MATEMATIKA
OPERASI BENTUK ALJABAR
SRIWATI TI DANGGA D(4 ANGGA WAKTU 8SRIWA x 40 menit kali e!tem"an# e!tem"an#
KELAS $III SE%ESTER GANJIL Nama :......................................................... NIS NIS :... :..... .... .... .... .... .... ..... ..... .... .... .... ..... ..... .... .... ..... ..... .... .... .... ..... ..... .... .... .... .... SEKOLA& %ENENGA& PERTA%A PERTA%A Kelas Ke las :..... :........ ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ..... .. Kelompok :................................................ :........................................................... ...........
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1" Men#$%ti &n men#m'(n )!n #m %n# &in*tn% 2" Men#$!#i &n men#$%ti pe!i'(* )*)*!+ &isip'in+ tn##*n#),-+ pe&*'i .to'e!nsi+ #oton# !o%on#/+ snt*n+ pe!% &i!i+ &'m -e!inte!(si se! ee(ti &en#n 'in#(*n#n sosi' &n 3"1 Men*n)*((n pe!i'(* te'iti &n ses*i p!ose&*! &'m me'(*(n (ti5its 'm &'m )n#(*n pe!#*'n 3"
&n (e-e!&nn%"
&i !*m$+ se(o'$+ &n ms%!(t
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se-#i
pen#et$*n .(t*'+ (onsept*'+
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imp'ementsi
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me!n#(i+ memo&ii(si+ &n mem-*t/ &n !n$ -st!( .men*'is+ mem-+ men#$it*n#+ men##m-!+ &n men#!n#/ ses*i &en#n %n# &ipe')!i &i se(o'$ &n s*m-e! 'in %n# sm &'m s*&*t pn&n#4teo!i
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P& -$n )! &n LKS ini &ipe')!i tentn#7 1" Pen#e!tin 5!i-e'+ Koeisien &n (onstnt 2" Pen#e!tin S*(* A')-! 3" S*(*8s*(* se)enis &'m A')-! " Ope!si Bent*( A')-! . Tm-$+ K*!n#+ K'i + B#i &n Pn#(t/ Be-e!p -#in te!se-*t &is)i(n &'m -e-e!p ms'$" Unt*( me'ti$ (emmp*n -e!pi(i! mtemti( An&+ se-i(n% setip pe!ms'$n %n# &is)i(n An& se'esi(n sen&i!i te!'e-i$ &$*'* se-e'*m -e!&is(*si &en#n o!n# 'in t* n##ot (e'ompo(m*" Pe!$ti(n pet*n)*( pen##*nn B$n A)! ini #! An& &pt men#isi Lem-! Ke!) Sis, .LKS/"
1" B'$ setip ms'$ %n# &i-e!i(n"
2" P$mi &n ),-'$ setip ms'$ te!se-*t se! mn&i!i" 3" Dis(*si(n &en#n -$s %n# snt*n ),-n setip ms'$ te!se-*t -e!sm n##ot (e'ompo(m*" " Mint'$ -nt*n #*!* )i( An& men&pt ms'$ (eti( men%e'esi(n ms'$ %n# &i-e!i(n" 9" T*'is'$ ),-n (e'ompo(m* %n# p'in# tept p& LKS %n# &i-e!i(n &en#n men##*n(n pensi' *nt*( &i)*(n p& &is(*si (e's" :" Be!&s!(n p!oses peme$n ms'$ %n# An& '(*(n+ pe!$ti(n'$ !n#(*mn %n# m*n#(in &item*(n" ;" <(in'$ -$, &en#n -e!*s$ An& psti -is" Pe!%'$ te!$&p (emmp*n An& &n te!$&p o!n#8o!n# &i se(it! An&"
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St*n Pen&i&i(n 7 SMP4MTs Mt Pe')!n
7 Mtemti(
Ke's4 Semeste!
7 VIII 4 I
Po(o( B$sn
7 Ope!si Bent*( A')-!
A'o(si >(t*
7 2 ??0 menit .1 ??pe!tem*n/
P& mte!i81 B$n A)! ini An& (n mempe')!i pen#e!tin 5!i-e'+ (onstnt+ (oeisien &n s*(* se!t ope!si pen)*m'$n &n pen#*!n#n p& -ent*( ')-! -e!&s!(n ms'$ %n# &i-e!i(n se!t ! menent*(n so'*sin%"
Pe!$ti(n ms'$ -e!i(*t=
P( B&!*n men)*' -e!mm8mm )enis -*n#" B*n# %n# &i)*'n% &i(e'ompo((n men*!*t )enisn%" A& m,!+ me'ti+
n##!e( &n 'inn%" H!# msin#8msin# -*n#
pe!tn#(i -e!se'isi$ Rp2000+00" 1" Ji( nm -*n# %n# &i)*' %n# &i)*' P( B&!*n msin#8msin# &i,(i'i o'e$ s*t* 'm-n#
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'm-n#
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%n#
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Ji( $!# 1 tn#(i
m,!
