ludoM edoK
FKT.TAM 02 1- 10
YNU kinkeT satlukaF fitomotO kinkeT nakididneP nasuruJ
TIMIL SATIUYNITNOK NAD ISGNUF
)X( f = )X( f X
C
C
mil X = X X C
: nusuyneP
.T.M ,.dP.M ,ibutraM
)4 PS( naraggnagneP nad margorP nanusuyneP naanacnereP metsiS T nakididneP nasuruJ fitomotO kinke
002 5
2
RATNAGNEP ATAK
luduj nagned ludoM isgnuF haubeS satiuynitnoK nad timiL ini
kutnebmem kutnu hailuk nataigek malad naudnap iagabes nakanugid
utas halas bus - “ :utiay ,isnetepmok nad ,tafis ,pesnok nakanuggneM
la isalupinam ini ludoM .“isgnuf timil halasam nahacemep malad rabaj
I retsemes id akitametaM hailuk atresep aumes kutnu nakanugid tapad
iregeN satisrevinU kinkeT satlukaF fitomotO kinkeT idutS margorP adap
.atrakaygoY
miL rasad pesnok nakijasid ini ludom adaP satiuynitnoK nad ti
malad iapmujid kaynab gnay aynnahalasamrep nad isgnuF haubeS
.sitkarp nupuam sitiroet araces kiab ,kinket gnadib id aynnaparenep
sahabmem 1 rajaleb nataigeK .rajaleb nataigek agit sata iridret ini ludoM
.rabajlA isgnuF timiL :gnatnet K gnatnet sahabmem 2 rajaleb nataige : timiL
.irtemonogirT isgnuF K rajaleb nataige 3 gnatnet sahabmem : satiuynitnoK
.isgnuF haubeS
awsisaham hadum nagned ini ludom irajalepmem tapad kutnU
namahamep nad nauhategnep iaynupmem halet nakparahid gnatnet
pesnok - gnay rasad pesnok pesnok amaturet ini lah malad ,ayngnajnunem
gnatnet isgnuF rabajlA nad irtemonogirT isgnuF .
,atrakaygoY 5002 rebotkO
nusuyneP
.T.M ,.dP.M ,ibutraM
3
LUDOM ISI RATFAD
namalaH
AH LUPMAS NAMAL ............................................................................ 1 RATNAGNEP ATAK ............................................................................. 2
ISI RATFAD ................................................... ....................................... 3 YRASSOLG / NAHALITSIREP .... . ......................................................... 5
NAULUHADNEP . I ................................................................................. 6
ispirkseD .A ..... .... ........................................................................ . ....... 6
......................................................................................... taraysarP .B 6
.......................... ludoM naanuggneP kujnuteP .C ................................ 7
.......................................................... awsisaham igab kujnuteP .1 7
igab kujnuteP .2 nesod ...................................................... ............ 7
kA naujuT .D .................................................................................. rih 8
.................................................................................... isnetepmoK .E 8
....................................... naupmameK keC .F ..................................... 9
NARAJALEBMEP .II ...................................................................... . ....... 01
awsisahaM rajaleB anacneR .A ......................................................... 01
nataigeK .B ............................................................................. rajaleB 01
1 rajaleB nataigeK .1 ............. ........................................................ 01
...................... 1 rajaleb nataigek naujuT .a . ........ ...................... . 01
iretam naiarU .b ... ..................................................... . ................ . 01
........................................................................ 1 namukgnaR .c 1 .. 8
............................. 1 saguT .d ..................................................... . 02
......................................................................... 1 fitamrof seT .e . 02
bawaj icnuK .f set .. 1 fitamrof . ................................................... . 02
4
namalaH
2 rajaleB nataigeK .2 ........................................................... .......... 12
....................................................... 2 rajaleb nataigek naujuT .a 12
............................................ 2 iretam naiarU .b ........................... 12
......................................................................... 2 namukgnaR .c . 22
.................................................................................. 2 saguT .d . 32
fitamrof seT .e ... 2 ........... ........................................................... . 32
bawaj icnuK .f set fitamrof 2 ............... ...................................... .. 42
3 rajaleB nataigeK . 3 ........................................................... ......... 42
rajaleb nataigek naujuT .a 3 ....................................................... 42
iretam naiarU .b 3 ....................................................................... 42
namukgnaR .c 3 ..................................................... .................... 25
saguT .d 3 .................................................................................. 26
fitamrof seT .e ... 3 ...................................................................... 26
bawaj icnuK .f set fitamrof 3 ....... ........ ...................................... 27
ISAULAVE .III .............................................................................. ...... .. 28
.......................................................................... naaynatreP .A ....... . 28
............................................................................. nabawaJ icnuK .B 29
........................................................................ nasululeK airetirK .C 29
PUTUNEP .VI ................. ...................................................................... .. 03
AKATSUP RATFAD ............................................................................ . 13
5
/ NAHALITSIREP YRASSOLG
isgnuF ksiD uynitno nuf haubes halada : gnay isg kadit uata ulales kadit
upmem surenem suret isgnuf haubes uata kitit paites id agrah iayn
uata kitit adap agrah iaynupmem kadit imalagnem hanrep gnay
.utnetret lavretni
uynitnoK isgnuF surenem suret uata ulales gnay isgnuf haubes halada :
upmem yn kitit paites id agrah ia .
irtemonogirT isgnuF halada : aynagrah gnay isgnuf haubes halada
utnetret tudus utaus agrah helo nakutnetid .
