Matemáticas, 5to de Primaria
August 4, 2022 | Author: Anonymous | Category: N/A
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Bc Iu`mbrhf mb c`s Aeij`s mb `itevem`mbs L`tblàtei`s 2, mbc sbouhmf iursf mbc Hevbc ^rel`ref, bs uh` fdr` ifcbitev` irb`m`, ifhibdem` y mesbð`m` pfr bc bquepf mb ehvbsteo`iefhbs pbm`oùoei`s mb Bmetfre`c Y`htecc`h`, Y. @., bh c` Tbpûdcei` Mflehei`h`, d`kf c` merbiieùh bmetfre`c mb Ic`ume` Ccedrb. Yu irb`ieùh y mbs`rrfccf j` bst`mf ` i`rof mbc seouebhtb bquepf; ]bxtf; @ct`or`ie` Y`htfs ]bxtf; Ecustr` Ecus tr`ieùh; ieùh; Tummy Hûðbz, Kf så Hûðbz @l`mf @l`mfy^f ^fc`h c`hif, if, ] ]ucef ucef L L`tfs, `tfs, Oueccbrlf ^årbz, O`drebc Fsv`cmf Kfså Acfrbs. Aftfor`aì`; www.pjftfs.ifl y @rijevf Y`htecc`h`
Bquepf tåiheif;
• Ifrrbiieùh mb bstecf; @hmrås Dc`hif Mì`z y Cues Dberf Àcv`rbz • Mesbðf oràaeif; Kfseb @hteou` • Ybp`r`ieùh mb ifcfr; Kfså Lfr`cbs ^br`ct` y Iås`r L`tì`s ^boubrf Merbitfr mb @rtb y ^rfmuiieùh; Lfesås Gbccy Y`ht`h` Yudmerbitfr` mb Merbiieùh mb @rtb; Cece`h Y`cibmf Abrhàhmbz @hmrås Lfceh` Lfcffh Bmetfr`; @hmrås Bmetfr`;
Bstb Bstb cedrf j` se semf mf rb` rb`cecez` z`mf mf mb ifh ifhafr afrle lem`m m`m ifh bc iurrì iurrìiu iucul cul veobh obhtb tbd`ieùh yieùh j` se semf mf LEHBTM. sf sflb lbtetemf mf ` c`ve `prf `prfd` mbc
^relbr` bmeieùh 4>02 ©4>0= dy Y`htecc`h`, Y. @. Bmet`mf pfr Y`htecc`h`, Y. @. I`ccb Ku`h Yàhijbz T`lìrbz Hf. 5, O`siub. @p`rt`mf ^fst`c; 00-429 • Y`htf Mflehof, Tbpûdcei` Mflehei`h`. ]bcs. (:>5) 1:4-09:4 / 1:5-??=5. A`x; (:>5) 1:5-0>44 wbd setb; www.s`htecc`h`.ifl.mf www.s`htecc`h`.ifl.mf
Tboestrf Ehmustre`c;2:-9=? EYDH;………………… Elprbsf pfr ……………………… Elprbsf bh Tbpûdcei` Mflehei`h` ^rehtbm eh Mflehei`h Tbpudcei
Mbpf Mbpfse set` t`mf mf mb ifhafr ifhafrle lem`m m`m ifh c` cby. Pubm`h reou Pubm`h reourf rfs` s`lbh lbhtb tb prfje prfjede dem`s, m`s, seh `utf `utfre rez` z`ieùh ieùh bsire bsiret` t` mb cfs tetu tetuc` c`rbs rbs mbc –Ifpyreojt“, –Ifpyreojt“, d`kf d`kf c`s s`hief s`hiefhbs hbs bst` bst`dcb dcbie iem`s m`s bh c`s cb ybs, c` rbprf rbprfmui muiieùh ieùh tft`c tft`c f p`rie`c p`rie`c mb bst` bst` fdr` pfr iu`cquebr iu`cquebr lbmef lbmef f prfib prfibme melebh lebhtf, tf, iflprbh iflprbhme memfs mfs c` rbprf rbprfor` or`aì` aì` y bc tr`t` tr`t`lebh lebhtf tf ehafrlà ehafrlàteteif, if, y c` mestre mestredu duieùh ieùh bh bkblpc` bkblpc`rbs rbs mb bcc` lbme`h lbme`htb tb `cque `cquecbr cbr f pråst` pråst`lf lf pûdce pûdceifs. ifs.
Ìhmeib Rhem`m 0; Hûlbrfs l`yfrbs qub bc leccùh ....................... ....................................... .................. ^àoeh` = • Hûl Hûlbrf brfss l` l`yf yfrbs rbs qub bc le leccccùh ùh • Cb Cbitu itur` r` y bs bsire iretu tur` r` mb mb hûl hûlbr brfs fs • Tb Tbcc`i `ieefh fhbs bs mb fr frmb mbhh • Tbmfhmbf Rhem`m 4; Fpbr`iefhbs `retlåtei`s ............. ............................. ............................... ...................... ....... ^àoeh` : • @meieùh • ^r ^rfp fpeb ebm` m`mb mbss mb c`s c`s fpbr` fpbr`ie iefh fhbs bs • ^ftbhie`s • Yustr` r`iiieùh • T` T`ììz iu`mr`m` • Lûc ûcttepcei` i`iieùh • Fp Fpbr` br`ie iefh fhbs bs ifl flde deh` h`m` m`ss • Meveseùh Rhem`m 9; Lûctepcfs y mevesfrbs ............................ ............................................ ............................. .............^àoeh` 01 • Lû Lûctcteepc pcfs fs y mev meveesfr frbs bs • Lì Lìhe helf lf ifl flûh ûh lû lûctctep epcf cf.. Làxelf iflûh mevesfr • Hû Hûlb lbrf rfss pre prelf lfss y if iflp lpub ubst stfs fs • Mb Mbsi siflp flpfs fsei eieù eùhh bh a` a`itf itfrbs rbs pre prelf lfss Rhem`m =; Ar`iiefhbs .............. .............................. ................................ ................................ ......................... ......... ^àoeh` 4> • Ar Ar`i `iie iefh fhbs bs bq bque uev` v`cb cbht htbs bs.. • Yu Yustr str`i `iie ieùh ùh mb ar ar`i `iie iefh fhbs bs Iflûh mbhfleh`mfr • Luc Luctetepc pcei` ei`ie ieùh ùh mb ar` ar`ii iief efhbs hbs • Ar` Ar`ii iief efhbs hbs el elprf prfpe pe`s `s y hûlb hûlbrf rfss lextfs lextfs • Me Meve vese seùh ùh mb ar ar`i `iie iefh fhbs bs • If Iflp lp`r` `r`ie ieùh ùh mb ar` ar`iiie iefh fhbs bs • Fp Fpbr` br`ie iefh fhbs bs ifl flde deh` h`m` m`ss • @me meiieùh mb ar` ar`iiie iefh fhbs bs Rhem`m 2; Hûlbrfs mbiel`cbs ......................... ........................................ ............................... .................. ^àoeh` 4: • Bsi Bsiretu retur` r` y cb cbitur` itur` mb hûlb hûlbrfs rfs mbi mbiel el`c `cbs bs • Luc Luctetepc pcei ei`i `ieù eùhh mb hûl hûlbrf brfss mbie mbiel` l`cb cbss • If Ifie iebh bhtb tbss mbi mbiel el`c `cbs bs • If Iflp` lp`r`i r`ieù eùhh mb mb hûl hûlbrf brfss mbi mbiel el`c `cbs bs • Mev Meves eseù eùhh mb mb mbi mbiel el`c `cbs bs pf pfrr bhtb bhtbrf rfss • @m @mei eieù eùhh mb hûl hûlbrf brfss mb mbie iel` l`cb cbss • Tb Tbmf mfhm hmbf bf mb mb hûlb hûlbrf rfss mbie mbiel` l`cb cbss • Yus Yustr`i tr`iie ieùh ùh mb hûl hûlbrf brfss mbi mbiel el`c `cbs bs 4
L`tblàtei`s 2
© Y`htecc`h`, Y. @. @.
Rhem`m 1; T`zfhbs y prfpfriefhbs ......................... ......................................... ......................... ......... ^àoeh` 91 • T`z T`zfh fhbs bs y prf prfpf pfri rieefh fhbs bs • ^fr friibh bht` t`kb kbss mb mb i`h i`htetem` m`mb mbss • Iu` u`rt` rt` prf prfppfri rieefh fh``c Rhem`m ?; Ifhibptfs mb Obflbtrì`................ ............................... ............................... .................. .. ^àoeh` => • ^u ^uht htfs fs,, rbit`s rbit`s,, r`yf r`yfss y sbo sbolb lbht htfs fs • Àho Àhouc ucfs. fs. Lbm Lbmem em`s `s y ic ic`se `seffi` ffi`ie ieùh ùh • Bc pc pc`h `hf. f. Orà Oràffi ffi`s `s i` i`rtb rtbse se`h `h`s `s • Àho Àhouc ucfs fs if ifho horubh rubhtb tbs.s. Ifh Ifhstrui struiie ieùh ùh • Tbit Tbit`s `s p`r`c p`r`cbc bc`s, `s, pbrpb pbrpbhme hmeiuc`r iuc`rbs bs y fdceiu`s eiu`s • Fp Fpbr` br`ie iefh fhbs bs ifh àh àhou oucf cfss Rhem`m :; ]reàhoucfs :; ]reàhoucfs ................ ............................... .............................. ............................... .......................... .......... ^àoeh` =1 • ]reàhoucfs • If Ifho horub rubhi hie` e` mb tre treàh àhou oucf cfss • Ic Ic`se `seffi` ffi`ie ieùh ùh mb cf cfss tre treàh àhouc oucfs fs • Yb Yblb lbkk`h `hz` z` mb mb tre treàh àhou ouccfs • Àh Àhou ouccfs mb uh tr treeàh àhou oucf cf Rhem`m 5; Cfhoetumbs, àrb` y vfculbh. Lbmem`s ........................ ............................ .... ^àoeh` 24 • Rh Rhem em`m `mbs bs mb cfh fhoe oetu tumm • Àrb Àrb`s `s c`t c`tbr` br`cc y tft tft`c `c mb uh uh pres presl` l` • Tbifrremfs • Rh Rheem` m`mb mbss mb vfc fcul ulbh bh
• • • •
^br brììlb lbtr trff mb mb uh` uh` ffo ffour ur`` Rhem`mbs mb mb àrb àrb`` Àrbb` mb Àr mb pf pfcìofhf hfss Àrbb` mbc iìri Àr riuucf
• • • •
Qfc fcul ulbh bh mb mbcc pr preesl sl`` Rheem` Rh m`mmbs mb pbsf Rhem`mbs mb mb l` l`s` Rhem`m Rhe m`mbs bs mb teteblp blpf. f. ]blp blpbr`t br`tur` ur`
Rhem`m 0>; Bst`mìstei`s y prfd`decem`mbs ................ .................................. ........................ ...... ^àoeh` 1= • Arb Arbiu iubhi bhie` e`ss `ds `dsfc fcut`s ut`s y rbc rbc`t `tev` ev`ss • Bxpb Bxpbrel relbht bhtfs fs mbt mbtbrle brlehe hest`s st`s y `c `cb` b`tf tfref refss • Orà Oràffi ffi`s `s bs bst` t`mì mìst stei ei`s `s • Bsp Bsp`i `ief ef mb uh bxp bxpbre brelbh lbhtf tf `c `cb`t b`tfre freff • Or Orààffi` ibcuc`r • ^rf rfdd`de deccem` m`mmbs • ^r ^rfl flbm bmef ef,, lf lfm` m` y lb lbme me`h `h`` • ^r ^rfl flbm bmef ef,, lf lfm` m` y lb lbme me`h `h`` © Y`htecc`h`, Y. @.