&'$ p+ -e!p $!# 1 tn#(i
me'ti@
8888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888 D'm pe!ms'$n $!# -*n# m,!+ &n -*n# me'ti+ &pt &i,(i'i &en#n 'm-n# te!tent*" Mis'(n se'isi$ $!# &i,(i'i &en#n 'm-n# + m( ni'i it* &ise-*t Mis'(n $!# 1 tn#(i m,! &'$ p m( $!# 1 tn#(i n##!e( &'$ p 000 "
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Jika Dila membeli 4 tangkai bunga mawar dan 7 tangkai bunga melati , Ilma 6 tangkai bunga mawar dan 5 tangkai bunga anggrek serta Alia 8 tangkai melati dan 3 tangkai anggrek ada !ak "adrun,
tuliskan ban#ak bunga mawar dan anggrek masing$masing dari Dila, Ilma dan
Alia dalam bentuk al%abar&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ Lambang yang digunakan untuk menyatakan banyaknya bunga mawar yang dibeli Nova dan Ilma disebut suku sejenis. Sedangkan konstanta pada suku disebut koefisien'
V!i-e' &'$ 'm-n# t* #-*n#n 'm-n# %n# me,(i'i sem-!n# n##ot &'m $imp*nn semestn%" Konstnt &'$ 'm-n# t* #-*n#n %n# men*n)*( n##ot te!se-*t &'m $imp*nn semestn%" S*(* st* .t*n##'/ &'$ sepe!n#(t 'm-n# ')-! %n# &pt -e!*p 5!i-e' t* (onstnt &n &it*'is tnp tn& ope!si tm-$ &n (*!n#" S*(* &* &'$ -ent*( ')-! %n# &i$*-*n#(n o'e$ st* ope!si
)*m'$ t* se'isi$" Bonto$7 2C 3+ 2 + 3 C 2 C S*(* ti# &'$ -ent*( ')-! %n# &i$*-*n#(n o'e$ &* ope!si
)*m'$ t* se'isi$" Bonto$7 2C 2 C 1+ 3 C % C%
Bent*( ')-! %n# memp*n%i 'e-i$ &!i &* s*(* &ise-*t s*(* -n%( Koeisien &'$ -#in (onstnt &!i s*t* s*(* ')-! %n# men%t(n -n%(n% 5!i-e'
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Lti$n 1 1"
2"
3"
"
Tent*(n (oeisien+ 5!i-e' &n (onstnt &!i -ent*( ')-! -e!i(*t= "
;C2 C 3
-"
E3 2C3 F C 1
"
2& F 9&
Tent*(n &* s*(* se)enis &!i so' -e!i(*t= "
83
-"
C2
Ke'ompo(n s*(*8s*(* %n# se)enis &n ti&( se)enis &!i -ent*( ')-! -e!i(*t= "
C2 F 2C% F 3C 2 9C%
-"
9-2 3- F 2 2 F 9-
P*t!i &n Anis$ men&is(*si(n -ent*( ')-! &n " Men*!*t P*t!i (oeisien &!i &'$ 81 &n (oeisien &!i &'$ 1" Se&n#(n men*!*t Anis$ (e&* -ent*( ')-! it* memp*n%i (oeisien 0" T*'is'$ ),-n %n# -en! &n )e's(n 'sn n&"
9" (entukan bentuk al%abar, k)e*isien, +ariabel dan k)stanta ada al%abar berikut ini a' 2 b' 4 .'
:" (entukan bentuk al%abar berikut ini a' 2a / 5b / 4a / 3b b' 3 ;"
(entukan suku se%enis atau bukan suku se%enis
a' b' .' d'
2- dan $33#2 dan #2 $4-2# dan 2-# 2 2-# dan 2ab
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Bahan jar dan LKS !
St*n Pen&i&i(n 7 SMP4MTs Mt Pe')!n
7 Mtemti(
Ke's4 Semeste!
