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TYT Matematik Ders İşleyiş Modülleri 6. Modül Oran Orantı

Published by Nesibe Aydın Eğitim Kurumları, 2019-08-23 00:52:06

Description: TYT Matematik Ders İşleyiş Modülleri 6. Modül Oran Orantı

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A 7.ôDFSJ8O.EUPQMBNLBÀUS GBJLJ[L[ËóSFODJHFMNJõ FSLFLWFL[ËóSFODJJTF UBNBNLVMMBOMBSBLNFUSFHFOJõMJóJOEFZPMZBQ- MZPS CBõLBTOGBHF¿NJõUJS 1. x = 2 ve x . y . z = 24 4. a - b = 1 \" # $ % & #VOBHÌSF ÌôSFODJEFôJöJNJTPOS2BTTyOGUBLJL[Ìô- ÖRNEK 4 a+b 4 m = t =3 SFODJTBZTOOFSLFLÌôSFODJPTMBEZVTôVOOBBPHSBÌOSFO [CLVBMÀVU-S PMEVôVOBHÌSF a2 - b2 kaçtS #VOB HÌSF TPO EVSVNEBLJ ZPMVO V[VOMVôV 2a . b QMBOMBOBOZPMV[VOMVôVOEBOLBÀLNGB[MBES OV[ D) 19n Ek) 12 A) 2 B) 4 C) 6 m-n t+k m kA) PMEVôVOBHÌSF c m.f p1ÀBSQNB)OO7TPOVC-) 8 D) 2 E) 11 \" # $ % & 5 DVOVCVMVOV[ 2 15 15 3 5. .JMMJ1JZBOHPJEBSFTJOJOZMCBõ¿FLJMJõJOEFCJMFUOV- NBSBMBS CFMJSMFOJSLFO Ð[FSJOEF GBSLM SBLBNMBSO ZB[M PMEVóV UPQVO CVMVOEVóV LVUVEBO TSBZMB SBTUHFMFUPQ¿FLJMJZPS 3. (Ë[EFhOJO UFMFGPO GBUVSBT 5- EJS (Ë[EF ZMO 95 JMLÐ¿BZOEBCVUBSJGFZJLVMMBOELUBOTPOSBJOUFSOFU 3 2. m=3 , n=4 2 8 LVMMBONOOBSUNBTTPOVDVÐDSFUJ5-PMBOCJS ¥FLJMFO UPQMBS TSBZMB TBóEBO TPMB EPóSV ZB[MB- 1. 2. 2 n4 k5 3. 9 4. ÐTUUBSJGFZFHF¿NJõUJS:MOBZOEBBCPOFTJPMEV- SBL CJMFU OVNBSBT PMVõUVSVMVZPS #ÐZÐL JLSBNJZF- óV(4.PQFSBUËSÐGJSNBTOEBOGBUVSBTOBFLËEF- OJO¿FLJMJõJOEF¿FLJMFOJMLÐ¿UPQUBOJMLJOJOPMEVóV 2 3 NFMJ PMBSBL ZFOJ CJS UFMFGPO BMNõUS $JIB[ CFEFMJ CJMJOJZPS ZMOTPOBMUBZOEBIFSBZ5-FLPMBSBLGBUVSB- PMEVôVOBHÌSF m2 + n2 PSBOLBÀUS 5. a = 3 ve b = 3 ZBZBOTUMBDBLUS k2 a+b 4 b+c 4 #VOB HÌSF (Ì[EFhOJO CV CJS ZMML LVMMBONMB- A) 1 3 C) 4 5 5 PMEVôVOBHÌSF a PSBOLBÀUS SEJLLBUFBMOEôOEBBZMLGBUVSBMBSOOPSUBMB- ,BMBOZFEJUPQVOOVNBSBMBSOOPSUBMBNBTUBN B) D) E) c NBTLBÀ5-EJS TBZPMEVôVOBHÌSF ÀFLJMJöTPOVDVCJMFUOVNB- 2 343 SBTBöBôEBLJMFSEFOIBOHJTJPMBCJMJS A) 9 B) 3 C) 1 D) 1 \" # $ % & 3 E) 1 9 \" # $ % & 1. D 2. B 3. A 31 4. C 5. B 3. a = c = 2 PMEVôVOBHÌSF 6. BCDPMEVôVOBHÌSF bd ab + c2 f a + b p.f c - d p a2 + bc ac PSBOLBÀUS ÀBSQNOOTPO VDVLBÀUS A) 1 B) 2 C) 3 D) 2 E) 3 A) 5 B) 12 C) 5 D) 13 E) 1 3 3 2 4 13 13 12 12 1. C 2. A 3. E 6 4. C 5. A 6. B

