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·/÷7&34÷5&:&)\";*3-*, 2. MODÜL 4\":*,·.&-&3÷#²-·/&#÷-.&3\"4:0/&-4\":*-\"3 www.aydinyayinlari.com.tr ÖRNEK 14 ÖRNEK 18 B C DWFEUBNTBZMBSES YHFS¿FMTBZES a = 18 = c = 6 x =\"- 5 = 7 -# 4 b 2d FöJUMJôJOFHÌSF\"#FOÀPLLBÀUS PMEVôVOBHÌSF B+C+ c +EUPQMBNOOFOLÑÀÑL EFôFSJLBÀUS A = x + #= 7 - x, A +#= 12 Z\"#= 36 E= -TFÀJMJSTF c = - C= -WFB= -PMVSj -40 66 ÖRNEK 15 ÖRNEK 19 OVNBSBM TBZGBEBO CBöMBZBO TBZGBML CJS LJUB \"MJhOJOLBUMEóCJSTOBWEBLJNZB NBUFNBUJL GJ[JL COTBZGBMBSOOVNBSBMBOESNBLJÀJOLBÀSBLBNLVM TPSVTVCVMVONBLUBES MBOMS \"MJhOJO IFS EFSTUFO FO B[ CJS TPSVZV DFWBQMBNö PM NBTJÀJOFOB[LBÀTPSVDFWBQMBNBMES ÷MLTBZGBJÀJO = 9 10 -TBZGBJÀJO &OÀPLTPSVZBTBIJQEFSTMFSJOTPSVMBSOBCJSFLMFOJS 100 -TBZGBJÀJO = 180 7 + 6 + 1 = 14 = 453 + 642 ÖRNEK 16 ÖRNEK 20 EFOZFLBEBSPMBOUÐNTBZMBSBõBóEBLJHJCJ YWFZSBLBNES x =wwwCJ¿JNJOEFZBOZBOBZB[MZPS 24 = y FöJUMJôJOJTBôMBZBOLBÀGBSLM Y Z JLJMJTJWBSES x #VOB HÌSF FMEF FEJMFO Y TBZTOO TPMEBO SBLB NLBÀUS 24 =y 72 5 j 72 - n 8643 UBOF 35 + 1 = 35 j n = 38 x 3468 1 $FWBQCVTBZOOCJSMFSCBTBNBôES ÖRNEK 17 ÖRNEK 21 C- 3a : [2a -C- B-C ] - a 7d^ - 5 hd 9 d - 4 = - 34 JGBEFTJOJOFOTBEFöFLMJOJCVMVOV[ :VLBSEBLJCPöLVUVDVLMBSBTSBTZMBIBOHJJöMFNMFS HFUJSJMNFMJEJS C- 3a : a - a =C- a -3 +, +, x 14. –40 15. 642 16. 8 17. CmBm 4 18. 36 19. 14 20. 4 21. Y
www.aydinyayinlari.com.tr 4\":*,·.&-&3÷#²-·/&#÷-.&3\"4:0/&-4\":*-\"3 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 22 ÖRNEK 25 3BLBNMBSGBSLMÑÀCBTBNBLMFOLÑÀÑLUBNTBZJMF \"CJSHFS¿FMTBZES SBLBNMBS GBSLM JLJ CBTBNBLM FO CÑZÑL UBN TBZOO A= 1 + a UPQMBNLBÀUS 4-a b+3 -987 + 98 = -891 PMEVôVOBHÌSF BWFCIBOHJEFôFSMFSJBMBNB[ Bâ Câ-3 ÖRNEK 23 18 8 ÖRNEK 26 10 14 CCJSJSSBTZPOFM BWFDJTFSBTZPOFMTBZMBSES B- C=D+ 1 6 PMEVôVOBHÌSF B+DLBÀUS a - 1 = 0 j c + 1 =ES a = 1 j c = -1 j a + c = 0 ôFLJMEFLJLVUVDVLMBSBIFSTBUSEB TÐUVOEBWFLËõFHFO- ÖRNEK 27 EFUPQMBNMBSBZOPMBOTBZMBSZFSMFõUJSJMFDFLUJS ,VUVDVLMBSB ZB[MNBT HFSFLFO FO CÑZÑL TBZ LBÀ a = 2b + 1 US b-3 = 18 PMEVôVOBHÌSF BOOIBOHJEFôFSJJÀJOCIFTBQMBOB NB[ ÖRNEK 24 BC- 3a =C+ 1 j a =JÀJO 3a + 1 YWFZUBNTBZMBSES -4 < x <Zâ C B- 2 ) = 3a + 1 j b = a-2 PMEVôVOB HÌSF Y - Z JGBEFTJOJO EFôFSJ FO ÀPL LBÀUS ÖRNEK 28 x = -WFZ= -BMOSTBDFWBQTGSCVMVOVS - 1 OJO UPQMBNBZB WF ÀBSQNBZB HÌSF UFSTMFSJOJO 2 UPQMBNLBÀUS 1 1 2 13 - Z -2 + = - 2 22 -2 22. –891 23. 18 24. 0 5 25. Bâ Câm 3 26. 0 27. 2 28. - 2
TEST - 1 4BZ,ÑNFMFSJ* 1. -3 + + 3 : [ 7 + - ] & 5. B+ C- ¿BSQNOEBIFSUFSJNBSUUSMS- JöMFNJOJOTPOVDVLBÀUS TBTPOV¿BSUNBLUBES \" # $ % #VOBHÌSF B+CUPQMBNLBÀUS \" # $ % & 2. -4, - WF TBZMBS JMF TBEFDF + ), ( - WF 6. x `;+ JÀJOBöBôEBLJMFSEFOIBOHJTJEBJNBCJS Y JöMFNMFSJOJ CJSFS LF[ LVMMBOMBSBL WF QBSBO SBTZPOFMTBZUBONMBNB[ UF[LVMMBONBEBOFMEFFEJMFCJMFDFLFOLÑÀÑL sa ZLBÀUS \" x + 1 # x - 1 $ 2x - 3 x2 x2 + 1 4x - 3 \" - # - $ - % & % x + 1 E 2x - 1 x2 - 4 1 - 4x 3. B C DWFYGBSLMQP[JUJGUBNTBZMBSWFYâEJS 7. BWFCUBNTBZMBSPMNBLÑ[FSF a2 +C2 +D2 = x 2a + 5b = 0 FöJUMJôJOJTBôMBZBOLBÀGBSLMYTBZTWBSES a + 2b + 4 JGBEFTJOEFCBöBôEBLJMFSEFOIBOHJTJPMBNB[ \" # $ % & \" # $ % & 8. 5BNTBZPMBO x - 2 TBZTOO¿BSQNBZBHËSF 4x + 3 UFSTJEFCJSUBNTBZES 4. B C D E FWFGCJSCJSJOEFOGBSLMSBLBNMBSPM #VOB HÌSF Y JO BMBCJMFDFôJ EFôFSMFS UPQMBN LBÀUS NBLÑ[FSF \" - 28 # - 5 $ - 7 BC+DE+ e . f 15 3 12 JGBEFTJOJOFOLÑÀÑLEFôFSJLBÀUS % - 1 & - 1 \" # $ % & 4 3 1. C 2. # 3. # 4. A 6 5. A 6. D 7. C 8. A
4BZ,ÑNFMFSJ* TEST - 2 1. x, y `/PMNBLÑ[FSF 5. B CWFDGBSLMSBLBNMBSES YZ+ 18 =Z 2a -C=C-D FöJUMJôJOJTBôMBZBOLBÀUBOF Y Z JLJMJTJWBSES FöJUMJôJOF HÌSF LBÀ GBSLM B C D TSBM ÑÀMÑTÑ \" # $ % & WBSES \" # $ % & 2. BWFCQP[JUJGUBNTBZMBS B<EJS 6. YCJSEPóBMTBZES 2a +C= 57 5x + 3 x -1 PMEVôVOBHÌSF CTBZTOOFOLÑÀÑLEFôFSJLB JGBEFTJOJOCJSUBNTBZPMEVôVCJMJOEJôJOFHÌSF US Y TBZTOO BMBDBô GBSLM EFôFSMFS UPQMBN LBÀ US \" # $ % & \" # $ % & 3. TBZGBMLCJSLJUBCOTBZGBMBSEFOCBöMBZB 7. Y Z [WFUCJSCJSJOEFOGBSLMQP[JUJGUBNTBZMBSES SBL OVNBSBMBOEôOEB LBÀ UBOF SBLBN LVMMB x = 6 =t OMS yz \" # $ % & PMEVôVOBHÌSF UOJn FOCÑZÑLEFôFSJJÀJOYJO FOLÑÀÑL EFôFSJLBÀUS \" # $ % & 4. B CWFDEPóBMTBZMBSES 8. BWFCUBNTBZMBSES 4a +C+D= 38 2 + 3 =1 FöJUMJôJOJTBôMBZBODTBZMBSOOFOCÑZÑLEFôF ab SJJMFFOLÑÀÑLEFôFSJOJOGBSLLBÀUS PMEVôVOB HÌSF C UBN TBZMBSOO UPQMBN LBÀ US \" # $ % & \" # $ % & 1. D 2. C 3. E 4. E 7 5. E 6. C 7. C 8. D
TEST - 3 4BZ,ÑNFMFSJ* 1. YWFZUBNTBZMBSES 5. ·ÀUBOFTJUBOCÑZÑLPMBOGBSLMEPôBMTBZ 1<x<6 OO UPQMBN PMEVôVOB HÌSF FO CÑZÑL TBZ FOÀPLLBÀUS 2 <Z< 9 \" # $ % & x+y a= x PMEVôVOBHÌSF BLBÀGBSLMUBNTBZEFôFSJBMS \" # $ % & 2. BWFCUBNTBZMBSES 6. 3BLBNMBS CJSCJSJOEFO GBSLM ÑÀ CBTBNBLM EÌSU -6 # a < 8 GBSLMTBZOOUPQMBNPMEVôVOBHÌSF CVTB -8 #C< - 4 ZMBSEBOFOCÑZÑôÑ FOB[LBÀUS #VOB HÌSF B2 - C2 JGBEFTJOJO BMBCJMFDFôJ FO LÑÀÑLEFôFSLBÀUS \" # $ % & \" - # - $ - % & 3. B CWFDCJSFSUBNTBZES 7. 5FSTUFOZB[MõMBSLFOEJTJJMFBZOPMBOTBZMBSB 3a -C= 0 1\"-÷/%30.÷,4\":*-\"3BEWFSJMJS BCD= 48 ±SOFóJO PMEVôVOB HÌSF D OJO BMBCJMFDFôJ LBÀ GBSLM EF 121 ôFSWBSES 23532 \" # $ % & 130013 4. #JSCJSJOEFOGBSLM ÑÀCBTBNBLMTBZOOUPQMB CJSFSQBMJOESPNJLTBZES NPMEVôVOBHÌSF CVTBZMBSOFOCÑZÑ 3BLBNMBSUPQMBNPMBOÑÀCBTBNBLMLBÀUB ôÑ FOB[LBÀUS OF1BMJOESPNJLTBZWBSES \" # $ % & \" # $ % & 1. A 2. A 3. # 4. C 8 5. E 6. C 7. C
4BZ,ÑNFMFSJ* TEST - 4 1. LJõJMJLCJSHSVQCJSPUFMEFLPOBLMBZBDBLUS 4. 0 2 2 0UFMEF EÌSEFS WF CFöFS ZBUBLM PEBMBS PMEVôV õFLJMEFLJTBZEPôSVTVJMFWFSJMFOLBQBMBSBML OBHÌSF CVHSVCVZFSMFöUJSNFLJÀJOIJÀCJSZBUBL UBLBÀUBOFTBZNBTBZTWBSES CPöLBMNBNBLÑ[FSFFOB[LBÀPEBHFSFLJS \" # $ % & \" # $ % & 2. EËOEÐSÐMEÐóÐOEFEFóFSJEFóJõNFZFOTBZMB- 5. BWFCTBZNBTBZMBSWF< a <EJS SB 4530#0(3\".\"5÷,4\":*-\"3 BEWFSJMJS #JSCJSJOEFOGBSLMB C TBZMBSTBZ ±SOFóJO EPóSVTVÐ[FSJOEFZFSMFõUJSJMEJóJOEFCTBZTPSUBODB TBZES 96 #VOB HÌSF B TBZTOO BMBCJMFDFôJ LBÀ EFôFS 1691 WBSES 61019 \" # $ % & TBZMBSTUSPCPHSBNBUJLË[FMMJóJUBõS #VOBHÌSF JLJCBTBNBLMCJSTUSBCPHSBNBUJLTB ZOO SBLBNMBS UPQMBN BöBôEBLJMFSEFO IBOHJ TJPMBCJMJS \" # $ % & 3. B CWFDOFHBUJGUBNTBZMBSES 6. BQP[JUJGUBNTBZES A= 3 + 4 + 6 #JSËóSFODJ-a -JMFB+BSBTOEBLJUBNTBZMB- abc SO¿BSQNOOUPQMBNOEBOFLTJLPMEVóVOVCV- MVZPS PMEVôVOB HÌSF \" FO CÑZÑL UBN TBZ EFôFSJOJ BMEôOEBB+C+DUPQMBNLBÀPMVS #VOBHÌSF BTBZTLBÀUS \" - # - $ - % - & -1 \" # $ % & 1. D 2. A 3. A 9 4. E 5. D 6. D
