari8 taksi #p0

,

%999

%

%99

+

...........

2

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

9

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

3

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

#. Gambar hubun"an terebut a#alah+

Gambar "ra!ik terebut berbentuk ................................................................... -ari tu"a b ,kamu telah mem$er&leh uatu $eramaan (aitu+

f ( x ) =1500 x + … Bila k&e!iien ariabel x a#alah a #an uku k&ntan a#alah b. Maka rumu !un"i menja#i f(x)

¿ … x+ …

6ika rumu !un"i f  x0 #i"anti #en"an y, maka (an" #a$at kalian $er&leh a#alah


y =… x + …

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
y =… x + 5000

Gambar

"ra!ik

terebut

berbentuk ........................................................................ = 1500 x + … Bila k&e!iien ariabel x a#alah a #an uku
¿ … x+ …

rumu !un"i f  x0 #i"anti #en"an y, maka (an" #a$at kalian $er&leh a#alah

y =… x + …

 6ika kalian ti#ak memahami materi (an" #ibaha, ba5alah kembali &al #en"an 5ermat



#an

in"atlah

k&ne$

erta

trate"i

(an"

#i$erlukan

#alam

men(eleaiakan &al a"ar kalian bia menja)ab &al (an" #iberikan. Keim$ulan+ Ber#aarkan bentuk umum #an "ra!ikn(a $eramaan ini #iebut $eramaan "ari luru. Menurut kamu $en"ertian #ari $eramaan "ari luru a#alah $eramaan

(an"

memiliki

bentuk

umum

f(x)

¿ … x + … atau y = … x + …dengan a,b ∈ R


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Selamat Berdiskusi...... embelajaran tidak di!apai Dengan kebetulan. "a harus di!ari Dengan semangat # disimak dengan tekun.

B. #ADIEN %. Pen&ertian radien

:ah$ untu# mengetahui apa itu gra"ien Gra#ien itu a$a Se mul abangunan i nidi bangun t e g akl ur us .Namun l amake l amaan bangunan i ni i7 perhati#an gambar me nj adimi r i ng.Ar s i t e k awaldar ibangunan Me nar a Pi s a adal ah Banno Pi s ano. "ibawah ini%

Me nar aPi s abe r adadiI t al i a.Me nar aPi s ai nimul aidi bang uns e ki t art ahun1173.

Me nar a Pi s a me mi l i kibe r at14. 500 t o n de ng an t i ngg i58 me t e r .Pada mas amas a

be r i kut nyas e j uml ahar s i t e ki kutme nyumbanggagas andal am pe mbangunanme nar a i ni .Se t i a pt a hun k e mi r i ng a n Me na r aPi s at e r usb e r t a mb ah.I t us e b ab ny ap ar aa hl i bangunan me nc oba me l akukan per bai kan agarpe ni nggal an s e j ar ah i nibi s at e t ap b e r t a ha n.Me nur utp e ne l i t i a n,k e mi r i ng a n Me na r a Pi s aa da l a h5 , 5 de r a j a t .Se t i a p t a hunn y ak e mi r i ng a n me na r ab e r t a mb ah 1 mi l i me t e rdi hi t ungs e c a r av e r t i k alda r i punc ak me nar a ke t anah. Apa s e be nar ny ay ang di maks ud de ng an ke mi r i ng an?


Ke mi r i ng andar is uat ug ar i sl ur usdis e bu g tr adi e n.

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Kerjakan dan diskusikan den&an teman se(an&kumu da'am )aktu 3 menitPerkirakan'a* )aktu /an& di(erikan untuk

men&erjakan tu&as den&an (aik a&ar (isa

se'esai tepat pada )aktun/a0-

a. A$a $erbe#aan $&ii tan""a #ari keti"a "ambar #iata7 6elakan4 b. A$a (an" #imaku# #en"an "ra#ien7 5. Gambarlah $&ii tan""alebih $a#amemahami k&&r#inat 'arteiu4 *ntuk $en"ertian "ra#ien, 6a)ab+ lakukanlah ke&iatan 9 berikut+  Memahami maalah+ 10 A$a (an" #itan(akan7 a.
 Menera$kan 8 men""unakan trate"i+ a.
,m

*m

0m

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b. <&ii tan""a $a#a keti"a "ambar menunjukkan "ra#ien #ari main"Dmain" tan""a. 6a#i, (an" #imaku# #en"an "ra#ien a#alah ...........................................................................................................................

5. Gambar $&ii tan""a "ambar terebut a#alah+




a.

:

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 Keim$ulan+ 6a#i, (an" #imaku# #en"an "ra#ien a#alah ..................................................................................................................................

Selamat Berdiskusi...

$elajar memang bukan satu%satunya tujuan hidup kita, tetapi jika itu saja tak mampu kita atasi lantas apa yang akan kita !apai& 'him MATEMATIKA SMP/MTs KELAS VIII

;

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+. Menentukan radien aris Lurus Setelah kamu men"etahui $en"ertian "ra#ien, lalu ba"aimanakah 5ara menentukan "ra#ien "ari luru7 %0 Menentukan &radien &aris 'urus /an& me'a'ui dua titik Karena uatu "ari luru #a$at #itentukan melalui #ua titik, maka untuk

menentukan "ra#ien uatu "ari luru #a$at #itentukan melalui #ua titik. x ,y A ( x 1 , y 1 ) Mial titik #an B 2 2 0 terletak $a#a uatu "ari a, untuk menentukan "ra#ien "ari a terlebih #ahulu #itentukan k&m$&nen x $erubahan nilai x0 #an k&m$&nen y $erubahan nilai y0 #ari titik A

x 2 , y 2 ¿

x1, y 1

0 #an titik B

.

Per%atikan gam$ar $erikut

6aris a melalui "ua titi# A( x .$ y .) "an B( x , $ y , ) $ sehingga #8mp8nen y pa"a garis a a"alah

y 2−…

"an #8mp8nen x pa"a garis a a"alah

x 2−…

% @engan

"emi#ian gra"ien garis lurus ang melalui titi# A( x .$ y .) "an B( x , $ y , ) a"alah y 2−…

#ntuk le$i% mema%ami 0ara menentukan gradien garis MATEMATIKA SMP/MTs KELAS VIII

39

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Kegiatan Kerjakan dan diskusikan den&an teman se(an&kumu da'am )aktu %, menit#. uatu "ari, titik (an" lain $a#a "ari g , namakan ' namakan "ari g . Tentukan Perkirakan'a* )aktu /an& di(erikan untuk men&erjakan tu&as den&an (aik titik a&ar -. *lan"i (isa se'esai#an tepat pada lan"lahDlan"kah )aktun/a0- a, b, 5 #i ata4

6a)ab+ -iketahui  titik $a#a bi#an" k&&r#inat, titik AD@, %0 #an titik B , D30 . maalah+  Memahami 10 A$a (an" #itan(akan7 a. ubun"kanlah  titik terebut, ehin""a #i$er&leh uatu "ari, namakan "ari g . a. Men"hubun"kan  titik (an" #iketahui. b. Tentukan eliih abi, #an eliih &r#inat $a#a titik terebut4 b. Menentukan eliih abi #an eliih &r#inat 5. Tentukan ba"i antara eliih &r#inat #en"an eliih abi4 5. hail .................................................................................................................. #. .................................................................................................................. 0 A$a (an" #iketahui7 -iketahui  titik $a#a bi#an" k&&r#inat, titik AD@, %0 #an titik B , D30.  Men(uun 8 meren5anakan trate"i+ a. ubun"kan  titik (an" #i ketahui $a#a k&&r#inat 'arteiu ehin""a



membentuk uatu "ari. b. Men"hitun" eliih abi #an eliih &r#inat $a#a titik terebut. 5. ....................................................................................................................... #. ....................................................................................................................... Menera$kan 8 men""unakan trate"i+ a. ubun"kanlah  titik terebut, ehin""a #i$er&leh

b. Seliih abi #ari #ua titik terebut (aitu Seliih &r#inat #ari #ua titik terebut (aitu

x 2− x 1=…− …= … y 2− y 1= …− … =…


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5. Seliih

y 2 − y 1 x2 − x1

&r#inat

=

#iba"i

eliih

abi

#ua

Seliih &r#inat #ari #ua titik terebut (aitu

x2 − x1

(aitu

x 2− x 1=…− …= …

Seliih abi #ari #ua titik terebut (aitu

y 2 − y 1

terebut,

… =… …

#. Titik '...,...0 , titik -...,...0

Seliih

titik

&r#inat

#iba"i eliih

abi

y 2− y 1= …−… = … #ua

titik

terebut

(aitu

= …=… …


terebut

beru$a ................................................................................. b. Seliih abi #ari #ua titik

terebut

(aitu ...................................................... Seliih &r#inat #ari



#ua

(aitu.................................................... 5. Seliih &r#inat #iba"i eliih

abi

(aitu........................... #. Titik '...,...0 , titik -...,...0 Seliih abi #ari