ÜNwİwVwE.ayRdinSyaİyTinlaEri.YcoEm.trHAZIRLIK ·/÷7&34÷5&:&)\";*3-*, MATEMATİK - 1 6. MODÜL ORAN VE ORANTI ³ Oran t 2 ³ Orantı t 2 ³ Orantının Özellikleri t 3 ³ Doğru Orantı t 10 ³ Ters Orantı t 10 ³ Aritmetik Ortalama t 12 ³ Geometrik Ortalama t 12 ³ Oran - Orantı Problemleri t 18 ³ Karma Testler t 25 ³ Yeni Nesil Sorular t 31 1

·/÷7&34÷5&:&)\";*3-*, 6. MODÜL ORAN VE ORANTI www.aydinyayinlari.com.tr ORAN VE ORANTI - I Oran 0SBOU TANIM TANIM \"ZOCJSJNEFLJJLJ¿PLMVóVOCJSCJSJOFCËMÐONFTJ- öLJWFZBEBIBGB[MBPSBOOFõJUMJóJOFPSBOUEFOJS OForanEFOJS a = c =k bd &OB[CJSJTGSEBOGBSLMPMBOBWFCSFFMTBZ- MBSWFSJMEJóJOEFBOOCZFPSBOBCWFZB a õFLMJOEFHËTUFSJMJS L PSBOUTBCJUJEJS b BD=CECJ¿JNJOEFEFHËTUFSJMJS õFLMJOEFHËTUFSJMJS aWFEZFEöMBS DWFCZFJÀMFSBEWFSJMJSö¿MFS 0SBOOCJSJNJZPLUVS ¿BSQNEõMBS¿BSQNOBFõJUUJS :BOJ ÖRNEK 1 a=c bd \"ZöFhOJOCPZVDN )BUJDFhOJOCPZVDNJTF)B- UJDFhOJOCPZVOVO\"ZöFhOJOCPZVOBPSBOOCVMVOV[ JTFBpE=DpCEJS )BUJDFhOJOCPZV 120 3.40 3 == = PMVS \"ZöFhOJOCPZV 80 2.40 2 ÖRNEK 3 3=x 26 PMEVôVOBHÌSF YJCVMVOV[ 2 . x = 3 . 6 & x =PMBSBLCVMVOVS ÖRNEK 2 ÖRNEK 4 #JSTOGUBFSLFL L[ËóSFODJCVMVONBLUBESöLJBZ m = t =3 TPOVOEBTOGMBSBSBTËóSFODJEFóJõJNJTSBTOEBTOGB nk GBSLMJLJ[L[ËóSFODJMFSHFMNJõ FSLFLWFL[ËóSFO- PMEVôVOBHÌSF c m - n m.f t + k pÀBSQNOOTPOV- DJJTFCBõLBTOGBHF¿NJõUJS mk #VOBHÌSF ÌôSFODJEFôJöJNJTPOSBTTOGUBLJL[Ìô- DVOVCVMVOV[ SFODJTBZTOOFSLFLÌôSFODJTBZTOBPSBOOCVMV- OV[ ÷LJJLJ[L[HFMJQ L[HJEJODFL[ÌôSFODJOÑGVTVEFôJö- NF[&SLFLMFSJTFB[BMS4POEVSVNEB ,[\" &SLFL\" 5 N=OWFU=LJTF ,[ \" 10 d m-n n.d t+k n=d 3n - n n.d 3k + k n &SLFL\" 5 = 2 PMBSBLCVMVOVS m k 3n k CVMVOVS 5 2n 4k 8 =·= 3n k 3 3 2. 2 2 8 1. 3. 9 4. 2 3

