#ÌMÑOFCJMNF TEST - 24 1. #FöCBTBNBLM\"\"TBZTOOJMFCÌMÑNÑO 5. L QP[JUJG CJS UBN TBZES Y TBZT SBLBNMBS UPQMB- EFOLBMBOPMEVôVOBHÌSF \"SBLBNLBÀUS NL-WFZTBZTSBLBNMBSUPQMBNL+PMBO UBNTBZMBSES \" # $ % & #VOBHÌSF YWFZOJOYZöFLMJOEFZBOZBOBZB [MNBTJMFFMEFFEJMFDFLTBZOOJMFCÌMÑNÑO EFOFMEFFEJMFOLBMBOLBÀUS \" # $ % & 2. ¶¿CBTBNBLM\"#$EPóBMTBZTJ¿JO 6. \"#JLJCBTBNBLMEPóBMTBZES r ¥JGUTBZES AB A.B A.B A + B r VOCJSLBUOEBOGB[MBES 2 2 r \"=$EJS PMEVôVOBHÌSF \"#$TBZTLBÀUS 22 10 \" # $ % & :VLBSEBLJCÌMNFJöMFNMFSJOFHÌSF LBÀUBOF\"# JLJCBTBNBLMTBZTWBSES \" # $ % & 3. \" O =O4 -O2 +O+PMBSBLUBONMBOZPS 7. OTBZTEFOCÐZÐLUFLSBLBNESOUBOFJLJCBTB- \" TBZT BöBôEBLJMFSEFO IBOHJTJ JMF UBN NBLMEPóBMTBZOOIFSCJSJOJOOJMFCËMÐNÐOEFOFM- CÌMÑOFNF[ EFFEJMFOLBMBOMBSCJSCJSJOEFOGBSLMES #VOB HÌSF CV JLJ CBTBNBLM TBZMBSO UPQMBN OOOJMFCÌMÑNÑOEFOLBMBOLBÀUS \" # $ % & \" # $ % & 4. 101 + 10 + 10 ++ 1017 8. \"#JLJCBTBNBLMEPóBMTBZ YWFZQP[JUJGUBNTBZ- UPQMBNOOJMFCÌMÑNÑOEFOLBMBOLBÀUS MBSES \"Y=#Z=\"# \" # $ % & LPöVMVOVTBôMBZBOLBÀUBOF\"#TBZTWBSES \" # $ % & 1. E 2. D 3. D 4. E 49 5. D 6. # 7. A 8. C
·/÷7&34÷5&:&)\";*3-*, 2. MODÜL 4\":*,·.&-&3÷#²-·/&#÷-.&3\"4:0/&-4\":*-\"3 www.aydinyayinlari.com.tr &,0,�#* �# ÖRNEK 3 TANIM a = 8 , b = D= E= 18 , e = 2 , f = 1 WFSJMJZPS 34 öLJZBEBEBIBGB[MBEPóBMTBZZBZOBOEBCË- MFCJMFOEPóBMTBZMBSOFOCÐZÐóÐOF FOCÑZÑL \"öBôEBLJJöMFNMFSJZBQO[ PSUBLCÌMFO �# EFOJS B &,0, B C = ? C �# B C = ? D �# D E = ? E &,0, D E = ? F &,0, F G = ? ÖRNEK 1 WF TBZMBSOO FO CÑZÑL PSUBL CÌMFOMFSJOJ B &,0, = 120 CVMVOV[ C �# = 1 D &,0, = 18 24 36 42 2 * )FSÑÀTBZZBZOBOEBCÌ E �# = 9 12 18 21 2 F &,0,d 2 , 1 n = EKOK^ 2, 1 h = 2 = 2 6 9 21 MFCJMFOBTBMTBZMBSOÀBSQ 3 4 EBOB^ 3, 4 h 1 3 9 21 2 13 7 ÖRNEK 4 11 7 N�#UVS 3* a2CD BC2D , aCD2 1 3 �# = 6 JGBEFMFSJOJOJOFOLÑÀÑLPSUBLLBUOCVMVOV[ 7 &,0, B2C3D BC2D3 B3CD2) =B3C3D3 EKOK TANIM öLJ ZB EB EBIB GB[MB EPóBM TBZOO IFS CJSJOF UBN CËMÐOFCJMFO EPóBM TBZMBSO FO LпÐóÐOF FOLÑÀÑLPSUBLLBU &,0, EFOJS ÖRNEK 2 ÖRNEK 5 WFTBZMBSOOFOLÑÀÑLPSUBLLBUOCVMVOV[ a4C2D BC, a2CD2E2 JGBEFMFSJOJOFOCÑZÑLPSUBLCÌMFOJOJCVMVOV[ 8 12 2 &MEF FEJMFO UÑN TBZMBSO ÀBSQN 4 62 &,0,UVS �# B4C2D BC3 B2CD2E2) =BC 2 32 &,0, = 23 . 3 = 24 1 33 1 %m/*m ÖRNEK 6 BWFCBSBMBSOEBBTBMTBZMBSJTF BEPôBMTBZTJMFOO&,0,V �#VPM �# B C = &,0, B C =BC EVôVOBHÌSF BLBÀUS BTBZT CTBZTOOUBNLBU B=JTFB= 48 a =CL L` N+ JTF �# B C =C &,0, B C = a &,0, B C �# B C =BC EKOK f a , x p = EKOK_ a, x i b y EBOB_ b, y i 1. 6 2. 24 50 3. B C D E F 4. B3C3D3 5. BC6. 48
www.aydinyayinlari.com.tr 4\":*,·.&-&3÷#²-·/&#÷-.&3\"4:0/&-4\":*-\"3 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, %m/*m ÖRNEK 10 \"SEõLQP[JUJGUBNTBZMBSBSBMBSOEBBTBMES BWFCQP[JUJGUBNTBZMBSES �# B C WF a = 5 ÖRNEK 7 b 11 \"WF#BSEõLQP[JUJGUBNTBZMBSES PMEVôVOBHÌSF B-CGBSLLBÀUS &,0, \" # �# \" # PMEVôVOBHÌSF \"+#LBÀUS a5 = JTFB=LWFC=L �# \" # = &,0, \" # =\"# \"#+ 1 = 241 j\"#= 240 b 11 j\" WF# j\" # L=�# B C L= B= C= 44 jB-C= -24 %m/*m ÖRNEK 11 \"<#PMNBLÐ[FSF YWFZQP[JUJGUBNTBZMBSES �# \" # #\"< B #&,0, \" # &,0, Y Z =WFY=Z PMEVôVOBHÌSF Y+ZUPQMBNLBÀUS ÖRNEK 8 x = 3 & x = 3k, y = 5k \"WF#CJSCJSJOEFOGBSLMQP[JUJGUBNTBZMBSES y5 &,0, \" # PMEVôVOBHÌSF \"+#TBZTOOFOLÑÀÑLWFFOCÑ &,0, Y Z = 90 =LjL= 6 j x +Z= 48 ZÑLEFôFSMFSJUPQMBNLBÀUS ÖRNEK 12 &,0, \" # = 36 A = #=JTF \"+# NBY= 54 \"WF#CJSCJSJOEFOGBSLMQP[JUJGUBNTBZMBSES A = #=JTF \"+# NJO =JTF = 54 + 13 = 67 �# \" # =WF<\"+ B < 102 LPöVMVOVTBôMBZBOLBÀGBSLM\"TBZTCVMVOBCJMJS ÖRNEK 9 �# \" # =JTFYWFZBSBMBSOEBBTBMTBZMBSPM \"=2 NBLÑ[FSF \"=YWF#=ZPMBDBLUS 51 < 17(x +Z <JTF< x +Z< 6 B = 22 A = jUBOF $= 22 ÖRNEK 13 PMEVôVOB HÌSF EKOK_ A, B, C i JöMFNJOJO TPOVDV \"WF#BSEõL¿JGUEPóBMTBZMBSES �# \" # +&,0, \" # = LBÀUS EBOB_ A, B, C i PMEVôVOBHÌSF \"+#UPQMBNLBÀUS EKOK^ A, B, C h 332 �# \" # =WF&,0, \" # = 144 A =OWF#= O+ PMEVôVOEBO 2 .3 .5 144 =O O+ 1 ) j 72 =O O+ 1 ) = = 180 jO= \"= #= \"+#= 34 EBOB^ A, B, C h 2.3.5 7. 31 8. 67 9. 180 51 10. –24 11. 48 12. 4 13. 34
·/÷7&34÷5&:&)\";*3-*, 2. MODÜL 4\":*,·.&-&3÷#²-·/&#÷-.&3\"4:0/&-4\":*-\"3 www.aydinyayinlari.com.tr ÖRNEK 14 ÖRNEK 18 \"WF#QP[JUJGUBNTBZMBSES AB C x \" #WF$EPóBMTBZMBSOO¿BS- �# \" # =WF&,0, \" # = 180 ab c PMEVôVOBHÌSF \"+#UPQMBNFOB[LBÀUS ad e x QBOMBSB BZSMNõ CJ¿JNJ ZBOEBLJ gf e y HJCJEJS 180 = 22.32.5 = 15.22.3 gf h z A = 15x jY PMBCJMJS#=ZjY PMBCJMJS ik l t #VOB HÌSF Ekok (A, B, C) A +#= 60 + 45 = 105 11 1 t Ebob (A, B, C) ÖRNEK 15 LBÀUS YWFZQP[JUJGUBNTBZMBSES 22 x - y = 2 WF&,0, Y Z -�# YZ = x+y 7 x .y.z.t PMEVôVOBHÌSF Y+ZUPQMBNLBÀUS ? = = x.y.z 7x -Z= 2x +ZjY ZjY L Z L 2 &,0, Y Z =LWF�# YZ =L L-L= 176 jL JTFY+Z=L= 56 x.t ÖRNEK 19 x =+WFZ= 4! + PMEVôVOBHÌSF �# Y Z LBÀUS x = 3! (1 + 4.5) =WFZ= 4! (1 + 5.6) = 4!.31 �# Y Z = 3! ÖRNEK 16 ÖRNEK 20 \" #WF$EPóBMTBZMBSES BQP[JUJGUBNTBZES &,0, \" # $ = PMEVôVOBHÌSF \"+#+$UPQMBNFOB[ LBÀUS &,0, B =WF�# B = 1 560 = 24.5.7 j A = #= $= 7 PMEVôVOB HÌSF B TBZTOO BMBCJMFDFôJ LBÀ EFôFS A +#+ C = 28 WBSES 1008 = 24.32 = 24 = 22. 32 B= B=WFZBB= 7 . 32 jEFôFS ÖRNEK 17 ÖRNEK 21 \"WF#BSBMBSOEBBTBMTBZMBSES a <WF�# B = 8 &,0, \" # =WF 14 + B = 20 LPöVMMBSOBVZHVOLBÀGBSLMBQP[JUJGUBNTBZTWBS ES A PMEVôVOBHÌSF \"+#UPQMBNLBÀUS 144 = 24.32 = 8.2.32 B=L LTBZTJMF2BSBMBSOEBBTBMPMNBM 14 + 8AB = 20A & A = 7 L= B= jUBOF 126 52 18. YZ[ 19. 3! 20. 3 21. 4 =JTF#= 18 $FWBQ+ 18 = 25 14. 105 15. 56 16. 28 17. 25
www.aydinyayinlari.com.tr 4\":*,·.&-&3÷#²-·/&#÷-.&3\"4:0/&-4\":*-\"3 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 22 ÖRNEK 26 \" #WF$QP[JUJGUBNTBZMBSES YQP[JUJGCJSUBNTBZES \"#=WF\"$= 108 x >PMEVôVOBHÌSF �# Y+ Y2 - Y3 + JGB PMEVôVOBHÌSF \"TBZTLBÀGBSLMEFôFSBMBCJMJS EFTJOJOFöJUJOJCVMVOV[ \"TBZTPSUBLÀBSQBOES x2 - 1 = ^ x - 1 h^ x + 1 h 4&? =^x+1h &O CÑZÑL EFôFSJ �# PMBDBLUS %JôFS EF ôFSMFSJJTF�# JOQP[JUJGCÌMFOMFSJEJS 3 + 1 = ^ x + 1 h^ 2 - x + 1 h A =�# = 36 = 22.32 OO + 1) . 52 + 1) =UBOFQP[JUJGCÌMFOJWBSES x x $FWBQ ÖRNEK 27 ÖRNEK 23 2 , 3 ve 7 Y ZWF[UBNTBZMBSES Y=Z=[ 35 11 PMEVôVOBHÌSF Y+Z+[OJOÑÀCBTBNBLMFOLÑÀÑL EFôFSJLBÀUS TBZMBSOB UBN CÌMÑOFCJMFO QP[JUJG JLJ CBTBNBLM FO CÑZÑLEPôBMTBZLBÀUS &,0, =PMEVôVJÀJO Y=Z=[=L x =L Z=L [=LPMVSY+Z+[=L \"SBEôO[TBZYPMTVO L= -BMOSTB j -994 xx x 3x 5x 11x CVMVOVS ÖRNEK 24 ,, j ,, 23 7 BCJSEPóBMTBZES 23 7 &,0, B = 120 3 5 11 PMEVôVOBHÌSF BTBZTOOLBÀGBSLMEFôFSJWBSES x = EKOK =LJTFY=UÑS B= B= jUBOF ÖRNEK 28 \"WF#QP[JUJGUBNTBZES A >#PMEVôVOBHÌSF �# \" \"-# -�# # \"-# JöMFNJOJOTPOVDVLBÀUS �# \" # TBZT \"-# TBZTOO ÀBSQBOMBSOEBO CJSJ PMEVôVJÀJO�# \" \"-# =�# # \"-# CVMV OVSWFGBSLMTGSPMVS ÖRNEK 29 ÖRNEK 25 1P[JUJGUBNTBZMBSLÐNFTJOEF =�# Y Z a b =&,0, B C x YQP[JUJGCJSUBNTBZES Z x >WF&,0, Y- 1, x, x + = PMBSBLUBONMBOZPS PMEVôVOBHÌSF YTBZTOOBMBDBôEFôFSMFSUPQMBN 18 JöMFNMFSJOJOTPOVDVLBÀUS LBÀUS 30 60 = 22JTF&,0, =&,0, = 60 24 j x =WFZBY= 5 j = 4 + 5 = 9 3018=&,0, = 90 9024=�# = 6 j 6 22. 9 23. –994 24. 3 25. 9 53 26. x+1 27. 84 28. 0 29. 6