#ua

(aitu ....................................................... Seliih &r#inat #ari

#ua

(aitu .................................................... Seliih &r#inat #iba"i eliih

abi

titik #ua

terebut

titik

terebut,

titik

terebut

titik

terebut

#ua

titik

terebut

(aitu............................. 6ika kalian ti#ak memahami materi (an" #ibaha, ba5alah kembali &al #en"an 5ermat #an in"atlah k&ne$ erta trate"i (an" #i$erlukan #alam



men(eleaiakan &al a"ar kalian bia menja)ab &al (an" #iberikan. Keim$ulan+ Selamat Ber#aarkan hail $a#a ke"iatan #iata 5ara men5ari "ra#ien "ari luru (an"

Berdiskusi ...........


melalui

#ua

titik

a#alah .................................................

A ( x 1 , y 1 ) danB ( x 2 ,3 y2)

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Pembelajaran ti"a# "i;apai @engan #ebetulan ia harus "i;ari @engan semangat  "isima# "engan te#un%

+0 Menentukan radien aris Lurus /an& Sa'in& Sejajar

Per%atikan gam$ar di$a3a% ini

Gambar #iam$in" a#alah "ariD"ari (an" alin" ejajar. *ntuk menentukan "ra#ien #ari main"Dmain" "ari terebut #a$at #i$ilih #ua buah titik (an" terletak $a#a main"Dmain" "ari #an (an" #iketahui k&&r#inatn(a. Setelah #i$ilih #ua titik $a#a main"Dmain" "ari terebut kemu#ian #ihitun" "ra#ienn(a #en"an men""unakan rumu "ra#ien "ari (an" melalui #ua titik

− -ari "ambar #iata #i$er&leh+  Titik D@,90 #an 9,@0 Gra#ienn(a 

y 2 − y 1 x2 − x1

=

… −0 … = =… 0 −… …

 Titik D,90 #an 9,0 Gra#ienn(a 

y 2 − y 1 x2 − x1

=

Setelah #ihitun" "ra#ien #ari keem$at "ari terebut tern(ata ama (aitu .............................. -en"an #emikian #a$at #iambil keim$ulan bah)a GariD"ari (an" ejajar mem$un(ai "ra#ien (an" ............................................. .

… −0 … = =… 0 −… …

 Titik 9,90 #an 3,30 Gra#ienn(a 


33

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*ntuk lebih memahami menentukan "ari luru (an" ejajar lakukanlah ke&iatan  berikut ini. Kerjakan dan diskusikan den&an teman se(an&kumu da'am )aktu %, menitPerkirakan'a* )aktu /an& di(erikan untuk men&erjakan tu&as den&an (aik a&ar (isa

Ke iatan 4


-iketahui $a#a bi#an" k&&r#inat 5arteiu "ari a melalui titik D,0 #an 1,0, "ari b melalui titik D1,10 #an titik ,10, "ari c melalui titik D3.D10 #an titik 1,D10, #an "ari d melalui titik D1, D0 #an 1, D0. a. Gambarlah "ari a, b, c, d $a#a k&&r#inat 'arteiu4 b. itun"lah "ra#ien #ari "ari a, b, c, d terebut4 6a)ab+  Memahami maalah+ 10 A$a (an" #itan(akan7 a. Gambar "ari a, b, c ,d $a#a k&&r#inat 5arteiu. b. ......................................................................................................................... .. 0 A$a (an" #iketahui7 Gari a melalui titik D,0 #an 1,0, "ari b melalui titik D1,10 #an titik ,10, "ari c melalui titik D3.D10 #an titik 1,D10, #an "ari d melalui titik D1, D0 #an



1, D0. Men(uun 8 meren5anakan trate"i+ a. Men""ambar "ari a, b, c, d $a#a k&&r#inat 5arteiu. b. ............................................................................................................................... ..


3@

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 Menera$kan 8 men""unakan trate"i+ a.

b. Gari a melalui titik D,0 #an 1,0, y 2− y 1 2−… … = = =… m a= Gra#ien "ari a a#alah x 2− x 1 1 −… … Gari b melalui titik D1,10 #an titik ,10, y 2− y 1 …−1 … = = =… m b= Gra#ien "ari b a#alah x 2− x 1 2−… … Gari c melalui titik D3.D10 #an titik 1,D10, y 2− y 1 −1−(−1 ) … = = =… mc = Gra#ien "ari c a#alah x 2− x1 … −… … Gari d melalui titik D1, D0 #an 1, D0 y 2− y1 1− … … = = =… md = Gra#ien "ari d a#alah x 2− x 1 … − … …


terebut

beru$a................................................................................................. Gra#ien "ari

MATEMATIKA SMP/MTs KELAS VIII a#alah................................................................................................... Gra#ien "ari a#alah...................................................................................................

a 3% b

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 6ika kalian ti#ak memahami materi (an" #ibaha, ba5alah kembali &al #en"an 5ermat #an in"atlah k&ne$ erta trate"i (an" #i$erlukan #alam



men(eleaiakan &al a"ar kalian bia menja)ab &al (an" #iberikan. Keim$ulan+ Ber#aarkan ke"iatan #i ata, "ariD"ari (an" ejajar mem$un(ai "ra#ien ............................................................................................................................ ..

'elamat $erdiskusi......)))

*idak ada namanya satu ja+aban tepat Di dunia nyata, pilih apapun Dan buatlah jadi ja+abanmu Maka itulah ja+abanmu.

20 Menentukan &radien &aris /an& sa'in& te&ak 'urus

Per%atikan gam$ar di$a3a% ini


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Gambar 1

Gambar 

am(ar %

am(ar +

Titik $a#a "ari p (aitu 9,10 #an 1,30

Titik $a#a "ari a (aitu 1,DD30 #an D1,30

Gra#ien

"ari

@0

(¿¿ p )=

m y 2− y 1

−

p

Gra#ien

"ari

a

m

=

… −1

−

=…

(¿¿ a )=

y 2− y 1

−

=

…−3

− −

=…

ail kali ke#ua "ra#ien $a#a "ambar 1+ m p × m q=… × …= … ail kali ke#ua "ra#ien $a#a "ambar + m a × m b=… × …= …

-en"an #emikian #a$at #iambil keim$ulan bah)a hail kali "ra#ien "ariD "ari (an" alin" te"ak luru a#alah .... *ntuk lebih memahami menentukan "ari luru (an" te"ak luru lakukanlah ke&iatan ; berikut ini.

Ke iatan 5

Kerjakan dan diskusikan den&an teman se(an&kumu da'am )aktu %, menit-

Perkirakan'a* )aktu /an& di(erikan untuk



-iketahui "ari g melalui titik D1,%0 #an titik ,D@0 #an "ari h melalui titik 3,D0 #an ,D 10. a. Gambarlah "ra!ik "ari g #an h! b. Tentukan "ra#ien "ari g #an "ari h! 5. Tentukan hail kali antara "ra#ien "ari g #en"an "ra#ien "ari h! 6a)ab+  Memahami maalah+ 10 A$a (an" #itan(akan7 a. Gambar "ra!ik "ari g #an h

3C MATEMATIKA SMP/MTs KELAS VIII b. Gra#ien "ari g #an h. 5. ................................................................................................................. .

