Simulado Extra - Prova 2 - 3º Ano

 

Xmk mkul ulb bga Dxt xtrb rb ‘ Pra ravb vb MM MM DUBKD OBHMAOBL GA DOXMOA KÍGMA PSA^B GD HMÊOHMBX GB OBWTSDZB D XTBX WDHOALAIMBX PSA^B GD KBWDKÂWMHB D XTBX WDHOALAIMBX

3032 DXWB PSA^B XAKDOWD PAGDSÂ XDS BPLMHBGB  DXWB  B PBSWMS GA GMB 08/09/3032, ÀX 28E00*. 28E00*. LDMB BWDOWBKDOWD BWDOWBKDOWD BX MOXWSTÉÔDX XDITMOWDX XDITMO WDX 2 

3 

8 

7 

4 

> 

9 

5 

= 

Dstd HBGDSOA GD RTDXWÔDX haotík =0 qudstôds oukdrbgbs gd =2 b 250, gmspastbs gb sdiumotd kbodmrb:

20  Sdsdrvd

as 80 kmoutas nmobms pbrb kbrhbr sdu HBSWÈA-SDXPA HBSWÈA-SDXPAXWB. XWB. As rbshuoeas d bs kbrhbéôds bssmoblbgbs oa HBGDSOA GD RTDXWÔDX oèa sdrèa haosmgdrbgas ob bvblmbéèa.

b. bs qudstôds gd oúkdra =2 b 284 sèa rdlbtmvbs rdlbtmvbs à ârdb ârdb gd Hmêohmbs gb Obturdzb d subs Wdhoalaimbs6

22 Ruboga

c. bs qudstôds gd oúkdra oúkdra 28> b 250 250 sèa rdlbtmvbs à ârdb ârdb gd Kbtdkâtmhb d subs Wdhoalaimbs.

23 ^ahê

Haonmrb sd a sdu HBGDSOA GD RTDXWÔDX haotík b qubotmgbgd qubotmgbgd gd qudstôds d sd dssbs qudstôds dstèa ob argdk kdohmaobgb ob mostruéèa botdrmar. Hbsa a hbgdroa dstdjb mohakpldta, tdoeb qublqudr gdndmta au bprdsdotd gmvdriêohmb, hakuomqud ba bplmhbgar gb sblb pbrb qud dld takd bs pravmgêohmbs hbcëvdms. Dshrdvb d bssmod sdu oakd oas dspbéas dspbéas prøprmas ga HBSWÈA-SDXPA HBSWÈA-SDXPAXWB XWB hak hbodtb dsndrairânmhb gd tmotb prdtb. Oèa gacrd, oèa bkbssd odk rbsurd rbsurd a HBSWÈA-SDXPAXWB, HBSWÈA-SDXPAXWB, pams dld oèa pagdrâ sdr sucstmtuëga. Pbrb hbgb hbgb ukb gbs qudstôds acjdtmvbs, sèa bprdsdotbgbs bprdsdotbgbs 4 apéôds apéôds mgdotmnmhbgbs mgdotmnmhbgbs hak bs ldtrbs , , , d . Bpdobs ukb rdspaogd harrdtbkdotd à qudstèa. Tsd a høgmia prdsdotd odstb hbpb pbrb prddohedr a hbkpa harrdspaogdotd harrdspaogdotd oa HBSWÈA-SDXPAXWB. Hak sdu SB (Sdimstra (Sdimstra Bhbgêkmha), Bhbgêkmha), prddoheb a hbkpa hbkpa harrdspaogdotd ba høgmia ga bluoa. Xd a sdu SB oèa bprdsdotbr 9 gëimtas, prddoheb as prmkdmras dspbéas d gdmxd as gdkbms dk crboha. Oa HBSWÈA-SDXPAXWB, HBSWÈA-SDXPAXWB, prddoheb prddoheb taga a dspbéa gdstmobga à apéèa dshalemgb dshalemgb pbrb b rdspastb. B kbrhbéèa dk kbms gd ukb apéèa boulb b qudstèa, kdska qud ukb gbs rdspastbs dstdjb harrdtb. A tdkpa tdkpa gmspaoëvdl gmspaoëvdl pbrb dstbs pravbs pravbs í gd hmoha earbs.

*gd bharga hak a earârma gd Crbsëlmb

tdrkmobr bs pravbs, bhdod pbrb hebkbr a bplmhbgar d dotrdiud dstd HBGDSOA GD RTDXWÔDX d a HBSWÈA-SD HBSWÈA-SDXPAXWB. XPAXWB. pagdrâ gdmxbr a lahbl gd pravb sakdotd bpøs gdharrmgbs gubs earbs ga moëhma gb bplmhbéèa d pagdrâ ldvbr sdu HBGDSOA GD RTDXWÔDX ba gdmxbr dk gdnmomtmva b sblb gd pravbs oas últmkas 80 kmoutas qud botdhdgdk a tírkmoa gbs pravbs.

28  ^ahê sdrâ dxhluëga ga Dxbkd, b qublqudr tdkpa, oa hbsa gd:

b. prdstbr, dk qublqudr gahukdota, gdhlbrbéèa gdhlbrbéèa nblsb au modxbtb6 modxbtb6 c. bimr hak moharrdéèa moharrdéèa au gdshartdsmb pbrb hak qublqudr pbrtmhmpbotd pbrtmhmpbotd au pdssab dovalvmgb oa prahdssa gd bplmhbéèa gbs pravbs6 h. pdrturcbr, gd qublqudr qublqudr kaga, b argdk argdk oa lahbl gd bplmhbéèa gbs pravbs, moharrdoga dk hakpartbkdota mogdvmga gurbotd b rdblmzbéèa ga Dxbkd6 g. sd hakuomhbr, hakuomhbr, gurbotd bs pravbs, hak autra pbrtmhmpbotd vdrcblkdotd, par dshrmta au par qublqudr autrb narkb6 d. partbr qublqudr tmpa gd gd dqumpbkdota dqumpbkdota dldtr÷omha d gd hakuomhbéèa hakuomhbéèa gurbotd b rdblmzbéèa ga Dxbkd6 n. utmlmzbr au tdotbr utmlmzbr kdma nrbuguldota, nrbuguldota, dk cdodnëhma cdodnëhma prøprma au gd tdrhdmras, dk qublqudr dtbpb ga Dxbkd6 i. utmlmzbr lmvras, oatbs au mkprdssas gurbotd b rdblmzbéèa rdblmzbéèa ga Dxbkd6 e. sd busdotbr gb sblb gd pravbs ldvboga ldvboga haosmia a HBGDSOA GD RTDXWÔDX botds ga prbza dstbcdldhmga d / au a HBSWÈA-SDXPAXWB b qublqudr tdkpa.

 

HMÊOHMBX GB OBWTSDZB D XTBX WDHOALAIMBX

RTDXWÈA =8

Rudstôds gd =2 b 284

As sølmgas m÷omhas sèa narkbgas par kdma gd btrbéôds dldtrastâtmhbs d, bssmk, b naréb gb lmibéèa m÷omhb pagd sdr dstmkbgb b pbrtmr gb sdiumotd dqubéèa:

RTDXWÈA =2 A bhúkula gd hbribs dlítrmhbs sac ukb plbhb dldtr÷omhb pagd idrbr sírmas pracldkbs pbrb b mogústrmb, ukb vdz qud bliuos hmrhumtas dldtr÷omhas, par dxdkpla, gas hakputbgards, pagdk sdr prdjugmhbgas par dlbs.

N



f . z2 . z 3 3

g

Odssb dqubéèa, f í ukb haostbotd, z2 d z3 sèa bs hbribs gas ëaos, d g í b gmstãohmb dotrd dlds.

B mkbidk b sdiumr kastrb bliukbs lmoebs dqumpatdohmbms dqumpatdohm bms idrbgbs par ukb hbrib paotubl odibtmvb, qud sd dohaotrb sac ukb plbhb dldtr÷omhb.

BWFMOX, P. Y.6 JAODX, L. Prmohëpmas gd Ruëkmhb: qudstmaoboga b vmgb kagdrob d a kdma bkcmdotd. 8. dg. Sma gd Jbodmra: Iubobcbrb Faaibo, 300> (Bgbptbéèa).

Tkb mogústrmb odhdssmtb rdblmzbr a rdvdstmkdota gd sdus naroas hak kbtdrmbms rdnrbtârmas, gmspaoga bpdobs gas øxmgas gd kbioísma d gd cârma, rdprdsdotbgas, rdspdhtmvbkdotd, par KiA d CbA.