isgnuF timiL halada : isgnuf haubes itakedid gnay satab ialin uata agrah
gnalib nagned itnagid uti isgnuf lebairav akij ialin itakednem gnay na
utnetret .
isinifedreT : utaus awhab nakataynem kutnu halitsi haubes halada
.utnetret agrah iaynupmem nagnalib
6
I BAB NAULUHADNEP
ispirkseD .A
ludoM luduj nagned isgnuF satiuynitnoK nad timiL ini
sahabmem rasad pesnok gnatnet atres isgnuF satiuynitnoK nad timiL
aynnahalasamrep gnay id aynnaparenep malad iapmujid kaynab
.sitkarp nupuam sitiroet araces kiab ,kinket gnadib gnay iretaM
,rabajlA isgnuF timiL : pukacnem irajalepid irtemonogirT isgnuF timiL
d .isgnuF haubeS satiuynitnoK na
.rajaleb nataigek aud sata iridret ini ludoM 1 rajaleb nataigeK
:gnatnet sahabmem ,rabajlA isgnuF timiL 2 rajaleb nataigeK
:gnatnet sahabmem irtemonogirT isgnuF timiL rajaleb nataigeK . 3
:gnatnet sahabmem ynitnoK .isgnuF haubeS satiu paites adaP
nad laos hotnoc nagned ipakgnelid ulales rajaleb nataigek
nahital atreseb aynnasahabmep - utnabmem kutnu aynulrepes nahital
.nakparahid gnay isnetepmok iapacnem malad awsisaham
ludom irajalepmem iaseles haleteS nahurulesek araces ini
nakparahid awsisaham isnetepmok bus iaynupmem “ nakanuggneM
timil halasam nahacemep malad rabajla isalupinam nad ,tafis ,pesnok
“isgnuf
taraysarP .B
iretam isireb ini ludoM - iretam nagnukud nakulremem gnay iretam
ial gnay n iretam nupadA .aynmulebes irajalepid halet aynitsemes -
let aynsurahes gnay rasad iretam hailuk atresep helo imahafid ha id
pesnok halada amaturet fitomotO kinkeT nakididneP nasuruJ rasad
.irtemonogirT isgnuF nad rabajlA isgnuF : gnatnet
7
kujnuteP .C ludoM naanuggneP
awsisahaM igab kujnuteP .1
malad akam ,lamiskam gnay rajaleb lisah helorepid ragA
ulrep gnay rudesorp aparebeb ada ini ludom nakanuggnem
: nial aratna nakanaskalid nad ,nakitahrepid
amaskes nagned imahaf nad halacaB .a pesnok naiaru - pesnok
alup imahaf naidumek ,ini ludom adap nakijasid gnay sitiroet
pesnok naparenep - hotnoc malad tubesret pesnok - laos hotnoc
iretam ada hisam askapret aliB .aynnaiaseleynep arac atreseb
d imahafid asib muleb nad salej gnaruk gnay ne iab nag arap k
upmagnem gnay nesod adapek nakaynanem tapad awsisaham
.nahailukrep nataigek
,iridnam araces )nahital laos( fitamrof sagut paites nakajrek aboC .b
raseb aparebes iuhategnem kutnu nakduskamid ini lah
ret awsisaham paites ikilimid halet gnay namahamep padah
iretam - .rajaleb nataigek paites adap sahabid gnay iretam
iretam iasaugnem muleb awsisaham aynnaataynek malad alibapA .c
nad acabmem igal ignalu aboc ,nakparahid gnay level adap
nahital igal nakajregnem - halaynatreb ulrep ualak nad aynnahital
od adapek gnay nahailukrep nataigek upmagnem gnay nes
nakulremem natukgnasreb gnay iretam ualaK .natukgnasreb
taraysarp awhab naknikay akam )taraysarp( lawa namahamep
raneb duskamid gnay - .ihunepid hadus raneb
nesoD igaB kujnuteP .2
nataigek paites malaD nad sagut iaynupmem nesod ,nahailukrep
: kutnu narep
a. .rajaleb sesorp nakanacnerem malad awsisaham utnabmeM
b. sagut iulalem awsisaham gnibmibmeM - nahital uata sagut - nahital
.rajaleb bahat malad naksalejid gnay
8
c. ad urab pesnok imahamem malad awsisaham utnabmeM n
.nakulrepid alibapa awsisaham naaynatrep bawajnem
d. gnay nial rajaleb rebmus seskagnem kutnu awsisaham utnabmeM
.nakulrepid
e. .nakulrepid akij kopmolek rajaleb nataigek risinagrogneM
f. .nakulrepid akij gnipmadnep nesod/ilha gnaroes nakanacnereM
g. lave nakadagneM isnetepmok naiapacnep padahret isau
.nakutnetid halet gnay awsisaham naanaskalep tubesret isaulavE -
.rajaleb nataigek rihka paites adap ayn
rihkA naujuT .D
ludom malad rajaleb nataigek iretam hurules irajalepmem haleteS
parahid awsisaham ini nak tapad : “ nad ,tafis ,pesnok nakanuggneM
“isgnuf timil halasam nahacemep malad rabajla isalupinam .
isnetepmoK .E
ludoM FKT 02 1- luduj nagned 10 satiuynitnoK nad timiLisgnuF haubeS kutnebmem akgnar malad nususid ini bus -
isnetepmok “M rabajla isalupinam nad ,tafis ,pesnok nakanuggne
“isgnuf timil halasam nahacemep malad .