S






0 A$a (an" #iketahui7 Gari g melalui titik ... , ...0 #an titik ... , ...0 #an "ari h melalui titik ... , ...0 #an ... , ...0. Men(uun 8 meren5anakan trate"i+ a. Men""ambar "ra!ik "ari g #an h $a#a k&&r#inat 'arteiu. b. ........................................................................................................................ 5. ........................................................................................................................ Menera$kan 8 men""unakan trate"i+

a.

Gambar

terebut

(aitu.................................................................................... b. Titik $a#a "ari g (aitu D1,%0 #an ,D@0

m y 2− y 1 …−… (¿¿ )= = =… g Gra#ien "ari g x 2− x 1 …−…

¿

Titik $a#a "ari h (aitu 3,D0 #an ,D10

m y 2− y 1 …− … (¿¿ )= = =… h Gra#ien "ari h x 2− x 1 …− …

¿

5. ail kali ke#ua "ra#ien a#alah+

mg ×m h= …× … =…


Gra#ien

"ari

a#alah......................................................................................... ail kali ke#ua


a#alah...........................................................................

h "ra#ien 3:

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 6ika kalian ti#ak memahami materi (an" #ibaha, ba5alah kembali &al #en"an 5ermat #an in"atlah k&ne$ erta trate"i (an" #i$erlukan #alam men(eleaiakan



&al a"ar kalian bia menja)ab &al (an" #iberikan. Keim$ulan+ Ber#aarkan ke"iatan #i ata, hail kali #ari "ra#ien "ari (an" alin" te"ak luru a#alah...................................................................................................................

'elamat $erdiskusi .....)))

adilah seorang murid 'elama kamu masih memiliki sesuatu -ntuk dipelajari; Dan itu berarti seumur

A o Men!oba 3 Kerjakan'a* se1ara mandiri da'am )aktu %3 menitPerkirakan'a* )aktu /an& di(erikan a&ar (isa men&erjakan se'esai pada )aktun/a0-

1.
b.

y =3 x + 2

Manakah (an"

meru$akan $eramaan "ari luru #an bukan $eramaan "ari luru7

Berikan alaanmu4 6a)ab+  Memahamai maalah+ 10 A$a (an" #itan(akan7 Manakah #ari $eramaan terebut (an" meru$akan $eramaan "ari luru #an bukan $eramaan "ari luru.


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0 A$a (an" #iketahui7 2

Persamaan y = 3 x + 2 dan persamaan y = 3 x + 2

 Men(uun 8 meren5anakan trate"i+ Memahami #en"an 5ermat bentuk $eramaan terebut manakah (an" meru$akan



$eramaan "ari luru #an bukan meru$akan $eramaan "ari luru. Menera$kan 8 men""unakan trate"i+ =3 x +2 meru$akan $eramaan bentuk a.
y = ax + b

a =…danb =…

Sehin""a, ................................................................................................................. ........ 2

b. Bentuk



y =3 x + 2 bila #in(atakan #alam bentuk

y = ax + b ariabel x

ber$an"kat . Sehin""a,..........................................................................................................

y =3 x + 2

meru$akan .........................................................

 6ika kalian ti#ak memahami materi (an" #ibaha, ba5alah kembali &al #en"an 5ermat #an in"atlah k&ne$ erta trate"i (an" #i$erlukan #alam men(eleaiakan &al



a"ar kalian bia menja)ab &al (an" #iberikan. Keim$ulan+ an" meru$akan $eramaan "ari luru a#alah ................... #an (an" bukan

$eramaan "ari luru a#alah................................................................................. . Tentukanlah "ra#ien "ari (an" melalui titikDtitik k&&r#inat berikut+ a. A  3,10 #an B  , @ 0 b. ' D, D3 0 #an -  D@, 0 6a)ab+  Memahami maalah+ 10 A$a (an" #itan(akan7 .................................................................................................................................. ............................................................................................................................

0 A$a (an" #iketahui7 ....................................................................................................................... ....................................................................................................................... .....


@9

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 Men(uun 8 meren5anakan trate"i+







........................................................................................................................................ ........................................................................................................................................ ........................................................................................................................................ .................................................................................................................................... Menera$kan 8 men""unakan trate"i+ ........................................................................................................................................ ........................................................................................................................................ ........................................................................................................................................ ........................................................................................................................................ .......................................................................................................................................


&al a"ar kalian bia menja)ab &al (an" #iberikan. Keim$ulan+ ........................................................................................................................................ ........................................................................................................................................ ...................................................................................................................................

3. Tentukan a$akah ke#ua "ari berikut ejajar atau alin" te"ak l uru7 a.

Gari $ (an" melalui A  @, 0 #an B 9, 90 #an "ari  (an" melalui ' D, @0 #an -

9, 90. b. Gari r (an" melalui E , D30 #an F  :, 0 #an "ari  (an" melalui G  @, 0 #an  9, 90. 6a)ab+  Memahami maalah+ 10 A$a (an" #itan(akan7 ................................................................................................................................. ............................................................................................................................. 0 A$a (an" #iketahui7 ................................................................................................................................. ............................................................................................................................


@1

S


 Men(uun 8 meren5anakan trate"i+







...................................................................................................................................... ...................................................................................................................................... ...................................................................................................................................... ...................................................................................................................................... . Menera$kan 8 men""unakan trate"i+ ...................................................................................................................................... ...................................................................................................................................... ...................................................................................................................................... ...................................................................................................................................... ...................................................................................................................................... ...................................................................................................................................... ...................................................................................................................................... ...................................................................................................................................... ............


&al a"ar kalian bia menja)ab &al (an" #iberikan. Keim$ulan+ ...................................................................................................................................... ...................................................................................................................................... ..................................................................................................................................


@

S


#E"LEKSI 1. Bentuk umum $eramaan "ari luru a#alah ................................................................................................................. ................................................................................................. . Menurut kamu (an" #imaku# #en"an "ra#ien a#alah ................................................................................................................. ................................................................................................. x ,y B ( x 2 , y 2) 3. Gra#ien "ari luru (an" melalui titik A 1 1 0 #an

a#alah ................................................................................................................. ................................................................................................. @. Menurut kamu (an" #i maku# "ra#ien "ari ejajar a#alah ................................................................................................................. ................................................................................................. %. Menurut kamu (an" #imaku# "ra#ien "ari (an" alin" te"ak luru a#alah ................................................................................................................. .................................................................................................

enilaian Tu&as Ke'ompo k

No Ke&iatan 2 Ke&iatan 9 Ke&iatan 3 Ke&iatan  Ke&iatan ; Mandiri % + 2 4um'a* skor

Nilai:

skor %, %, %, %, %, %3 %3 +, %,,

Ni'ai 5 jum'a* skor

Catatan Guru:


Paraf :

@3

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LEMBA# KEIATAN SIS$A 9

•

• •

•

: 1. Memahami bentuk aljabar, relai, !un"i, #an $eramaan "ari luru. Kompetensi Dasar : 1. Menentukan "ra#ien, $eramaan #an "ra!ik "ari luru. Indikator : 1..3. Menentukan $eramaan "ari luru (an" melalui #ua titik . 1..@. Menentukan $eramaan "ari luru (an" melalui atu titik #en"an "ra#ien tertentu. Tujuan : 1. Si)a #a$at menentukan $eramaan "ari luru (an" melalui #ua titik . . Si)a #a$at menentukan $eramaan "ari luru (an" melalui atu titik #en"an "ra#ien tertentu. Standar Kompetensi

7. MENENTUKAN PE#SAMAAN A#IS LU#US %. Persamaan aris Lurus Yan& Me'a'ui Satu Titik Den&an radien Tertentu. x , y . Mialkan uatu "ari mem$un(ai "ra#ien m #an melalui ebuah titik ( 1 1 )

Bentuk $eramaan "ari terebut a#alah y  mx 2 c. *ntuk menentukan $eramaan "ari terebut $erhatikan lan"kahDlan"kah berikut.

