www.aydinyayinlari.com.tr 7&3÷ 4\":.\"7&0-\"4*-*, 8. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 5 ÖRNEK 8 #JS EÐ[MFNEF CVMVOBO UBOF OPLUBEBO UBOFTJ EPó- #JSCJSJOF QBSBMFM ZBUBZ EPôSV JMF CJSCJSJOF QBSBMFM SVTBMES (FSJZF LBMBO OPLUBEBO IFSIBOHJ пРEPóSV- EÑöFZEPôSVLFTJöUJSJMEJôJOEFLBÀQBSBMFMLFOBSFM- TBMEFóJMEJS EFFEJMJS ,ÌöFMFSJCVOPLUBMBSPMBOLBÀGBSLMÑÀHFOPMVöUVSV- MBCJMJS 43 f p.f p = 18 22 4 46 46 f p + f p f p + f p f p = 100 3 12 21 ÖRNEK 9 ÖRNEK 6 %Ñ[MFNEFLJGBSLMOPLUBJMFFOÀPLLBÀUBOFÀPLHFO PMVöUVSVMBCJMJS 77777 f p + f p + f p + f p + f p = 99 34567 õFLJMEFLBÀUBOFEÌSUHFOWBSES ÖRNEK 7 43 f p.3 + f p.4 = 18 + 12 = 30 22 A G ÖRNEK 10 H A BD E F C õFLJMEFLBÀUBOFÑÀHFOWBSES ,ÌöFMFSJ\"WF#PMBOÑÀHFO BC õFLJMEFLJOPLUBJMFPMVöUVSVMBCJMFDFLEÌSUHFOMFSJO 4 TBZTLBÀUS #LÌöFMJÑÀHFOMer: f p.4 12 4 6 5 2 f p - >f p + f p + f pH = 474 5 \"LÌöFMJÑÀHFOMFSf p.3 4 444 2 24 + 30 - 12 = 42 49 8. 18 9. 42 10. 474 100 6. 99 7. 42
·/÷7&34÷5&:&)\";*3-*, 8. MODÜL 7&3÷ 4\":.\"7&0-\"4*-*, www.aydinyayinlari.com.tr ÖRNEK 11 ÖRNEK 14 YLBSFMJLCJSEBNBUBIUBTOEB CVLBSFMFSMFPMVö- UVSVMBOWFBMBOÀJGUTBZPMBOLBSFMFSJOTBZTLBÀUS #JSLBSFOJOBMBOCS2 dir.) 2x2lik & 7.7 = 49 _ b 4x4lik & 5.5 = 25 bb ` 84 tane 6x6lık & 3.3 = 9 b bb õFLJMEF CVMVOBO OPLUB JMF PMVöUVSVMBCJMFDFL ÑÀ- 8 x 8 lik & 1.1 = 1 a HFOTBZTLBÀUS %m/*m 12 5 f p - f p = 210 O UBOF ¿FNCFS FO GB[MB 2.c n m LBEBS 33 2 GBSLMOPLUBEBLFTJõJS ÖRNEK 12 OUBOFпHFOFOGB[MB 6.c n m LBEBS GBSLM d6 d7 d8 d9 2 d1 nPLUBEBLJLFTJõJS d2 d3 O UBOF LBSF FO GB[MB d4 8.c n m LBEBS GBSLM d5 2 OPLUBEBLFTJõJS d1 // d2 // d3 // d4 // d d // d // d // d ÖRNEK 15 7 %Ñ[MFNEFGBSLMÀFNCFSFOÀPLLBÀOPLUBEBLFTJöJS õFLJMEFUBSBMCÌMHFZJJÀJOFBMBOLBÀEÌSUHFOWBSES 7 2·f p = 42 2322 f p.f p.f p.f p = 24 2 1111 ÖRNEK 13 ÖRNEK 16 #JS ÀFNCFSJO Ñ[FSJOEF CVMVOBO GBSLM OPLUB JMF GBSLM ÀFNCFS JMF GBSLM ÑÀHFO FO ÀPL LBÀ OPLUB- PMVöUVSVMBCJMFDFLUÑNEPôSVMBSOÀFNCFSJOJÀCÌMHF- EBLFTJöJSMFS TJOEFLBÀLFTJöJNOPLUBTPMVöVS 5 4 54 10 10.9.8.7 = 210 f p.2 + f p.6 + f pf p.6 f p= 4 4.3.2 2 2 11 20 + 36 + 120 = 176 11. 210 12. 24 13. 210 14. 84 42 16. 176
,PNCJOBTZPO TEST - 25 1. 6[BZEBÑÀÑCJSEPôSVÑ[FSJOEFCVMVONBZBOBM- %Ñ[MFNÑ[FSJOEFLJEPôSVFOGB[MBLBÀOPLUB- UOPLUBLBÀEÑ[MFNCFMJSUJS EBLFTJöFCJMJS \" # $ % & \" # $ % & 2. d 6. #JS ÀFNCFS Ñ[FSJOEF CVMVOBO GBSLM OPLUBOO A BCDE IFSIBOHJ JLJTJ JMF PMVöUVSVMBO EPôSVMBSO ÀFN- CFS JÀFSJTJOEF WF Ñ[FSJOEF FO ÀPL LBÀ UBOF LF- d2 TJNOPLUBTWBSES F KL M \" # $ % & :VLBSEBLJOPLUBJMFLBÀEÌSUHFOÀJ[JMFCJMJS \" # $ % & 3. 7. C õFLJMEFLJOPLUBEBOFOGB[MBLBÀUBOFÑÀHFO B PMVöUVSVMBCJMJS \" # $ % & A DEF GH :VLBSEBLJOPLUBJMFLBÀÑÀHFOÀJ[JMFCJMJS \" # $ % & 4. L 8. ôFLJMEFGBSLMOPLUBCVMVONBLUBES K d M AB C D E F G #VOBHÌSF LÌöFMFSJCVOPLUBMBSÑ[FSJOEFCVMV- OBOFOÀPLLBÀGBSLMÑÀHFOÀJ[JMFCJMJS õFLJMEFLJ OPLUBEBO FO GB[MB LBÀ GBSLM ÀPL- HFOPMVöUVSVMVS \" # $ % & \" # $ % & 1. E 2. E 3. E 4. E \" 6. $ 7. E 8. D
TEST - 26 ,PNCJOBTZPO 1. ôFLJMEFLJOPLUBEBOÐEPóSVTBMES 4. A õFLJMEFCJSLFOBSDNPMBOUBOFLBSFPMEV- #VOBHÌSF CJSLÌöFTJ\"PMBOLBÀÑÀHFOPMVöUV- ôVOBHÌSF BMBODN2EFOCÑZÑLPMBOLBÀUBOF SVMBCJMJS EJLEÌSUHFOWBSES \" # $ % & \" # $ % & A 2. D C E D BFG HK LC õFLJMEFLBÀUBOFGBSLMÑÀHFOWBSES A \" # $ % & B 6. õFLJMEF WFSJMFO OPLUBOO FO B[ JLJTJOEFO HFÀNFLLPöVMVJMFLBÀGBSLMEPôSVÀJ[JMFCJMJS E \" # $ % & F 3. #JSEÐ[MFNÐ[FSJOEFLJEPóSVEBOTBEFDFÐCJSCJ- B CD SJOFQBSBMFMPMVQ EJóFSÐCJS\"OPLUBTOEBOHF¿- A NFLUFEJS #V EPôSVMBSO LFTJöNFTJZMF FO ÀPL LBÀ OPLUB G PMVöVS \" # $ % & H K õFLJMEFLJJLJLFTJöFOEPôSVWFÀFNCFSÑ[FSJOEF- LJOPLUBZLVMMBOBSBLLBÀGBSLMÑÀHFOÀJ[JMFCJ- MJS \" # $ % & 1. D 2. B 3. B 4. $ D 6. $
,PNCJOBTZPO TEST - 27 1. ôFLJMEFLJ TFSBNJL HËS- 4. ôFLJMEF CJSJNLBSFMFSF CËMÐONÐõ UBSMB HËSÐMNFLUF- TFMJOEF CJS EJLEËSUHFO TF¿JMJQ SFOLMFOEJSJMF- dir. DFLUJS #VTFÀJNLBÀGBSLMöFLJMEFZBQMS #V UBSMBOO UBSBM CËMNFMFSJOF FLJN ZBQMNBZBDBL- \" # $ % & US &LJN ZBQMNBZBO CÌMÑNMFSJ JÀJOF BMNBZBO LBÀ 2. LBSFöFLMJOEFUBSMBWBSES \" # $ % & ôFLJMEFLJ CJSJNLÐQUFO PMVõNVõ ZBQEB OPLUB 1 br HËSÐMNFLUFEJS 1 br #V OPLUBMBSEBO LBÀ GBSLM ÑÀHFO PMVöUVSVMBCJ- MJS YCJSJNLBSFEFOPMVöBOöFLJMEFBMBOUFLTB- ZPMBOLBÀEJLEÌSUHFOWBSES \" # $ % & \" # $ % & 3. %BJSFEJMJNJ CJSEBJSFEFNFSLF[B¿OOJ¿CËMHFTJO- 6. ôFLJMË[EFõLÐQMFSEFOPMVõNVõCJSNFSEJWFOEJS EFLJZBZMBTOSMBMBOES#VLTNTFLUËSPMBSBLEB BEMBOESMS 180° OA :VLBSEB \" NFSLF[MJ ZBSN EBJSFEFO PMVõNVõ CJS õFLJMEFLBÀUBOFEJLEÌSUHFOQSJ[NBTWBSES BSBCBI[HËTUFSHFQBOFMJHËSÐMNFLUFEJS \" # $ % & #VI[HÌTUFSHFTJOEFLBÀTFLUÌSWBSES \" # $ % & 1. \" 2. E 3. D 4. B $ 6. D
·/÷7&34÷5&:&)\";*3-*, 8. MODÜL 7&3÷ 4\":.\"7&0-\"4*-*, www.aydinyayinlari.com.tr 1\"4$\"-·¦(&/÷WF#÷/0.\"¦*-*.* 1BTDBM·ÀHFOJ TANIM TANIM 1 1 + 2 = 3 ya da 11 Y Z` R - {}PMNBLÐ[FSF 1 21 2 + 2 = 3 13 31 0 1 1 n `/PMNBLÐ[FSF Y+ZJGBEFTJOJOLVWWFUMFSJ BMOSTB 1 4 6 41 (x + y) = 1 (x + y)1 = 1.x + 1.y 1BTDBMпHFOJOIFSIBOHJCJSOTBUSOOSTSB- (x + y)2 = 1.x2+ 2.x.y + 1.y2 TOEBLJ TBZ JMF S + TSBTOEBLJ TBZ UPQMB- (x + y)3 = 1.x3 + 3.x2.y + 3.x.y2 + 1.y3 OSTB1BTDBMпHFOJOJO O+ TBUSOO S+1 ). TSBTOEBLJTBZFMEFFEJMJS h cnm+c n m=cn+1m (x + y)n = c n m.xn.y0 + c n mxn–1y + . . . + c n mx0 yn r r+1 r+1 01 n B¿MNMBSFMEFFEJMJS #VFõJUMJóF1BTDBMÌ[EFöMJôJ denir. öTQBULPNCJOBTZPOUBONOEBOZBQMS #VB¿MNMBSEBLJUFSJNMFSJOLBUTBZMBSPSUBMBOB- SBLZB[MSTB 1 ÖRNEK 1 11 121 c 14 m + c 14 m + c 15 m + c 16 m 3456 13 31 JöMFNJOJOTPOVDVLBÀUS õFLMJOEFLJTBZMBSEBOPMVõBOпHFOFMEFFEJMJS #VпHFOF1BTDBMÑÀHFOJBEWFSJMJS %m/*m 14 14 15 f p+f p=f p 1 = 2 TBUS 0 10 34 4 15 15 16 1 1 1 +1 = 2 TBUS 1 + 1 f p+f p=f p 0 1 45 5 16 16 17 1 2 1 1 + 2 + 1 = 2 TBUS 2 + 2 + 2 f p+f p=f p 13 0 1 2 56 6 1 + 3 + 3 + 1 = 2 TBUS ÖRNEK 2 31 3 + 3 + 3 + 3 1BTDBM ÑÀHFOJOEF TBUSO FMFNBO LÑNFMFSEF 0 1 2 3 OFZJUFNTJMFEFS 1BTDBM пHFOJOJO IFS CJS TBUSOEBLJ TBZMBSO FMFNBOM CJS LÑNFOJO FMFNBOM BMU LÑNF TBZTO UPQMBN FMFNBOTBZTTBUSOVNBSBTOOFL- 6 TJóJ PMBO LÐNFOJO BMU LÐNF TBZTO WFSJS ±S- OFóJO TBUS FMFNBOMCJSLÐNFOJO WF UFNTJMFEFSf p FMFNBOMBMULÐNFTBZTES 2 1BTDBMпHFOJOJO O+ TBUSOEBLJTBZMBSO UPQMBN FMFNBOTBZTOPMBOLÐNFOJOBMULÐ- NFTBZTOWFSJS Bu dVSVNEB c n m+c n m+c n m+ ... +c n m = 2n 012 n CVMVOVS 17 1. f p 2. FMFNBOMCJSLÑNFOJOFMFNBOMBMULÑNF 6 TBZTOUFNTJMFEFS
www.aydinyayinlari.com.tr 7&3÷ 4\":.\"7&0-\"4*-*, 8. MODÜL ·/÷7&34÷5&:&)\";*3-*, #JOPN\"ÀMN ÖRNEK 4 TANIM (3x - 4y)n Y Z`3 O S`/ S#OPMNBLÐ[FSF BÀMNOEBUFSJNCVMVOEVôVOBHÌSF CVUFSJNMFSJO (x + y)n = c n m xn.y + c n m xn-1.y1 + LBUTBZMBSUPQMBNLBÀUS 01 c n m xn-2.y2 + ... + c n m xn-1.yr + ... + O+ 1 = O= 7 21 x = Z= 1 (3x -Z 7 = (- 7 = -1 c n m x1.yn-1 + c n m x.yn n+1 n ES YJOB[BMBOLVWWFUMFSJOFHËSF %m/*m ÖRNEK 5 ( x + y ) n JGBEFTJOJOB¿MNOEB (a3 +C)17 BÀMNBOOB[BMBOLVWWFUMFSJCJÀJNJOEFEÑ[FOMFOJS- TFCBöUBOUFSJNOFPMVS n +UBOFUFSJNWBSES r+1=8 r=7 ,BUTBZMBSUPQMBNCVMVOVSLFOY= 1 ve y = 1 f 17 p.^ 3 h10 .^ 5 h7 a b BMOSTB 7 c n m + c n m + . . . + c n m = 2n FõJUMJóJFMde edilir. f 17 p.a30.b35 01 n 7 #BõUBO S+ 1). terim c n m xn–r.yr dir. ÖRNEK 6 r (4x3 - y2) Sondan (r + 1). terim c n m xr.yn–r dir. r BÀMNYJOB[BMBOLVWWFUMFSJCJÀJNJOEFEÑ[FOMFOJS- TFTPOEBOUFSJNOFPMVS 0SUBEBLJUFSJNCVMVOVSLFOr = n BMOS 2 #JS UFSJNJO CBõUBO WF TPOEBO CVMVOEVóV ZFS UPQMBNOOCJSFLTJóJUFSJNTBZTOWFSJS r + 1= S= 4 f 6 p.^ 3 h4.a - 2 k2 4x y 4 8 . x12Z4 ÖRNEK 3 ÖRNEK 7 ( x +Z 4JGBEFTJOJOBÀMNOZB[O[ f x3 - 1 12 x2 f 4 p.x4.^ 2y h0 + f 4 p.x3.^ 2y h1 + f 4 p.x2.^ 2y h2 p = x36 + . . . 012 BÀMNOEBTPOEBOUFSJNOFEJS +f 4 p.x1.^ 2y h3 + f 4 px0.^ 2y h4 34 r + 1= 6 r = = x4 + 8x3Z+ 24x2Z2 +YZ3 +Z4 f 12 p.^ 3 h5 .f - 1 7 x 2 p 5 x 12 -f p.x 5 3. x4 Y3Z Y2Z2 YZ3 Z4 4. –1 f 17 p 30 35 6. 8.x12Z4 7. -d 12 nx 5 a b 7
·/÷7&34÷5&:&)\";*3-*, 8. MODÜL 7&3÷ 4\":.\"7&0-\"4*-*, www.aydinyayinlari.com.tr ÖRNEK 8 ÖRNEK 11 ( x3 - 3y )12 = x + ... f x2 - 12 6 BÀMNOEBTPOEBOUFSJNOFEJS x3 p BÀMNOEBY2MJUFSJNJOLBUTBZTOFEJS r + 1= 9 r = 8 f 12 p^ 3 h8 ^ - 3y h4 6 2 h6 - r.f 12 r x f p.^ x - 3 p 8 r x f 12 p.81.x 24 4 .y 2(6 -S - 3r = 2 j r = 2 8 f 6 p ^ - 12 h2 = 2160 2 ÖRNEK 9 ÖRNEK 12 f x2 - 1 6 f 25x4 - y3 n . . . + Ax16y18 + . . . x3 p p= 5 BÀMNOEBPSUBEBLJUFSJNOFEJS PMEVôVOBHÌSF \"LBÀUS 6 3r r= =3 d n n a 25x4 kn–r.f - y p 2 r5 f 6 p.^ x2 h3.f - 1 3 3r = 18 j r = 6 3 3 p x -20.x-3 O- = 16 jO f 10 p.a 25x4 k4.f - y 36 10 A = 25.f p p & 65 6 ÖRNEK 10 ÖRNEK 13 f 2x2 + y3 12 f x3 + 1 8 p 2x p 4 BÀMNOEBLJUFSJNMFSEFOCJSJ\"Y18 ZOPMEVôVOBHÌ- BÀMNOEBTBCJUUFSJNLBÀUS SF \"LBÀUS f 8 p.^ 3 h8–r . d 1 r x n r 2x 3r 12 y f p ^ 2 h12–r . f p 24 - 3r = r j r=6 2x r4 8 1 6 7 f p.d 62 n= 16 24 - 2r = 18 j r = 3 f 12 p^ 2 h9.d 1 3 12 n = 8.f p 343 8. f 12 p81.x24.y4 9. –20x–3 12 11. 2160 10 7 8 10. 8.f p 12. 25·f p 13. 3 6 16
www.aydinyayinlari.com.tr 7&3÷ 4\":.\"7&0-\"4*-*, 8. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 14 ÖRNEK 16 f x2 - k 12 c 30 m + c 30 m + . . . + c 30 m x4 02 30 p TPOVDVOFEJS BÀMNOEBTBCJUUFSJNPMEVôVOBHÌSF LLBÀUS 229 f 12 p.^ 2 h12–r . f - k r x 4 p r x 24 - 2r = 4r j r = 4 f 12 p.^ - k h4 = 495 ÖRNEK 17 4 k=±1 c 18 m + c 18 m + . . . + c 18 m = A PMEVóVOBHËSF 35 17 c 18 m + c 18 m + . . . + c 18 m 02 18 ÖRNEK 15 UPQMBN\"DJOTJOEFOOFEJS ( x - 2 )4 ( x2 - 1 ) = ... +LY3 + ... PMEVôVOBHÌSF LLBÀUS 18 18 18 18 18 18 f p+f p+...+f p=f p+f p+...+f p <1 14344424441743 0 2 18 f 4 p.x3.^ - 2 h1.f 5 p^ - 1 h5 $ 3 1A 8x 18 18 18 15 f p+f p+...+f p= A+1 f 4 p.x1.^ - 2 h3.f 5 p x2.^ - 1 h4 \" - 3 j -Y3 02 18 160x 34 k = - %m/*m ÖRNEK 18 n `/PMNBLÐ[FSF (x - 2)BÀMNOEBY4MÑWFYMJUFSJNJOLBUTBZMBSUPQ- MBNOFEJS ^ 1 + x hn = c n m + c n mx + c n mx2 + . . . + c n mxn 01 2 n f 5 p.x4.^ - 2 h1 4 ^ 1 - x hn = c n m - c n mx + c n mx2. . . .c n m^ - x hn \" - 10x 01 2 n 1 WFFõJUMJLUFY =EFóFSJJ¿JO f 5 p.x1.^ - 2 h4 \" 80.x 4 2n = c n m + c n m + . . . + c n m -10 + 80 = 70 01 n 0 = c n m - c n m. . .c n m = 2n–1 01 n O¿JGUJTFc n m + c n m + . . . + c n m = 2n–1 ÖRNEK 19 02 n (x + 3y2)7 = x7 + ... +LY4.y + ... c n m + c n m + . . . + c n m = 2n–1 FöJUMJôJOEFLIBOHJTBZZHÌTUFSNFLUFEJS 13 n-1 OUFLJTFc n m + c n m + . . . + c n m = 2n–1 02 n-1 7 px4.a 2 k3 7.6.5 4 6 f j x .27.y c n m + c n m + . . . + c n m = 2n–1 3y 3 3.2.1 13 n 46 )FSJLJEVSVNEBda sonuç 2n-1 dir. =35.27 .x .y ise k = k.9 14. ±1 m 16. 229 17. \" 18. 70 19.