7 VIII 4 I
Po(o( B$sn
7 Ope!si Bent*( A')-!
A'o(si >(t*
7 2 0 menit .1 pe!tem*n/
P& mte!i82 -$n A)! ini n& akan memela%ari .ara men%umlakan dan mengurangkan suku$ suku se%enis ada bentuk al%abar "
Pe!$ti(n ms'$ -e!i(*t=
D* $!i '#i No5 (n me!%(n *'n# t$*nn%" Unt*( men%m-*t $!i -$#in% it* No5 &n i-*n% pe!#i (e ps!" Se'in mem-e'i -e!mm8mm (*e me!e( )*# mem-e'i -*$8-*$n &int!n% pe' &n )e!*( "Keti( smpi &i st* to(o A+ te!n%t pe!se&in to(o te!se-*t $n% tin##' 10 -*$ pe' &en#n -e!t msin#8msin# 100 ons &n 10 -*$ )e!*( &en#n -e!t msin#8msin# 200 ons" K!en -!n# %n# &i-, s*&$ te!''* -n%( m( me!e( mem*t*s(n $n% mem-e'i 2 (# .2000 ons/ pe' &n )e!*(" H!# msin#8msin# -*$ pe! (# -e!se'isi$ Rp2000+00"
1"
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Ap-i'+ pe' &i'm-n#(n &en#n C &n )e!*( &i'm-n#(n &en#n %+ t*'is'$ &'m -ent*( ')-!88888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888
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3"
Ji( No5 mem*t*s(n *nt*( mem-e'i '#i : pe' &n ; )e!*( &n sete'$ ti- &i !*m$ te!n%t %$ No5 te'$ mem-e'i 3; -*$ pe' &n 0 -*$ )e!*(+ -e!p )*m'$ pe' &n
)e!*(
No5
se(!n#@
88888888888888888888888
T*'is'$
-ent*(
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Ap-i' &!i )*m'$ te!se-*t te!&pt 2 -*$ pe' &n 1 -*$ )e!*( %n# -*s*(+ -e!p )*m'$ -*$ %n# &imi'i(i No5@8888888888888888888888888888T*'is'$ -ent*( ')-!n%
Pen)*m'$n &n pen#*!n#n -ent*( ')-! &pt &i'(*(n &en#n men)*m'$(n t* mempe!(*!n#(n (eoisien8(oeisien &!i s*(*8s*(* %n# se)enis"
Lti$n 2 1" Se&e!$n(n -ent*(8-ent*( ')-! -e!i(*t" " :mn 3mn -" 1:C 3 3C " C % C 3 &" 2p 3p2 2G 9G2 3p
2" Tent*(n $si' &!i7 " pen)*m'$n 10C2 :C% 12 &n C2 2C% 10+ -" pen#*!n#n p2 10p 19 &!i p2 10p 9"
3"
Di me) m(n te!&pt 9 pi!in#+ 9 #e's &n 9 sen&o( m(n" A&i( men#m-i' 1 pi!in# &n 1 sen&o( m(n (em*&in i-* menm-$(n '#i 2 pi!in#+ 1 #e's &n 3 sen&o( m(n -e!p )*m'$ pe!'tn m(n %n# & &ime) m(n te!se-*t@
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" P( Tni meme'i$! 3 (m-in#+ 9 %m &n 10 -e-e(" P& s*t* st &i men)*' 1 (m-in# &n 2 -e-e( (e ps!" P& st 'in &i mem-e'i '#i 3 %m &n 2 -e-e(" Be!p )*m'$ te!n( p( tni se(!n#@ 9"
Di to(o tnmn te!&pt 9 tnmn -*n# m,!+ 10 Tnmn -*n# me'ti &n tnmn -*n# -o#en5i'" Te!)*' 2 tnmn -*n# m,! &n 2 -*n# -o#en5i'" To(o te!se-*t mem-e'i '#i 2 tnmn -*n# m,!+ 2 tnmn -*n# me'ti &n tnmn -*n# -o#en5i'" Be!p )*m'$ tnmn -*n# &i to(o te!se-*t@
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Bahan jar dan LKS "
St*n Pen&i&i(n 7 SMP4MTs Mt Pe')!n
7 Mtemti(
Ke's4 Semeste!