·/÷7&34÷5&:&)\";*3-*, 2. MODÜL 4\":*,·.&-&3÷#²-·/&#÷-.&3\"4:0/&-4\":*-\"3 www.aydinyayinlari.com.tr 4\":*,·.&-&3÷** 5FLWF¦JGU4BZMBS ÖRNEK 4 7$1,0%m/*m B CWFDCJSFSUBNTBZ b . c - 8 = 2a + 4 OCJSUBNTBZPMNBLÐ[FSF 7 ¥JGUTBZMBS- O 5FL4BZMBS- O- PMEVôVOB HÌSF BöBôEBLJMFSEFO IBOHJTJ LFTJOMJLMF EPôSVEVS T±T=Ç T±Ç=T DZÇ=Ç Ç±T=T \" BUFL CWFD¿JGU T.T=T T.Ç=Ç # DUFLTBZ $ BWFC¿JGU Ç.Ç=Ç Ç.T=Ç % CWFDEFOFOB[CJSJUFL & CWFDEFOFOB[CJSJ¿JGU TO = T , ÇO =¥ O`/+ a0 = Bá ÖRNEK 1 CD= 8 + 7 . 2(a + 2) CD=ÀJGUj$FWBQ&PMVS \"öBôEBLJMFSEFOLBÀUBOFTJUFLTBZES I. 88 + 77 + 66 II. 3792 - 15143 III. 51998 . 61996 IV. 15 . 57 . 96 ÖRNEK 5 4BEFDF*UFLTBZES YCJSUBNTBZPMNBLÑ[FSF BöBôEBLJMFSEFOIBOHJTJ EBJNBUFLTBZES \" Y- Y+ # Y2 + x + 4 ÖRNEK 2 $ Y2 -Y % Y3 - x2 + 5 B m CJS UFL TBZ JTF BöBôEBLJ JGBEFMFSJO IBOHJMF & Y+ Y- SJUFLTBZES I. B+ II. B+ $FWBQ%öLLESYZFSJOFUFLWFZBÀJGUTBZZB[NBLJGB III. B- B- IV. aa + 1 EFOJOUFLPMVöVOVCP[NB[ a -UFLJTFBÀJGUTBZES#VOBHÌSF TBEFDF*UFLTB ÖRNEK 6 ZES Y WF Z QP[JUJG UFL TBZMBS PMNBL Ñ[FSF BöBôEBLJMFS ÖRNEK 3 EFOIBOHJTJÀJGUTBZES B CWFDEPôBMTBZMBSWFB+C+DÀJGUTBZPMEVôV \" Y2 + 5x + # YxZ $ YZ OBHÌSF BöBôEBLJJGBEFMFSEFOIBOHJMFSJEPôSVEVS I. BWFCUFLJTFD¿JGUUJS % YZ YZ & YZ +Zx + 9 II. BWFC¿JGUJTFD¿JGUUJS III. BUFLJTFC+D¿JGUUJS $FWBQ & EJS YZ WF Zx + 9 UFL TBZES UPQMBNMBS ÀJGU IV. CWFDUFLJTFB-CUFLUJS PMVS 4BEFDF***ZBOMöUSBUFLJTFC+DÀJGUPMBNB[ 1. 1 2. I 3. I, II, IV 10 4. E 5. D 6. E
www.aydinyayinlari.com.tr 4\":*,·.&-&3÷#²-·/&#÷-.&3\"4:0/&-4\":*-\"3 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, %m/*m ÖRNEK 9 1P[JUJGTBZMBSOUÐNLVWWFUMFSJQP[JUJGUJS B CWFDQP[JUJGUBNTBZMBSPMNBLÑ[FSF a > 0 ise aO > 0 a2 b3 - c2 = c2 2 /FHBUJGTBZMBSO¿JGULVWWFUMFSJQP[JUJG UFLLVW- WFUMFSJOFHBUJGUJS FöJUMJôJ JÀJO BöBôEBLJMFSEFO IBOHJTJ EBJNB EPôSV a <WFO¿JGUJTFBO > 0 EVS a <WFOUFLJTFBO < 0 \" a vFCUFLJTFD¿JGUUJS ÖRNEK 7 # BC¿JGUJTFDUFLUJS $ BUFLC¿JGUJTFDUFLUJS B QP[JUJG UFL TBZ PMEVôVOB HÌSF BöBôEBLJMFSEFO % D¿JGUCUFLJTFBUFLUJS LBÀUBOFTJEBJNBÀJGUUJS & B¿JGUCUFLJTFD¿JGUUJS I. 2a2 + a + 1 a2C3 - c2 = 2c2 II. B+ 2 + 5 a2C3 = 3c2 Z& BÀJGU CUFLJTFDÀJGU III. aa + 1 - B+ a ¦5 ¦ I. 2a2 + a + 1 =¦+ T + T =¦ ÖRNEK 10 ÖRNEK 8 B CWFDTBZNBTBZMBSES abc - 5ab = 2b B CWFDQP[JUJGUBNTBZMBSPMNBLÑ[FSF c 3a + b = 4 FöJUMJôJOF HÌSF BöBôEBLJMFSEFO IBOHJTJ LFTJOMJLMF c ZBOMöUS PMEVôVOBHÌSF BöBôEBLJMFSEFOIBOHJTJ EBJNB EPô \" B CWFDUFL # BWFCUFL D¿JGU SVEVS $ BUFL CWFD¿JGU % B¿JGU CWFDUFL \" BC¿JGUUJS # BCUFLUJS $ a UFLUJS & B CWFD¿JGU b % B+C¿JGUUJS & BmCUFLUJS #LFTJOMJLMFZBOMö BCD-BC=CD 3a +C= 4c Z a +C=ÀJGU TT a.b^ c - 5 h = 2bc .. ¦¦ T T çift ise tektir. 7. 1 8. D 11 9. E 10. E
·/÷7&34÷5&:&)\";*3-*, 2. MODÜL 4\":*,·.&-&3÷#²-·/&#÷-.&3\"4:0/&-4\":*-\"3 www.aydinyayinlari.com.tr ÖRNEK 11 \"SEöL4BZMBS B¿JGUEPóBMTBZES %m/*m a2006 +C2007 1FõQFõFPMBOMBSBSBTOEBLJGBSLBZOPMBOTBZ- MBSB\"SEöL4BZMBSEFOJS TBZT UFL EPôBM TBZ PMEVôVOB HÌSF BöBôEBLJMFS Terim Say›s› = Son Sayı - ‹lk Sayı +1 EFOIBOHJTJÀJGUTBZES Ortak Fark \" B3 -C # B+ C-B $ C2 -C Terim Say›s› Toplam = ( ‹lk Sayı + Son Sayı ) % C3 B+ & B-C 2 BÀJGU CUFLPMBDBLUS$öLLOEBC2 -C= T - T =¦ n (n + 1) PMVS 1 + 2 + 3 + ... +O= 2 2 + 4 + 6 + ... + O =O O+ 1 + 3 + 5 + ... + O- =O2 ÖRNEK 12 ÖRNEK 14 a2UFLUBNTBZPMNBLÑ[FSF \"öBôEBLJUPQMBNMBSIFTBQMBZO[ I. a4 +¿JGUTBZES II. a2 -QP[JUJG¿JGUTBZES a) 1 + 2 + 3 + ... + 25 C 1 + 3 + 5 + ..... + 43 III. a6 +QP[JUJGUFLTBZES c) 2 + 4 + 6 + ..... + 64 E 5 + 8 + 11 + 14 + .... + 77 JGBEFMFSJOEFOIBOHJMFSJLFTJOMJLMFEPôSVEVS 25 . 26 Z = 222 = 484 I. a4 + 1 = T + T =¦ a) = 325 II. a2 - 1 Za = 1 V a = -JTFTPOVÀTGS III. a2UFLJTFB6 + 4 = T +¦= T 2 C O- 1 = 43 Zn = 22 c) 2n = 64 Zn = 32 Z 1056 E 54= 77 - 5 + 1 = 25 Z5PQ= 25 ( 5+77 ) = 1025 32 ÖRNEK 15 1P[JUJGJLJCBTBNBLMGBSLMTBZOOUPQMBNOOFO LÑÀÑLEFôFSJLBÀUS ÖRNEK 13 4BZMBSFOLÑÀÑLTFÀJMNFMJ \"WF$¿JGUTBZ #UFLTBZPMNBLÐ[FSF Son sayı - 10 \" # $LPöVMVOVTBôMBZBOLBÀUBOFÑÀCBTBNBL M\"#$EPôBMTBZTZB[MBCJMJS + 1 = 12 Z4POTBZ= 21 1 5PQMBN= 21 ( 10 + 21 ) = 6 . 31 = 186 2 A <#< C ¦ 5¦ ÖRNEK 16 23 4, 6, 8 Z 3 \"SEöL ÀJGU EPôBM TBZOO UPQMBN PMEVôVOB HÌSF CVOMBSOFOLÑÀÑôÑLBÀUS 25 6, 8 Z 2 45 6, 8 Z 2 27 8Z1 47 8Z1 67 8Z1 660 44 - ilk sayı EFôFSCVMVOVS = 44 \" + 1 = 8 \" ? = 30 15 2 11. C 12. *WF***13. 10 12 14. B C D E 15. 186 16. 30
www.aydinyayinlari.com.tr 4\":*,·.&-&3÷#²-·/&#÷-.&3\"4:0/&-4\":*-\"3 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 17 ÖRNEK 22 B CWFDBSEõLQP[JUJGUBNTBZMBSES 4BZMBSO CÐZÐLMÐóÐ LBEBS OPLUB ZBSENZMB CJS пHFO PMVõUVSBCJMFO TBZMBSB ·ÀHFO ZB EB ·ÀHFOTFM TBZMBS a <C<DWFf 1 - 1 p f 1 - 1 p f 1 - 1 p = 14 BEWFSJMJS a b c 17 PMEVôVOBHÌSF BTBZTLBÀUS a - 1 b - 1 c - 1 14 . . = \" a = 15 a b c 17 ÖRNEK 18 :VLBSEBLJ õFLJMEF TBZTOO CJS пHFOTFM TBZ PMEV- óVHËSÐMNFLUFEJS 2n +WFO-TBZMBSBSEöLJLJUFLUBNTBZPM EVôVOBHÌSF OOJOBMBDBôEFôFSMFSUPQMBNLBÀUS \"ZSDBпHFOTBZMBS 2n + 1 - ( 3n - 7 ) = -n + 8 = 2 Zn = 6 1+2+3+...+n = n^n+1h , n! N (3n - 7) - ( 2n + 1 ) = n - 8 = 2 Zn = 10 Z = 16 2 ÖRNEK 19 FõJUMJóJJMFEFFMEFFEJMFCJMJS \"SEöLÑÀEPôBMTBZOOÀBSQNPMEVôVOBHÌSF (ÐOFõ NBUFNBUJLEFSTJOEFCJOPNLBUTBZMBSOLVMMBOB- UPQMBNMBSLBÀUS SBLPMVõUVSVMBO1BTDBM¶¿HFOJZBSENZMBO`/ Y+Z O B¿MNOEBLJLBUTBZMBSCVMBCJMFDFóJOJËóSFOJZPS 210 = 21 . 10 = 7.83.2 .5 =PMVQ+ 6 + 5 = 18 6 CVMVOVS ÖRNEK 20 123 \"SEöLJLJÀJGUTBZOOLBSFMFSJGBSLPMEVôVOBHÌ SF CVTBZMBSOUPQMBNMBSFOÀPLLBÀUS 2 x2 - y2 =JTF Y+ y )( x - y ) = 84 x + y = 42 ÖRNEK 21 (ÑOFö Y + y )8 BÀMNOEBLJ LBUTBZMBS 1BTDBM ÑÀ HFOJ PMVöUVSBSBL CVMNBL JÀJO LBÀ UBOF TBZ LVMMBO \"SEöLEÌSUUFLTBZOOUPQMBNNPMEVôVOBHÌSF FO NBMES CÑZÑLTBZOONUÑSÑOEFOFöJUJOFEJS 9.10 TBZTBZ-TBZTBZ = 45 2 Z Z Z m m1 m3 ++ 4 42 42 m+6 ?= 4 17. 15 m+6 13 22. 45 18. 16 19. 18 20. 42 21. 4
TEST - 5 4BZ,ÑNFMFSJ** 1. YWFZCJSFSUBNTBZES 4. Y ZWF[HFSÀFMTBZMBS -Y Z- YZ= Z[2 > Z+ z3 < 0 JöMFNJOJO TPOVDV ÀJGU TBZ JTF BöBôEBLJMFSEFO PMEVôVOB HÌSF Y Z WF [ OJO EPôSV TSBMBOö IBOHJTJEBJNBUFLTBZES BöBôEBLJMFSEFOIBOHJTJEJS \" Zx # Y+Z $ Y+Z \" [<Z<Y # [< x <Z $ Y<Z< z % YZ- & Y2 +Z % Y< z <Z & Z< x < z 2. YWFZCJSFSUBNTBZES 5. 50 - 1 + 48 - 3 + ... + 2 - 49 & ( 3x - CJSÀJGUTBZWF Z2 + CJSUFLTBZPM EVôVOBHÌSF JöMFNJOJOTPOVDVLBÀUS \" # $ % * YZ-Z II. 4x -Z III. 3x +Z- 4 JGBEFMFSJOEFOIBOHJMFSJEBJNBUFLTBZES \" :BMO[* # :BMO[** $ :BMO[*** 6. 1 . 1 + 1 . 1 + . . . + 1 . 1 34 45 101 102 % **WF*** & * **WF*** JöMFNJOJOTPOVDVLBÀUS \" 9 # 11 $ 31 35 34 100 % 41 & 43 101 102 3. a < C < 0 < D PMEVôVOB HÌSF BöBôEBLJMFSEFO 7. \"SEöLÀJGUTBZOOUPQMBNPMEVôVOBHÌ IBOHJTJEBJNBQP[JUJGUJS SF CV TBZMBS LÑÀÑLUFO CÑZÑôF TSBMBOEôOEB ( - TBZTCBöUBOLBÀODTSBEBES \" b - c # a - b $ c - a c-a c-b b \" # $ % & % a + b & c c b-a 1. D 2. C 3. E 14 4. # 5. C 6. # 7. C