www.aydinyayinlari.com.tr ORAN VE ORANTI 6. MODÜL ·/÷7&34÷5&:&)\";*3-*, 0SBOUOO²[FMMJLMFSJ %m/*m %m/*m a=c=e bd f #JSPSBOUEBJ¿MFSWFZBEõMBSLFOEJBSBTOEBZFS Ð¿MÐPSBOUT BDF=CEGCJ¿JNJOEFZB[- EFóJõUJSFCJMJS#VEVSVNEBPSBOMBSEFóJõTFCJMF MS PSBOUOOFõJUMJóJEFóJõNF[ a = c JTF a = b WFZB d = c bd cd ba ÖRNEK 8 PMBCJMJS BCD= ÖRNEK 5 PMEVôVOBHÌSF b + 2a PSBOOCVMVOV[ a=2 c-a b3 PMEVôVOBHÌSF a + b PSBOOCVMVOV[ a =L C= LWFD=LZB[BMN a-b b + 2a 7k 7 = = PMBSBLCVMVOVS ab c- a 3k 3 = = k PSBOUTPMVöVS ÖRNEK 9 23 BL CLJTF YZ[& a + b 2k + 3k 5k PSBOUTWFY- 2y +[=FöJUMJôJOFHÌSF YZ[ÀBS- QNOCVMVOV[ = = = - 5 PMBSBLCVMVOVS a - b 2k - 3k - k x =L Z=LWF[=LZB[BMN LmL+L= 12 &L= 12 &L=UÑS ÖRNEK 6 YZ[= 6.9.12 =PMBSBLCVMVOVS a = 1 WF x.a + b = 2 b3 b-a PMEVôVOBHÌSF YEFôFSJOJCVMVOV[ b = 3a JTF x.a + 3a =2 3a - a JTFYpB+ 3a = 4a &YpB= a & x =PMBSBLCVMVOVS ÖRNEK 7 ÖRNEK 10 a+b = 2 B=C=DWF 1 + 1 + 1 = 1 a-b 3 abc 4 PMEVôVOBHÌSF a.b PSBOOCVMVOV[ PMEVôVOBHÌSF BOOEFôFSJOJCVMVOV[ a2 + b2 kkk 3a +C= 2a -CJTF a = - 5b JTF a= , b= , c= - 5b.b - 5.b 2 5 237 111237 1 = = - PMBSBLCVMVOVS a + b + c = k + k + k = 4 & k = 48 ^ - 5b h2 + b2 2 26 k 48 26.b JTFB= = =PMBSBLCVMVOVS 22 5. –5 5 3 7 9. 24 6. 1 7. - 3 26

·/÷7&34÷5&:&)\";*3-*, 6. MODÜL ORAN VE ORANTI www.aydinyayinlari.com.tr %m/*m ÖRNEK 13 a = c = k PMEVóVOBHËSF a = b = c WFB-C+D= bd 234 a + c = a - c = k ES FöJUMJLMFSJOFHÌSF B+C+DOJOEFôFSJOJCVMVOV[ b+d b-d abc 3a - 2b 4c = = = k& = = =k 234 6 - 6 16 ÖRNEK 11 3a - 2b + 4c 48 = = = k=3 a=b=c 234 16 16 FõJUMJóJWFSJMJZPS a + b + c = 2k + 3k + 4k = 9k = 27 a +C+D=PMEVôVOBHÌSF B+DOJOEFôFSJOJCV- MVOV[ ÖRNEK 14 abc a+b+c a = c = e = 1 PMNBLÐ[FSF = = =k& =k bd f 4 234 9 B-D+F=WF-E+G= PMEVôVOBHÌSF CEFôFSJOJCVMVOV[ a +C+D=L=JTFL=UÑS ac a+ c = k & a +D=L=CVMVOVS = =k& 24 6 2a - c 3e 1 2a - c + 3e 1 = = = JTF = 2b - d 3f 4 2b - d + 3f 4 18 1 & = & 72 =C+ 24 &C= 24 2b + 24 4 ÖRNEK 12 %m/*m 1 = 2 = 3 =1 a = c = k PMEVóVOBHËSF 4x - y 4y - z 4z - x 10 bd PSBOUTOEBY+ y +[OJOEFôFSJOJCVMVOV[ a.c = a2 = c2 = k2 EJS 1+ 2+ 3 = 1 b.d b2 d2 4x - y + 4y - z + 4z - x 10 6 21 = 3^ x + y + z h = x + y + z = 10 &YZ[PMB- rBLCVMVOVS %m/*m ÖRNEK 15 NWFOTGSEBOGBSLMHFS¿FLTBZMBSPMTVO a = b = 4 WFY + y = xy3 PMEVôVOBHÌSF B2 +C2OJOEFôFSJOJCVMVOV[ a = c = k PMEVóVOB HËSF m.a + n.c = k 16 + b 16 + b 16 a b a a ==& =& = bd m.b + n.d 9 9 54 9 x + EJS xy y & + = 96 a b 11. 12. 4 13. 27 14. 24 15. 96