 ‘23^

Haosmgdrboga qud dssds kbtdrmbms gdvdk supartbr bltëssmkbs tdkpdrbturbs, b kdlear dshaleb sdrmb pdlb utmlmzbéèa ga

 B S

  

Gbgas: Oúkdras bt÷kmhas: Ki ; 23, Cb ; 4>.

‘

  3  S

     S     8

 B

CbA, pams a hâtmao bprdsdotb kdoar rbma d hbrib.

 C

CbA, pams a hâtmao bprdsdotb kbmards vblards gd rbma d gd hbrib.

 H

KiA, pams a hâtmao bprdsdotb kdoards vblards gd rbma d gd hbrib. CbA, pams b gmstãohmb dotrd as ëaos í kbmar, kbs bs hbribs sèa miubms.

C

 G

Hbsa uk tíhomha prdhmsd kavdr ukb hbrib dlítrmhb gd > ´H ga paota B pbrb a paota C, dld prdhmsbrâ dxdrhdr dx drhdr uk trbcblea, dk kmhrajaulds, gd

 D

KiA, pams b gmstãohmb dotrd as ëaos í kdoar, kbs bs hbribs sèa miubms.

 ‘>.

RTDXWÈA =7

 C

+23.

 H

 ‘37.

 G

+8>.

 D

 ‘75.

Hak pmstb sdhb, as rmshas gd bhmgdotds hak hbkmoeôds par haotb gd gdrrbpbidos í cbmxa, kbs, hak bs heuvbs, dssd dss d rmsha kbms qud gacrb. A hadnmhmdotd gd btrmta dotrd a podu d a bsnblta, dk pmstb sdhb, í gd hdrhb gd 0,>, d dk haogméôds kdleards, hak podus oavas d bsnblta cak pagd sdr bmogb kbmar. Ruboga hakdéb b heavdr, dssd oúkdra hbm pbrb 0,3, mssa parqud b prmkdmrb heuvb sd kmsturb hak b sujdmrb ga bsnblta, haka padmrb, øldas d irbxbs, pø gd carrbhebs gas podus d autras kbtdrmbms qud trbosnarkbk a bsnblta dk uk “sbcèa‛. Pbrb vdrmnmhbr sd eâ rmsha gd bhmgdotd, pagd-sd alebr pdla rdtravmsar d vdr a rbstra gd âiub sbmoga gas podus. Hbsa ebjb aogbs, d oèa uk sprby sbmoga gb lbtdrbl ga podu, a kdlear í rdguzmr b vdlahmgbgd.

 B

RTDXWÈA =3 B cmølaib Írmhb gb Xmlvb, gb Nbhulgbgd gd Doidoebrmb gd Blmkdotas, haosdiumu msalbr oavbs lmoebidos gd nuoias nmlbkdotasas d ldvdgurbs b pbrtmr gd bkastrbs gd nalebs, nrutas d sdkdotds, prdsdotds obs rdimôds gd Kbtb Btlãotmhb d bkbz÷omhb. Dssbs lmoebidos kastrbrbk patdohmbl pbrb b praguéèa gd dozmkbs hak bplmhbéôds ob mogústrmb gd cmahakcustëvdms, par dxdkpla. IBSGDOBL, M. Gmspaoëvdl dk:

RTDXWÈA =5

Bs hdrãkmhbs sèa haostmtuëgbs cbsmhbkdotd gd ukb kmsturb gd brimlb d gd øxmgas kdtâlmhas. Tk nbta motdrdssbotd b rdspdmta gd utdosëlmas ndmtas gdssd kbtdrmbl í qud dlds pagdk sdr utmlmzbgas haka bkalbgards gd nbhbs, msta í, ba sdrdk nrmhhmaobgas ob supdrnëhmd ga kdtbl, sèa hbpbzds gd rmshbr b supdrnëhmd gdld. Acsdrvd:

Tkb dxpdrmêohmb rdblmzbgb dk 2=35 pdla kmhracmølaia moilês Nrdgdrmhf Irmnnmte kastrau, pbrb surprdsb idrbl, qud cbhtírmbs hbpbzds gd hbusbr ukb gadoéb pagmbk, kdska gdpams gd kartbs, “pbssbr‛ dssb hbpbhmgbgd pbrb cbhtírmbs vmvbs qud b tmoebk pdrgmga, kbs oèa gdshacrmu haka mssa aharrmb. Dssd domikb sø sdrmb gdhmnrbga pastdrmarkdotd, pastdrmarkdotd, hak a trbcblea gd três kígmhas oartd-bkdrmhboas ‘ Aswblg W. Bvdry,, Halmo K. KbhLdag d Kbhlyo KhHbrty. Bvdry Gmspaoëvdl dk: .. gam: 20.202>/s27 20.202>/s2792-7=33(02)03 92-7=33(02)03300-0. 300-0. PKMG: 22==5 22==5904 904 (Bgbptbéèa).

B gmstrmcuméèa gdssb gadoéb pdla Crbsml gdkaostrb b odhdssmgbgd gb nlardstb bkbz÷omhb pbrb a(b)  B

prdsdrvbéèa gas vdtards movdrtdcrbgas ga Wrypboasakb hruzm.

 C

drrbgmhbéèa ga bidotd dtmaløimha qud hbusb b gadoéb oa cmakb.

 H  G

haotrald gb mondhéèa eukbob par kdma gd trmbtakëodas mondhtbgas. mostblbéèa gd hakpdtméèa dotrd a Wrypboasakb d a Plbskagmuk.

 D

dstbcdldhmkdota gbs narkbs lbtdotds ga hmhla gd vmgb ga pratazaârma.

C D SOA TL L M X M X WD KB GD D OX M OA

DODK ‘ ^AL. DUWSB ‘ 3032

HOBW ‘ PSA^B MM ‘ PÂIMOB 4

 

RTDXWÈA 202

RTDXWÈA 208

Tk dxpdrmkdota nam rdblmzbga pbrb tdstbr b sdldtmvmgbgd gd ukb kdkcrbob ibsasb pbrb a HA3. Odssd dxpdrmkdota, utmlmzau-sd b rdbéèa gd hakcustèa hakpldtb ga dtboal ibsasa haka naotd gd dkmssèa gdssd iâs. Dssb rdbéèa praguzmu 3 kal gd HA 3 qud, bpøs pbssbr pdlb kdkcrbob, nam brkbzdobga dk uk rdhmpmdotd ndhebga haotdoga uk êkcala køvdl, b 89 ºH. Momhmblkdotd, b prdssèa oa motdrmar ga rdhmpmdotd drb gd > btk, kbs, hak a tdkpa, a iâs dxpbogmu sd hakpartboga gd kbodmrb mgdbl. Acsdrvd Acs drvd a irânmha b sdiumr, qud rdprdsdotb dssb trbosnarkbéèa:

Wagbs bs rdbéôds dxplasmvbs praguzdk irbogd qubotmgbgd gd hblar, qud tdk uk dndmta mkprdssmaobotd gd bukdotbr b prdssèa gas ibsds ‘ qubota kbms bltb b tdkpdrbturb, kbmar b prdssèa. B omtrailmhdrmob í ukb kalíhulb bltbkdotd mostâvdl, qud dxplagd sd bqudhmgb au kbrtdlbgb. Doqubota b pølvarb pagd sdr kbousdbgb hak rdlbtmvb sdiurboéb, b omtrailmhdrmob í kumta mkprdvmsëvdl, pagdoga dxplagmr dspaotbodbkdotd dk vmrtugd gd uk

p / btk

heaqud au gd bqudhmkdota. B sdiumotd dqubéèa cblbohdbgb rdprdsdotb b rdbéèa gd gdhakpasméèa gb omtrailmhdrmob: 7H8E4O8A=( ) ↓ >O3(i) + 23HA3(i) + 20E3A(i) + A3(i) l

Haosmgdrd qud bpdobs 20% gd ilmhdrmob rdbidk botds gd a brtdnbta qud b haotík sdr dstmlebébga d qud b rdbéèa í tèa râpmgb qud b ilmhdrmob oèa vbparmzb botds gb dxplasèa.

>

B qubotmgbgd gd kbtírmb gd ibsds narkbgas quboga >52 i gd omtrailmhdrmob sèa halahbgas pbrb rdbimr í Gbga: Kbssb kalbr dk i.kal ‘2: H8E4O8A= ; 339.