L`tblàtei`s 2
9
Aeij` 0; Hûlbrfs
l`yfrbs qub bc leccùh
Rhem`m
0
Hûlbrfs l`yfrbs l`yfrbs qub bc leccùh
Iflpcbt` bc bc iu`mrf. 0. Iflpcbt` Hûlbrf
I
:2 410 5>5
Leccfhbs M
R
:
2
I
Lecc`rbs M
R
Rhem`mbs I M R
4
1
0
5
>
5
9= :4: :01 52 2=> :4: 4: :92 59> 01 ==2 ?94 =2 1?: 5>0 50 91? 2=9
4. Ehmei` Ehmei` quå quå v`cfr tebhb c` iear` = bh i`m` uhf mb bstfs hûlbrfs. :=2 2?1
41 ?:2 :1=
925 ?=9
?1 =4: :94
4 94= >11
0= 541 09:
9=2 199
=: 221 :19
9. Iflpcbt` Iflpcbt` c`s c`s sbrebs seouebhtbs. • Yul` Yul` 0 0 >>> >>>
2 >>> >>>
• Yul` 0> Yul` 0> >>> >>>
5 >>> >>>
• Yul` 4> Yul` 4> >>> >>>
=> >>> >>>
• Yul` 9> Yul` 9> >>> >>>
42 >>> >>>
=
L`tblàtei`s 2
© Y`htecc`h`, Y. @.
Rhem`m
Aeij` 4; Cbitur`
y bsiretur` mb hûlbrfs
0 0. Rhb Rhb ifh ifh uh` acbij` i`m` hfldrb ` su hûlbrf ifrrbspfhmebhtb.
44 >>> >>>
Iu`rbht` leccfhbs.
52 >>2 >>>
Fijbht` y iehif leccfhbs. ]rbeht` y sbes leccfhbs.
?: >>> >>>
Ybtbht` y fijf leccfhbs.
=> >>> >>>
Qbehtemùs leccfhbs.
91 >>> >>>
Hfvbht` y iehif leccfhbs iehif lec.
:2 >>> >>>
4. Bsiredb bc hûlbrf qub sb tb pemb bh i`m` i`sf. • Iehif leccfhbs, iehif lec sebtb. • Iu`rbht` leccfhbs, quehebhtfs lec hfvbht` y iehif. • Ybtbht` y uh leccfhbs, iu`trfiebhtfs sbtbht` y trbs lec sbesiebhtfs hubvb. • Puehib leccfhbs, fijfiebhtfs lec iehiubht`. • Fijf leccfhbs, mfs lec trbs.
9. Bsiredb iùlf sb cbb i`m` hûlbrf. • 29 1?: 0>> • 91 =42 4>> • :2 45: >>> • 1> 521 9>> • 1 :>> =20 © Y`htecc`h`, Y. @.
L`tblàtei`s 2
2
Rhem`m
Aeij` 9; Tbc`iefhbs
mb frmbh
0 0. Iflp`r` Iflp`r` cfs cfs p`rbs mb hûlbrfs y, cubof, bsiredb bsiredb bc bc seohf 8 f 3 sboûh ifhvbho`.
• 9= 42> 5=2 VVVVV 42 42> :21.
• :1 ?2> :=4 VVVVV 2> 4=5 >>>.
• =1 >=> 2>? VVVVV 42 =52 121.
• 91 52> 1?> VVVVV 91 52> ?1>.
• :: 921 :=? VVVVV :: =42 2>1.
• ?> >4> >>9 VVVVV ?> >>4 05>.
4. Aìk`tb Aìk`tb bh bh cfs hûlbrfs mbc i`rtbc y, mbspuås, t`ij` t`ij` cfs cfs qub sfh lbhfrbs mb 0 2>> >>>. 0 0:2 551 21 :?> >1:
0 =2> >>>
2 :2> 42>
0 1:1 :2>
4 =55 212
?21 :5=
• Bsiredb cfs Bsiredb cfs hûlbrfs qub t`ij`stb, mb l`yfr ` lbhfr.
• Bsiredb cfs Bsiredb cfs hûlbrfs qub hf t`ij`stb, mb lbhfr ` l`yfr.
9. Iflpcbt` Iflpcbt` bc bc seouebhtb iu`mrf. @htbrefr
Hûlbrf
^fstbrefr
09 2:? 12= ?5 221 :9> 1? 129 :50 42 =94 10= ?1 054 921 ::? ?2= 940
1
L`tblàtei`s 2
© Y`htecc`h`, Y. @.
Rhem`m
Aeij` =; Tbmfhmbf
0 0. Tbmfhmb` Tbmfhmb` iflf iflf sb tb ehmei`.
@ c` uhem`m mb leccùh làs ibri`h`
@ c` mbibh` mb leccùh làs ibri`h`
= 521 ?=:
5 42> >>>
0 :>5 :0:
2 :44 102
4 1=5 421
9 =2: 01?
2: :9> 1:>
29 9?: 50=
0: 129 504
?9 144 :02
4? 501 2:>
45 =9: 2:1
4. ]`ij` ]`ij` c` c` lbkfr `prfxel`ieùh. 41 :92 4>>
41 >>> >>>
0= 042 9=2
4? >>> >>>
02 >>> >>>
0 >29 04=
0 >>> >>>
9 5:2 >>>
4 >>> >>>
= >>> >>>
92 ?:2 4>>
92 :>> >>>
© Y`htecc`h`, Y. @.
0= >>> >>>
9 >>> >>>
4=2 91>
92 ?>> >>>
4=1 >>>
4=2 >>>
L`tblàtei`s 2
?
Aeij` 2; @meieùh
Rhem`m
4
Fpbr`iefhbs `retlåtei`s
0. Tbsubcvb bc seouebhtb prfdcbl` bh tu iu`mbrhf.
• Bh c` ifhstruiieù ifhstruiieùh h mb c` c` bsiubc` Y`ht` L`rt` sb o`st`rfh 94 :4= 1?2 pbsfs pbsfs y bh c` ifhstruiieùh mb c` bsiubc` Bc Auturf sb o`st`rfh 92 ?94 022 pbsfs mflehei`hfs. mflehei`h fs. ¶Iuàhtf sb o`stù o `stù bh tft`c bh c`s mfs ifhstruii ifhstruiiefhbs6 efhbs6
M`tfs;
Fpbr`ieùh;
Tbspubst`; Yb o`st`rfh pbsfs.
4. Babitû` c`s seouebhtbs fpbr`iefhbs bh tu iu`mbrhf.
:
9=: =4: + 1?2 ?94
9> =42 1>> + 592 :90
: =94 ?21 + 5 9?1 004
=94 ?>2 + 592 102
94 :92 5>1 + =1 ?12 >>5
592 1?> + 49= :02
?4: 10= + 0=1 :4?
0 942 1?> + 4 9=4 5>>
L`tblàtei`s 2
© Y`htecc`h`, Y. @.
Rhem`m
Aeij` 1; Yustr`iieùh
4 0. Tbsubcvb bc seouebhtb prfdcbl` bh tu iu`mbrhf.
• Bc prbsupubstf prbsupubstf mb l`tbre`cbs p`r` c` ifhstruiieùh ifhstruiieùh mb uh bmeaeief bs mb : ?42 1?> pbsfs y mb l`hf mb fdr` mb 1 :=5 ?52 pbsfs. ¶Bh iuàhtf supbr` bc ifstf mb l`tbre`cbs `c mb l`hf mb fdr`6
M`tfs;
Fpbr`ieùh;
Tbspubst`; Bc ifstf mb l`tbre`cbs supbr` `c ifstf mb l`hf mb fdr` bh
.
4. Babitû` c`s seouebhtbs sustr`iiefhbs bh tu iu`mbrhf.
© Y`htecc`h`, Y. @.
592 :?2 ’ 19= 41>
0 942 1?2 ’ 552 ?1>
4 9:5 4>> ’ 0 9?2 1?4
:95 10= ’ ?92 4>>
5 ?91 :>= ’ 1 1=2 ?>4
9> =42 ?:> ’ 42 494 ?>>
2 ?54 =2> ’ 9 592 =>>
:5: ?92 ’ 194 =>4
L`tblàtei`s 2
5
Rhem`m
Aeij` ?; Luctepcei`ieùh
4 0. Tbsubcvb.
• Cues` rb`cez` bc ehvbht`ref ehvbht`ref mb uh` uh` z`p`tbrì`. J` ifht`mf 2=2 i`k`s mb z`p`tfs p`r` jfldrbs ` ?1 pbsfs i`m` uh` y =:9 i`k`s mb z`p`tfs mb lukbrbs ` :1 pbsfs i`m` uh`. @. ¶Iuàc bs bc ifstf tft`c tft`c mb cfs z`p`tfs mb jfldrbs6 jfldrbs6 D. ¶Iuàc bs bc ifstf tft`c mb mb cfs z`p`tfs mb mb lukbrbs6 I. ¶Iuàc bs bc ifstf mb cfs z`p`tfs mb jfldrbs y lukbrbs6 M. ¶Iuàht`s i`k`s mb z`p`tfs z`p`tfs j`y bh tft`c6
M`tfs;
Fpbr`ieùh;
Tbspubst`s; @
D
I
M
4. Bh uh` ou`ou` ve`k`h, me`re`lbhtb, 0 92> p`s`kbrfs. Ye i`m` pbrsfh` p`o` 42 pbsfs
pfr su p`s`kb, ¶iuàhtf mehbrf fdtebhb bc ijfabr pfr bc p`of mb tfmfs sus p`s`kbrfs6
M`tfs; Fpbr`ieùh;
Tbspubst`; Fdtebhb
0>
L`tblàtei`s 2
pbsfs.
© Y`htecc`h`, Y. @.
Rhem`m
Aeij` :; Meveseùh
4 0. Tb`cez` c`s mevesefhbs seouebhtbs y, cubof, iflprubd` tus rbsuct`mfs.
9 1:2 02
?25 9:= 401
Iflprfd`ieùh;
Iflprfd`ieùh;
2 :?1 =9
=9 401 92
Iflprfd`ieùh;
Iflprfd`ieùh;
4. Iflpcbt` c` t`dc`.
Mevembhmf
==2
Mevesfr
Ifiebhtb
Tbsemuf
49
:
02
00
>
9
0
1
54= 21
© Y`htecc`h`, Y. @.
L`tblàtei`s 2
00
Rhem`m
Aeij` 5; ^rfpebm`mbs
mb c`s fpbr`iefhbs
4 0. Iflpcbt` cfs bsp`iefs bh dc`hif `pcei`hmf, bh i`m` i`sf, uh` prfpebm`m mb c` sul`
f mb c` luctepcei`ieùh. •
=2> + VVVVV < < 5> + VVVVV + VVVVV .
•
(5:> + VVVVV ) + :2 x 12 < 12 x 0:> • 9> + (=9 + 02) < (9> + =9) + 02
9. ¶Mfhmb bstà bc brrfr6 Bhieårr`cf y, cubof, bsirìdbcf bh afrl` ifrrbit`.
^rfpebm`m `sfie`tev` mb c` sul` f mb c` luctepcei luctepcei`ieùh `ieùh
04
Rhem`m
09 x (4 + 9) < (09 x 4) + (09 x 9)
02 + (0: + 04) < 02 + (0: + 04)
4> + (5 + 9) < (4> + 5) + 9
0: x (2 + 1) < (0: x 2) + 1
L`tblàtei`s 2
© Y`htecc`h`, Y. @.
Aeij` 0>; ^ftbhie`s
4 0. Rhb i`m` hûlbrf ` c` pftbhie`.