4BZ,ÑNFMFSJ** TEST - 6 1. BWFCUBNTBZMBSES 5. YCJSEPóBMTBZES a = 5 -CPMEVôVOBHÌSF 1 - x + x2 - x3CJSUFLTBZPMEVôVOBHÌSF I. aCUFLTBZ * BQP[JUJGUBNTBZJTFYa + x II. a -C$ 0 ** BQP[JUJGUBNTBZJTFYa + 2 *** C< 0 ise a > 0 *** BQP[JUJGUBNTBZJTFBx - x JGBEFMFSJOEFOIBOHJMFSJEBJNBEPôSVEVS JGBEFMFSJOEFOIBOHJMFSJEBJNBÀJGUTBZES \" :BMO[* # :BMO[** $ :BMO[*** \" :BMO[* # :BMO[** $ :BMO[*** % *WF*** & * **WF*** % *WF** & **WF*** 6. B C DWFEUBNTBZMBSWFDJMFETGSEBOGBSLMES a <C< 0 <D+E 2. B CWFDHFS¿FMTBZMBSES PMEVôVOBHÌSF BöBôEBLJMFSEFOIBOHJTJEBJNB EPôSVEVS C2D3 > 0 a3D< 0 BC< 0 \" a2. b + c < 0 # b2. c + d < 0 d2 a2 PMEVôVOBHÌSF B CWFDOJOJöBSFUMFSJTSBTZMB IBOHJTJEJS $ c2. d + a < 0 % d2. a + b < 0 b2 c2 \" -, -, - # +, +, + $ +, +, - % +, -, + & -, +, + & a2. b + d < 0 c2 3. B CWFDBSEöLUFLTBZMBSPMNBLÑ[FSF 7. B CWFDBSEõL¿JGUTBZMBSES a <C<DJÀJO a <C<DPMEVôVOBHÌSF b + c JöMFNJOJOTPOV a B-D C-D B-C DVOVOFOLÑÀÑLQP[JUJGUBNTBZEFôFSJLBÀUS ÀBSQNBöBôEBLJMFSEFOIBOHJTJOFUBNCÌMÑOF NF[ \" # $ % & \" # $ % & 8. B CWFDQP[JUJGUBNTBZMBSES a.b - 3 = 2b c 4. -10 - 7 - 4 - 1 + 2 + 5 + .... + 41 PMEVôVOBHÌSF BöBôEBLJMFSEFOIBOHJTJEPôSV EVS UPQMBNOOTPOVDVLBÀUS \" # $ % & \" BUFL C¿JGU # BUFL CUFL $ CUFL D¿JGU % CUFL DUFL & BUFL DUFL 1. D 2. E 3. C 4. D 15 5. D 6. D 7. C 8. #
TEST - 7 4BZ,ÑNFMFSJ** 1. OCJSUBNTBZES 4. \"SEõLпUBNTBZOO¿BSQNOBPSUBEBLJTBZFL- 1 + 3 + 5 ... +O- 1 MFOJODFFMEFFEJMFOTBZ\"WF\"OOSBLBNMBSUPQMB- JöMFNJOJOTPOVDVCJSÀJGUTBZPMEVôVOBHÌSF O N#TBZTES TBZTOO FOLÑÀÑLJLJCBTBNBLMEFôFSJLBÀUS \" TBZT ÑÀ CBTBNBLM FO LÑÀÑL EFôFSJOJ BME \" # $ % & ôOEB * \"UFLTBZES ** #UFLTBZES *** \"+#UFLTBZES JGBEFMFSJOEFOIBOHJMFSJEBJNBEPôSVEVS \" :BMO[* # :BMO[** $ :BMO[*** % *WF*** & **WF*** 2. B C DWFEUBNTBZMBSES 5. ôFLJMEF PLMBSO CBõMBOH¿ OPLUBMBSOEBLJ TBZMBSO a <C< 0 <D<E UPQMBNPLMBSOCJUJõOPLUBTOEBLJTBZZBFõJUUJS abcd PMEVôVCJMJOEJôJOFHÌSF I. c > d ef k ba ** C- a >E-D xy *** BE<CD JGBEFMFSJOEFOIBOHJMFSJEBJNBEPôSVEVS 80 B C DWFEBSEöLUFLTBZMBSWFB<C< c <E \" :BMO[* # :BMO[** $ :BMO[*** PMEVôVOBHÌSF B+F+YLBÀUS % *WF** & **WF*** \" # $ % & 6. B CWFDUBNTBZMBSES a2 +C< 0 C3 +D> 0 3. 3 - 5 + 7 - 8 + . . . + 47 - 38 PMEVôVOBHÌSF BöBôEBLJMFSEFOIBOHJTJEPôSV 2323 23 PMBCJMJS JöMFNJOJOTPOVDVLBÀUS \" B<C<D< # C< a < 0 <D \" - 21 # 43 $ % & $ D< 0 < a <C % D<C< 0 < a 13 16 & C<D< 0 < a 1. # 2. C 3. C 16 4. D 5. D 6. #
4BZ,ÑNFMFSJ** TEST - 8 1. BWFCUBNTBZMBSES 4. \"õBóEB QP[JUJG BSEõL ¿JGU UBN TBZMBS IFS TBUSB 4a +C=PMEVôVOBHÌSF TBUSOVNBSBTLBEBS¿JGUTBZ TSBEBLJ¿JGUTBZEBO CBõMBZBSBLZB[MZPS * BC# 0 II. a +COJOBMBDBóEFóFSMFSBSEõLUBNTBZMBS- TBUS 2 TBUS 4, 6 ES TBUS 8, 10, 12 *** BTBZTFOLпÐLQP[JUJGEFóFSJBMEóOEBCTB- TBUS 14, 16, 18, 20 ZTFOCÐZÐLOFHBUJGEFóFSJOJBMS #VOBHÌSF TBUSOTPOVOBHFMJOEJôJOEFZB[ MBOTPOTBZJMFCFSBCFSZB[MBOTBZMBSOUPQMB JGBEFMFSJOEFOIBOHJMFSJEBJNBEPôSVEVS NLBÀUS \" :BMO[* # :BMO[** $ :BMO[*** % *WF** & * **WF*** \" # $ % & 2. \"SEõLJLJQP[JUJG¿JGUUBNTBZEBOLпÐLPMBOOCFõ LBUJMFCÐZÐLPMBOOEËSULBUOOUPQMBNEJS #VOBHÌSF CÑZÑLTBZLBÀUS \" # $ % & 3. B CWFDBSEöLQP[JUJGÀJGUUBNTBZMBSPMEVôVOB 5. \"JLJCBTBNBLMBTBMTBZWF#BTBMTBZES HÌSF NWFOTGSEBOGBSLMUBNTBZMBSPMNBLÐ[FSF r C =O+ 1 ve D = 2m I. 5a -C+DUFLTBZES r -#< C <\"WF-#< D <\" II. 5a -C-D + a -¿JGUTBZES CJMHJMFSJWFSJMJZPS III. 5a +C-D +D¿JGUTBZES #VOBHÌSF \"+#TBZTFOLÑÀÑLEFôFSJOJBME IV. 5a +DC+D¿JGUTBZES ôOEB D OJOBMBCJMFDFôJGBSLMUBNTBZEFôFS JGBEFMFSJOEFOIBOHJMFSJEBJNBEPôSVEVS C MFSUPQMBNLBÀUS \" :BMO[* # :BMO[** $ *WF*** \" - # - $ - % - & -28 % *WF*7 & * ** ***WF*7 1. D 2. D 3. D 17 4. D 5. E
·/÷7&34÷5&:&)\";*3-*, 2. MODÜL 4\":*,·.&-&3÷#²-·/&#÷-.&3\"4:0/&-4\":*-\"3 www.aydinyayinlari.com.tr 4\":*,·.&-&3÷*** #BTBNBL¦Ì[ÑNMFNF ÖRNEK 3 TANIM Y ZWF[CJSFSSBLBNES x + 1 =Z- 1 = z \"#$%EËSUCBTBNBLMTBZ A BC D LPõVMVOB VZHVO п CBTBNBLM GBSLM EPóBM TBZMBS ZB[- MZPS #JSMFS#BTBNBó 0) 0OMBS#BTBNBó ) a) ,BÀEPôBMTBZZB[MBCJMJS :Ð[MFS#BTBNBó 2) C :B[MBCJMFOFOCÑZÑLWFFOLÑÀÑLTBZOOGBSL #JOMFS#BTBNBó ) LBÀUS #BTBNBLMBSEBLVMMBOMBOSBLBNMBSTBZEFóFS- B Y ZWFZB[EFOCJSJOFCBLNBLZFUFSMJ EFôFSMFST MFSJEJS SBMPMVöVS x = 1, ... , 7 j x = 7 4BZ EFóFSJ JMF CBTBNBóO ¿BSQN CBTBNBL EFóFSJEJS C - 132 = 666 ¶¿ ZÐ[ PO JLJ TBZTOO ZÐ[MFS CBTBNBóOO ÖRNEK 4 TBZEFóFSJUÐS#BTBNBLEFóFSJEÐS #\"4\".\", ¦²;·.-&.& 4BZOO CBTBNBL YSBLBNMBSGBSLMCJSEPóBMTBZES EFóFSMFSJOJOUPQMBNES YTBZTOOSBLBNMBSÀBSQNPMEVôVOBHÌSF CB \"#$= 100.A +#+ C TBNBLTBZTFOÀPLLBÀPMBCJMJS ÖRNEK 1 3BLBNMBSGBSLMJLJCBTBNBLMFOCÑZÑLUBNTBZJMF 120 = 5! = 1, 2, 3, 4, 5 jCBTBNBLM ÑÀCBTBNBLMFOLÑÀÑLUBNTBZOOGBSLLBÀUS 98 - (-999) = 1097 ÖRNEK 2 ÖRNEK 5 3BLBNMBSUPQMBNPMBOEÌSUCBTBNBLM SBLBNMBS 3BLBNMBSGBSLM пCBTBNBLM EËSUGBSLMEPóBMTBZOO GBSLMFOCÑZÑLEPôBMTBZ SBLBNMBSUPQMBNPMBO UPQMBNES ÑÀCBTBNBLMSBLBNMBSGBSLMFOLÑÀÑLEPôBMTBZOO #VTBZMBSOFOCÑZÑôÑ FOÀPLLBÀUS UPQMBNLBÀUS 102 + 103 + 104 + x = 1186 TBZ x = 877 jY TBZ = 10169 1. 1097 2. 10169 18 3. B C 4. 5 5. 876
www.aydinyayinlari.com.tr 4\":*,·.&-&3÷#²-·/&#÷-.&3\"4:0/&-4\":*-\"3 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 6 ÖRNEK 10 #JSCJSJOEFO GBSLM ÑÀ CBTBNBLM ÑÀ EPôBM TBZOO öLJ CBTBNBLM BC TBZT SBLBNMBS ZFS EFóJõUJSJMJQ FMEF UPQMBNPMEVôVOBHÌSF CVTBZMBSOFOLÑÀÑôÑ FEJMFOTBZJMFUPQMBOODBTPOV¿PMVZPS FOGB[MBLBÀUS #V LPöVMB VZBO LBÀ GBSLM BC JLJ CBTBNBLM TBZT WBSES 643 214 214 215 j 213 BC+CB=JTF B+C = 88 213 214 216 a+b=8 01234567 j8 87654321 ÖRNEK 7 ÖRNEK 11 B CWFDGBSLMSBLBNMBSES ÷LJ CBTBNBLM BC TBZT SBLBNMBS UPQMBNOO LB B+C D= 22 UPMEVôVOBHÌSF CVLPöVMBVZBOLBÀUBOFJLJCBTB PMEVôVOBHÌSF FOLÑÀÑLBCDTBZTLBÀUS NBLMTBZZB[MBCJMJS (a +C D= 22 10a +C= 7a +C j4 [[[ a = 2b 1 5 2 = 152 1234 2468 ÖRNEK 8 ÖRNEK 12 BWFCCJSFSSBLBNES ·À CBTBNBLM BCD WF JLJ CBTBNBLM BC EPôBM TB a #C< 5 ZMBSOOUPQMBNJTF a +C+DUPQMBNLBÀUS LPöVMVOB VZHVO LBÀ GBSLM BC JLJ CBTBNBLM TBZT BCD+BC= 110a +C+ c = 280 WBSES [ [[ 2 5 5 j 12 a # C< 5 44 ÖRNEK 13 3 2 BCDпCBTBNBLMTBZT CBDпCBTBNBLMTBZTOEBO 1 jCUBOFBWBSES+ 3 + 2 + 1 = 10 GB[MBES ÖRNEK 9 #V LPöVMB VZBO LBÀ UBOF ÑÀ CBTBNBLM BCD TBZT ZB[MBCJMJS öLJCBTBNBLMCJSTBZOOSBLBNMBSZFSEFóJõUJSJMJSTF TB- ZOOEFóFSJBSUZPS BCD-CBD= 90 (a -C = 540 #VTBZOOSBLBNMBSGBSLOOQP[JUJGEFôFSJLBÀUS a–b=6 jUBOFj 3.10 = 30 CB-BC= 27 123 C- a) = 27 jC- a = 3 789 6. 213 7. 152 8. 10 9. 3 19 10. 8 11. 4 12. 12 13. 30
·/÷7&34÷5&:&)\";*3-*, 2. MODÜL 4\":*,·.&-&3÷#²-·/&#÷-.&3\"4:0/&-4\":*-\"3 www.aydinyayinlari.com.tr ÖRNEK 14 ÖRNEK 17 BBCCEËSUCBTBNBLM BBWFCCJLJCBTBNBLMTBZMBSES BWFDCJSFSSBLBNES BD+DB= 1111 BBCC= BB+CC PMEVôVOBHÌSF b LBÀUS PMEVôVOB HÌSF CV LPöVMB VZHVO LBÀ UBOF BD ÑÀ CBTBNBLMTBZTZB[MBCJMJS a 100aa +CC= 12.aa +CC a0c + c0a = 101(a + c) = 1111 jUBOF 88aa =CC a + c = 11 88 bb b 11 = aa & a = 8 23456789 98765432 ÖRNEK 15 ÖRNEK 18 YZ ZYWFYYJLJCBTBNBLMTBZMBSES C+D= 12 xy + yx = 5 PMEVôVOB HÌSF BC WF BD JLJ CBTBNBLM TBZMBSOO xx 3 UPQMBNFOÀPLLBÀUS PMEVôVOBHÌSF Y ZUPQMBNFOÀPL LBÀUS BC+ ac = 20a +C+ c = 20.9 + 12 = 192 11^ x + y h x + y y5y2 ÖRNEK 19 11x = x = 1 + x = 3 & x = 3 BCJLJCBTBNBLMTBZES j 6 + 9 = 15 BC=C2 LPöVMVOVTBôMBZBOLBÀGBSLMBCJLJCBTBNBLMTBZ ÖRNEK 16 TWBSES B CWFDSBLBNES #VLPöVMBVZBOSBLBNMBSTBEFDFWFES #BTBNBLÀÌ[ÑNMFNFTJZBQMNöI»MJ 25 = 52WF= 62 107 + a.104+C2 +D ÖRNEK 20 PMBOTBZZCVMVOV[ BC CBWFDJLJCBTBNBLMTBZMBSPMNBLÐ[FSF = 1.107+0.106+0.105+ a.104 + 0.103 + 0.103 +C2 + 0.10+c BC-CB=D =BCD PMEVôVOBHÌSF ( a . c -CD JGBEFTJOJOEFôFSJLBÀUS BC-CB= 5c j 9 (<a - b) = 55c 64 = c(a -C = 4.6 = 24 14. 8 15. 15 16. BCD 20 17. 8 18. 192 19. 2 20. 24