iapacnem kutnU bus - surah uluhad hibelret ,tubesret isnetepmok
bus iapacid tapad - aynajrek kujnu airetirk atreseb isnetepmok bus
am nagned rajaleb pukgnil iulalem iagabes narajalebmep kokop iret
tukireb :
9
F . naupmameK keC
jalepmem mulebeS ira ludoM 102 FKT – adnat nagned halisi ,ini 10
( kec ikilimid halet gnay isnetepmok nakkujnunem gnay naaynatrep )
: nakbawajgnuggnatrepid tapad nad rujuj nagned awsisaham
buS
isnetepmoK naaynatreP
nabawaJ “aY“ nabawaJ aliB nakajreK aY kadiT
anuggneM -
,pesnok nak nad ,tafis
isalupinam rabajla
malad nahacemep
halasam nad timilstiuynitnok
isgnuf .
,naitregnep :naksalejnem upmam ayaS .1
tafis nad ,isaton - .isgnuf timil tafis
1 fitamroF seT
1 romoN
asamrep nakiaseleynem tapad ayaS .2 - .rabajla isgnuf timil nahal
1 fitamroF seT
2 romoN asamrep nakiaseleynem tapad ayaS .3 -
.irtemonogirt isgnuf timil nahal
2 fitamroF seT
asamrep nakiaseleynem tapad ayaS .4 - isgnuf haubes satiuynitnok nahal
3 fitamroF seT
bawajnem awsisaham alibapA kadiT ini ludom irajalep akam
bawajid gnay iretam iauses kadiT .tubesret
buSisnetepmoK
airetirK ajreK kujnU
pukgniLrajaleB
narajalebmeP kokoP iretaM
pakiS nauhategneP nalipmarteK
anuggneM - ,pesnok nak
,tafis nad isalupinam
rabajla malad
nahacemep halasam
timil nadtiuynitnok s
isgnuf .
naksalejneM .1
naitregnep , isaton nad
tafis - il tafis tim. isgnuf
2 iaseleyneM . -mrep nak asa -
timil nahal isgnuf a rabajl
3 iaseleyneM . -asamrep nak -
timil nahal isgnuf
irtemonogirt .5 naksalejneM .4
satiuynitnok haubes
isgnuf
aitregneP .1 n ,
isaton nadtafis - tafis timil
. isgnuf
2 . L isgnuf timi a rabajl .
3 . L isgnuf timi irtemonogirT
4 . satiuynitnoK haubes
isgnuf
nad itileT
tamrec malad
silunem lobmis
alem nad -rep nakuk -
nagnutih
naitregneP .1 ,
isaton nad ,tafis - tafis timil
. isgnuf 2 . L isgnuf timi
a rabajl .
3 . L isgnuf timi irtemonogirT
4 . satiuynitnoK haubes
isgnuf
gnutihgneM
nagned rudesorp lisah nad
raneb gnay
01
II BAB NARAJALEBMEP
awsisahaM rajaleB anacneR .A hawab id lebat isignem nagned rajaleb nataigek anacner haltauB
.iaseles haletes nesod adapek rajaleb itkub halatnim nad ini
nataigeK sineJ laggnaT utkaW tapmeTrajaleB
nasalAnahabureP
faraPnesoD
nad isaton ,naitregneP .1 tafis - isgnuf timil tafis
rabajla isgnuf timiL .2
nogirt isgnuf timiL .3 .irtemo haubes satiuynitnoK .4
isgnuf
.rajaleB nataigeK .B
: 1 rajaleB nataigeK .1 rabajlA isgnuF timiL
: 1 rajaleB nataigeK naujuT .a 1 .) tafis nad isaton ,naitregnep naksalejnem tapad awsisahaM -
.isgnuf timil tafis
2 .) aM m tapad awsisah ne iaseley ep nak isgnuf timil nahalasamr
.rabajla
: 1 iretaM naiarU .b tafiS nad isatoN ,naitregneP .)1 - tafis isgnuF timiL .
kutnU isgnuf timil gnatnet naitregnep imahamem tapad
gnuf haub aud irad ialin nakitahrep akam akij tukireb X is
gnisam - isgnuf halada amatrep isgnuF .aynagrah iracid gnisam
isgnuf halada audek isgnuf gnades ,surul gnidnabreb gnay
.kilabret gnidnabreb gnay
11
: aynlasim ,surul gnidnabreb isgnuf kutnU .)a X
f = )X( nagned ( X ) ilsa nagnalib = 4
X 004 001 2 1 40,0 400,0 4000,0 .......
)X( f 001 52 5,0 52,0 10,0 100,0 1000,0 .......
iraD rah irebid X akij awhab salej kapmat sata id ratfad ag
aggnihes ,licek nikam aguj )X( f agrah akam licek nikam
“ gnay X kutnu ilakes licek tama tagnas nakatakid ( ”
“ naka aguj )X( f agrah akam ) lon itakednem tama tagnasilakes licek araces silutid ini naataynreP .) lon itakednem ( ”
: isaton nagned sitametam
X X 0 = timil takgnisid gnires uata 0 = mil X 4 0 X 4 0
ayntujnaleS ,awhab nakitkubid tapad aguj akij nikam X
X kutnU .alup raseb nikames naka )X( f agrah akam raseb
kat itakednem nakatakid ( ”ilakes raseb tama tagnas“ gnay
ama tagnas“ naka aguj ) X( f agrah akam ) aggnihret t
araces silutid ini naataynreP .)aggnihret kat( ”ilakes raseb
: isaton nagned sitametam
X X
= timil takgnisid gnires uata mil = X 4 X 4
kutnu awhab mumu araces naklupmisid tapad aynrihkA
: ukalreb tapad surul gnidnabreb isgnuf aumes
= )X( f timil 0 nad = )X( f timil X 0 X
21
b gnidnabreb isgnuf kutnU .) kilabret : aynlasim ,
4 = )X( f gned ( na X ) ilsa nagnalib =
X
X 1 2 8 04 004 000.4 000.04 ....... )X( f 4 2 5,0 1,0 10,0 100,0 1000,0 .......