9=9
==
142 ?45
? 424
94
42
421
91
9
4. Bsiredb bc v`cfr mb cfs c`mfs mb i`m` uhf mb cfs iu`mr`mfs seouebhtbs. seouebhtbs.
91 il4
• C`mf; VVVVVVV C`mf; VVVVVVV
:0 il4
1= il4
=5 il4
• C`mf; VVVVVVV C`mf; VVVVVVV
• C`mf; VVVVVVV C`mf; VVVVVVV
• C`mf; VVVVVV C`mf; VVVVVV
9. @p`rb` i`m` iu`mrf mb c` ezquebrm` ifh c` sul` mb iu`mr`mfs mb c` mbrbij`.
Iu`mr`mf
Yul` mb iu`mr`mfs
24
14 + :4
9>4
0:4 + 4=4
024
94 + =4
0>4
54 + 044
=. ]`ij` cfs hûlbrfs qub tebhbh r`ìz iu`mr`m` bx`it`.
4
2 12
© Y`htecc`h`, Y. @.
0= ?4
42 :0
91 040
=5 0==
L`tblàtei`s 2
Rhem`m
Aeij` 00; T`ìz
iu`mr`m`
09
4 0. Bsiredb bh afrl` mb r`mei`c. 4
4
• 5 < :0
• ? < =5
4
4
• 2 < 42
• 00 < 040
4
4
• : < 1=
• 1 < 91
4. Bsiredb c` bxprbseùh pftbhie`c bquev`cbhtb.
•
91
< 1
• 0== < 04 • 421 < 01
4
<
4
<
• 0>> < 0>
4
<
4
<
• 142 < 42
4
<
4
<
• 910 < 05
9. Bsiredb c` r`ìz iu`mr`m` mb i`m` uhf mb cfs hûlbrfs seouebhtbs.
•
42
<
•
142 <
•
=5 <
•
:0
<
•
442 <
•
0>> <
•
0== <
•
040 <
•
1= <
=. Iflpcbt`.
0=
•
< 5 pfrqub
x
< :0
•
< ? pfrqub
x
< =5
•
< 0> pfrqub
x
< 0>>
•
< : pfrqub
x
< 1=
L`tblàtei`s 2
© Y`htecc`h`, Y. @.
Rhem`m
Aeij` 04; Fpbr`iefhbs
ifldeh`m`s
4 0. Hf fcvembs bc frmbh kbràrqueif mb c`s fpbr`iefhbs, y i`ciuc`.
• 0= ’ 2 + 1
• 42 ’ (: + ?)
• : x (02 ’ 0>)
• 9: + (1 x ?)
• (4 x :) + (9 x 1)
• (2 x 5) ’ (9 x 2)
• ?x4+1 <
• 44 ’ (? ’ 2)
• 42 + 9 x 2
• 4x=+:x4
4. Tbsubcvb cfs prfdcbl`s seouebhtbs. seouebhtbs.
• Hfbce` j` ter`mf uh tft`c mb 0= rfccfs mb 91 aftfs i`m` uhf. J` rbvbc`mf y` 004 aftfs. ¶Iuàht`s aftfs cb a`ct`h pfr rbvbc`r ` Hfbce`6
M`tfs;
Tbsfcuieùh;
Tbspubst`; Cb a`ct`h pfr rbvbc`r VVVVVVVVVV rbvbc`r VVVVVVVVVVVVVV VVVV aftfs. aftfs.
• L`rifs y trbs mb sus `leofs aubrfh `c iehb. I`m` I`m` bhtr`m` ifstù ?2 pbsfs. I`m` uhf o`stù 042 pbsfs. ¶Iuàhtf o`st`rfh bh tft`c L`rifs y sus `leofs6 M`tfs;
Tbsfcuieùh;
tft`c VVVVVVVVVVVVVV VV pbsfs. pbsfs. Tbspubst`; O`st`rfh bh tft`c VVVVVVVVVVVV © Y`htecc`h`, Y. @.
L`tblàtei`s 2
Aeij` 09; Lûctepcfs
y mevesfrbs
02
Rhem`m
9
Lûctepcfs y mevesfrbs
0. Cbb Cbb mbtbhem`lbhtb mbtbhem`lbhtb i`m` bhuhie`mf. Yeoub Yeoub c`s c`s ehstruiief ehstruiiefhbs. hbs.
C` a`lece` ^årbz @ca`rf bstà iflpubst` pfr = lebldrfs. Bc hfldrb mbc p`pà bs Ku`h, su bspfs` sb cc`l` @h` y sus jekfs sfh ^bmrf y L`rt`. C` bm`m mb Ku`h bs 91 `ðfs, @h` tebhb 92 `ðfs, ^bmrf tebhb 04 `ðfs y L`rt` tebhb 0> `ðfs. • @meveh` @meveh` ` ` queåh sb rbaebrb i`m` uh` mb c`s `aerl`iefhbs. Bsiredb bc Bsiredb bc hfldrb bh bc bsp`ief ifrrbspfhmebhtb. ’ Yu bm`m bs uh lûctepcf lûctepcf mb 5; 5; ’ Yu bm`m bs uh lûctepcf lûctepcf mb ?; ?; ’ Yu bm`m hf bs uh lûctepcf mb mb 4; ’ Yu bm`m bs uh lûctepcf lûctepcf mb 2 y mb 4; ’ Yus bm`mbs bm`mbs sfh lûctepcfs lûctepcfs mb 2;
y
’ Yus bm`mbs bm`mbs sfh lûctepcfs lûctepcfs mb 1;
y
4. @hft` @hft` bc bc hûlbrf `c iu`c ifrrbspfhmbh cfs mevesfrbs m`mfs.
Hûlbrf
Mevesfrbs
Hûlbrf
Mevesfrbs
0, 4, 9, =, 1, 5, 0:, 91
0, 2
01, :, =, 4, 0
5, 9, 0
0, 04, 4, 9, 1, =
0, 9, 2, 02
9, ?, 0, 40
=0, 0
9. @hft` @hft` mbhtrf mbhtrf mb i`m` bcba`htb, cfs mevesfrbs ehmei`mfs.
Mevesfrbs mb 4:
01
Mevesfrbs mb 0?
Mevesfrbs mb 9>
L`tblàtei`s 2
© Y`htecc`h`, Y. @.
Rhem`m
Aeij` 0=; Hûlbrfs
prelfs y iflpubstfs
9 0. Ifcfrb` mb `l`reccf cfs hûlblfs prelfs y mb vbrmb cfs iflpubstfs.
22
45
5? 9?
4:
=2 =0
=?
05
40
4?
12
49
=9
=5
90
4> 2?
29
25
00
04 ?
4. Bsiredb Bsiredb cf cf qub sb tb pemb.
• ]fmfs cfs hûlbrfs prelfs qub j`y bhtrb 0 y 49. • ]fmfs cfs hûlbrfs prelfs qub j`y bhtrb 42 y ?>. • ]fmfs cfs hûlbrfs prelfs qub j`y bhtrb 2> y 0>>. 9. Bsiredb cf qub sb tb pemb.
• ]fmfs cfs hûlbrfs iflpubstfs qub j`y bhtrb 4 y 9>.
• ]fmfs cfs hûlbrfs iflpubstfs bhtrb 94 y 1>.
• ]fmfs cfs hûlbrfs iflpubstfs bhtrb 14 y 5>.
L`tblàtei`s 2
© Y`htecc`h`, Y. @.
Rhem`m
Aeij` 02; Mbsiflpfseieùh
bh a`itfrbs prelfs
0?
9 0. Rs` Rs` àrdfcbs àrdfcbs mb a`itfrbs p`r` mbsiflpfhbr cfs seouebhtbs hûlbrfs
bh sus a`itfrbs prelfs. 01>
• 01> <
1>>
• 1>> <
=4
• =4<
5>
=2
• 1> <
• := <
• 04> <
1>
:=
04>
0:
• 4:> <
• 5> <
• =2 <
4:>
21
• 21 <
?>
• ?> <
L`tblàtei`s 2
:5
• :5 < © Y`htecc`h`, Y. @.
Rhem`m
9
Aeij` 01; Lìhelf
iflûh lûctepcf. Làxelf iflûh mevesfr
0. Fdtåh bc lìhelf iflûh lûctepcf mb i`m` p`rbk` mb hûlbrfs.
• 5 y 04
• 0: y 0>>
l.i.l. (5, l.i.l. (5, 04) <
l.i.l. (0:, l.i.l. (0:, 0>>) <
• 9> y 01
• 4: y 91
l.i.l. (9>, 01) <
l.i.l. (4:, l.i.l. (4:, 91) <
4. I`ciuc` I`ciuc` bc bc làxelf iflûh mevesfr mb cfs seouebhtbs p`rbs mb hûlbrfs.
• 9> y 1>
• 42 y 1>
l.i.l. (9>, l.i.l. (9>, 1>) <
l.i.l. (42, l.i.l. (42, 1>) <
9. Tbsubcvb bc prfdcbl` seouebhtb.
• C` sbðfr` G`rc` tebhb 0: p`cbt`s, 4= dfldfhbs dfldfhbs y 91 i`r`lbcfs. i`r`lbcfs. Cfs quebrb rbp`rter ` sus hebtfs, bh i`htem`mbs eou`cbs. ¶Iuàht`s auhm`s mb ofcfseh`s pubmb prbp`r`r c` sbðfr` G`rc` p`r` sus hebtfs6 M`tfs;
Fpbr`iefhbs;
Tbspubst`; ^ubmb Tbspubst`; ^ubmb prbp`r`r VVVVVVVV prbp`r`r VVVVVVVV auhm`s auhm`s mb ofcfseh`s. L`tblàtei`s 2
© Y`htecc`h`, Y. @.
Aeij` 0?; Ar`iiefhbs
Rhem`m
bquev`cbhtbs. Iflûh mbhfleh`mfr
05
=
Ar`iiefhbs
0. Bsiredb c`s
ar`iiefhbs bquev`cbhtbs.
= 0>
<
0 1
<
= :
<
4 9
<
1 01
<
2 0>
<
4. Ifhvebrtb c`s
seouebhtbs ar`iiefhbs bh ftr`s ifh uh mbhfleh`mfr iflûh.
0 9
7
4 2
7
= 1
: 2
7
2 =
7
4 9
2 7 04
: 9
7
0 4
9
7
=
7
0
=
7
9
7
5
9
0
7
:
4
2
4
0>
:
?
9. ]`ij` c`s
= :
04
1
ar`iiefhbs bquev`cbhtbs ` c` m`m`. 4> :>
01 4= 4>
?
7
= 01 0 4
4 =
0> 4>
4= =:
2 0> 4 =
L`tblàtei`s 2
0 4 4> 9>
4 2 4> => © Y`htecc`h`, Y. @.
Rhem`m
=
Aeij` 0:; Ar`iiefhbs
elprfpe`s y hûlbrfs lextfs
0. ]r`hsafrl` c`s
ar`iiefhbs elprfpe`s bh hûlbrfs lextfs.
2> 41
42 0>
4: 04
9> 1
9: 5
0: ?
4. ]r`hsafrl` cfs
hûlbrfs lextfs bh ar`iiefhbs elprfpe`s.
0 < • 00 5
• :
4 < 2
• 5
9 < :
4 < 2
• ?
1 < 0>
• =
9 < :
• 9
9. Tbc`iefh` i`m`
9 5
=
9= =
hûlbrf lextf ifh su ar`iieùh elprfpe` bquev`cbhtb. :
4 =
4: 9
1
4 9
=
95 5
=. Fdsbrv` y, cubof, iflpcbt` ` quå hûlbrf Mbspuås, c`s c` ifhvbrseùh ` uh` ar`iieùh elprfpe`. j`zaeour`s
9 0>
=9 0>
4> 9
lextf ifrrbspfhmbh.
Ar`iieùh lext`
Ar`iieùh elprfpe`
L`tblàtei`s 2
© Y`htecc`h`, Y. @.
Rhem`m
=
0 9
5
Aeij` 05; Iflp`r`ieùh
mb ar`iiefhbs
40
0. Cbb bc
tbxtf y, cubof, ifhtbst`.