TEST - 25 &,0,�#* 1. WFTBZMBSOOFOLÑÀÑLPSUBLLBUBöB 5. YQP[JUJGCJSUBNTBZES ôEBLJMFSEFOIBOHJTJEJS 2x + 4x 37 \" # $ % & UPQMBNCJSUBNTBZPMEVôVOBHÌSF YTBZTOO FOLÑÀÑLEFôFSJLBÀUS \" # $ % & 2. WFTBZMBSOOFOCÑZÑLPSUBLCÌMFOJBöB 6. A = 3 ôEBLJMFSEFOIBOHJTJEJS 2 B= 5 \" # $ % & 4 PMEVôVOB HÌSF &,0, \" # BöBôEBLJMFSEFO IBOHJTJEJS \" 15 # 15 $ 15 % 21 & 25 8 4 222 3. YQP[JUJGCJSUBNTBZES 7. \"WF#QP[JUJGUBNTBZMBSES �# Y = 1 * \"WF#BSBMBSOEBBTBMTBZMBS &,0, Y =Y ** \"WF#BSEõLTBZMBS PMEVôVOBHÌSF YTBZTBöBôEBLJMFSEFOIBOHJ *** \"WF#BSEõL¿JGUTBZMBS *7 \"TBZT#TBZTOOUBNLBU TJPMBCJMJS :VLBSEBLJMFSEFOLBÀUBOFTJOEFWFSJMFO \" # $ % & \"WF#TBZMBSOOFOCÑZÑLPSUBLCÌMFOJEJS \" # $ % & 4. \"=2 8. \"= 8 + 8! B =2 B = 12 + 12! PMEVôVOB HÌSF �# \" # + &,0, \" # PMEVôVOB HÌSF �# \" # BöBôEBLJMFSEFO UPQMBNBöBôEBLJMFSEFOIBOHJTJEJS IBOHJTJEJS \" # $ % & \" # $ % & 1. D 2. D 3. E 4. A 54 5. E 6. C 7. # 8. D
&,0,�#* TEST - 26 1. YQP[JUJGCJSUBNTBZES 5. \"JMF#QP[JUJGUBNTBZMBSWF\">#PMNBLÐ[FSF \"= x2 - 2x + 1 �# \" # TBZT\"-#ZFFõJUZBEB\"-#OJO B = x - 1 ¿BSQBOMBSOEBOCJSJEJSYWFZQP[JUJGUBNTBZMBSES PMEVôVOB HÌSF &,0, \" # BöBôEBLJMFSEFO x -Z= 12 IBOHJTJEJS \" Y4 - 2x + x2 + x - 2 PMEVôVOBHÌSF �# Y Z LBÀGBSLMEFôFSBMB # Y4 - x - x + 1 CJMJS $ Y4 + 2x + x2 - x - 1 % Y4 + x + x2 + x + 1 \" # $ % & & Y4 - 1 6. BWFCQP[JUJGUBNTBZMBSES 2. \" #WF$CJSFSQP[JUJGUBNTBZES &,0, B C +�# B C = \"#= a =3 #$= PMEVôVOBHÌSF \"+$UPQMBNOOFOLÑÀÑLEF a+b 8 PMEVôVOB HÌSF B + C UPQMBN BöBôEBLJMFSEFO ôFSJLBÀUS IBOHJTJEJS \" # $ % & \" # $ % & 3. \"WF#CJSCJSJOEFOGBSLMQP[JUJGUBNTBZMBSES 7. B C DWFEUBNTBZMBSES &,0, \" # = 72 2a =C=D=E PMEVôVOBHÌSF \"+#UPQMBNOOFOCÑZÑLWF PMEVôVOBHÌSF B+C +D+EUPQMBNOOÑÀCB FOLÑÀÑLEFôFSMFSJUPQMBNLBÀUS TBNBLMFOLÑÀÑLEFôFSJLBÀUS \" # $ % & \" # $ % & 4. \"QP[JUJGUBNTBZES 8. YQP[JUJGUBNTBZES �# \" = YWFTBZMBSOOFOLпÐLPSUBLLBUES. &,0, \" = #VOBHÌSF YTBZTLBÀGBSLMEFôFSBMS PMEVôVOB HÌSF \" TBZTOO BMBCJMFDFôJ FO LÑ \" # $ % & ÀÑLEFôFSLBÀUS \" # $ % & 1. # 2. D 3. # 4. A 55 5. D 6. C 7. D 8. #
TEST - 27 &,0,�#* 1. \"WF#QP[JUJGUBNTBZMBSBSBMBSOEBBTBMES 5. YWFZCJSCJSJOEFOGBSLMQP[JUJGUBNTBZMBSES \"#=PMEVôVOBHÌSF x+y &,0, \" # +�# \" # EBOB_ x, y i = UPQMBNOOTPOVDVLBÀUS 3 \" # $ % & y PMEVôVOB HÌSF JöMFNJOJO FO LÑÀÑL QP[JUJG x UBNTBZEFôFSJLBÀUS \" # $ % & 2. \"= xZ4[2 6. \" #WF$CJSCJSJOEFOGBSLMQP[JUJGUBNTBZMBSES B = x2Z2[ EBOB_ A, B i = 2 $= x4Z[ EBOB_ A, C i 3 PMEVôVOBHÌSF A +#+$UPQMBNOOFOLÑÀÑL EFôFSJLBÀUS Y Z [GBSLMBTBMTBZMBSPMEVóVOBHËSF \" # $ % & �# \" # $ BöBôEBLJMFSEFOIBOHJTJEJS \" YZ2[2 # Y2Z[2 $ Y2Z2[ % Y2[ & Z2[ 3. BWFCCJSCJSJOEFOGBSLMQP[JUJGUBNTBZES 7. 1 ve 1 QP[JUJGUBNTBZMBSES \"= 108a ab \"= 144b b = 18b - 1 a PMEVôVOBHÌSF B+CFOB[LBÀUS EBOBf 1 , 1 p = 6 ab PMEVôVOBHÌSF 1 LBÀUS a+b \" 1 # 1 $ % & 36 12 \" # $ % & 8. YWFZBSBMBSOEBBTBMQP[JUJGUBNTBZMBSES ,PPSEJOBUEÑ[MFNJOEF 4. BWFCCJSCJSJOEFOGBSLMQP[JUJGUBNTBZES \" �# Y Z &,0, Y Z a + b = 48 OPLUBMBS BöBôEBLJ EPôSVMBSO IBOHJTJOJO Ñ[F PMEVôVOBHÌSF &,0, B C FOÀPLLBÀUS SJOEFCVMVOVS \" # $ % & \" Y= # Z= $ Y+Z= 1 % Z=Y & Z= 2x 1. D 2. C 3. E 4. C 56 5. A 6. D 7. C 8. A
&,0,�#* TEST - 28 1. \" #WF$EPóBMTBZMBSOOFOB[JLJUBOFTJCJSCJSJO- 5. \"= 18! EFOGBSLMES B = 88 �# \" # $ = x x =�# \" # PMEVôVOBHÌSF YTBZTOOQP[JUJGCÌMFOTBZT PMEVôVOBHÌSF \"+#+$UPQMBNOOFOLÑÀÑL LBÀUS EFôFSJLBÀUS \" # $ % & \" Y # Y $ Y % Y & Y 2. r \" #WF$CJSEFOCÐZÐLSBLBNMBSES 6. YWFZBSBMBSOEBBTBMQP[JUJGUBNTBZMBSES r \" #WF$TBZMBSOOIFSIBOHJJLJTJBSEõLEFóJM- &,0, Y Z = 120 EJS x + 90 - 14 = 0 #VOB HÌSF &,0, \" # $ CJSCJSJOEFO GBSLM y LBÀGBSLMUFLTBZEFôFSJWBSES PMEVôVOBHÌSF YTBZTBöBôEBLJMFSEFOIBOHJ TJEJS \" # $ % & \" # $ % & 3. \"WF#CJSEFOCÐZÐLWFCJSCJSJOEFOGBSLMUBNTBZ- 7. 1P[JUJGUBNTBZMBSEB MBSES &,0, B C = a AB PMEVôVOBHÌSF �# C- C+B B+ TP EKOK f , p OVDVBöBôEBLJMFSEFOIBOHJTJEJS EBOB_ A, B i EBOB_ A, B i \" B- C B+ $ B2 - a + 1 JöMFNJOJOTPOVDVBöBôEBLJMFSEFOIBOHJTJPMB CJMJS \" # $ % & % B2 + a + & B2 - a 4. \"#JLJCBTBNBLMEPóBMTBZWFOCJSEFOCÐZÐLQP- 8. YQP[JUJGUBNTBZES [JUJGUBNTBZES �# Y + Y + TBZT BöBôEBLJMFSEFO AB + AB IBOHJTJPMBNB[ n n+1 \" # $ % & UPQMBNOUBNTBZZBQBO\"#JLJCBTBNBLMTBZ TFOCÑZÑLEFôFSJOJBMEôOEB\"+#LBÀPMVS \" # $ % & 1. # 2. # 3. D 4. C 57 5. D 6. A 7. D 8. E
·/÷7&34÷5&:&)\";*3-*, 2. MODÜL 4\":*,·.&-&3÷#²-·/&#÷-.&3\"4:0/&-4\":*-\"3 www.aydinyayinlari.com.tr &,0,�#** �#WF&,0,JMF÷MHJMJ1SPCMFNMFS ÖRNEK 4 ÖRNEK 1 ¶¿CBTBNBLMCJSEPóBMTBZ rJMFCËMÐOEÐóÐOEFLBMBO #JSLVUVEBLJLBMFNMFSпFSпFSWFEËSEFSEËSEFSTBZME- rJMFCËMÐOEÐóÐOEFLBMBO óOEBBSUNBNBLUBES rJMFCËMÐOEÐóÐOEFLBMBO CVMVONBLUBES #VOB HÌSF LVUVEBLJ LBMFN TBZT BöBôEBLJMFSEFO #VTBZOOBMBCJMFDFôJFOLÑÀÑLJLJEFôFSJOUPQMBN IBOHJTJPMBNB[ LBÀUS \" # $ % & A =B+ 1 =C+ 3 =D+ 6 A + 2 = B+ 1) = C+ 1) = D+ 1) &,0, = 12 &,0, = 120 ,BMFNTBZTOB\"EFOJSTF\"=L L` Z+) A + 2 =L L` Z+) A =PMBNB[ L= 1 j A = 118 L= 2 j A = 238 j 356 ÖRNEK 2 (ÐOFõ PZVODBLMBSOCFõFSMJWFBMUõBSMHSVQMBSBBZSO- ÖRNEK 5 DBJLJPZVODBLBSUNBLUBES B CWFDQP[JUJGUBNTBZMBSES &OB[UBOFPZVODBôPMNBTOJTUFZFO(ÑOFö CB \"= 2a + 1 = 4b +=D- 12 CBTOEBOLBÀPZVODBLEBIBJTUFNFMJEJS PMEVôVOBHÌSF FOLÑÀÑL\"TBZTOOSBLBNMBSUPQ MBNLBÀUS 0ZVODBLTBZTOB\"EFOJSTF A = 5x + 2 =Z+ 2 A = B- 1) + 3 =C+ 3 = D- 3) + 3 A - 2 = 5x =Z (A - 2)NJO =&,0, = 30 A - 3 = B- 1) =C= D- 3) A - 2 =L L` Z+) A = 32 j 4 &,0, = 20 A - 3 =L L` Z+) L= 1 j A - 3 = \"= 23 j 5 ÖRNEK 3 ÖRNEK 6 B CWFDQP[JUJGUBNTBZMBSES WFMJUSFMJL[FZUJOZBóEPMVG¿MBS LBSõUSM- NBEBOFõJUIBDJNMJõJõFMFSFEPMEVSVMBDBLUS \"=B+ 2 = 4b + 2 =D+ 2 #VOBHÌSF FOB[LBÀöJöFLVMMBOMNBMES PMEVôVOB HÌSF \" TBZTOO ÑÀ CBTBNBLM FO CÑZÑL #VMVOBDBL�#EFôFSJöJöFOJOIBDNJOJWFSFDFLUJS EFôFSJLBÀUS �# = 20 MUJÀJO= 21 =öJöF A =B+ 2 =C+ 2 =D+ 2 MUJÀJO=öJöF A - 2 =B=C=D MUJÀJO=öJöFjöJöF (A - 2)NJO =&,0, = 60 A - 2 =L L` Z+) L= 16 j A - 2 = 960 j A = 962 1. E 2. 4 3. 962 58 4. 356 5. 5 6. 47
www.aydinyayinlari.com.tr 4\":*,·.&-&3÷#²-·/&#÷-.&3\"4:0/&-4\":*-\"3 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 7 ÖRNEK 10 \"MJ õFLJMEFLJ EFNJS ¿VCVLMBS Fõ V[VOMVLMV QBS¿BMBSB ,FOBSV[VOMVLMBSDNWFDNPMBOEJLEËSUHFOMFSLVM- BZSNBTJ¿JOCJSEFNJSDJVTUBTJMFBOMBõZPS MBOMBSBLFOLпÐLBMBOBTBIJQCJSLBSFFMEFFEJMNFLJT- UFOJZPS 24m AB #VJöJÀJOFOB[LBÀEJLEÌSUHFOLVMMBOMNBMES 42m EKOK = = 40 A^ Kare h CD = 40.40 36m EF A^ Dikdörtgen h 5.8 6TUB IFS CJS LFTJN JÀJO 5- ÑDSFU BMBDBôOB HÌSF \"MJhOJOÌEFZFDFôJQBSBFOB[LBÀMJSBES 40 cm = 40 1BSÀBMBSOFOV[VOCPZBTBIJQPMNBMBSHFSFLJS 40 cm �# = 6 =QBSÀB LFTJN ÖRNEK 11 =QBSÀB LFTJN =QBSÀB LFTJNjLFTJN 5BCBOBZSUMBSDNWFDNPMBOCJSPEBOOUBCB- 14.5 = 70 TL OË[EFõLBSFGBZBOTMBSJMFLBQMBOBDBLUS #VJöJÀJOFOB[LBÀBEFUGBZBOTLVMMBOMNBMES ÖRNEK 8 �# = 60 ,FOBSV[VOMVLMBSNWFNPMBOEJLEËSUHFOõFLMJO- 'BZBOTMBSOCJSBZSUDN EFLJCJSCBI¿FOJOFUSBGOBLËõFMFSFEFCJSFSUBOFHFMFDFL Alan^ Oda tabanı h 360.420 õFLJMEFBóB¿EJLJMFDFLUJS = 42 #VJöJÀJOFOB[LBÀBôBÀHFSFLJS Alan^ Fayans h 60.60 �# = 4 Çevre 2^ 36 + 28 h = = 32 Ebob 4 ÖRNEK 9 ÖRNEK 12 ,FOBS V[VOMVLMBS N WF N PMBO EJLEËSUHFO CJ¿J- #PZVUMBS DN DN WF DN PMBO EJLEÌSUHFO NJOEFLJ CJS CBI¿F LBSF õFLMJOEF QBS¿BMBSB BZSMQ PMV- QSJ[NBT öFLMJOEFLJ Fö UVôMBMBSEBO FO B[ LBÀ UBOF õBOUÐNLBSFQBS¿BMBSOLËõFMFSJOFCJSFSBóB¿EJLJMJZPS TJZMFCJSLÑQCMPLZBQMBCJMJS #VJöJUBNBNMBNBLJÀJOFOB[LBÀBôBÀHFSFLJS �# = 12 &,0, = 180 60 BôBÀ =\"ôBÀTBZTY%JLFZEPôSV ,ÑQÑOCJSBZSUDN 48 BôBÀ = d 48 + 1 n.d 60 + 1 n Hacim ^ küp h 180.180.180 BôBÀ = = 1080 BôBÀ Hacim ^ DP h 15.18.20 BôBÀ EBOB EBOB 6. dikey = 5.6 = 30 5. dikey 4. dikey 3. dikey 2. dikey 1. dikey 7. 70 8. 32 9. 30 59 10. 40 11. 42 12. 1080