TEST - 28 #JOPN\"ÀMN 1. f x2 - 1 15 4. f x2 – 1 10 x3 x p p BÀMNOEBTBCJUUFSJNLBÀUS JGBEFTJOJOBÀMNOEBTBCJUUFSJNLBÀUS A) - c 15 m.2 B) -c 15 m $ c 15 m \" # $ % & 5 5 5 D) c 15 m.2 E) c 10 m 5 5 f k - n x3 xp 2. ^ a2 - 3b3 hn YJOBSUBOLVWWFUMFSJOFHÌSF BÀMEôOEBTPOEBO ÑODÑUFSJNPMEVôVOBHÌSF LLBÀUS JGBEFTJOJOBÀMNOEBLJUFSJNMFSEFOCJSJYB4C9 PMEVôVOBHÌSF Y+OLBÀUS \" m # m $ % & A) - # - $ - & - D) - 6. f 1 - x2 9 3 7 p 3. f 2x - p x2 2 JGBEFTJBÀMEôOEBTBCJUUFSJNLBÀUS JGBEFTJ Y JO B[BMBO LVWWFUJOF HÌSF BÀMEôOEB A) - # m $ - 21 CBöUBOÑODÑUFSJNJOLBUTBZTLBÀUS 2 D) 2- E) 21 \" # $ % & 1. $ 2. D 3. \" 4. E B 6. $
#JOPN\"ÀMN TEST - 29 1. ax – y2 n = xn... + k.x4y4 + ... 4. fx+ 1 8 k x2 p FõJUMJóJWFSJMJZPS BÀMNOEBY2MJUFSJNJOLBUTBZTLBÀUS #VOBHÌSF O+LLBÀUS \" # $ % & \" # $ % & 2. f x3 - a 5 ( 2x - 1 )4. ( x2 + 1 )3 = .... +LY4 + ... x2 p PMEVôVOBHÌSF LLBÀUS \" # $ % & BÀMNOEB TBCJU UFSJN - PMEVôVOB HÌSF B LBÀUS \" # $ % & 3. f x3 - 3 n 6. c n m.7n + c n m.7n – 1 + . . . + c n m.7 + c n m = 272 01 n–1 n p x BÀMNOEBLBUTBZMBSUPQMBNPMEVôVOBHÌ- PMEVôVOBHÌSF OLBÀUS SF JGBEFOJOTBCJUUFSJNJLBÀUS \" # $ % & \" # $ & 7 % 1. $ 2. B 3. B 4. E $ 6. D
TEST - 30 #JOPN\"ÀMN 1. ( 2x3 + x2 ) 4. ( x - 1 )4 . ( x2 + 2 )3 BÀMNOEBCBöUBOUFSJNBöBôEBLJMFSEFOIBO- JGBEFTJOJOBÀMNOEBY6MUFSJNJOLBUTBZTLBÀ- HJTJEJS US A) 12.x13 # Y14 $ Y \" # $ % & % Y & Y17 x - y 8 f y2 x2 p 2. f x3 - 1 12 JGBEFTJOJOB¿MNOEBUFSJNMFSEFOCJSJ A UÐS ^ xy h4 x p BÀMNOEBTBCJUUFSJNLBÀUS #VOBHÌSF \"LBÀUS \" # $ % - & - \" # $ % & 6. f x3 - 2 8 x2 p 3. f x2 - 2 10 JGBEFTJ Y JO B[BMBO LVWWFUMFSJOF HÌSF BÀME- x3 ôOEB PSUBEBLJ UFSJN BöBôEBLJMFSEFO IBOHJTJ p PMVS BÀMNOEBLJTBCJUUFSJNLBÀUS \" Y4 B) 16 $ 1120 x4 x A) # 3 $ 3 E) 7.2 D) 1120 & Y4 % 4 x4 1. B 2. E 3. \" 60 4. $ $ 6. E
#JOPN\"ÀMN TEST - 31 1. (a3 -C)n 4. (x + 2)4 . (x2 - 1)3 = ... +LY4 + ... BÀMNOEBLJ UFSJNMFSEFO CJSJ \"B C JTF \" PMEVôVOBHÌSF LLBÀUS LBÀUS A) - # - $ % & A) - # - $ - D) - & - 10 fx+ 1 3n x2 f 2x5 + 1 p p 8x2 2. BÀMNOEBY29 MVUFSJNJOLBUTBZTLBÀUS BÀMNOEBTBCJUUFSJNBöBôEBLJMFSEFOIBOHJTJ- EJS \" # $ % & \" $ O n # $ O O $ $ O O- % $ O Om & $ O O+ 1) 3. f 4x4 - 1 9 6. c 8 m + c 9 m + c 10 m 2x2 p 33 3 JöMFNJOJOTPOVDVBöBôEBLJMFSEFOIBOHJTJEJS BÀMNOEBTBCJUUFSJNLBÀUS A) - # - $ A) c 11 m - c 8 m B) c 11 m % & 74 4 $ c 12 m D) c 11 m + c 12 m 5 45 E) c 12 m - c 8 m 42 1. \" 2. D 3. D 61 4. $ B 6. \"
·/÷7&34÷5&:&)\";*3-*, 8. MODÜL 7&3÷ 4\":.\"7&0-\"4*-*, www.aydinyayinlari.com.tr 0-\"4*-*,* %FOFZ ¦LU ²SOFL6[BZ SONUÇ 7$1,0%m/*m O UBOF NBEFOJ QBSBOO CJS NBEFOJ QBSBOO O LF[ IBWBZB BUMNBT EFOFZJOEF ËSOFL V[BZO ±ODFEFOTPOVDVCJMJONFZFOPMBZMBSOHFS¿FL- FMFNBOTBZT2O dir. MFõNFEVSVNMBSOBJMJõLJOWFSJUPQMBNBTÐSFDJOF EFOFZBEWFSJMJS #VTPOV¿UBOZPMB¿LBSBLBõBóEBLJCPõMVLMBSEPM- EVSVOV[ #JS EFOFZ TPOVDVOEB LBSõMBõMBCJMFDFL PMBT UÐNEVSVNMBSOIFSCJSJOFÀLU denir. r UBOF[BSOIBWBZBBUMNBTEFOFZJOEFËSOFLV[B- ZOFMFNBOTBZT 61 dir. %FOFZ TPOVDVOEB FMEF FEJMFO CÐUÐO ¿LUMBSO LÐNFTJOF JTF ÌSOFL V[BZ BE WFSJMJS WF & JMF r UBOF[BSOIBWBZBBUMNBTEFOFZJOEFËSOFLV[B- HËTUFSJMJS ZOFMFNBOTBZT 62 dir. #JSNBEFOJQBSBOOLF[IBWBZBBUMNBTEF- r OUBOF[BSOIBWBZBBUMNBTEFOFZJOEFËSOFLV[B- OFZJOEFËSOFLV[BZ ZOFMFNBOTBZT 6O dir. E = {5 :} s ( E ) = 21 \"óB¿õFNBT Y T ÷NL»OT[,FTJO \"ZSL\"ZSL0MNBZBO0MBZMBS TANIM #JSNBEFOJQBSBOOLF[IBWBZBBUMNBTEF- &ËSOFLV[BZOBLFTJOPMBZ CPõLÐNFZFJN- OFZJOEFËSOFLV[BZ L»OT[PMBZ denir. &ËSOFLV[BZOO\"WF#HJCJJLJPMBZJ¿JO E = { : : : 5 5 : 5 5 } A a B =JTF\"WF#PMBZMBSOBBZSLPMBZ- s ( E ) = 22 MBS denir. A a # á JTF \" WF # PMBZMBS BZSL PMNBZBO \"óB¿õFNBT PMBZMBSES Y 5ÑNMFZFO TANIM YT #JS&ËSOFLV[BZOOJTUFOFOLPõVMMBSTBóMBZBO BMU LÐNFTJ EõOEB LBMBO FMFNBOMBSOO LÐNF- Y sine CJSPMBZOUÑNMFZFOJdenir. T ÖRNEK 2 T #JS[BSOBUMNBTEFOFZJOEF[BSOÐTUZÐ[ÐOFHFMFOTB- ÖRNEK 1 ZOO B 5FLTBZHFMNFPMBZO #JSNBEFOJQBSBOOLF[IBWBZBBUMNBTEFOFZJOEF C \"TBMTBZHFMNFPMBZOMJTUFZÌOUFNJJMFZB[O[ ÌSOFLV[BZOWFEJZBHSBNOZB[O[ B \"= { } : C #= { } :T :: TT : :T T : T T 62 2. B \" \\ ^C # \\ ^
www.aydinyayinlari.com.tr 7&3÷ 4\":.\"7&0-\"4*-*, 8. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 3 bilgi #JSLVUVEBLJMBNCBEBOUBOFTJTBóMBNES#VLVUVEBO #JS ¿JGU [BSO BUMNBT EFOFZJOEF ÐTU ZÐ[MFSJOF SBTUHFMFUBOFMBNCBBMOEóOEB HFMFO TBZMBSO UPQMBN WF LB¿ EVSVN PMEVóV B ²SOFLV[BZOFMFNBOTBZTLBÀUS BõBóEBLJUBCMPEBLJHJCJEJS C #VLVUVEBOBMOBOMBNCBMBSEBOCJSJOJOTBôMBN 5PQMBN 2 3 4 7 11 12 CJSJOJO CP[VL PMNBT $ PMBZ PMEVôVOB HÌSF $ 5BOF 12344 3 2 1 PMBZOOFMFNBOTBZTLBÀUS ±SOFóJO JLJ[BSOBUMNBTPMBZOEBÐTUZÐ[ÐOF 6 HFMFO TBZMBSO UPQMBNOO EFO CÐZÐL PMNB B f p = 15 durumu 4 + 3 + 2 + 1 =UBOFEJS 2 0MBTML'POLTJZPOV 42 7$1,0%m/*m C f p.f p = 8 #JS & ËSOFL V[BZOO UÐN BMU LÐNFMFSJOJO LÐ- 11 mesi EAPMTVOG&A Z [ ]UBONMWFBõB- óEBLJBLTJZPNMBSHFS¿FLMFZFO1GPOLTJZPOV- ÖRNEK 4 OB PMBTML GPOLTJZPOV 1 \" EFóFSJOF EF \" PMBZOOPMBTMóEFOJS #JS ¿JGU [BSO BUMNBT EFOFZJOEF [BSMBSO ÐTU ZÐ[MFSJOF HFMFOTBZMBSO J A e EAJ¿JO# P ( A ) # 1 \"¥BSQNMBSOOFO¿PLPMNBPMBZ JJ P ( E ) = 1 #&õJUPMNBPMBZ $5PQMBNMBSOOFOB[PMNBPMBZ JJJ A ` EA B ` EA ve A aB = Ø ise õFLMJOEFWFSJMJZPS P ( A bB ) = P ( A ) + P ( B ) #VOBHËSF B \" #WF$PMBZMBSOMJTUFZÌOUFNJJMFZB[O[ ²[FMJLMFS C \" #WF$PMBZMBSOOBZSLPMBOWFBZSLPMNB- r P( Ø ) = ZBOMBSCVMVOV[ r A e B ise P(A) # P(B) r A a #áJTF B \"= { } B = { } P ( A b B ) = P( A ) + P ( B ) - P ( A aB ) r 1 \" CJSPMBZOPMBTMó 1 \" BZOPMBZO ${ } C \"a$= qPMEVôVOEBO\"JMF$BZSLPMBZMBSES PMNBNBPMBTMóJTF \" a # â q PMEVôVOEBO \" JMF # BZSL PMNBZBO P ( A ) + P ( A) = 1 = P ( E ) r P(A - B) = P ( A a B) =1 \" m1 \"a B ) PMBZMBSES B a$âq#JMF$BZSLPMNBZBOPMBZMBSES &ö0MVNMV²SOFL6[BZ ±SOFLV[BZ&= { e1 F2 Fn }PMBOCJS1 PMBTMLGPOLTJZPOVJ¿JO P(e1) = P(e2) = ... = P(en) ise E ye FöPMVNMVÌSOFLV[BZdenir. &õPMVNMVCJSËSOFLV[BZEBCJS\"PMBZOOPMB- s (A) TMó P (A) = s (E) 3. B C 63
·/÷7&34÷5&:&)\";*3-*, 8. MODÜL 7&3÷ 4\":.\"7&0-\"4*-*, www.aydinyayinlari.com.tr ÖRNEK 5 ÖRNEK 8 #JSËSOFLV[BZO\"WF#PMBZMBSJ¿JO1 \" = 1 )JMFTJ[JLJ[BSOCJSMJLUFBUMNBTEFOFZJOEF P(A b B) = 3 ve P(A a B) = 2 ise 2 B ·TUF HFMFO TBZMBSO UPQMBNMBSOO PMNBT 55 PMBTMôLBÀUS C ÷LJTJOJOEFBZOHFMNFTJPMBTMôLBÀUS a P ( B ) C P ( A a#h D 1 \"hb #h PMBTMLMBSLBÀUS B \"= { } B 3 = 1 + P^ B h - 2 T & = 62 = 36 52 5 P^ A h = 5 36 P^ B h = 1 2 C #= { } P^ B h = 6 1 = C P^ A + B' h = 1 - 2 = 1 36 6 2 5 10 D p^ A' , B' h = 1 - 2 = 3 55 ÖRNEK 6 ÖRNEK 9 #JS LPõVZB LBUMBO п BUMFU WBSES \"UMFUMFSEFO CJSJODJTJ- #JSUPSCBEBCÐZÐLMÐLMFSJBZONBWJ LSN[ CFZB[ OJO ZBSõ LB[BONB PMBTMó JLJODJ BUMFUJO ZBSõ LB[BO- UPQWBSES5PSCBEBOBZOBOEBUPQ¿FLJMJZPS NBPMBTMóOOZBSTOB пÐODÐBUMFUJOLB[BONBPMBTM- #VUPQMBSEBO óOOJTFпLBUOBFõJUUJS B ¶¿ÐOÐOEFNBWJPMNBT C öLJTJOJOLSN[CJSJOJONBWJPMNBT #VOB HÌSF ZBSö CJSJODJ BUMFUJO LB[BONB PMBTMô D ¶¿ÐOÐOEFGBSLMSFOLUFPMNBT LBÀUS E 4BEFDFCJSJOJOCFZB[PMNBT PMBTMLMBSOCVMVOV[ 12 3 3x + 6x + x =1 1 4 x= fp 10 3 3 41 B = = 3x = 10 9 84 21 fp 3 34 f pf p 22 12 1 C = = ÖRNEK 7 9 84 7 fp )JMFTJ[CJS[BSBUMEôOEB 3 B 5FLTBZHFMNFTJPMBTMôLBÀUS C \"TBMTBZHFMNFTJPMBTMôLBÀUS 432 f pf pf p B \"= { } &= { } 111 P^ A h = 3 = 1 24 2 62 D = = 9 84 7 C #= { } P^ B h = 3 = 1 fp 62 3 27 f p.f p 12 2.21 1 E = = 9 84 2 fp 3 11 3 3 11 64 51 1 121 B C D 6. 7. B C 8. B C 9. B C D E 2 10 5 10 22 36 6 21 7 7 2
www.aydinyayinlari.com.tr 7&3÷ 4\":.\"7&0-\"4*-*, 8. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 10 ÖRNEK 13 #JSTOGUBL[WFFSLFLWBSES,[MBSOJ FS- #JSPEBEBFWMJ¿JGUWBSES LFLMFSJOTJHË[MÐLMÐEÐS #VPEBEBOSBTUHFMFJLJLJöJTFÀJMEJôJOEF CVJLJLJöJ- OJOLBSLPDBPMNBPMBTMôLBÀUS #V TOGUBO SBTUHFMF TFÀJMFO CJS ÌôSFODJOJO L[ WFZB HÌ[MÑLMÑPMNBPMBTMôLBÀUS 12 1 1 ·= K E 8 12 12 11 11 4 12 Gözlüklü Gözlüksüz 4 + 8 + 12 2 ÖRNEK 14 = #JS¿JGU[BSBUMZPS 36 3 ·TU ZÑ[F HFMFO TBZMBSO BZO WFZB UPQMBNMBSOO EBOCÑZÑLPMNBPMBTMôLBÀUS ÖRNEK 11 P^ A , B h = 6 + 6 - 2 10 5 == #JSTOGUBLJËóSFODJMFSJOFSLFLL[ES&S- 36 36 36 36 18 LFLMFSJO WF L[MBSO V JO ÐTUÐOEF OPU BM- NõUS ÖRNEK 15 (FMJöJHÑ[FM TFÀJMFO CJS ÌôSFODJOJO JO ÑTUÑOEF OPU #JSLVNCBSBEBLVSVõEFóFSJOEFNBEFOJQBSBWBS- BMNöPMNBPMBTMôLBÀUS ES #VOMBSEBO UBOFTJ LVSVõMVL HFSJ LBMBOMBS LV- SVõMVLUVS K 8 in üstü 12x 3BTUHFMF BMOBO NBEFOJ QBSBEBO CJSJOJO LVSVö- +E MVL EJôFSJLJTJOJOLVSVöMVLPMNBPMBTMôLBÀUS 100x + 24x 36x %36 ÖRNEK 12 86 f p.f p %Ð[HÐOCJSQBSBLF[IBWBZBBUMZPS #VOB HÌSF LF[ ZB[ LF[ UVSB HFMNFTJ PMBTM- 1 2 30 ôLBÀUS = 14 91 fp 3 :::55Z d 1 5 5! ÖRNEK 16 n. A = { } #= {B C D E}LÐNFMFSJWFSJMJZPS\"EBO 2 3! .2! #ZFUBONMUÐNGPOLTJZPOMBSCJSFSLBSUBZB[MQCJSUPS- 10 5 CBZBLPOVZPS = 5PSCBEBOCJSLBSUÀFLJMEJôJOEF CVLBSUUBZB[MGPOL- 32 16 TJZPOVOCJSFCJSGPOLTJZPOPMNBPMBTMôLBÀUS 4.3.2 3 = 3 8 4 2 5 1 5 30 3 10. 11. %36 12. 13. 14. 16. 11 18 91 8 3 16