Cfs bstume`htbs mb 2» iursf v`h ` iffpbr`r p`r` j`ibr uh s`drfsf dezifijf mb h`r`hk`. Àhobc ccbvù 2 9/= t`z`s mb j`reh` y G`te` 4 1/= t`z`s mb j`reh`. Jflbrf `pfrtù 2/1 cetrfs mb cbijb y ]`vetf 4 0/9 cetrfs. Y`l`htj` ccbvù 4 0/4 t`z`s mb kuof mb h`r`hk` y Cues 4=/0> t`z`s mb kuof mb h`r`hk`. • ¶Pueåh ccbvù làs j`reh`, Àhobc f G`te`6 Mbtbrlìh`cf. • ¶Pueåh ccbvù ccbvù làs kuof mb h`r`hk`, Y`l`htj` f Cues6 I`ciûc`cf. • ¶Jflbrf ccbvù làs cetrfs mb cbijb qub ]`vetf6 I`ciûc`cf. • ¶Iùlf frmbh`rì`s, mb lbhfr ` l`yfr, c`s ar`iiefhbs ar`iiefhbs mbc prfdcbl`6 Frmåh`c`s.
4. Rdei` c`s
seouebhtbs ar`iiefhbs bh c` rbit` hulårei`.
1
9
=
= 0
4
2 9
4 0 4 0
44
9 9 =
0 0 4
: =
9
5 9 4
=
00 9
2
04 9 9
L`tblàtei`s 2
=
© Y`htecc`h`, Y. @.
Rhem`m
=
Aeij` 4>; @meieùh
mb ar`iiefhbs
0. @hft` bc
rbsuct`mf mb i`m` sul`. ^eht` mbc leslf ifcfr cfs pbibs qub ifhtbho`h bc leslf rbsuct`mf.
= + :
= < :
2 + 1
4. Babitû`,
0 + 9
0 < 4
1 < 2
0 + 9
9 0= + < 2 02
: 09 + < 1 04
oràaei`lbhtb, c`s sul`s seouebhtbs. +
<
+
<
+
<
+
<
9. Babitû` c`s
seouebhtbs sul`s.
• 9 + 1 <
+
<
• 2 2 + 2 = < 1 0>
+
<
• = + 4 <
+
<
• 9 1 + 4 2 < : 1
+
<
• 4 + 9 <
+
<
• = = + = 0 < 5 9
+
<
2
5
0>
=
2
4
L`tblàtei`s 2
© Y`htecc`h`, Y. @.
Rhem`m
=
1 < 1
Aeij` 40; Yustr`iieùh
mb ar`iiefhbs
49
0. Babitû`
oràaei`lbhtb.
’
<
’
4. Babitû` c`s
<
’
<
seouebhtbs rbst`s.
• ? ’ 9 <
’
<
• ?
4 =
’ 2
1 0>
<
’
<
• = ’ 4 <
’
<
• 5
9 1
’ :
2 5
<
’
<
• 1 ’ 4 <
’
<
• 1
9 ?
’ 9
= ?
<
’
<
2
2
9
1
5
=
9. @p`rb` i`m`
4=
<
’
fpbr`ieùh mb rbst` ifh su rbsuct`mf.
5 V 9 = =
? V 1 = :
4 V 9 =
0? V : 1 9
4 0 V 0 4 9 9
4 9
0
2 =
9 4
0 1
L`tblàtei`s 2
© Y`htecc`h`, Y. @.
Rhem`m
=
Aeij` 44; Luctepcei`ieùh
mb ar`iiefhbs
0. I`ciuc` cfs
prfmuitfs seouebhtbs.
• 4 x = : 2
• = 4: x ? =:
• 2 24 x 0 4?
9 x : 1 2
• : 9= x 1 42
• 1 x 9 5 0>
•
• 4 09 x = 42
1 9 • :1 x 5
4. Iflpcbt` c`s
•
9 x :
0
0
• 1 9 x 4 =
luctepcei`iefhbs ifh c`s ar`iiefhbs seouebhtbs. < 1 =>
•
x = < : 2 02
•
9 x
=
L`tblàtei`s 2
© Y`htecc`h`, Y. @.
Rhem`m
=
< 02 4>
Aeij` 49; Meveseùh
mb ar`iiefhbs
42
0. Babitû`,
p`sf ` p`sf, c`s mevesefhbs seouebhtbs.
• = ÿ 1 <
ÿ
<
2 ? • 0> ÿ : <
ÿ
<
• 4 ÿ = <
ÿ
<
2
1
4. I`ciuc` c`s
:
0>
mevesefhbs seouebhtbs.
• 1 4: ÿ = ?2 <
? • 4 42 ÿ = 0> <
• 9 42 ÿ : = < ?
• 1 2: ÿ 9 = < 2
9. Tbsubcvb.
• Yb rbp`rtbh 9 04 cetrfs mb kuof bh v`sfs mb 9/04 cetrfs mb i`p`iem`m. ¶Iuàhtfs v`sfs sb ccbh`ràh6 M`tfs;
Fpbr`ieùh;
• Yb rbp`rtbh 1 cedr`s cedr`s mb s`cijeij`s bh bhv`sbs mb 9/: cedr`s. ¶Iuàhtfs bhv`sbs mb s`cijeij`s sb prbp`r`ràh6 M`tfs;
; Fpbr`ieùh
Tbspubst`; Yb prbp`r`ràh VVVVV Tbspubst`; Yb ccbh`ràh VVVVVV v`sfs.
41
bhv`sbs.
L`tblàtei`s 2
© Y`htecc`h`, Y. @.
Rhem`m
=
Aeij` 4=; Fpbr`iefhbs
ifldeh`m`s
0. Tbsubcvb c`s
fpbr`iefhbs seouebhtbs.
• 9
= :
+4
9 :
x
4 9
• :
4 9
’ 4
0 4
x
= :
0. Tbsubcvb cfs
• 0
• 2
4 2
4 =
+=
’ 4
9 1
9 1
ÿ
9 2
+9
4 1
seouebhtbs prfdcbl`s.
• Kfså tebhb iu`trf cetrfs y lbmef mb kuof. ^fr c` l`ð`h`, Kfså dbdeù uh cetrf, trbs fit`vfs mb kuof y pfr c` t`rmb, dbdeù mfs cetrfs, uh fit`vf. ¶Iuàhtfs cetrfs mb kuof
• @h` y sus jbrl`hfs tebhbh iehif bhtbrfs, uh lbmef mb uh` t`rt`. Iflebrfh, `c lbmefmì`, mfs bhtbrfs, trbs sbxtfs mb t`rt`, y pfr c` hfijb, uh bhtbrf, mfs sbxtfs mb t`rt`.
dbdeù bh tft`c6 ¶Puå i`htem`m mb kuofKfså cb qubm`6 Fpbr`ieùh;
¶Puå i`htem`m t`rt` bh tft`c6 ¶Puå mb p`rtb mbiflebrfh c` t`rt` cbs qubmù6 Fpbr`ieùh;
Tbspubst`; Iflebrfh VVVVVVV Tbspubst`; Dbdeù VVVVVVV cetrfs
y cb qubm`h VVVVVVV cetrfs.
mb t`rt`. Cbs qubmù VVVVVVV p`rtb mb c` t`rt`. L`tblàtei`s 2
© Y`htecc`h`, Y. @.
Aeij` 42; Bsiretur`
y cbitur` mb hûlbrfs mbiel`cbs
Rhem`m
2
Hûlbrfs mbiel`cbs
4?
c` t`dc` ifh c`s bxprbsefhbs qub a`ct`h. 0. Iflpcbt` Iflpcbt` c`
Hûlbrf mbiel`c
Ar`iieùh mbiel`c
Ar`iieùh mbiel`c
4.1 ]rbeht` y mfs ibhtåsel`s. = 2>0 0> >>> 4.094 Lec iu`trfiebht`s mfs mebzlecåsel`s. 04.9
4. Fdsbrv` bc iu`mrf seouebhtb y, cubof, iflpcåt`cf. Cbitur` mbc hûlbrf
Hûlbrf >.>>9
Mfs bhtbrfs, trbs ibhtåsel`s. 42.04=4 Iehif bhtbrfs, mfib mebzlecåsel`s. 91.>1 Iu`rbht` y mfs bhtbrfs, fijf måiel`s. >.>>>59 1.094 Puehib bhtbrfs, sebhtb lecåsel`s.
4:
L`tblàtei`s 2
© Y`htecc`h`, Y. @.
Rhem`m
2
Aeij` 41; Iflp`r`ieùh
mb hûlbrfs mbiel`cbs
0. Ifhtbst`. Bh c` i`rrbr` mb 0>> lbtrfs pc`hfs, L`hubc c` rb`cezù bh uh teblpf mb 00.20 lehutfs, L`rì` bh 0>.:2 sbouhmfs, Kfså bh 02.49 sbouhmfs y @h` bh 5.5: sbouhmfs. • ¶Pueåh o`hù c` iflpbtbhie`6 • ¶Pueåh ccboù bh ûctelf cuo`r6
4. ^eht` mbc leslf ifcfr cfs i`r`ifcbs qub ifhtebhbh bxprbsefhbs bquev`cbhtbs. Cubof, frmåh`c`s mb l`yfr ` lbhfr.
0.:
5 2 0: 0>>
0? =
>.0:
=42 0>>
=.42
9. Iflp`r` cfs seouebhtbs hûlbrfs mbiel`cbs. • 91.042
91.42
• =.41
2.1
• =4.?
=4.>?
• ?4.92
?4.4
• 0=2.9
0=2.>>
• ?=.041
?=.=
• =5.1
=5.>?
• 0492.54
0942.5>
L`tblàtei`s 2
© Y`htecc`h`, Y. @.
Rhem`m
2 0. Babitû` c`s sul`s.
Aeij` 4?; @meieùh
mb hûlbrfs mbiel`cbs
45
• :=2.?: + 1?9.22
• 2=9.?19 + =:.19>
• =>.?1 + 52.99
• ?15.21 + 9:=.?12
• 5.?1=9 + :.?21=
• 55.?2 + :2.4:
4. Babitû` c`s rbst`s.
• ?=2.1? ’ 9=4.?99
• : 21?.40 ’ 9 402.14
• >.1??? ’ >.>>0=
9. Tb`cez` c`s fpbr`iefhbs seouebhtbs. • :=1.?> + 12=.44 ’ :14.5=9
<
’
<
• 25=.>9 + 04=.?9 ’ 401.9=2
<
’
<
• >.5=2? + >.>92= ’ >.>>=29
<
’
<
9>
L`tblàtei`s 2
© Y`htecc`h`, Y. @.
Rhem`m
2 0. Babitû` c`s sustr`iiefhbs.
Aeij` 4:; Yustr`iieùh
mb hûlbrfs mbiel`cbs
• :=2.?: ’ 1?9.22
• 2=9.?19 ’ =:.19>
• =>.?1 ’ 52.99
• ?15.21 ’ 9:=.?12
• 5.?1=9 ’ :.?21=
• 55.?2 ’ :2.4:
• ?=2.1? ’ 9=4.?99
• :21?.40 ’ 9402.14
• >.1??? ’ >.>>0=
4. Tb`cez` c`s fpbr`iefhbs ifldeh`m`s. • (:=1.?> + 12=.44) ’ :14.5=9 <
’
<
• (25=.>9 x 04=.?9) ’ 401.9=2 <
’
<
• >.5=2? ’ (>.>92= + >.>>=29) <
’
< L`tblàtei`s 2
© Y`htecc`h`, Y. @.
Rhem`m
Aeij` 45; Luctepcei`ieùh
mb hûlbrfs mbiel`cbs
2 0. Bsiredb pfr quå a`itfr, 0>, 0>> f 0 >>>, sb luctepceiù bh i`m` i`sf.