Pnmobl ^momhmbl

80

^/L

A valukd momhmbl ahupbga pdla iâs, dk lmtra, drb gd, bpraxmkbgbkdotd, Gbga: Haostbotd gas ibsds ; 0,053 btk.L.kal ‘2 F ‘2.  B

0,3.

 C

2,0.

 H

2,9.

 G

9,4.

 D

5,4.

 B

0,=0.

 C

3,25.

 H  G

7,40. 2>,4.

 D

3=,00.

RTDXWÈA 207

RTDXWÈA 203 B dxprdssèa gas idoøtmpas ga smstdkb sboiuëoda BCA dstâ rdlbhmaobgb hak a lahus iêomha gdoakmobga E, aogd dstâ a bldla E (gakmobotd) au e (rdhdssmva). A bldla E praguz ukb dozmkb (dozmkb E) qud trbosnarkb ukb sucstãohmb prdhursarb dk botëidoa E, qud, par sub vdz, í trbosnarkbga dk botëidoa B au C par béèa, rdspdhtmvbkdotd, gd dozmkbs smotdtmzbgbs sac a hakboga gas bldlas MB au MC. Haka a bldla m í mobtmva, oèa prakavd qublqudr trbosnarkbéèa oa botëidoa E. Pdssabs hak idoøtmpa ee oèa praguzdk b dozmkb E d dxprdssbk uk ndoøtmpa gdoakmobga nblsa A. Gmspaoëvdl dk: Dotrd bs brkbs quëkmhbs oèa ldtbms, gdstbhbk-sd as bidotds lbhrmkaiêodas, qud hbusbk mrrmtbéèa oas aleas, bhakpboebgb par lbhrmkbéèa, haka tbkcík mrrmtbéôds ob pdld d vmbs rdspmrbtørmbs. Dssds bidotds sèa pauha au kagdrbgbkdotd salúvdms dk saluéèa bquasb d valâtdms à tdkpdrbturb bkcmdotd. Xèa gmspdrsas par kdma gd sprbys  dk rdhmpmdotds prdssurmzbgas, haotdoga a bidotd d uk prapdldotd ibsasa, au dk gmkmoutas hbrtuheas dxplasmvas qud valbtmzbk a bidotd laia botds gb rupturb ga rdhmpmdotd. Tkb irbobgb gd HX (3-hlaracdozmlmgdoa kblaoaomtrmlb) pagd narkbr ukb ouvdk gd 4 b 20 kdtras gd gmãkdtra qud pagd pdrsmstmr par 20 b 24 kmoutas. BKASMK, O. K. dt bl. Ruëkmhb d brkbs oèa ldtbms: iâs lbhrmkaiêoma dk naha. Sdvmstb Ruëkmhb Oavb ob Dshalb, v. 89, o. 3, 3024 (Bgbptbéèa).

pr + vi+

pr  vi

 C pr + vi

B râpmgb dxpbosèa ga bidotd lbhrmkaiêoda ba sd rakpdr a rdhmpmdotd dstâ rdlbhmaobgb, prmohmpblkdotd, ba(à)  B

gmkmouméèa gd prdssèa hbusbgb pdlb râpmgb dxpasméèa ga iâs às haogméôds btkasnírmhbs.

 C

gmspdrsèa ga bidotd lbhrmkaiêoda hbusbgb pdlb dxpasméèa bas vdotas kbms nartds.

 H

bltdrbéèa gb haostbotd gas ibsds mgdbms gdvmga às vbrmbéôds crushbs qud a smstdkb sanrd.

 G

bukdota ob qubotmgbgd gd kbtírmb gd ibsds dk vmrtugd gb valbtmlmzbéèa ga bidotd lbhrmkaiêoda.

 D

gmkmouméèa gb tdkpdrbturb ga smstdkb hbusbgb pdla haotbta ga bidotd lbhrmkaiêoda hak a br nrma.

pr  vi+

C D SOA TL L M X M X WD KB GD D OX M OA

DODK ‘ ^AL. DUWSB ‘ 3032

HOBW ‘ PSA^B MM ‘ PÂIMOB 9

 

RTDXWÈA 209

Bs três dspíhmds gdshrmtbs sèa b Hyhlapds xmoiudosms, dohaotrbgb prøxmka à rdimèa ga Sma Umoiu, ob Bkbz÷omb, b Hyhlapds runus, prdsdotd ob rdimèa gd Saog÷omb d oakdbgb bssmk gdvmga à sub har bvdrkdlebgb, d b Hyhlapds teakbsm, qud vmvd ob kbridk gmrdmtb ga Sma Bkbzaobs, dotrd a dstbga ga Bhrd d a Pdru.

B gdshacdrtb ga ndo÷kdoa gb dxpbosèa ga Tomvdrsa, ndmtb par Dgwmo Euccld ob gíhbgb gd 2=30, pdrkmtmu b dlbcarbéèa gb empøtdsd gd qud, sd a Tomvdrsa dstâ dxpbogmoga, dld drb kdoar oa pbssbga. Bssmk, sd nassd passëvdl valtbr oa tdkpa, bs iblâxmbs sdrmbk vmstbs hbgb vdz kbms prøxmkbs ukbs gbs autrbs, pagdoga mkbimobr qud hedibrmb b uk mostbotd dk qud tuga a qud hakpôd a Tomvdrsa eajd dstbrmb rduomga dk uk paota monmomtbkdotd gdosa d qudotd qud hakdéau b dxpbogmr, hebkbga Cmi Cboi. Xupaoga qud b vdlahmgbgd gd dxpbosèa gdsgd dssd mostbotd btí eajd nam haostbotd, bstr÷oakas haosdiumrbk dstmkbr b mgbgd ga Tomvdrsa usboga b Ldm gd Euccld, dk qud b vdlahmgbgd gd bnbstbkdota í praparhmaobl à gmstãohmb gbs iblâxmbs btí oøs, sdoga b haostbotd gd praparhmaoblmgbgd b haostbotd gd Euccld (E0), huja vblar í gd 92 fk . s ‘2. Kps ‘2 (93,7 . 20 ‘23 boa ‘2).

 B

ba kdska rdmoa, bpdsbr gd ahupbrdk nmlas cmaløimhas

 C

gmndrdotds. ba kdska iêodra, bpdsbr gd sd trbtbrdk gd dspíhmds gmndrdotds.

Gmspaoëvdl dk: gd julea gd 2=>= d gurau hdrhb gd 2=4 earbs. Tk gas kakdotas kbms kbm s mkpartbotds gb emstørmb gb kmssèa bhaotdhdu dotrd 27e47kmo d 33e4=kmo, quboga b vdlahmgbgd gb obvd hbmu gd 8,=8 fk/s pbrb 3,33 fk/s gdvmga à naréb gb irbvmgbgd gb Wdrrb. B pbrtmr gd dotèa, b obvd sd kavdu hak vdlahmgbgd haostbotd btí dotrbr ob dsndrb gd monluêohmb gb Lub. Gmspaoëvdl dk: 54 O.  G 3 =20 O.  D 4 59> O.

DODK ‘ ^AL. DUWSB ‘ 3032

C D SOA TL L M X M X WD KB GD D OX M OA

 

RTDXWÈA 223 Hdtabhmgasd í a bhúkula sboiuëoda gd harpas hdt÷omhas ‘ âhmgas nrbhas praguzmgas b pbrtmr gb bhdtml-HaB ‘ gdmxboga a kdma hak a pE kbms cbmxa qud a oarkbl. Haka qubsd tagbs bs rdbéôds quëkmhbs qud bhaotdhdk obs hílulbs gdpdogdk gd uk pE dstâvdl au qud sø pdrkmtb ukb vbrmbéèa kumta lmidmrb, dssb bhmgdz í kumta gdsnbvarâvdl ba nuohmaobkdota hdlulbr. B mkbidk mlustrb as kdhbomskas dovalvmgas oa gdsdovalvmkdota gd hdtabhmgasd dk hbsas gd gmbcdtds. Ob busêohmb gb mosulmob, b ilmhasd oèa í trbosndrmgb ba hmtaplbskb.

Gmspaoëvdl dk: 4 ºH, au kdska supdrmards. Gmspaoëvdl dk: 0°.

 D

204.

 D

290°.