·/÷7&34÷5&:&)\";*3-*, 2. MODÜL 4\":*,·.&-&3÷#²-·/&#÷-.&3\"4:0/&-4\":*-\"3 www.aydinyayinlari.com.tr ÖRNEK 13 ÖRNEK 16 #PZVUMBSN N NPMBOEJLEËSUHFOMFSQSJ[NBTCJ- #PZVUMBSNFUSFWFYNFUSFPMBOCJSEJLEËSUHFOFõLB- ¿JNJOEFLJCJSPEB LÐQCJ¿JNJOEFLJFõLVUVMBSMBEPMEVSV- SFMFSFCËMÐOFDFLUJS MBDBLUS &MEFFEJMFOLBSFMFSJOTBZTPMEVôVOBHÌSF YBöB #VOBHÌSF LÑQCJÀJNJOEFLJLVUVMBSEBOFOB[LBÀUB ôEBLJMFSEFOIBOHJTJPMBCJMJS OFHFSFLMJEJS \" # $ % & �# = 2 ,ÑQLVUVMBSOCJSBZSUN Alan^ Dikdörtgen h 12.x = = 12 Hacim ^ oda h 4.6.12 Alan^ Kare h EBOB.EBOB = = 36 j�#2 = x j x =PMBCJMJS Hacim ^ kutu h 2.2.2 ÖRNEK 14 ÖRNEK 17 #PZVUMBS DN DN WF DN PMBO EJLEËSUHFO QSJ[NB ôFLJMEF CJS PEBOO LBSF UBCBOOO GBZBOTMBS JMF EËõFO- õFLMJOEFLJ UBIUB CMPLMBS ÐTU ÐTUF WF ZBO ZBOB EJ[JMFSFL NFTJHËTUFSJMNJõUJS LÐQMFSZBQMBDBLUS AAA 5BIUB CMPLMBSEBO UPQMBNEB UBOF CVMVOEVôVOB HÌSF FOB[TBZEBFöLÑQMFSZBQMSTBLBÀUBOFTJBS UBS &,0, = 20 BB Hacim^ Küp h 20.20.20 = = 200 Hacim ^ D.P h 2.4.5 A A A BB YYCPZVUMBSOEBLJLÑQJÀJOCMPLHFSFLJS Y Y CPZVUVOEBLJ LÑQMFSEFO UBOFTJ JMF ZFOJ LÑQMFS ZBQMBCJMJS 5PQMBNEB UBOF LÑQ ZBQMS WF HF SFLMJLÑQTBZTUBOFEJSUBOFTJBSUBS A 30 cm B 40 cm 50 cm 20 cm ÖRNEK 15 0EBOO UBCBO N2 EFO CÑZÑL PMEVôVOB HÌSF PEBOOUBCBOFOB[LBÀN2PMNBMES #JSIBWV[B\"MJTBBUUFCJS &SEJTBBUUFCJSWF(ÐOFõ TBBUUFCJSHJUNFLUFEJS 1m UBOFTJ JMF CJS AA A LBSFPMVöBDBLUS )FQTJ CFSBCFS BZO BOEB IBWV[B HJUNFMFSJOEFO (Ñ OFöJOJODJLF[HJEJöJOFLBEBSHFÀFOTÑSFJÀJOEF\"MJ 1m B B B B B =N2 WF&SEJLBÀLF[CFSBCFSIBWV[BHJUNJöMFSEJS AA (ÑOFöLF[HJEJöJ=TBBU &,0, = 12 TBBU \"MJ WF &SEJhOJO CJSMJLUF IBWV[B HJEJö TÑSFMFSJ EJSTBBUJÀJOEF =EFGBCJSMJLUFHJEFDFLMFSEJS 13. 36 14. 36 15. 4 60 16. C 17. 4
&,0,�#** TEST - 29 1. B CWFDQP[JUJGUBNTBZMBSES 4. \"MJhOJOCJMZFMFSJOJOTBZTEFOGB[MBES\"MJCJMZF- \"= 8a + 4 =C+ 4 =D+ 4 MFSJOJBSWFõFSTBZEóOEBIFSTFGFSJOEFCJM- FöJUMJôJOF HÌSF \" TBZTOO FO LÑÀÑL EFôFSJ ZFBSUUSZPS LBÀUS #VOBHÌSF \"MJhOJOFOB[LBÀCJMZFTJWBSES \" # $ % & \" # $ % & 2. B C DQP[JUJGUBNTBZMBSES 5. ôFLJMEFLJEJLEËSUHFOQSJ[NBTOOUÐNZÐ[FZMFSJCP- Aa Ab A9 ZBOQ IJ¿ QBS¿B BSUNBZBDBL õFLJMEF FO CÐZÐL IB- DJNMJFõLÐQMFSFBZSMBDBLUS 8 6C 48 cm 647 18 cm PMEVôVOBHÌSF ÑÀCBTBNBLMFOLÑÀÑL\"TBZ 36 cm TOOSBLBNMBSUPQMBNLBÀUS #VOB HÌSF FMEF FEJMFO LÑQMFSJO LBÀ UBOFTJOJO \" # $ % & ZBMO[CJSZÑ[ÑCPZBMES \" # $ % & 3. Y Z [QP[JUJGUBNTBZMBSES 6. WFTBZMBSOOCJSBTBZTJMFCÌMÑNÑOEFO \"= 7x =Z=[ LBMBO TSBTZMB WF PMEVôVOB HÌSF B TBZT FöJUMJôJOJTBôMBZBOFOLÑÀÑL\"TBZTLBÀUS OO FO CÑZÑL EFôFSJOJO SBLBNMBS UPQMBN LBÀ US \" # $ % & \" # $ % & 1. C 2. C 3. A 61 4. C 5. C 6. C
TEST - 30 &,0,�#** 1. #JSHSVQËóSFODJ\"TOGOEBLJTSBMBSBпFSMJPUVSVS- 4. JMF CÌMÑOEÑôÑOEF JMF CÌMÑOEÑôÑOEF MBSTBËóSFODJBZBLUBLBMZPS#TOGOEBLJTSBMB- LBMBO WFSFO ÑÀ CBTBNBLM LBÀ EPôBM TBZ WBS SBEËSEFSMJPUVSVSMBSTBCJSTSBCPõLBMZPS ES (SVQUBLJÌôSFODJTBZTOOEFOGB[MBPMEVôV \" # $ % & CJMJOEJôJOF HÌSF CV HSVQUB FO B[ LBÀ ÌôSFODJ WBSES \" # $ % & 2. &OLÑÀÑLPSUBLLBUMBSPMBOGBSLMJLJQP[JUJG 5. TBZTOBFOLÑÀÑLIBOHJEPôBMTBZFLMFOJS UBNTBZOOUPQMBNFOÀPLYWFFOB[ZPMEVôV TF WFJMFUBNCÌMÑOFCJMJS OBHÌSF Y-ZLBÀUS \" # $ % & \" # $ % & 3. #JSNBLJOFZBSENZMBDN DNWFDNCPZ- 6. B C DQP[JUJGUBNTBZMBSES MBSOEBLJ¿VCVLMBS FõJUV[VOMVLUBFOCÐZÐLQBS¿B- \"=B=C-=D- MBSBELEBCËMÐOFCJMJZPS PMEVôVOB HÌSF \" TBZTOO FO LÑÀÑL EFôFSJ #VOB HÌSF FO LTB ÀVCVôVO LFTJN JöMFNJ LBÀ LBÀUS EBLJLBTÑSNÑöUÑS \" # $ % & \" # $ % & 1. C 2. D 3. C 62 4. A 5. D 6. E
&,0,�#** TEST - 31 1. YQP[JUJGCJSUBNTBZES 4. #JSJEJóFSJOJOLBUOEBOFLTJLPMBOJLJTBZNBTB- WFYTBZTOO�#VWF&,0,V ZTOO&,0,VWF�#VUÐS PMEVôVOBHÌSF FOLÑÀÑLYTBZTOOQP[JUJGCÌ #VTBZMBSOUPQMBNLBÀUS MFOTBZTLBÀUS \" # $ % & \" # $ % & 5. \"õBóEBLJ õFLJMEF CJSJ EJLEËSUHFO EJóFSJ LBSF õFL- MJOEFJ¿J¿FJLJCBI¿FHËSÐMNFLUFEJS)FSJLJCBI¿F- OJOFUSBGOBLËõFMFSFEFCJSFSUBOFHFMNFLLPõVMVZ- MBFõJUBSBMLMBSJMFGJEBOEJLJMFDFLUJS 2. ¶¿GBSLMUPSCBEBLH LHWFYLHVOCVMVONBL- D 36 m C UBES'BSLMUPSCBMBSEBLJVOMBSIJ¿LBSõUSMNBZBDBL 24 m K 16 m WF IJ¿ BSUNBZBDBL õFLJMEF FõJU BóSMLUB QBLFU 16 m F ZBQMZPS A EB #VOBHÌSF YLHVOJÀJOLVMMBOMBOQBLFUTBZT #VJöJÀJO FOB[LBÀGJEBOHFSFLJS BöBôEBLJMFSEFOIBOHJTJPMBCJMJS \" # $ % & \" # $ % & 3. YQP[JUJGUBNTBZES 6. B CWFDQP[JUJGUBNTBZMBSES �# Y = x \"= 4a -= C+ + 2 = D- - 8 FõJUMJóJWFSJMJZPS \" FOLÑÀÑLEFôFSJOJBMEôOEBB+C+DUPQMB #VOBHÌSF YLBÀGBSLMEFôFSBMS NLBÀUS \" # $ % & \" # $ % & 1. D 2. A 3. A 63 4. # 5. # 6. C
TEST - 32 &,0,�#** 1. #PZVUMBSDNWFDNPMBOEJLEËSUHFOõFLMJOEFLJ 5. \"SEõLJLJQP[JUJGUBNTBZOO¿BSQNMBSOB�#V CJSLBSUPOFOCÐZÐLBMBOMLBSFMFSFCËMÐOFDFLUJS FLMFOJODFFMEFFEJMJZPS #V TBZMBSO &,0, V BöBôEBLJMFSEFO IBOHJTJ #VJöMFNJOTPOVOEBFOB[LBÀLBSFFMEFFEJMFCJ MJS EJS \" # $ % & \" # $ % & 2. 0UPNBUJLпTBBUUFOIFSCJSJTSBTJMFEL EL WFELEBCJS¿BMNBLUBES 4BBUEFBZOBOEBÀBMBOTBBUMFSCJSEBIB 6. .FINFU (ÐOFõZBõOEBES.FINFUWF(Ð- TBBULBÀUBUFLSBSCJSMJLUFÀBMBDBLUS OFõLBSUMBSOÐ[FSJOFEFOCBõMBZBSBLLFOEJZBõMB- \" # $ SOBLBEBSPMBOTBZMBSZB[ZPSMBS:BõMBSJMF�# VLFOEJTJOJWFSFOTBZMBSOZB[MPMEVóVLBSUMBSBMQ % & EBIBTPOSBCVTBZMBSEBOEBBZOPMBOMBSCJSLVUV- ZBBUZPSMBS #VOBHÌSF LVUVEBLBÀLBSUCVMVOVS \" # $ % & 3. %BJSFTFM CJS QJTUUF ZBSõBO п ZBSõNBD TSBTZMB WFELEBCJSUVSBUBCJMNFLUFEJS \"ZOBOEBBZOZÌOEFIBSFLFUFEFOZBSöNBD MBS UFLSBS CBöMBOHÀ OPLUBTOEB CVMVöUVLMBSO EB FOÀPLUVSBUBOLBÀUVSBUNöUS \" # $ % & 7. 1P[JUJG CJS UBN TBZOO FLTJôJ JMF GB[MBTOO �#VBöBôEBLJMFSEFOIBOHJTJPMBCJMJS \" # $ % & 4. JMFCÌMÑOFCJMFOBSEöLJLJTBZOO&,0,V PMEVôVOBHÌSF CVTBZMBSOUPQMBNLBÀUS \" # $ % & 1. A 2. C 3. # 4. # 64 5. A 6. # 7. #
www.aydinyayinlari.com.tr 4\":*,·.&-&3÷#²-·/&#÷-.&3\"4:0/&-4\":*-\"3 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, &,0,�#*** Periyodik Tekrar Eden Olayları İçeren ÖRNEK 4 Problemler ÖRNEK 1 #JSFMFLUSJLQBOPTVOEBLJEËSUGBSLMMBNCB WF EBLJLBEBCJSZBOQTËONFLUFEJS #JSEPLUPSCFõHÐOEFCJSOËCFUUVUVZPS %ÌSEÑ CJSMJLUF BZO BOEB ZBOELUBO FO B[ LBÀ TBBU TPOSBUFLSBSCJSMJLUFZBOBSMBS ÷MLOÌCFUJOJDVNBHÑOÑUVUBOCVEPLUPSTFLJ[JODJOÌ CFUJOJIBOHJHÑOUVUBS &,0, =EL EL TBBUUJS 8 - 1 = 7 j 7 . 5 = 35 j 35 7 5 0 ,BMBOTGSPMEVôVOEBODVNBHÑOÑ ÖRNEK 5 ÖRNEK 2 ¶¿¿BMBSTBBUTSBTZMB 1 , 5 ve 7 TBBUUFCJS¿BMNBL- 46 8 #JSIFNõJSFHÐOEFCJSOËCFUUVUNBLUBES UBES ·ÀÑODÑOÌCFUJOJQB[BSHÑOÑUVUBOCVIFNöJSFEPLV [VODVOÌCFUJOJIBOHJHÑOUVUBS öMLLF[TBBUEBCJSMJLUFÀBMELMBSOBHÌSFUFLSBS TBBULBÀUBCJSMJLUFÀBMBSMBS 9 - 3 = 6 j 6 . 7 = 42 j EKOKd 1 , 5 , 7 n = EKOK^ 1, 5, 7 h = 35 = 17, 5 42 7 468 EBOB^ 4, 6, 8 h 2 0 j TB TBEL ,BMBOTGSPMEVôVOEBOQB[BSHÑOÑ j 07.00 ÖRNEK 3 ÖRNEK 6 #JSBTLFSBMUHÐOEFCJSOËCFUUVUVZPS ¶¿ CJTJLMFUMJ EBJSFTFM CJS QJTUJO FUSBGOEB TSBTZMB EL 0O TFLJ[JODJ OÌCFUJOJ DVNBSUFTJ HÑOÑ UVUBO CV BT ELWFELEBCJSUVSBUBCJMJZPS LFS BMUODOÌCFUJOJIBOHJHÑOUVUNVöUVS \"ZOOPLUBEBOBZOBOEBBZOZÌOEFIBSFLFUFCBö 18 - 6 = 12 j 12 . 6 = 72 j 72 7 MBZBOCVCJTJLMFUMJMFSJLJODJLF[ZBOZBOBHFMEJLMFSJO EF TBBU PMEVôVOB HÌSF IBSFLFUF TBBU LBÀUB 2 CBöMBNöMBSES ,BMBOEJS$VNBSUFTJEFOHFSJZFTBZMS1FSöFNCFHÑ OÑ &,0, =EL CVMVöNBEL=TBEL PMEVôVOEBOTBBUUFCBöMBNöUS 1. $VNB 2. 1B[BS3. 1FSöFNCF 65 4. 2 5. 07.00 6. 10.25