·/÷7&34÷5&:&)\";*3-*, 8. MODÜL 7&3÷ 4\":.\"7&0-\"4*-*, www.aydinyayinlari.com.tr ÖRNEK 17 ÖRNEK 20 \"UPSCBTOEBCFZB[ TBS #UPSCBTOEBCFZB[ öLJBWDEBOCJSJOJOIFEFGJWVSNBPMBTMó 2 WFEJóFSJOJO TBSUPQWBSES 5 \"EBOUPQÀFLJMJQ#ZFBUMELUBOTPOSB#EFOÀF- LJMFOCJSUPQVOTBSPMNBPMBTMôLBÀUS IFEFGJWVSNBPMBTMó 1 UÐS 4 #4+44 4 4 5 5 41 )FEFGJO ·+·= B ÷LJBWDUBSBGOEBOWVSVMNBPMBTMô 9 8 9 8 72 C CJSBWDUBSBGOEBOWVSVMNBPMBTMô D WVSVMBNBNB PMBTMôOFEJS ÖRNEK 18 21 1 B · = \"WF#UPSCBMBSOOIFSJLJTJOEFEFCFZB[ NBWJUPQ WBSES 5 4 10 \" EBO CJS UPQ BMOQ SFOHJOF CBLMNBEBO # ZF TPO- 23 31 9 SBEBO#EFOCJSUPQBMOQSFOHJOFCBLMNBEBO\"ZB C · + · = LPOEVôVOEBSFOLCBLNOEBOJMLEVSVNVFMEFFUNF 5 4 5 4 20 PMBTMôLBÀUS 33 9 D · = B .B + M.M 5 4 20 4 5 6 7 31 ·+·= ÖRNEK 21 10 11 10 11 55 öSFN CVMVUMV HÐOMFSEF CBML ZBLBMBNB PMBTMóOO CVMVUTV[HÐOMFSEFJTF PMEVóVOVCFMJSMJZPS#FMJSMJCJS HÐOÐOCVMVUMVPMNBTPMBTMóJTF UÐS\"õBóEBPMBT- MLBóB¿õFNBTHËSÐMNFLUFEJS #PöMVLMBS UBNBNMBZQ öLMBSEBLJ TPSVMBS ZBOUMBZ- O[ 0,3 Bulutlu 0,1 #BMLWBS Gün 0,9 #BMLZPL #BMLWBS 0,7 0,65 #BMLZPL Bulutsuz 0,35 ÖRNEK 19 B ÷SFNhJO CVMVUMV CJS HÑOEF CBML UVUNB PMBTMô LBÀUS #JSEBJSFJÀJOEFBMOBOCJSOPLUBOOEBJSFOJONFSLF- [JOFÀFWSFTJOEFOEBIBZBLOPMNBPMBTMôLBÀUS C ÷SFNhJOCBMLUVUNBPMBTMôLBÀUS 2 B = π .r 1 C + 2 = 4 π .4r 41 31 1 199 17. 18. 19. 66 20. B C D 21. B C 10 20 20 72 55 4
www.aydinyayinlari.com.tr 7&3÷ 4\":.\"7&0-\"4*-*, 8. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 22 ÖRNEK 24 ôFLJMEFLJLVUVMBSEBTBZMBSCJSCJSJOEFOGBSLMFOB[CJSFS \"ZõFEBLUJMPTVOEBUFNJ[MJLJ¿JOTËLUÐóÐUVõVSBTUHFMF LVSVZFNJõCVMVONBLUBES ZFSJOFUBLNõUS UBOFGTUL \"UBOFGOEL UBOFDFWJ[ B tane badem #V LVSVZFNJõMFSJO UBNBN CJS UPSCBEB LBSõUSMZPS #V \"ZõF EBIB TPOSB EBLUJMPTVOEB ZFOJ ZB[BDBó SPNBOO UPSCBEBOSBTUHFMFCJSLVSVZFNJõ¿FLJMEJóJOEFGOEL¿FL- ZB[NBZBCBõMBS%BLUJMPEBTSBTZMB) \" : \" 5UVõMBS- NFPMBTMóFOB[ DFWJ[¿FLNFPMBTMóFOGB[MBES OBCBTBSBLSPNBOOOCBõMóOZB[NBLJTUFNJõUJS 5PSCBEB UBOF LVSVZFNJö CVMVOEVôVOB HÌSF GO- #VOB HÌSF \"ZöFhOJO SPNBOOO JTNJOJ EBLUJMPEB ELTBZTOOBMBCJMFDFôJEFôFSMFSUPQMBNLBÀUS EPôSVCJÀJNEFZB[NBPMBTMôLBÀUS \"+ B + 8 + 14 = \"+ B = 14 1 B = 9 j\"= \"UVöV PMBTMLMBZFSJOFEPôSVUBLMNöUS \"< 8 < B < 14 B = 10 j\"= 4 #= 11 j\"= 3 5 \"< B < 8 < 14 #= 12 j\"= 2 11 1 B = 13 j+\"= 1 EVSVNVJÀJO ·= 5 5 25 \"CVMVOBNB[ ÖRNEK 23 ÖRNEK 25 ôFLJMEF \" OPLUBTOEB EVSBO GBSFOJO HJUUJóJ ZPMEBO HFSJ 6¿MBS CPODVL PMBO Ë[EFõ EËONFNFLõBSUZMBZPMBMNBLUBES UPQMVJóOFBMOZPS#VJóOFMFS- MF V¿MBS CJSCJSJOF UFNBT FEF- BE DFL CJ¿JNEF SBTUHFMF BõBóEB CJS ËSOFóJ HËSÐMFO BMUHFOMFS F PMVõUVSVMVZPS A CG #V EJ[JMJNMFSEF CJSCJSJZMF UFNBT FEFO CPODVL CV- D MVONBNBPMBTMôLBÀUS #VOB HÌSF GBSFOJO % WFZB ' EF CVMVOBO QFZOJSMFSF VMBöNBPMBTMôLBÀUS B E 16 1 1 dn 3 91 21 A 9F = 1 1 3 C 9G 2 32 veya D 1 1 1 10 5 6 += = 6 9 36 18 (6) (4) 22. 5 67 1 1 23. 24. 18 25 32
TEST - 32 0MBTML 1. #JSUPSCBEBZFõJM TBS NBWJCJMZFWBSES %Ð[HÐOCJS[BSLF[BUMZPS 5PSCBEBOSBTUHFMFTFÀJMFOCJSCJMZFOJOZFöJMWF- LF[HFMNFPMBTMôLBÀUS ZBTBSPMNBPMBTMôLBÀUS 15 B) 25 $ 25 15 35 A) 1 B) 7 $ 5 D) 1 E) 1 A) 65 66 D) E) 6 12 7 3 2 65 66 65 2. ¶¿ËóSFODJEFOIFSCJSJOJOCJSQSPCMFNJ¿Ë[NFPMBT- 6. öLJ[BSCJSMJLUFBUMZPS MLMBS 2 , 3 ve 3 tir. ·TUF HFMFO TBZMBSO UPQMBNOO LBSF LÌLÑOÑO 34 5 CJSUBNTBZPMNBPMBTMôLBÀUS #VÌôSFODJMFSEFOFOB[CJSJOJOCVQSPCMFNJÀÌ[- NFPMBTMôLBÀUS A) 1 B) 7 $ 1 D) 2 E) 1 6 36 3 3 2 A) 1 B) 2 $ 7 D) 17 29 30 E) 15 30 30 30 3. TBZTOOSBLBNMBSOOZFSMFSJEFóJõ- 7. #JS UPSCBEB EFO F LBEBS OVNBSBMBOESMNõ UJSJMFSFLCBTBNBLMTBZMBSPMVõUVSVMVZPS UPQMBSWBSES#VUPSCBEBOBZOBOEBUPQ¿FLJMJZPS #VOBHÌSF JMLWFTPOCBTBNBôOBZOPMNBPMB- #VOBHÌSF UPQMBSOÑ[FSJOEFLJTBZMBSEBOCJSJOJO TMôLBÀUS JMF CÌMÑOÑQ JMF CÌMÑOFNFZFO EJôFSJOJO JMF CÌMÑOÑQ JMF CÌMÑOFNFZFO TBZ PMNB PMBTMô A) 1 B) 1 $ 1 D) 1 E) 1 LBÀUS 7 14 18 21 23 A) 1 B) 2 $ 4 D) 7 E) 14 25 25 25 25 25 4. ôFLJMEFLJOPLUBMBSLVMMBOMBSBLPMVõUVSVMBOEËSUHFO- 8. ôFLJMEFLJOPLUBMBSEBOSBTUHFMFпOPLUBTF¿JMJZPS MFSEFOCJSUBOFTJTF¿JMJZPS GFE K H L G F A E HO B D C #VOB HÌSF TFÀJMFO CV EÌSUHFOJO CJS LFOBSOO D BC \"$LJSJöJPMNBPMBTMôLBÀUS #VOBHÌSF TFÀJMFOCVOPLUBMBSEBOCJSJOJOTBEF- A) 1 B) 1 $ 1 D) 1 E) 1 DFEÌSUHFOÑ[FSJOEFPMNBPMBTMôLBÀUS 12 10 7 4 3 2 B) 3 $ 4 3 5 A) 7 7 D) E) 7 8 8 1. B 2. E 3. B 4. B 68 B 6. B 7. B 8. B
0MBTML TEST - 33 1. \"UPSCBTOEBTJZBI LSN[ #UPSCBTOEBTJ- #JS UPSCBEB CFZB[ TBS WF NBWJ UPQ WBSES ZBI LSN[CJMZFWBSES\"EBOCJSCJMZFBMOQ# ¥FLJMFOUPQMBSHFSJBUMNBLõBSUZMBUPQ¿FLJMJZPS ZF #EFOCJSCJMZFBMQ\"UPSCBTOBBUMZPSWFCVJõ- MFNCJSLB¿EFGBUFLSBSMBOZPS #VOB HÌSF ÀFLJMFO UPQVO BZO SFOLUF PMNB PMBTMôLBÀUS \" UPSCBTOEBO ÀFLJMFDFL CJMZFOJO TJZBI PMEV- A) 121 B) 123 $ 1 ôVLFTJOPMEVôVBOEB #EFOÀFLJMFDFLCJMZFOJO 1000 1000 4 LSN[PMNBPMBTMôLBÀUS D) 34 E) 17 A) 1 B) 2 $ 4 5 E) 2 125 125 9 9 9 D) 3 9 2. #JSBWDOOIFEFGJWVSNBPMBTMó 2 UÐS 6. ÷ÀJOEFCFZB[ LSN[WFTBSUPQCVMVOBOCJS 3 UPSCBEBOÀFLJMFOUPQVOÑÀÑOÑOEFGBSLMSFOLUF #VBWDIFEFGFBUöZBQUôOEBÑOEFIFEFGJ HFMNFPMBTMôLBÀUS WVSNBNBPMBTMôLBÀUS A) 1 B) 1 $ 2 D) 3 E) 3 22 11 11 11 22 A) 22 B) 29 $ 38 D) 40 E) 43 243 243 243 243 243 3. öLJ[BSCJSMJLUFBUMZPS ·TUZÑ[FZFHFMFOTBZMBSUPQMBNOOÑOLBUPM- 7. ÷ÀJOEFCFZB[ LSN[WFTBSUPQCVMVOBO EVôVCJMJOEJôJOFHÌSF CVTBZMBSEBOCJSJOJOUFL CJSJOJOÀJGUHFMNFPMBTMôLBÀUS CJSUPSCBEBOSBTUHFMFÀFLJMFOCJSUPQVOCFZB[ZB EBLSN[HFMNFPMBTMôLBÀUS A) 1 B) 1 $ 1 D) 1 E) 1 A) 1 B) 1 $ 1 D) 7 E) 3 2 3 4 5 6 12 4 3 12 4 4. öLJ[BSBUMZPS 8. TBZTOOQP[JUJGCÌMFOMFSJOEFOCJSJSBTUHF- ;BSMBSEBOCJSJOJOUFL EJôFSJOJOÀJGUTBZHFMEJôJ MF TFÀJMJSTF TFÀJMFO CV TBZOO TBZTOO CJS CJMJOEJôJOFHÌSF UPQMBNMBSOOPMNBPMBTMô LBUPMNBPMBTMôLBÀUS LBÀUS A) 1 B) 1 $ 1 D) 1 E) 1 A) 1 B) 2 $ 1 D) 1 E) 1 10 5 4 7 14 9 9 3 4 6 1. D 2. D 3. \" 4. B 69 E 6. D 7. D 8. $
TEST - 34 0MBTML 1. A = { }LÐNFTJOJOBMULÐNFMFSJOEFO 6. A = { } CJSUBOFTJTF¿JMJZPS LÑNFTJOJOFMFNBOMBSBSBTOEBOSBTUHFMFJLJUB- OFTJ TFÀJMEJôJOEF CVOMBSO UPQMBNOO ÀJGU TBZ #VOBHÌSF TFÀJMFOLÑNFOJOFOB[FMFNBOMPM- NBPMBTMôLBÀUS PMNBPMBTMôLBÀUS 29 B) 7 $ 21 5 1 A) 1 B) 2 $ 3 D) 2 E) 7 A) D) E) 3 5 5 15 15 128 32 128 32 8 2. ÷ÀJOEFCFZB[ LSN[WFTBSUPQCVMVOBO 7. ÷ÀJOEFCFZB[ LSN[WFTBSUPQCVMVOBO CJSUPSCBEBOÀFLJMFOUPQVOJLJTJOJOEFTBSHFM- CJS UPSCBEBO BZO BOEB ÀFLJMFO UPQVO GBSLM NFPMBTMôLBÀUS SFOLUFHFMNFPMBTMôLBÀUS 5 B) 5 $ 5 10 3 A) 19 B) 23 $ 29 D) 47 E) 47 A) D) E) 66 66 66 66 132 44 22 33 33 22 3. GBSLM[BSG QPTUBLVUVTVOBBUMZPS 8. ÷ÀJOEFCFZB[ LSN[WFTBSUPQCVMVOBO #VOBHÌSF BUMBO[BSGMBSOÑÀÑOÑOEFBZOQPT- CJSUPSCBEBOBZOBOEBÀFLJMFOUPQVOÑÀÑOÑO UBLVUVTVOEBPMNBPMBTMôLBÀUS EFBZOSFOLHFMNFPMBTMôLBÀUS A) 1 B) 3 $ 6 D) 2 E) 1 5 B) 1 $ 3 D) 1 E) 1 125 125 125 25 25 A) 11 44 22 44 44 4. %ËSUFWMJ¿JGUBSBTOEBOLJõJSBTUHFMFTF¿JMFDFLUJS 9. öLJ[BSBUMZPS·TUFHFMFOTBZMBSOUPQMBNOO EFOCÑZÑLPMNBPMBTMôLBÀUS #VOBHÌSF TFÀJMFOLJöJMFSJOLBS–LPDBPMNBPMB- A) 1 B) 1 $ 1 55 TMôLBÀUS 3 4 6 D) E) 18 12 A) 1 B) 1 $ 1 D) 1 E) 2 3 4 6 7 7 \"UPSCBTOEBLSN[ TBSUPQ #UPSCBTOEB 10. öLJ[BSBZOBOEBBUMZPS LSN[ TBSUPQWBSES #VOBHÌSF \"WF#UPSCBMBSOEBOBZOBOEBCJSFS ;BSMBSEBOCJSJOJOEJôFSJOEFOGB[MBPMNBPMBT- UPQBMOEôOEBBZOSFOLUFOPMNBPMBTMôLBÀ- MôLBÀUS US A) 1 B) 2 $ 1 D) 5 E) 7 23 B) 11 $ 21 19 E) 17 9 9 3 36 36 A) D) 40 20 40 40 40 1. \" 2. $ 3. E 4. D $ 70 6. B 7. D 8. $ 9. D 10. B