KBW ‘ PSA^B MM ‘ PÂIMOB 2>

DODK ‘ ^AL. DUWSB ‘ 3032

C D SOA TL L M X M X WD KB GD D OX M OA

 

RTDXWÈA 270 Ruboga sd pdosb dk haoedhdr b hmgbgd gd Oavb Arldbos, a Nrdohe Rubrtdr í b prmkdmrb rdimèa qud gdvd sd tdr dk kdotd. Bnmobl, í odssd luibr qud sd dohaotrbk bs prmohmpbms btrbéôds gb hmgbgd, mohlumoga b vmgb oaturob d b brqumtdturb qud nbz gd Oavb Arldbos ukb hmgbgd úomhb dk taga as DTB. A Nrdohe Rubrtdr dstdogd-sd ba laoia ga Sma Kmssmssmppm gdsgd b Sub Hbobl btí b Bvdomgb Dsplbobgd, tatblmzboga 23 qubrtdmrôds, ukb gmstãohmb gd 2,77 fk6 d gb Sub Gdhbtur à Sub Sbkpbrt, hak sdtd qubrtdmrôds,

RTDXWÈA 273 Pbrb b haostruéèa ga kasbmha bprdsdotbga b sdiumr, utmlmzbrdkas bpdobs palëiaoas d hmrhuondrêohmbs. A pbssa momhmbl í b haondhéèa gb cbsd gd sdu pbgrèa, mlustrbgb ob mkbidk.

ukb gmstãohmb gd >=0 k. Gmspaoëvdl dk: 7 pdssabs (qud hakpbrtmlebrbk a past), 2 >00 qud rdbimrbk b dld d autrbs 394 qud hakdotbrbk. B hbéulb gb nbkëlmb qudrmb sbcdr a katmva gd vmrdk “trdzd uomgbgds dk uk pbhatd gd ouiidts‛, jâ qud “28 í uk oúkdra prmka d, partbota, sø í passëvdl gmvmgmr ukb qubotmgbgd miubl m iubl dotrd as haosukmgards sd vahê dstmvdr sazmoea au ouk cboga gd trdzd‛. B hlmdotd justmnmhau sub gúvmgb dxplmhboga qud í “b mrkè kbms oavb‛, a qud sdkprd b nbz nmhbr hak uk b kdoas. B dkprdsb gas ouiidts   rdspaogdu monarkboga qud dlds sèa vdogmgas dk pbhatds haotdoga 3== i au 928 i, d qud b qubotmgbgd gd ouiidts oas pbhatds pagd vbrmbr. Gmspaoëvdl dk: . 8.

 D

RTDXWÈA 278 B tdkpdrbturb gd ukb gdtdrkmobgb hmgbgd vbrmau, gurbotd uk gmb, sdiuoga b nuoéèa

 

   

W t

t

3

>



7t



23 ,

dk qud W í b tdkpdrbturb dk irbus Hdlsmus (°H) d 0 < t ≧ 37

rdprdsdotb bs earbs ga gmb acsdrvbga. B tdkpdrbturb gb hmgbgd nam miubl b 80 °H às  B 0 d 37 earbs.  C 3 d 23 earbs.  H 7 d 30 earbs.  G > d 25 earbs.  D 20 d 27 earbs.

DODK ‘ ^AL. DUWSB ‘ 3032

KBW ‘ PSA^B MM ‘ PÂIMOB 29

 

Xdoga S 2  a rdogmkdota gbs kâqumobs gd N 2, d S 3  a

RTDXWÈA 277 A trbgmhmaobl jaia gb vdleb í uk jaia, dk uk tbculdmra gd = hbsbs, oa qubl, pbrb vdohdr, vdohd r, a jaibgar gdvd blmoebr 8 pdébs miubms: earmzaotblkdotd, vdrtmhblkdotd au gmbiaoblkdotd. Gams bkmias gmsputbrbk ukb vdrsèa bprmkarbgb gdssd  jaia dk uk tbculdmra gd 2> hbsbs, oa qubl, pbrb vdohdr, a  jaibgar gdvd blmoebr 7 pdébs miubms gb kdskb kbodmrb qud nbrmb oa jaia trbgmhmaobl.

rdogmkdota gd N3, b rbzèa  B  C  H

Dk uk gdtdrkmobga kakdota gb pbrtmgb, a tbculdmra sd dohaotrbvb haonarkd b nmiurb b sdiumr:

S2 S3

 í miubl b

8 = 4 8 3 4

 G  D

= 2 8

 

RTDXWÈA 27>

Xbcdoga qud a bkmia hak bs pdébs hmrhulbrds nam a vdohdgar, sdk qud ebjb ratbéèa gb mkbidk, b nmiurb qud hakpldtb harrdtbkdotd bs hbsbs dk crboha ga tbculdmra bprdsdotbga í:  B

A smstdkb gd sdldéèa pbrb a moirdssa gd bluoas dk ukb nbhulgbgd utmlmzb haka hrmtírma pbrb hlbssmnmhbéèa gas hbogmgbtas b kígmb brmtkítmhb gbs oatbs actmgbs obs qubtra ârdbs gd haoedhmkdota d ob rdgbéèa bvblmbgbs oa Dxbkd Obhmaobl ga Dosmoa Kígma. Tk dstugbotd qud prdtdogd haoharrdr b ukb vbib odssb nbhulgbgd utmlmzau uk smkulbgar pbrb dstmkbr b sub oatb dk hbgb ukb gbs ârdbs, dxhdta ob rdgbéèa. Gdssb narkb, dld utmlmzbrâ bs oatbs actmgbs btrbvís ga smkulbgar d b oatb gd hartd ga hursa prdtdogmga oa boa botdrmar pbrb bvblmbr b passmcmlmgbgd gd sub bpravbéèa odssb mostmtuméèa. Haosmgdrboga qud bs oatbs gbs qubtra ârdbs, sdiuoga a smkulbgar, narbk 538, 4>>, >29 d 940, d qud b oatb gd hartd ga hursa prdtdogmga oa boa botdrmar nam 98>, pbrb ukb boâlmsd rdbl gb passmcmlmgbgd gd bpravbéèa oa hursa, b oatb këomkb qud dld gdvd haosmgdrbr pbrb sub rdgbéèa í miubl b

 C

 H

 G

 B

>5=,0.

 C

>=5,7.

 H

938,>.

 G

=37,0.

 D

=85,0.

RTDXWÈA 279 Dk ukb gdtdrkmobgb dkprdsb, eâ dldméôds pbrb kdkcras gb HMPB (Hakmssèa Motdrob gd Prdvdoéèa gd Bhmgdotds) gd três dk três boas, pbrb crmibgmstbs gd qubtra dk qubtra boas d pbrb kdkcras ga haosdlea nmshbl gd hmoha dk hmoha boas.

 D

Xd dk 3030 aharrdrbk bs três dldméôds smkultbodbkdotd, a prøxmka boa dk qud dssbs dldméôds aharrdrèa ba kdska tdkpa sdrâ RTDXWÈA 274 Wrês kâqumobs gb nâcrmhb N2, hak kdska rdogmkdota, haosdiudk praguzmr 25 pdébs dk uk gmb. Hmoha kâqumobs gb nâcrmhb N3 , hak rdogmkdota miubl dotrd sm, parík gmndrdotd ga rdogmkdota gbs kâqumobs gd N2, haosdiudk praguzmr 20 pdébs dk uk gmb. KBW ‘ PSA^B MM ‘ PÂIMOB 25

 B

3083.

 C

3084.

 H

3040.

 G

30>0.

 D

3050.

DODK ‘ ^AL. DUWSB ‘ 3032

C D SOA TL L M X M X WD KB GD D OX M OA

 

RTDXWÈA 275 Obs mogústrmbs butakatmvbs sèa ndmtas bhakpboebkdotas haostbotds ga oúkdra gd pdébs praguzmgbs pdlbs kâqumobs. Parík, gdvmga b nblebs ga apdrbgar, gdndmtas au qudcrbs gd hakpaodotds, b qubotmgbgd gd pdébs praguzmgbs pagd vbrmbr gurbotd a gmb. Prdahupbga hak b smtubéèa, a doidoedmra gb hakpboemb pdgmu ba dstbimârma qud, gurbotd uk gmb gb sdkbob, kdgmssd a oúkdra gd pdébs praguzmgbs. A rdsultbga nam bprdsdotbga haonarkd a irânmha b sdiumr: Oúkdra gd pdébs praguzmgbs

2 300 2 200 2 000 =00 500 900 >00 400 700 800 300 200 0 0

2

3

8

7

4

>

9

5

= 20 20 22 23 28 27 24 2> 29 25 2= 30 32 33 38 37 Earbs

A dstbimârma dlbcarau, tbkcík, uk rdlbtørma hak as prmohmpbms bhaotdhmkdotas oa pdrëaga oa qubl a oúkdra gd pdébs praguzmgbs nam rdguzmga hak b kbmar motdosmgbgd, haosmgdrboga b vbrmbéèa ga oúkdra gd pdébs par earb. Xbcdoga qud a dstbimârma hukprmu b tbrdnb, a pdrëaga mogmhbga oa rdlbtørma tdvd b gurbéèa gd  B 3 earbs.  C 8 earbs.  H 7 earbs.  G 4 earbs.  D > earbs. RTDXWÈA 27= Tkb dqumpd gd tapøirbnas dstbvb nbzdoga a dstuga gd ukb rdimèa plbob d pasmhmaoau gams tdagalmtas miubms b hdrtbs gmstãohmbs gd gams prígmas, b 2 k ga heèa, haonarkd mkbidk. Pbrb b kdgméèa ga prígma kbms blta, a ãoiula gd vmsèa ga tdagalmta hak b earmzaotbl nam gd 80°, d pbrb b kdgméèa ga prígma kbms cbmxa, a ãoiula gd vmsèa ga tdagalmta hak b earmzaotbl nam gd 74°.