·/÷7&34÷5&:&)\";*3-*, 2. MODÜL 4\":*,·.&-&3÷#²-·/&#÷-.&3\"4:0/&-4\":*-\"3 www.aydinyayinlari.com.tr ÖRNEK 7 ÖRNEK 10 #JSMJNBOBHÐOEFCJS\"HFNJTJ HÐOEFCJS#HFNJ- (FPNFUSJEFB¿ËM¿ÐCJSJNJPMBOEFSFDFOJOBTLBUMBS TJWFHÐOEFCJS$HFNJTJHFMNFLUFEJS EFSFDF=ELWFEL=TBOJZF PMBSBLUBONMBOS #VOBHÌSF HFNJMFSBZOHÑOMJNBOBHFMEJLUFOFOB[ LBÀHÑOTPOSBUFLSBSCJSMJLUFBZOMJNBOBHFMJSMFS öFLMJOEF UBONMBOBO CJS EFSFDF TBZBDOEB TB OJZFMJL CJS BÀOO HÌSÑOUÑTÑ BöBôEBLJMFSEFO IBOHJ &,0, =PMEVôVOEBO TJEJS HÑOTPOSBUFLSBSCJSMJLUFBZOMJNBOBHFMJSMFS A) B) 002 40 36 002 39 4 6 C) D) 003 42 32 002 36 1 6 ÖRNEK 8 E) 002 41 36 WFTBZMBSOOQP[JUJGUBNTBZLBUMBS WFTB- USEBLJLVUVMBSBLFOEJEFóFSMFSJJMFTÐUVOOVNBSBMBSBZO 9376 3600 PMBDBLõFLJMEFZFSMFõUJSJMJZPS 2 TÐUVO 2176 60 j 002 . 36 . 16 TÐUVO 36 TÐUVO 16 TBUS TBUS 4 8 TBUS 10 #VOBHÌSF JMLEFGBLBÀODTÑUVOEBLJLVUVMBSOÑÀÑ EFEPMVPMBDBLUS &,0, = PMEVôVOEBO TÑUVOEBLJ ÑÀ LV ÖRNEK 11 UVEPMVEVS 0LVM JEBSFTJ CFTMFONF ¿BOUBTOEB CVMVONBT HFSFLFO J¿FDFLMFSMJTUFTJOJBõBóEBLJHJCJCFMJSMJZPS 1B[BSUFTJ 4BM ¦BSöBNCB 1FSöFNCF $VNB 4ÐU -JNPOBUB 1PSUBLBM 7JõOFTVZV &MNB TVZV ÖRNEK 9 TVZV BZ=HÐOPMBSBLWFSJMJZPS 1B[BSUFTJ HÑOÑ PLVMV BÀMBO .FINFUhJO HÑO \"ZOZMJÀJOEF/JTBOTBMHÑOÑLVUMBOEôOBHÌSF CFTMFONFÀBOUBTOEBIBOHJJÀFDFLCVMVOVS &LJNIBOHJHÑOLVUMBOS /JTBO-&LJNBSBT+ 6 =HÑO 179 5 186 7 ,BMBOUÑS4BMEBOEÌSUHÑOTPOSBDVNBS 4 4 UFTJPMVS ,BMBO UÑS 1B[BSUFTJEFO CBöMBZBSBL HÑO QFSöFN CFHÑOÑPMVS 1FSöFNCFHÑOÑWJöOFTVZV 7. 120 8. 60 9. $VNBSUFTJ 66 10. D 11. 7JöOFTVZV
www.aydinyayinlari.com.tr 4\":*,·.&-&3÷#²-·/&#÷-.&3\"4:0/&-4\":*-\"3 .0%·- ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 12 ÖRNEK 14 )FSBENDNPMBOCJSLBSODBDNMJLCJSUFQFZFUS- #JSQJMPUEËSUHÐOCPZVODBUPQMBNTBBUV¿VõZBQQJLJ NBOSLFOIFSTFGFSJOEFBENUSNBOQBENHFSJLB- HÐOEJOMFOJZPS ZZPS ÷MLVÀVöVOBTBMHÑOÑÀLBOCVQJMPUTBBUVÀVöV #VOB HÌSF LBSODB UFQFZF VMBöUôOEB UPQMBN LBÀ FOHFÀIBOHJHÑOJÀJOEFUBNBNMBS BENBUNöUS 1JMPUJÀJOQFSJZPUHÑOEÑS )FSBENEBBENUSNBOZPS 135 : 15 = 9 j 9 . 6 = 54 25 3 j BEN j1B[BSVÀVöBÀLNBM%FNFLLJDVNB 8 UBNBNMBS 54 7 1 5 ÖRNEK 15 ôFLJMEFCJSLPOUSPMTÐ[LBWõBLUBTPMBEËOÐõÐWFEÐ[HJ- EJõJ EÐ[FOMFZFO [BNBO HËTUFSHFMJ USBGJL MBNCBMBS WFSJM- NJõUJS ÖRNEK 13 r 4PMBEËOÐõMBNCBTOEBTBOJZFLSN[ TBOJZF TBS TBOJZFZFõJMõLZBOZPS .FINFU#FZEÐ[FOMJPMBSBL r %Ð[HJEJõMBNCBTOEBTBOJZFLSN[ TBOJZF r \"SBDZMBHÐOEFCJSEFQPZBLUIBSDBZQEJóFSHÐ- TBSWFTBOJZFZFõJMZBOZPS OÐOTBCBIEFQPTVOVUBNPMBSBLEPMEVSVZPS r )FSTBOJZFCJSBSB¿TPMBEËOFCJMJZPSWFCJSBSB¿LBW- r )FSHÐO HÐOCPZVLNZPMLBUFEJZPS õBóEÐ[HF¿FCJMJZPS r \"SBDOLNEFCJSCBLNBHËUÐSÐZPS 5SBGJL MBNCBMBSOO IFS JLJTJ EF TBBU EB LSN- .FINFU#FZLFTJOUJTJ[PMBSBLIFSHÐOBSBDOLVMMBONB- [ZBOZPS ZBEFWBNFEJZPS #VOBHÌSF TBBU53FLBEBSLBWöBLUBOUPQMBN #JSTBMHÑOÑIFNZBLUBMQIFNEFBSBDOCBLNB LBÀBSBÀHFÀNJöUJS HÌUÑSNFL [PSVOEB LBMBO .FINFU #FZ CJS TPOSBLJ LF[ IBOHJ HÑO BZO EVSVNMB LBSö LBSöZB LBMBDBL JMF BSBTOEB TPMB HJEFO BSBÀ EÑ[ US HJEFOBSBÀ JMF53BSBTOEBIFNTPMBIFNEÑ[HJEFO .FINFU#FZ BSBDOCBLNBHÑOEFCJSHÌUÑSÑZPS öFSBSBÀUPQMBNBSBÀ &,0, = 300 7 6 ,BMBOES4BMEBOHÑOTPOSBQB[BSUFTJPMVS 12. 57 13. Pazartesi 67 14. Cuma 15. 184
TEST - 33 &,0,�#*** 1. #JSIFNõJSFCFõHÐOEFCJSOËCFUUVUVZPS 4. #JSËóSFODJHÐOEFCJSNBUFNBUJLEFOFNFTJ¿Ë[Ð- ZPS %PLV[VODVOÌCFUJOJQB[BSUFTJUVUBOCVIFNöJ ÷ML EFOFNFTJOJ DVNBSUFTJ HÑOÑ ÀÌ[FO ÌôSFODJ SFÑÀÑODÑOÌCFUJOJIBOHJHÑOUVUNVöUVS BMUODEFOFNFTJOJIBOHJHÑOÀÌ[FS \" 1FSõFNCF # $VNB \" 1B[BSUFTJ # 4BM $ $VNBSUFTJ % 1B[BS $ ¥BSõBNCB % 1FSõFNCF & 1B[BSUFTJ & $VNB 2. \" #WF$MBNCBMBSTSBTZMBEL ELWFEL 5. #JSEPLUPSBMUHÐOEFCJS CJSIFNõJSFEËSUHÐOEFCJS BSBZMBZBOQTËOÐZPSMBS OËCFUUVUVZPS #FSBCFS JML ZBOöMBSOEBO ÑÀÑODÑ ZBONBMBSOB #FSBCFS JML OÌCFUMFSJOJ QB[BSUFTJ UVUUVLMBSOB LBEBS HFÀFO TÑSFEF # MBNCBT LBÀ LF[ ZBOQ HÌSF CFSBCFS EÌSEÑODÑ OÌCFUMFSJOJ IBOHJ HÑO TÌONÑöUÑS UVUBSMBS \" # $ % & \" $VNBSUFTJ # $VNB $ 1FSõFNCF % ¥BSõBNCB & 4BM 3. :FEJIBSGMJ4\":*-\"3LFMJNFTJEFGBZBOZBOBZB- 6. .\"3.\"3\"LFMJNFTJZFUFSMJTBZEBZBOZBOBZB[M- [MZPS ZPS #VOB HÌSF CBöUBO IBSG BöBôEBLJMFSEFO #VOB HÌSF CV ZB[MNEB IBSGF LBEBS LBÀ IBOHJTJEJS UBOF\"IBSGJLVMMBOMNöUS \" # $ % & \" 4 # \" $ : % - & 3 1. C 2. D 3. # 68 4. C 5. E 6. C
&,0,�#*** TEST - 34 1. #VHÑO HÑOMFSEFO DVNB PMEVôVOB HÌSF 4. %ÌSEÑOLBUPMBOIFSIBOHJCJSZMJÀFSJTJOEF HÑOTPOSBIBOHJHÑOPMBDBLUS 0DBL DVNB HÑOÑ JTF .BZT IBOHJ HÑOF EFOLHFMNJöUJS \" 1FSõFNCF # ¥BSõBNCB \" 1B[BS # $VNBSUFTJ $ 4BM % 1B[BSUFTJ $ $VNB % 1FSõFNCF & 1B[BS & ¥BSõBNCB 2. \"MJ #BOVWF$BOBZOHÐOTQPSTBMPOVOBHJUNFZF 5. #JS UFMFGPO VZHVMBNBT LVMMBODMBSOB VZHVMBNB- CBõMZPSMBS ZUFMFGPOVOBJMLJOEJSFOLVMMBODTOEBOCBõMBZBSBL TSBTZMBBõBóEBWFSJMFOBMHPSJUNBZLVMMBOBSBL \"MJHÑOEFCJS #BOVHÑOEFCJSWF$BOHÑO EF CJS TQPS TBMPOVOB HJUUJôJOF HÌSF LBÀ HÑO BYC TPOSBJMLLF[ÑÀÑTQPSTBMPOVOBBZOHÑOHJEFS õFLMJOEFHËSÐMFOõJGSFMFSÐSFUJZPS MFS BEFOCÐZÐLiBuEFóJõLFOJZFSJOFEBIB \" # $ % & ËODFZB[MNBNõFOLпÐLBTBMTBZES CBEBOTPOSBHFMFOJMLBTBMTBZES YBJMFCBSBTOEBiYuEFóJõLFOJZFSJOF EBIBËODFZB[MNBNõFOLпÐL¿JGUTBZES ôJGSFBYC BJMFCBSBTOEBY BJMFCBSBTOEBY ZFSJOFZB[MBCJM- ZFSJOFZB[MBCJMF- DFL¿JGUTBZMBS DFL¿JGUTBZMBS UÐLFONFEJ UÐLFOEJ #VBMHPSJUNBJMFÐSFUJMFOJMLпõJGSFTSBTZMB LVMMBODJ¿JO 3. #JS SBEZP QSPHSBNOEB CBõMBOH¿UBO JUJCBSFO TSB- LVMMBODJ¿JO TZMB EBLJLBMLQBS¿BWFEBLJLBSFLMBNZB- LVMMBODJ¿JO ZOJMF EBLJLBMLDBOMUFMFGPOCBóMBOUTZBQM- ZPS õFLMJOEFEJS #VOB HÌSF JLJ TBBU TÑSFO QSPHSBN CPZVODB 6ZHVMBNBOO TSBEBLJ LVMMBOD JÀJO ÑSFUUJôJ UPQMBNLBÀEJOMFZJDJDBOMZBZOBCBôMBONöUS öJGSFBöBôEBLJMFSEFOIBOHJTJEJS \" # $ % & \" # $ % & 1. A 2. # 3. C 69 4. E 5. D
TEST - 35 &,0,�#*** 1. #JSEPLUPSHÐOEF CJSIFNõJSFHÐOEFCJSOËCFU 4. \"MJTFLJ[HÐOEFCJSBOOFBOOFTJOF[JZBSFUFHJEJZPS UVUNBLUBES 5FZ[FTJJTFпHÐOEFCJSBOOFTJOJ[JZBSFUFEJZPS #FSBCFS JML OÌCFUMFSJOJ QB[BS HÑOÑ UVUBSMBSTB \"MJWFUFZ[FTJJMLLF[ÀBSöBNCBHÑOÑBOOFBOOF CFSBCFSBMUODOÌCFUMFSJOJIBOHJHÑOUVUBSMBS TJOJOFWJOEFLBSöMBöULMBSOBHÌSFBMUODLBSö MBöNBMBSIBOHJHÑOPMBDBLUS \" 1B[BSUFTJ # 4BM $ ¥BSõBNCB % 1FSõFNCF \" 1FSõFNCF # $VNB & $VNB $ $VNBSUFTJ % 1B[BS & 1B[BSUFTJ 2. #JSMJNBOBCJSHFNJTFLJ[HÐOEFCJSZBOBõNBLUBES 1B[BS HÑOMFSJ LBQBM PMBO CV MJNBOB BZO HFNJ EÌSEÑODÑ LF[ QB[BSUFTJ HÑOÑ HFMEJôJOF HÌSF EPLV[VODVLF[IBOHJHÑOHFMJS \" 1B[BSUFTJ # 4BM $ ¥BSõBNCB % 1FSõFNCF 5. #JSLPOGFLTJZPOJõ¿JTJIBGUBMLTBBUMJLNFTBJTJOJ & $VNB r )BGUBJ¿JIFSHÐOTBCBI-WFËóMFEFO TPOSB-TBBUMFSJBSBTOEB 3. #VHÑOHÑOMFSEFOÀBSöBNCBWFTBBUPMEV r )BGUBTPOVDVNBSUFTJHÐOÐËóMFEFOTPOSB ôVOBHÌSF TBBUELTPOSBTBöBôEBLJMFS - TBBUMFSJ BSBTOEB ¿BMõBSBL UB- EFOIBOHJTJEJS NBNMBNBLUBES \" 1B[BSUFTJHÐOÐTBBU ,POGFLTJZPOJõ¿JTJCJSHËNMFLÐSFUNFLJ¿JOLFTJOUJ- # 4BMHÐOÐTBBU TJ[PMBSBLELZBJIUJZB¿EVZVZPS $ $VNBHÐOÐTBBU % 1FSõFNCFHÐOÐTBBU ÷ML HÌNMFôJ ÑSFUNFZF DVNBSUFTJ HÑOÑ UF & ¥BSõBNCBHÐOÐTBBU CBöMBZBO CV JöÀJ HÌNMFôJ BöBôEBLJ [BNBO EJMJNMFSJOEFOIBOHJTJOEFUBNBNMBS \" 4BM TBBUEJMJNJ # ¥BSõBNCB TBBUEJMJNJ $ 1FSõFNCF TBBUEJMJNJ % $VNB TBBUEJMJNJ & $VNBSUFTJ TBBUEJMJNJ 1. E 2. E 3. E 70 4. A 5. D