0MBTML TEST - 35 1. YUBNTBZPMNBLÐ[FSF¿J[JMFCJMJSпHFOMFSBSBTO- EFOFLBEBS EBIJM PMBOTBZMBSBSBTO- EBOCJSJTF¿JMJZPS EBO TFÀJMFO JLJ TBZEBO CJSJOJO EJôFSJOJO JLJ LBU A PMNBPMBTMôLBÀUS 8 15 A) 1 B) 2 $ 1 D) 4 E) 5 99 99 33 99 99 Bx C 6. #JSTOGUBLJËóSFODJOJOVFSLFLWFL[MBSO 3 7 TJHË[MÐLMÐEÐS #VOB HÌSF TFÀJMFO ÑÀHFOEF \" BÀTOO HFOJö #VOBHÌSF TOGUBOSBTUHFMFTFÀJMFOJLJÌôSFODJ- BÀPMNBPMBTMôLBÀUS OJOJLJTJOJOEFHÌ[MÑLTÑ[L[ÌôSFODJPMNBPMB- TMôLBÀUS A) 2 B) 1 $ 4 D) 1 E) 2 15 5 15 3 3 A) 5 B) 7 $ 11 D) 11 E) 7 184 69 138 69 184 2. A = {- - - }LÐNFTJOEFOSBTUHFMF JLJTBZTF¿JMJZPS #VOBHÌSF TFÀJMFOJLJTBZOOÀBSQNOOQP[JUJG 7. A = { }LÐNFTJOJOFMFNBOMBSOEBO PMNBPMBTMôLBÀUS 2 tanesi seçiliyor. A) 2 B) 3 $ 4 D) 8 E) 11 4FÀJMFOTBZMBSOUPQMBNOOÀJGUTBZPMNBPMB- 7 7 21 21 21 TMôLBÀUS 2 B) 3 $ 2 3 4 A) 5 7 D) E) 5 7 7 3. \"LVUVTVOEBNBWJ LSN[ #LVUVTVOEBNBWJ 8. A F B G LSN[ UPQ CVMVONBLUBES \" LVUVTVOEBO CJS UPQ BMOQ#LVUVTVOBBUMZPS#LVUVTVOEBOCJSUPQ¿F- C LJMJZPS #VOB HÌSF ÀFLJMFO UPQVO NBWJ HFMNF PMBTMô LBÀUS A) 5 B) 4 $ 5 D) 4 E) 41 H D 9 9 11 11 99 I E 4. QBSBCJSMJLUFBUMZPS õFLJMEFLJ OPLUBEBO IFSIBOHJ ÑÀÑ TFÀJMEJôJO- EFTBEFDFCJSJOJOÀFNCFSÑ[FSJOEFPMNBPMBTM- ôLBÀUS ·ÀÑOÑOZB[JLJTJOJOUVSBHFMNFPMBTMôLBÀUS A) 1 B) 10 $ 1 D) 2 E) 1 2 21 3 7 4 3 B) 1 $ 5 3 7 A) 4 D) E) 16 16 8 16 1. D 2. B 3. E 4. $ 71 \" 6. B 7. D 8. B
TEST - 36 0MBTML 1. #JMHJTBZBSNÐIFOEJTMFSJWFFMFLUSJLNÐIFOEJTMFSJOJO FSLFLWFL[ËóSFODJOJOCVMVOEVóVCJSËóSFODJ CVMVOEVóVLJõJMJLCJSUPQMBOUEBCBZBOWF HSVCVOEBLJõJMJLCJSLPNJTZPOLVSVMBDBLUS CJMHJTBZBSNÐIFOEJTJCVMVONBLUBES&SLFLFMFLUSJL NÐIFOEJTMFSJOJOTBZTCBZBOFMFLUSJLNÐIFOEJTMF- #VOBHÌSF LPNJTZPOEBFOGB[MBCJSL[ÌôSFODJ- SJOJOTBZTOEBOJLJGB[MBES OJOCVMVONBPMBTMôLBÀUS #VOB HÌSF HSVQUBO TFÀJMFO CJS LJöJOJO CBZBO A) 1 B) 19 $ 8 D) 3 E) 3 CJMHJTBZBSNÑIFOEJTJPMNBPMBTMôLBÀUS 2 42 21 7 14 A) 1 B) 1 $ 1 D) 1 5 36 18 12 9 E) 36 2. öLJ[BSCJSMJLUFBUMZPS 6. ö¿JOEFFõJUTBZEBTBSWFLSN[UPQCVMVOBOCJSUPS- ·TUF HFMFO TBZMBSO CJSCJSJOEFO GBSLM HFMNF CBEBO¿FLJMFOUPQVOGBSLMSFOLUFHFMNFPMBTMó PMBTMôLBÀUS 15 dur. 29 #VOBHÌSF CVUPSCBEBLBÀUPQWBSES \" # $ % & A) 2 B) 3 $ 5 D) 5 E) 5 3 4 12 18 6 7. A = { } 3. ÷ÀJOEFCFZB[ LSN[WFTBSUPQCVMVOBO LÑNFTJOJO FMFNBOMBSOEBO SBTUHFMF TFÀJMFO TBZOOÀBSQNOOÀJGUTBZPMNBTPMBTMôLBÀ- CJS UPSCBEBO ÀFLJMFO UPQVO JLJTJOJO EF BZO US SFOLHFMNFPMBTMôLBÀUS A) 19 B) 15 $ 47 D) 29 E) 1 1 B) 2 $ 4 5 11 66 44 66 66 3 A) 7 7 D) E) 7 7 14 4. ÷ÀJOEFCFZB[ LSN[WFTBSUPQCVMVOBO 8. \" # $ п BZSL PMBZES WF CJSMFõJNMFSJ CJS ËSOFL CJSUPSCBEBOÀFLJMFOUPQVOJLJTJOJOTBS EJôF- V[BZCFMJSUNFLUFEJS SJOJOLSN[HFMNFPMBTMôLBÀUS P ( A ) + P( B ) = 2 1 # +1 $h = 3 A) 2 B) 1 $ 3 D) 2 E) 1 54 33 33 11 11 11 PMEVôVOBHÌSF 1 \" LBÀUS A) 1 B) 1 $ 3 D) 1 E) 1 20 10 20 5 4 1. E 2. E 3. \" 4. D 72 B 6. $ 7. D 8. \"
0MBTML TEST - 37 1. ¶¿ BTLFS LBSF CJ¿JNJOEFLJ CJS BSB[JEF ^\" ! - .h 4. \"MJ WF CBCBT EBNB PZOBNBLUBES 0ZVOV LB[BO- PLMBSZMBHËTUFSJMFOEPóSVMUVEBNBZOUBSBNBTZB- NB PMBTMLMBS ZBõMBS JMF EPóSV PSBOUM WF PZVOVO QBDBLUS CFSBCFSFCJUNFPMBTMóZBõMBSGBSLJMFEPóSVPSBO- UMES #VOBHÌSF IBOHJNBZOUBSBNBöFLMJJMFBSB[JEF CVMVOBOCJSNBZOUFTQJUFUNFPMBTMôFOÀPL- \"MJ WF CBCBT ZBöOEB PMEVôVOB HÌSF tur PZVOV\"MJOJOLB[BONBPMBTMôLBÀUS A) B) A) 5 B) 1 $ 3 D) 6 E) 3 18 2 16 25 7 C) D) \"WF# &ËSOFLV[BZOEBBZSLPMBZMBSPMNBLÐ[F- E) SF P^ Alh = 3 ve P^ Blh = 2 tir. 45 #VÌSOFLV[BZEB\"WF#PMBZMBSOOJLJTJOEFOEF BZSLCJSPMBZOPMBTMôBöBôEBLJMFSEFOIBOHJ- si PMBNB[ A) 3 B) 1 $ 1 D) 1 E) 1 20 5 8 7 9 2. E = { B C D}ËSOFLV[BZWFSJMTJO 6. #JSQBSBBUMZPS CJS[BSZVWBSMBOZPSWFCJSUPSCBEB- #VOBHÌSF BöBôEBLJMFSEFOIBOHJTJ&EFUBON- LJUPQUBOCJSJTJSBTUHFMFTF¿JMJZPS MCJSPMBZES #VEFOFZJOÌSOFLV[BZOOÀLUTBZTLBÀUS \" # \\ ^ $ \\q ^ \" # $ % & % \\ B^ & { { 1 } } 3. \"õBóEBLJEFOFZMFSFBJUËSOFLV[BZMBSCVMVOVZPS 7. \"ZõFWF)BOEBONVUGBLUBLFLZBQNBLJ¿JOFOB[ #VOBHÌSF IBOHJEFOFZFBJUÌSOFLV[BZFöPMB- TBBU FOGB[MB TBBUWBLJUHF¿JSNFLUFEJSMFS TMEFôJMEJS #VOBHÌSF BZONVUGBLUBBZOBOEBLFLZBQNB- A) NBWJWFLSN[UPQCVMVOBOCJSUPSCBEBOCJS ZB CBöMBZBO \"ZöFhOJO )BOEBOhEBO FO B[ ZBSN UPQ¿FLJMNFTJ TBBUÌODFLFLJZBQNBPMBTMôLBÀUS B) #JS¿JGU[BSBUMQÐTUZÐ[FHFMFOTBZMBSO¿BSQ- A) 1 B) 7 $ 1 D) 2 E) 1 NOOZB[MNBT 6 9 27 9 8 $ #JSNBEFOJQBSBOOBSUBSEBLF[BUMNBT D) öLJ CBTBNBLM UBN LBSF EPóBM TBZMBSEBO CJSJOJO seçilmesi E) EFOLпÐLBTBMTBZMBSEBOCJSJOJOTF¿JMNFTJ 1. E 2. D 3. B 73 4. \" B 6. D 7. B
TEST - 38 0MBTML 1. \"PMBZ &ËSOFLV[BZOEBCJSPMBZPMNBLÐ[FSF 4. ,FOEJBSBMBSOEBCJSLPõVZBSõZBQBOпBSLBEBõ- P^Ah + 2.P^Alh = P^Eh UBO&NSFOJOLB[BONBPMBTMó ,FNBMJOLB[BONB PMBTMóOOZBSTWF:BTJOJOLB[BONBPMBTMóEJ- PMEVôVOBHÌSF \"PMBZJMFJMHJMJOFTÌZMFOFCJMJS óFS JLJTJOJO LB[BONB PMBTMLMBSOO UPQMBN LBEBS- \" öNLBOT[PMBZES ES # ,FTJOPMBZES $ P^ A h = 2 UÐS #VOBHÌSF CVZBSö,FNBMJOLB[BONBPMBTMô 3 LBÀUS D) P^ Al h = 2 UÐS 3 A) 1 B) 2 $ 1 3 E) 1 E) P(A) < P(E) 2 3 3 D) 4 4 #JS[BSBUNBEFOFZJOEF \"PMBZi¶TUZÐ[FHFMFOTBZOO¿JGUTBZPMNBTuWF #PMBZi¶TUZÐ[FHFMFOTBZOOUFOCÐZÐLPMNB- TuPMBSBLWFSJMJZPS 2. \"WF# &ËSOFLV[BZOEBJLJPMBZPMTVO #VEFOFZJOÌSOFLV[BZO\"WF#PMBZMBSZMBCJS- MJLUF 7FOO öFNBTOEB HÌTUFSJNJ BöBôEBLJMFS- #VPMBZMBSOPMBTMLMBSBöBôEBLJMFSEFOIBOHJTJ EFOIBOHJTJEJS HJCJPMVSTBCVPMBZMBSBZSLPMBNB[ A) P^ A h P^ B h 1B B) 1 B EA 6 EA 3 2 2 45 3 25 A) 3 6 1 4 5 4 2 3 B) 2 7 3 3 C) B D) B 7 $ 3 1 EA EA 5 8 2 4 5 3 4 5 D) 1 6 26 3 2 1 1 E) 6 7 E) B 14 EA 35 2 6 3. #JSTOGUBOTF¿JMFOCJSËóSFODJOJOFSLFLPMNBPMBT- 6. A = { }LÐNFTJOJOFMFNBOMBMULÐNFMFSJ- Mó 3 tir. OJOIFSCJSJCJSLBSUBZB[MQUPSCBZBBUMZPS 5 #VOBHÌSF UPSCBEBOSBTUHFMFÀFLJMFOLBSUUBBS- #V TOGUB L[ ÌôSFODJ PMEVôVOB HÌSF TOG EöLTBZMBSOZB[MNöPMNBPMBTMôLBÀUS NFWDVEVLBÀUS A) 1 B) 1 $ 2 D) 1 E) 3 \" # $ % & 4 3 3 2 4 1. B 2. \" 3. E 74 4. $ $ 6. D
0MBTML TEST - 39 1. 4. õFLJMEFLJ FöLFOBS ÑÀHFOMFS LBUMBOQ PMVöUVSV- \"¿LIBMJWFSJMFOLÐQLBUMBOQCJS[BSFMEFFEJMJZPS MBOEÑ[HÑOEÌSUZÑ[MÑöFLMJOEFLJ[BSBUMEôOEB HÌSÑOFOZÑ[MFSEFUPQMBNUBOFOPLUBHÌSÑMNF #VOBHÌSF EÑ[CJS[FNJOFBUMBOCV[BSOHÌSÑ- PMBTMôLBÀUS OFOZÑ[MFSJOEFTBEFDFUBOFJöFLMJPMNBPMB- TMôLBÀUS A) 1 B) 1 $ 3 D) 1 E) 2 A) 2 B) 1 $ 1 D) 1 E) 1 4 2 4 3 3 3 3 2 6 JMF UBN CÌMÑOFO JLJ CBTBNBLM EPôBM TBZMBS- EBOTFÀJMFOCJSTBZOOBZO[BNBOEBJMFCÌMÑ- OFCJMFOCJSTBZPMNBPMBTMôLBÀUS 2. ö¿JOEFUPQCVMVOBOCJSUPSCBEBONBWJUPQ¿FLNF A) 1 B) 2 $ 3 D) 1 E) 1 4 5 8 5 6 PMBTMó 2 UÐS 3 6. TPSVEBOTJOJOZBOUMBOBDBôCJSTOBWBHJSFO #VOB HÌSF UPSCBZB IBOHJ SFOL WF TBZEB UPQ ÌôSFODJOJOGBSLMTPSVMBSZBOUMBNöPMNBPMB- BUMSTBNBWJUPQÀFLNFPMBTMô 3 PMVS TMôLBÀUS 4 A) 1 B) 3 $ 1 D) 3 E) 9 10 10 5 25 10 3FOL 4BZ A) 4BS 3 y B) Mavi 2 $ Mavi 1 7. D) :FõJM 2 E) :FõJM 1 (4, 4) x O(0, 0) (2, 0) 3. WFZBõMBSOEBпLJõJOJOLBUMEóCJSZBS- %JL LPPSEJOBU TJTUFNJOJO OPLUBTOEB CVMVOBO LJõJ TBóB WF ZVLBS OPLUBTOEB CVMVOBO LJõJ õLB[BONBPMBTMLMBSZBõMBSJMFUFSTPSBOUMES TPMBWFBõBóBZOCÐZÐLMÐLUFWFTBCJUI[MBSMBJMFSMF- NFLUFEJSMFS #VOB HÌSF CV ZBSö FO CÑZÑLMFSJOJO LB[BONB #V LJöJMFS BZO BOEB IBSFLFU FUUJLMFSJOF HÌSF PMBTMôLBÀUS LBSöMBöNBPMBTMLMBSLBÀUS A) 5 B) 12 $ 7 D) 2 E) 10 3 B) 1 $ 5 1 15 27 43 15 7 37 A) D) E) 64 16 32 32 64 1. B 2. B 3. E 4. B D 6. B 7. $
TEST - 40 0MBTML 1. SBLBNMBSJMFZB[MBCJMFOCJSCJSJOEFOGBSLMп \"ZõF &DF #VSDVWF$FSFOJTJNMJEËSUBSLBEBõTB- CBTBNBLMTBZMBSEBOSBTUHFMFCJSUBOFTJTF¿JMJZPS EFDF ¿FõJU FUFL ¿FõJU FMCJTF ¿FõJU QBOUPMPO CVMVOBOCJSNBóB[BEBO BMõWFSJõZBQBDBLUS #VTBZOOPMNBPMBTMôLBÀUS A) 1 B) 1 $ 1 D) 1 E) 1 27 18 9 6 3 2. A = { }LÐNFTJOJOFMFNBOMBSOLVMMBOB- r \"ZõFFUFLZBEBQBOUPMPOBMBDBLUS r &DFFUFLHJZNFZJUFSDJIFUNFNFLUFEJS SBLZB[MBCJMFDFLCJSCJSJOEFOGBSLMJLJCBTBNBLMEP- r $FSFOJMF#VSDVBZO¿FõJULZBGFUBMNBZBDBLMBS- óBMTBZMBSEBOSBTUHFMFCJSJTF¿JMJZPS ES #VTFÀJMFOTBZOOEBOCÑZÑLCJSTBZPMNB r )FSLFTTBEFDFCJSQBS¿BLZBGFUBMBDBLUS PMBTMôLBÀUS 1 B) 3 $ 2 91 A) 10 5 D) E) 4 20 2 #VOBHÌSF $FSFOhJOFUFLBMNBPMBTMôLBÀUS A) 3 B) 1 $ 3 D) 1 E) 3 4 4 8 8 16 3. #JSUPSCBEBEFOBLBEBSOVNBSBMBONõCF- 6. UBOF TJZBI UBOF CFZB[ CJMZF GBSLM JLJ LVUVZB ZB[WFNBWJUPQWBSES ZFSMFõUJSJMNFLJTUFOJZPS#JMZFMFSZFSMFõUJSJMJQSBTUHF- MFCJSLVUVTF¿JMJZPS#VLVUVEBOEBSBTUHFMFCJSCJM- 5PSCBEBOCFZB[WFNBWJSFOLMJCJSFSUPQÀFLJM- ZF¿FLJMJZPS NJöJTFTBZMBSUPQMBNOOPMNBPMBTMôLBÀ- US 7 B) 2 $ 4 3 1 ¦FLJMFO CJMZFOJO CFZB[ PMNB PMBTMô FO GB[MB A) D) E) LBÀUS 100 25 25 25 5 A) 1 B) 5 $ 5 11 2 8 7 D) E) 1 14 4. A = { }PMNBLÐ[FSF 7. #JS UPLB LVUVTVOEB NBWJ TBS UPLB WBSES \" EBO \" ZB UBONMBOBO CJS G GPOLTJZPOMBSOO \"EFOhJOFMJOEFJTFNBWJ TBSUPLBWBSES5P- BSBTOEBOSBTUHFMFTFÀJMFOCJSGPOLTJZPOVO LB LVUVTVOEBO SBTUHFMF BMOBO CJS UPLBOO TBS PM- NBPMBTMóOO 3 olmBTOJTUFZFO\"EFO UPLBMB- G +G +G = 7 10 LPöVMVOVTBôMBNBPMBTMôLBÀUS SOEBOBUBOFTJOJLVUVZBBUZPS A) 1 B) 3 $ 4 D) 1 E) 9 #VOBHÌSF BOOBMBCJMFDFôJLBÀEFôFSWBSES 25 25 75 7 125 \" # $ % & 1. B 2. D 3. B 4. B 76 $ 6. $ 7. $