www.aydinyayinlari.com.tr 4\":*,·.&-&3÷#²-·/&#÷-.&3\"4:0/&-4\":*-\"3 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 21 ÖRNEK 25 ÷LJCBTBNBLMBCTBZTSBLBNMBSUPQMBNOOYLB B C D Y ZGBSLMSBLBNMBSWFBCD DCB YZпCBTB- UOB CBTBZTEBSBLBNMBSUPQMBNOOY-LBUOB NBLMTBZMBSES FöJUPMEVôVOBHÌSF YLBÀUS BCD - DCB = YZ PMEVôVOBHÌSF Y+ y + c +C+ a UPQMBNFOÀPL BC= 2x (a +C LBÀUS + CB= (3x - 4) (a +C BCD-DCB= 99 (a - c) = xy7 11 (a +C = (5x - 4) (a +C j x = 3 99 . 3 = 297 = 2 + 9 + 8 + 7 + 5 = 31 ÖRNEK 22 ÖRNEK 26 )FSCJSJCBTBNBLMTBZOOCJSMFSCBTBNBôOEBLJ BC JLJ CBTBNBLM TBZTOO TPMVOB TBóOB ZB[ME- SBLBNTBZTBMEFôFSJCÑZÑUÑMÑS POMBSCBTBNBôO óOEBFMEFFEJMFOEËSUCBTBNBLMTBZJMLTBZEBO EBLJSBLBNLÑÀÑMUÑMÑSWFTBEFDFUBOFTJOJOZÑ[ GB[MBES MFSCBTBNBôOEBLJSBLBNCÑZÑUÑMÑSTFCVTBZOO #VOBHÌSF BCJLJCBTBNBLMTBZTLBÀUS UPQMBNOEBLJEFôJöJNOFEJS BC=BC+ 1209 BCD+ 7 - 140 + 300 =BCD+ 167 1002 +BC=BC+ 1209 BC= 207 jBC= 23 ÖRNEK 23 ÖRNEK 27 B CWFDTGSEBOWFCJSCJSJOEFOGBSLMSBLBNMBSES \"#$ п CBTBNBLM CJS TBZES .FINFU IFTBQ NBLJOF- TJJMF #V SBLBNMBSMB ZB[MBCJMFDFL UÑN ÑÀ CBTBNBLM TB ZMBSO UPQMBN BöBôEBLJMFSEFO IBOHJTJOF LFTJOMJL \"#$ MF CÌMÑOÑS JõMFNJOJ ZBQNBL JTUJZPS 'BLBU BS[BM PMBO IFTBQ NBLJ- \" # $ % & OFTJ\"SBLBNZFSJOFGB[MBTO #WF$SBLBNMBSZFSMF- SJOFJLJõFSFLTJLMFSJOJZB[ZPS )FSSBLBNöBSLF[GBSLMCBTBNBLMBSEBCVMVOBCJMJS²S OFôJOZJJODFMFZFMJN 1 87 8 7 87 ++ \"2, \"2, \"2, BCDMFSJOUPQMBN (a +C+ c) = 3.37.23.7 (a +C+ c) JTF = 37.7 = 259 ÖRNEK 24 #VOBHÌSF .FINFUhJOCVMNBLJTUFEJôJTPOVÀJMFCVM EVôVTPOVDVOGBSLOONVUMBLEFôFSJLBÀUS B CWFDQP[JUJGUBNTBZMBS BWFBCJLJCBTBNBL MTBZMBSWFB+BC=PMEVôVOBHÌSF BCBöB 10 [100 (A + 1) + #- 2) + (C - 2)] = [\"#$+ 78] . 10 ôEBLJMFSEFOIBOHJTJEJS =\"#$+ 780 =GB[MB 20 + a + 10a +C= 90 11a +C= 70 j 64 21. 3 22. BSUBS23. #24. 24 21 25. 31 26. 23 27. 780
·/÷7&34÷5&:&)\";*3-*, 2. MODÜL 4\":*,·.&-&3÷#²-·/&#÷-.&3\"4:0/&-4\":*-\"3 www.aydinyayinlari.com.tr ÖRNEK 29 ÖRNEK 32 BCDEEËSUCBTBNBLMCJSTBZWFYHFS¿FMTBZES \"# :BOEBLJUPQMBNBJöMFNJOEFIFSIBSGGBSL + $% MCJSSBLBNHÌTUFSEJôJOFHÌSF a . x = 2, 124 _ b % A +#+ C +%UPQMBNLBÀUS b . x = 3, 17 b ` c . x = 7, 3 bb d . x = 17 a 7 PMEVôVOB HÌSF BCDE Y ÀBSQNOO TPOVDVOV CV AB5 8 j MVOV[ 7 + C3D 8 D13 BCDEY= 1000ax +CY+ 10cx +EY ÖRNEK 33 = 2124 + 317 + 73 + 17 = 2531 )FSIBSGGBSLMSBLBNHÌTUFSNFLÑ[FSF ab2 ZBOEBLJ UPQMBNB JöMFNJOF HÌSF B C D + cab ÀBSQNLBÀUS 906 ÖRNEK 30 4 4 x >Z YZZWFZYYпCBTBNBLMTBZMBSES 6 ab2 2 + cab YZZ+ZYY= 1443 PMEVôVOBHÌSF ZB[MBCJMFDFLJLJCBTBNBLMYZTBZ 906 MBSLBÀUBOFEJS ÖRNEK 34 111(x + y) = 1443 x + y = 13 xyz I :BOEBLJ¿BSQNBJõMFNJ*7TBUSZBO- 94 x II MõMLMBCJSCBTBNBLTBóBLBZESMBSBL 85 III ZBQMNõUS 76 abc UBOF IV #VOBHÌSF EPôSVTPOVÀLBÀUS + def abc = xyz.3 j 610 =YZ[jYZ[= 122 = 122.23 = 2806 def = xyz.2 ÖRNEK 31 ÖRNEK 35 aab :BOEBLJ¿LBSNBJõMFNJOEFBWFCCJSFSSB- a7 :BOEBLJ ÀBSQNB JöMFNJOF HÌSF Y – bba LBNES x CD LBÀUS rr + rr #VOBHÌSF B+CFOÀPLLBÀUS 7x5 BBC-CCB= 545 a7 5 109 (a -C = 545 j a -C= 5 4 85 j (a +C NBY = 9 + 4 = 13 x bc 68 + 7x5 6 29. 2531 30. 3 31. 13 22 32. 22 33. 48 34. 2806 35. 6
4BZ,ÑNFMFSJ*** TEST - 9 1. ·À CBTBNBLM SBLBNMBS BTBM WF GBSLM PMBO FO 5. 5PQMBNMBS PMBO BTBM SBLBNMBSO ÀBSQNMBS CÑZÑL ÀJGU UBN TBZ JMF JLJ CBTBNBLM FO LÑÀÑL FOÀPLLBÀUS ÀJGUUBNTBZOOUPQMBNLBÀUS \" # $ % & \" # $ % & 2. B CWFDCJSFSSBLBNES 6. B CWFDCJSFSSBLBNES a <C< 5 <D< 8 a+b = 4 = b+c 3c4 PMEVôVOBHÌSF ÑÀCBTBNBLMLBÀGBSLMBCDEP ôBMTBZTWBSES PMEVôVOB HÌSF CV SBLBNMBS LVMMBOMBSBL ZB[ MBCJMFOÑÀCBTBNBLMTBZMBSLBÀUBOFEJS \" # $ % & \" # $ % & 3. 3BLBNMBSÀBSQNUFLTBZPMBOLBÀUBOFJLJCB 7. ÷LJCBTBNBLMÑÀEPôBMTBZOOUPQMBNPM TBNBLMEPôBMTBZWBSES EVôVOBHÌSF CVTBZMBSOFOCÑZÑôÑLBÀGBSLM EFôFSBMBCJMJS \" # $ % & \" # $ % & 4. BCDSBLBNMBSGBSLMпCBTBNBLMEPóBMTBZMBSES 8. BCDEEËSUCBTBNBLMWFBCJLJCBTBNBLMTBZMBSES #VOBHÌSF C-DGBSLFOÀPLPMBOLBÀGBSLM BC 2 =D2 +E2 BCDTBZTZB[MBCJMJS PMEVôVOB HÌSF BCDE TBZT LBÀ GBSLM EFôFS \" # $ % & BMS \" # $ % & 1. A 2. # 3. C 4. D 23 5. A 6. # 7. # 8. A
TEST - 10 4BZ,ÑNFMFSJ*** 1. 3BLBNMBS TGSEBO GBSLM ÑÀ CBTBNBLM CJS TB 5. \"#$ #$\"WF##0пCBTBNBLMEPóBMTBZMBSES ZOO POMBS WF ZÑ[MFS CBTBNBôOEBLJ SBLBNMBS \"#$+#$\"-##0= 224 ZFSEFôJöUJSJMEJôJOEFFMEFFEJMFOZFOJTBZJMFFT PMEVôVOBHÌSF \"#JLJCBTBNBLMTBZTOO FO LJTBZBSBTOEBLJGBSLFOÀPLLBÀPMBCJMJS LÑÀÑLEFôFSJLBÀUS \" # $ % & \" # $ % & 2. #JSCJSMFSJOEFOGBSLMJLJCBTBNBLMÑÀEPôBMTB 6. \"#WF#\"JLJCBTBNBLMEPóBMTBZMBSPMNBLÐ[FSF ZOO UPQMBNOO BMBCJMFDFôJ LBÀ GBSLM EFôFS \"#-#\" WBSES GBSLCJSEPóBMTBZOOLBSFTJOFFõJUUJS \" # $ % & #VOB HÌSF CV LPöVMV TBôMBZBO LBÀ GBSLM \"# TBZTWBSES \" # $ % & 3. EFOBLBEBSPMBOEPóBMTBZMBSZBOZBOBZB[- 7. \"EËSUCBTBNBLMWF\"пCBTBNBLMTBZMBS- MBSBL ES \" TBZTFMEFFEJMJZPS #VOB HÌSF \" TBZTOO \" TBZT UÑSÑO #VOBHÌSF \"TBZTOO73MFSCBTBNBôOEBLJ EFOEFôFSJBöBôEBLJMFSEFOIBOHJTJEJS TBZLBÀUS \" \" + # \" + 504 \" # $ % & $ \" + % \" + 540E & \" + 504 4. ¶¿CBTBNBLM\"#$EPóBMTBZTOOJLJLBUOEBOPO- 8. \"#$пCBTBNBLMWF#$JLJCBTBNBLMTBZMBSES MBSCBTBNBóOOCBTBNBLEFóFSJ¿LBSMSTBTPOV¿ ABC = 51 PMVZPS BC #VOBHÌSF \"+#+$LBÀUS PMEVôVOBHÌSF \"+#+$BöBôEBLJMFSEFOIBO HJTJPMBNB[ \" # $ % & \" # $ % & 1. # 2. C 3. # 4. A 24 5. A 6. E 7. E 8. E
4BZ,ÑNFMFSJ*** TEST - 11 1. A = B ve B = C 5. \"#WF#\"JLJCBTBNBLMTBZMBSES 32 AB + A = 27 BA + B 17 LPöVMMBSOB VZHVO PMBSBL ZB[MBCJMFO ÑÀ CBTB PMEVôVOBHÌSF A +#LBÀUS NBLM\"#$TBZTOOSBLBNMBSUPQMBNLBÀUS \" # $ % & \" # $ % & 2. YZ[ п CBTBNBLM WF YZ JLJ CBTBNBLM CJSFS EPóBM 6. \"MJ CJS\"TBZTOOJMF¿BSQNBLJTUFSLFOZBOMõ- TBZES MLMBCJSMFSWFPOMBSCBTBNBóOOZFSMFSJOJEFóJõUJSF- YZ[+YZ= 235 SFLJõMFNZBQQTPOVDVGB[MBCVMVZPS YZ[= YZ +E #VOBHÌSF \"TBZTOOPOMBSWFCJSMFSCBTBNB FõJUMJLMFSJWFSJMJZPS ôOEBLJSBLBNMBSOGBSLLBÀUS #VOBHÌSF [+ELBÀUS \" # $ % & \" # $ % & 3. \"#$%EËSUCBTBNBLMEPóBMTBZMBSOPMVõUVSNBL 7. \" Y 0OMBS CBTBNBóOEBLJ SBLBNMBSO UPQMBN J¿JO CJSMFS CBTBNBóOEBLJ SBLBNMBSO UPQMBNOB FõJU PMBOBSEõLпEPóBMTBZEBOPSUBEBPMBOES r 4BEFDF SBLBNMBSLVMMBOMBDBLUS x #PMEVôVOBHÌSF YJOBMBCJMFDFôJLBÀGBSL r 3BLBNMBSCJSCJSJOEFOGBSLMES MEFôFSWBSES r \"+#= C +%EJS \" # $ % & LPõVMMBSWFSJMJZPS #VOBHÌSF \"#$%TBZMBSLÑÀÑLUFOCÑZÑôFT SBMBOEôOEB CBöUBO TBZ BöBôEBLJMFSEFO IBOHJTJEJS \" # $ % & 4. \"= 1017-WFSJMJZPS 8. \" :BOEBLJÀLBSNBJöMFNJOFHÌSF A +#LBÀUS #VOB HÌSF \" TBZTOO SBLBNMBS UPQMBN LBÀ – # US \" # $ % & \" # $ % & 1. D 2. C 3. C 4. # 25 5. D 6. A 7. # 8. A