iraD agrah irebid X akij awhab salej kapmat sata id ratfad
akam raseb nikam kutnu aggnihes ,licek nikam )X( f agrah
“ gnay X ilakes raseb tama tagnas itakednem nakatakid ( ”
“ naka )X( f agrah akam ) aggnihret kat licek tama tagnasilakes araces silutid ini naataynreP .) lon itakednem ( ”
: isaton nagned sitametam
4 4 0 = timil takgnisid gnires uata 0 = mil X X X X
ayntujnaleS ,awhab nakitkubid tapad aguj akij nikam X
gnay X kutnU .raseb nikames naka )X( f agrah akam licek
“ ilakes licek tama tagnas ) lon itakednem nakatakid ( ”
“ naka )X( f agrah akam ilakes raseb tama tagnas kat( ”
ynreP .)aggnihret nagned sitametam araces silutid ini naata
: isaton
4 4
= timil takgnisid gnires uata = mil X 0 X X X 0
kutnu awhab mumu araces naklupmisid tapad aynrihkA
: ukalreb tapad kilabret gnidnabreb isgnuf aumes
0 = )X( f timil nad = )X( f timil X X 0
31
iraD naitregnep haubes libmaid tapad tubesret naiaru
: awhab isgnuF timiL gnay satab agrah haubes halada
airav akij tubesret isgnuf helo itakedid utaus itnagid aynleb
aynsalej hibel kutnU .utnetret agrah itakednem gnay agrah
: tukireb hotnoc nakitahrep
( timil X = ) 4 + 6 = 4 + 2 X 2
adaP akgna tubesret hotnoc 6 halada timil uata agrah
satab gnay akgna itnagid X akij ) 4 + X ( isgnuf irad
aynlasim ,2 itakednem 100,2 naklisahgnem gnay 100,6
uata 9999,1 naklisahgnem gnay 9999,5 uti agrah audek
akgna itakednem ataynret 6 akgna idaJ . 6 agrah halnakub
gnay akgna ( satab agrah aynah ipatet ,kaske .) itakedid
isgnuf timil agrah akam amas gnay naralanep nagneD
kutneb nagned - : aynlasim ,nakutnetid tapad aynnial kutneb
X2 ( timil .)1( 2 X4 + – 2 = ) 3 . 12 4 + . 1 – 3 = 3 X 1
timil .)2( X3 ( 2 3 = ) 5 + X4 + . 2 4 + . = 5 + + = 5 + X
6 X6 . 21 2 = = = timil .)3(
X 2 X 2 2 – 0 2
X 6 6 0 6 0 = = = timil .)4(
X 5 X5 6 . 03 6
2 2 2 0 = = = timil .)5(
X .5 4 + X5 4 +
2 2 3 + X . 3 + 3 + = = = = timil .)6(
X 5 5 5 5
41
tafiS – isgnuF timiL tafis :
lisah padahret narusulenep iraD - timil nagnutihrep lisah
tafis iaynupmem isgnuf timil awhab naktubesid tapad isgnuf -
: tukireb iagabes tafis
k = k timil .)1( X C
C = X timil .)2(
X C
timil .)3( )X( f timil .k = )X( f . k
X X C C
)X( f [ timil .)4( + )X( f timil = ] )X( g + )X( g timil
X X C X C C
)X( f [ timil .)5( . mil = ] )X( g )X( f ti . )X( g timil
X X C X C C
)X( f [ timil .)6( : )X( f timil = ] )X( g : )X( g timil
X X C X C C
] )X( f [ timil .)7( n = ] )X( f timil [ n X X C C
timil .)8( = ] )X( f )X( f timil X X C C
natataC 0 = )X( g timil agrah lasa 6 romon tafis kutnU : X C
)X( f timil : 8 romon tafis kutnU > 0
X C
51
rabajlA isgnuF timiL .)2
halet anamiagabes isgnuf timil pisnirp nakrasadreB
iaruid akam rabajla isgnuf halada )X( f akij ,sata id nak
: tukireb iagabes namodep nagned gnutihid tapad aynagrah
) liir nad natsnok nagnalib halada k nad C (
k = )C( f alibapa k = )X( f timil .)a X C
k = )X( f timil .)b = )C( f alibapa
X 0 C
0 alibapa 0 = )X( f timil .)c = )C( f
X k C
k ( f alibapa 0 = )X( f timil .)d = )
X
= )X( f timil .)e isinifedret kadit uata utnetret kadit alibapa X C
0 ( uata ; : halada )c( f agrah – )
0
apureb isgnuf haubes timil nagnutihrep lisah ataynret akiJ
kutneb aratna id utas halas - kutneb isinifedret kadit sata id
kutneb ( e ) burep nakukalid surah akam naajregnep arac naha ,
uata ulud aynlaos kutneb nakanahredeynem nagned aynlasim
arates gnay nial kutneb nagned laos kutneb nakataynem
aggnihes .) isinifedret ( utnetret kutneb malad lisah helorepid
os kutneb naanahredeynep arac nupadA aynlasim tubesret la
nawakes kutneb nagned nakilagnem ,nakrotkafmem nagned
61
nad ,aguj nawakes kutneb nagned aynigabmem naidumek
bes a .aynlaos kutneb gnutnagret ayniag
laoS hotnoC :
gnutiH hal isgnuf timil - isgnuf ini tukireb !