www.aydinyayinlari.com.tr 7&3÷ 4\":.\"7&0-\"4*-*, 8. MODÜL ·/÷7&34÷5&:&)\";*3-*, 0-\"4*-*,** #BôNT[0MBZMBS ÖRNEK 1 7$1,0%m/*m #JS [BS WF CJS NBEFOJ QBSBOO BUMNBT PMBZOEB [B- SOBTBMTBZWFQBSBOOZB[HFMNFPMBTMôLBÀUS & ËSOFL V[BZOO IFSIBOHJ JLJ PMBZ \" WF # PM- TVO \" WF # PMBZMBSOO CJSJOJO HFS¿FLMFõNFTJ 1 \"a# =1 \" 1 # WFZBHFS¿FLMFõNFNFTJEJóFSJOJOHFS¿FLMFõNF- [[ NFTJEJóFSJOJOHFS¿FLMFõNFTJPMBTMóOEFóJõ- 31 1 UJSNJZPSTBCVJLJPMBZBCBôNT[PMBZMBS denir. \"WF#CBóNT[PMBZMBSWF = .= 1 \" á 1 # áPMNBLÐ[FSF 62 4 P ( A a B ) = P ( A ) . P ( B ) dir. ,PöVMMV0MBTML ÖRNEK 2 7$1,0%m/*m #JS[BSWFCJSNBEFOJQBSBIBWBZBBUMZPS &ËSOFLV[BZOOIFSIBOHJJLJPMBZ \"WF#PM- ;BSO ÑTU ZÑ[ÑOF UFL TBZ WFZB QBSBOO UVSB HFMNF sun. PMBTMôLBÀUS P ( B ) >JTF#PMBZOOHFS¿FLMFõNFTJIºMJO- 1 \"b# =1 \" +1 # m1 \"a# =1 \" +1 # -1 \" 1 # EF\"PMBZOOPMBTMóOB \"PMBZOO#ZFCBó- 1 1 11 3 = +-·= MLPõVMMVPMBTMóWFZB\"OO#LPõVMMVPMBTM- 2 2 22 4 óEFOJSWF1 \"=# CJ¿JNJOEFHËTUFSJMJS 1 \"=# P (A + B) dir. P (B) &FõPMVNMVËSOFLV[BZJTF 1 \"=# = s (A + B) dir. s (B) ÖRNEK 3 \"MJhOJOTBUSBO¿ZBSõNBTOLB[BONBPMBTMó 1 3 7FMJhOJO 3 ve SF[FShJO 3 UÐS 54 #VÑÀPMBZCJSCJSJOEFOCBôNT[PMEVôVOBHÌSF \"MJ WF7FMJhOJOLB[BONB 4F[FShJOLB[BOBNBNBPMBTMô LBÀUS UYARI 1 \"MJhOJOLB[BONBPMBTMô ,PõVMMVPMBTMLIFTBQMBOSLFO #PMBZOOJ¿JOEFWBSPMBO\"PMBZTBZT 3 #PMBZOOFMFNBOTBZT 3 PSBOLVMMBOMS 7FMJhOJOLB[BONBPMBTMô 5 1 4F[FShJOLB[BOBNBNBPMBTMô 4 131 1 ·· = 3 5 4 20 77 1 3 1 1. 2. 3. 4 4 20
·/÷7&34÷5&:&)\";*3-*, 8. MODÜL 7&3÷ 4\":.\"7&0-\"4*-*, www.aydinyayinlari.com.tr ÖRNEK 4 ÖRNEK 6 FSLFLWFL[EBO FSLFLWFL[OTB¿MBSTB- { } LÐNFTJOJO FMFNBOMBSOEBO SBTUHF- SES MFJLJTJTF¿JMJZPS #VOBHÌSF HSVQUBOSBTUHFMFTFÀJMFOCJSJL[JTFTBS TBÀMPMNBPMBTMôLBÀUS 4FÀJMFOTBZMBSOUPQMBNÀJGUPMEVôVOBHÌSF IFSJLJ- TJOJOEFUFLTBZPMNBPMBTMôLBÀUS P^ S \\ K h = P^ S + K h = s^ S + K h = 3 5PQMBNMBSÀJGUPMEVôVOBHÌSF ¦+¦ZBEB5+5PM- P^ K h s^ K h 8 NBMÀJGUZBEBUFLTBZTFÀJMNFMJEJS 3 {1, 3, 5} herhangi ikisi 2 P T\\Ç = 33 {2, 4, 6} + herhangi ikisi 22 {1, 3, 5} herhangi ikisi 1 = 2 ÖRNEK 5 &ËSOFLV[BZOOJLJPMBZ\"WF#PMTVO P (Aı) = 1 , P (Bı) = 2 , P (A , B) = 7 ise 23 12 B 1 \"=# ÖRNEK 7 C 1 \"h=#h ôFLJMEFCJSTJOFNBTBMPOVOVOPUVSNBEÐ[FOJHËSÐMNFL- UFEJS&MBhOOEBBSBMBSOEBCVMVOEVóVLJõJMJLHSVQTJOF- D 1 \"=#h NBZBHJUNJõMFSEJS PMBTMLMBSLBÀUS B 1 \"b# =1 \" +1 # -1 \"a# 1 PERDE 1 \"=# = P^ A + B h 4 3 A == B P^ B h 14 C D 3 E 5 12345678 C 1 \"h=#h = P^ A' + B' h 12 5 #V LJöJOJO ZBO ZBOB PUVSEVôV CJMJOEJôJOF HÌSF == &MBhOO$OVNBSBMLPMUVôBPUVSNBPMBTMôLBÀUS P^ B' h 28 =BSEöLCFöLJöJMJLZFSWBSES 3 4.4! 1 = 1 20.5! 25 D 1 \"=#h = P^ A + B' h 4 3 == P^ B' h 28 3 AB 11 1 4 12 45 12 3 35 3 4. B C D 78 1 1 48 8 6. 7. 8 2 25
www.aydinyayinlari.com.tr 7&3÷ 4\":.\"7&0-\"4*-*, 8. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 8 ÖRNEK 10 \"UPSCBTOEBUVSVODV NBWJ #UPSCBTOEBUVSVO- #JSTOGUBLJËóSFODJMFSJOVGJ[JLUFO LJNZB- DV NBWJUPQWBSES3BTUHFMFTF¿JMFOCJSUPSCBEBOCJS EBOWFVEBIFSJLJEFSTUFOLBMNõUS UPQBMOZPS #VTOGUBOSBTUHFMFTF¿JMFOCJSËóSFODJOJO \"MOBOUPQVONBWJPMEVôVCJMJOEJôJOFHÌSF\"UPSCB- B ,JNZBEBO LBMEô CJMJOEJôJOF HÌSF GJ[JLUFO EF TOEBOBMONöPMNBPMBTMôLBÀUS LBMNöPMNBT AB C 'J[JLUFO HFÀUJôJ CJMJOEJôJOF HÌSF LJNZBEBO LBM- 3T 2T NöPMNBTPMBTMLMBSLBÀUS 4M 5M a) F K 1 1 '=, = 4 14 4 %20 %10 %30 · = %40 27 9 14 15 ·+· 27 27 C P^ K / F' h = 3 7 ÖRNEK 9 ÖRNEK 11 A = {B C D E F G}LÐNFTJOJOBMULÐNFMFSJCJSFSLBS- #JS[BSBSUBSEBLF[BUMZPS UB ZB[MQ CJS LVUVZB LPOVZPS #V LVUVEBO SBTUHFMF CJS B #JSJODJ BUöUB HFMEJôJ CJMJOEJôJOF HÌSF [BSMBS- LBSU¿FLJMJZPS EBLJTBZMBSUPQMBNOOEFOCÑZÑLPMNBT ¦FLJMFO LBSUUBLJ LÑNFOJO FMFNBOM CJS LÑNF PMEV- ôVCJMJOEJôJOFHÌSFCVLÑNFEFCOJOCVMVONBPMB- C #JSJODJ BUöUB ÀJGU TBZ HFMEJôJ CJMJOEJôJOF HÌSF TMôLBÀUS JLJODJ BUöUB HFMFO TBZOO CJSJODJ BUöUBLJ TBZ- EBOEBIBCÑZÑLCJSTBZPMNBTPMBTMLMBSLBÀ- 6 US FMFNBOMBMULÑNFMFSJf p i6s4te4n4e7n d4ur4u4m8 45 B ^144,414h,4^ 44,424h,4^ 44,443 2h,^44,444h,4^ 44,454h,4^ 44,446 3h FMFNBOMCOJOCVMVOEVôVBMULÑNFMFSJf p tüm durum 53 fp 1 32 3 = C =EVSVN 63 fp 4 ÷TUFOFO ^ 2, 3 h^ 2, 4 h^ 2, 5 h^ 2, 6 h 4 6 durum ^ 4, 5 h^ 4, 6 h 1 3 4 2 79 13 11 8. 9. 10. B C 11. B C 47 33 9 3
·/÷7&34÷5&:&)\";*3-*, 8. MODÜL 7&3÷ 4\":.\"7&0-\"4*-*, www.aydinyayinlari.com.tr ÖRNEK 12 ÖRNEK 15 \"ZUVó WF öMLFShJO FMMFSJOEF UBOF BOBIUBS WBSES #V ôFLJMEFBEFUQPTUBLVUVTVHËSÐMNFLUFEJS BOBIUBSMBSEBO UBOFTJ \"ZUVóhVO EPMBCO UBOFTJ öM- LFShJOEPMBCOB¿NBLUBES)FSIBOHJJLJBOBIUBSMB\"ZUVó LFOEJEPMBCO öMLFSLFOEJEPMBCOB¿NBZEFOJZPS 4BEFDF CJS EPMBCO BÀMEô CJMJOEJôJOF HÌSF \"Z- UVôhVOEPMBCOOBÀMNöPMNBPMBTMôLBÀUS \"OBI- UBSEFOFEJLUFOTPOSBZFSJOFLPOVMVZPS \"ÀMEBÀMNBE+BÀMNBEBÀME=5ÑNEVSVN 11 22 5 1 ·+·= 33 33 9 11 1 91 ÷TUFOJMFOEVSVN · = = 33 9 55 9 ÖRNEK 13 1PTUBD GBSLM SFLMBN CSPõÐSÐOÐ QPTUB LVUVMBSOB BUB- DBLUS B C DTGSEBOGBSLMSBLBNMBSPMNBLÐ[FSF BCD пCB- TBNBLMTBZMBSZB[MZPS 5FLCJSTSBOOUBNBNFOCPöLBMEôCJMJOEJôJOFHÌSF CFMJSMJJLJCSPöÑSÑOBZOTSBEBPMNBPMBTMôLBÀUS #VOBHÌSF CVTBZMBSEBOSBTUHFMFTFÀJMFOCJSUBOFTJ- OJOUFLPMEVôVCJMJOEJôJOFHÌSF SBLBNMBSBSBTOEB 3 2 3 2! . 3! a <C<DJMJöLJTJOJOPMNBPMBTMôLBÀUS f p. f p. f p. 1 1 2 [[[[[ 8. 7. 5 #Pö T- \"ZOTBUSEBPMB- \"ZO CSP- %JôFS . = 280 tane tek sayı SBTFÀJ- DBLCSPöÑSMFSF öÑSMFSJO TB- CSPöÑSMFS NJ \" 1, 3, 5, 7, 9 , ZFSTFÀJNJ USEBLJ ZFS EFôJöJN D= 3 j 1 _ = 216 b 4 6 b D=j f p = b 2 b5 ` 6 b 28 D= 7 j f p = b 2 bb a ÖRNEK 16 8 28 D= 9 j f p = FSLFLËóSFODJ L[ËóSFODJWFYËóSFUNFOBSBTOEBO 2 SBTUHFMFLJõJTF¿JMJZPS ÖRNEK 14 4F¿JMFO LJõJMFSEFO CJSJOJO ËóSFUNFO PMEVóV CJMJOEJóJOF HËSF EJóFSJOJOEFËóSFUNFOPMNBPMBTMóOFEJS TPSV- SBLBNMBSCJSFSLF[LVMMBOMBSBLZB[MBO TVOVODFWBCOO 1 UFOLÑÀÑLPMNBTJÀJOYFOÀPL ÑÀCBTBNBLMCJSTBZOOJMFCÌMÑOEÑôÑCJMJOEJôJOF HÌSF UFLPMNBPMBTMôLBÀUS 3 LBÀPMNBMES 3! x = = 3 dn 2! LBMBOOWFSFOMFSZ Z 3! = 6 2 x-1 1 =< LBMBOOOWFSFOMFSZ Z 3! = 6 2^ x + 4 h 3 x x+4 p d n.f 3! 11 LBMBOOWFSFOMFSZ Z = 3 + 2! x < 11 5ÑNEVSVN FOÀPL 5 5FL UBOF4POVÀ 18 1 5 5 80 216 16. 10 12. 13. 14. 5 28 18
#BôNT[0MBZMBS,PöVMMV0MBTML TEST - 41 1. #JSTOGUBËóSFODJWBSES#VOMBSEBOTJNBUF- 4. \"UPSCBTOEBLSN[ CFZB[ #UPSCBTOEBLS- NBUJLUFO JGJ[JLUFOWFJIFNNBUFNBUJLIFNGJ- N[ CFZB[UPQWBSES3BTUHFMFCJSUPSCBTF¿JMJQ [JLUFO CÐUÐOMFNFZF LBMNõUS 3BTUHFMF TF¿JMFO CJS J¿JOEFOCJSUPQBMOZPS ËóSFODJOJO NBUFNBUJLUFO CÐUÐOMFNFZF LBMEó CJMJ- niyor. ¦FLJMFOUPQVOCFZB[PMEVôVCJMJOEJôJOFHÌSF \" UPSCBTOEBOÀFLJMNJöPMNBPMBTMôLBÀUS #V ÌôSFODJOJO GJ[JLUFO EF CÑUÑOMFNFZF LBMNB A) 21 B) 22 $ 23 D) 24 E) 25 PMBTMôLBÀUS 59 59 59 59 29 A) 1 B) 5 $ 7 3 3 4 D) E) 12 12 20 5 2. #JSTOGUBLJËóSFODJMFSJOFSLFLUJS&SLFLMFSJO \"WF# &ËSOFLV[BZOEBJLJPMBZPMTVO VWFL[MBSOTOGMBSOHF¿NJõUJS P^ Blh = 3 , P^ A + B h = 2 85 PMEVôVOBHÌSF 1 \"=# PMBTMôOCVMVOV[ 3BTUHFMFTFÀJMFOCJSÌôSFODJOJOTOGHFÀUJôJCJ- 16 B) 8 $ 7 6 E) 1 MJOEJôJOFHÌSF FSLFLPMNBPMBTMôLBÀUS A) D) A) 9 B) 3 $ 1 D) 3 E) 3 25 25 25 25 8 25 25 3 10 5 3. #BTLFUCPM WPMFZCPMWFGVUCPMEBOFOB[CJSJOJPZOB- 6. UBOFLVUVWBS)FSLVUVEBJLJ¿FLNFDFWBS,VUV- ZBOMBSEBOPMVõBOCJSHSVQUB TBEFDFCJSPZVOPZOB- MBSOCJSJOJOJLJ¿FLNFDFTJOFCJSFSBMUO EJóFSJOJOJLJ ZBOMBSOTBZMBSFõJUWFUÐS4BEFDFJLJPZVOPZ- ¿FLNFDFTJOEFOCJSJOFCJSBMUO EJóFSJOFCJSHÐNÐõ OBZBOMBSO TBZMBS FõJU WF ES )FS п PZVOV EB LBMBOLVUVOVO¿FLNFDFMFSJOFBZSBZSCJSFSHÐNÐõ PZOBZBOMBSOTBZTEJS BUMZPS #V HSVQUBO SBTUHFMF TFÀJMFO CJSJOJO FO B[ JLJ 3BTUHFMF BÀMBO ÀFLNFDFEFO BMUO ÀLUô CJMJO- PZVO PZOBEô CJMJOEJôJOF HÌSF IFS ÑÀ PZVOV EJôJOFHÌSF EJôFSCJSÀFLNFDFEFOEFBMUOÀL- EBPZOVZPSPMNBPMBTMôLBÀUS NBPMBTMôLBÀUS 1 B) 1 $ 1 1 1 1 B) 1 $ 1 2 3 A) 5 D) E) A) 2 4 D) E) 2 10 20 40 3 3 4 1. B 2. $ 3. $ 81 4. D \" 6. D