90
• :.1
x
< : 1>>
• 9.450 x
< 94.50
• 2.94
x
< 29.4
• 04.9
x
< 0 49>
• 1.0=2 x
< 10=.2
• 2.0
x
< 2 0>>
• 9.2
< 92
• >.>0: x
x
< >.0:
4. Mbsiudrb. • Fdsbrv` c` ic`vb, seoub c`s acbij`s y, mbspuås, rb`cez` c`s fpbr`iefhbs qub sb tb ehmei`h. Bhifhtr`ràs bc hfldrb mb uh l`lìabrf mflehei`hf bh vì`s mb bxtehieùh. Ic`vb @ ; >
:2.>1
x:
x 4.2
R ; 4
x=
E ; 9 ] ; 2 K
x 04.2
x >.2
; =
Bc l`lìabrf bs
.
9. Cbb y, cubof, rbsubcvb bc prfdcbl` seouebhtb. • C` t`s` mb i`ldef mbc mùc`r bs mb TM$==.?2 pfr 0 mùc`r. Ye sb v`h ` i`lde`r pfr pbsfs 02>.2> mùc`rbs, ¶` iuàhtfs pbsfs bquev`cb bst` i`htem`m6
M`tfs;
Fpbr`ieùh;
Tbspubst`; Bquev`cbh ` TM$ 94
.
L`tblàtei`s 2
© Y`htecc`h`, Y. @.
Rhem`m
2 0. Fdtåh cfs ifiebhtbs mbiel`cbs bh i`m` i`sf.
Aeij` 9>; Ifiebhtbs
mbiel`cbs
09
9
00
4
=?
2
0=
9
41
9
4>
9
?=
=
49
?
=5
2
9>
=
50
5
1:
:
L`tblàtei`s 2
© Y`htecc`h`, Y. @.
Rhem`m
2 0. Tbsubcvb bc prfdcbl`.
Aeij` 90; Meveseùh
mb mbiel`cbs pfr bhtbrfs
99
• Rh i`dcb mb 9=.:> lbtrfs sb mevemb bh : p`rtbs eou`cbs. ¶Iuàhtf lemb i`m` p`rtb mbc i`dcb6
M`tfs;
Fpbr`ieùh;
lemb VVVVVVVVVVVVVV lbtrfs. lbtrfs. Tbspubst`; I`m` p`rtb lemb VVVVVVVVVVVVVV
4. Babitû` Babitû` c`s c`s seouebhtbs mevesefhbs mb hûlbrfs mbiel`cbs pfr bhtbrfs.
• 12.9?
:
• 52.42 2
9=
• :?.54 ?
• 42.?1 =
• 002.1>2 5
• 19?.: 9
L`tblàtei`s 2
© Y`htecc`h`, Y. @.
Rhem`m
Aeij` 94; Tbmfhmbf
mb hûlbrfs mbiel`cbs
2 0. @prfxel` cfs ifiebhtbs seouebhtbs j`st` bc cuo`r mbiel`c qub sb ehmei`.
J`st` c`s måiel`s
J`st` c`s ibhtåsel`s
J`st` c`s lecåsel`s
• ?2.= ÿ 9.1
• =92.99 ÿ 42
• 921.=? ÿ 12.0=
• ?1.>: ÿ 9.=2
• :4.02 ÿ >.02
• 41.?: ÿ >.2:1
4. Tbsubcvb cfs prfdcbl`s. • T`a`bc tebhb 2=.?2 cedr`s mb `rrfz y c`s quebrb rbp`rter ` sus trbs jbrl`h`s. ¶Iuàht`s cedr`s mb `rrfz mbdb m`rcb ` i`m` uh`6
M`tfs;
Fpbr`ieùh;
Tbspubst`; Mbdb m`rcb VVVVVVV cedr`s mb `rrfz, `prfxel`m`lbhtb.
• Leoubc bh uh` c` sul` mb TM$4 2>9.>> pfr = lfijec`s. ¶Iuàc bsp`où bc ifstf mb tebhm` i`m` lfijec`6
M`tfs;
Fpbr`ieùh;
Tbspubst`; I`m` lfijec` iubst` TM$VVVVVVVVVVVVV. L`tblàtei`s 2
© Y`htecc`h`, Y. @.
Aeij` 99; T`zfhbs
Rhem`m
1
T`zfhbs y prfpfriefhbs
y prfpfriefhbs
92
0. Iflpcbt` c` t`dc` ifh c`s bxprbsefhbs qub a`ct`h. T`zùh
Yb bsiredb t`ldeåh
Yb cbb
9/04 ?/0>
? ; 0>
=/?
Iu`trf bs ` sebtb
4/2 1/? 5/01
5; 01
9/1
]rbs bs ` sbes
2/0> 4/?
4;?
=/9
4. Bhiebrr` Bhiebrr` c`s c`s r`zfhbs bquev`cbhtbs ` c`s m`m`s. 4 9
0 4 1 5
0> 02 4 1
2 0>
= 1
1 02
0> 4> 02 42
2 02 42 9>
0 4
4> =>
9. Bhiebrr` Bhiebrr` c`s c`s r`zfhbs qub afrl`h uh` prfpfrieùh.
91
9 5
<
02 =2
4 1
<
0> 9>
2 02
<
2 9>
4= 51
<
?4 5
? =4
<
94 04:
9 5
<
02 =2
04 ?4
<
2 9>
= 0>
<
4= 1>
02 04
<
94 4>
L`tblàtei`s 2
© Y`htecc`h`, Y. @.
Rhem`m
Aeij` 9= ; Iu`rt`
1 0. Mbtbrleh` Mbtbrleh` bc bc v`cfr mbc lbmef f mbc bxtrblf mbsifhfiemf.
prfpfriefh`c
04 2 < x 0>
x
x <
x 1 < 2 02
<
x <
: x < 9 02
x <
x
<
x
<
x <
x
x <
4 2 < = x
<
x <
x <
x <
Iflpcbt` c`s c`s t`dc`s mb prfpfriefh`cem`m seouebhtbs. 4. Iflpcbt`
Heðfs
0
Jbc`mfs
9
Bquepfs
0
Kuo`mfrbs
00
9
1
04
9
44
==
9. Tbsubcvb cfs prfdcbl`s seouebhtbs. • Rh ifrrbmfr rbifrrb 0> l bh 0 lehutf. ¶Iuàhtfs lbtrfs rbifrrbrà bh 2> lehutfs6
• ^`r` j`ibr 9 cedr`s mb dezifijf sb us`rfh 5 jubvfs. ¶Iuàht`s cedr`s mb dezifijf sb j`ràh ifh 0: jubvfs6
Tbsfcuieùh;; Tbsfcuieùh
Tbsfcuieùh;; Tbsfcuieùh
Tbspubst`;; Tbifrrbrà VVVVVVV Tbspubst` Tbifrrbrà VVVVVVV lbtrfs. lbtrfs.
Tbspubst`;; Yb j`ràh VVVVVVVV Tbspubst` j`ràh VVVVVVVVV V cedr`s. cedr`s. L`tblàtei`s 2
© Y`htecc`h`, Y. @.
Rhem`m
Aeij` 92; ^fribht`kbs
1 0. I`ciuc` I`ciuc` cfs cfs pfribht`kbs seouebhtbs. seouebhtbs. • 42 % mb : >>>
• 44 % mb 0 ?2>
mb i`htem`mbs
9?
• =9 % mb 5>2
• 59 % mb 2>>
4. Bsiredb Bsiredb cfs cfs seouebhtbs pfribht`kbs pfribht`kbs bh afrl` mb ar`iieùh.
• =9 %
• 5? %
• :? %
• 04 %
• =2 %
• 01 %
• 42 %
• ?9 %
9. Tbsubcvb Tbsubcvb y, y, cubof, rbspfhmb rbspfhmb.. • ¶Mb quå hûlbrf bs 4>> bc 2> %6
• ¶Mb quå hûlbrf bs 9> bc 4> %6
• ¶Mb quå hûlbrf bs ?2 bc 02 %6
• ¶Mb quå hûlbrf bs 0>> bc 0> %6
9:
L`tblàtei`s 2
© Y`htecc`h`, Y. @.
Rhem`m
Aeij` 91; Aeij`
`meiefh`c
1 0. M`m`s c`s r`zfhbs, iflpcbt` iflpcbt` c`s c`s prfpfriefhbs.
9
<
40
4 < =
2
1
0 < 9>
0> < 4>
: < 01
<
4. Bsiredb Bsiredb bh bh cfs rbiu`mrfs c`s prfpfriefhbs, cubof, iflprubd` iflprubd` qub qub bc prfmuitf mb sus lbmefs bs eou`c `c prfmuitf mb sus bxtrblfs. • = bs ` 0>, iflf 4= bs ` 1>. x
<
x
x
<
x
x
<
x
• 9 bs ` 2, iflf 1 bs ` 0>.
• 4 bs bs ` 1, iflf 02 bs ` =2.
9. Iflpcbt` bc iu`mrf. ^rfpfrieùh
Bxtrblfs
Lbmefs
Yb cbb
9/2 < 1/0> 5/4> < 91/:> 4/1 < 9>/5> ?/= < 40/04 02/= < =2/04 0/2 < 5/=2 L`tblàtei`s 2
© Y`htecc`h`, Y. @.
Aeij` 91; ^uhtfs,
Rhem`m
?
rbit`s, r`yfs y sbolbhtfs
Ifhibptfs mb Obflbtrì`. Àhoucfs
0. Hfldr` cfs bcblbhtfs obflåtreifs.
95
D @
@
@
I
D
4. ]r`z` cf qub sb tb ehmei`.
• ]rbs cìhb`s cìhb`s rbit`s rbit`s qub qub p`sbh p`sbh pfr pfr bc puhtf @. • Rh r`yf qub p`rt` mbc puhtf D. • Rh sbolbhtf sbolbhtf qub p`sb pfr cfs puhtfs puhtfs D y I.
@
I D
=>
L`tblàtei`s 2
© Y`htecc`h`, Y. @.
Aeij` 9? ; Bc
Rhem`m
?
pc`hf. Oràaei`s i`rtbse`h`s
0. L`ri` cfs puhtfs (Z, U) y, cubof, ûhbcfs. Ifhtbst`; ¶Puå rbsuctù6 U
]`dc` mb m`tfs
=>
Z
U
0>
0>
00
02
04
4>
09
42
0=
9>
92 9> 42 4> 02 0> 2 0>
00
04
09
0=
Z
02
4. Tbprbsbht` c`s iffrmbh`m`s mb cfs puhtfs mb i`m` uh` mb c`s rbit`s seouebhtbs.
U ? 1 2 = 9 4 0
O I D
B
,
)
D; (
,
)
I; (
,
)
O; (
,
)
J; (
,
)
E; (
,
)
M; (
,
)
B; (
,
)
A; (
,
)
J E
@ M
@; (
A
0 4 9 = 2 1 ? :
Z
9. Fdsbrv` c`s oràaei`s y, cubof, ifhtbst` .
• ¶Puå mì` y ` quå jfr` sb rboestrù c` l`yfr l`yfr tblpbr`tur`6
9> 4: ` r 41 • ¶Iuàc aub c` lbhfr tblpbr`tur` rboestr`m` u t ` r 4= bc mflehof6 b p l44 b ]4> • ¶Puå tblpbr`tur` sb rboestrù bc sàd`mf 0: ` c`s :;>>6 >
Yàd`mf
Mflehof
?
:
5
0> 00 04
L`tblàtei`s 2
© Y`htecc`h`, Y. @.
Rhem`m
?