www.aydinyayinlari.com.tr 4\":*,·.&-&3÷#²-·/&#÷-.&3\"4:0/&-4\":*-\"3 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, 3BTZPOFM4BZMBS 3\"4:0/&-4\":*-\"3* ÖRNEK 3 7$1,0%m/*m B 4 1 UBNTBZMLFTSJOJCJMFõJLLFTJSPMBSBLZB[O[ 2 a, b `;WFCáPMNBLÐ[FSF a õFLMJOEFZB[MBCJMFOTBZMBSBLFTJS SBTZP C) 9 CJMFõJLLFTSJOJUBNTBZMLFTJSPMBSBLZB[O[ b 4 OFMTBZ EFOJS 91 a $ Pay B C 2 b $ Payda 24 Bá a =UBONT[, 0 = 0 , 0 =CFMJSTJ[ 0 a0 #BTJULFTJS PBZQBZEBTOEBONVUMBLEFóFSDF %m/*m LпÐLPMBOLFTJSMFSEJS-JMFBSBTOEBEFóFS BMS L TGSEBOGBSLMUBNTBZPMTVO a = a.k jHFOJõMFUNFJõMFNJ 2 .- 1 ,... b b.k 34 a = a : k jTBEFMFõUJSNFJõMFNJ #JMFöJL LFTJS 1BZ QBZEBTOEBO NVUMBL EF- b b:k óFSDF CÐZÐL ZB EB FõJU PMBO LFTJSMFSEJS 5BN TBZMBSCJSFSCJMFõJLLFTJSEJS 4BEFMFõUJSNF WF HFOJõMFUNF JõMFNMFSJ JMF FMEF 9 , - 3 , 4, . . . FEJMFOLFTJSMFSFEFOLLFTJSMFSEFOJS 72 2 = 4 = 6 = .... 5BNTBZMLFTJS a b õFLMJOEFLJLFTJSMFSEJS 369 c ÖRNEK 4 a b = a + b WF- a b = -f a + b p \"öBôEBLJMFSEFOIBOHJMFSJOJOEPôSVPMEVôVOVCVMV cc c c OV[ 2 1 =2+ 1 = 7 I. 6 = 36 %PôSV 3 33 7 42 :BOMö - 3 1 = - f 3 + 1 p = - 13 :BOMö II. 20 = 80 4 44 25 105 ÖRNEK 1 III. 105 = 25 70 14 a + 1 CBTJULFTJSEJS 6 ÖRNEK 5 BUBNTBZTLBÀGBSLMEFôFSBMS x ≠ - 2 WFLCJSUBNTBZPMNBLÐ[FSF 3 | |B+ 1 <JTFEFôFS 12x + k 3x + 2 ÖRNEK 2 JGBEFTJCJSTBCJUTBZZBFöJUJTFLUBNTBZTLBÀUS 2x + 4 CJSCJMFõJLLFTJSEJS 10 12 k = &k=8 YUBNTBZTOOFOCÑZÑL OFHBUJGEFôFSJLBÀUS 32 | |2x + 4 $ 10 j x = - 7 1. 11 2. –7 71 91 4. *%PôSV **:BOMö ***:BOMö 5. 8 3. B C 2 24
·/÷7&34÷5&:&)\";*3-*, 2. MODÜL 4\":*,·.&-&3÷#²-·/&#÷-.&3\"4:0/&-4\":*-\"3 www.aydinyayinlari.com.tr ÷SSBTZPOFM4BZMBS ÖRNEK 7 TANIM 15 5 TBZT TBZTOOLBÀLBUES B CCJSFSUBNTBZ CáPMTVO a õFLMJOEF 44 11 ZB[MBCJMFOTBZMBSES b Q = ( a : a, b ! Z, b ≠ 0 2 15 5 3 b = k· JTFk = 44 11 4 1 ,- 2 HJCJ , 7, . . . 34 a õFLMJOEFZB[MBNBZBOTBZMBSBJSSBTZPOFM b TBZMBSEFOJS 2 , 3 , π , . . .HJCJ ÖRNEK 8 3BTZPOFM4BZMBSEB%ÌSU÷öMFN 3 5:3 %m/*m 65 5PQMBNB¦LBSNB 6 JöMFNJOJOTPOVDVLBÀUS a ± x = a.y ± b.x by b.y 31 36 1 5 1 ·:·= · = 5 6 1 5 10 18 36 (y) (b) ¦BSQNB a · x = a.x b y b.y #ÌMNF ÖRNEK 9 a x = a · y = a.y 5 - 1:1 - 1.1 : 3 2 3 42 JöMFNJOJOTPOVDVLBÀUS b y b x b.x a 5 1 3 1 5 3 1 40 - 36 - 3 1 b a.y -·- = - - = = 3 2 1 8 3 2 8 24 24 = x b.x y ÖRNEK 6 \"öBôEBLJJöMFNMFSJOTPOVÀMBSOCVMVOV[ B 1 + 7 C 3 - 5 ÖRNEK 10 32 46 D 30 · 14 E 15 : 5 >f 3 1 - 5 11 1 7 15 24 p·2 H : 2 4 4 3 10 JöMFNJOJOTPOVDVLBÀUS 23 1 =d 13 - 21 n· 7 G· 10 = - 2· 7 · 10 = - 20 B C - 4 4 3 21 3 21 9 6 12 D E 23 1 72 3 1 1 - 20 6. B C - D E 7. 8. 9. 10. 4 36 24 9 6 12
www.aydinyayinlari.com.tr 4\":*,·.&-&3÷#²-·/&#÷-.&3\"4:0/&-4\":*-\"3 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 11 ÖRNEK 14 2- 2 f 1 - 1 pf 1 - 1 pf 1 - 1 pgf 1 - 1 p = 1 1+ 3 345 n 32 2 PMEVôVOBHÌSF OLBÀUS 2+ 1 2 3 4 ... n-1 = 1 jO= 64 3- 1 · · 2 345 n 32 JöMFNJOJOTPOVDVLBÀUS ÖRNEK 15 25 A = 5 + 7 + 9 PMEVóVOBHËSF 1+ 11 13 15 27 + 20 + 39 3 3 25 11 13 15 == UPQMBNOO\"UÑSÑOEFOEFôFSJOFEJS 2 12 36 2+ ÷TUFOJMFOF#EFOJSTF#- A =JTF#= A + 5 55 ÖRNEK 12 4 =1 3+ 6 5+ 3 3x + 1 PMEVôVOBHÌSF YLBÀUS ÖRNEK 16 4 j 3x + 1 = 3 406 - 405 =1 2 407 JöMFNJOJOTPOVDVLBÀUS 3+ 6 4 x= 812 - 810 5+ 3 3 407 3x + 1 1 1BZEBQBSBOUF[JOFBMOS 1 1 2 ÖRNEK 13 ÖRNEK 17 1+ 2 B CCJSFSUBNTBZ CáPMNBLÐ[FSF 1- 2 1- 3 r D a = [ a TBZTOOUPQMBNBJõMFNJOFHËSFUFSTJ] x-2 bb JGBEFTJYJOLBÀGBSLMEFôFSJJÀJOUBONT[ES r a D = [ a saZTOO¿BSQNBJõMFNJOFHËSFUFSTJ] bb 2 2 2 PMBSBLUBONMBOZPS 1+ =1+ =1+ D 11 D JöMFNJOJOTPOVDVLBÀUS 2 2 2x - 4 · 1- 1- 1- 22 3 x-5 x-5 1- x-2 x-2 x=2 x=5 11 1 2 2x - 10 # = - WF # =JTF = -1 =1+ =1- j x = -1 j UBOF 22 2 - x+1 x+1 x-5 25 2 13. 3 73 14. 64 15. A + 5 1 11. 12. 16. 17. –1 2 36 3
·/÷7&34÷5&:&)\";*3-*, 2. MODÜL 4\":*,·.&-&3÷#²-·/&#÷-.&3\"4:0/&-4\":*-\"3 www.aydinyayinlari.com.tr ÖRNEK 18 ÖRNEK 21 #JS LFTSJO QBZOB FLMFZJQ QBZEBTOEBO ¿LBSMODB \"MJ #BOVWF$BOJTJNMJпLBSEFõJOFOLпÐóÐZBõO- LFTJS 5 FFõJUPMVZPS EBLJ\"MJhEJS#VLBSEFõMFSCJSQBTUBZZBõMBSUPQMBNLB- EBSFõQBS¿BZBCËMÐQ ZBõMBSLBEBSQBS¿BBMBSBLQBZMB- 3 õZPSMBS 1BZWFQBZEBMBSOOUPQMBNPMBOCVLFTSJOQBZWF \"MJhOJOQBZOBQBTUBOO 4 JEÑöUÑôÑOFHÌSF LBS QBZEBTOOÀBSQNLBÀUS 15 EFöMFSJOFOCÑZÑôÑPMBO$BOhOQBZFOB[LBÀUS x x+3 5 & = jx=2 48 7-x 7-x-2 3 \"MJ = BME1BTUBQBSÀBZBCÌMÑOEÑ 7-x=5 15 30 12 2 = 2 . 5 = 10 #+ C =JTF$BOQBZZBOJ = QBZBME 30 5 ÖRNEK 19 ÖRNEK 22 ôFLJMEF \"#$% LBSF [\"$] LËõFHFOEJS \"#$% LBSFTJ Fõ f 1 –4 1 –3 CÐZÐLMÐLUFLBSFMFSFBZSMNõUS p -f p DC 22 1 2 JöMFNJOJOTPOVDVLBÀUS (16 - 8) . 2 = 16 AB 5BSBMBMBOMBSUPQMBNOOUÑNBMBOBPSBOOHÌTUFSFO LFTJSLBÀUS 3 ·ÀHFOMFSCJSMFöUJSJMJSTFLBSFFMEFFEJMJS? = 16 ÖRNEK 20 ÖRNEK 23 \" #WF$QP[JUJGHFS¿FMTBZMBSWF\" # $EJS x - 4 + y + 2 = 3PMEVóVOBHËSF 1+1+1= 1 x-1 y+5 A B C 15 1 + 1 JöMFNJOJOTPOVDVLBÀUS PMEVôVOBHÌSF $TBZTOOBMBCJMFDFôJFOLÑÀÑLUBN x-1 y+5 TBZEFôFSLBÀUS x-1 -3 y+5 -3 111 3= + + + A <#<$JTF > > x-1 x-1 y+5 y+5 ABC 111 1 + + < JTF< C j C = 46 C C C 15 3 = 2 - 3f 1 + 1 p j - 1 = 1 + 1 x-1 y+5 3 x-1 y+5 74 23 1 18. 10 19. 16 20. 46 21. 22. 23. - 5 16 3
3BTZPOFM4BZMBS* TEST - 36 1. 3a + 1 5. f 5 + 3 + 1 p - f 5 - 7 - 3 p 8 10 4 4 10 8 19 JGBEFTJCJSCJMFöJLLFTJSJTFBOOBMBCJMFDFôJFO JöMFNJOJOTPOVDVLBÀUS LÑÀÑLQP[JUJGUBNTBZLBÀUS \" # $ % & \" - # - $ % & 2. 2x + 1 6. 111 + 91 - 21 9 555 65 35 CJS CBTJU LFTJS PMEVôVOB HÌSF Y UBN TBZTOO JöMFNJOJOTPOVDVLBÀUS BMBDBôEFôFSMFSUPQMBNLBÀUS \" - # $ % & \" - # - $ - % & f1 1 +2 2 p:f1 3 +3 3 p 7. YCJSUBNTBZWFZCJSCBTJULFTJSEJS Z=- x 3. 33 22 PMEVôVOBHÌSF Y Z- JöMFNJOJOTPOVDVBöB ôEBLJMFSEFOIBOHJTJEJS f2 3 -1 3 p:f1 3 - 3 p 22 42 JöMFNJOJOTPOVDVLBÀUS \" # $ % - & - \" 1 # 2 $ 3 % 4 & 5 7 7 7 7 7 4. 2 + 5 = 5 8. %FóFSJ 3 PMBOCJSLFTSJOQBZOEBO¿LBSMSWF 3- 1 4 2- 1 QBZEBTOBFLMFOJSTFEFóFSJ 2 PMNBLUBES x 3 PMEVôVOBHÌSF YLBÀUS #VOBHÌSF JMLLFTSJOQBZWFQBZEBTOOUPQMBN \" 3 # 4 $ 5 % 6 & 7 LBÀUS 2 5 4 55 \" # $ % & 1. # 2. # 3. A 4. # 75 5. D 6. # 7. E 8. #
TEST - 37 3BTZPOFM4BZMBS* 3+4 f 1 + 1 p f 1 + 1 p :15 23 1. 4 5 5. 4+5 34 f 1 - 1 p f 1- 1 p: 6 JöMFNJOJOTPOVDVLBÀUS 35 JöMFNJOJOTPOVDVBöBôEBLJMFSEFOIBOHJTJEJS \" 2 # 3 $ 5 % & \" 2 # 3 $ 4 % 3 & 3 5 6 3 4 32 4 - 16 2021 1 - 2020 2 2. 9 - 2 6. 7 7 43 2020 3 - 2019 4 3 77 JöMFNJOJOTPOVDVLBÀUS JöMFNJOJOTPOVDVBöBôEBLJMFSEFOIBOHJTJEJS $ 5 % & 10 \" - 2 # - 1 $ 1 % 2 & 3 3 7 77 7 \" - # 3. f 1 - 2 p.f 1 - 2 p·f 1 - 4 p 7. f 1 - 1 p f 1 - 1 p f 1 - 1 p 359 4 9 16 JöMFNJOJOTPOVDVLBÀUS JöMFNJOJOTPOVDVLBÀUS \" 1 # 3 $ 5 % 1 & -1 \" 1 # 1 $ 1 % 5 & 7 3 5 99 16 9 8 88 4. 3–2 = 10–1 3+ 1 1+ 2 9–1 + 1 x–1 8. 4 PMEVôVOBHÌSF YBöBôEBLJMFSEFOIBOHJTJEJS 3- 1 1- 2 4 JöMFNJOJOTPOVDVLBÀUS \" # $ % & \" 3 # 5 $ % & 8 8 1. # 2. # 3. D 4. A 76 5. D 6. E 7. D 8. E