TEST - 42 #BôNT[0MBZMBS,PöVMMV0MBTML 1. #JS¿JGU[BSBUMEóOEBÐTUZÐ[FHFMFOTBZMBSOUPQ- 4. %JDMF±óSFUNFOËóSFODJMFSJOF MBNOOFOB[PMEVóVCJMJOJZPS A = {B C D E} #VOBHÌSF [BSMBSEBOFOB[CJSJOJOPMNBPMB- B = { } LÐNFMFSJOJ UBONMBZQ \" EBO # ZF TMôLBÀUS GPOLTJZPOMBSUBONMBNBMBSOJTUFNJõUJS 3 B) 2 $ 1 3 4 5BONMBOBOGPOLTJZPOMBSEBOJ¿JOFGPOLTJZPOUBON- A) 5 2 D) E) MBZBO ËóSFODJMFSJOJO TBZTO CFMJSMJZPS #V TBZ ZB- [MBCJMFDFLUÐNJ¿JOFGPOLTJZPOMBSOTBZTJMFBZO- 10 5 5 ES 4OGUB TFÀJMFO CJS ÌôSFODJOJO JÀJOF GPOLTJZPO UBONMBEôCJMJOEJôJOFHÌSF TBCJUGPOLTJZPOPM- NBPMBTMôLBÀUS 2. A) 1 B) 1 $ 2 1 2 D) E) 15 3 5 15 #JSCBTLFUCPMLBSöMBöNBTOEBTBZTJTUFNJ #JSUJZBUSPTBIOFTJOEFпHFOõFLMJOEFLJCJSLVNBõ- r ¶¿TBZ¿J[HJTJEõOEBOBUMBOIFSCBTLFUJ¿JO MBEFLPSZBQMBDBLUS TBZ HG K r ¶¿TBZ¿J[HJTJJ¿JOEFBUMBOIFSCBTLFUJ¿JOTB- F Z E r 'BVM TPOVDV BUMBO IFS CBTLFU J¿JO JTF TBZ BMONBLUBES D C #FSLFCJSCBTLFUCPMLBSõMBõNBTOEBTBZBUZPS AB #VOBHÌSF BUUôTBZMBSBSBTOEBPMEVôVCJ- MJOEJôJOFHÌSF PMNBNBPMBTMôLBÀUS A) 1 B) 1 $ 1 D) 4 E) 2 11 6 3 11 5 3. OVNBSBMÀJGULSN[WFÀJGUCFZB[ OV- , OPLUBT LÐQ õFLMJOEFLJ TBIOFOJO UBWBOO PSUB OPLUBTES %FLPS õFLJMEFLJ OPLUBEBO Ð TF¿JMJQ NBSBMÀJGUTJZBI OVNBSBMÀJGULSN[ ZBQMBDBLUS ÀJGU TJZBI UFSMJôJO CVMVOEVôV CJS LVUVEBO SBTU- HFMFTFÀJMFOJLJUFSMJôJOBZOSFOLMJPMEVôVCJMJO- %FLPSVO CJS VDVOVO UBSBM CÌMNFEF PMEVôV CJ- EJôJOFHÌSFCJSCJSJOJOFöJPMNBPMBTMôLBÀUS MJOEJôJOFHÌSF EJôFSLÌöFMFSJOJO\" # $ %EFO IFSIBOHJJLJTJOJOPMNBPMBTMôLBÀUS 9 B) 1 $ 4 5 E) 2 A) 8 B) 1 $ 5 D) 3 E) 3 A) 5 5 D) 13 3 13 7 8 26 13 5 1. $ 2. D 3. D 82 4. B $
#BôNT[0MBZMBS,PöVMMV0MBTML TEST - 43 1. A = { }LÐNFTJOJOFMFNBOMBSLVMMB- 4. FWMJ ¿JGU JMF CFLBSEBO PMVõBO LJõJMJL BSLBEBõ OMBSBLSBLBNMBSGBSLMCBTBNBLMUÐNEPóBMTB- HSVCVCJSLBOFQFZFZBOZBOBPUVSBDBLMBSES ZMBSCJSLºóEBZB[MZPS #FLBSMBSOZBOZBOBPMNBEôCJMJOEJôJOFHÌSF #V L»ôUMBSEBO SBTUHFMF TFÀJMFO CJS UBOFTJOJO ÀJGUMFSJOIFSCJSJOJOFöMFSJZMFZBOZBOBPMNBPMB- Ñ[FSJOEFLJTBZOOÀJGUPMEVôVCJMJOEJôJOFHÌSF TMôLBÀUS TBZZPMVöUVSBOSBLBNMBSOTPMEBOTBôBLÑÀÑL- UFOCÑZÑôFEPôSVTSBMBONöPMNBPMBTMôLBÀ- 1 B) 1 $ 1 2 1 US A) 5 D) E) 20 30 5 10 1 B) 1 $ 11 4 1 A) 9 D) E) 6 360 45 8 ,BSFMJEFGUFSJOTBEFDFCS2MJLLTNõFLJMEFHË- SÐMNFLUFEJS 2. \"-&-\"%& LFMJNFTJOJO IBSGMFSJOJO SBTUHFMF TSBMBO- NBTZMBLFMJNFMFSPMVõUVSVMVZPS ÷ML\"IBSGJOJOJML&IBSGJOEFOÌODFHFMEJôJCJMJO- &MJGEFGUFSJOFNBWJSFOLMJCBOUWFË[EFõZFõJMSFOLMJ EJôJOFHÌSF &IBSGMFSJOJOCJSBSBEBPMNBPMBTM- CBOUMBSõFLJMEFLJIºMMFSJZMFZBQõUSBDBLUS ôLBÀUS %FGUFSF ZBQöUSMBO CBOUO EJôFS CBOUMBS JMF PS- A) 1 B) 1 $ 4 D) 8 E) 4 UBLLÌöFWFZBLFOBSBTBIJQPMNBEôCJMJOEJôJOF 21 7 7 21 21 HÌSF ZFöJM CBOUMBSO BZO TBUSEB PMNB PMBTMô LBÀUS A) 1 B) 1 $ 1 D) 1 E) 3 3 2 12 6 5 3. #JS BZ J¿FSJTJOEF CFMMJ BSBMLMBSEB HÐO LBS ZBó- 6. 3BLBNMBSGBSLM SBLBNMBSOOTBZEFóFSMFSJ¿BSQ- NBLUBES ,BS HFDF ZBóEóOEB HÐOEÐ[ ZBóNV- NPMBOTBZMBSEBOCJSTBZTF¿JMJZPS ZPSWFZBHÐOEÐ[ZBóEóOEBHFDFZBóNBNBLUBES 5PQMBNEBHÐOEÐ[WFHFDFLBSZBóNBNõUS 4FÀJMFO TBZOO UFL PMEVôV CJMJOEJôJOF HÌSF CBTBNBLMPMNBTPMBTMôLBÀUS ,BSOHÑOEÑ[ZBôNBEôCJMJOEJôJOFHÌSF HFDF A) 1 B) 3 $ 3 D) 2 8 EFZBôNBNöPMNBPMBTMôLBÀUS 20 20 10 5 E) 21 A) 1 B) 7 $ 4 D) 4 E) 7 7 11 13 11 13 1. $ 2. D 3. B 83 4. E E 6. E
TEST - 44 #BôNT[0MBZMBS,PöVMMV0MBTML 1. #JSEËOFSLBQOO EBJSFõFLMJOEFCJSBMBOJ¿FSJTJOEF 3. ôFLJMEFLJNBOUBSQBOPEBFõJUBSBMLMBSMBUBLMNõ EËOFOпLBOBEWBSES BEFUSBQUJZFNFWDVUUVS ¥Lõ 1 1 2 3 32 1 br 1 br 1 br (JSJõ 1 br 13 2 Kanatlar ,BSFCJSL»ôEOQBOPZBBTMEôCJMJOEJôJOFHÌ- SF L»ôEOCS2MJLCJSL»ôUPMNBPMBTMôLBÀ- ¶¿LBQLBOBE CVBMBOпFõJUCËMÐNFBZSNBLUBES US ¥Lõ A) 1 B) 1 $ 1 D) 1 E) 1 5 4 3 2 1 3 2 4. LJõJMJLCJSPSLFTUSBEBFSLFLMFSJOUBOFTJ %ËOÐõ 3 yönü PSLFTUSBOOJTFËEÐMTBIJCJEJS (JSJõ :VLBSEB LBOBUMBSO п GBSLM LPOVNV HËSÐMNFLUF- #VOBHÌSF PSLFTUSBEBOSBTUHFMFTFÀJMFOLJöJ- EJS,BOBUB¿LMLMBSHJSJõWF¿LõB¿LMLMBSJMFBZ- OJO EF ÌEÑM TBIJCJ PMEVôV CJMJOEJôJOF HÌSF TB- OES EFDFCJSJOJOLBEOPMNBPMBTMôLBÀUS 7 B) 3 $ 27 9 27 A) D) E) ,BQ ZVLBSEBLJ LPOVNEBZLFO EËONFZF EFWBN 220 110 55 70 220 FEFSLFOLJõJHJSJõLTNOEBLBQZBZËOFMNJõMFSEJS MJL EÌONF ZBQUô CJMJOFO LBQOO ÌOÑOEF \"TM $FSFO \"INFUWF#VSBLZVSUEõOB¿LNBLJ¿JO CFLMFZFO LJöJOJO LBSö UBSBGB HFÀUJôJ CJMJOEJ- ôJOF HÌSF BZO CÌMNFEF HFÀNJö PMNB PMBTMô LJNMJLLPOUSPMÐOEFOHF¿FDFLMFSEJS LBÀUS ,JNMJLMFSJOJ QPMJT NFNVSVOEBO UFTMJN BMELMB- A) 1 B) 1 $ 1 D) 1 E) 1 SOEB \"INFUhJO LJNMJôJOJO EPôSV WFSJMEJôJ CJMJO- 2 4 8 16 32 EJôJOFHÌSF BöBôEBLJMFSEFOIBOHJTJZBOMöUS A) %JóFSLJõJMFSJOEFLFOEJLJNMJLMFSJOJBMNBPMBTMó 2. 2m3m CS BZSU V[VOMVLMBS PMBO CJS EJLEËSUHFOMFS 1 ES 6 QSJ[NBT õFLMJOEFLJ UBIUB CMPóVO LBSõMLM ZÐ[MFSJ BZOPMBDBLõFLJMEFNBWJ LSN[WFTBSZBCPZBO- B) \"INFUEõOEBTBEFDFCJSLJõJOJOLFOEJLJNMJóJOJ ZPS %BIB TPOSB UBIUB CMPL CJSJN LÐQMFSF BZSMZPS ,ÐQMFSEFOCJSJTF¿JMJZPS alma olaTMó 1 dir. 2 $ \"INFUEõOEBIJ¿CJSJOJOLFOEJLJNMJóJOJBMNBNB PMBTMó 1 ES 6 4FÀJMFOLÑCÑONBWJZFCPZBMCJSZÑ[ÑOÑOPMEV- D) &OB[JLJLJõJOJOLFOEJLJNMJóJOJBMNBPMBTMó 1 ôVCJMJOEJôJOFHÌSF SFOHJEFCVMVOEVSNBPMB- TMôLBÀUS ES 6 A) 1 B) 1 $ 1 D) 2 E) 1 E) &OGB[MBJLJLJõJOJOLFOEJLJNMJóJOJBMNBPMBTMó 5 2 6 5 8 5 ES. 6 1. $ 2. B 84 3. \" 4. E $
www.aydinyayinlari.com.tr 7&3÷ 4\":.\"7&0-\"4*-*, 8. MODÜL ·/÷7&34÷5&:&)\";*3-*, %FOFZTFM-5FPSJL0MBTML 0-\"4*-*,*** ÖRNEK 1 7$1,0%m/*m /FIJSCJSUPSCBZBGBSLMSFOLUFCJMZFLPZNVõUVS(Ë[MF- SJOJLBQBUBSBLSBTUHFMFCJSCJMZFBMNõUS )JMFTJ[CJSNBEFOJQBSBZBUBSBLFMEFFEJMFOTP- OV¿MBSJODFMFZFMJN #VCJMZFOJO/FIJSJOJTUFEJôJSFOLUFPMNBPMBTMôOF ÀFöJUCJSPMBTMLUS \"Uö4BZT (FMFO5VSB (FMFO:B[ 5FPSJL 4BZT 4BZT 4 ÖRNEK 2 #JSNBEFOJQBSBBSUBSEBLF[IBWBZBBUMZPSLF[ZB- [LF[UVSBHFMEJóJHËSÐMÐZPS 5BCMPEB WFSJMFOMFSF HËSF NBEFOJ QBSB LF[ #VOBHÌSF LF[BUMEôOEBQBSBOOUVSBHFMNFPMB- TMôOFÀFöJUCJSPMBTMLUS BUMEóOEBUBOFTJUVSBHFMNFLUFEJS 5VSBHFMNFPMBTMó= 4 = 0, 4 5FPSJL 10 ÖRNEK 3 .BEFOJQBSBLF[BUMEóOEBUBOFTJUVSB öLJBSLBEBõUBO±[MFNBUõZBQBSBL[BSOHFMNFPMB- HFMNFLUFEJS TMóOIFTBQMZPS'BUPõEBBUõZBQBSBLQBSBOOUV- 5VSBHFMNFPMBTMó= 46 = 0, 46 SBHFMNFPMBTMóOIFTBQMZPS :VLBSEB CFMJSUJMFO EVSVN IBOHJ ÀFöJU PMBTMôB ÌS- 100 OFLUJS .BEFOJ QBSB LF[ BUMEóOEB UBOFTJ UVSBHFMNFLUFEJS %FOFZTFM 5VSBHFMNFPMBTMó = 492 = 0, 492 ÖRNEK 4 1000 5BCMPEBFMEFFdilen sonV¿MBSBHËSF FMEFFUUJ- r .JMMJ1JZBOHP:MCBõ±[FM¥FLJMJõJJ¿JO óJNJ[ PMBTML IFTBCOB EFOFZTFM PMBTML BE r 4ÐMFZNBOBEFU verilir. r 5BIJSBEFU r )BZEBSBEFU \"TMOEB IJMFTJ[ CJS NBEFOJ QBSBOO ÐTU ZÐ[ÐOF r 5BZZBSBEFU ZB[ZBEBUVSBHFMNFPMBTMóUFPSJLPMBSBL 1 r 4FMJNBEFU CJMFUBMNõMBSES 2 #VOB HÌSF CV EÌSU LJöJEFO IBOHJTJOF .JMMJ 1JZBOHP dir. :MCBö²[FM¦FLJMJöJ÷LSBNJZFTJOJOÀLNBPMBTMôUF- PSJLPMBSBLEBIBZBLOES 5BCMPEBOEB HËSÐMFDFóJ HJCJ EFOFZ TBZT art- UL¿BEFOFZTFMPMBTMLEFóFSJUFPSJLPMBTMLEF- 5BZZBS óFSJOFZBLMBõNBLUBES SONUÇ #JSPMBTMLEFOFZJTPOVDVOEBFMEFFEJMFOWFSJ- MFSF HËSF IFTBQMBOBO PMBTMóB EFOFZTFM PMB- TML CJS PMBTML EFOFZJOEFO CFLMFOFO PMBTM- óBUFPSJLPMBTMLBEWFSJMJS 1. UFPSJL 2. UFPSJL3. EFOFZTFM4. 5BZZBS
TEST - 45 %FOFZTFM5FPSJL0MBTML 1. #JS[BSLF[IBWBZBBUMZPS¶TUZÐ[FHFMFOTP- 3. OV¿MBSBõBóEBLJHJCJEJS r LF[ r LF[ r LF[ r LF[ r LF[ r LF[ #JS BOLFU GJSNBTOO LJõJZF VZHVMBEó NFTMFL BOLFUJOF HFMJZPS ;BSO ÑTU ZÑ[ÑOF BTBM TBZ HFMNF PMBZOO EF- r ËóSFUNFO OFZTFMPMBTMôOFEJS r NJNBS r EPLUPS A) 1 B) 13 $ 33 18 9 r TFSCFTUNFTMFL 2 D) E) r FD[BD 25 50 25 10 LBUMNõUS 2. öLJ[BSIBWBZBBUMZPS;BSMBSOÐTUZÐ[MFSJOFHFMFO #VOB HÌSF SBTUHFMF TFÀJMFO CJS LJöJOJO ÌôSFU- NFOPMNBPMBZOOUFPSJLPMBTMôOFEJS TBZMBSOUPQMBNOOOPUFEJMEJóJEFOFZMFSZBQMZPS A) 1 B) 1 $ 1 D) 1 E) 4 %FOFZTPOV¿MBSBõBóEBLJHJCJEJS 6 3 10 2 9 ;BSMBSO·TU 0MBZO(FSÀFLMFöNF 4. %Ð[FOMFOFOCJSBEBZBSõNBTOEBL[MBSWFFSLFLMFS :Ñ[FZMFSJOF(FMFO 4BZT 4BZMBSO5PQMBN ZBSõNBLUBESFSLFLWFL[ZBSõNBDOOCV- 4 MVOEVóVBEBEBEÐ[FOMFOFOZBSõNBOOUBOFTJ- 2 7 OJL[HSVCV UBOFTJOJFSLFLHSVCVLB[BONõUS 3 2 4 7 7 11 4 11 12 #VOBHÌSF [BSMBSOÑTUÑOEFLJOVNBSBMBSOUPQ- #VOBHÌSF ZBSöNBZL[HSVCVOVOLB[BONBT MBNOOPMNBPMBZOOUFPSJLPMBTMôEFOFZTFM PMBZOOEFOFZTFMPMBTMôLBÀUS PMBTMLUBOLBÀGB[MBES A) 1 # $ 2 51 1 B) 3 $ 2 1 1 5 7 D) E) A) 5 5 D) E) 13 2 2 3 6 1. B 2. D 3. B 86 4. B $
7FSJ 4BZNBWF0MBTML KARMA TEST - 1 1. \"INFU (ËLIBO .ÐHF HÐOEF PSUBMBNB TPSV ôFLJMEFLJHSBGJLUFÐMLFNJ[FZMEBHFMFOUVSJTUTBZ- ¿Ë[NFLUFEJS MBSWFSJMNJõUJS #VHSVCBHÑOEFUBOFTPSVÀÌ[FO#VSDVFLMF- Turist Say›s› (bin) OJODFPMVöBOZFOJHSVQHÑOEFPSUBMBNBLBÀUB- OFTPSVÀÌ[FS \" # $ % & Y›llar 2. TBZTOO CÑUÑO BTBM ÀBSQBOMBS öFLMJOEF PMVöUVSVMBOTBZEJ[JTJOJONFEZBOLBÀUS \" # $ % & #VOB HÌSF UVSJTU TBZMBSOO TUBOEBSU TBQNBT LBÀUS 10 5 10 3 15 $ 50 A) B) 3 3 3. ôFLJMEFLJHSBGJLMFSEFOHSBGJLCBI¿WBOO[BNBOB 55 5 15 D) E) CBóMFMJOEFLJUPIVNNJLUBSEFóJõJNJOJTJ[BNB- OBCBóMFLUJóJBMBOHËTUFSNFLUFEJS 2 2 Tohum (kg) Alan (m2) 6. ôFLJMEF \"WF#LFOUMFSJBSBTOEBCVMVOBO11 ve P2 42 250 QPTUBOFMFSJOJOLFOUMFSFWFCJSCJSMFSJOFPMBOV[BLML- 37 MBSHËTUFSJMNFLUFEJS A 50 B 20 P1 P2 10 2 Saat 2 Saat #VOBHÌSF \"EBO#ZFTBCJUI[MBZPMBMBOCJS HSBùL HSBùL BSBDO11 ve P2QPTUBOFMFSJOFV[BLMLMBSUPQMB- NOO [BNBOB HÌSF EFôJöJNJOJ HÌTUFSFO HSBGJL #V CBIÀWBO N2 BMBO EJLUJôJOEF FMJOEF BöBôEBLJMFSEFOIBOHJTJEJS LBÀLHMLUPIVNVLBMNöUS \" # $ % & A) 6[BLML LN B) 6[BLML LN 90 70 50 4. Çekirdek (SBGJL CJS LVSVZFNJõ Zaman Zaman UBCBóOEBLJZFNJõMFSJO C) 6[BLML LN D) 6[BLML LN F›st›k 60° EBóMNO HËTUFSNFL- 90 O tedir. 90 100° 50 70 70° F›nd›k Leblebi Zaman Zaman E) 6[BLML LN #JS QBLFUUF CVMVOBO GTUôO HSBN MFCMFCJOJO 90 HSBNOEBOHSGB[MBPMEVôVOBHÌSF CVQBLFU 70 LBÀHSBNMLUS 50 \" # $ % & Zaman 1. E 2. B 3. \" 4. E 87 B 6. E