www.aydinyayinlari.com.tr ORAN VE ORANTI 6. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 16 ÖRNEK 19 a=c=e= 7 ^ 7 - 2 h WF ^ 7 + 2 h TBZMBS JMF EÌSEÑODÑ bd f PSBOUMPMBOTBZZCVMVOV[ PMEVôVOBHÌSF f.d.a PSBOOOEFôFSJOJCVMVOV[ b.e.c 5 7+ 2 & 5x = 7 - 2 & x = 1 = 7- 2 x f.d.a f d a f d a 1 1 1 = e.c.b = e.c.b = . . 7= b.e.c 77 7 ÖRNEK 17 ÖRNEK 20 B C DQP[JUJGHFS¿FLTBZMBSPMNBLÐ[FSF ,BSFõFLMJOEFLJCJSLBSUPOËODFõFLJMEFLJHJCJOVNBSBMBO- a = b = c WFB +C +D = ESMQEËSUFõQBS¿BZBBZSMZPS%BIBTPOSBOVNBSB- 234 MCËMÐNFõ OVNBSBMCËMÐNFõ OVNBSBMCËMÐN Fõ OVNBSBMCËMÐNJTFFõLBSFõFLMJOEFLJQBS- FõJUMJLMFSJWFSJMJZPS ¿BMBSBBZSMZPS #VOBHÌSF B+COJOEFôFSJOJCVMVOV[ 12 a 222 b c = = = 2 JTF 4 9 16 k 22 2 2a + b + 2c 2 196 =k & = k=2 49 49 a +C=L= 5.2 =PMBSBLCVMVOVS %m/*m 34 B C D TBZMBSOO EËSEÐODÐ PSBOUMT Y JTF WF OVNBSBM CËMÐNÐO QBS¿BMBS NBWJ SFOHF WF a = c PMVS OVNBSBMCËMÐNÐOQBS¿BMBSJTFLSN[SFOHFCPZBOZPS bx 4PO EVSVNEBLJ NBWJ SFOLMJ QBSÀB TBZTOO LSN[ SFOLMJQBSÀBTBZTOBPSBOOCVMVOV[ ÖRNEK 18 CÌMÑNQBSÀBNBWJ CÌMÑN LSN[ CÌMÑN WF TBZMBS JMF EÌSEÑODÑ PSBOUM PMBO TBZ- NBWJ CÌMÑN LSN[ ZCVMVOV[ M 4 + 16 20 10 = = = PMBSBLCVMVOVS K 9 + 25 34 17 4 20 JTF x =PMBSBLCVMVOVS = 10 x 1 17. 5 19. 1 10 16. 7 17

TEST - 1 0SBOUOO²[FMMJLMFSJ 1. x = 2 WFYZ[= 4. a - b = 1 2y a+b 4 PMEVôVOBHÌSF [LBÀUS PMEVôVOBHÌSF a2 - b2 LBÀUS 2a . b \" # $ % & \" 1 # 7 $ 8 % 2 & 11 2 15 15 3 5 2. m = 3 n = 4 n 4 k5 PMEVôVOBHÌSF m2 + n2 PSBOLBÀUS 5. a = 3 WF b = 3 k2 a+b 4 b+c 4 \" # 3 $ 4 % 5 & 5 PMEVôVOBHÌSF a PSBOLBÀUS 2 3 43 c \" # $ % 1 & 1 3 9 3. a = c = 2 PMEVôVOBHÌSF 6. BCDPMEVôVOBHÌSF bd ab + c2 a2 + bc f a + b p.f c - d p PSBOLBÀUS ac ÀBSQNOOTPO VDVLBÀUS \" 1 # 2 $ 3 % & 3 \" 5 # 12 $ 5 % 13 E 3 3 2 4 13 13 12 12 1. C 2. A 3. E 6 4. C 5. A 6. B

0SBOUOO²[FMMJLMFSJ TEST - 2 1. a = 1 WF c = 2 PMEVóVOBHËSF 4. a.b = a.c = b.c WF b5 a3 436 a + 2c a +C+D= b-c PMEVôVOBHÌSF BLBÀUS PSBOLBÀUS \" # $ % & \" 5 # 5 $ 7 % 7 & 1 12 13 12 13 2 2. a - b = 3 PMEVôVOBHÌSF 5. a = b = c = 2 a+b 4 xyz3 a2 - 7b2 a2 + ab PMEVôVOBHÌSF BöBôEBLJMFSEFOIBOHJTJZBOMö US PSBOLBÀUS \" y + z = 3 # 2a2 - 3bc = 4 b+c 2 2x2 - 3yz 9 $ a . b + c2 = 4 % a3 = x3 xy + z2 9 8 27 \" 3 # $ 2 % 7 & 41 & a2 + b2 + c2 = 2 4 3 8 56 x2 + y2 + z2 3 3. BYCZD[WF 1 + 1 – 1 = 2 6. m + 1 = 2 , n + 1 = 3 PMEVôVOBHÌSF xyz nm m2 + mn n2 PMEVôVOBHÌSF a +C-DLBÀUS PSBOLBÀUS \" # $ 1 % 1 & 1 \" 2 # 10 $ 2 % 10 & 10 20 2 9 33 9 1. D 2. A 3. B 7 4. B 5. E 6. D