.)a l ( timi X5 2 – 3X ) 4 + ( timil .)e X5 2 – ) X4 X X 2
X X3 2 + 3 + X2
b .) l timi f .) l timi X X 5 – X 5 4X2 + 3 X – 2
X2 – 3 + X4 X2 – 9 + X6
c .) l timi g .) l timi X X3 1 2 X + – X 2 X 3 2 X + – 21
4 3X + 5
d .) l timi h .) l timi X X 5 + X 3 X – 2
bawaJ :
.)a l ( timi X5 2 – X3 4 + ) = 2.5 2 – 3 2. 4 + = 81 X 2
5.3 X3 51
)b . l timi = = = X X 5 – 5 5 – 5 0
X2 – 3 + X4 12 – 4. 3 + 1 0
c .) l timi = = = 0 X X3 1 2 X + – 3 2 .12 1 + – 2 2
4 4 4
d .) l timi = = = 0 X 5 + X 5 +
( timil .)e X5 2 – ( = ) X4 5. 2 – .4 = ) –
X
71
habuid surah akam ,isinifedret kadit kutneb aynlisah anerak
: tukireb iagabes arac nagned
( X5 2 + X4 ) ( timil X5 2 – ) X4 = ( timil X5 2 – ) X4 . X X ( X5 2 + X4 )
( X5 2 – X4 ).( X5 2 + X4 ) X5 2 – X4 timil = = timil
X ( X5 2 + X4 ) X X5 2 + X4
ualak hisam ini kutneb adap nakisutitsbusid X agrah
inifedret kat kutneb tapadid aumes aynmulebes akam ,igal is
X :utiay ( iggnitret takgnap X igabid ukus 2 uata X 4 )
X5 2 / X2 – X4 / X2
= : idajnem timil X ( X5 2 / X 4 + X4 / X4 )
5 – 4 / X 5 – /4 = timil =
X 5 / X2 + 4 / X3 5 / 2 + 4 / 3
5 – 0 5 = = =
0 + 0 0
X2 3 + X2 + 2 2 + . 3 + f .) l timi )isinifedret kat( = =
X 4X2 + 3 X – 2 4. 2 3 + . – 2
habuid surah akam ,isinifedret kadit kutneb aynlisah anerak
utiay X nagned ukus aumes igabmem arac nagned 2.
X2 3 + X2 + X2 / X2 2 + X/ X2 X/3 + 2 l timi timil =
X 4X2 + 3 X – 2 X 4X2 / X2+ 3 /X X2 – /2 X2
1 2 + / X/3 + X 2 1 2 + / /3 + 2 1 0 + 0 +
= = timil =
81
X 4 + 3/ X – /2 X2 4 + 3/ – /2 2 4 0 + – 0
= ¼
X2 – 3 9 + X6 2 – 6. 0 9 + 3 g .) l timi ) isinifedret kat ( = =
X X 3 2 X + – 3 21 2 3 + – 0 21
: aynnakrotkafmem arac nagned utiay ,habuid surah akam
X2 – X( 9 + X6 – X( ) 3 – X )3 – 3 l timi timil = timil = X X 3 2 X + – X 21 X( 3 X( )4 + – X )3 X 3 4 +
3 – 0 3 = timil = ---- = 0
X 3 3 7 4 +
3X + 3 5 X /3X + 3/5 X + 1 3/5 X h .) l timi = l timi timil =
X 3 X – X 2 3X 3/ X – 3/2 X X 1 – 3/2 X
0 + 1
= = 1 1 – 0
.c namukgnaR : 1 tregneP .)1 tafiS nad isatoN ,nai - isgnuF timiL tafis .