KARMA TEST - 2 7FSJ 4BZNBWF0MBTML 1. 1. 2. 3. 4. 4FSLBOBËóSFUNFOJBõBóEBLJWFSJHSVCVOVOTUBO- ²ôSFODJOPUMBS 3 4 3 EBSUTBQNBTOIFTBQMBNBZËEFWPMBSBLWFriyor. 5BCMPEBCJSËóSFODJOJONBUFNBUJLEFSTJOEFOBMEó CFõTOBWTPOVDVWFSJMNJõUJS 4FSLBO IFTBQMBNBMBSO ZBQBSLFO IFS CJS WFSJ JMF #VOBHÌSF OPUMBSOTUBOEBSUTBQNBTLBÀUS BSJUNFUJL PSUBMBNB BSBTOEBLJ GBSL CVMNBL ZFSJOF IFSCJS WFSJ JMF NFEZBO BSBTOEBLJ GBSL CVMBSBL Jõ- \" # $ % & lemlerine devam ediyor. #VOBHÌSF CVMEVôVTUBOEBSUTBQNBJMFCVMNBT HFSFLFOTUBOEBSUTBQNBBSBTOEBLJGBSLLBÀUS \" # $ % & 2. TBZEJ[JTJOJONPEVJMFNFEZBOOOUPQMBNLBÀ- US \" # $ % & 3. ôFLJMEFLJHSBGJLUFCJSTOGUBLJËóSFODMJFSJOGJ[JLEFS- 6. * #JSWFSJHSVCVOVOFOLпÐLEFóFSJEBIBEB TJOEFOBMEóOPUMBSWFSJMNJõUJS LпÐMÐSTFNFEZBOEBLпÐMÐS Ö€renci Say›s› ** 5FQFEFóFSJPMNBZBOCJSWFSJHSVCVOVOUÐNWF- SJMFSJCJSCJSJOEFOGBSLMES 7 6 ***\"SJUNFUJL PSUBMBNBMBS BZO JLJ WFSJ HSVCVOVO 5 TUBOEBSUTBQNBMBSEBBZOES 4 3 *7#JSWFSJHSVCVOVOUÐNEFóFSMFSJBZOJTFB¿LML 2 WFTUBOEBSUTBQNBTCJSCJSMFSJJMFBZOES 1 :VLBSEBLJCJMHJMFSEFOIBOHJMFSJEPôSVEVS 0 123 4 \" :BMO[* # :BMO[*** $ **WF*7 % *WF*** & *WF*7 5 Notlar #VOBHÌSF TOGOOPUPSUBMBNBTZBLMBöLLBÀ- US \" # $ % & 7. { } 4. FMFNBOMCJSLÑNF IJÀCJSJCPöPMNBZBOÑÀBZ- LÑNFTJOEFOSBTUHFMFBMOBOCJS9TBZTOO x3 - 2x2JGBEFTJOJCJSUBNTBZOOLBSFTJZBQNB SLLÑNFZFLBÀEFôJöJLöFLJMEFBZSMBCJMJS PMBTMôLBÀUS \" # $ % & A) 1 B) 1 $ 2 D) 3 E) 4 10 9 5 10 9 1. \" 2. $ 3. E 4. B 88 \" 6. $ 7. B
7FSJ 4BZNBWF0MBTML KARMA TEST - 3 1. #JSEFOFZJO\" #WF$HJCJBZSEVSVNJMFTPOV¿- 4. #JSLÐQÐOZÐ[ÐNBWJ ZÐ[ÐZFõJMWFZÐ[ÐLS- MBOEóPSUBZB¿LZPS N[SFOHFCPZBOZPS#VLÐQEÐ[CJS[FNJOFBUM- EóOEBHËSÐOFOZÐ[MFSJOYSFOHJOFCPZBMZÐ[MFSJO \" #OJOLBULBEBS # $OJOLBULBEBSHÌ[- UBNBNOJ¿FSNFTJWFUBNBNOJ¿FSNFNFTJPMBZMB- MFNMFOFCJMEJôJOFHÌSF CVEFOFZEFOFMEFFEJMF- SBZSLPMNBZBOPMBZMBSES DFL Fö PMBTM ÌSOFL V[BZ BöBôEBLJMFSEFO IBO- HJTJHJCJPMNBMES #VOB HÌSF Y ZFSJOF BöBôEBLJMFSEFO IBOHJTJ HFMFNF[ A) {\" # $} B) {\" # # $ $ $} \" .BWJ # ,SN[ $ {\" \" \" \" \" \" # # # $} D) {\" \" # # # $} $ :FõJM % .BWJWFZBZFõJM E) {\" # # # $ $} & .BWJWFZBLSN[ 2. ±LTÐSÐL õJLBZFUJ JMF LFOEJTJOF CBõWVSBO CJS IBT- 0[BOWFBSLBEBõ#FSBOiUBõ LºóU NBLBTuPZOV- UBOO \" # WF $ IBTUBMó PMEVóVOV UFõIJTFUNJõCJSEPLUPSBZOõJLBZFUMFHFMFOZFOJCJS ZPS#VPZVOEBFMJZMFUBõZBQBONBLBTZBQBO NB- IBTUBTOEBOTPOSBCVPSBOMBSOIFQTJOJEÐõÐSNÐõ- LBTZBQBOLºóUZBQBOWFLºóUZBQBOUBõZBQBO UÐS ZFONFLUFEJS 0ZVODVMBS BZO õFZJ ZBQBSMBSTB P FM CFSBCFSFCJUNFLUFEJS #VOBHÌSF EPLUPSVOZFOJIBTUBJMFJMHJMJZBQUL- MBSOEBOIBOHJTJEPôSVEVS 0[BO PZOBZBDBLMBS IFS FMEF UBö ZBQBDBôOB #FSBOJTFIJÀÑTUÑTUFBZOöFZJZBQNBZBDBôOB A) #VIBTUBJ¿JO\" #WF$EBOGBSLMCJSUFõIJTUFCV- HÌSF PZVOVFMTPOVOEB0[BOOLB[BONBPMB- MVONVõUVS TMôLBÀUS B) #VIBTUBOO\"IBTUBMóPMEVóVOVUFõIJTFUNJõ- \" # 1 $ 1 D) 1 E) 1 tir. 2 3 4 $ #VIBTUBOO#IBTUBMóPMEVóVOVUFõIJTFUNJõUJS 6. #JS[FZUJOBóBDOHËWEFTJOEFOTBCJUCJSHпMFTBM- D) #VIBTUBOO$IBTUBMóPMEVóVOVUFõIJTFUNJõUJS E) ±ODFLJ ZBQUó UFõIJTMFSEF ZBOMõML PMEVóVOV MBZBOCJSNBLJOF[FZUJOMFSJOEBMOEBOEÐõNFTJOJLP- MBZMBõUSNBLUBES BOMBNõUS #VOB HÌSF CJS [FZUJOJO EÑöNF PMBTMôOO NB- 3. 4\"3*.4\",LFMJNFTJOJOIFSCJSIBSGJCJSLBSUBZB[- LJOFOJOÀBMöNBTÑSFTJOFCBôMHSBGJôJBöBôEB- LJMFSEFOIBOHJTJPMNBMES MBSBLCJSLVUVZBBUMZPS A) 0MBTML B) 0MBTML #VLVUVEBOSBTUHFMFÀFLJMFOCJSLBSUOÑ[FSJOEF- LJ IBSGJ HÌ[MFNMFNF EFOFZJOJO Fö PMBTM ÌSOFL 11 V[BZBöBôEBLJMFSEFOIBOHJTJPMBCJMJS Zaman Zaman A) {4 \" 3 * . 4 \" ,} D) 0MBTML B) {4 \" 3 * . ,} C) 0MBTML 1 $ {4 3 . , {\" *}} 1 D) {S1 \"1 3 * . 42 \"2 ,} E) {\" * {4 . ,}} Zaman Zaman E) 0MBTML 1 Zaman 1. $ 2. \" 3. D 89 4. B D 6. B
KARMA TEST - 4 7FSJ 4BZNBWF0MBTML 1. \" &ËSOFLV[BZOEBCJSPMBZPMNBLÐ[FSF 4. D C \"#$%LBSFTJOJOLËõFHFO- MFSJOJO LFTJN OPLUBT & P^ A h = 2 UÐS E EJS&OPLUBTOEBCVMVOBO 3 A CJS LBSODB \" # $ WF % OPLUBMBSOEBLJZFNMFSJLB- #VOBHÌSF BöBôEBLJMFSEFOIBOHJTJCJSJNLBO- SFOJOLFOBSWFLËõFHFOMF- T[PMBZES SJOJO PMVõUVSEVóV ZPMMBS CPZVODB IBSFLFU FEFSFL A) A b\"h # \" $ \"h B D) A a\"h & &hb A FO LTB yoldan toplaya- DBLUS 2. #JS[BSBUNBEFOFZJOEF\"ZõFÐTUZÐ[FHFMFOTBZ- #VOBHÌSF CVLBSODBOOJMLBMEôZFNJO\"EBO OOWFZBPMBCJMFDFóJOJ #FSSBEBÐTUZÐ[FHFMFO WFTPOBMEôZFNJO%EFOPMNBPMBTMôLBÀUS TBZOO WFZBPMBCJMFDFóJOJUBINJOFEJZPS öQVDV=\"óB¿EJZBHSBN #VOB HÌSF CV EFOFZJO ÌSOFL V[BZ & WF \"ZöF A) 3 B) 3 $ 1 D) 1 E) 1 JMF #FSSBOO UBINJOMFSJOJ JÀFSFO PMBZMBS \" JMF # 5 8 8 4 2 7FOOöFNBTOEBOBTMHÌTUFSJMJS A) E A B B) E AB \"õBóEBNBEFOJQBSBOOZB[WFUVSBHFMNFPMBT- 1 5 13 MLMBSZMBÐ[FSMFSJOFZBUSMBOCBIJTNJLUBSMBSWFSJMJZPS 5 6 24 34 6 Para 0MBTML #BIJT * : 5- 2 ** 5 5- *** : 5- C) E A B D) E AB *7 5 5- V : 5- 351 5 4 1 5 5- 4 62 3 : 5- 5 5- 62 : 5- 5 5- E) E A 4B 15 32 6 3. 5JDUBDUPFPZVOVOEBJLJPZVODVTSBZMBi9uWFi0u #VOBHÌSF FOÀPLHFUJSJOJOIBOHJQBSBZBZBUS- MBOCBIJTUFOHFMNFTJCFLMFOJS TFNCPMMFSJOJYMÐLCJSUBCMPZBZFSMFõUJSJZPSMBS4B- US TÐUVO WFZB ¿BQSB[ CPZVODB LFOEJ TFNCPMMFSJOJ \" * # ** $ *** % *7 & 7 JMLZB[BOPZVODVPZVOVLB[BONBLUBES\"õBóEBLJ PZVOBi9uJMFCBõMBONõUS 6. öLJ[BSôFLJMmEFLJHJCJCJSCJSJOFZBQõUSMBSBLôFLJMm2 XOO EFLJHJCJZFQZFOJCJS[BSFMEFFEJMJZPS X ôFLJMm ôFLJMm XO :FOJ PMVöBO [BS EÑ[ CJS [FNJOEF EJLEÌSUHFO #VOBHÌSF PZVOVOEFWBNOEBi0uTFNCPMÑOÑZB- ZÑ[MFSJ[FNJOFHFMFDFLöFLJMEFZVWBSMBOSTBÑTU [BOPZVODVOVOPZVOVLB[BONBPMBTMôLBÀUS ZÑ[F HFMFO TBZMBS UPQMBNOO PMNB PMBTMô LBÀUS #JS[BSOLBSõMLMZÑ[MFSJOEFLJTBZMBSUPQ- MBNEJS A) 1 B) 1 $ 1 D) 1 & \" # 1 $ 1 D) 1 E) 3 6 4 3 2 2 3 4 4 1. D 2. \" 3. E 90 4. $ E 6. \"
7FSJ 4BZNBWF0MBTML KARMA TEST - 5 1. #JSPMBZOPMNBPMBTMóOO 3. LJõJMJLCJSUPQMBOUËODFTJOEFIFSLFTJ¿JOJTJNMFSJ- öTUFOJMFOPMBTEVSVNMBSOTBZT OJOZB[MPMEVóVCJSEPTZBIB[SMBONõUS5PQMBOU- 5ÐNPMBTEVSVNMBSOTBZT ZBJMLHFMFOLJõJEPTZBEBLJJTJNMFSFCBLNBEBOSBTU- HFMFCJSEPTZBBMNõUS JMFIFTBQMBOEóOCJMJZPSV[ %BIBTPOSBLJLBUMNDMBSJTFFóFSJTJNMFSJWBSTBP EPTZBZBMNõUS:PLTBSBTUHFMFCJSEPTZBZBMNõ- US 5- #VOB HÌSF UPQMBOUZB TPO HFMFO LJöJOJO LFOEJ EPTZBTOBMNBPMBTMôLBÀUS 5- A) 1 B) 1 $ 1 D) 2 E) 3 2 4 6 3 5 %FSJOLVNCBSBTOEBCJSJLUJSEJóJMJSBMLWFLVSVõ- 4. (2x + y)7B¿MNOEBLJUFSJNMFSEFOSBTUHFMFJLJUBOF- MVLNBEFOJQBSBMBSMBLFOEJTJOFWJUSJOEFHËSEÐóÐFM- CJTFWFBZBLLBCZBMNBLJTUJZPS si seçiliyor. 1BSBT FMCJTFZJ BMNBZB ZFUJZPS %FSJOhJO LVNCBSB- #VOB HÌSF TFÀJMFO JLJ UFSJNJO LBUTBZMBSOO TOEB CJSJLFO QBSBMBSO BSBTOEBO SBTUHFMF ¿FLJMFO UPQMBNOOUFLPMNBPMBTMôLBÀUS CJSNBEFOJQBSBOOLVSVõPMNBPMBTMó 4 tir. 5 A) 1 B) 1 $ 1 D) 1 E) 1 #VOBHÌSF %FSJOhJOBMöWFSJöUFOTPOSBLBÀMJSBT 8 28 4 7 14 LBMNöUS \" # $ % & 2. 'BISJ QBSB LPMFLTJZPOV J¿JO LPMFLTJZPO QBSBMBSO÷/(÷-5&3& \"õBóEB9 :WF;CBOLBMBSZMB¿BMõBOMBSO NFN- 364:\" ÐMLF ÐMLF LMBTËSMFNFLUFEJS ,MBTËSMFSJOEFO BMU UB- OVOJZFUZÐ[EFMFSJBõBóEBLJTÐUVOHSBGJóJOEFHËTUF- OFTJBõBóEBHËSÐMNFLUFEJS\"-.\"/:\" SJMNJõUJS #V CBOLBMBS LVMMBOBO LJõJMFSJO TBZDB EB- ,0-0.#÷:\" óMNJTFEBJSFHSBGJóJOEFHËTUFSJMNJõUJS &MJOEFZFOJBMEóCJS,PMPNCJZBWF\"MNBOZBQBSBT1\",÷45\"/ CVMVOBO'BISJ LMBTËSMFSFCBLNBEBOQBSBMBSGBSLM Memnuniyet yüzdesi LMBTËSMFSFZFSMFõUJSJZPS ÷5\"-:\" #VOBHÌSF 'BISJhOJOCVQBSBMBSEBOFOB[CJSJOJ 50 EPôSVLMBTÌSFZFSMFöUJSNJöPMNBPMBTMôZÑ[EF Z LBÀUS \" # $ % & 40 140° X 30 Y X YZ Banka 9 CBOLBTOEBO NFNOVO LBMBOMBSO TBZT : CBOLBTOEBO NFNOVO LBMBOMBSO TBZT PMEVôVOBHÌSF ;CBOLBTOEBONFNOVOLBMBO- MBSOTBZTLBÀUS \" # $ % & 1. \" 2. B 91 3. E 4. B B