7 VIII 4 I
Po(o( B$sn
7 Ope!si Bent*( A')-!
A'o(si >(t*
7 2 0 menit .1 pe!tem*n/
P& mte!i83 -$n A)! ini An& (n -e')! pe!('in &n pem-#in -ent*( ')-!" Pe!$ti(n ms'$ -e!i(*t= P( A&i (n mem-*t Se-*$ (o'm -e!-ent*( pe!se#i pn)n# &en#n '*s (o'm 130 m 2" Pn)n# (o'm 3 mete! 'e-i$ pn)n# &!i 'e-!n%
1'
T*'is(n pn)n# &n 'e-! (o'm te!se-*t &'m -ent*( ')-!=888888888888888888888888888888
2'
Tent*(n (e'i'in# (o'm te!se-*t8888888888888888888888888888888888888888888888888888888888888888888888888
3'
Ji( L*s (o'm 03
m2 &n 'e-! (o'm 19 m+ $it*n# pn)n# (o'm
te!se-*t=888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888
P( An&!e memp*n%i se-i&n# (e-*n &i smpin# !*m$n%" Ke-*n te!se-*t -e!-ent*( pe!se#i pn)n# &en#n pn)n# .C 1/m &n 'e-! .C 2/m"
1"
Hit*n# '*s (e-*n P( An&!e &'m C888888888888888888888888888888888888888888888888888888888888888888
2'
Hit*n# (e'i'in# (e-*n P( An&!e te!se-*t=8888888888888888888888888888888888888888888888888888888888888
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Pe!('in s*(* t*n##' &en#n s*(* t*n##' Mis'(n te!&pt -ent*( ')-! 2 &n - m( pe!('in 2 &n - &pt &it*'is &en#n 2Pe!('in s*(* t*n##' &en#n s*(* &*+ ti# t* s*(* -n%( Mis'(n te!&pt -ent*( ')-! C &n C% m( $si' ('i C &n C% &pt &it*'is C. C% / CC% C Be#it* )*# $'n% pe!('in s*(* t*n##' &en#n s*(* ti# &n s*(* -n%(" Pe!('in s*(* &* &en#n s*(* &* Pe!('in s*(* &* &en#n s*(* &* &pt &i!i &en#n men##*n(n $*(*m &ist!i-*ti &n s(em H*(*m &ist!i-*ti Pe!('in &* s*(* -ent*( ')-! . -/ &n . &/ &en#n $o(*m &ist!i-*ti &pt &it*'is se-#i -e!i(*t" . -/. &/ . -/ . -/& - & -& & - -& Den#n s(em Se! s(em+ pe!('in &it*'is7 ! sepe!ti ini me!*p(n ! 'in %n# &pt &i#*n(n *nt*( men%e'esi(n pe!('in nt! &* -*$ s*(* -ent*( ')-!"
Hsi' pem-#in &* -ent*( ')-! &pt &in%t(n &'m -ent*( %n# p'in# se&e!$n &en#n meme!$ti(n (to!8(to! t* 5!i-'e %n# sm" Bent*( ')-! 2 &n memp*n%i to! %n# sm %it* + se$in## $si' pem-#in 2 7 &pt &ise&e!$n(n %it* 2"
atian 3
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1' unakan ukum distributi* untuk men#elesaikan erkalian berikut' a' 2- / 3
.' 3-# / 5
b' 5 #
d' 5 2
2' (entukan asil dari a' - / 1- / 2 b' - / 82- / 4 .' - 2- / 5
3'
(entukan asil embagian berikut' a' 8- 4
.' 16a2b 2ab
b 15 3 d' 8-2 / 2- 2#2 2# 4' (entukan asil embagian dari a' 12 b'
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St*n Pen&i&i(n 7 SMP4MTs Mt Pe')!n
7 Mtemti(
Ke's4 Semeste!
7 VIII 4 I
Po(o( B$sn
7 Ope!si Bent*( A')-!
A'o(si >(t*
7 2 0 menit .1 pe!tem*n/
P& mte!i8 -$n A)! ini An& (n -e')! pe!pn#(tn -ent*( ')-!"