Subtitui titik

( x

1

, y 1)

ke $eramaan y  mx 2 c.

y  mx 2 c ⇔ y 1= m x 1+ c ⇔c

= y 1−m x 1

Subtituikan nilai 5 ke $eramaan y  mx 2 c. y  mx 2 c y =mx + y 1−m x 1

B

4adi< persamaan &aris /an& me'a'ui satu titik den&an &radien m ada'a* .......................................................

#ntuk le$i% mema%ami menentukan &ersamaan garis yang melalui se$ua% KELAS titik den MATEMATIKA an radien SMP/MTs m lakukan keVIIIiatan

Kegiatan

@@

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Kerjakan dan diskusikan den&an teman se(an&kumu da'am )aktu %, menitPerkirakan'a* )aktu /an& di(erikan untuk


se'esai tepat pada )aktun/a01

Tentukan $eramaan "ari (an" melalui titik 3, %0 #an ber"ra#ien

2

6a)ab+  Memahami maalah+ 10 A$a (an" #itan(akan7 Menentukan $eramaan "ari (an" melalui titi k ... ...0 #an ber"ra#ien ............. 0 A$a (an" #iketahui7 ..............................................................................................................................  Men(uun 8 meren5anakan trate"i+


terebut. Menera$kan 8 men""unakan trate"i+

y − y 1= m( x − x1 ) 1

y −5 = ( x −3 ) 2

y =… x − … + … y =… x + …atau 2 y =… + …  Keim$ulan+ hasil jawaban Pemeri#saan 6a#i untuk menentukan $eramaan "ari (an" melalui titik 3, %0 #an ber"ra#ien

1 2 1

Persamaan garis ang melalui titi# (0$?) "an bergra"ien

2 a#alah men""unakan rumu $eramaan ................................... ehin""a hail (an"

#i$er&leh a"alah%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  6ika kalian ti#ak memahami materi (an" #ibaha, ba5alah kembali &al #en"an a#alah ........................................................................................................................

5ermat

#an

in"atlah

k&ne$

erta

trate"i

(an"

#i$erlukan

#alam

men(eleaiakan &al a"ar kalian bia menja)ab &al (an" #iberikan.


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Selamat Berdiskusi....

Kunci keberhasilan adalah disaat kita tahu kalau kita salah dan segera memperbaikinya. !ario "eguh#

+. Persamaan aris Lurus Yan& Me'a'ui Dua Titik

( x

1

, y 1 ) dan ( x 2 , y 2 )

*ntuk men"etahui ba"aimana 5ara menentukan $eramaan "ari (an" melalui #ua titik $erhatikan lan"kah berikut+ %. Tulilah rumu untuk mem$er&leh $eramaan (an" melalui atu titik #en"an "ra#ien m.

¿ y − y 1= m ¿ %%%%%%%%%%%%%%%)

. 6ika #iketahui titik

( x 1 , y 1) #an ( x 2 , y 2) , 5arilah "ra#ien "ari (an" melalui

#ua titik terebut4 Namailah "ra#ien terebut #en"an m. y 2− y 1 = m Gra#ien "ari (an" melalui #ua titik a#alah … … .. 3. Gantilah m $a#a ja)aban n&m&r 1 #en"an m (an" #i$er&leh #ari ja)aban n&m&r 4

¿

y − y 1 … … .. y 2− y 1 ¿ ...............0 atau y 2 − y 1 = … … . y − y 1= … … .. 6a#i, untuk menentukan $eramaan "ari (an" melalui #ua titik a#alah ...........................................................................................

-ntuk lebih memahami !ara menentukan persamaan MATEMATIKA SMP/MTsgaris KELAS VIII melalui dua titik lakukanlah

@

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Kegiatan Kerjakan dan diskusikan den&an teman se(an&kumu da'am )aktu %, menitPerkirakan'a* )aktu /an& di(erikan untuk men&erjakan tu&as den&an (aik a&ar (isa se'esai tepat pada )aktun/a0-

Tentukan $eramaan "ari (an" melalui titik 3, ?%0 #an ?, ?30. 6a)ab+

 Memahami maalah+



10 A$a (an" #itan(akan7
y − y 1 y 2 − y 1

= ……

..

…….

 Menera$kan 8 men""unakan trate"i+ y − y 1 y 2 − y 1

=

… . −… … −…

y −… x−… = −3 −… −2 −… y + … x − … = … … … ( y + … ) =… ( x −… ) … y = … x − …+…

 Keim$ulan+

6a#i $eramaan "ari (an" melalui #ua titik (aitu #en"an men""unakan …untuk y = …menentukan x +… rumu ............................................................................................................................ y =… x + …atau … y =… x −… Sehin""a hail (an" #i$er&leh #ari &al #iata a#alah ....................................................


 6ika kalian ti#ak memahami materi (an" #ibaha, ba5alah kembali &al #en"an 5ermat #an in"atlah k&ne$ erta trate"i (an" #i$erlukan #alam men(eleaiakan


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Selamat Berdiskusi....

 Menera$kan 8 men""unakan trate"i+ ..........................................................................................................................................

/rang%orang yang berhenti belajar .......................................................................................................................................... akan menjadi pemilik masa lalu, .......................................................................................................................................... /rang%orang yang masih terus .......................................................................................................................................... belajar akan menjadi pemilik masa .......................................................................................................................................... depan. ... “Mario *eguh” 


.......................................................................................................................................... ...................................................................................................................................... 6ika kalian ti#ak memahami materi (an" #ibaha, ba5alah kembali &al #en"an 5ermat #an in"atlah k&ne$ erta trate"i (an" #i$erlukan #alam men(eleaiakan &al a"ar

kalian bia menja)ab &al (an" #iberikan.  Keim$ulan+ ............................................................................................................................................. Kerjakan'a* se1ara mandiri da'am )aktu +, menit..................................................................................................................................... Perkirakan'a* )aktu /an& di(erikan (isa men&erjakan se'esai pada )aktun/a0. Tentukan $eramaan "ari (an" a&ar melalui titikDtitik k&&r#inat A 3, 30 #an B , 104 1. 6a)ab+ Tentukan $eramaan "ari (an" melalui titik P 3, %0 #an memiliki "ra#ien ?.  Memahami maalah+ 6a)ab+ 10 A$a (an" #itan(akan7 maalah+  Memahami ......................................................................................................................... 10 A$a (an" #itan(akan7 0 .............................................................................................................................. A$a (an" #iketahui7 ......................................................................................................................... 0 A$a (an" #iketahui7 meren5anakan trate"i+  Men(uun8 .............................................................................................................................. .......................................................................................................................................... meren5anakan trate"i+  Men(uun8 .......................................................................................................................................... .............................................................................................................................................. ....................................................................................................................................... ..............................................................................................................................................

 ........................................................................................................................................... Menera$kan 8 men""unakan trate"i+ .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... ..........................................................................................................................................

.. 

@:

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 Keim$ulan+ ........................................................................................................................................... .....................................................................................................................................

Selamat 7enger8akan. MATEMATIKA SMP/MTs KELAS VIII

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-ntuk menang orang tidak harus menang. $erhasil menghindari kekalahan besar, adalah juga kemenangan.

#E"LEKSI 1. Rumu untuk menentukan $eramaan "ari luru (an" melalui atu titik #en"an "ra#ien m a#alah ..................................................................................................... . Rumu untuk menentukan $eramaan "ari luru (an" melalui #ua titik a#alah .....................................................................................................