TEST - 12 4BZ,ÑNFMFSJ*** 1. \"#JLJCBTBNBLMTBZMBSES 5. BCD JöMFNJOFHÌSF B+C+ c +EUPQ MBNLBÀUS \"#=\"+# x E PMEVôVOB HÌSF \"# OJO BMBCJMFDFôJ EFôFSMFS rrrr UPQMBNLBÀUS + 936 \" # $ % & 10920 \" # $ % & 2. \"# WF $% JLJ CBTBNBLM TBZMBSES \"# TBZT $% 6. )FSIBSGGBSLMSBLBNHËTUFSNFLÐ[FSF TBZTOOWFZBLBUES AB6 #VOBHÌSF LBÀGBSLM\"#TBZTZB[MBCJMJS + C5D \" # $ % & D13 WFSJMJZPS :VLBSEBLJUPQMBNBJöMFNJOFHÌSF A +#+ C +%UPQMBNLBÀUS \" # $ % & 3. 3BLBNMBSÀBSQNPMBOEÌSUCBTBNBLMTBZ 7. 849 :BOEBLJ UPQMBNB JöMFNJOEF IFS SBLBN CJS LFSF LVMMBOMNBL Ñ[F MBS CÑZÑLUFO LÑÀÑôF TSBMBOEôOEB CBöUBO + x5y SF x +ZUPQMBNLBÀUS TBZOOSBLBNMBSUPQMBNLBÀUS 1ab6 \" # $ % & \" # $ % & 4. \"пCBTBNBLMTBZESYJTFJLJCBTBNBLMJLJGBSL- 8. 3 2 9 :BOEBLJÀBSQNBJöMFNJOEFTP OVDVO SBLBNMBS UPQMBN LBÀ MEPóBMTBZOOUPQMBNES x rr US rrr \"- x = 53 + rrr PMEVôVOBHÌSF \"TBZTLBÀGBSLMEFôFSBMBCJ rr MJS \" # $ % & \" # $ % & 1. # 2. C 3. C 4. C 26 5. A 6. E 7. C 8. #
4BZ,ÑNFMFSJ*** TEST - 13 1. \"õBóEB WFSJMFO UPQMBNB JõMFNJOEF IFS IBSG GBSLM 5. \"#$%SBLBNMBSGBSLMEËSUCBTBNBLMTBZES CJSSBLBNHËTUFSNFLUFEJS \" %WF# $ AB PMEVôVOBHÌSF LBÀGBSLM\"#$%TBZTZB[MBCJ BA MJS AA + BB \" # $ % & 176 #VOBHÌSF \"+#UPQMBNLBÀUS \" # $ % & 2. xy (I) :BOEBLJ JõMFNEF ZBOMõMLMB *7 x 25 (II) TBUSCJSCBTBNBLTBóBLBZESMB- 6. \"#пCBTBNBLMWF\"#JLJCBTBNBLMTBZMBSES abc (III) SBLUPQMBONõUS #VOBHÌSF + def (IV) \"# \"# UPQMBNBöBôEBLJMFSEFOIBOHJTJPMBNB[ 504 (V) \" # $ % & #VOBHÌSF Y+ZLBÀUS \" # $ % & 3. r \"CJSEPóBMTBZES | | | |7. \"#$пHFOJOEF \"# ve \"$ V[VOMVLMBSCJSFSSB- r 0 #\" LBNES r \"TBZTOOLBSFTJOJOCBTBNBLTBZTSBLBNMBS A UPQMBNOBFõJUUJS :VLBSEBWFSJMFOMFSFHÌSF \"TBZTLBÀGBSLMEF ôFSBMBCJMJS \" # $ % & 4. \"#$WF\"$#пCBTBNBLMTBZMBSWFLQP[JUJGCJS BC UBNTBZES | |#$ =CSPMEVôVOBHÌSF LBÀGBSLM\"#$ÑÀ \"#$-\"$# L HFOJÀJ[JMFCJMJS \" # $ % & PMEVôVOB HÌSF L TBZT LBÀ GBSLM EFôFS BMBCJ MJS 5. C 6. D 7. A \" # $ % & 1. A 2. C 3. # 4. E 27
·/÷7&34÷5&:&)\";*3-*, 2. MODÜL 4\":*,·.&-&3÷#²-·/&#÷-.&3\"4:0/&-4\":*-\"3 www.aydinyayinlari.com.tr 4\":*,·.&-&3÷*7 \"TBM4BZMBS ÖRNEK 4 TANIM )BOHJSBLBNMBSJMFBSBMBSOEBBTBMES EFOCÐZÐL CJSWFLFOEJTJOEFOCBõLBQP[JUJG WF CËMFOJPMNBZBOEPóBMTBZMBSES ÖRNEK 1 \"öBôEBLJMFSEFOIBOHJMFSJBTBMTBZES I. 1 II. 3 III. 22 ÖRNEK 5 IV. 41 V. 57 VI. 83 VII. 111 VIII. 131 x -WFZ+BSBMBSOEBBTBMTBZMBSES Y- = Z+ II, IV, VI, VIII PMEVôVOBHÌSF Y+ZLBÀUS ÖRNEK 2 x - 5 21 3 = = & x - 5 = 3, y + 3 = 5 Y ZCJSFSEPôBMTBZWF Y+ Z- = 17PMEV ôVOBHÌSF Y+ZUPQMBNLBÀUS y + 3 35 5 x = 8, y = 2 j x + y = 10 3y - 5 = 1, y =WFY+ 3 = 17, x = 7 x+y=9 ÖRNEK 6 \"SBMBSOEB\"TBM4BZMBS x +JMFZ+BSBMBSOEBBTBMTBZMBSPMNBLÑ[FSF TANIM Y+ Z+ = 105 ve x >Z EFOCBõLBPSUBLCËMFOJCVMVONBZBOTBZMBSB PMEVôVOBHÌSF Y-ZGBSLFOÀPLLBÀUS BSBMBSOEBBTBMTBZMBSEFOJS 105 = 105.1 = (x + 1) . (y + 3) x + 1 = 105, y + 3 = 1 j x = 104 j y = -2 x - y = 106 ÖRNEK 3 ÖRNEK 7 \"öBôEBLJTBZÀJGUMFSJOEFOIBOHJMFSJBSBMBSOEBBTBM 2x +JMFZ-BSBMBSOEBBTBMQP[JUJGUBNTBZMBSES ES 18x -Z+ 59 = 0 I. 2 ve 3 II. 7 ve 9 III. 1 ve 5 PMEVôVOBHÌSF Y+ZUPQMBNLBÀUS IV. 8 ve 15 V. 10 ve 12 VI. 21 ve 24 18x + 59 = 7y j 18x + 45 = 7y - 14 I, II, III, IV 9(2x + 5) = 7(y - 2) 2x + 5 7 = & x = 1, y = 11 j x + y = 12 y-2 9 1. II, IV, VI, VIII 2. 9 3. I, II, III, IV 28 4. 1, 2, 4, 7, 8 5. 10 6. 106 7. 12
www.aydinyayinlari.com.tr 4\":*,·.&-&3÷#²-·/&#÷-.&3\"4:0/&-4\":*-\"3 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, %m/*m ÖRNEK 9 \" B C DQP[JUJGUBNTBZMBSWFY Z [BTBMTBZ- TBZTOO QP[JUJG UBN TBZ CËMFOMFSJOJO TBZT MBSPMTVO\"EPóBMTBZTOO PMEVóVOBHËSF CVTBZOO a) #BTBNBLTBZTLBÀUS \"TBM¿BSQBOMBSOUÐSÐOEFOZB[MN C \"TBMÀBSQBOMBSOFMFSEJS \"= xaZC . zD 36.10n = 22.32.2n.5n = 2n+2. 32. 5n j (n + 3) . 3 . (n + 1) = 144 j n = 5 \"TBM¿BSQBOMBSY ZWF[ a) 36.105 CBTBNBLM C WF 1P[JUJGUBNTBZCËMFOMFSJOJOTBZT ÖRNEK 10 B+ C+ D+ 12 . 15nTBZTOOUBOFUBNTBZCÌMFOJPMEVôV 5BNTBZCËMFOMFSJOJOUPQMBN OBHÌSF OLBÀUS xa + 1 - 1 · yb + 1 - 1 · zc+ 1 - 1 x-1 y-1 z-1 Po[JUJGUBNTBZCËMFOMFSJOJO¿BSQN 1 ^a+1h^b+1h^c+1h A2 \"EBOLпÐLWF\"JMFBSBMBSOEBBTBMEPóBMTB- ZMBSOTBZT A· x - 1 · y - 1 · z - 1 xyz ÖRNEK 8 12.15n = 22. 3 . 3n. 5n = 22.3n+1. 5n j 3.(n + 2) . (n + 1) = 90 j n = 4 TBZTOO a) 5BNCÌMFOMFSJLBÀUBOFEJS ÖRNEK 11 C 1P[JUJGUBNTBZCÌMFOMFSJOJOUPQMBNLBÀUS c) 1P[JUJGUBNTBZCÌMFOMFSJOJOÀBSQNLBÀUS TBZTOOQP[JUJGÀJGUTBZCÌMFOMFSJOJOTBZTLBÀ E ,FOEJTJOEFOLÑÀÑLBSBMBSOEBBTBMPMEVôVLBÀ US EPôBMTBZWBSES 24 = 23 . 3 a) 2.4.2 = 16 4 - 1 32 - 1 144 = 24.32 2 C · = 60 2-1 3-1 Çift sayı Pozitif Tek sayı 1 ^ 3 + 1 h^ 1 + 1 h 4 bölenlerinin = bölenlerin - bölenlerin c) 24 2 = 24 sayısı sayısı sayısı 21 = 5.3 - 3 = 12 E 24· · = 8 32 8. B C D 4E 29 9. B C 10. 4 11. 12
·/÷7&34÷5&:&)\";*3-*, 2. MODÜL 4\":*,·.&-&3÷#²-·/&#÷-.&3\"4:0/&-4\":*-\"3 www.aydinyayinlari.com.tr ÖRNEK 12 &O,ÑÀÑL,VWWFUF5BNBNMBNB TBZTOO BTBM PMNBZBO UBN TBZ CÌMFOMFSJOJO ÖRNEK 16 UPQMBNLBÀUS B C`/+JÀJO 168 = 23 . 3 . 7 150 . a =C3 JTUFOJMFOBTBMCÌMFOMFSUPQMBNOOUFSTJöBSFUMJTJEJS = - (2 + 3 + 7) = -12 FöJUMJôJOEFBEPôBMTBZTOOFOLÑÀÑLEFôFSJLBÀ US 2 . 3 . 52.a =C3 a = 22. 32. 5 = 180 ÖRNEK 13 ÖRNEK 17 5BNTBZCÌMFOMFSJOJOTBZTPMBOFOLÑÀÑLQP[JUJG \"=WF#CJSQP[JUJGUBNTBZES UBNTBZLBÀUS \"#JöMFNTPOVDVOVOCJSUBNLBSFZFFöJUPMNBTJÀJO #TBZTOOBMBDBôFOLÑÀÑLEFôFSLBÀUS 5#4= 8 j1#4= 4 = 2.2 = (1 + 1) (1 + 1) = 21.31 = 6 #= x2 23 . 3 . 52#= x2 #= 2.3 = 6 ÖRNEK 14 ÖRNEK 18 \"= 35.37 +TBZTWFSJMJZPS 180. a2 =C3 \"TBZTOOQP[JUJGBTBMPMNBZBOCÌMFOTBZTBöBô FöJUMJôJOEF B WF C QP[JUJG UBN TBZMBSOO FO LÑÀÑL EBLJMFSEFOIBOHJTJEJS EFôFSMFSJUPQMBNLBÀUS A = (36 - 1) . (36 + 1) + 1 = 362 = 64 22 . 32 . 5 . a2 =C3 A = 24.34 j 5.5 - 2 = 23 a = 22.32.5 = 180 C= 4.9.5 = 180 180 + 180 = 360 ÖRNEK 15 ÖRNEK 19 1P[JUJG CÌMFO TBZT PMBO JLJ CBTBNBLM LBÀ EPôBM BWFCTGSEBOGBSLMJLJUBNTBZMBSES TBZWBSES B- 4 =C 1#4= 3 jBC= x2 FöJUMJôJOJ TBôMBZBO FO CÑZÑL B OFHBUJG UBN TBZT 4PSVMBOUBCBOBTBMTBZPMBOLBSFTBZMBSES LBÀUS WF (a – 3)4 = 34C a = - C= 23 12. –12 13. 6 14. 23 15. 2 30 16. 180 17. 6 18. 360 19. –3