Jfr`
Aeij` 9:; Tbit`s
p`r`cbc`s, pbrpbhmeiuc`rbs y fdceiu`s
0. Ic`seaei` c`s seouebhtbs rbit`s bh p`r`cbc`s, pbrpbhmeiuc`rbs u fdceiu`s.
=0
pbrpbhmeiuc`rbs y fdceiu`s. 4. Embhteaei` bh c`s aeour`s c`s rbit`s p`r`cbc`s, pbrpbhmeiuc`rbs
=4
L`tblàtei`s 2
© Y`htecc`h`, Y. @.
Aeij` 95; Àhoucfs.
Rhem`m
?
Lbmem`s y ic`seaei`ieùh
0. Fdsbrv` bc medukf, cubof, lemb cfs àhoucfs y, mbspuås, iflpcbt`.
:
2
• Bc àhoucf 0 lemb • Bc àhoucf 4 lemb
=
• Bc àhoucf 9 lemb
4 ?
• Bc àhoucf = lemb • Bc àhoucf 2 lemb
9
• Bc àhoucf 1 lemb • Bc àhoucf ? lemb
1
0
• Bc àhoucf : lemb
4. Lemb i`m` uhf mb cfs àhoucfs y, cubof, bsiredb se bs `oumf, rbitf u fdtusf.
• Lbmem`;
• Lbmem`;
• Bs uh àhoucf;
• Bs uh àhoucf;
• Lbmem`;
• Lbmem`;
• Bs uh àhoucf;
• Bs uh àhoucf; L`tblàtei`s 2
© Y`htecc`h`, Y. @.
Aeij` =>; Àhoucfs
Rhem`m
?
ifhorubhtbs. Ifhstruiieùh
0. Lemb ifh bc tr`hspfrt`mfr cfs àhoucfs mb c`s aeour`s y, cubof, l`ri` ifh rfkf
cfs qub sfh ifhorubhtbs.
=9
4. Ifhstruyb àhoucfs ifhorubhtbs ` cfs àhoucfs rbprbsbht`m rbprbsbht`mfs. fs.
=2¾
==
0=>¾
:>¾
L`tblàtei`s 2
© Y`htecc`h`, Y. @.
Aeij` =0; Fpbr`iefhbs
Rhem`m
?
ifh àhoucfs
0. Iflpcbt`.
• Bc supcblbhtf mb uh àhoucf mb 1>» bs uh àhoucf mb VVVVVVVV.
• Bc àhoucf qub lemb eou`c qub su iflpcblbhtf bs VVVVVVVVVVVVV. VVVVVVVV VVVVV.
• Bc supcblbhtf mb uh àhoucf mb =2» bs uh àhoucf mb VVVVVVVV.
• Bc àhoucf qub lemb eou`c qub su supcblbhtf bs VVVVVVVV
• Bc supcblbhtf mb 0:>» bs VVVVVVVVVVVVVVV.
• Bc iflpcblbhtf mb uh àhoucf mb 2>» bs VVVVVVVVVVVVVVVVV VVVVVVVV VVVVVVVVV..
4. Ehmei` cfs àhoucfs à houcfs iflpcblbht`refs iflpcblbht`refs y supcblbht`refs mb c` aeour` seouebhtb.
4
0
9 1
?
:
= 2 09 04
01
Yfh iflpcblbht`refs cfs p`rbs mb àhoucfs;
Yfh supcblbht`refs cfs p`rbs mb àhoucfs;
L`tblàtei`s 2
© Y`htecc`h`, Y. @.
Aeij` =4; ]reàhoucfs
Rhem`m
:
]reàhoucfs ] reàhoucfs
0. Bsiredb c`s p`rtbs mbc treàhoucf y, cubof, rbspfhmb.
I
=2
@
D
4. ]r`z` cfs treàhoucfs qub pubm`s uhebhmf trbs puhtfs mestehtfs.
D M
@
I
=1
L`tblàtei`s 2
© Y`htecc`h`, Y. @.
Rhem`m
Aeij` =9 ; Ic`seaei`ieùh
:
mb cfs treàhoucfs
0. Fdsbrv` c` aeour` y, cubof, ic`seaei` cfs treàhoucfs mb `iubrmf ` sus c`mfs.
9 4
=
1
2 0
?
• Bc treàhoucf 0 bs • Bc treàhoucf 4 bs • Bc treàhoucf 9 bs • Bc treàhoucf = bs • Bc treàhoucf 2 bs • Bc treàhoucf 1 bs • Bc treàhoucf ? bs 4. ¶Iùlf bs i`m` treàhoucf6 L`ri` ifh uh` Z sus i`r`itbrìstei`s.
Bquecàtbrf Esùsibcbs Bsi`cbhf 4. Iflpcbt` .
• Bc treàhoucf treàhoucf qub tebhb sus sus trbs c`mfs eou`cbs eou`cbs sb cc`l`; • Bc treàhoucf treàhoucf ifh mfs c`mfs c`mfs eou`cbs eou`cbs bs uh treàhoucf; treàhoucf; • Bc treàhoucf treàhoucf qub hf tebhb tebhb sus c`mfs eou`cbs eou`cbs sb cc`l`; L`tblàtei`s 2
© Y`htecc`h`, Y. @.
Rhem`m
Aeij` ==; Àhoucfs
:
mb uh treàhoucf
0. ]r`z` cfs sbes àhoucfs bxtbrhfs mb treàhoucf @DI. Mbspuås, ifcfrå`cfs.
D
=?
@
I
4. Rs` bc tr`hspfrt`mfr y lemb lemb cfs àhoucfs ehtbrefrbs mb cfs treàhoucfs y iflprubd`
qub c` sul` mb sus lbmem`s bs 0:>¾.
P
H
F
L
^
T
• Tbspfhmb. ¶Iuàc bs c` lbmem` mbsifhfiem`, x6
x
:>¾
?>¾
x =>¾
=:
04>¾
L`tblàtei`s 2
© Y`htecc`h`, Y. @.
Rhem`m
:
Aeij` =2; Ifhorubhie`
mb treàhoucfs
0. Fdsbrv` c` bstrbcc` mb sbes puht`s y, cubof, ifhtbst`.
• ¶Iuàhtfs treàhoucfs vbs bh c` bstrbcc`6 bstrbcc`6 • ¶Iuàhtfs treàhoucfs sfh ifhorubhtbs6 • ¶^ubmbs embhteaei embhteaei`r `r p`r`cbcfor`lfs6 p`r`cbcfor`lfs6 ¶Iuàhtfs6
• ¶J`y rfldfs rfldfs bh c` aeour`6 ¶Iuàhtfs6 ¶Iuàhtfs6 • ¶Puå p`r`cbcfor`lfs sfh rfldfembs6 • ¶Qbs tr`pbiefs bh c`s aeour`s6 aeour`s6 Embhteaìi`cfs.
4. L`ri` ifh
c`s aeour`s ifhorubhtbs.
9. Fdsbrv` c`s aeour`s y, cubof, bsiredb c` lbmem` mbc c`mf l`ri`mf ifh c` x.
0 il
x
=.4 il
9 il
9 il
9 il
9 il
x
• Bc c`mf x lemb lemb VVVVVVVV VVVVVVVVVVVVV VVVVV il.
• Bc c`mf x lemb lemb VVVVVVVVVVVVVV VVVVVVVVVVVVVV il.
L`tblàtei`s 2
© Y`htecc`h`, Y. @.
Rhem`m
Aeij` =1;
Yblbk`hz` mb treàhoucfs
: 0. Embhteaei` cfs treàhoucfs qub sfh sblbk`htbs.
J
O
H
B
M
L
^
=5
E
D
A
G
I • Yfh sblbk`htbs
y
.
• Yfh sblbk`htbs
y
.
4. L`ri` ifh
2>
T Y
C
K @
P
c`s aeour`s sblbk`htbs.
L`tblàtei`s 2
© Y`htecc`h`, Y. @.
Rhem`m
Aeij` `meiefh`c;
Cfhoetumbs mbsifhfiem`s bh aeour`s ifhorubhtbs
:
0. Fdsbrv` c`s aeour`s y, mbspuås, bsiredb c` lbme` mbc c`mf l`ri`mf ifh c` x.
x
1 il 9 il
4 il 2 il
2 il 9 il
x
• Bc c`mf x lemb
il.
• Bc c`mf x lemb
4 il
il.
4 il
x
= il
= il
= il x
4 il
• Bc c`mf x lemb
il.
• Bc c`mf x lemb
il.
2 il : il
x
04 il
x
© Y`htecc`h`, Y. @.
L`tblàtei`s 2
Aeij` =:; Rhem`mbs
Rhem`m
5
mb cfhoetum
Cfhoetumbs, àrb` y vfculbh. Lbmem`s
0. Aìk`tb bh
cfs bkblpcfs y, cubof, rb`cez` c`s ifhvbrsefhbs.
Bkblpcf; 02 l ` il.
Bkblpcf; 1>> l ` gl.
20
02 l x 0>> < 0 2>> il.
1>> l ÿ 0 >>> < >.1 gl.
• =l
VVVV VVVV ÿ VV VVVV VVVV < VV VVVV VVVV ml ml.. < VVVVV x VVVVV < VVVVV il. • 92 il < VV
• 5l
< VVVVV
VVVVV < VVVVV ml. • 4:> il < VVVVV
VVVV < VVVVV l.
• =2 l < VVVVV
VVVVV < VVVVV ll. • 1>> l < VVVVV
VVVV < VVVVV gl.
• ?1 jl < VVVVV
VVVVV < VVVVV il. • 9:> m`l < VVVVV
VVVV < VVVVV gl.
• 42 gl < VVVVV
VVVVV < VVVVV il. • 5 ll
< VVVVV
VVVV < VVVVV ml.
• 2 jl < VVVVV
VVVVV < VVVVVV l. • 5 jl
< VVVVV
VVVV < VVVVV gl.
• :l
VVVV < VVVVVV il. • :>> l
< VVVVV
VVVV < VVVVV gl.
< VVVVV
4. Aìk`tb bh
bc bkblpcf y, cubof, rb`cez` c`s ifhvbrsefhbs mb uhem`mbs mb cfhoetum mbc Yestbl` Ehocås. Bkblpcf; 2 puco`m`s ` il.
2 x 4.2= il < 04.? il • 04 at < VVVVVVVVVVVVVV eh.
• 2 ym < VVVVVVVVVVVVVVat.
• 04 at < VVVVVVVVVVVVVV il.
• 2 ym < VVVVVVVVVVVVVV il.
• 4 le < VVVVVVVVVVVVVV ym.
• 0> eh < VVVVVVVVVVVVVV il.
• 4 le < VVVVVVVVVVVVVV gl.
• 2 le < VVVVVVVVVVVVVV gl.
24
© Y`htecc`h`, Y. @.
L`tblàtei`s 2
Rhem`m
Aeij` =5 ; Tbifrremfs
5 0. Cbb mbtbhem`lbhtb
cf qub meib @htfhe` y, cubof, `vbreou` ` quå tebhm` quebrb er. Ye vfy pfr bc i`lehf @, rbifrrf làs mb 0>> l, se vfy pfr bc i`lehf D, rbifrrf lbhfs mb 4>> l.
^`stbcbrì` >.2 jl ^`h`mbrì` => l 5 m`l Arutbrì` :> l
4. I`ciuc` y,
>.09 gl
cubof, rbspfhmb .
• ¶Iuàhtfs lbtrfs tebhb bc rbifrremf mbsmb bc puhtf @ j`st` c` p`stbcbrì`6
• ¶Iuàhtfs lbtrfs tebhb bc rbifrremf mbsmb bc puhtf @ j`st` c` p`h`mbrì`6
• ¶Iuàhtfs lbtrfs tebhb bc rbifrremf mbsmb bc puhtf D j`st` c` arutbrì`6
• ¶Iuàhtfs lbtrfs tebhb bc rbifrremf mbsmb bc puhtf D j`st` c` p`h`mbrì`6
© Y`htecc`h`, Y. @.