Penialian

Tu&as Ke'ompok

No Ke&iatan = Ke&iatan > Mandiri % + 4um'a* skor

•

•

•

•

Skor +, +, 2, 2, %,,

Ni'ai 5 skor

Catatan Guru: Paraf : Nilai: Standar Kompetensi : 1. Memahami bentuk aljabar, relai, !un"i, #an $eramaan "ari luru. Kompetensi Dasar : 1. Menentukan "ra#ien, $eramaan #an "ra!ik "ari luru. LEMBA# KEIATAN SIS$A $eramaan "ari 3luru (an" alin" ejajar. Indikator : 1..%. Menentukan 1... Menentukan $eramaan "ari luru (an" alin" te"ak luru. 1..C. Menentukan $eramaan "ari luru (an" alin" berim$it. 1..:. Menentukan $eramaan "ari luru (an" alin" ber$&t&n"an. Tujuan : 1. Si)a #a$at menentukan $eramaan "ari luru (an" alin" ejajar . . Si)a #a$at menentukan $eramaan "ari luru (an" alin" te"ak luru. 3. Si)a #a$at menentukan $eramaan "ari (an" alin" berim$it. @. Si)a #a$at menentukan $eramaan "ari (an" alin" ber$&t&n"an. %9 MATEMATIKA SMP/MTs KELAS VIII

S


2. Persamaan aris Lurus Yan& Sa'in& Sejajar

Per%atikan gam$ar $erikut ini:

Gambar terebut menunjukkan "ari l #en"an $eramaan y  mx 2 c ber"ra#ien m #an "ari g ejajar #en"an l . Karena "ari g 88 l maka mg  ml  m. Gari g melalui titik 

x1 , y 1

0 #an ber"ra#ien m, ehin""a $eramaan "arin(a a#alah

4adi< persamaan &aris /an& sa'in& sejajar ada'a* ........................................................................................ ...........

#ntuk le$i% mema%ami &ersamaan garis yang saling se8a8ar lakukanla% kegiatan 19 $eriku


Kegiatan 19

%1

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Kerjakan dan diskusikan den&an teman se(an&kumu da'am )aktu %, menit Menera$kan 8 men""unakan trate"i+ Perkirakan'a* )aktu /an& di(erikan untuk men&erjakan tu&as den&an (aik a&ar (isa Rumu $eramaan "ari (an" alin" ejajar a#alah se'esai tepat y pada − y 1)aktun/a0 x 1  m x ? 0 Tentukan $eramaan "ari (an" melalui titik  ,30 #an ejajar #en"an "ari y −3 =… ( x −6 ) 4 x + 3 y − 6=0 . y −3 =… x −…

6a)ab+

y =… x + … + 3

 Memahami maalah+ 

  

+ …#itan(akan7 … x(an" 10 y = A$a

%

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Selamat $erdiskusi...

/rang%orang besar hanya menyampaikan pendapat jika diminta, dan itu pun setelah mendengarkan orang lain dengan seksama. “Mario *e uh”

9. Persamaan aris Yan& Sa'in& Te&ak Lurus

Per%atikan gam$ar di $a3a% ini:


%3

S


mg ×m l=−1

atau

m g=

− 1 −1 = ml

m

. Karena "ari g melalui

( x

1

, y1 )

#an

Kerjakan dan diskusikan den&an teman se(an&kumu da'am )aktu %, menit-

6a#i, $eramaan "ari (an" melalui Perkirakan'a* )aktu /an& di(erikan untuk

( x 1 , y 1) #an te"ak luru #en"an men&erjakan tu&as den&an (aik

a&ar (isa

"ari y mx 2 c a#alah .......................................................................... se'esai tepat pada)aktun/a0Tentukan $eramaan "ari (an" melalui titik ?1, 30 #an te"ak luru "ari  x ? 3 y  4 6a)ab+

 Memahami maalah+ 10 A$a (an" #itan(akan7


............................................................................................................................... Men(uun 8 meren5anakan trate"i+ #ntuk le$i% mema%ami Menentukan "ra#ien #ari $eramaan  x ? 3 y  , (akni #en"an men"ubah $eramaan  x

&ersamaan garis yang saling tegak lurus lakukanla%

? 3 y   menja#i bentuk

Kegiatan 

−3 y =−2 x −6, → y =

−2 x + 2 −3

, ehin""a #a$at #iketahui

"ra#ien #ari "ari terebut a#alah ................................................................................ Menera$kan8 men""unakan trate"i+ Gra#ien "ari  x ? 3 y   a#alah .................................................................................
y − y 1= y  3 = y −3 =

( x − x1 )

m

−1 ( x −(−1 )) …

−1 …

( x +1 )

y =… x +MATEMATIKA …+3 SMP/MTs KELAS VIII y =… x + …

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




kalian bia menja)ab &al (an" #iberikan. Keim$ulan+ 6a#i untuk menentukan $eramaan "ari (an" alin" te"ak luru (aitu #en"an men""unakan rumu.................................................................................................. Sehin""a hail (an" #i$er&leh #ari &al #iata a#alah ..............................................

Selamat Berdiskusi

Anda mengetahui apa yang seharusnya tidak dilakukan MATEMATIKA SMP/MTs KELAS VIII ketika anda gagal. adi anda men!iptakan pengetahuan baru dan itu bukan kegagalan. “ ”

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3. Persamaan aris Yan& Sa'in& Berimpit

Per%atikan gam$ar $erikut

+ c1 )aktu y =m2 xda'am Kerjakan den&an$eramaan teman se(an&kumu %, ke menit"ra#ienn(a ama. dan 6ikadiskusikan "ari a #en"an #i"eer kanan, maka Perkirakan'a* )aktu /an& di(erikan untuk


uatu aat "ari a terebut akan berim$it #en"an "ari b.
y = y ⇔ m 1 x + c1= m2 x + c 2 berim$it,Tentukan maka akan berlaku+ antara "ari hubun"an #en"an $eramaan m 1=m 2 Sehin""a l#i$er&leh 6 8 14 =0 #an 2 ! x − y −

c 1= c 2

4

6a)ab+

bah)a "ariD"ari #en"an $eramaan

l 1 ! 3 x − 4 y − 7=0

#an

. -en"an #emikian, #a$at #iambil keim$ulan

y =m 1 x + c1

#an

y =m 2 x + c2

berim$it, jika han(a

 Memahami maalah+ 10 A$a (an" #itan(akan7 m = m c = c



ax + b + c =0 ubun"an #ua "ari terebut. 0 A$a (an" #iketahui7 ...................................................................................................................................... -ntuk lebih ................................................................................................................................ memahaminya Men(uun 8 meren5anakan trate"i+

lakukanlah kegiatan 01

*ntuk menentukan hubun"an ke#ua "ari terebut, maka #itentukan hubun"an

Ke iatan 12

antara k&e!iien x , k&e!eien y #an k&ntantan(a.

 Menera$kan 8 men""unakan trate"i+ 3 x −4 y −7 =0 maka+ *ntuk "ariMATEMATIKA #en"an $eramaan SMP/MTs KELAS VIII

… , c 1=…

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6 x −8 y − 14 =0

Se#an"kan untuk "ari #en"an $eramaan

maka+

a2= 6 ⇔ 2 × 3= 6 ⇔ 2 ×a1 b2= … ⇔ 2 ×… =… ⇔ 2 ×b 1 c 2=… ⇔ 2 × …= … ⇔ 2 × c 1 Karena , D:, #an D1@ meru$akan keli$atan #ari

....................#en"an "ari

l2

3,− 4,−7

maka "ari

l1

.


Gari

l1

....................#en"an "ari

l2

.

 Keim$ulan+ ubun"an

antara

"ari

#en"an

$eramaan

l 1 ! 3 x − 4 y − 7=0

#an

l 2 ! 6 x −8 y −14 =0 a#alah ......................................................................................................................


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Selamat Berdiskusi..

Kesabaran memang penuh ujian, jika kalian selalu lulus kemenangan itu akan permanen selamanya. “

. Persamaan aris Yan& Sa'in& Berpoton&an.