3BTZPOFM4BZMBS* TEST - 38 1. 4BZEPóSVTVOVO - 14 ile 11 BSBTOEBLJCËMÐ- 5. 2a - 6 JGBEFTJWF¿BSQNBZBHËSFUFSTJUBNTBZES 15 15 a+3 NÐBMUFõQBS¿BZBCËMÐONÐõUÐS #VOBHÌSF BTBZTOOBMBDBôEFôFSMFSUPQMBN A BC DE LBÀUS – 14 11 \" # $ % & 1 15 15 3 #VOBHÌSF TGSBFOZBLOOPLUBIBOHJTJEJS \" \" # # $ $ % % & & 6. a = 3b - 2 2b + 1 2. 3 - 1 PMEVôVOBHÌSF BTBZTOOIBOHJEFôFSJJÀJOC IFTBQMBOBNB[ 1+ 1 1+ 1 \" - 1 # 1 $ % 3 & x 22 2 JGBEFTJOJUBONT[ZBQBOLBÀGBSLMYHFSÀFMTB ZTWBSES \" # $ % & Hn tane 7. 3 + 33 + . . . + 33. . .3 7 77 77 . . . 7 UPQMBNOOTPOVDVUBNTBZES 3. B CWFDQP[JUJGUBNTBZMBSES #VOBHÌSF OTBZTOOFOLÑÀÑLEFôFSJLBÀUS a + 1 = 18 \" # $ % & 1+ b 7 c PMEVôVOBHÌSF B+C+DUPQMBNLBÀUS \" # $ % & 8. A = 7 - 3 - 5 PMEVôVOBHÌSF 15 8 11 8 + 11 - 6 15 8 11 2x - y UPQMBNOO \" UÑSÑOEFO EFôFSJ BöBôEBLJMFSEFO IBOHJTJEJS 4. = 0 5x - 10 PMEVôVOBHÌSF ZTBZTBöBôEBLJMFSEFOIBOHJ \" +\" # m\" $ +\" TJPMBNB[ \" 1 # $ % & % m\" & m\" 2 1. C 2. D 3. A 4. D 77 5. C 6. D 7. C 8. #
TEST - 39 3BTZPOFM4BZMBS* 1. 4. a = 1 a - 4 2020 PMEVôVOBHÌSF a JöMFNJOJOTPOVDVBöBô a+4 EBLJMFSEFOIBOHJTJEJS \" 1 # 1 $ - 1 2020 2018 2018 ôFLJMCJSJNLBSFMFSEFOPMVõNVõUVS % - 1 & - 1 2020 2022 5BSBMCÌMHFMFSJOBMBOMBSPSBOOHÌTUFSFOLFTJS BöBôEBLJMFSEFOIBOHJTJPMBCJMJS \" 1 # 1 $ 1 % 2 & 3 4 3 234 5. ôFLJMEÐ[HÐOBMUHFOMFSJMFPMVõUVSVMNVõUVS 2. YCJSSBTZPOFMTBZES 5BSBMBMBOOUÑNBMBOBPSBOBöBôEBLJLFTJSMFS EFOIBOHJTJJMFJGBEFFEJMFCJMJS BY2 - 7! = 0 PMEVôVOB HÌSF B TBZTOO FO LÑÀÑL EFôFSJ LBÀUS \" # $ % & \" 1 # 1 $ 1 % 1 & 1 2 3 4 56 3. \"#TBZTSBTZPOFMTBZES 6. 1 < x < 2 * \" #SBTZPOFMTBZES 12 72 9 ** A SBTZPOFMTBZES FöJUTJ[MJôJOJTBôMBZBOLBÀGBSLMYUBNTBZTWBS B ES *** \"B irrasZPOFMTBZES JGBEFMFSJOEFOIBOHJMFSJEBJNBEPôSVEVS \" :BMO[* # :BMO[*** $ *WF** % *WF*** & **WF*** \" # $ % & 1. D 2. E 3. A 78 4. C 5. A 6. #
www.aydinyayinlari.com.tr 4\":*,·.&-&3÷#²-·/&#÷-.&3\"4:0/&-4\":*-\"3 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, 0OEBMLM4BZMBS 3\"4:0/&-4\":*-\"3** ÖRNEK 2 TANIM \"öBôEBLJJöMFNMFSJZBQO[ B 0,1 + 0,01 + 0,001 C 1BZEBTVOQP[JUJGUBNTBZLBUMBSõFLMJOEF ZB[MBCJMFOLFTJSMFSFEFOJS 1, 44 E - 0,84 D ÖRNEK 1 0, 012 \"öBôEB WFSJMFO LFTJSMFSJO POEBMLM BÀMNMBSO CV MVOV[ B C D E - B 8 C 3 D 21 %m/*m 10 5 25 6 Virgülden sonra n E 123 F 11 tane basamak varsa 100 1000 f) 125 B C E F D G 0OEBMLM4BZMBSEB%ÌSU÷öMFN 0,00 ... a = a.10–n 0,2 =-1 =- =- %m/*m ÖRNEK 3 5PQMBNB–¦LBSNB (0, 00045) . (0, 000032) . (0, 0006) (0, 0009) . (0, 0016) . (0, 000036) 7JSHÐMMFSBMUBMUBHFUJSJMJSWFCPõMVLMBSTGSJMFEPM- JöMFNJOJOTPOVDVLBÀUS EVSVMVS + = ? - = ? –5 –6 –4 45.10 .32.10 .6.10 + 00 + 00 1,814 1,214 –4 –4 –6 9.10 .16.10 .36.10 –15 –1 6.45.32.10 10.10 1 == –14 6 6 ¦BSQNB 9.26.36.10 0OEBMLMTBZMBSLFTJSF¿FWJSFSFL¿BSQNBLUFS- ÖRNEK 4 DJIFEJMNFMJEJS = 8 · 3 = 24 (0, 761 + 5, 239) . (0, 4.2 + 0, 2) (0, 2.0, 03 + 2, 994) . (0, 03 + 0, 46 + 0, 51) 1000 10 10000 JöMFNJOJOTPOVDVLBÀUS = 0,0024 #ÌMNF 6.1 0OEBMLMTBZMBSOWJSHÐMEFOTPOSBLJCBTBNBL =2 TBZT TGS LVMMBOMBSBL FõJUMFONFTJ WF WJSHÐM ZPLNVõHJCJJõMFNZBQMNBTUFSDJIFEJMFCJMJS 3.1 0, 5 = 0, 500 = 500 = 4 0, 125 0, 125 125 1.B C D E F G 79 2. B C D E m 3. 1 4. 2 6
·/÷7&34÷5&:&)\";*3-*, 2. MODÜL 4\":*,·.&-&3÷#²-·/&#÷-.&3\"4:0/&-4\":*-\"3 www.aydinyayinlari.com.tr ÖRNEK 5 %FWJSMJ0OEBML4BZ \"õBóEBLJõFLJMMFSFõCJSJNLBSFMFSJMFPMVõUVSVMNVõUVS %m/*m 5BSBMCËMHFMFSJOBMBOMBSUPQMBNOOõFLMJOBMBOOBPSBO CJSSBTZPOFMTBZZBLBSõMLHFMNFLUFEJS %FWJSMJPOEBMLLFTJSMFSSBTZPOFMTBZZB¿FWSJMJS- #VOBHÌSF LFO + Sayının Devretmeyen f p-f p JöMFNJOJOTPOVDVLBÀUS tamamı kısım 4 3 10 8 4 J Virgülden sonra devreden N K O + == KK kadar 9 devretmeyen OO 10 8 10 5 L kadar 0 P 10 ZËOUFNJLVMMBOMS ÖRNEK 8 \"öBôEBLJ EFWJSMJ POEBML LFTJSMFSJ SBTZPOFM TBZZB ÀFWJSJOJ[ B 0, 3 C 0, 24 D 1, 123 ÖRNEK 6 E 2, 9 F - 3, 18 f) 1, 007 \"WF#CJSFSSBLBNES 31 24 8 r\"- B = B = C = r B =\" #-# \"- PMEVôVOBHÌSF \"SBLBNLBÀUS 93 99 33 E 2, 9 = 3 AB - BA - 15 9.5 - 15 1123 - 112 337 B = = = 3 jA = 8 D = 1007 - 100 907 f) = 10 10 900 300 900 900 F -d 318 - 31 n = - 287 90 90 ÖRNEK 7 ÖRNEK 9 \"CJSHFS¿FLTBZES 0, 27 + 0, 36 + 0, 07 A+ 1 JöMFNJOJOTPOVDVLBÀUS 40 0, 25 - 0, 16 - 0, 01 CJS UBN TBZ PMEVôVOB HÌSF \" TBZTOO WJSHÑMEFO TPOSBLJLTNOCVMVOV[ 27 + 36 + 7 70 99 99 99 99 70.90 100 == = 23 15 1 7 7.99 11 1 25 = A + 0, 025 -- A+ =A+ 40 1000 90 90 90 90 j A =Y YUBNTBZ 4 80 1 8 337 E F - 287 907 100 5. 6. 8 7. 975 8. B C D f) 9. 3 33 300 90 900 11 5
www.aydinyayinlari.com.tr 4\":*,·.&-&3÷#²-·/&#÷-.&3\"4:0/&-4\":*-\"3 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 10 ÖRNEK 12 \"öBôEBLJMFSEFO IBOHJTJ 0, 26 ile 0, 3 TBZMBS BSB a = 17 , b = 5 , c = 10 TOEBES 14 2 7 \" 16 # 17 $ 3 % 7 & 9 TBZMBSOLÑÀÑLUFOCÑZÑôFTSBMBZO[ 45 45 10 20 20 4BZMBSCJMFöJLLFTJSMFSWFQBZJMFQBZEBBSBTGBSLFöJU 24 30 3 17 10 5 <x< &x= 90 90 10 < < jB<D<C 14 7 2 ÖRNEK 11 ÖRNEK 13 BWFCTGSEBOWFCJSCJSJOEFOGBSLMSBLBNMBSES a = 5 , b = 11 , c = 7 a, 0b + b, 0a 8 15 40 = 273 0, 0a - 0, 0b TBZMBSOLÑÀÑLUFOCÑZÑôFTSBMBZO[ PMEVôVOBHÌSF B+CUPQMBNFOÀPL LBÀUS 1BZEBMBSEFFöJUMFOJS 75 88 21 jD<B<C a = ,b = , c = 120 120 120 ba 91 ^ a + b h a+ +b+ 90 90 90 = = 273 ab 1 ^a-bh - 90 90 90 a+b a1 = 3 & = & 4 + 8 = 12 a-b b2 3BTZPOFM4BZMBSEB4SBMBNB ÖRNEK 14 %m/*m a = - 13 , b = - 29 , c = - 11 7 23 17 1BZEBMBSFõJUJTFQBZCÐZÐLPMBOCÐZÐLUÐS 2<3<4 TBZMBSOLÑÀÑLUFOCÑZÑôFTSBMBZO[ 555 11 29 13 jB C D 1BZMBSFõJUJTFQBZEBTLпÐLPMBOEBIBCÐZÐL- 1P[JUJGPMBSBL < < UÐS 17 23 7 2<2<2 13 29 11 753 /FHBUJGPMBSBL - < - < - 1BZ WF QBZEBMBS BSBTOEBLJ GBSLO FõJU PMEVóV 7 23 17 EVSVNEB ÖRNEK 15 r 4BZMBS CBTJU LFTJSMFS JTF QBZ CÐZÐL PMBO CÐZÐLUÐS 4 < a <3 25 75 5 4 < 10 < 19 FöJUTJ[MJôJOEFBOOFOLÑÀÑLUBNTBZEFôFSJLBÀUS 7 13 22 r 4BZMBSCJMFõJLLFTJSMFSJTFQBZCÐZÐLPMBO 12 a 15 LпÐLUÐS < < JTFB= 13 11 < 9 < 7 6 42 75 75 75 10. C 11. 12 81 12. B D C 13. D B C14. B C D15. 13
TEST - 40 3BTZPOFM4BZMBS** 0, 1 + 0, 2 5. \"WF#CJSCJSJOEFOGBSLMSBLBNMBSES 1. ·0,6 A +#=PMEVôVOBHÌSF \" #+\" # -1 0, 4 - 0, 04 JöMFNJOJOTPOVDVFOÀPLLBÀUS JöMFNJOJOTPOVDVLBÀUS \" # $ % & \" 1 # $ % & 2 2. 8 · 0, 1 0, 02 + 0, 03 0, 006 JöMFNJOJOTPOVDVLBÀUS \" # $ % & a 0, 761 + 5239.10–3 k.a 2.0, 4 + 2.10–1 k 6. a _ 0, 2 i.3.10–2 + 2, 994 k._ 0, 03 + 0, 46 + 0, 51 i JöMFNJOJOTPOVDVLBÀUS \" # $ % & 0, 012 0, 14 0, 015 3. + - 0, 02 0, 07 0, 003 JöMFNJOJOTPOVDVBöBôEBLJMFSEFOIBOHJTJEJS \" - # - $ -2,8 7. x =Z % - & -4,2 YCJSUBNTBZPMEVôVOBHÌSF ZTBZTOOFOLÑ ÀÑL EFôFSJLBÀUS \" # $ % & 2+ 3 0, 02 0, 014 6, 68 –1 4. 0, 04 6.10–2 5.102 JöMFNJOJOTPOVDVLBÀUS 8. f - -p 0, 2 1, 4 66, 8 \" -1 # -1 $ -1 JöMFNJOJOTPOVDVLBÀUS & -1 % -1 \" - # - $ % & 1. A 2. D 3. # 4. A 82 5. E 6. # 7. # 8. A