L`tblàtei`s 2
Rhem`m
Aeij` 2>; ^brìlbtrf
mb uh` aeour`
5 0. I`ciuc` bc
pbrìlbtrf.
• ¶Puå pbrìlbtrf tebhb uh tbrrbhf rbit`houc`r mb 02 l mb c`rof pfr 0> l mb `hijf6 Fpbr`ieùh;
• ¶Iuàc bs c` ieriuhabrbhie` mb c` ]ebrr`, se su r`mef bs mb ? >>> gecùlbtrfs6 Fpbr`ieùh;
29
Tbspubst`; C` ieriuhabrbhie`
bs VVVVVVVV l. l. Tbspubst`; Bc pbrìlbtrf bs VVVVVVVV 4. I`ciuc` bc
bs VVVVVVVV bs VVVVVVVV gl. gl.
pbrìlbtrf mb cfs pfcìofhfs rbouc`rbs seouebhtbs.
1 il
1 il
9 il
1 il • Cfhoetum mbc c`mf
il
• Cfhoetum mbc c`mf
il
• Aùrluc`
il
• Aùrluc`
il
• ^brìlbtrf
il
• ^brìlbtrf
il
9. I`ciuc` bc
c`mf mbsifhfiemf, ifhfiemf bc pbrìlbtrf mb i`m` aeour`. =l x ^brìlbtrf < 9> l 0> l
1l 1l 2=
0> l
:l
x < VVVVVVVVV l
^brìlbtrf < 9= l
x
x < VVVVVVVVV l © Y`htecc`h`, Y. @.
L`tblàtei`s 2
Rhem`m
Aeij` 20; Rhem`mbs
mb àrb`
5 0. Tbc`iefh` ifh
uh` acbij` c` uhem`m mb àrb` ifh qub lbmerì`s c`s supbraeiebs m`m`s.
• C` supbraeieb mb c` ieum`m mb Y`htf Mflehof.
• C` supbraeieb mbc s`cùh
gl4
• C` supbraeieb mb c` pfrt`m` mb tu cedrf mb L`tblàtei`s.
• C` supbraeieb mb uh` aftf
l4
mb ic`sbs.
• C` supbraeieb mb uh` t`rkbt` mb iråmetf.
4. Fdsbrv` bc
bhl`ri`m`.
• C` supbraeieb mbc àrb` mb uh bmeaeief.
il4
bkblpcf y, cubof, iflpcbt`.
Bkblpcf; : ml4 ` il4.
Bkblpcf; 2 >>> ll4 ` il4.
: x 0>> < :>> il4.
< VVVVVVVVV
VVVVVVVVVVV < VVVVVVVVVVV il4.
• 2 >>> il4 < VVVVVVVVV
VVVVVVVVVVV < VVVVVVVVVVV l4.
• >.>1 jl4
< VVVVVVVVV
VVVVVVVVVVV < VVVVVVVVVVV l4.
• 42 ml4
< VVVVVVVVV
VVVVVVVVVVV < VVVVVVVVVVV l4.
• 92> jl4
< VVVVVVVVV
VVVVVVVVVVV < VVVVVVVVVVV il4.
• 9 ml4
2 >>> ÿ 0>> < 2> il4.
22 © Y`htecc`h`, Y. @.
L`tblàtei`s 2
Rhem`m
Aeij` 24; Àrb`
5 0. Lemb ifh
uh` rboc` cfs c`mfs mb i`m` pfcìofhf y, cubof, i`ciuc` su àrb`.
mb pfcìofhfs
• D`sb
• Fpbr`ieùh;
• Bc àrb` bs mb 4. I`ciuc` bc
• D`sb
• @ctur`
• @ctur`
• Fpbr`ieùh;
• Bc àrb` bs mb
il4.
il4.
àrb` mb c` ijeijeou`.
9> il == il
1> il • Tbspubst`; Bc àrb` mb c` ijeijeou` bs mb VVVVVVV il 4.
9. I`ciuc` bc
àrb` mb cfs seouebhtbs pfcìofhfs rbouc`rbs.
1.:: il
^brìlbtrf < VVVVVV il. x 4
0> il 21
<
0:.0 il
^brìlbtrf < VVVVVV il. x 4
il4.
Bc àrb` bs mb VVVVV il 4.
i l i 0 2
il4.
<
Bc àrb` bs mb VVVVV il 4. © Y`htecc`h`, Y. @.
L`tblàtei`s 2
Rhem`m
Aeij` 29; Àrb`
5 0. Tbsubcvb bc
seouebhtb prfdcbl`. • Bh bc ibhtrf mb uh p`rqub j`y uh` aubhtb ifh afrl` ieriuc`r ieriuc`r qub tebhb uh meàlbtrf mb 92> il. ¶Iuàc bs bc àrb` qub fiup` c` aubhtb bh bc p`rqub6 M`tfs;
Fpbr`ieùh;
mbc iìriucf
Tbspubst`; C` aubhtb fiup` uh àrb`
mb VVVVVVVVVVVVVVV il4.
4. Lemb bc
meàlbtrf f r`mefs y, mbspuås, i`ciuc` bc àrb` mb cfs iìriucfs.
Àrb` + VVVVVVVVVV il4.
Àrb` < VVVVVVVVVV il4.
2?
© Y`htecc`h`, Y. @.
L`tblàtei`s 2
Rhem`m
Aeij` 2=; Àrb`s
c`tbr`c y tft`c mb uh presl`
5 0. Tbsubcvb.
• Rh` i`k` mb d`sb iu`mr`m` mbdb sbr afrr`m` ifh p`pbc p`r` prbp`r`r uh rbo`cf. ¶Puå i`htem`m mb p`pbc sb hbibset`rà p`r` iudrer c` i`k`6 M`tfs;
Fpbr`ieùh;
0>> il
l i > 1
1> il
Tbspubst`; Yb hbibset`ràh VVVVVVVVVV il4
mb p`pbc. 4. I`ciuc` bc
àrb` tft`c mb cfs seouebhtbs presl`s. • C`s `rest`s `rest`s mb c`s d`sbs mb uh presl` rbit`houc`r lembh : il y 1 il y c` `ctur` 5 il. Àrb` c`tbr`c VVVVVVVVVV il4.
Àrb` tft`c VVVVVVVVVV il4.
• C`s `rest`s mb c`s d`sbs mb uh presl` mb d`sb iu`mr`m` lembh 1 ml y c` `ctur` 9 ml. Àrb` c`tbr`c VVVVVVVVVV ml4.
Àrb` tft`c VVVVVVVVVV ml4.
2:
© Y`htecc`h`, Y. @.
L`tblàtei`s 2
Rhem`m
Aeij` 22; Rhem`mbs
mb vfculbh
5 0.
¶Bh quå uhem`mbs bxprbs`rì`s bc vfculbh mb cfs seouebhtbs fdkbtfs6 Bhiebrr` c` uhem`m bcboem`.
Bc vfculbh mb uh` pesieh`
gl9
l9
il9
Bc vfculbh mb uh` iudbt` mb `ou`
m`l9
l9
il9
Bc vfculbh mbc oftbrf mb uh lbmei`lbhtf
ll9
il9
ml9
4. Tb`cez` bh
tu iu`mbrhf c`s seouebhtbs ifhvbrsefhbs mb uhem`mbs mb vfculbh.
=>> il9
<
l9
0> m`l9
>.?2 l9
<
ml9
>.>>1 gl9 <
jl9
l9
: >>> l9
ml9
91 >>> il9 <
l9
<
<
L`tblàtei`s 2
© Y`htecc`h`, Y. @.
Rhem`m
Aeij` 21; Qfculbh
5 0. I`ciuc` bc
vfculbh mb cfs seouebhtbs iubrpfs.
1.9 il 4=.2 il
1.9 il
mbc presl`
25
1.9 il
0=> il4
Tbspubst`; Bc vfculbh bs 4. Tbsubcvb cfs
il9.
Tbspubst`; Bc vfculbh bs
il9.
seouebhtbs prfdcbl`s.
• Rh` ifculh` mbifr`tev` a`drei`m` bh ybsf mb d`sb iu`mr`m` mb :2 il mb c`mf y uh` `ctur` mb 0=2 il. ¶Iuàc bs bc vfculbh mb c` ifculh`6 Tbspubst`; Bc vfculbh mb c` ifculh`
M`tfs;
bs VVVVVVVVVV il9. Fpbr`ieùh;
• Rh` pbibr` tebhb uh c`rof mb 1> il, bc `hijf mb =2 il y c` `ctur` mb ?2 il. ¶Iuàc bs bc vfculbh mb c` pbibr`6 Tbspubst`; Bc vfculbh mb c` pbibr`
M`tfs;
bs VVVVVVVVVV il. Fpbr`ieùh;
1>
L`tblàtei`s 2
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Rhem`m
Aeij` 2?; Rhem`mbs
5 0. ]r`hsafrl` bh
tu iu`mbrhf c`s lbmem`s mb pbsf seouebhtbs.
2 cd
fz
01> fz
cd
2 >>> cd
t
>.242 cd
fz
0> qq
cd
4t
cd
04 cd
fz
: fz
cd
mb pbsf
01 fz
4. Tbsubcvb
cd
2 cd
fz
cfs seouebhtbs prfdcbl`s.
• Rh i`leùh i`ro` 2 tfhbc`m`s mb `rbh`. ¶Iuàht`s cedr`s mb `rbh` i`ro` bc i`leùh6 Tbspubst`; Bc i`leùh i`ro`
M`tfs;
VVVVVVVVVV cd mb `rbh`. Fpbr`ieùh;
• Rh p`qubtb mb i`rhb pbs` 51 fhz`s. ¶Iuàht`s cedr`s mb i`rhb tebhb bc p`qubtb6 M`tfs;
Tbspubst`; Bc p`qubtb tebhb
VVVVVVVVVV cedr`s mb i`rhb. Fpbr`ieùh;
L`tblàtei`s 2
© Y`htecc`h`, Y. @.
10
Rhem`m
Aeij` 2:; Rhem`mbs
mb l`s`
5 0. Iflpcbt` c`s
bxprbsefhbs mb cfs rbiu`mrfs.
• 2 gecfor`lfs <
or`lfs.
• 9 2>> or`lfs <
gecfor`lfs.
• 0> gecfor`lfs <
or`lfs.
• = >>> or`lfs <
gecfor`lfs. gecfor`lfs.
• 4= gecfor`lfs <
or`lfs.
• 4:> or`lfs
<
• 92 gecfor`lfs <
or`lfs.
• >.>>02 gecfor`lfs <
leceor`lfs.
• 1> or`lfs
<
leceor`lfs.
• :2> leceor`lfs
<
or`lfs.
• >.>1 or`lfs
<
leceor`lfs.
• 2 gecfor`lfs
<
or`lfs.
or`lfs.
• 9 >>> or`lfs
<
gecfor`lfs.
• 042 leceor`lfs < 4. Tbsubcvb bc
seouebhtb prfdcbl`.
• @hmrås rbiedb uh p`qubtb qub pbs` =2 gecfor`lfs y quebrb s`dbr su pbsf bh or`lfs. ¶Puå fpbr`ieùh mbdb rb`cez`r6 M`tfs;
Fpbr`ieùh; Tbspubst`; Bc pbsf mbc p`qubtb
bs VVVVVVVVVV or`lfs.
14
L`tblàtei`s 2
© Y`htecc`h`, Y. @.
Rhem`m
Aeij` 1>; Rhem`mbs
mb teblpf. ]blpbr`tur`
5 0. Iflpcbt` c`s
bquev`cbhie`s seouebhtbs.
• 02 mì`s
<
jfr`s.
• 1 trelbstrbs <
lbsbs.
• 92 mì`s
<
jfr`s.
• 2 sblbstrbs <
`ðfs.
• 4 måi`m`s <
`ðfs.
• 4 seocfs
lecbhefs.