Perhatikan gambar disamping!

A (−2, 2 ) , B ( 2, 2 ) , " ( −1 , 4 ) , # ( 1, 5 ) , $ (3, 5 ) .

GariD"ari a, b, c #an d alin" ber$&t&n"an #i atu titik.

Dari gambar tersebut bisa di buat tabel sebagai berikut:


%:

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aris

Komponen ?

−2 −2=−4

AB

y

Komponen /

( ) radien x

2 −2 = 0

0

−4 2− 4 =−2

2−(−1 ) =3

B7

=0

−2 −2 = 3

2−1 =1

BD

2−5 =−3

3

−3

=−3 1 Kerjakan dan diskusikan den&an teman se(an&kumu da'am )aktu %, menit−3 2−3 =−1 2−5 =−3 BE Perkirakan'a* )aktu /an& di(erikan untuk men&erjakan tu&as den&an (aik a&ar =3 (isa se'esai −1 tepat pada )aktun/a0Tentukan hubun"an antara "ari #en"an $eramaan

h1 ! 6 x −3 y −5 =0

#en"an "ari

-ari tabel terebut #a$at #iim$ulkan bah)a "ra#ien #ari "ariD"ari (an" ber$&t&n"an ti#ak h2 ! 3 x + 4 y + 6 =0 4 ama. -en"an #emikian, #a$at #ikatakan bah)a #ua "ari akan alin" ber$&t&n"an jika 6a)ab+ memiliki "ra#ien (an" ti#ak ama atau k&e!iien #ari x, y, #an bilan"an k&ntann(a bukan


meru$akan keli$atan (an" ama #ari k&e!iien x, y, #an bilan"an k&ntan lainn(a.



10 A$a (an" #itan(akan7 ubun"an #ua "ari #ari $eramaan terebut. 0 A$a (an" #iketahui7 .................................................................................................................................... Men(uun 8 meren5anakan trate"i. Untuk lebih memahaminya −3berikut y −5 =0 6 x13 lakukanlah kegiatan ini #an 3 x + 4 y + 6 =0 ke#alam *bah terlebih #ahulu $eramaan

Ke iatan 1 bentuk

y =mx + c , kemu#ian 5ari "ra#ien #ari $eramaan terebut.

 Menera$kan 8 men""unakan trate"i+
h1 ! 6 x −3 y −5 =0

#iubah ke #alam $eramaan

y =mx + c menja#i

3 y =6 x −5

y =… x −

5

y =… x −

5

3

3

⇒ m1

=…

h2 ! 3 x + 4 y + 6 =0

#iubah ke #alam $eramaan

y =mx + c menja#i

−4 y =3 x + 6 y =… x −

6

y =… x −

6

4MATEMATIKA SMP/MTs KELAS VIII

4

⇒ m2

=…

%;

S




Ke#ua "ari terebut alin"...................................................................................... Keim$ulan+ ........................................................................................................................................... ......................................................................................................................................

Selamat Berdiskusi...

Kepintaran seseorang dapat diketahui dari tiap ja+abannya. Kebijaksanaan seseorang dapat diketahui daro setiap pertanyaannya. “Mario *eguh”


9

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Ayo 7en0o$a

Kerjakan'a* se1ara mandiri da'am )aktu +, menitPerkirakan'a* )aktu /an& di(erikan a&ar (isa men&erjakan se'esai pada )aktun/a0-

1. Tentukan a$akah ke#ua "ari berikut ejajar atau alin" te"ak luru7 8 meren5anakan trate"i+  Men(uun a. Gari $ (an" melalui A  @, 0 #an B 9, 90 #an "ari  (an" melalui ' D, @0 #an .......................................................................................................................................... - 9, 90. .......................................................................................................................................... b. Gari r (an" melalui E , D30 #an F  :, 0 #an "ari  (an" melalui G  @, 0 #an ..........................................................................................................................................  9, 90. .......................................................................................................................................... 6a)ab+ 8 men""unakan trate"i+  Memahami maalah+  Menera$kan .......................................................................................................................................... 10 A$a (an" #itan(akan7 .......................................................................................................................................... .................................................................................................................................. .......................................................................................................................................... ........................................................................................................................... 0 A$a (an" #iketahui7 .......................................................................................................................................... .................................................................................................................................. .......................................................................................................................................... ........................................................................................................................... ..........................................................................................................................................





.......................................................................................................................................... .......................................................................................................................................... ............


kalian bia menja)ab &al (an" #iberikan. Keim$ulan+ .......................................................................................................................................... ..........................................................................................................................................

....................................................................................................................................... 2 x + 4 y + 3= 0 6 x + 12 y + 9 =0 % . Buktikan "ari berhim$it #en"an "ari 6a)ab+  Memahami maalah+ 10 A$a (an" #itan(akan7 ........................................................................................................................... 0 A$a (an" #iketahui7 ...........................................................................................................................  Men(uun8 meren5anakan trate"i+ .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... ............


1

S


 Men""unakan 8 menera$kan trate"i+





......................................................................................................................................... ......................................................................................................................................... ......................................................................................................................................... ......................................................................................................................................... ......................................................................................................................................... ......................................................................................................................................... ......................................................................................................................................... ......................................................................................................................................... ......................................................................................................................................... .....
a"ar kalian bia menja)ab &al (an" #iberikan.  Keim$ulan+ ......................................................................................................................................... ......................................................................................................................................... ......................................................................................................................................... h1 ! 6 x −3 y −5 h2 ! 3 x + 4 y + 6 3. Tentukan hubun"an "ari #en"an "ari 6a)ab+  Memahami maalah+ 30 A$a (an" #itan(akan7 ........................................................................................................................... @0 A$a (an" #iketahui7 ...........................................................................................................................  Men(uun8 meren5anakan trate"i+ ......................................................................................................................................... ......................................................................................................................................... ......................................................................................................................................... ......................................................................................................................................... ........  Men""unakan 8 menera$kan trate"i+ ......................................................................................................................................... ......................................................................................................................................... ......................................................................................................................................... ......................................................................................................................................... ......................................................................................................................................... .........................................................................................................................................  MATEMATIKA SMP/MTs KELAS VIII ......................................................................................................................................... ......................................................................................................................................... .........................................................................................................................................

S





........................................................................................................................................... ........................................................................................................................................... ..................................................................................................................................... 6ika kalian ti#ak memahami materi (an" #ibaha, ba5alah kembali &al #en"an 5ermat #an in"atlah k&ne$ erta trate"i (an" #i$erlukan #alam men(eleaiakan &al a"ar



kalian bia menja)ab &al (an" #iberikan. Keim$ulan+ ........................................................................................................................................... ........................................................................................................................................... .....................................................................................................................................

Selamat 7enger8akan...


3

S


Ketika kamu berhenti mengejar apa yang bukan untukmu, maka *uhan akan mempertemukan kamu dengan apa yang baik untukmu. “ ”

#E"LEKSI %. Rumu untuk menentukan $eramaan "ari luru (an" ejajar a#alah .......................................................................................................... +. Rumu untuk menentukan $eramaan "ari luru (an" te"ak luru a#alah .......................................................................................................... ax + by + c =0 3. Se5ara umum "ari #en"an $eramaan akan berim$it #en"an

"ari (an" $eramaann(a

px + qy + r =0

, jika

............................................................................................................................ ........................................................................................ @. -ua "ari akan alin" ber$&t&n"an jika ............................................................................................................................ ........................................................................................