3BTZPOFM4BZMBS** TEST - 41 1. 3 - 2 + 1 = x 5. 0, 1 + 0, 11 + 0, 111 3, 2 3, 02 3, 002 JöMFNJOJOTPOVDVLBÀUS PMEVôVOBHÌSF \" 0, 3 # 0, 30 $ 0, 33 & 0, 17 6, 2 5, 02 4, 002 % 0, 7 -+ 3, 2 3, 02 3, 002 JGBEFTJOJO Y UÑSÑOEFO EFôFSJ BöBôEBLJMFSEFO IBOHJTJEJS \" Y+ # Y+ $ Y- 1 % -Y & Y- 2 0, 4 . 0, 6 6. \" -1 -2 - 2. # - -4 - 0, 26 PMEVôVOBHÌSF A JöMFNJOJOTPOVDVLBÀUS B JöMFNJOJOTPOVDVLBÀUS \" # $ % 1 & 1 \" 11 # 10 $ 9 % 99 & 24 10 100 9 9 10 10 99 7. 1, 9 + 0, 19 + 0, 0019 + 0, 000019 + . . . UPQMBNOOTPOVDVBöBôEBLJMFSEFOIBOHJTJEJS 3. 2, 1- 2, 2 + 1, 3 - 0, 3 \" 0, 202 # 2, 02 $ 2, 20 JöMFNJOJOTPOVDVLBÀUS % 2, 002 & 2, 202 \" 0, 6 # 0, 7 $ 0, 8 % & 1, 1 8. A = 0, 123 4. \" B = 0, 123 # C = 0, 123 PMEVôVOBHÌSF A JöMFNJOJOTPOVDVLBÀUS B TBZMBSOO LÑÀÑLUFO CÑZÑôF EPôSV TSBMBOö BöBôEBLJMFSEFOIBOHJTJEJS \" 0, 1 # 0, 3 $ 0, 6 % 0, 7 & 0, 17 \" \" # $ # \" $ # $ $ # \" % $ \" # & # \" $ 1. # 2. # 3. C 4. C 83 5. A 6. A 7. C 8. C
TEST - 42 3BTZPOFM4BZMBS** 1. * 12 < 13 < 15 5. \" #WF$QP[JUJGUBNTBZMBSES 15 10 7 5=6=8 A.B B.C A.C ** 3 < 2 < 5 PMEVôVOBHÌSF BöBôEBLJMFSEFOIBOHJTJEPôSV 537 EVS *** 15 < 15 < 15 \" $< B <\" # #<$<\" $ #<\"<$ 782 % \"< B <$ & \"<$< B TSBMBNBMBSOEBOIBOHJMFSJEPôSVEVS \" :BMO[* # :BMO[** $ :BMO[*** % *WF** & *WF*** 2. A = 23 , B = 203 , C = 2003 6. 0, 35 < x < 0, 39 20 200 2000 PMEVôVOBHÌSF YTBZTBöBôEBLJMFSEFOIBOHJ TJPMBCJMJS TBZTOO LÑÀÑLUFO CÑZÑôF EPôSV TSBMBOö BöBôEBLJMFSEFOIBOHJTJEJS \" 1 # 2 $ 17 % 2 & 19 5 9 \" \"<$<# # $< B <\" $ #<\"<$ 45 5 45 % #<$<\" & \"< B <$ 3. \"QP[JUJGUBNTBZES 7. A = - 5 , B = - 6 , C = - 7 11 13 15 1<A<5 398 PMEVôVOB HÌSF BöBôEBLJ TSBMBNBMBSEBO IBO HJTJEPôSVEVS PMEVôVOB HÌSF \" TBZTOO BMBCJMFDFôJ LBÀ EF ôFSWBSES \" \"< B <$ # \"<$<# $ #<\"<$ \" # $ % & % #<$<\" & $< B <\" 4. \"OFHBUJGUBNTBZES 8. A = - 1, 103 , B = - 1, 103 , C = - 1, 103 \"=# #=$ PMEVôVOB HÌSF \" # WF $ TBZMBS BSBTOEBLJ PMEVôVOB HÌSF BöBôEBLJ TSBMBNBMBSEBO IBO EPôSVTSBMBNBBöBôEBLJMFSEFOIBOHJTJEJS HJTJEPôSVEVS \" $< B <\" # $<\"<# $ #<$<\" \" \"< B <$ # \"<$<# $ #<\"<$ % #<\"<$ & \"< B <$ % #<$<\" & $< B <\" 1. D 2. # 3. A 4. C 84 5. C 6. C 7. E 8. #
4BZ,ÑNFMFSJ#ÌMÑOFCJMNF3BTZPOFM4BZMBS KARMA TEST - 1 1. + 5. \"CJSUBNTBZES4BEFDFUPQMBNB ¿LBSNB ¿BSQ- JöMFNJOJOTPOVDVLBÀUS NB CËMNF WF ÐTU BMNB JõMFNMFSJ SBLBNMBSOB VZ- HVMBOBSBL\"TBZTFMEFFEJMFCJMJZPSJTF\"TBZTOB \" # $ % & '3*&%.\"/4\":*4* BEWFSJMJS ±SOFóJOCJS'SJFENBOTBZTES 2. 4x + 24 ¥ÐOLÐ2 =FMEFFEJMFCJMJS \"öBôEBLJMFSEFO IBOHJTJ CJS 'SJFENBO TBZT x ES JGBEFTJCJSUBNTBZPMEVôVOBHÌSF YJOBMBCJMF \" # $ % & DFôJLBÀGBSLMUBNTBZEFôFSJWBSES 6. BWFCCJSFSUBNTBZES \" # $ % & -8 < a < -7 < b < PMEVôVOBHÌSF a FOB[LBÀUS b \" -7 B - $ - % - & - 3. YWFZUBNTBZMBSPMNBLÑ[FSF 7. BC2D < 0 YZ- 4x -Z+= 0 aCD< 0 a2CD < 0 FöJUMJôJOEFY+ZUPQMBNOOBMBCJMFDFôJEFôFSMFS UPQMBNLBÀUS PMEVôVOBHÌSF B CWFDOJOJöBSFUMFSJTSBTZMB BöBôEBLJMFSEFOIBOHJTJEJS \" # $ % & \" - + - # + - - $ + + - % + + + & + - + 4. ÷LJUBOFTJEFOCÑZÑLEPôBMTBZOOUPQMBN 8. YWFZOFHBUJGUBNTBZMBSES PMEVôVOB HÌSF CV TBZMBSO FO CÑZÑôÑ FO x.y + y ÀPLLBÀUS =-3 \" # $ % & x PMEVôVOBHÌSF YTBZTOOBMBCJMFDFôJEFôFSMFS ÀBSQNLBÀUS \" # $ % & 1. E 2. D 3. D 4. E 85 5. E 6. A 7. C 8. C
KARMA TEST - 2 4BZ,ÑNFMFSJ#ÌMÑOFCJMNF3BTZPOFM4BZMBS 1. \"= 5. \" # $BSEõLQP[JUJGTBZMBSWF\"< B <$EJS B = A = 2x x+y $=2 , B = x -Z+ 1 , C = y2 PMEVôVOBHÌSF YZLBÀUS PMEVôVOB HÌSF BöBôEBLJ TSBMBNBMBSEBO IBO \" # $ % & HJTJEPôSVEVS \" $<\"<# # $< B <\" $ #<$<\" % #<\"<$ & \"< B <$ 2. OCJSHFS¿FLTBZES 6. #JSLÐQÐOZÐ[FZMFSJÐ[FSJOFBSEõL¿JGUTBZMBSZB[- O2+ÀJGUTBZPMEVôVOBHÌSF BöBôEBLJMFSEFO MZPS IBOHJTJLFTJOMJLMFUFLTBZES #VTBZMBSOUPQMBNFOLÑÀÑLJLJODJTBZOOÑÀ LBU PMEVôVOB HÌSF ZB[MBO FO CÑZÑL TBZ LBÀ US \" O- # O+ $ O2 - 7 \" # $ % & -2 % O+ & O2 + 2 3. B CWFDBSEõLQP[JUJG¿JGUTBZMBSESB< b <DPM- 7. 3BLBNMBSOO LÐQMFSJ UPQMBN LFOEJTJOF FõJU PMBO EVóVOBHËSF TBZMBSB \"3.4530/(4\":*-\"3* BEWFSJMJS a - 2 + c + 10 ²SOFôJO = 1 + + b+4 a+6 PMEVóVOEBOCJS\"SNTUSPOHTBZTES JöMFNJOJOTPOVDVLBÀUS \" ÑÀ CBTBNBLM TBZT CJS \"SNTUSPOH TBZT PMEVôVOBHÌSF \"SBLBNLBÀGBSLMEFôFSBMS \" # $ % & \" # $ % & 4. \"SEõLпUFLTBZOO¿BSQNCVTBZMBSEBOCÐZÐL J 1- 1 N–1 K O PMNBZBO JLJTJOF BZS BZS CËMÐOÐQ TPOV¿MBS UPQMB- K O OODBFMEFFEJMJZPS 8. K 3+ 2 O ·6–1 #V TBZMBSEBO FO CÑZÑL PMBO BöBôEBLJMFSEFO K2 1+ 1 O IBOHJTJEJS K 3 O L P \" # $ % & JöMFNJOJOTPOVDVLBÀUS \" 1 # 1 $ 6 % & 11 6 11 1. A 2. E 3. # 4. A 86 5. C 6. C 7. # 8. A
4BZ,ÑNFMFSJ#ÌMÑOFCJMNF3BTZPOFM4BZMBS KARMA TEST - 3 1. \" # \" # A B 5. a - 7a - _ 2a + b - _ b - a i - 2a iA - b JöMFNJOJOTPOVDVBöBôEBLJMFSEFOIBOHJTJEJS 9 \" B+C # B-C $ B+ 2b :VLBSEBLJ CÌMNF JöMFNJOF HÌSF CÌMÑN BöBô % B-C & B+ b EBLJMFSEFOIBOHJTJEJS \" # $ % & 6. \"WF#QP[JUJGUBNTBZMBSES \" - B =Q PMEVôVOB HÌSF \"# OJO Q BTBM TBZT UÑSÑOEFO EFôFSJBöBôEBLJMFSEFOIBOHJTJEJS 2. YCJSUBNTBZ \"#WF#\"JLJCBTBNBLMTBZMBSES p+1 p-1 p-1 \" # $ x =\"#-#\" 2 2 3 PMEVôVOBHÌSF \"SBLBNLBÀGBSLMEFôFSBMBCJ MJS p+1 2p + 1 % & \" # $ % & 3 3 3. \"SBMBSOEBLJGBSLJLJPMBOBTBMTBZMBSB÷,÷;\"4\"- 7. \"-WF\"+#BSBMBSOEBBTBMTBZMBSES SAYILAREFOJS \"-#- 21 = 0 ±SOFóJO WFJLJ[BTBMTBZMBSES PMEVôVOBHÌSF #TBZTBöBôEBLJMFSEFOIBOHJ \"öBôEBLJTBZMBSEBOIBOHJTJJLJ[BTBMTBZMBSO TJEJS UPQMBNPMBCJMJS \" - # - $ - % & \" # $ % & 8. 1P[JUJG UBN CËMFOMFSJOJO TBZTOB UBN CËMÐOFCJMFO 4. A :BOEBLJ CÌMNF JöMFNJOF HÌSF \" TBZMBSB TAU SAYILARI BEWFSJMJS B TBZTOO BMBCJMFDFôJ LBÀ GBSLM ±SOFóJO TBZTOO BMUUBOFQP- EPôBMTBZEFôFSWBSES \" # $ % & [JUJGCËMFOJWBSES =UBNTBZPMEVóVOEBO CJSUBVTBZTES \"öBôEBLJMFSEFO IBOHJTJ CJS 5BV TBZT EFôJM EJS \" # $ % & 1. C 2. C 3. D 4. C 87 5. D 6. C 7. C 8. D
KARMA TEST - 4 4BZ,ÑNFMFSJ#ÌMÑOFCJMNF3BTZPOFM4BZMBS 1. 41! - 5. %ÌSU CBTBNBLM \"# WF #\" EPôBM TBZMBS TBZTOO TPO EÌSU CBTBNBôOEBLJ SBLBNMBS BSBTOEBLJ GBSL BöBôEBLJMFSEFO IBOHJTJ JMF EB UPQMBNLBÀUS JNBUBNCÌMÑOÑS \" # $ % & \" # $ % & 2. \"= 0! + 1! + 2! ++ 6. \"#$пCBTBNBLMTBZES PMEVôVOB HÌSF \" TBZTOO JMF CÌMÑNÑOEFO \"= 2B LBMBOLBÀUS B =$ PMEVôVOBHÌSF \"#$TBZMBSOOUPQMBNOOJMF CÌMÑNÑOEFOLBMBOLBÀUS \" # $ % & \" # $ % & 3. \"= 2 - 2 - 2 - 7. OQP[JUJGCJSUBNTBZES PMEVôVOB HÌSF \" TBZTOO TPOEBO LBÀ CBTB A =O+TBZTJMFUBNCÌMÑOFCJMEJôJOFHÌ NBôTGSES SF O TBZTOO JLJ CBTBNBLM FO CÑZÑL EFôFSJ LBÀUS \" # $ % & \" # $ % & 4. #FõCBTBNBLMSBLBNMBSGBSLM\"#TBZTOO 8. 1, 08 - 8, 4 + 216 JMFCËMÐNÐOEFOLBMBOUJS 0, 036 0, 12 7, 2 JöMFNJOJOTPOVDVLBÀUS #VOBHÌSF \"SBLBNGBSLMEFôFSBMS \" - # - $ - % & \" # $ % & 1. # 2. # 3. C 4. # 88 5. A 6. D 7. # 8. C
4BZ,ÑNFMFSJ#ÌMÑOFCJMNF3BTZPOFM4BZMBS KARMA TEST - 5 1. \"= 122 5. x = - Z=WF[=PMEVóVOBHËSF B =2 xz - x.y.z + f z –x y –y p -f p $= y2 JöMFNJOJOTPOVDVLBÀUS PMEVôVOBHÌSF &,0, \" # $ BöBôEBLJMFSEFO \" - # - $ % & IBOHJTJEJS \" # 4 $ % & 7 2. ,FOBSV[VOMVLMBSNWFNPMBOEJLEËSUHFOCJ- 6. 0 < A <#< 1 <$PMEVôVOBHÌSF ¿JNJOEFLJCJSCBI¿FFOCÐZÐLBMBOMLBSFQBS¿BMBSB * A < B BZSMQIFSQBS¿BOOLËõFMFSJOFCJSFSGJEBOEJLJMFDFL- CC UJS ** - C < - C #VJöMFNJÀJOLBÀGJEBOHFSFLJS AB \" # $ % & *** A < B BC JGBEFMFSJOEFOIBOHJMFSJLFTJOMJLMF EPôSVEVS \" :BMO[* # :BMO[** $ :BMO[*** % *WF** & * **WF*** 3. \" #WF$TGSEBOWFCJSCJSJOEFOGBSLMSBLBNMBSES 9 - 3 -5 #VOBHÌSF �# \" # $ LBÀGBSLMEFôFSBMS 7. 16 11 8 2 + 5 -3 11 12 8 JöMFNJOJOTPOVDVLBÀUS \" # $ % & \" - # - 2 $ - 3 % - 9 & - 5 3 257 4. \"WF#QP[JUJGUBNTBZMBSES 8. ¶¿ZBSõNBDLBQBMCJSFóSJõFLMJOEFLJQJTUUFCJSUV- &,0, \" # = 22 SVTSBTZMB WFTBBUUFUBNBNMBZBCJMJZPS PMEVôVOBHÌSF \"TBZTLBÀGBSLMEFôFSBMS \"ZO BOEB BZO OPLUBEBO BZO ZÌOEF IBSFLFU \" # $ % & FEFOZBSöNBDMBSOCJSJODJLBSöMBöNBMBSOBLB EBSHFÀFOTÑSFEFFOI[MZBSöNBDLBÀUVSBU NöPMVS \" # $ % & 1. C 2. A 3. C 4. C 89 5. E 6. D 7. C 8. A