80°

74°

2k

2k xk

yk

Xbcdoga qud, bpøs bs kdgméôds, b dqumpd haostbtau qud bs blturbs gas prígmas kbms blta d kbms cbmxa sèa, rdspdhtmvbkdotd, >0 k d 70 k, b sakb gbs gmstãohmbs x d y gas tdagalmtas bas prígmas í, dk kdtra, gd  B

4= 8

+

8= 3.

 C

4= 8

+

8=.

 H

0 8

+

8=.

 G

5= 3

+

8=.

 D

5= 8 .

C D SOA TL L M X M X WD KB GD D OX M OA

DODK ‘ ^AL. DUWSB ‘ 3032

KBW ‘ PSA^B MM ‘ PÂIMOB 2=

 

RTDXWÈA 240

RTDXWÈA 248

Tkb pdssab prdhmsb rdblmzbr uk gdslahbkdota gdotra gd sub hmgbgd. Dlb gdhmgmu utmlmzbr uk sdrvméa gd hbraob pbib pdla bplmhbtmva gd sdu hdlulbr. B nmk gd dhaoakmzbr, dlb ndz ukb pdsqumsb gd vblards, smkulboga sub harrmgb. Xbcd-sd qud oa bplmhbtmva B dxmstd ukb tbrmnb nmxb gd S$ 8,30 d hacrb-sd S$ 2,50 par quml÷kdtra ragbga d S$ 0,24 par kmouta gd vmbidk. Oa bplmhbtmva C, í hacrbga S$ 2,70 par quml÷kdtra ragbga d S$ 0,74 par kmouta gd vmbidk.

Pbrb rdvdstmr a nuoga gbs dkcblbidos gd sdus pragutas, ukb nâcrmhb utmlmzb a sdiumotd prahdssa: gd ukb naleb qubgrbgb, sèa rdtmrbgas qubtra hartds gd três tmpas gmndrdotds, haonarkd b mlustrbéèa b sdiumr. Hbgb tmpa gd hartd í usbga pbrb rdvdstmr a nuoga gd uk praguta gmndrdotd, pagdoga ebvdr  juoéèa dotrd as tmpas gdpdogdoga gb ârdb b sdr rdvdstmgb. k

Ba hblhulbr a vblar tatbl b sdr pbia, dlb pdrhdcdu qud, pbrb dssb vmbidk, pbibrmb S$ 237,50 dk bkcbs bs apéôds gd trbospartd.

M

MM

MM

MMM

Haosmgdrboga qud bkcas as sdrvméas ibstbrbk a kdska tdkpa d pdrharrdrbk b kdskb gmstãohmb, b rbzèa dotrd a tdkpa tatbl gd vmbidk, dk kmoutas, d b gmstãohmb tatbl pdrharrmgb, dk quml÷kdtras, í, bpraxmkbgbkdotd,  B

0,>>.

 C

0,94.

 H

2,88.

 G

2,42.

 D

2,5>.

As tmpas M d MMM sèa qubgrbgas, d as hartds ga tmpa MM sèa rdtãoiulas.

RTDXWÈA 242 Wrês haldhmaobgards gd kadgbs, Lbëod d Pbula, sd dohaotrbrbk pbrb haovdrsbr sacrdPalmbob, sdus bhdrvas.

Gd bharga hak bs monarkbéôds, b ârdb ga nuoga gb dkcblbidk qud pagd sdr rdvdstmgb par gams hartds ga tmpa MM í miubl b:

Ba taga, dlds tmoebk 39> kadgbs, dotrd bs qubms 309 oèa sd rdpdtmbk ob haldéèa uk ga autra. Lbëod passum = kadgbs b kbms qud Pbula, d Palmbob passum = kadgbs b kdoas qud Pbula.

 B

(k + o)3

 C

3(k + o)

 H

(ko)3

Pbula pdrhdcdu qud passum 73 kadgbs dk hakuk hak Lbëod d 30 kadgbs dk hakuk hak Palmbob. Palmbob pdrhdcdu qud passum 34 kadgbs dk hakuk hak Lbëod.

 G

ko

 D

3ko

A oúkdra gd kadgbs qud as três passudk dk hakuk í miubl b  B 94.  C >=.  H 25.  G  D

=. >.

RTDXWÈA 247 Tk mostmtuta gd dstbtëstmhb ndz ukb pdsqumsb hak uk irupa gd javdos, usboga-as haka bkastrb pbrb dstmkbr a tdkpa kígma gmârma dk qud as javdos crbsmldmras usbk bs rdgds sahmbms. B tbcdlb b sdiumr kastrb as gbgas haldtbgas odssb pdsqumsb: Mgbgd gas dotrdvmstbgas

RTDXWÈA 243 Pbrb b lmkpdzb ga rdsdrvbtørma gd âiub gd uk haogakëoma, narbk odhdssârmas a ndhebkdota ga rdimstra d a dshabkdota tatbl gb âiub prdsdotd oa rdsdrvbtørma. Xbcd-sd qud a valukd gd âiub rdtmrbga ga rdsdrvbtørma, dk lmtra, bpøs t earbs ga moëhma ga dshabkdota í gbga par ^(t) ; 80(40 ‘ t) 3,

24 d 2> 29 d 25 2= d 30 32 b 34

dk qud 0 ≧ t ≧ 40.

Gdssb narkb, bpøs 7 earbs gd dshabkdota, qubl valukd gd âiub bmogb prdhmsbvb sdr dshabga gdssd rdsdrvbtørma1

Tsa gmârma gbs rdgds sahmbms (earbs) > 4 4 7

Oº gd javdos dotrdvmstbgas 34 80 34 30

Gd bharga hak dssb pdsqumsb, a tdkpa kígma gmârma gd usa gbs rdgds sahmbms par javdos gd 24 b 34 boas í gd

 B

230 lmtras.

 B

8,30 e.

 C

2 850 lmtras.

 C

4,04 e.

 H

22 430 lmtras.

 H

4,34 e.

 G

>8 750 lmtras.

 G

>,34 e.

 D

94 000 lmtras.

 D

>,40 e.

KBW ‘ PSA^B MM ‘ PÂIMOB 30

o

DODK ‘ ^AL. DUWSB ‘ 3032

C D SOA TL L M X M X WD KB GD D OX M OA

 

RTDXWÈA 244 Tkb trbospartbgarb passum gams kagdlas gd vbiôds: U d ]. ]. As gdsdoeas, narb gd dshblb, gbs vmstbs vm stbs lbtdrbms gdssds gdss ds vbiôds dstèa mogmhbgas b sdiumr, hak bs kdgmgbs prmohmpbms: 20,5 kdtras

3,8 kdtras

^bièa U

3,05 kdtras

Gdssb kbodmrb, hbsa dssb ârdb sdjb gmvmgmgb miublkdotd dotrd as bidotds gd sdiurboéb, b ârdb gdstmobgb bas humgbgas gd hbgb uk gdlds, dk kdtra qubgrbga, sdrâ gd  B 300.  C 400.  H 3 000.  G 3 400.  D 4 000. RTDXWÈA 245

= kdtras 22,> kdtras

3,8= kdtras

^bièa ]

3,8= kdtras

= kdtras

Haosmgdrboga a narkbta d bs kdgmgbs gas gdsdoeas qud rdprdsdotbk b vmstb lbtdrbl gas vbiôds U d ], dlds pagdk sdr hlbssmnmhbgas, rdspdhtmvbkdotd, dk  B

trbpízma dshbldoa d trbpízma dqumlâtdra.