Penilaian Tu&as

No Skor Ke&iatan %, %, Ke&iatan %% %, Ke&iatan Ke'ompok Ke&iatan %+ %, Ke&iatan %2 %, %.a %, SMP/MTs KELAS VIII MATEMATIKA %.( %, A/o men1o(a + +, 2 +, 4 ' * k %,,

@

S


Nilai  jumlah Sk&r

Catatan Guru:

Nilai:

Paraf :

LEMBA# KEIATAN SIS$A 

•

• •

•

: 1. Memahami bentuk aljabar, relai, !un"i, #an $era maan "ari luru. Kompetensi Dasar : 1. Menentukan "ra#ien, $eramaan #an "ra!ik "ari luru. Indikator : 1..C. Men""ambar "ra!ik "ari luru melalui #ua titik . 1..:. Men""ambar "ra!ik "ari luru melalui atu titik #en"an "ra#ien tertentu. 1..;. Men""ambar "ra!ik "ari luru jika $era maan(a #iketahui Tujuan : 1. Si)a #a$at men""ambar "ra!ik "ari luru melalui #ua titik . . Si)a #a$at men""ambar "ra!ik "ari luru melalui atu titik #en"an "ra#ien tertentu. 3 Si)a #a$at men""ambar "ra!ik "ari luru jika $eramaan "arin(a #iketahui. Standar Kompetensi

D. MENAMBA# #A"IK A#IS LU#US %. Men&&am(ar ra8ik aris Lurus Me'a'ui Dua Titik.

Telah kalian ketahui bah)a melalui #ua buah titik #a$at #itarik ebuah "ari luru. . -en"an #emikian untuk men""ambar "ra!ik "ari luru #a$at #ilakukan #en"an (arat minimal ter#a at #ua titik. *ntuk den&an lebih teman memahami ba"aimana 5ara %, menitKerjakan dan diskusikan se(an&kumu da'am )aktu Kegiatan

men""ambar "ra!ik melalui #ua titik, lakukanlah Perkirakan'a* )aktu /an& di(erikan untuk ke"iatan 1@ berikut ini. men&erjakan tu&as den&an (aik a&ar (isa se'esai tepat pada )aktun/a0-

Gambarlah "ra!ik "ari luru (an" melalui ke#ua titik berikut $a#a bi#an" k&&r#inat 'arteiu.


a. A1, 0 #an B?, 30 b. 'C, 90 #an -?1, %0

%

S








6a)ab+ Memahami maalah+ 10 A$a (an" #itan(akan7 Gambar "ra!ik "ari luru (an" melalui #ua titik. 0 A$a (an" #iketahui7 .................................................................................................................................... .................................................................................................................................... ............................................................................................................................... Men(uun 8 meren5anakan trate"i+ Membuat 8 men""ambar "ra!ik $a#a k&&r#inat 'arteiu. -an men"hubun"kan titikD titik (an" telah #iketahui, ehin""a membentuk uatu "ra!ik "ari luru. Menera$kan 8 men""unakan trate"i+ a. Gambar "ra!ik (an" melalui titik A1, 0 #an B?, 30, kemu#ian hubun"kan ke#ua titik terebut.

b. Gambar "ra!ik (an" melalui titik 'C, 90 #an -?1, %0, $a#a k&&r#inat



'arteiu #iata, kemu#ian hubun"kan ke#ua titik terebut.



S


 6ika kalian ti#ak memahami materi (an" #ibaha, ba5alah kembali &al #en"an 5ermat #an in"atlah k&ne$ erta trate"i (an" #i$erlukan #alam men(eleaiakan &al a"ar



kalian bia menja)ab &al (an" #iberikan. Keim$ulan+ Gra!ik #ari $eramaan ? $eramaan terebut beru$a.................................................


/rang bijak belajar kala mereka bisa; /rang bodoh belajar Kala mereka harus. Arthur 2ellesley

+. Men&&am(ar ra8ik aris Lurus Me'a'ui Satu Titik Den&an radien Tertentu.

( x

1

, y 1)

#en"an "ra#ien m

*ntuk lebih memahamin(a lakukanlah ke"iatan 1% berikut ini.

Kegiatan Kerjakan dan diskusikan den&an teman se(an&kumu da'am )aktu %, menitPerkirakan'a* )aktu /an& di(erikan untuk men&erjakan tu&as den&an (aik a&ar C MATEMATIKA (isa se'esai tepat pada )aktun/a0- SMP/MTs KELAS VIII

−1 Gambarlah "ari (an" melalalui titik < , 90 #en"an "ra#ien

2

4

S


6a)ab+  Memahami maalah+ 10 A$a (an" #itan(akan7 Gambar "ari (an" melalalui titik < , 90 #en"an "ra#ien



¿−

1 2 4

0 A$a (an" #iketahui7 ........................................................................................................................... Men(uun 8 meren5anakan trate"i+ −1 *ntuk men""ambar "ari (an" melalui titik < , 90 #an ber"ra#ien lan"kahD 2 lan"kahn(a a#alah eba"ai berikut+ Gambar titik <, 90 $a#a bi#an" k&&r#inat 'arteiu. − Karena "ra#ien a#alah $erban#in"an antara k&m$&nen y #an k&m$&nen x, maka −

m=

& y −1 = 2 &x

#iterukan #en"an



,

& y  ?1, artin(a ke ba)ah 1 atuan #ari titik < , 90

& x  , artin(a ke kanan  atuan, ehi n""a #i$er&leh titik

J@, ?10. ubun"kan titik < #an titik J. − Menera$kan 8 men""unakan trate"i+


Gra!ik terebut beru$a ............................................................................................. 6ika kalian ti#ak memahami materi (an" #ibaha, ba5alah kembali &al #en"an 5ermat #an in"atlah k&ne$ erta trate"i (an" #i$erlukan #alam men(eleaiakan &al a"ar kalian bia menja)ab &al (an" #iberikan.


:

S


 Keim$ulan+ -ari ke"iatan #iata untuk men""ambar "ra!ik "ari luru melalui atu titik #en"an "ra#ien tertentu a#alah ......................................................................................................................................... ......................................................................................................................................... ...................................................................................................................................

Selamat Berdiskusi.......

$elajar memang bukan stu% satunya *ujuan hidup kita, tetapi jika itu saja *ak mampu kita atasi lantas apa

2. Men&&am(ar ra8ik aris Lurus 4ika Persamaan arisn/a Diketa*ui. Telah kalian ketahui bah)a melalui #ua buah titik #a$at

#itarik ebuah "ari luru. -en"an #emikian untuk

"ngat ..

men""ambar "ra!ik "ari luru #a$at #ilakukan #en"an (arat minimal ter#a$at #ua titik.

a0 Men&&am(ar &aris 'urus (er(entuk

Kegiatan

y =mx

*ntuk men"etahui ba"aimana 5ara men""ambar "ari luru bentuk (m/, lakukan ke"iatan 1 berikut ini

Kerjakan dan diskusikan den&an teman se(an&kumu da'am )aktu %, menitPerkirakan'a* )aktu MATEMATIKA /an& di(erikan untuk men&erjakan ; SMP/MTs KELAS tu&as VIII den&an (aik a&ar (isa se'esai tepat pada )aktun/a0-

Gambarlah "ra!ik "ari

y =3 x 4

S


6a)ab+






10 A$a (an" #itan(akan7 Gambar "ra!ik (  3/. 0 A$a (an" #iketahui7 .......................................................................................................................... Men(uun 8 meren5anakan trate"i+ Ambil ebaran" nilai / untuk menentukan nilai (. − Buat tabel $aan"an berututan. − Gambar "ra!ikn(a. − Menera$kan 8 men""unakan trate"i+ y = 3 x Gari Ambil x =0 ma'a y =3 ( … )= …

= = = Ambil x 2 ma'a y 3 ( … ) … Tabel $aan"an berurutan a#alah+

/ ( / , (0

9 ..... .... , ....0

 ..... .... , ....0

Gambar "ra!ikn(a (aitu+


C9

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




a"ar kalian bia menja)ab &al (an" #iberikan. Keim$ulan+ *ntuk men""ambar "ra!ik $a#a $eramaan (  3/ (aitu #en"an ......................................................................................................................................... .................................................................................................................................

Selamat Berdiskusi.....