www.aydinyayinlari.com.tr 4\":*,·.&-&3÷#²-·/&#÷-.&3\"4:0/&-4\":*-\"3 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 20 ÖRNEK 22 YWFZCJSFSUBNTBZES 10! + 9! JöMFNJOJOTPOVDVLBÀUS 2 + 222 + 332 Y=Z2 9! + 8! PMEVôVOBHÌSF ZTBZTOOFOLÑÀÑLEFôFSJLBÀUS 10! + 9! 9!^ 10 + 1 h 9.11 99 112 (1 + 4 + 9).x = y2 = == 112 . 2.7.x = y2 j -11.2.7 = -154 9! + 8! 8!^ 9 + 1 h 10 10 ÖRNEK 21 ÖRNEK 23 YWFZCJSFSUBNTBZES \"=+WF#=WFSJMJZPS 8.12.16. ... . 28 . x =Z2 #VOB HÌSF # TBZTOO \" TBZT UÑSÑOEFO ZB[Mö OCVMVOV[ PMEVôVOBHÌSF ZTBZTOOBTBMÀBSQBOMBSOOUPQMB NLBÀUS A = 15! (1 + 16) = 15! . 17 #= 17.16.15! = 16A 216 . 32 . 5 . 7 . x = y2 j = 2 + 3 + 5 + 7 = 17 7$1,0%m/*m ÖRNEK 24 OCJSQP[JUJGUBNTBZPMNBLÐ[FSF EFOOZF +++ ... + LBEBSPMBOEPóBMTBZMBSO¿BSQNOBOGBLUÌSJ UPQMBNOOCJSMFSCBTBNBôOEBLJSBLBNLBÀUS ZFMEFOJSOJMFHËTUFSJMJS 0! + 1! + 2! + 3! + 4! = 1 + 1 + 2 + 6 + 24 = 34 O= O- O #JSMFSCBTBNBôOEBLJSBLBNUÑS = 1 ÖRNEK 25 = 1 = 1. 2 = 2 n! + _ n + 2 i! = 7 = 1. 2 . 3 = 6 _ n + 2 i! - n! 5 = 1 . 2 . 3 . 4 = 24 PMEVôVOBHÌSF OEPôBMTBZTLBÀUS = 1 . 2 . 3 . 4 . 5 = 120 n!^ 1 + ^ n + 1 h^ n + 2 h h 2 + 3n + 3 7 )FS GBLUËSJZFM LFOEJTJOEFO LпÐL GBLUËSJZFMMFS UÐSÐOEFOZB[MBCJMJS n == === .... n!^ ^ n + 1 h^ n + 2 h - 1 h 2 5 O$PMNBLÐ[FSF + 3n + 1 n OTBZTOOCJSMFSCBTBNBóEBJNBTGSES j÷ÀMFSEöMBSÀBSQNZBQMSTBO=CVMVOVS 20. –154 21. 17 31 99 23. 16A 24. 4 25. 1 22. 10
·/÷7&34÷5&:&)\";*3-*, 2. MODÜL 4\":*,·.&-&3÷#²-·/&#÷-.&3\"4:0/&-4\":*-\"3 www.aydinyayinlari.com.tr ÖRNEK 26 ÖRNEK 30 OWFYQP[JUJGUBNTBZMBSES BWFCQP[JUJGUBNTBZMBSES = 2O. x B=C PMEVôVOBHÌSF CTBZTLBÀGBSLMEFôFSBMS PMEVôVOBHÌSF OTBZTOOBMBCJMFDFôJFOCÑZÑLEF ôFSLBÀUS 23 2 j 11 + 5 + 2 + 1 = 19 210!, 15!, 7! jUBOF 11 2 52 a! 22 = 210 = 15.14 = 7.6.5 1 b! 209!, 13!, 4! ÖRNEK 27 ÖRNEK 31 YWFZQP[JUJGUBNTBZMBSES \" B CWFDQP[JUJGUBNTBZMBSWFY Z [BTBMTBZMBSES 27! = y \"= xaZC . zD 8x PMEVôVOBHÌSF \"TBZTOOBMBCJMFDFôJLBÀGBSLMEF PMEVôVOBHÌSF YTBZTOOBMBDBôEFôFSMFSUPQMBN ôFSWBSES LBÀUS \"TBZTUBOFBTBMJMFZB[MBCJMJZPSTBLVMMBOMBOBTBM 27 2 j 223 = (23)7 . 2 MBS WFPMVSWFIFS[BNBOJOJLJLBUBSBTEFôFS = 87 . 2 j 1 + 2 + ... + 7 = 28 BMS jUBOF 13 2 6 2 32 ÖRNEK 32 1 #JSNBOBWFMJOEFCVMVOBOTPOUBOFBZOUÐSNFZWF- ÖRNEK 28 ZJIFSCJSJQP[JUJGCËMFOTBZTPMBOIFSIBOHJCJSTBZLB- EBSOQBLFUMFZJQJOEJSJNMJPMBSBLTBUNBZBLBSBSWFSJZPS TBZTOOTPOEBOLBÀCBTBNBôTGSES ÷ÀJOEFÀBSQBOBSBOS 33 5 j 57 jCBTBNBLTGSES 65 1 ÖRNEK 29 #VJOEJSJNEFOFOÀPLLBÀNÑöUFSJGBZMBEBMBOBCJMJS YWFZQP[JUJGUBNTBZMBSES 27 . 22+ 2.32 = 126 j NÑöUFSJ 52! = 38! .y 7x PMEVôVOBHÌSF YTBZTFOÀPLLBÀPMBCJMJS 52 7 38 7 j 8 - 5 =UBOF 77 5 1 8 tane 5 tane 26. 19 27. 28 28. 7 29. 3 32 30. 3 31. 5 32. 29
4BZ,ÑNFMFSJ*7 TEST - 14 1. \"#$% EËSU CBTBNBLM QP[JUJG UBN TBZ WF Y Z [ 5. A 2 :BOEBLJBTBM¿BSQBOMBSBBZSNBJõMFNJ- BTBMTBZMBSES B OFHËSF YZ[=\"#$% PMEVôVOB HÌSF \"#$% FO LÑÀÑL EFôFSJOJ BME C * $TBZTVOLBUES D ôOEBY+ y +[LBÀUS E 7 ** # TBZTOO UBN CËMFOMFSJOJO TBZT \" # $ % & F7 UÐS G ***'TBZTEJS *7 #TBZT &TBZTOOLBUES JGBEFMFSJOEFOIBOHJMFSJEBJNBEPôSVEVS \" *WF** # **WF*** $ *WF*7 % ** ***WF*7 & * ** ***WF*7 2. \"WF#CJSCJSJOEFOGBSLMBTBMSBLBNMBSWF\"#JLJCB- 6. ,FOEJTJWFIBSJÀCJSUFLQP[JUJGCÌMFOJPMBOFO TBNBLMQP[JUJGUBNTBZES LÑÀÑL ÑÀ CBTBNBLM TBZOO QP[JUJG CÌMFOMFSJ UPQMBNLBÀUS \"## 61 \" # $ % & LPöVMVOVTBôMBZBOLBÀGBSLM\"#JLJCBTBNBLM TBZWBSES \" # $ % & 3. YWFZQP[JUJGUBNTBZPMNBLÐ[FSF 7. n! = 20 2x -WFZ+BSBMBSOEBBTBMTBZMBSES _ n - 2 i! 2x - 3 = 18 4y + 3 38 PMEVôVOBHÌSF _ n + 2 i! LBÀUS oMEVôVOBHÌSF Y+ZLBÀUS n! \" # $ % & \" # $ % & 4. \"WF#BSBMBSOEBBTBMTBZMBSES 8. YCJSUBNTBZES \"+#= 14 2x PMEVôVOBHÌSF,\"#FOÀPLLBÀUS 3-x JGBEFTJCJSEPôBMTBZZBFöJUPMEVôVOBHÌSF YJO \" # $ % & FOLÑÀÑkEFôFSJLBÀUS \" - # - $ % & 1. # 2. A 3. C 4. C 33 5. C 6. E 7. # 8. C
TEST - 15 4BZ,ÑNFMFSJ*7 1. \"CJSBTBMTBZWF#CJSUBNTBZES 5. \" # $BTBMTBZMBSJ¿JO 222 + 332 + 442 =\"# r \"<#< C r \"+#= C FöJUMJôJOF HÌSF # TBZT LBÀ GBSLM EFôFS BMBCJ PMEVôVCJMJOEJôJOFHÌSF C -#LBÀUS MJS \" - # - $ % & \" # $ % & 2. - 6. 1P[JUJGCÌMFOTBZTPMBOFOÀPLÑÀCBTBNBLM TBZTOOTPOEBOLBÀCBTBNBôTGSES LBÀEPôBMTBZWBSES \" # $ % & \" # $ % & 3. ++++ ..... + 7. \"WF#QP[JUJGUBNTBZMBSES TBZTOOJMFCÌMÑNÑOEFOFMEFFEJMFOLBMBO A2 = 28 LBÀUS B PMEVôVOBHÌSF \"+#UPQMBNOOFOLÑÀÑLEF \" # $ & & ôFSJLBÀUS \" # $ % & 4. = 9O\" 8. C`;+ PMNBLÐ[FSF PMEVôVOBHÌSF \"EPôBMTBZOOFOLÑÀÑLEFôF B- 4 =C SJJÀJOO`/+LBÀUS PMEVôVOBHÌSF B+CUPQMBNOO FOLÑÀÑLEF ôFSJLBÀUS \" # $ % & \" # $ % & 1. A 2. E 3. A 4. C 34 5. D 6. D 7. A 8. A
4BZ,ÑNFMFSJ*7 TEST - 16 1. TBZTOO BTBM PMNBZBO UBN CÌMFOMFSJOJO 5. \"öBôEB WFSJMFO JGBEFMFSEFO LBÀ UBOFTJ EPôSV UPQMBNLBÀUS EVS r YZ= YZ \" - # - $ - % - & -10 r Y+Z= Y+Z r x! = f x p! y! y r Y-Z 2 = [ Y-Z 2 ] r YY= Y+ -Y \" # $ % & 2. \"=+++ ... + #=+++ ... + PMEVôVOBHÌSF #-\"GBSLOOCJSMFSCBTBNBô LBÀUS \" # $ % & 6. 200! 7 n–5 TBZTJMFUBNCÌMÑOFOFOLÑÀÑLQP[JUJGUBN saZPMEVôVOBHÌSF OLBÀUS \" # $ % & 3. YWFZQP[JUJGUBNTBZMBSPMNBLÑ[FSF 7. 6x - 15 Y= Z- x-1 PMEVôVOBHÌSF ZOJOBMBCJMFDFôJEFôFSMFSUPQ LFTSJOJQP[JUJGUBNTBZZBQBOYUBNTBZMBSOO MBNLBÀUS UPQMBNLBÀUS \" # $ % & \" # $ % & m 4. OTBZTOOTPOEBOÑÀCBTBNBôTGSPMEVôV 8. YWFZCJSFSEPôBMTBZ OBHÌSF OTBZTLBÀGBSLMEFôFSBMBCJMJS 108 . x2 =Z3 \" # $ % & PMEVôVOBHÌSF Y+ZOJOBMBCJMFDFôJFOLÑÀÑL EFôFSLBÀUS \" # $ % & 1. # 2. A 3. C 4. E 35 5. A 6. E 7. C 8. A
TEST - 17 4BZ,ÑNFMFSJ*7 1. YWFZQP[JUJGUBNTBZMBSES 5. 10022 - 1002 Y+ = Y3 -Y Z TBZTOOBTBMÀBSQBOMBSOOUPQMBNLBÀUS FöJUMJôJOFHÌSF Y-ZLBÀUS \" # $ % & \" # $ % & 2. Y ZWF[GBSLMEPóBMTBZMBSES 6. YWFZQP[JUJGUBNTBZMBSJÀJO YZ[= 12 _ _ 3! i! i! y.x! = PMEVôVOBHÌSF Y+ y +[UPQMBNOOFOLÑÀÑL EFôFSJLBÀUS 3! PMEVôVOBHÌSF x +ZUPQMBNOOFOLÑÀÑL EFôF \" # $ % & SJLBÀUS \" # $ % & (n - 1) ! .n (n + 1) ! 7. YCJSEPóBMTBZPMNBLÐ[FSF 3. : Y TBZTOO TPOEBO Z UBOF CBTBNBô TGS PM EVôVOB HÌSF Z TBZT BöBôEBLJMFSEFO IBOHJTJ 2n (n! ) 4n2 + 4n PMBNB[ JöMFNJOJOTPOVDVLBÀUS \" # $ % & \" 1 # 3 $ 2 n n+1 n-1 % 2 & n! 4. %CJSEPôBMTBZWFB C DGBSLMBTBMTBZMBSPM 8. \" Y YUFOCÐZÐLPMNBZBOBTBMTBZMBSO¿BSQN- NBLÑ[FSF ES D = a2 C3DE BCJSQP[JUJGUBNTBZPMNBLÑ[FSF TBZTOOBTBMPMNBZBOQP[JUJGUBNCÌMFOMFSJTB \" B =\" ZTPMEVôVOBHÌSF ETBZTLBÀUS FöJUMJôJOJTBôMBZBOLBÀUBOFBTBZTWBSES \" # $ % & \" # $ % & 1. C 2. C 3. D 4. E 36 5. D 6. C 7. D 8. C
4BZ,ÑNFMFSJ*7 TEST - 18 1. \"QP[JUJGUBNTBZTJ¿JO 4. YWFZQP[JUJGUBNTBZMBSES r \"< 73 3 . 6 . 9 ... 33 = 18xZ r \"WFBSBMBSOEBBTBM r \"WFBSBMBSOEBBTBM PMEVôVOBHÌSF YTBZTFOÀPLLBÀPMBCJMJS PMEVóVCJMJOJZPS #VOBHÌSF \"OOBMBCJMFDFôJLBÀEFôFSWBSES \" # $ % & \" # $ % & 5. Y ZWF[QP[JUJGUBNTBZMBSES 2. YWFZQP[JUJGUBNTBZMBSES x3 =Z= [- 2 Y=Z2 PMEVôVOB HÌSF Y + y + [ UPQMBNOO FO LÑÀÑL PMEVôVOB HÌSF Y TBZTOO FO LÑÀÑL EFôFSJ EFôFSJLBÀUS LBÀUS \" # $ % & \" # $ % & 6. \" Y YJOBTBM¿BSQBOMBSOOZBOZBOBZB[MNBT JMFFMEFFEJMFOTBZES A ( x ) =PMEVôVOBHÌSF YQP[JUJGUBNTBZT OO FOCÑZÑLJLJCBTBNBLMEFôFSJOJOQP[JUJGCÌ MFOTBZTLBÀUS \" # $ % & 3. QWFQ+TBZMBSOOIFSJLJTJEFBTBMTBZJTFQ 7. \" B CQP[JUJGUBNTBZ YWFZBTBMTBZMBSES TBZTOB SOPHIE–(&3.\"*/\"4\"-* BEWFSJMJS r \"= xaZC r \"TBZTOOQP[JUJGCËMFOMFSJOJO¿BSQN\"12 ±SOFóJO PMEVôVOB HÌSF B + C TBZTOO GBSLM EFôFSMFSJ UPQMBNLBÀUS Q=JTFQ+ 1 =PMEVóVOEBO \" # $ % & Q=CJS4PQIJFm(FSNBJOBTBMES #VOB HÌSF JLJ CBTBNBLM JML ZFEJ BTBM TBZEBO LBÀUBOFTJ4PQIJF–(FSNBJOBTBMEFôJMEJS \" # $ % & 1. # 2. # 3. C 37 4. A 5. # 6. A 7. E