 C

trbpízma dqumlâtdra d trbpízma msøshdlds.

 H

trbpízma dshbldoa d trbpízma msøshdlds.

 G

trbpízma rdtãoiula d trbpízma msøshdlds.

 D

trbpízma dqumlâtdra d trbpízma rdtãoiula.

Prígmas biarb tbkcík têk sdla Prahdl Alebr a sdla Prahdl, bqudld qud mogmhb a haosuka gd dodrimb, jâ í eâcmta haosalmgbga dotrd as crbsmldmras ba hakprbr bpbrdleas dlítrmhas. Biarb, qudk dstâ btrâs gd mkøvdms pbrb hakprbr au bluibr pagd sd surprddogdr: bqudlb haostruéèa ob qubl dstâ gd alea tbkcík pagd tdr sdla gd dnmhmêohmb dodriítmhb. Oa moëhma ga kês, a Mokdtra d b Dldtracrâs lboébrbk b Dtmqudtb gd Dnmhmêohmb Dodriítmhb gd Dgmnmhbéôds Hakdrhmbms, gd Xdrvméas d Púclmhas. Hbgb dgmnëhma rdhdcd ukb hlbssmnmhbéèa dotrd B (a kdlear oëvdl gd dnmhmêohmb) d D (a pmar oëvdl). As prígmas qud rdhdcdrdk hlbssmnmhbéèa B iboebrèa a sdla Prahdl Dgmnmhb. Kbms dnmhmdotd

 B

 Bhmkb gd =4%

C

[=0%, =4%[

RTDXWÈA 24> Tkb mogústrmb nbrkbhêutmhb gdsdovalvdu uk oava kdgmhbkdota pbrb a trbtbkdota gd rdbéôds blírimhbs. Bpøs rdhdcdr b bpravbéèa ga Kmomstírma gb Xbúgd pbrb b sub hakdrhmblmzbéèa, dssb mogústrmb rdblmzau uk dstuga pbrb gdtdrkmobr qubl gdvdrmb sdr a prdéa gd vdogb gdssd kdgmhbkdota. Oa nmobl gdssd dstuga, haohlumu-sd qud a prdéa mgdbl gd vdogb gdssd kdgmhbkdota sdrmb gdnmomga pdlb nuoéèa n(x) ; 3x ‘ >, dk qud x harrdspaogd ba husta gd praguéèa, qud, par sub vdz, pagd sdr hblhulbga pdlb nuoéèa x ; i(k) ; k + 2,

2.

 C

3.

 H

8.

 G

7.

 D

4.

Kdoas dnmhmdotd Gmspaoëvdl dk: 8, ob hrbtdrb gd uk vulhèa dxtmota, pbrb dstugbr b maoasndrb tdrrdstrd.

Gmspaoëvdl dk: bcr. 3032.

Bs tarrds gd sustdotbéèa gas hbcas ga Sbgmatdldshøpma gd Brdhmca dstbvbk pasmhmaobgbs gd tbl narkb qud a tapa gd hbgb ukb drb a vírtmhd gd uk trmãoiula dqumlâtdra mkbimoârma gd lbga x kdtras. Ob vmstb supdrmar gdssd haojuota, botdob d tarrds, drb passëvdl pdrhdcdr qud a hdotra gb botdob pbrbcølmhb hamohmgmb hak a mohdotra gdssd trmãoiula mkbimoârma, sdoga a rbma gb hmrhuondrêohmb moshrmtb b dssd trmãoiula miubl b 240 kdtras, haonarkd rdprdsdotbéèa b sdiumr.

Botdob pbrbcølmhb

xk 240 k

Gd bharga hak bs monarkbéôds, b kdgmgb x ga lbga l bga ga trmãoiula dqumlâtdra narkbga pdla tapa gbs tarrds gd sustdotbéèa drb, dk kdtra, miubl b  B

800 .

 C

800 3 .

 H

800 8 .

 G

700 8 .

 D

300 300 8 0 .

RTDXWÈA 2>0 Dk ukb hakpdtméèa dotrd três ialdmras gd uk hlucd, dlds gdvdk gdndogdr a kdska oúkdra gd pdoblmgbgds. Ba tírkmoa gb hakpdtméèa, a hlucd gmvmgmrâ S$ 2 287,00 dotrd as três, dk pbrtds movdrsbkdotd praparhmaobms à qubotmgbgd gd pdoblmgbgds oèa gdndogmgbs par hbgb uk. Xbcd-sd qud a ialdmra M sanrdu três ials, a ialdmra MM sanrdu sdms ials d a ialdmra MMM sanrdu sdtd ials. Gd bharga hak bs monarkbéôds, as vblards rdhdcmgas pdlas ialdmras M, MM d MMM, odssb argdk, dk rdbl, sèa miubms b  B 343, 3=7 d 455.  C  H  G  D

455, 33>, 3=7 743 dd 343. 74>. 74>, 743 d 33>. 895, 895 d 895.

KBW ‘ PSA^B MM ‘ PÂIMOB 33

DODK ‘ ^AL. DUWSB ‘ 3032

C D SOA TL L M X M X WD KB GD D OX M OA

 

RTDXWÈA 2>2 Xhrbccld, tbkcík haoedhmga haka Pblbvrbs Hruzbgbs oa Crbsml, í uk jaia gd pblbvrbs hlâssmha d gmvdrtmga dk uk tbculdmra 24 Ù 24. A acjdtmva í nbzdr kbms paotas jaiboga pblbvrbs ob earmzaotbl, vdrtmhbl au gmbiaobl qud sd haodhtbk às  jaibgbs gas autras jaibgards jaibgards oa tbculdmra. Oa hbota mondrmar gd hbgb pdéb, í mogmhbgb b paotubéèa gb ldtrb, ldtrb, sdoga qud ldtrbs kdoas nrdqudotds passudk paotubéôds kbms bltbs. B paotubéèa gd ukb pblbvrb í gbgb pdlb sakb gbs paotubéôds gbs ldtrbs. Hbsa ukb gbs ldtrbs gb pblbvrb sdjb halahbgb oa tbculdmra obs hbsbs dspdhmbms WP (trmplmhb b paotubéèa gb pblbvrb), GP (guplmhb b paotubéèa gb pblbvrb), WL (trmplmhb a vblar gb ldtrb) au GL (guplmhb a vblar gb ldtrb), a vblar nmobl gb pblbvrb bukdotb haonarkd b hbsb usbgb. Gmspaoëvdl dk: 3 Dk irbogd pbrtd gbs kâqumobs d dqumpbkdotas, b vdlahmgbgd momhmbl, ba bhmaobr a dqumpbkdota, í cbmxb b nmk nm k gd sd dvmtbr bhmgdotds. Oa dotbota, b vdlahmgbgd gd apdrbéèa pagd sdr bukdotbgb gd bharga hak b odhdssmgbgd ga usuârma. Oa kboubl gd ukb gdtdrkmobgb kâqumob, sèa bprdsdotbgbs monarkbéôds b rdspdmta gbs três prmkdmrbs vdlahmgbgds gmspaoëvdms (M, MM d MMM) d gb bltdrbéèa sanrmgb hak b kugboéb gd M pbrb MM d gd MM pbrb MMM, haonarkd b tbcdlb b sdiumr: ^dl a h m g bg d

M

Sdlbéèa

^dlahmgbgd momhmbl

MM Bukdota gd 30% gd vdlahmgbgd dk rdlbéèa à vdlahmgbgd M

MMM Bukdota gd 40% gd vdlahmgbgd dk rdlbéèa à vdlahmgbgd MM

Hak cbsd odssbs monarkbéôds, b vdlahmgbgd MMM gb kâqumob, quboga hakpbrbgb hak b vdlahmgbgd momhmbl, rdprdsdotb uk bukdota gd  B

84%.

 C

74%.

 H

>0%.

 G

90%.

 D

50%.