An& te'$ mempe')!i &einisi -i'n#n -e!pn#(t" P& -#in ini mte!i te!se-*t (n &i(em-n#(n+ %it* memn#(t(n -ent*( ')-!" Sepe!ti %n# te'$ (m* (et$*i+ -i'n#n -e!pn#(t &i&einisi(n se-#i -e!i(*t"
Unt*( -i'n#n !ii' &n n -i'n#n s'i" Pemn#(tn p& -ent* ')-! &'$ pe!('in -e!*'n# &!i -i'n#n po(o(
J&i
Dn sete!*sn% Se(!n#+ -#imn &en#n -ent*( . -/ 2" Bent*( . -/ 2 me!*p(n -ent*( 'in
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&!i . -/ . -/" J&i+ &en#n men##*n(n sit &ist!i-*ti+ -ent*( . -/ 2 &pt &it*'is7
. -/ 2 . -/ . -/ . -/ . -/ 2 - - - 2 2 2- - 2
Den#n ! %n# sm+ -ent*( . -/ 2 )*# &pt &it*'is se-#i7 . -/ 2 . -/ . -/ . -/ . -/.-/ 2 - - - 2 2 2- - 2 Se'n)*tn%+ (n &i*!i(n -ent*( . -/ 3+ se-#i -e!i(*t" . -/ 3 . -/ . -/ 2 . -/ . 2 2- - 2/
.-/2 2 2- - 2
.2 2- - 2 / - . 2 2- - 2 / 3 22- -2 2- 2-2 -3 3 22- 2- - 2 2-2 -3
.men##*n(n ! s(em/ .s*(* %n# se)enis &i(e'ompo((n/ .ope!si(n s*(*8s*(* %n# se)enis/
3 32- 3- 2 -3
Unt*( men#*!i(n -ent*( ')-! . -/ 2+ . - / 3+ &n . -/ + (m* &pt men%e'esi(nn% &'m ,(t* sin#(t" A(n tetpi+ -#imn &en#n -ent*( ')-! . -/9+ . -/ :+ . -/;+ &n sete!*sn%@ Tent* s) (m* )*# &pt men#*!i(nn%+ mes(ip*n (n meme!'*(n ,(t* %n# 'e-i$ 'm" Unt*( mem*&$(n pen#*!in pe!pn#(tn -ent*(8-ent*( ')-! te!se-*t+ (m* -is men##*n(n po' se#iti# Ps' " Se(!n#+ pe!$ti(n po' se#iti# Ps' -e!i(*t"
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13
H*-*n#n nt! se#iti# Ps' &en#n pe!pn#(tn s*(* &* -ent*( ')-! &'$ se-#i -e!i(*t"
Se-e'*mn%+ (m* te'$ men#et$*i -$, -ent*( ')-! . -/ 2 &pt &i*!i(n men)&i 2 2- - 2" Ji( (oeisien8(oeisienn% &i-n&in#(n &en#n -!is (eti# po' se#iti# Ps'+ $si'n% psti sm+ %it* 1+ 2+ 1" Ini -e!!ti+ -ent*( ')-! . -/ 2 men#i(*ti po' se#iti# Ps'" Se(!n#+ pe!$ti(n 5!i-e' p& -ent*( 2 2- - 2" Sem(in (e (nn+ pn#(t sem(in -e!(*!n# . 2 (em*&in /" Se-'i(n%+ sem(in (e (nn pn#(t - sem(in -e!tm-$ .- (em*&in - 2/" J&i+ &en#n men##*n(n po' se#iti# Ps' &n t*!n pe!pn#(tn 5!i-e'+ -ent*(8-ent*( pe!pn#(tn s*(* &* . -/3+ . -/+ . -/ 9+ &n sete!*sn% &pt &i*!i(n se-#i -e!i(*t" . -/ 3 3 32- 3- 2 -3 . -/ 3- :2-2 -3 - . -/ 9 9 9- 103-2 102-3 9- -9 &n sete!*sn%"
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Pe!pn#(tn -ent*( ')-! . -/ n &en#n n -i'n#n s'i )*# men#i(*ti po' se#iti# Ps'" A(n tetpi+ tn& setip (oeisienn% se''* -e!#nti &!i ./ (e ./+ -e#it* sete!*sn%" Pe')!i'$ *!in -e!i(*t"
. -/ 2 2 2- - 2 . -/ 3 3 32- 3-2 -3 . -/ 3- :2-2 -3 - . -/ 9 9 9- 103-2 102-3 9- -9
Lti$n
1"
Tent*(n $si' pe!pn#(tn -ent*( ')-! -e!i(*t" " .9 /3 -" .2C% /2 " .9C% 3/ &" .3 pG /
2" Tent*(n $si' pe!pn#(tn -ent*( ')-! -e!i(*t" " .2C 3/2 -" .C % /3 3" J-!(n pe!pn#(tn -ent*( ')-! -e!i(*t" " .C /3 -" . 9/ " .2C % /3 &" .3 2/9
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