/rang bijak belajar kala mereka bisa, /rang bodoh belajar kala mereka harus.

(0 Men&&am(ar ra8ik aris Lurus Ber(entuk

Kegiatan

y =mx + c

*ntuk men"etahui ba"aimana 5ara men""ambar "ari luru bentuk

y =mx + c , lakukan ke"iatan 1C berikut ini.




=2 x + 4 4 KELAS VIII Gambaralah "ra!ik #ari "ari y SMP/MTs MATEMATIKA

C1

S


6a)ab+




10 A$a (an" #itan(akan7 ............................................................................................................................ 0 A$a (an" #iketahui7 ............................................................................................................................. Men(uun 8 meren5anakan trate"i+ Ambil ebaran" nilai / #an (. − Buat tabel $aan"an berututan. − Gambar "ra!ikn(a. − Menra$kan 8 men""unakan trate"i+

*ntuk

y =0 ma'a y =2 x −4 … =2 x − 4

2 x =…

Tabel $aan"an berurutann(a a#alah+

/ ( / , (0

9 ...... .... , ....0

..... 9 .... , ....0

x =…

Gambar "ra!ikn(a a#alah+


C

S



y =0 ma'a x =…





a"ar kalian bia menja)ab &al (an" #iberikan. Keim$ulan+ *ntuk men""ambar "ari $a#a $eramaan

y =2 x + 4 a#alah

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

Selamat Berdiskusi ........

*ujuan dari belajar adalah untuk tumbuh; Dan akal kita , berbeda dari tubuh kita, bisa terus bertumbuh selama kita hidup.

10 Men&&am(ar aris Lurus Ber(entuk

Kegiatan

*ntuk

men"etahui

ax + by + c =0

ba"aimana

men""ambar "ari luru bentuk

5ara

y =mx + c




x + 3 y = 6 4 Gambarlah "ra!ik $eramaan "ari luru 2 KELAS MATEMATIKA SMP/MTs VIII

C3

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6a)ab+

 Memahami maalah+ 10 A$a (an" #itan(akan7 Gambar "ra!ik $eramaan





2 x + 3 y = 6

0 A$a (an" #iketahui7 ........................................................................................................................... Men(uun 8 meren5anakan trate"i+ Ambil ebaran" nilai / #an (. − Buat tabel $aan"an berututan. − Gambar "ra!ikn(a. − Menera$kan 8 men""unakan trate"i+ 2 x + 3 y = 6

*ntuk /  9 maka 2 ( … ) + 3 y =6

*ntuk (  9 maka 2 x + … =6

… + 3 y = 6 Tabel $aan"an berurutann(a a#alah+ 3 y =6 6

=/ =

9 ( ..... / , (0 .... , ....0 Gambar "ra!ikn(a a#alah+

2 x + 3 ( … )=6

2 x =6

x =

6

… ...... 9 .... , ....0


C@

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


Tabel $aan"an berurutann(a a#alah....................................................................... Gambar terebut beru$a........................................................................................... 6ika kalian ti#ak memahami materi (an" #ibaha, ba5alah kembali &al #en"an 5ermat #an in"atlah k&ne$ erta trate"i (an" #i$erlukan #alam men(eleaiakan &al a"ar



kalian bia menja)ab &al (an" #iberikan. Keim$ulan+ *ntuk men""ambar "ra!ik "ari luru $eramaan

2 x + 3 y = 6

a#alah

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


$erpikir adalah pekerjaan tersulit yang pernah ada, yang mana mungkin karena itulah makannya sedikit yang melakukann a.

Ayo Kerjakan'a* se1ara mandiri da'am )aktu 2, menitPerkirakan'a* )aktu /an& di(erikan a&ar (isa men&erjakan se'esai pada )aktun/a0-

1. Gambarlah "ra!ik "ari luru (an" melalui titik+ a. A3, ?0 #an B?1, 30 b. J?%, 90 #an R3, @0 6a)ab+  Memahami maalah+ 10 A$a (an" #itan(akan7 ..................................................................................................................................


C%

S




0 A$a (an" #iketahui7 ........................................................................................................................... Men(uun 8 meren5anakan trate"i+ .............................................................................................................................................. .............................................................................................................................................. ........................................................................................................................................

 Menera$kan8 men""unakan trate"i+ a.

b.




....................................................................................................................................... 6ika kalian ti#ak memahami materi (an" #ibaha, ba5alah kembali &al #en"an 5ermat #an in"atlah k&ne$ erta trate"i (an" #i$erlukan #alam men(eleaiakan &al a"ar kalian bia menja)ab &al (an" #iberikan.


C

S


 Keim$ulan+ ............................................................................................................................................. ..................................................................................................................................... . Gambarlah "ari luru (an" melalui titik A1, 30 #an ber"ra#ien  6a)ab+  Memahami maalah+ 10 A$a (an" #itan(akan7 kalian ti#ak memahami materi (an" #ibaha, ba5alah kembali &al #en"an 5ermat  6ika......................................................................................................................................



#an................................................................................................................................ in"atlah k&ne$ erta trate"i (an" #i$erlukan #alam men(eleaiakan &al a"ar 0 A$abia (an" #iketahui7 kalian menja)ab &al (an" #iberikan. ...................................................................................................................................... Keim$ulan+

.......................................................................................................................................... ................................................................................................................................ 8 meren5anakan trate"i+  Men(uun .......................................................................................................................................... ............................................................................................................................................. ....................................................................................................................................... ............................................................................................................................................. 3. Gambarlah "ari #en"an $eramaan berikut #an jelakan #en"an 5ara a$a kalian ....................................................................................................................................... men"erjakann(a4  Menera$kan 8 men""unakan trate"i+ y =2 x

a.

b. 5.

y =2 x + 4 2 x + 4 y =12

6a)ab+

 Memahami maalah+ 10 A$a (an" #itan(akan7 a. ..................................................................................................................... b. .................................................................................................................... 5. ..................................................................................................................... 0 A$a (an" #iketahui7 a. ............................................................................................................................. 
......

.................................................................................................................................... .... b. .................................................................................................................................... .................................................................................................................................... 5.



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

............................................................................................................................. Menera$kan 8 men""unakan trate"i+ a. .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... ..................................................................................................................................


CC

S


Gambar "ra!ikn(a+

b. ....................................................................................................................... ...................................................................................................................... .. ...................................................................................................................... . Gambar "ra!ikn(a+


C:

5. ...................................................................................................................... ..

S


Gambar "ra!ikn(a+


.................................................................................................................................... ....................................................................................................................................

................................................................................................................................. b. .................................................................................................................................... .................................................................................................................................... 5.

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



. Keim$ulan+ ........................................................................................................................................... ........................................................................................................................................... .....................................................................................................................................


C;

S


#E"LEKSI %. Ba"aimana 5ara men""ambar "ra!ik "ari luru bentuk (  m/7 ............................................................................................................................. ............................................................................................................................. ................................................................ +. Ba"aimana 5ara men""ambar "ra!ik "ari luru bentuk (  m/257 ............................................................................................................................. ............................................................................................................................. ................................................................. 2. Ba"aimana 5ara men""ambar "ra!ik "ari luru bentuk a/2b(25  97 ............................................................................................................................. ............................................................................................................................. .................................................................


:9

S


Penilaian

Tu&as

No soa' Ke&iatan %9 Ke&iatan %3 Ke&iatan Ke&iatan % Ke'ompok Ke&iatan %; Nilai: Ke&iatan %= % A/o men1o(a + 2 4um'a* skor

Skor %, %, %, %, %, %3 %3 +, %,,

Ni'ai 5 jum'a* skor Catatan Guru:

Paraf :

A;AR P#S;AKA

A#ina)an, M, ', #kk. 99:0. Serb Pe"a #atemat$a %"t$ S#P&#' ela * . 6akarta + Erlan""a. arta, I. 99%0. #atemat$a Berma$"a. Surakarta + Ma#iatama.


:1

LKS AKUUH 2

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