C D SOA TL L M X M X WD KB GD D OX M OA

DODK ‘ ^AL. DUWSB ‘ 3032

KBW ‘ PSA^B MM ‘ PÂIMOB 38

 

RTDXWÈA 2>8 Haka hblhulbr a MBH Pbrb gdsdovalvdr a ëogmhd gd iargurb harparbl, Smhebrg Cdrikbo, gb Tomvdrsmgbgd ga Xul gb Hblmnøromb, dk Las Boidlds, d haldibs boblmsbrbk monarkbéôds gd hdrhb gd 2 900 bkdrmhboas gd armidk kdxmhbob. Dlds prahurbrbk bs hbrbhtdrëstmhbs, tbms haka iêodra, mgbgd, blturb, pdsa, hmrhuondrêohmb ga qubgrml au bliukb hakcmobéèa gdssds trbéas qud kdlear sd harrdlbhmaobssd hak b iargurb harparbl kdgmgb btrbvís ga usa gd ukb tíhomhb hak rbma-x. As pdsqumsbgards gdshacrmrbk qud b hmrhuondrêohmb ga qubgrml d b blturb dstbvbk nartdkdotd lmibgbs à iargurb harparbl. B pbrtmr gdssbs hbrbhtdrëstmhbs, as pdsqumsbgards gdsdovalvdrbk ukb dqubéèa pbrb a hâlhula ga ëogmhd gd bgmpasmgbgd harparbl:

Xbcdoga qud b pdssab hakprbrâ sakdotd b qubotmgbgd gd pbpíms odhdssârmb pbrb b mostblbéèa, a vblar qud dlb ibstbrâ hak b hakprb gas pbpíms gd pbrdgd d sub bplmhbéèa í  B

S$ 782,94.

 C

S$ 88=,00.

 H

S$ 393,94.

 G

S$ 342,94.

 D

S$ 24=,00.

RTDXWÈA 2>4 A irânmha b sdiumr rdprdsdotb as movdstmkdotas gb Pdtracrbs ba laoia ga pdrëaga gd 3004 b 300=. Movdstmkdota gb Pd Pdtracrbs tracrbs S$ Cmleèa 92

MBH

 

HRubgrml



2,4

 Blturb 

  25



Gmspaoëvdl dk: 0> 3009 3009 30 3005 05 30 300= 0=

Gmspaoëvdl dk: 2>3

 G

25x ‘ 8> 0=2

 D

25x + 8> 0=2

RTDXWÈA 2>>

 H    Rubgrml   Blturb   8   MBH  

8



 

RTDXWÈA 2>7

Tkb pdssab rdblmzau ukb hakprb oa sbhalèa. Ba hedibr dk hbsb, vmu qud ebvmb hakprbga takbtds b S$ 8,00 a qumlairbkb, hdcalbs b S$ 7,00 a qumlairbkb d hdoaurbs b S$ 4,00 a qumlairbkb, d, par dssds três mtdos, pbiau S$ 70,00. Gurbotd b hakprb, dlb oèa boatau b qubotmgbgd qubotmgbg d qud hakprau gd hbgb praguta, parík sbcmb qud b qubotmgbgd gd takbtds drb b kdskb qud b gd hdoaurbs d uk qumlairbkb kdoar ga qud b qubotmgbgd gd hdcalbs.

Tkb pdssab dstâ rdnarkboga b sblb gd sub hbsb d usbrâ gams tmpas gmndrdotds gd pbpdl gd pbrdgd dk ukb pbrdgd gd hakprmkdota 34 gk par 825 hk gd blturb. A pbpdl gd pbrdgd ga tmpa B sdrâ bplmhbga dk gams tdréas gb blturb d dk taga a hakprmkdota gb pbrdgd, jâ a pbpdl ga tmpa C sdrâ bplmhbga oa tdréa rdstbotd gb blturb d dk taga a hakprmkdota gb pbrdgd.

 B

8,0.

Ba nbzdr a arébkdota pbrb b mostblbéèa gdssds pbpíms

 C

8,4.

 H

7,0.

 G

7,4.

 D

4,0.

gd pbrdgd, dssb pdssab vdrmnmhau qud a kdtra qubgrbga ga pbpdl ga tmpa B hustb S$ 80,00, qud a kdtra qubgrbga ga pbpdl ga tmpa C hustb S$ 84,00 d qud a husta gd mostblbéèa gas gams pbpíms gd pbrdgd í S$ 250,00. KBW ‘ PSA^B MM ‘ PÂIMOB 37

87 3>

3

 Blturb     MBH  25  

74

Haosmgdrboga-sd qud b pbrtmr gd 3005 a hrdshmkdota sd kbotdvd lmodbr, b nuoéèa qud gdshrdvd dssd hakpartbkdota, pbrb x ∅ {3005, 300=, 3020, 3022, ...}, í dxprdssb par:

8

 

48

  a    è    e    l    m    C    $    S

Gd bharga hak bs monarkbéôds, b qubotmgbgd hakprbgb gd hdcalbs, dk qumlairbkb, í miubl b

DODK ‘ ^AL. DUWSB ‘ 3032

C D SOA TL L M X M X WD KB GD D OX M OA

 

RTDXWÈA 2>9 B haosultb pdrmøgmhb hak a gdotmstb í mkpartbotd pbrb sd prdvdomr gmvdrsbs gadoébs d kbotdr b sbúgd cuhbl. Tkb pdsqumsb nam rdblmzbgb hak pdssabs gd gmvdrsas oëvdms gd dshalbrmgbgd b rdspdmta ga tdkpa gdharrmga gdsgd b últmkb haosultb hak a gdotmstb. A irânmha b sdiumr dxmcd as rdsultbgas, dk parhdotbidk, gdssb pdsqumsb. Rubota tdkpa nbz gdsgd b sub últmkb mgb ba gdotmstb1    ) 74    %    (   s 70   a    g   b 84    t

   m   s   v 80   d   r    t   o 34   d   s 30   a    g     k 24   d   i 20   b    t   o   d 4   h   r   a    P 0

73

70

88

83 39

39

37   32 33 32 30

35

35 37 32

 

38

37

8 kdsds

32

> kdsds

28

2 boa =

Nuogbkdotbl mohakpldta

Nuogbkdotbl hakpldta

Kígma mohakpldta

Kígma hakpldta

Kbms gd 2 boa

Tomvdrsmtârma

Gmspaoëvdl dk: = Kâqumob partâtml gdssblmomzb âiub d b tarob mgdbl pbrb a haosuka A Gdsaodlbtar í ukb kâqumob mogmvmgubl hbpbz gd gdssblmomzbr b âiub ga kbr, gdmxboga-b patâvdl d mgdbl pbrb a haosuka eukboa. Pbrb qud dld sdjb bhdssëvdl às rdimôds kbms hbrdotds au bnbstbgbs, b kâqumob í dqumpbgb hak plbhbs natavaltbmhbs, qud narodhdk tagb b dodrimb odhdssârmb pbrb a sdu nuohmaobkdota, mogdpdogdotdkdotd gbs rdgds gd trboskmssèa.

Gd bharga hak bs monarkbéôds d haosmgdrboga a kês hak 80 gmbs, b qubotmgbgd gd lmxa, dk taodlbgb, trbtbgb kdosblkdotd par dssb kâqumob, gdsgd qud dlb nuohmaod momotdrruptbkdotd par dssd pdrëaga, í miubl b  B

242 300,00.

 C

> 800,00.

 H

4 070,00.

 G

242,30.

 D

>,80.

RTDXWÈA 292 Tk sdrrbledmra prdtdogd rdblmzbr uk hartd trbosvdrsbl, rdprdsdotbga pdla sdikdota KO, dk ukb pdéb trbpdzamgbl, haonarkd b nmiurb b sdiumr, dk qud  BC / / HG // KO.  B 8,0 k K

C 8,4 k O >,4 k

G

H

Gd bharga hak as hrmbgards, dk 5 earbs gd trbcblea gmârma gb kâqumob, í passëvdl gdssblmomzbr 4 lmtras gd âiub

Pbrb rdimstrbr tagbs bs gmkdosôds odhdssârmbs pbrb b

par gmb, qud pagdk sdr haosukmgas mkdgmbtbkdotd, sdk b odhdssmgbgd gd nmltras au dldkdotas quëkmhas pbrb b rdtmrbgb gd paludotds.

rdblmzbéèa ga sdrvméa, nam odhdssârma gdtdrkmobr b kdgmgb ga sdikdota KG, sdoga dstb, dk kdtra, bpraxmkbgbkdotd miubl b

Gmspaoëvdl dk: 0 lmtras gd âiub. A tatbl gd kâqumobs qud gdvd sdr bgqumrmga par dssd rdstburbotd pbrb sbtmsnbzdr bs haogméôds gdsdjbgbs í  B

83.

 C

2>.

 H

23.

 G  D

5. >.

 B

9,0.

 C

>,4.

 H

4,>.

 G

4,0.

 D

7,3.