·/÷7&34÷5&:&)\";*3-*, 2. MODÜL 4\":*,·.&-&3÷#²-·/&#÷-.&3\"4:0/&-4\":*-\"3 www.aydinyayinlari.com.tr #²-.& %PôBM4BZMBSEB#ÌMNF÷öMFNJ ÖRNEK 4 7$1,0%m/*m \" #WF$EPóBMTBZMBSES \" # $WF,EPóBMTBZMBS #áES AB BC \"=#$+, #,<# 7 \"#ËMÐOFO AB ##ËMFO PMEVôVOBHÌSF \"TBZTOOBMBCJMFDFôJFOLÑÀÑLEF C $#ËMÐN ôFSLBÀUS K ,,BMBO A =#+WF#= 5C +JTF A = 3(5C + 4) + 7 = 15C + 19, ,=JTF\"TBZT#TBZTOBUBNCËMÐONÐõUÐS C >JTF$NJO = 5 ,<$JTF#WF$ZFSEFóJõUJSFCJMJS A = 15. 5 + 19 = 94 ÖRNEK 1 B C B C a b :BOEBLJCÌMNFJöMFNJOEFCÌMÑN JMFLBMBOOUPQMBNLBÀUS abab4 ab000 ab0 4 ÖRNEK 5 = ++ ab ab ab ab = 1010 + 4 j 1010 + 4 = 1014 \"WF#EPóBMTBZMBSES ab AB :BOEBLJCÌMNFJöMFNJOEF \"+#= 134 ÖRNEK 2 PMEVôVOBHÌSF \"TBZTLBÀUS \"CJSEPóBMTBZES \" \"m A =#+ 1 = 134 -# PMEVôVOBHÌSF \"TBZTLBÀUS #= 133 j#= 19 j A = 115 A + 23 = 5 (A - 4) + 3 A + 20 = 5A - 20 j 40 = 4A j A = 10 ÖRNEK 3 ÖRNEK 6 \" # $WF,EPóBMTBZMBS \" #WF$EPóBMTBZMBSWF#á$EJS AB BC A AB :BOEBLJCËMNFJõMFNJOEFCËMFOWF 7 K C CËMÐNZFSEFóJõUJSFCJMNFLUFEJS 2 PMEVôVOBHÌSF ,TBZTLBÀUS 7 #VOBHÌSF \"TBZOOFOLÑÀÑLEFôFSJLBÀUS A =#+ #= 7C + 2, A = 5 ( 7C + 2) + 3 = 35C + 13 7 <#WF<$JTF#=WF$=BMOBCJMJS 35C + 13 35 A = 9.8 + 7 = 79 13 j K = 13 1. 1014 2. 10 3. 13 38 4. 94 5. 115 6. 79
www.aydinyayinlari.com.tr 4\":*,·.&-&3÷#²-·/&#÷-.&3\"4:0/&-4\":*-\"3 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 7 :BOEBLJ CÌMNF JöMFNJOEF CÌMÑOFO %m/*m TBZLBÀUS g \" # $ Y ZWFOEPóBMTBZMBSWFDáES – g AC ve BC g ise – xy A+B C A–B C #ÌMFO=JTFCÌMFO= 28 x+y x–y #ÌMÑOFO= 28.35 + 5 = 985 A.B C An C ÖRNEK 8 x . y xn 6g 1a :BOEBLJ CÌMNF JöMFNJOEF B LBÀ GBSLM ,BMBO$EFOCÐZÐL¿LBSTBUFLSBS$ZFCËMÐO- 5. . EFôFSBMBCJMJS NFMJEJS a = 1, 2, 3 ,BMBO OFHBUJG ¿LBSTB $ OJO LBUMBS FLMFOFSFL QP[JUJGZBQMNBMES ÖRNEK 9 A6 ÖRNEK 11 – y+4 A4 A EPôBM TBZOO JMF CÌMÑNÑOEFO LBMBO PMEVôV – 2y + 4 4 OBHÌSF A2 +\"TBZTOOJMFCÌMÑNÑOEFOLBMBO LBÀUS 2 A2OJOJMFCÌMÑNÑOEFOLBMBO2 = 4 PMEVôVOBHÌSF ZLBÀUS \"OOJMFCÌMÑNÑOEFOLBMBO= 6 j 4 + 6 = 10 j 10 5 j0 0 A = 4 (2y + 4) + 2 = 6 (y + 4) + 4 j y = 5 ÖRNEK 12 AEPôBMTBZTOOJMFCÌMÑNÑOEFOLBMBOPMEVôV OBHÌSF BöBôEBLJMFSEFOIBOHJTJJMFUBNCÌMÑOÑS ÖRNEK 10 \" \"+ # \"- $ \"+ 2 2A5 B3 :BOEBLJCÌMNFJöMFNJOEF\"+#LBÀ % \"+ & \"- 1 –9 US 18 õLMBSEB\"ZFSJOFL+ZB[MSTB\"-TBZTOOOO 205 + A.10 = #+ 3) + 18 LBUPMEVôVHÌSÑMÑS 160 =#- 10A $FWBQ&EJS [[ 2 + 2=4 7. 985 8. 3 9. 5 10. 4 39 11. 0 12. E
TEST - 19 #ÌMNF 1. \" #WF$EPóBMTBZMBSES BC 5. \"WF#EPóBMTBZMBSES AB A #m C må# PMEVôVOB HÌSF \" TBZTOO FO LÑÀÑL EFôFSJ :VLBSEBWFSJMFOCÌMNFJöMFNJOFHÌSF \"TBZT LBÀUS OOBMBDBôEFôFSMFSUPQMBNLBÀUS \" # $ % & \" # $ % & 2. BCBCD CFö CBTBNBLM TBZT BC JLJ CBTBNBLM TBZTOBCÌMÑOEÑôÑOEF CÌMÑNJMFLBMBOOUPQ MBNFOÀPL LBÀPMBCJMJS \" # $ % & 6. #JSEPôBMTBZOOJMFCÌMÑNÑOEFOFMEFFEJMFO GBSLMLBMBOMBSOUPQMBNBöBôEBLJMFSEFOIBOHJ TJPMBNB[ \" # $ % & 3. B C D 1 6 BCDEËSUCBTBNBLMEPóBMTB- ZES m rrr YZ :VLBSEBLJ CÌMNF JöMFNJOF HÌSF LBÀ GBSLM YZ JLJCBTBNBLMEPôBMTBZTWBSES \" # $ % & 7. \"CJSQP[JUJGUBNTBZES A # # 4. A :BOEBLJCÌMNFJöMFNJOEF\"WFY 2.B x + 2 CJSFSEPôBMTBZPMEVôVOBHÌSF :VLBSEBLJCÌMNFJöMFNJOFHÌSF \"TBZTOOFO \" OO BMBCJMFDFôJ FO CÑZÑL EF LÑÀÑLEFôFSJLBÀUS x ôFSLBÀUS \" # $ % & \" # $ % & 1. D 2. E 3. # 4. C 40 5. C 6. A 7. D
#ÌMNF TEST - 20 1. ++ 5. \" #WFYQP[JUJGUBNTBZMBSES UPQMBNBöBôEBLJTBZMBSEBOIBOHJTJOFUBN CÌ A B MÑOFNF[ Y x \" # $ % & k :VLBSEBWFSJMFOCÌMNFJöMFNMFSJOFHÌSF \"- # TBZTOOFOLÑÀÑLEFôFSJLBÀUS \" # $ % & 2. \"EPóBMTBZTOOJMFCËMÐNÐOEFOLBMBOUÐS #VOBHÌSF \"- 4 )2 . ( A + 5 )3TBZOOJMFCÌ MÑNÑOEFOLBMBOLBÀUS \" # $ % & 3. \" #WF$EPóBMTBZMBSES 6. \"#$ÑÀCBTBNBLMTBZTOO \"#JLJCBTBNBLM A TBZTOBCÌMÑNÑOEFOFMEFFEJMFOLBMBOFOÀPL B LBÀPMBCJMJS \" # $ % & A C 2 PMEVôVOBHÌSF #+$UPQMBNOOFOLÑÀÑLEF ôFSJLBÀUS \" # $ % & 4. \"WF#EPóBMTBZMBSES 7. \"WF#EPóBMTBZMBSES \"må# A A+B B 70 2 PMEVôVOB HÌSF \"2 - #2 TBZTOO JMF CÌMÑ NÑOEFOLBMBOLBÀUS PMEVôVOB HÌSF \"# TBZTOO JMF CÌMÑNÑO EFOLBMBOLBÀUS \" # $ % & \" # $ % & 1. D 2. C 3. E 4. D 41 5. C 6. E 7. A
·/÷7&34÷5&:&)\";*3-*, 2. MODÜL 4\":*,·.&-&3÷#²-·/&#÷-.&3\"4:0/&-4\":*-\"3 www.aydinyayinlari.com.tr #ÌMÑOFCJMNF,VSBMMBS #²-·/&#÷-.& ÖRNEK 1 7$1,0%m/*m 3BLBNMBSGBSLM\"#CFõCBTBNBLMEPóBMTBZTOO JMFCËMÐNÐOEFOLBMBOEJS JMF#ÌMÑOFCJMNF #JSMFSCBTBNBóOEBLJSBLBN¿JGUTBZPMNBMES #VTBZJMFUBNCÌMÑOFCJMEJôJOFHÌSF \"SBLBNLBÀ GBSLMEFôFSBMBCJMJS JMF#ÌMÑOFCJMNF JMFUBNCÌMÑOÑZPSTB\"WFZB\" 4BZOOSBLBNMBSUPQMBNÐOLBUPMNBMES 4 + A + 1 + 3 + 2 = 10 + A j A = 4 + A + 1 + 3 + 6 = 14 + A j A = \"TBZTGBSLMEFôFSBMS JMF#ÌMÑOFCJMNF 4BZOO TPO JLJ CBTBNBóOEB CVMVOBO TBZ ÖRNEK 2 ÐOLBUPMNBMES %ÌSUCBTBNBLM\"#TBZTOOJMFCÌMÑNÑOEFOLB MBOWFJMFCÌMÑNÑOEFOLBMBOPMEVôVOBHÌSF A +#UPQMBNOOFOCÑZÑLEFôFSJLBÀUS JMF#ÌMÑOFCJMNF 4BZOOCJSMFSCBTBNBóOEBLJSBLBNWFZB JMFLBMBOJTF\"WFZB\"JMFLBMBOJTF 8 + A + 1 + 3= 12 + A j A = PMNBMES 8 + A + 1 + 8 = 17 + A j A = = 8 + 9 = 17 JMF#ÌMÑOFCJMNF 4BZOOTPOпCBTBNBóOEBCVMVOBOTBZJO LBUPMNBMES JMF#ÌMÑOFCJMNF ÖRNEK 3 4BZOOSBLBNMBSUPQMBNVOLBUPMNBMES BBBBZFEJCBTBNBLMTBZTOOJMFCÌMÑNÑOEFO LBMBOPMEVôVOBHÌSF BLBÀUS JMF#ÌMÑOFCJMNF #JSMFSCBTBNBóOEBTGSPMNBMES BBBBj 9 +B=L+ 2 jB= 5 JMF#ÌMÑOFCJMNF ÖRNEK 4 4BZOOSBLBNMBSTBóEBOTPMBEPóSV - + - +õFLMJOEFJõBSFUMFOEJSJMFSFLUPQMBOS BCBCFöCBTBNBLMTBZTJMFUBNCÌMÑOÑZPSTB B LBÀGBSLMEFôFSBMS 4POV¿JOUBNTBZCJSLBUPMNBMES j ( 0 + - ( 1 + = 0 BSBLBNOOJMLEFôFSJPMBDBLWFEFôFSMFSJEÌSEFSEÌ SFSBSUBDBLUSWFjUBOF - + - +JMFUBNCËMÐOÐS j + - = 11 + - +JMFUBNCËMÐOÐS j ( 1 + - ( 7 + = -11 - + - +JMFUBNCËMÐOÐS 42 1. 6 2. 17 3. 5 4. 2
www.aydinyayinlari.com.tr 4\":*,·.&-&3÷#²-·/&#÷-.&3\"4:0/&-4\":*-\"3 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 5 ÖRNEK 8 BCBMUCBTBNBLMTBZTJMFCÌMÑOFCJMEJôJOF :FEJCBTBNBLMBCTBZTJMFUBNCËMÐOFCJMFO HÌSF B+CUPQMBNLBÀUS UFLTBZES #VOBHÌSF BCEÌSUCBTBNBLMTBZTOOJMFCÌMÑ BC NÑOEFOLBMBOLBÀUS -+-+-+ (3 + 4 + 7) - C+B+ 5) =L 4POCBTBNBLUJSJMFCÌMÑOFCJMNFJODFMFOJSTF 14 - 5 - B+C =Lj 9 - B+C =Lj 9 =B+C 5 . 11 jB \"SBMBSOEB\"TBM4BZMBSO¦BSQNJMF#ÌMÑOFCJMNF +-+-+-+ 18 - (11 +B = 7 -B=PMNBMB= 7 %m/*m 7275 j 7 + 2 + 7 + 5 = 21 j 3 #ËMÐOFCJMNFLVSBMWFSJMNFZFOTBZMBSJMFJODF- ÖRNEK 9 MFNF ZBQBSLFO BSBMBSOEB BTBM ¿BSQBOMBSOO LVSBMMBSJMFJõMFNZBQMS %ËSUCBTBNBLMBCTBZTJMFCËMÐOEÐóÐOEFLBMB- OOWFSNFLUFEJS ±SOFóJOCJSTBZOO #VOB HÌSF B SBLBNOO BMBCJMFDFôJ EFôFSMFS UPQMB r JMFCËMÐOFCJMNFTJJ¿JOWFF NLBÀUS r JMFCËMÐOFCJMNFTJJ¿JOWFF r JMFCËMÐOFCJMNFTJJ¿JOWFF JMFCÌMÑNÑOEFOLBMBOEJSC=WFZBC=PMVS UBNCËMÐONFTJHFSFLJS JMFCÌMÑNÑOEFOLBMBOEJS C=JLFOB=WFC=JLFOB=CVMVOVS ÖRNEK 6 $FWBQ #Fõ CBTBNBLM WF SBLBNMBS GBSLM \"#\" TBZT JMF ÖRNEK 10 UBNCËMÐOFCJMNFLUFEJS #VOBHÌSF #SBLBNOOBMBCJMFDFôJLBÀGBSLMEFôFS \"#EÌSUCBTBNBLMTBZESLCJSQP[JUJGUBNTBZPM WBSES NBLÑ[FSF \"#=L+FöJUMJôJTBôMBOEôOBHÌ SF \"SBLBNLBÀGBSLMEFôFSBMS 15 =PMEVôVJÀJOÌODFTPOSBJMFCÌMÑOFCJMNFJO DFMFONFMJ#WFZB# JMFCÌMÑNÑOEFOLBMBOJTF#=WFZBEJSJMFCÌ MÑNÑOEFOLBMBOJTF#=JLFO\"= WF#= 8 [[ JLFO\"= 7 +# +# 5PQMBNEFôFSUBöS [[ #= #= 5PQMBNUBOF ÖRNEK 7 ÖRNEK 11 #FöCBTBNBLM\"#TBZTJMFUBNCÌMÑOFCJMEJ #Fö CBTBNBLM \"## TBZTOO JMF CÌMÑNÑOEFO ôJOFHÌSF \"+#UPQMBNLBÀGBSLMEFôFSBMS LBMBOPMEVôVOBHÌSF \"SBLBNOOBMBCJMFDFôJLBÀ GBSLMEFôFSWBSES 36 =WF#= WF\"= EFôFSMFSJOJBMBCJ MJS5PQMBNMBSEBOJLJTPOVÀÀLBS 36 =JTF\"##= 4x +WF\"##=Z+PMVS #=JTF\"= #=JTF\"= #=JTF\"= EFôFS 5. 9 6. 6 7. 2 43 8. 3 9. 7 10. 7 11. 4