• 02 lbsbs <
mì`s.
4. Fdsbrv` bc
<
seouebhtb l`p` qub ehmei` tblpbr`tur`s mb mesteht`s zfh`s mbc p`ìs y, cubof, rbspfhmb.
H Lfhtb Ireste
Làx. 90 »I Lìh. 44 »I
F
B
Y`hte`of Y`l`hà
Làx. 90 »I Lìh. 40 »I
Làx. 4: »I Lìh. 40 »I
Y`h Irestùd`c
Làx. 90 »I Lìh. 0: »I
Y
C` Tfl`h`
Làx. 45 »I Lìh. 40 »I
Y`htf Mflehof
Làx. 9> »I Lìh. 05 »I
D`r`jfh`
Làx. 45 »I Lìh. 40 »I
• • • • • •
¶Bh iuàcbs ieum`mbs sfh làs arì`s c`s hfijbs6 ¶Bh quå ieum`m bs l`yfr c` meabrbhie` bhtrb c` tblpbr`tur` làxel` y c` lìhel`6 ¶Bh quå ieum`m sb rboestrù c` lbhfr meabrbhie` meabrbhie` bhtrb c` tblpbr`tur` làxel` y c` lìhel`6 ¶Iuàcbs sfh c`s c`s tblpbr`tur`s làxel` y lìhel` lìhel` mb Y`l`hà6 ¶Iuàc bs c` meabrbhie` mb tblpbr`tur`s bh c` prfvehie` mb D`r`jfh`6 ¶Iuàcbs prfvehie`s tebhbh c`s lesl`s tblpbr`tur`s6 L`tblàtei`s 2
© Y`htecc`h`, Y. @.
Aeij` 10; Arbiubhie`s
`dsfcut`s y rbc`tev`s
Rhem`m
0>
Bst`mìstei` y prfd`decem`mbs
0. Ifh cfs m`tfs mb cfs lbmefs mb tr`hspfrtb làs us`mfs, ifhstruyb uh` t`dc`
mb arbiubhie`s y, cubof, rbspfhmb .
Ifhstruyb `quì; ?:
92
19
=4
02
• ¶Iuàc bs bc lbmef lbmef mb tr`hspfrtb làs us`mf6
• ¶Iuàc bs bc lbmef lbmef mb tr`hspfrtb lbhfs us`mf6 us`mf6 • ¶Iuàht`s pbrsfh`s pbrsfh`s aubrfh bhiubst`m`s bh tft`c6
4. Bsiredb c` arbiubhie` `dsfcut` mb i`m` m`tf.
• Bsiredb `quì c` arbiubhie` rbc`tev` mb cfs m`tfs y, cubof, iflprubd` qub c` sul` mb c`s lesl`s bs eou`c ` c` uhem`m.
1=
L`tblàtei`s 2
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Rhem`m
Aeij` 14 ; Oràaei`s
0> 0. Yb iubstefh`rfh v`re`s pbrsfh`s `ibri` mb sus arut`s prbabrem`s.
Iflpcbt` c` t`dc` mb m`tfs seouebhtb y, cubof, rbspfhmb rbspfhmb. Arut`
Ifhtbf
Arbiubhie`
L`hof
0=
H`r`hk`
0?
Ouehbf ^eð`
0:
]ft`c
bst`mìstei`s
• ]ft`c mb pbrsfh`s bhiubst`m`s; • I`htem`m mb pbrsfh`s qub qub prbaebrbh prbaebrbh c` peð`; @jfr`, ifhstruyb bc oràaeif mb d`rr`s ifh cfs m`tfs mb c` t`dc` mb arbiubhie`.
^fr ûctelf, ifhstruyb c` oràaei` pfceofh`c.
L`tblàtei`s 2
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Rhem`m
Aeij` 19; Oràaei`
ieriuc`r
0> 0. Ifhstruyb c` oràaei` ieriuc`r ifrrbspfhmebhtb ifrrbspfhmebhtb ` i`m` setu`ieùh.
• :> bstume`htbs bhiubst`mfs `ibri` mb su prbabrbhie` pfr bc d`cfhibstf, bc dåesdfc y bc aûtdfc ifhtbst`rfh cf seouebhtb. Mbpfrtb
Hûlbrf mb bstume`htbs qub cf prbaebrbh
D`cfhibstf Dåesdfc
42 =>
Aûtdfc
02
Oràaei` ieriuc`r
12
’ ^fribht`kb mb bstume`htbs bstume`htbs qub prbaebrbh bc dåesdfc. ’ ^fribht`kb mb bstume`htbs bstume`htbs qub prbaebrbh bc d`cfhibstf. ’ ^fribht`kb mb bstume`htbs bstume`htbs qub prbaebrbh bc aûtdfc.
• Mb uh orupf mb heðfs y heð`s bhiubst`mfs, sfdrb iuàcbs `itevem`mbs prbaebrbh bh c`s v`i`iefhbs, rbsuctù qub uh 91% mbsb` er ` c` pc`y`, uh 4>% mbsb` er `c i`lpf, uh 41% prbaebrb kuo`r bh bc p`rqub y uh 0:% veset`r lusbfs. @itevem`mbs bh c`s v`i`iefhbs
11
^fribht`kb mbc tft`c mb heðfs y heð`s bhiubst`mfs
Er ` c` pc`y`
91%
Er `c i`lpf
4>%
Kuo`r bh bc p`rqub
41%
Qeset`r lusbfs
0:%
L`tblàtei`s 2
Oràaei` ieriuc`r
© Y`htecc`h`, Y. @.
Rhem`m
Aeij` 1=; ^rflbmef,
lfm` y lbme`h`
0> 0. I`ciuc` bc prflbmef mb cfs m`tfs seouebhtbs.
• C`s i`ceaei`ief i`ceaei`iefhbs hbs mb 0> bstume`htbs bh uh bx`lbh mb L`tblàtei`s; :2 7 5> 7 0>> 7 ?1 7 10 7 25 7 :: 7 54 7 ?> 7 :>
^rflbmef <
<
• Cfs i`rrfs i`rrfs p`rqub`mfs p`rqub`mfs bh ? mì`s mb c` sbl`h` bh bh
uh` pc`z` iflbrie`c; 42> 7 4:> 7 45> 7 9=> 7 =0: 7 9:> 7 902
<
^rflbmef <
• C` prel` prel` mbc mbc mùc`r mùc`r j` v`re`mf bh bh sbes sbes sbl`h`s sbl`h`s bh c` l`hbr` qub sb lubstr` ` ifhtehu`ieùh; 95 7 9:7 => 7 9: 7 9? 7 95
^rflbmef <
<
4. Mbtbrleh` c` lfm` y c` lbme`h` mb cfs m`tfs seouebhtbs.
• C` i`htem`m i`htem`m mb deiecbt`s deiecbt`s vbhmem`s pfr uh` uh` kuoubtbrì` kuoubtbrì` bh uh` sbl`h` aub; 9> 7 =2 7 40 7 0: 7 9> 7 44 7 9>
Lfm` <
Lbme`h` < L`tblàtei`s 2
© Y`htecc`h`, Y. @.
Rhem`m
Aeij` 12; Bxpbrelbhtfs
mbtbrlehest`s y `cb`tfrefs
0> 0. Ic`seaei` cfs bxpbrelb bxpbrelbhtfs htfs bh mbtbrlehest`s f `cb`tfrefs, cubof, rbc`iefh`.
• C`hz`r uh m`mf y fdtbhbr bc 1.
• Iflprfd`r qub bc `ou` jebrvb jebrvb `c i`cbht`rsb. i`cbht`rsb.
• Fdtbhbr bc prblef l`yfr bh c` cftbrì`.
1?
• Rh cìquemf cìquemf sb mbrr`l` `c ver`r uh` ifp`.
• Fdtbhbr i`r` `c c`hz`r uh` lfhbm`.
• Iflprfd`r qub uh` uh` pebmr` pebmr` c`hz`m` j`ie` `rred` `rred` i`b làs t`rmb. t`rmb.
• Rh trfzf mb p`pbc sb qubl` bh bc aubof.
• Y`i`r uh` uh` dfc` dfc` vbrmb mfhmb sfcf j`y j`y dfc`s dfc`s vbrmbs. vbrmbs.
• Bxtr`br uh i`rt` `l`recc` mfhmb mfhmb j`y `l`recc`s, `l`recc`s, `zucbs y dc`hi`s. dc`hi`s.
1:
L`tblàtei`s 2
© Y`htecc`h`, Y. @.
Rhem`m
Aeij` 11; Bsp`ief
lubstr`c mb uh bxpbrelbhtf `cb`tfref
0> 0. Bsiredb bc bsp`ief lubstr`c mb cfs seouebhtbs bxpbrelbhtfs `cb`tfrefs.
BY^@IEF LRBY]T@C Y`i`r uh` dfc` mb uh` tùldfc` qub ifhtebhb uh` dfc` `l`recc`, uh` hbor` y uh` dc`hi`.
C`hz`r uh m`mf ifh c`s cbtr`s
@, D, I, M, B y A.
Cfs rbsuct`mfs elp`rbs `c c`hz`r uh m`mf mb 1 i`r`s.
C`hz`r 9 lfhbm`s `c `erb.
C`hz`r mfs m`mfs y `hft`r c` sul` mb `ldfs.
L`tblàtei`s 2
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Rhem`m
Aeij` 1?; ^rfd`decem`mbs
0> 0. Mbtbrleh` c` prfd`decem`m mb fiurrbhie` fiurrbhie` mb i`m` i`sf.
• Bh uh ifrr`c j`y 2 ifhbkfs dc`hifs, 9 l`rrfhbs y ? hborfs. ’ ¶Iuàc bs c` prfd`decem`m prfd`decem`m mb mb bxtr`br uh uh ifhbkf dc`hif6 ’ ¶Iuàc bs c` prfd`decem`m prfd`decem`m mb mb bxtr`br uh uh ifhbkf l`rrùh6 ’ ¶Iuàc bs c` prfd`decem`m prfd`decem`m mb mb bxtr`br uh uh ifhbkf hborf6 4. Bxprbs` cfs rbsuct`mfs a`vfr`dcbs y pfsedcbs bh cfs seouebhtbs bxpbrelbhtfs bxpbrelbhtfs `cb`tfrefs.
15
• Tbsuct`mf iruz `c ter`r uh` lfhbm`. A`vfr`dcbs
^fsedcbs
• Tbsuct`mfs lbhfrbs qub = bh bc bxpbrelbhtf mb ter`r uh m`mf. A`vfr`dcbs
^fsedcbs
9. Ehvbht` uh bxpbrelbhtf y, cubof, bsiredb cfs rbsuct`mfs a`vfr`dcbs y pfsedcbs.
?>
L`tblàtei`s 2
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Rhem`m
Aeij` `meiefh`c; ^rflbmef,
lfm` y lbme`h`
0> 0. Aìk`tb bh c`s t`dc`s mb arbiubhie`s y, cubof, i`ciuc` bc prflbmef, c` lfm`
y c` lbme`h` mb cfs m`tfs `orup`mfs.
@itevem`mbs bh c`s v`i`iefhbs
Hûlbrf mb heðfs y heð`s
Er ` c` pc`y`
0:
Er `c i`lpf
0>
Kuo`r bh bc p`rqub
09
Qeset`r lusbfs
5
^rflbmef
Lfm` Lbme`h`
Mbpfrtb
Hûlbrf mb bstume`htbs qub cf prbaebrbh
D`cfhibstf
42
Dåesdfc
=>
^rflbmef
Lfm` 02
Aûtdfc
Lbme`h`
Arut`
Arbiubhie`
^rflbmef
L`hof
0=
H`r`hk`
0?
Ouehbf
0:
Lfm`
^eð`
5
Lbme`h`
© Y`htecc`h`, Y. @.
L`tblàtei`s 2
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