.)a isgnuF timiL helo itakedid gnay satab agrah haubes halada
gnay agrah utaus itnagid aynlebairav akij tubesret isgnuf
.utnetret agrah itakednem
.)b isgnuf timiL X kutnu X itakednem C on nagned silutid isat :
)C( f = )X( f timil X C
tafiS .)c - : isgnuf timil tafis nagned ( , k C R lae )
k = k timil .)1( X C
C = X timil .)2(
91
X C
imil .)3( )X( f timil .k = )X( f . k t X X C C
)X( f [ timil .)4( + )X( f timil = ] )X( g + )X( g timil X X C X C C
)X( f [ timil .)5( . timil = ] )X( g )X( f . )X( g timil X X C X C C
)X( f [ timil .)6( : )X( f timil = ] )X( g : )X( g timil X X C X C C
] )X( f [ timil .)7( n = ] )X( f timil [ n X X C C
timil .)8( = ] )X( f )X( f timil X X C C
natataC 0 = )X( g timil agrah lasa )6( romon tafis kutnU : X C
)X( f timil : )8( romon tafis kutnU > 0 X C
rabajlA isgnuF timiL .)2
akiJ halada )X( f timil agrah akam ,rabajla isgnuf haubes
: tukireb iagabes namodep nagned iracid tapad )X( f irad
k = )C( f alibapa k = )X( f timil .)a
X C k
= )X( f timil .)b = )C( f alibapa X 0 C
0
= )C( f alibapa 0 = )X( f timil .)c X k C
k
( f alibapa 0 = )X( f timil .)d = ) X
02
= )X( f timil .)e isinifedret kadit uata utnetret kadit alibapaX C
0 ( uata ; : halada )C( f agrah – )
0 .d 1 saguT :
isgnuf timil halgnutiH - : ini tukireb isgnuf
X2 – 4 X4 – 3X2 – X2 timil .)2 timil .)7 -
X 2 X2 – 3X 2 + X 0 X2 5 – 52 – X 2 1+X 3 +
timil .)3 timil .)8 - X 0 X X 2X – 1
( timil .)4 X2 3 + X – X2 – X 3( timil .)9 ) X – 4 – 9X2 – )3 X X
.e fitamrof seT : 1 .)1 tafis nad isaton ,naitregnep : halnaksaleJ - ! isgnuf timil tafis
.)2 isgnuf timil halgnutiH - ! tukireb isgnuf
X2 + 2X – 51 3 4 a .) timil d ( timil .) – ) X 5 X2 – 25 X 2 X2 – 4 X – 2 X2 – 4 3 + X X3 – 3X2 – X 4 + b timil .) e timil .) -
X 3 X2 – X – 6 X X2 2 + 3X3 – 7 3 – 9 – X2 5X 1+ + 7 c timil .) f timil .) -
X 0 X5 X 5X – 02
.f fitamroF seT bawaJ icnuK : 1 .)1 isgnuF timiL itakedid gnay satab agrah haubes halada helo
gnay nagnalib utaus itnagid aynlebairav akij tubesret isgnuf .utnetret agrah itakednem isgnuf timiL X kutnu X itakednem C
isaton nagned silutid )C( f = )X( f timil : X C
12
isgnuf timiL tafis iaynupmem - afis tafis itrepes t - isarepo tafis.natsnok nagnalib rabajlaa/kitamtira
.)2 a .) .)c 51/1 e .) 3/1
b .) 5/2 d .) .)f 5
2 . rajaleB nataigeK 2 : gnuF timiL irtemonogirT is
rajaleB nataigeK naujuT .a 2 : isgnuf timil nahalasamrep nakiaseleynem tapad awsisahaM
.irtemonogirt
iretaM naiarU .b 2 :
irtemonogirT isgnuF timiL
il rasad edi nagneD isgnuF timil nagned amas gnay tim
malad id akam ,aynmulebes nakiaruid anamiagabes rabajlA
sumur tapadid irtemonogirT - : tukireb iagabes rasad sumur
X nis X timil . 1 = 1 uata timil = 1
X X X 0 X nis 0
X gt X timil . 2 = 1 uata timil = 1
X X 0 X X gt 0
tukireb iagabes idajnem saulrep id tapad tubesret sumur audeK :
Xa nis Xa timil . 3 1 = uata timil 1 =
X X Xa 0 Xa nis 0
Xa Xa gt timil . 4 1 = uata timil 1 =
X X Xa 0 Xa gt 0
nis n Xa a n X n
22
timil . 5 1 = ata u timil 1 = X a 0 n X n X nis 0 n Xa
gt n a Xa n X n timil . 6 1 = uata timil 1 =
X a 0 n X n X gt 0 n Xa
hotnoC isgnuf timil nakutneT : – : ini hawab id isgnuf
X3 nis gt X6 timil .1 ---------- timil .3 ----------
X X X 0 X7 nis 0 X gt s ni 2 3X
timil .2 --------- timil .4 -- -------- X X X5 0 0 7X2
bawaJ :
3 X3 nis X3 nis
.1 timil timil = . = 1. = 3 3 X X X 0 1 X3 0
4 4 X4 gt X4 gt 4
timil .2 timil = 1 = . = - X 0 X X5 X4 0 5 5 5
gt X7 X6 gt 6X 6 6 6
timil .3 = timil = 1 1 = - X X X7 nis 0 7 X6 X7 nis 0 7 7
s ni 2 3 X nis 2 3 X 9
timil .4 timil = . - X 0 7X2 X 0 9X2 7
9 9
. 1 = = - 7 7
.c namukgnaR 2 :
apad raseb sirag araces irtemonogirT isgnuF timiL nakadebid t