KARMA TEST - 6 4BZ,ÑNFMFSJ#ÌMÑOFCJMNF3BTZPOFM4BZMBS 1. ,FOEJTJIBSJ¿QP[JUJGUBNTBZCËMFOMFSJOJOUPQMBN- 4. &óFS CJS FõJUMJLUF FõJUMJóJO JõMFN UBSBG EËOEÐ- OBFõJUPMBOTBZMBSBMÜKEMMEL SAYIBEWFSJMJS SÐMEÐóÐOEFTPOV¿EFóJõNJZPSTBCVFõJUMJLMFSF 4530#0(3\".\"5÷,&õ÷5-÷,-&3BEWFSJMJS ±SOFóJO NÐLFNNFMTBZES ±SOFóJO #ËMFOMFSJ ES ++= 1 + 2 +=CVMVOVS \"ZSDB Q WF Q - BTBM TBZMBS PMNBL LPõVMVZMB ++= NÐLFNNFMTBZMBS 91 - 16 +YJöMFNJOJOCJSTUSPCPHSBNBUJLFöJUMJL 2Q-1 Q - PMVöUVSNBT JÀJO Y ZFSJOF BöBôEBLJMFSEFO IBO HJTJZB[MBNB[ JõMFNJJMFEFFMEFFEJMFCJMJS \" # $ % & #VOBHÌSF BöBôEBLJMFSEFOIBOHJTJCJSNÑLFN NFMTBZES \" # $ % & 2. \"= 22 + 44 +++ 5. 12x PMEVôVOBHÌSF \"TBZTOOQP[JUJGCÌMFOMFSJOJO TBZTOOQP[JUJGUFLCÌMFOTBZTY+PMEVôVOB TBZTLBÀUS HÌSF QP[JUJGÀJGUCÌMFOTBZTLBÀUS \" # $ % & \" # $ % & I 6. YWFZQP[JUJGUBNTBZES 3. x II Y=Z PMEVôVOBHÌSF Y+ZUPQMBNFOB[LBÀUS III + IV \" # $ % & 27 V :VLBSEBLJ¿BSQNBJõMFNJOEFIFSCJSOPLUBGBSLMCJS SBLBNHËTUFSNFLUFEJS #VOBHÌSF **WF***TBUSMBSEBLJTBZMBSOUPQMB NLBÀUS \" # $ % & 1. D 2. A 3. D 90 4. C 5. D 6. D
<(1m1(6m/6258/$54BZ,ÑNFMFSJ#ÌMÑOFCJMNF3BTZPOFM4BZMBS 1. 11 1 3. \"#пCBTBNBLMTBZES 1= 1! 1 2= 2! 1 AB5 = A! + B! + 5! 11 40585 = 4! + 0! + 5! + 8! + 5! 1 FõJUMJLMFSJWFSJMJZPS 1 #VOBHÌSF \"+#UPQMBNOOTPOVDVLBÀUS Theodorus Spirali \" # $ % & &JOTUFJO ZB EB 1JTBHPS 4QJSBMJ PMBSBL EB CJMJ OFO5IFPEPSVT4QJSBMJOEFEJLLFOBSV[VOMVLMB SSBTZPOFMTBZPMBOCFöJODJÑÀHFOFMEFFEJMJO DFZFLBEBSLBÀUBOFÑÀHFOÀJ[JMNFTJHFSFLJS \" # $ % & 4. YCJSUBNTBZES X JõMFNJJ¿JOFZB[MBOYTBZTOOLBUOO FLTJóJOF\"TBZTBEOWFSJS 2. 1.1 = 1 JõMFNJ \" TBZTOO GB[MBTOO ZBSTOB X #TBZTBEOWFSJS 11.11 = 121 111.111 = 12321 X JõMFNJ \" WF # TBZMBSOO UPQMBNOO 1111.1111 = 1234321 GB[MBTOB$TBZTBEOWFSJS h JõMFNJ $ TBZTOB Y TBZTOO JLJ LBU- PMEVôVOBHÌSF X O FLMFZJQ ¿LBSUBSBL TPOVDB % TBZ- (>111. . .1) 1(144121. .4.413) TBEOWFSJS n tane n tane * X + X = 12 ÀBSQNOO TPOVDVOVO SBLBNMBS UPQMBN BöB ** X + X = 12 ôEBLJMFSEFOIBOHJTJOFFöJUUJS *** X - X = 12 \" 1 + 2 +++O # 1 ++++ O- JGBEFMFSJOEFOIBOHJMFSJEPôSVPMBCJMJS $ 2 + 4 +++O % 12 + 22+2 ++O2 \" :BMO[* # :BMO[** $ :BMO[*** & 1 + 2 + ++O % *WF** & *WF*** 1. D 2. # 91 3. C 4. A
<(1m1(6m/6258/$5 4BZ,ÑNFMFSJ#ÌMÑOFCJMNF3BTZPOFM4BZMBS 1. \"õBóEBLJ FõJUMJLMFSEF TBUS OVNBSBT JMF TBUSEBLJ 3. \"õBóEB WFSJMFO FõJUMJLMFSJO ZBOTNBMBSOEB FMEF TBZMBSEBOCJSUBOFTJJMFCFMJSMJCJSCBóMBOULVSVMBCJMJS FEJMFOFõJUMJLMFSJOEFEPóSVPMEVóVHËSÐMNFLUFEJS 2 + 42 = 2 TBUS 102 = 100 001 = 012 102 + 112 + 122 = 2 + 142 TBUS 112 = 121 121 = 112 212 + 222 +2 + 242 = 2 +2 + 272 TBUS 1A2 = 1BB BB1 = A12 2 +2 +2 +2 + 402 = 412 + 422+2 + 442 TBUS 132 = 169 961 = 312 h #VOBHÌSF TBUSOTBôEBOJLJODJTSBEBCV #VOBHÌSF \"+#UPQMBNLBÀUS MVOBOTBZOOUBCBOLBÀUS \" # $ % & \" # $ % & 2. ôFLJMEF 4. ôFLJMEF.VóMBhEBOZPMB¿LQö[NJShFHJUNFLUFPMBO r #JSLFOBSV[VOMVóV 2 CSPMBOLBSFõFLMJOEFLJ CJS¿PLBSB¿UBOTBEFDF\" # $WF%OPLUBMBSOEBLJ LVUVMBSOJ¿JOFIBSGMFSZB[MNõUS BSB¿MBSOCFMMJCJSBOEBLJLPOVNMBSHËTUFSJMNJõUJS r ,VUVMBS CBõMBOH¿ OPLUBTOEB EJL LFTJõFO ZB- ö[NJS UBZEBTBóB EJLFZEFZVLBSEPóSVBSUBOJLJTBZ D EPóSVTVÐ[FSJOFõFLJMEFLJHJCJZFSMFõUJSJMNJõUJS C r )FS CJS IBSG IFN ZBUBZ IFN EJLFZ TBZ EPóSV- AB TV Ð[FSJOEF CVMVOEVLMBS BSBMLUBLJ UBNTBZ ZB EB UBN TBZMBS JGBEF FUNFLUFEJS :BOJ CJS IBSG .VóMB CJSEFO GB[MB UBN TBZ JMF FõMFõFCJMJS ±SOFóJO # IBSGJZBUBZTBZEPóSVTVOBHËSFTBZTOEJLFZ r #WF\"BSB¿MBSBSBTOEBLJV[BLMLN TBZEPóSVTVOBHËSF WFTBZMBSOJGBEFFU- r #WF$BSB¿MBSBSBTOEBLJV[BLMLN NFLUFEJS r #WF%BSB¿MBSBSBTOEBLJV[BLMLN B = 1 , B =WFZB#=PMBCJMJS PMEVôVOB HÌSF BZO BOEB \" + # OPLUBTOEB CVMVOBO BSBÀ JMF $ + % OPLUBTOEB CVMVOBO r ôFLJMEFLJIBSGMFSJMFZB[MBCJMFOJTJNMFS IBSGMFSJO BSBÀBSBTOEBLJV[BLMLLBÀNFUSFEJS HËTUFSEJóJUBNTBZMBSOUPQMBNJMFFõMFõUJSJMNJõ- UJS#JSJTNFCJSEFOGB[MBTBZLBSõMLHFMFCJMJS \" # $ ±SOFóJO \"-öJTNJ\" -WFöIBSGMFSJOFLBSõMLHF- % & MFOTBZMBSOUPQMBNJMFFõMFõNFLUFEJS A BC ÇDE F GòH I ö J KL MN OÖP R O #VOBHÌSF &3,\"/–¦÷ó%&.JöMFNJOJOTPOVDV FOÀPLLBÀUS \" # $ % & 1. C 2. C 92 3. # 4. E
<(1m1(6m/6258/$54BZ,ÑNFMFSJ#ÌMÑOFCJMNF3BTZPOFM4BZMBS 1. ,BSHP GJSNBT FMFNBO CJS QBLFUJ BESFTJOF UFTMJN 3. \"#$пCBTBNBLMTBZES FUNFLÐ[FSFZPMB¿LBS%PóSVNBIBMMFZFHFMEJóJO- * \"#$ =\"#+ B +#$ EF NBIBMMFOJOZBSBNB[¿PDVLMBSOOTPLBLOVNB- SBTZB[MUBCFMBMBSOOÐTUWJEBMBSO¿LBSUUóOWF PMBSBLUBONMBOZPS UBCFMBMBSOUFSTEVSEVóVOVËóSFOJS * ²SOFôJO #427 = 42 + 2 + 27 =EJS 12456. SOKAK *\"#$ = 12456. SOKAK PMEVôVOB HÌSF \" SBLBNOO BMBNBZBDBô LBÀ GBSLMEFôFSWBSES \" # $ % & #VOB SBóNFO LBSHP FMFNBO QBLFUJ EPóSV BESFTF UFTMJNFUNJõUJS %PôSVBESFTUFCVMVOBOTPLBLOVNBSBTBöBô EBLJMFSEFOIBOHJTJPMBCJMJS \" # $ % & 4. &LJO WF &TSB EJLEËSUHFO õFLMJOEF CJSFS LºóE IFS EFGBTOEBV[VOLFOBSMBSOUBNPSUBTOEBO LBSõML- M LFOBSMBS ÐTU ÐTUF HFMFDFL õFLJMEF LBUMBZBCJMJZPS- MBS B D 2. 1P[JUJG CËMFOMFSJOJO UPQMBN LFOEJTJOJO JLJ LBUOEBO A C CÐZÐLPMBOTBZMBSB7&3ö.-ö4\":*EFOJS &LJOLºóEOBZOõFLJMEFQFõQFõFZFEJEFGB &TSB ²SOFôJO LºóEOBZOõFLJMEFQFõQFõFCFõEFGBLBUMBZBSBL IFSJLJTJEFCJSFSLBSFFMEFFEJZPS CJSWFSJNMJTBZES¥ÐOLÐ #VLBSFMFSJOZÑ[FZBMBOMBSFöJUPMEVôVOBHÌSF 1 + 2 ++ 4 +++ 12 + 18 += &LJOhJO CBöMBOHÀUBLJ L»ôEOO ZÑ[FZ BMBOOO &TSBhOO CBöMBOHÀUBLJ L»ôEOO ZÑ[FZ BMBOOB = 72 PSBOOHÌTUFSFOLFTJSBöBôEBLJMFSEFOIBOHJTJ EJS >CVMVOVS ÷LJCBTBNBLMFOLÑÀÑLWFSJNMJTBZOOSBLBNMB SUPQMBNBöBôEBLJMFSEFOIBOHJTJEJS \" # $ % & \" 2 # 1 $ 5 % 1 & 1 3 4 7 8 16 1. D 2. C 93 3. D 4. #
<(1m1(6m/6258/$5 4BZ,ÑNFMFSJ#ÌMÑOFCJMNF3BTZPOFM4BZMBS 1. 6= A + B C: A= E 3. \"õBóEBLJEFTFOFõLBSUPOMBSLVMMBOMBSBLZBQMNõ- ++ + US 4= C – D D: B= F TBUS TBUS = TBUS TBUS = = 12 6 G PMEVôVOBHÌSF (TBZTLBÀUS \" # $ % & TBUS #VOBHÌSF LVMMBOMBOLBSUPOTBZTLBÀUS \" # $ % & 2. #BOV ±óSFUNFO ËóSFODJ PMBO CJS TOGUB QSPKF 4. ,//±-¥¶¶%òöôö.:5/òö%ö3 ËEFWMFSJWFSFDFLUJS -35// #B[ ÌôSFODJMFSJOF BZO ÌEFWJ WFSNFZJ QMBOMB :VLBSEBËOFNMJCJSCJMJNJOTBOOEÐOZBDBÐOMÐCJS ZBO #BOV ²ôSFUNFO CV ÌôSFODJMFSJ CFMJSMFNFL TË[ÐWFJTNJOEFLJCB[IBSGMFSEFOFUBNTBZMBS LVMMBOMBSBL LPEMBONõUS )FS CJS LFMJNF LPEMBNB- JÀJOTSBTZMB EBLVMMBOMBOTBZMBSOUPQMBNZMBWFIFSCJSDÐNMF J¿FSEJóJLFMJNFMFSJOJOLPEMBSOOUPQMBNZMBFõMFõUJSJ- * )FSIBOHJCJSËóSFODJJ¿JOTOGMJTUFTJOEFLJTSB MJZPS OVNBSBTOB CBLBSBL MJTUFEF ËODFTJOEF CVMV- 6/²3 OBOËóSFODJTBZTOY TPOSBTOEBCVMVOBOËó- ;&-ö)\" #6 )\"'5\" #&ô %&/&.& 4*/\"7*/\" ,\"5*-%* SFODJTBZTOZPMBSBLCFMJSMJZPS $·.-÷õó%,÷:-3%/)/÷÷÷- ** )FSCJSËóSFODJJ¿JO x WF y TBZMBSOIFTBQ- õ-õ÷3 yx MZPS \" # $ % & *** x WFZB y TBZT UBNTBZ¿LBOËóSFODJMFSJ- yx OFBZOËEFWJ EJóFSËóSFODJMFSJOFEFCVËEFW- EFOWFCJSCJSJOEFOGBSLMËEFWMFSWFSJZPS #BOV ²ôSFUNFOhJO CV TOGUBLJ ÌôSFODJTJOF WFSEJôJGBSLMÌEFWTBZTLBÀUS \" # $ % & 1. C 2. A 94 3. C 4. E
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