RTDXWÈA 293 Tkb dkprdsb gdsdovalvdu ukb plbtbnarkb qud andrdhd a sdrvméa gd hblhulbr b pracbcmlmgbgd gd sd bhdrtbr ukb bpastb dk jaias gb Latdrmb Ndgdrbl. Dssb pracbcmlmgbgd

RTDXWÈA 290 Gmrdéèa Gmrdéè a vbm narodhdr dqumpbkdota gdstmobga ba trbtbkdota gd rdsëguas

í hblhulbgb dk pbrb nuoéèa gb qubotmgbgd gd ob oúkdras qud, aí  jaibgar dshaled bpastbr. bpastbr . Par Par dxdkpla, kdib-sdob, kdib-sdob passëvdl bpastbr gd > b 24 oúkdras, dotrd as >0 gmspaoëvdms. Dotèa, pbrb hblhulbr b pracbcmlmgbgd gd bhdrta ob kdib-sdob, b plbtbnarkb idrb ukb nuoéèa qud gdpdogd gb qubotmgbgd gd oúkdras qud a jaibgar dshaledr, sdoga dstb gd > b 24. Gdssb narkb, sd uk hlmdotd dshaledr b kdib-sdob, dld pagd hblhulbr, usboga dssb plbtbnarkb, b pracbcmlmgbgd gd sd bhdrtbr gdsgd qud mosmrb uk oúkdra gd > b 24.

Btdota às qudstôds bkcmdotbms d hmdotd ga hakprakmssa gd tagas pbrb b gdstmobéèa bgdqubgb gas rdsëguas, a irupa kmodmra Gmrdéèa Haosultarmb & Doidoebrmb, dspdhmblmzbga dk prdstbéèa gd sdrvméas, gmvdrsmnmhau sdu ldqud gd btubéèa d bpastb dk uk oava omhea gd odiøhma: b kaotbidk d rdvdogb gd dqumpbkdotas hak tdhoalaimb jbpaodsb pbrb a trbtbkdota bgdqubga ga lmxa.

 B

G ; {2, 3, ..., 27, 24}

B tdhoalaimb tdk hbpbhmgbgd pbrb trbtbr 320 fi gd lmxa

 C

G ; {2, 3, ..., 4=, >0}

par earb d bpdobs ukb kâqumob btdogd, par dxdkpla, bs odhdssmgbgds gd uk kuomhëpma gd btí 30 kml ebcmtbotds.

 H

G ; {>, 9, ..., 4=, >0}

 G

G ; {>, 9, ..., 27, 24}

 D

G ; {9, 5, ..., 28, 27}

Gmspaoëvdl dk: H.  C  H  G  D

2,3H. 3,3H. 8,3H. 7,>H.

RTDXWÈA 29> Dk uk rdstburbotd, a idrdotd rdimstrb a oúkdra gd dotrdibs rdblmzbgbs gurbotd as gams turoas gd nuohmaobkdota, tbrgd d oamtd. B tbcdlb b sdiumr bprdsdotb bs boatbéôds ga idrdotd oa pdrëaga gd sdiuogb b sdxtb-ndmrb gd ukb sdkbob: Gm b Wu r o a Rubotmgbgd gd dotrdibs rdblmzbgbs

Xdi u o g b Wbr g d Oa m t d 30

27

Wdr é b Wbr g d Oa m t d 2=

23

Ru br t b Wbr g d Oa m t d 30

27

Ru m o t b Wbr g d Oa m t d 33

28

Xdx t b Wbr g d Oa m t d 33

27

Haka pbrtd gb boâlmsd gas gbgas, nam haosmgdrbga a vblar ga køgula gb gmndrdoéb gbs vbrmãohmbs ga oúkdra gd dotrdibs gdssds gams turoas gurbotd dssd pdrëaga. Gdssb kbodmrb, dssd vblar sd dohaotrb dotrd  B 0 d 2.  C 2 d 3.  H 3 d 8.  G 8 d 7.  D 7 d 4. RTDXWÈA 299 Tkb pdssab gdsdjb nbzdr bliuos bjustds ob dstruturb BCH gd sdu vbrbl gd heèa, haka a ga kagdla mlustrbga b sdiumr, gd kbodmrb qud dssb dstruturb nmqud nmxb d kbms rdnarébgb.

Pbrb nbzdr dssds bjustds, dlb vbm mostblbr gubs ebstds kdtâlmhbs. Tkb ebstd pbrtmrâ gd B btí dohaotrbr pdrpdogmhulbrkdotd a lbga CH, d b autrb ebstd pbrtmrâ gd C btí dohaotrbr pdrpdogmhulbrkdotd a lbga  BH . Dssb pdssab nmxbrâ bs gubs ebstds hak uk pbrbnusa, qud sdrâ halahbga oa paota gd dohaotra gbs ebstds. Gdssb narkb, a pbrbnusa sdrâ mostblbga oa  B

cbrmhdotra gd BCH.

 C

mohdotra gd BCH.

 H

dxhdotra gd BCH.

 G

artahdotra gd BCH.

 D

hmrhuohdotra gd BCH.

KBW ‘ PSA^B MM ‘ PÂIMOB 35

DODK ‘ ^AL. DUWSB ‘ 3032

C D SOA TL L M X M X WD KB GD D OX M OA

 

RTDXWÈA 295 B qubotmgbgd R gd axmiêoma gmspaoëvdl pbrb hdrta tmpa gd kdriulea í gbgb pdlb nuoéèa R(t) ; ‘ >t + (H + G), dk qud t í a tdkpa gd kdriulea, dk kmoutas, H í b hbpbhmgbgd gd axmiêoma oas hmlmogras utmlmzbgas, dk lmtras, d G, a valukd gd br oas pulkôds ga kdriulebgar, dk lmtras. Dk uk trdmobkdota, sèa utmlmzbgas hmlmogras gd >0 lmtras gd hbpbhmgbgd. Sdhakdogb-sd, par katmvas gd sdiurboéb, qud a tdkpa kâxmka gd kdriulea sdjb gd =0% ga tdkpa odhdssârma pbrb taga a axmiêoma gmspaoëvdl sd dsiatbr. Gdssb kbodmrb, a tdkpa kâxmka gd kdriulea gd ukb pdssab dqumpbgb hak gams hmlmogras d qud tdoeb b hbpbhmgbgd pulkaobr gd > lmtras í miubl b  B  C

20,5 kmoutas. 23,0 kmoutas.

 H

25,= kmoutas.

 G

33,0 kmoutas.

 D

37,7 kmoutas.

RTDXWÈA 29= DG

Tk pmotar, pbrb hrmbr dndmtas gd pranuogmgbgd dk sub pmoturb, gdsdoeau uk dscaéa, haonarkd mlustrbga b sdiumr, dk qud / / NH // BC, B, N d G dstèa blmoebgas, D BC  9> d GNH  >8. 

 



G

D

>8° H N

x

9>°  B

C

Pbrb dspdhmnmhbr, dk sdu dscaéa, qubms ârdbs sdrmbk pmotbgbs pbrb idrbr a dndmta gd pranuogmgbgd, nam odhdssârma hblhulbr a vblar ga ãoiula DÃG ; x, qud, dk irbu, í miubl b  B

9>.

 C

>8.

 H

72.

 G

27.

 D

28.

RTDXWÈA 250 Gams bkmias, Jaèa d Pdgra, haosdiumrbk dhaoakmzbr S$ 40 000,00 hbgb uk. Bkcas gdhmgmrbk movdstmr taga a hbpmtbl qud passuëbk b ukb kdskb tbxb gd juras, gurbotd a kdska tdkpa, parík Jaèa bplmhau dk uk movdstmkdota b juras smkplds d Pdgra dk uk movdstmkdota b juras hakpastas. Xbcdoga qud b tbxb gdssbs bplmhbéôds drb gd 77% ba boa d qud hbgb hbpmtbl nam bplmhbga par sdms kdsds, qubl b gmndrdoéb dotrd as rdogmkdotas actmgas pdlas bkmias odssds movdstmkdotas gurbotd dssd tdkpa1  B

S$ 2 000,00

 C

S$ 3 000,00

 H

S$ 8 000,00

 G

S$ 7 000,00

 D

S$ 4 000,00

C D SOA TL L M X M X WD KB GD D OX M OA

DODK ‘ ^AL. DUWSB ‘ 3032

KBW ‘ PSA^B MM ‘ PÂIMOB 3=

 

Bvdomgb Sbjb Ibcbilmb, 3 930 Dstarml, Cdla Earmzaotd - KI Wdl. (82) 803=-7=7=

YYY.CDSOATLLM.HAK.CS/XMXWDKB