nem aj : mumu sumur aud id ) liir nagnalib halada n nad a akij (
nis n Xa a n X n 1 timil . 1 = uata timil 1 =
32
X a 0 n X n X nis 0 n Xa
gt n a Xa n X n 2 timil . 1 = uata timil 1 =
X a 0 n X n X gt 0 n Xa
.d 2 saguT : isgnuf timil halgnutiH – isgnuf irtemonogirT : ini tukireb
X2 soc + 1 X gt timil .1 --------- timil .6 ---------------
X X X3 nis 0 X soc 0
X nis X5 gt – X soc timil .2 ------- timil .7 ------------------
X X X3 0 1 0 – X2 nis
nis 2 gt + X 2 1 X – X2 soc timil .3 -------------------- timil .8 ---------------
X 0 2/1 X 2 X X 0 2
1 – X soc X( timil .9 – X( gtoc .) 5 – 5 )
timil .4 ------------- X 5 X X 0 2
X3 nis . X nis X nis . X
timil .5 ----------------- timil .01 -----------------
X 1 0 – X4 soc X 1 0 – X4 soc
.e fitamrof seT 2 : isgnuf timil halgnutiH – isgnuf irtemonogirT ini tukireb
nis 3 X 1) timil . --------- )4 . X( timil – )2 esoc X( c – )2
X 0 gt 8 X X 2
tg3 2 X . X3 nis 4 nis X 2) timil . ------- )5 timil . -- ----------------
X 0 5X3 X 0 1 – soc 01 X
nis 2 3 gt + X 2 4 1 X – soc 7 X 3) timil . -------- ------------ )6 timil . ------ ---------
X 0 5 X 2 X 0 4 X 2
42
fitamroF seT bawaJ icnuK .f : 2
.)1 8/3 .)4 1
)2 . 5/8 .)5 52/6
.)3 5 .)6 6 8/1
3 . rajaleB nataigeK 3 : isgnuF haubeS satiuynitnoK
rajaleB nataigeK naujuT .a 3 : awsisahaM ad nem tap p nakiaseley nahalasamre satiuynitnok
.isgnuf haubes
iretaM naiarU .b 3 :
isgnuF haubeS satiuynitnoK
alibapa C = X kitit id uynitnok nakatakid )X( f isgnuf haubeS
tarays ihunemem - : ini hawab id tarays
.a ifedret )C( f .ada )C( f agrah aynitra ,isin
.b ada aguj ) X ( f timil X C
.c ) C ( f = ) X ( f timil
X C
kadit sata id tarays agitek irad hibel uata utas halas ualaK
d gnay isgnuf akam ,ihunepid isgnuf iagabes nakatakid naikime
gnay .C = X id )uynitnok kadit( uynitnoksid gnay isgnuf ayntujnaleS
.uynitnok isgnuf iagabes tubesid kitit paites id uynitnok
hotnoC :
.a X = )X( f isgnuF 2 paites kutnu babes ,kitit paites id uynitnok 3 +
tarays ihunepid ulales C = X - isgnuf haubes nauynitnokek tarays .
X 2 .b = )X( f isgnuF ------- sid )2( f babes ,2 = X kitit id uynitnok = ---
X – 2 0
isinifedret kadit )2( f aggnihes .
52
X 2 + 2 6 .c = )X( f isgnuF -------- = ) 2 ( f babes ,2 = X id uynitnoksid -
X – 2 0
X kutnu )X( f timil nupiksem utnetret kadit itrareb gnay .ada 2
satiuynitnok nataraysrep nakitahrepmem nagned ayntujnaleS
lavretni nakutnetid aguj tapad ,isgnuf utaus - anam id lavretni
nok kadit isgnuf haubes .uynit
hotnoC : isgnuf hakanam lavretni adaP - isgnuf tukireb sid .uynitnok
4 .)1 = )X( f X - 2 .)2 = )X( f --------------
²X - 9
bawaJ : 1) = )X( f . X - 2
)X( f alib uynitnok kadit gnay isgnuf idajnem naka )X( f
hawab id akij idajret utiay ,)layahk( aynagrah ada kadit
fitagen agrahreb raka , X : aggnihes - 0 < 2 2 < X
)X( f idaJ sid : lavretni adap uynitnok X { | } 2 < X
4 2) . = )X( f -------------
²X - 9
²X akij uynitnoksid naka ini isgnuF - 9 ≤ 0
²X - 9 ≤ 0
X ( - ) 3 . ) 3 +X ( ≤ 0
- 3 ≤ X ≤ 3
)X( f idaJ sid : lavretni adap uynitnok
X { - 3 ≤ X ≤ } 3
.c namukgnaR 3 :
C = X kitit id uynitnok nakatakid )X( f isgnuf haubeS
tarays ihunemem alibapa - : ini hawab id tarays
62
.a .ada )C( f agrah aynitra ,isinifedret )C( f
.b ada aguj ) X ( f timil X 0
.c ) C ( f = ) X ( f timil
X 0
k irad hibel uata utas halas ualaK kadit sata id tarays agite
isgnuf iagabes nakatakid naikimed gnay isgnuf akam ,ihunepid
isgnuf ayntujnaleS .C = X id )uynitnok kadit( uynitnoksid gnay
uynitnok isgnuf iagabes tubesid kitit paites id uynitnok gnay : 3 saguT .d
.)1 isgnuf hakanaM - isgnuf nakapurem gnay ini tukireb isgnuf
uynitnok aynitkub nakkujnut nad ,kitit paites id .?