·/÷7&34÷5&:&)\";*3-*, 2. MODÜL 4\":*,·.&-&3÷#²-·/&#÷-.&3\"4:0/&-4\":*-\"3 www.aydinyayinlari.com.tr ÖRNEK 12 ÖRNEK 15 BCTBZTOOJMFCÌMÑNÑOEFOLBMBOPMEVôVOB ¶¿CBTBNBLMCJS4EPóBMTBZTOO 5 LBUJLJCBTBNBL- HÌSF FMEF FEJMFCJMFDFL FO CÑZÑL BC JLJ CBTBNBL 8 MTBZTLBÀUS MCJS5EPóBMTBZTOBFõJUUJS 12 =JTFB+WFC+PMVS C=JTFB= WFC=JTFB= #VOB HÌSF FO CÑZÑL 4 EPôBM TBZTOO JMF CÌMÑ j 87 NÑOEFOLBMBOLBÀUS 8T 8.95 = 152 j 1 + 5 + 2 = 8 j = 8 S= &S= 55 ÖRNEK 13 ÖRNEK 16 \"#WF\"#EËSUCBTBNBLMTBZMBSES 0! + 1! + 2! + 3! + ... +UPQMBNOOJMFCÌMÑ NÑOEFOFMEFFEJMFOLBMBOLBÀUS 1A2B 13 ve 2A1B 13 18 =ÀBSQBOMBSWFTPOSBTOEBPMBDBLUS 6k 0! + 1! + 2! + 3! + 4! + 5! = 154 154 = 18 . 8 +PMEVôVOEBOLBMBOEVS :VLBSEBLJ CÌMNF JöMFNMFSJOF HÌSF L EPôBM TBZT LBÀUS \"#= 2010 +\"#= 13x +L ÖRNEK 17 \"#= 1020 +\"#=Z+ 6 ÷LJ CBTBNBLM EPôBM TBZMBSEBO LBÀ UBOFTJ WFZB - JMFUBNCÌMÑOFCJMJS 990 =13 (x -Z +L- 6 99 3 ve 9 3 j 33 – 3 = 30 (3 e tam) 33 3 996 = 13 ( ;x - y ) +LjL= 8 76 99 5 ve 9 5 j 19 – 1 = 18 (5 e tam) 19 1 99 15 j 6 (15 e tam) 6 = 30 + 18 - 6 =UBOF ÖRNEK 14 ÖRNEK 18 %ËSUCBTBNBLM\"#TBZTOOJMFCËMÐNÐOEFOLBMBO #FõCBTBNBLM\"\"##TBZTOOJMFCËMÐNÐOEFOLB- EJS MBOEJS #VTBZJMFUBNCÌMÑOFCJMEJôJOFHÌSF \"SBLBNOO BMBDBôEFôFSMFSLBÀUBOFEJS #VOBHÌSF \"SBLBNOOBMBCJMFDFôJLBÀGBSLMEFôFS WBSES L+JTF\"WFZB\"WFZB\"CVMVOVS #VTBZMBSJÀJOJMFCÌMÑOFCJMNFJODFMFOEJôJOEFJTF JÀJOWFJMFCÌMÑOFCJMNFJODFMFONFMJ A = CVMVOVS ,BMBOJTFJÀJOLBMBO JÀJOLBMBO $FWBQEFôFS \"\"PMNBM1 + /2A j A = 12. 87 13. 8 14. 3 44 15. 8 16. 10 17. 42 18. 3
www.aydinyayinlari.com.tr 4\":*,·.&-&3÷#²-·/&#÷-.&3\"4:0/&-4\":*-\"3 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 19 ÖRNEK 22 CBTBNBLM EPôBM TBZTOO JMF CÌMÑ \" #WF$BSEõLSBLBNMBSES NÑOEFOFMEFFEJMFOLBMBOLBÀUS ·À CBTBNBLM \"#$ EPôBM TBZMBSOO IFSIBOHJ JLJTJ OJO UPQMBN FO LÑÀÑL IBOHJ BTBM TBZ JMF LFTJOMJLMF 44 =JTFJMFCÌMÑNÑOEFOLBMBO JMFCÌMÑ UBNCÌMÑOÑS NÑOEFOLBMBOCVMVOVS 4141 ... 4 =B+ 2 =C+ 9 3BLBNUPQMBNMBSLFTJOMJLMFÑOLBUPMBDBLUS 14414441.2. .44+4423 = 4^ a + 1 h = 11^ b + 1 h 4BZOO GB[MBT JMF UBN CÌMÑOÑS #V EVSVNEB LB ÖRNEK 23 MBOEJS öLJCBTBNBLM\"#EPóBMTBZMBSWFFUBNCËMÐOFCJM- ÖRNEK 20 NFLUFEJS \"# TBZMBSOO BMBCJMFDFôJ EFôFSMFS UPQMBNOO JMF BC EËSU CBTBNBLM TBZTOO JMF CËMÐNÐOEFO LB- CÌMÑNÑOEFOLBMBOLBÀUS MBOEJS #VOBHÌSF B+COJOBMBCJMFDFôJFOCÑZÑLEFôFSJMF \"#TBZMBSWFLBUMBSPMNBM FOLÑÀÑLEFôFSJOUPQMBNLBÀUS 20 + 40 + 60 +TBZTOOSBLBNMBSUPQMBNPMBDB ôOEBOJMFCÌMÑNEFOLBMBOWFSJS 15 =JTFLWFQ+EJSBWFZBBPMVS B=JTFB+C=JTFFOCÑZÑL ÖRNEK 24 B=JTFB+C=JTFFOLÑÀÑL #FõCBTBNBLMBCDTBZTOOJMFCËMÐNÐOEFOLBMBO = 14 + 2 =CVMVOVS WFB#CEJS #VTBZJMFUBNCÌMÑOFCJMEJôJOFHÌSF LBÀGBSLM ÖRNEK 21 B C TSBMJLJMJTJCVMVOBCJMJS YWFOQP[JUJGCJSFSUBNTBZES JTFUBOF x n YTBZTOOOLF[ZBOZBOBZB[MNBTJMFFMEFFEJ- ÖRNEK 25 MFOTBZES ±SOFóJO 23 = 232323 \"TBZNBTBZTOOJMFCËMÐNÐOEFOLBMBO #TBZ- NBTBZTOOJMFCËMÐNÐOEFOLBMBOEJS 3 #VOBHÌSF \"2#+\"#2UPQMBNOOJMFCÌMÑNÑO EFOLBMBOLBÀUS 254 = 254254 A = 16x +WF#=Z+ EFSTFL 2 A2#+\"#2 =\"# \"+# = (16x + Z+ 18) (16x +Z+ 31) A = 2019 j (16x + 8 + Z+ 16 + 2) (16x +Z+ 24 + 17) j 5 . 2 . 7 = 350 j 350 43 . 8 + 6 n $FWBQCVMVOVS õFLMJOEFUBONMBOZPS \"TBZTOOBUBNCÌMÑOFCJMNFTJJÀJOFOB[LBÀCB TBNBLMPMNBTHFSFLJS BCÌMÑOFCJMNFJÀJOUBOF FCÌMÑOFCJMNFJÀJO UBOFHFSFLMJ &,0, =JTF= 132 19. 42 20. 16 21. 132 45 22. 3 23. 2 24. 3 25. 6
TEST - 21 #ÌMÑOFCJMNF 1. \"öBôEBLJTBZMBSEBOIBOHJTJJMFUBNCÌMÑOÑS 5. \"#TBZTJMFUBNCÌMÑOFCJMFOUFLTBZPM \" # $ % & EVôVOBHÌSF \"LBÀGBSLMEFôFSBMS \" # $ % & 2. ¶¿CBTBNBLMBTBZTJMFUBNCËMÐOÐZPS 6. 0! + 2! + 4! +++ 2020! #VOBHÌSF BLBÀGBSLMEFôFSBMS TBZTOOJMFCÌMÑNÑOEFOLBMBOLBÀUS \" # $ % & \" # $ % & 3. 3BLBNMBSGBSLMEÌSUCBTBNBLMFOLÑÀÑLEPôBM 7. %ËSUCBTBNBLM\"#$%TBZTOOCJSMFSWFPOMBSCB- TBZOOJMFCÌMÑNÑOEFOLBMBOLBÀUS TBNBLMBSOEBLJTBZMBSZFSEFóJõUJSJQ¿LBSMODBFM- EF FEJMFO TBZOO JMF UBN CËMÐOFCJMNFTJ JTUFOJ- \" # $ % & ZPS #VOB HÌSF $ WF % SBLBNMBS BSBTOEBLJ GBSL BöBôEBLJMFSEFOIBOHJTJPMBCJMJS \" # $ % & 4. #FõCBTBNBLM\"#TBZTJMFUBNCËMÐOÐZPS 8. TBZTBöBôEBLJMFSEFOIBOHJTJOFUBNCÌMÑ #VOBHÌSF \"+#TBZTLBÀGBSLMEFôFSBMS OFNF[ \" # $ % & \" # $ % & 1. # 2. C 3. A 4. # 46 5. # 6. C 7. D 8. E
#ÌMÑOFCJMNF TEST - 22 1. OQP[JUJGUBNTBZES 5. %ËSUCBTBNBLMJMFUBNCËMÐOFCJMFO\"#TBZT- 3O TBZMBSOO JMF CÌMÑNÑOEFO FMEF FEJMFO OOJMFCËMÐNÐOEFOLBMBOUÐS LBMBOMBSUPQMBNLBÀUS \"SBLBNOOBMBDBôEFôFSMFSUPQMBNLBÀUS \" # $ % & \" # $ % & 2. \"MU CBTBNBLM \"#\"# TBZT BöBôEBLJMFSEFO 6. %ËSUCBTBNBLM\"#TBZTOOJMFCËMÐNÐOEFO IBOHJTJOFEBJNBUBNCÌMÑOÑS LBMBOUJS #VOB HÌSF \"# TBZTOO FO CÑZÑL ZBQBO \" SBLBNLBÀUS \" # $ % & \" # $ % & 3. ¶¿ CBTBNBLM SBLBNMBS GBSLM \"# TBZTOO JMF 7. 5PQMBNMBSPMBOJLJQP[JUJGUBNTBZEBOCÐZÐóÐ CËMÐNÐOEFOLBMBOEJS LпÐóÐOFCËMÐOEÐóÐOEFCËMÐNLBMBOEJS #VOBHÌSF LÑÀÑLTBZLBÀUS #VOBHÌSF SBLBNMBSGBSLMLBÀ\"#TBZTZB[ MBCJMJS \" # $ % & \" # $ % & 4. \"EPóBMTBZT WFZFUBNCËMÐOFCJMNFLUFEJS 8. BCEËSUCBTBNBLMTBZTOOJMFCËMÐNÐOEFO #VOBHÌSF \"TBZTBöBôEBLJMFSEFOIBOHJTJOF LBMBOEJS UBNCÌMÑOFCJMJS #VOBHÌSF B+COJOBMBCJMFDFôJFOCÑZÑLEFôFS \" # $ % & JMFFOLÑÀÑLEFôFSJOUPQMBNLBÀUS \" # $ % & 1. # 2. E 3. # 4. C 47 5. E 6. E 7. # 8. #
TEST - 23 #ÌMÑOFCJMNF 1. \"= 5. #FõCBTBNBLMSBLBNMBSGBSLM\"#EPóBMTBZ- FöJUMJôJOFHÌSF \"SBLBNLBÀPMNBMES TOOJMFCËMÐNÐOEFOLBMBOUÐS #VOB HÌSF \"# TBZTOO SBLBNMBS UPQMBN \" # $ % & LBÀUS \" # $ % & 2. ¶¿CBTBNBLM\"#$TBZTOOJMFCËMÐNÐOEFOLB- 6. \"MUCBTBNBLM\"#$TBZTJMFCËMÐOEÐóÐOEF MBOUÐS LBMBOFMEFFEJMJZPS \"#$ TBZTOO SBLBNMBS ÑÀFS BSUUSMBSBL FMEF #VTBZMBSZB[MSLFOBZOTBZJÀFSJTJOEFFOÀPL FEJMFDFLTBZOOJMFCÌMÑNÑOEFOLBMBOLBÀUS LVMMBOMBOSBLBNBöBôEBLJMFSEFOIBOHJTJEJS \" # $ % & \" # $ % & 3. %ÌSUCBTBNBLM\"#%TBZTJÀJO r \"< B << D 7. %ËSUCBTBNBLM\"\"0#TBZTOOJMFCËMÐNÐOEFO r JMFUBNCËMÐOÐS LBMBOEJS #VOBHÌSF \"+#UPQMBNFOB[LBÀUS PMEVôVOBHÌSF LBÀGBSLM\"#%TBZTZB[MBCJ \" # $ % & MJS \" # $ % & 4. 3BLBNMBSGBSLMYZ[CFõCBTBNBLMTBZTOO 8. %ËSUCBTBNBLM\"#TBZTOOJMFCËMÐNÐOEFO JMFCËMÐNÐOEFOLBMBOEJS LBMBOEVS #VOBHÌSF LBÀGBSLMYZ[TBZTZB[MBCJMJS #VOB HÌSF \"# EÌSU CBTBNBLM TBZTOO JMFCÌMÑNÑOEFOLBMBOLBÀUS \" # $ % & \" # $ % & 1. C 2. A 3. D 4. A 48 5. C 6. # 7. D 8. E
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