KARMA TEST - 6 7FSJ 4BZNBWF0MBTML 1. A = {B C D E F } 4. \"MUZÐ[ÐCVMVOBOCJS[BSOIFSCJSZÐ[ÐOEFCJSLFMJ- LÑNFTJOJOBMULÑNFMFSJOJOLBÀUBOFTJOEFFOB[ NFOJOIBSGMFSJZB[MES;BSIBWBZBBUMEóOEBÐTU IBSG FOGB[MBSBLBNCVMVOVS ZÐ[FTFTMJIBSGHFMNFPMBTMó 1 veÐTUZÐ[FTFSU \" # $ % & 3 TFTTJ[CJSIBSGJOHFMNFPMBTMó 1 dir. 2 #VOB HÌSF [BSO ZÑ[MFSJOEF ZB[M PMBO IBSGMF- SJO PMVöUVSEVôV LFMJNF BöBôEBLJMFSEFO IBOHJ- TJPMBCJMJS \" '65#0- # %\",ö,\" $ #\"3%\", % #0:\".\" & 5¶3,¥& 2. A = {- - } LÐNFTJOJOUÐNBMULÐNFMFSJZB[MZPS #VOBHÌSF ZB[MBOCVBMULÑNFMFSEFOLBÀUBOF- TJOJOFMFNBOMBSUPQMBNES \" # $ % & :BöMBSÀBSQNOOPMEVôVCJMJOFOÑÀLBSEF- öJOZBöMBSOUBINJOFUNFZFÀBMöBOCJSLJöJLBS- EFöMFSJOZBöMBSOLFTJOPMBSBLCVMBCJMNFTJJÀJO FOB[LBÀUBINJOZBQNBMES \" # $ % & 3. \" #WF$FWMFSJBSBTOEBZPMMBSõFLJMEFHËTUFSJMNJõ- tir. ABC Ali Erdem 6. 4BZMBSOCÐZÐLMÐóÐLBEBSOPLUBZBSENZMBCJSп- ôFLJMEF\"FWJWF#FWJBSBTOEBZPM #FWJWF$FWJ HFOPMVõUVSBCJMFOTBZMBSBÑÀHFOTFMTBZMBS denir. BSBTOEB ZPM CVMVONBLUBES :PMMBS FõJU V[VOMVL- UBES \" FWJOEFO $ FWJOEFLJ BLSBCBTOB ZÐSÐZFDFL PMBO 1 1+2=3 1+2+3=6 \"MJWF$FWJOEFO\"FWJOEFLJBLSBCBTOBZÐSÐZFDFL PMBO&SEFNBZOBOEBIBSFLFUFUNJõMFSEJS :VLBSEBLJJMLпHFOTFMTBZHËSÐMNFLUFEJS r ,JõJMFSZÐSÐEÐLMFSJIFSZPMEBOCJSLF[HF¿FDFL- \"öBôEBLJMFSEFOIBOHJTJOÑÀHFOTFMTBZES lerdir. r &SEFN \"MJhEFOEBIBI[MES #VOBHÌSF \"MJWF&SEFNhJOLBSöMBöNBPMBTMô A) c n m B) c n + 1 m $ O O+ 1 ) OFEJS 2 2 1 B) 1 $ 1 1 1 D) c n - 1 m E) c 2n m A) 8 D) E) 2 n 4 16 32 64 1. D 2. $ 3. \" 92 4. E $ 6. B
7FSJ 4BZNBWF0MBTML <(1m1(6m/6258/$5 1. .FUFPSPMPKJ (FOFM .ÐEÐSMÐóÐ HÐOMÐL CJS BZEB 4. %JLLPPSEJOBUTJTUFNJOEF OPLUBTOEBCVMVOBO \"OLBSBhEBBõBóEBCFMJSUJMFOUBCMPEBHËSÐMEÐóÐEÐ- CJSIBSFLFUMJBõBóEBCFMJSUJMFOJLJLVSBMBHËSFIBSF- [FOEFZBóõOCFLMFOEJóJOJUBINJOFUNJõUJS LFUFUNFLUFEJS LVSBMCSTBóBWFCSZVLBS Ankara LVSBMCSTBóBWFCSZVLBS ,BSM :BóNVSMV y \" &TSBCVBZOHÐOÐ\"OLBSBhEBCVMVOBDBLUS x &ôFS ZVLBSEBLJ EÑ[FOMJ UBINJO HFSÀFLMFöFDFL O PMVSTB&TSBhOOLBSZBôöOHÌSNFPMBTMôLBÀ- US A) 1 B) 1 $ 1 D) 1 E) 1 25 20 10 5 3 2. 19 m m 25 = 28 #VOB HÌSF CV IBSFLFUMJ \" OPLUBTOB LBÀGBSLMZPMJ[MFZFSFLHJEFCJMJS 5 \" # $ % & :VLBSEBLJ JöMFN UBCMPTVOEB UBSBM CÌMNFMFSF +WFZB-LPOVMBSBLFöJUMJôJOTBôMBONBPMBTMô LBÀUS \" # 1 $ 1 D) 7 E) 1 24 20 120 2 3. ö¿MFSJOEF.VSBUhOEBCVMVOEVóVBMULJõJEFOпÐCJS A = { } GPUPóSBG ¿FLUJSFDFLUJS #V LJõJMFSEFO IFSIBOHJ CJSJO- LÑNFTJOJOFMFNBOMBSLVMMBOMBSBLZB[MBCJMFDFL EF HË[MÐLEF õBQLBEB CVMVONBNBLUBES 'PUPóSBG EÌSUCBTBNBLMSBLBNMBSGBSLMTBZMBSMBPMVöUV- ¿FLJNJJ¿JOHJSJMFOTUÐEZPEBCJSHË[MÐLWFCJSõBQLB SVMBDBLTBZEJ[JTJOJOSBOKLBÀUS WBSES \" # $ % & 'PUPóSBG¿ 6. ,BUTBZMBS EPóBM TBZMBSEBO PMVõBO EFSFDFEFO * .VSBUhOFOTBóEBCVMVONBTO ** #JSLJõJOJOHË[MÐLUBLNBTO CJSQPMJOPNVOLBUTBZMBSUPQMBNUÐS *** %JóFSCJSLJõJOJOEFõBQLBUBLNBTO #VEVSVNBVZBOLBÀGBSLMQPMJOPNZB[MBCJMJS istiyor. \" # $ % & #VOB HÌSF LBÀ GBSLM GPUPôSBG ÀFLJNJ ZBQMBCJ- MJS \" # $ % & 1. $ 2. \" 3. E 93 4. D D 6. $
<(1m1(6m/6258/$5 7FSJ 4BZNBWF0MBTML 1. ôFLJMEFLJпUPSCBZBHFMJõJHÐ[FMEBóUMNõCJMZF 3. #JSHSVQBSLBEBõPZVOFWJOFHJUNFZFLBSBSWFSJSMFS JMFCJSPZVOPZOBOZPS 0ZVOFWJOEFUBSBMZFSEFOCBõMBZQ¿LõOPLUBTOB WBSNBMBSHFSFLFOMBCJSFOUPZVOVOVPZOBNBZBLB- rar verirler. ¥Lõ I II III #VPZVOVOJLJLVSBMõVõFLJMEFCFMJSMFOJZPS LVSBM)FSIBOHJJLJUPSCBEBOCJSFSCJMZFBMOQ CV (JSJõ CJMZFMFSEJóFSUPSCBEBLJCJMZFMFSFFLMFOJS#ËZMFMJLMF CJMZFFLMFOFOUPSCBZBLVSBMVZHVMBONõPMVS LVSBM)FSIBOHJCJSUPSCBEBOJLJCJMZFBMOQ CV 0ZVO CJSFZTFM PZOBOZPS PMVQ IFSLFT PZVOB LBUM- CJMZFMFSEJóFSJLJUPSCBZBCJSFSUBOFEBóUMZPS#ËZ- NõUS MFMJLMFCJMZFBMOBOUPSCBZBLVSBMVZHVMBONõPMVS (SVQUBLJMFSJOIFSCJSJGBSLMZPMMBSEBOÀLöOPL- 5PSCBMBSEB LVSBMMBSO VZHVMBONBT JÀJO ZFUFS- UBTOBWBSEôOBHÌSF HSVQUBLBÀLJöJWBSES MJ TBZEB CJMZF PMEVôV WBSTBZMSTB CV JLJ LVSBM GBSLM UPSCBMBSB BSLB BSLBZB VZHVMBOEôOEB \" # $ % & UPSCBEBLJ CJMZF TBZTOO EFôJöNFNF PMBTMô LBÀUS A) 1 B) 1 $ 3 D) 1 E) 1 2 4 8 8 3 2. #JS PZVO ¿BSLOEB Fõ CËMNFMJ ZBSõNBDMBS ¿BSLB 4. ôFLJMEF BEFU MBNCBEBO PMVõBO FMFLUSJL EFWSFTJ PLBUNBLUBESMBS,SN[CËMNFZFHFMFOPLJ¿JOZB- HËTUFSJMNJõUJS SõNBD IFEJZF LB[BOZPS WF UFLSBS ¿BSLB PL BUNB IBLLLB[BOZPS 0ZVOEBZBSõNBDTSBTZMBZBSõBDBLUS. #VOB HÌSF JML IFEJZFZJ ZBSöNBD WF JLJODJ -BNCBMBSV[VOTÐSFZBLMEóOEBJLJMBNCBOOJMFU- IFEJZFZJ ZBSöNBDOO ÀFWJSJöJOEF LB[BO- LFOMJóJOJLBZCFEFSFLTËOEÐóÐCJMJONFLUFEJS NBPMBTMôLBÀUS 625 B) 375 $ 125 #VOBHÌSF TÌOFOMBNCBMBSOZBOZBOBPMBOJLJ A) 212 211 MBNCBPMNBPMBTMôLBÀUS 212 375 225 8 B) 1 $ 5 41 D) E) A) 5 9 D) E) 211 212 45 15 3 1. E 2. E 94 3. B 4. B
7FSJ 4BZNBWF0MBTML <(1m1(6m/6258/$5 1. \"ZõF±óSFUNFOTOGUBCJSFULJOMJLZBQNBLJ¿JOËó- #PZVUMBSLNWFLNPMBOõFLJMEFLJEJLEËSUHFO SFODJMFSJ.BWJWF%VSVhZVUBIUBZBLBMESZPS0OMBS- BSTBOO \" OPLUBTOEBO # OPLUBTOB \"# EPóSVMUV- EBO UBIUBZB LBUTBZMBS SBLBNMBSEBO PMVõBO CJSFS TVOEBIBSFLFUFEFOCJSLJõJOJOEÐSCÐOÐZMFCFSBCFS EPóSV EFOLMFNJ ZB[NBMBSO JTUJZPS 4OGB ZËOFMJQ HËSÐõ NFTBGFMFSJ LN EJS \"# EPóSVTV BSTBZ JLJ EPóSVMBSOLFTJõJQLFTJõNFEJLMFSJOJLPOUSPMFUNFMF- FõJUQBS¿BZBCËMNFLUFEJS rini istiyor. 10 km #VOBHÌSF ZB[MBOEPôSVMBSOLFTJöNFPMBTMô LBÀUS A B 8 km A) 1 B) 23 $ 3 D) 7 25 2 E) 45 16 40 72 2. (ËLIBOWFöTNFUËóMFZFNFóJJ¿JOHJUUJLMFSJMPLBOUB- #VLJöJOJOBSTBOOJÀJOEFLJCFMMJCJSOPLUBZHÌS- NFPMBTMôLBÀUS EBNFOÐEFLJQJ[[B EËOFSWFQJEFEFOCJSJOJTJQBSJõ WFSFDFLMFSEJS 4JQBSJõ WFSNF TSBTOEB (ËLIBOhO A) 3 B) 2 $ 3 D) 4 E) 5 UFMFGPOV¿BMEóJ¿JOTJQBSJõJOJEBLJLBHF¿WFSJZPS 4 3 45 3 6 4JQBSJõMFSJOIB[SMBNBTÐSFMFSJBõBóEBLJHJCJEJS 6. #JSGPUPóSBGQBZMBõNTJUFTJOJOHËSTFMJBõBóEBLJHJ- Pizza: EBLJLB CJEJS %ÌOFSEBLJLB 1JEFEBLJLB #VOBHÌSF (ÌLIBOWF÷TNFUhJOWFSEJLMFSJTJQB- ÷TJN SJöMFSJOBZOBOEBIB[SPMNBPMBTMôLBÀUS Gönderi Takip Takipçi Profilini düzenle 1 B) 2 $ 1 D) 4 E) 2 A) 9 3 9 3 9 3. ÌôSFODJOJOLBUMEôEFOFNFTOBWOEBCJS ÌôSFODJOJO TSBMBNBTOO EJKJUBM TBBUUF HÌSÑMF- CJMNFPMBTMôLBÀUS A) 1 B) 1 $ 1 D) 1 E) 1 2 7 11 14 17 4. ,= { } #FSFOQSPGJMJOEFLJCFMMJJLJGPUPóSBGOGBSLMGPUPóSBG J¿FSJTJOEFBõBóEBLJLVSBMMBSBHËSFHËSÐONFTJOJJT- tiyor. L = f n1 p + f n2 p + . . . + f nK p + . . . + f n24 p + f n25 p #FSFO r1 r2 rK r24 r25 r GPUPóSBGOFOÐTUZBEBFOBMUTBUSEBZFSBMNB- PMNBL Ð[FSF , LÐNFTJOEFLJ FMFNBOMBSO ZBST - TOJTUFNFEJóJOF EFLJO,MFSJOZFSJOF EJóFSZBSTJTFS, lerin yerine ZB[MZPS r GPUPóSBGO GPUPóSBGJMFBZOTBUSEBZFSBM- NBTOJTUFNFEJóJOF )FSLEFôFSJOJÀJOS, <O,PMEVôVOBHÌSF -OJO HÌSF LBÀ GBSLM öFLJMEF QSPGJMEF CV GPUPôSBGMBS BMBCJMFDFôJFOLÑÀÑLEFôFSLBÀUS QBZMBöBCJMJS \" # $ \" # $ % & % & 1. B 2. B 3. D 4. \" B 6. $
<(1m1(6m/6258/$5 7FSJ 4BZNBWF0MBTML 1. Q5ÐNLBSFMFSEJLEËSUHFOEJS 3. \"õBóEBZBOZBOBEJ[JMNJõPMBOPZVO¿VCVóVWBSES q:5ÐNEJLEËSUHFOMFSLBSFEJS \"OBPLVMVËóSFODJMFSJOFSBLBNMBSËóSFUNFZJIFEFG- r: 1BSBMFMLFOBSOTJNFUSJFLTFOJZPLUVS MFZFO PZVOEB ¿VCVLMBSB IBMLB UBLMBSBL SBLBNMBS s: #JSпHFOJOпUBOFEõUFóFU¿FNCFSJWBSES ËóSFUJMNFLUFEJSöML¿VCVLUB TPO¿VCVLUBIBMLB ËOFSNFMFSJWFSJMJZPS CVMVONBLUBES p q ±óSFUNFOJ ZFUFSJ LBEBS IBMLB WFSEJóJ .BWJhZF CV s ¿VCVLMBSEBO CPõ PMBOMBSB IBMLB UBLNBTO GBLBU TPOEVSVNEBTPMEBOTBóB¿VCVLUBBSUBOTBZEB r IBMLBCVMVONBTOJTUFNJõUJS .Ð[FZZFO¿BSLBSUBSEBпLF[¿FWJSFDFLUJSöCSF- #VOBHÌSF .BWJPZVOVUBNBNMBEôOEBÑÀCPö OJOVDVOBEFOLHFMFOËOFSNFMFSTSBTZMBBõBóEB- ÀVCVôBUBLUôIBMLBMBSOBSEöLTBZPMNBPMB- LJUBCMPZBZFSMFõUJSJMFDFLUJS TMôLBÀUS 1. önerme 2. önerme 3. önerme A) 1 B) 2 $ 1 D) 1 E) 1 42 21 35 7 6 #VOB HÌSF PMVöBO CJMFöJL ÌOFSNFTJOJO EPôSV- MVLEFôFSJOJOPMNBPMBTMôOFEJS 21 B) 3 $ 1 71 A) 8 2 D) E) 64 32 3 2. öSFN /VSIBO &TSBWF%JDMFLFOEJBSBMBSOEBCJSZF- 4. NFL ZBSõNBT EÐ[FOMFNFZF LBSBS WFSJSMFS öML ZB- SõNBDOO%JDMFPMNBTOBLBSBSWFSJSMFS1VBOMBNB- OO QVBOPMBSBLZBQMBDBóZBSõNBEBZBSõ- NBDMBSOQVBOPMBTMLMJTUFMFSJBõBóEBLJHJCJEJS 1VBO 1 2 3 ,JöJ öSFN 111 /VSIBO 236 111 Esra 623 111 362 ±SOFóJO öSFNhJO QVBO WFSNF PMBTMó 1 &T- 'VOEBEPOEVSNBTOZFEJLUFOTPOSB¿VCVóVOVLS- 3 NõUS SBhOOQVBOWFSNFPMBTMó 1 dir. 2 #VOBHÌSF ÀVCVôVOQBSÀBMBSOEBOCJSJOJOEJôF- SJOEFOFOB[LBUCÑZÑLPMNBPMBTMôLBÀUS #VOBHÌSF %JDMFhOJOQVBOBMNBPMBTMôBöB- ôEBLJMFSEFOIBOHJTJEJS A) 1 B) 2 $ 1 D) 1 E) 2 3 3 5 2 5 1 B) 2 $ 23 23 23 A) 9 D) E) 9 216 54 108 1. B 2. E 96 3. D 4. $
CEVAP ANAHTARI 9(5m6$<0$9(2/$6,/,. r Sayfa 11, Örnek 4 4PSVTBZT 500 400 300 250 Aylar Ocak ôVCBU .BSU Nisan r Sayfa 11, Örnek 5 6[BLML 500 100 Zaman r Sayfa 62, Örnek 1 Y YT YY TT Y Y T T Y T T r Sayfa 63, Örnek 4 a) A = {(1, 1), (1, 2), (1, 3), (2, 1), (3, 1)} B = {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)} C {(4, 6), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6)} b) A a C = qPMEVóVOEBO\"JMF$BZSLPMBZMBSES A a#áqPMEVóVOEBO\"JMF#BZSLPMNBZBOPMBZ- MBSES B a$áq#JMF$BZSLPMNBZBOPMBZMBSES
Search