.a 2 + X = ) X ( f
X2 4 + = ) X ( f .b ------ -----
X – 2
X 2 X2 + + 8 = ) X ( f .c ------ ------------
4 + X
.)2 isgnuf hakanam lavretni uata kitit adaP - kadit ini tukireb isgnuf ? uynitnok
X X3 + 72
= ) X ( f .)a -------- = ) X ( f .c - -------- X – X 2 – 3
X5 – X 1 2 – 52 = ) X( f .)b ----------- = ) X ( f .d - -- -----------
X3 – X 2 2 – X3 – 01
.e fitamrof seT 3 : .)1 halnakataK gnuf is - uynitnok ini tukireb isgnuf kadit uata nad ,
.? aynitkub nakkujnut
72
.)a = ) X ( f 3 X – = )X( f .)d 4 X2 + X6 – 7
X2 + 9 X4 b) = ) X ( f . ------ ---- - .)e = )X( f - -
X – 3 X – 2
c) = ) X ( f . X4 2 6 +
.)2 isgnuf hakanam lavretni uata kitit adaP - kadit ini tukireb isgnuf ? uynitnok
5 X X3 + 1
= ) X ( f .)a -------- = ) X ( f .c - -------- X + 4 X – 1
2 X – 3 X2 + 2 1 + X = ) X( f .)b ----------- = ) X ( f .d - -- -----------
X + 6 X 2 – 4
.f fitamroF seT bawaJ icnuK 3 :
.)a .)1 agitek ihunepid ulales babes ,C = X kitit paites id uynitnoK
isgnuf satiuynitnok nataraysrep
.)b = X id uynitnok kadiT t )3( f babes 3 .isinifedret kadi
.)c X4 lavretni adap uynitnok kadiT 2 6 < < X uata 5,1
< X aumes kutnu babes isinifedret kadit )X( f 5,1
agitek ihunepid ulales babes ,C = X kitit paites id uynitnoK .)d
uynitnok nataraysrep isgnuf sati
X id uynitnok kadiT .)e ≤ ( f babes 2 ≤ .isinifedret kadit )2
2 .)a .) kitit adaP X = – 4
b .) : lavretni adaP X { X ≤ – 6 }
c .) kitit adaP X = 1
d .) kitit adaP X = 2 nad X = – 2
82
III BAB ISAULAVE
naaynatreP .A
.1 isgnuf timil halgnutiH - ! tukireb isgnuf ) 04 = eroks (
X2 + 4 X – 5 X5 3 + X2 2 – X3 1 + a timil . c timil . -
X 1 X2 – 1 X X3 3 + X4 2 – 5 4 – 61 + X5 3X –1 + 4 b timil . d timil . -
X 0 7X X 3X – 5
2 . isgnuf timil halgnutiH – isgnuf irtemonogirT ini tukireb ) 04 = eroks ( !
nis 4 2 X . X nis 3 nis X a timil . ------- c timil . -- ----------------
X 0 3X4 X 0 1 – soc 8X
nis 3 2 gt + X 3 X 1 – soc 5 X b timil . -------- ------------ d timil . ---------------
X 0 6 X 3 X 0 2 X 2
3 . halnakataK isgnuf - uynitnok ini tukireb isgnuf kadit uata nad , akij
) 02 = eroks ( ? aynkatel anam lavretni uata kitit adap ,kadit
.a = ) X ( f 2 X + X2 = )X( f .c 5 2 X5 + – 4
X2 + 61 X3 = ) X ( f .b ------ ---- - d . = )X( f - -
X – 4 X – 7
92
nabawaJ icnuK .B .1 .a 3 .c 1 ⅔
.b – 65/5 .d 1 3/
.2 .a 5 3/1 .c 23/3
.b ½ 1 .d ¼ 6
.3 C = X kitit paites id uynitnoK .a
4 = X kitit id uynitnok kadiT .b
C = X kitit paites id uynitnoK .c
X | X { lavretni adap uynitnok kadiT .d } 7 ≤
nasululeK airetirK .C
airetirK rokS 1( – )01 toboB ialiN nagnareteK
( fitingoK 3 .ds 1 romon laos ) 5
sulul taraySm ialin lamini
65
isaton silunem naitileteK 1
rudesorp natapeteK 2
nabawaj alumrof natapeteK 1
utkaw natapeteK 1
RIHKA IALIN
03
VI BAB
PUTUNEP
ludum halnaikimeD 102 FKT .TAM – luduj nagned 10 nad timiLsgnuF satiuynitnoK i sid iaseles halet ini nusu ipakgnelid nagned
icnuk atreseb rihka isaulave nupuam fitamrof set ,sagut/nahital aparebeb
awsisaham arap nakparahid ini ludom nautnab nagneD .aynnabawaj
akerem hakapa ,aynisnetepmok nagnabmekrep iridnes uatnamem tapad
eb halet ran - adap nimrecret anamiagabes isnetepmok ikilimem raneb
.muleb uata rajaleb nataigek paites adap nakparahid gnay naujut
laminim nasululek tarays iapacnem halet gnay awsisaham arap igaB
adap aynrajaleb nataigek nakitnehgnem tapad akerem akam ludom ini
.ayntukireb ludom ek naktujnalem nad tapad muleb akij aynkilabeS
ilabmek gnalugnem surah akerem akam ,laminim nasululek ihunemem
iretam naigab adap amaturet aynrajaleb - ayniasaukid muleb gnay iretam
( sulul muleb huggnus hibel surah akerem aynkiabes nad ) - huggnus
nautnab kusamret ada gnay satilisaf naktaafnamem nagned rajaleb malad
.ini hailukatam rotatilisaf iagabes nesod irad
13
AKATSUP RATFAD
seryA knarF , rJ ., 91 48 . : largetnI nad laisnerefiD .suluklaK audeK isidE
:atrakaJ .)nahamejreT( aggnalrE .
.3991 .E ,gizsyerK natujnaL kinkeT akitametaM .)nahamejreT( 2 & 1 ukuB.aidemarG .TP :atrakaJ
,.kkd olisuS namojN .8891 1 diliJ sitilanA irtemoeG nad suluklaK : atrakaJ .aggnalrE
.M ,legeipS .4891 .R natujnaL akitametaM aggnalrE :atrakaJ .)nahamejreT(
.6891 .A.K ,duortS utnu akitametaM kinkeT k .)nahamejreT( :atrakaJ.aggnalrE