TEST - 3 0SBOUOO²[FMMJLMFSJ 1. b + 2c = a + 2b - 6 = 2a + c + d = 3 4. x . z . n = 3 , m = 6 , x = 12 ac b ymk n k PMEVôVOBHÌSF ELBÀUS y PMEVôVOBHÌSF PSBOOFEJS \" # $ % & z \" # $ 3 % & 2 2 3 2. m = n = k WFN- O+L= 5. B CD Z+ a = b = k 2 33 27 PMEVôVOBHÌSF N+ n +LLBÀUS oMEVôVOBHÌSF 2a + 7b JGBEFTJBöBôEBLJMFS- EFOIBOHJTJOFFöJUUJS \" # $ % & A 9 k # 8 k $ 7 k % 3 k & 2 k 3. a = c = e = 2 x + y x - y xy bd f 3 6. = = B-D+F=WF 11 3 56 E-G= PMEVôVOBHÌSF Z-YLBÀUS PMEVôVOBHÌSF BLBÀUS \" # $ % & \" # 20 $ 20 % 40 & 40 3 939 1. E 2. E 3. E 4. E 5. A 6. B

0SBOUOO²[FMMJLMFSJ TEST - 4 1. y = 4 PMEVôVOBHÌSF 4. 2x + 5 = 4 5x =[WF z7 3y 3y + 5 = 3 x+y x-y 2x PSBOLBÀUS PMEVôVOBHÌSF x PSBOLBÀUS y $ % 21 & \" # $ % & 2 \" # 2. \"INFU #VSDVWF$BOFSJTJNMJÐ¿BSLBEBõMJSBZ 5. #JSLJUBQMLUBLJBLBEFNJLLJUBQMBSOTBZTOOEJóFS BSBMBSOEB QBZMBõZPSMBS \"INFU #VSDVhEBO MJSB LJUBQMBSBPSBO 5 EJS GB[MB #VSDVJTF$BOFShEFOMJSBGB[MBQBSBBMZPS 2 #VOBHÌSF \"INFUhJOQBSBTOO $BOFShJOQBSBT- #VOBHÌSF LJUBQMLUBLJUÑNLJUBQMBSOTBZTFO OBPSBOLBÀUS B[LBÀPMVS \" # $ % & \" # 6 $ 7 % 8 & 9 5 5 55 3. B C D E LD3 6. a -BC= B -C = PMEVôVOBHÌSF a PSBOLBÀUS b a = c = k JLFO 3a + mc = k \" 1 # 1 $ % & bd 3b + 5 3 2 PMEVôVOBHÌSF NLBÀUS \" 5 B 3 c $ 5 % E & D c 5d 1. E 2. C 3. C 9 4. A 5. D 6. E

·/÷7&34÷5&:&)\";*3-*, 6. MODÜL ORAN VE ORANTI www.aydinyayinlari.com.tr ORAN VE ORANTI - II %PôSV0SBOU 5FST0SBOU TANIM TANIM B WF C ¿PLMVLMBSOEBO B BSUBSLFO C EF BZO B WF C ¿PLMVLMBSOEBO B BSUBSLFO C EF BZO PSBOEB BSUZPSTB WFZB B B[BMSLFO C EF BZO PSBOEB B[BMZPSTB WFZB B B[BMSLFO C EF BZO PSBOEBB[BMZPSTBBJMFCEPóSVPSBOUMEFOJS PSBOEBBSUZPSTBBJMFCUFSTPSBOUMEFOJS a = k WFZBB=CpLEJS L! R+ b = k WFZBBpC=LEJS L! R+ b a b b a = b·k b= k a a a ÖRNEK 1 ÖRNEK 3 YJMFZEPóSVPSBOUMES B+TBZT b TBZTJMFUFSTPSBOUMES #VOBHÌSF Y=JLFO Z=JTFZ=JLFOYJOEF- 2 ôFSJOJCVMVOV[ a =JLFOC=PMVZPSTBC=JLFOBOOEFôFSJOJ x 63 CVMVOV[ y = k & 4 = k = 2 PMVS x3 b4 B p L& p L = & x = 36 24 2 22 57 B p &B& a = 23 ÖRNEK 2 ÖRNEK 4 #JSÐ¿HFOJOLFOBSMBS WFJMFPSBOUMES WFJMFUFSTPSBOUMJLJEPôBMTBZOOUPQMBNJTF #V ÑÀHFOJO ÀFWSFTJ DN PMEVôVOB HÌSF FO V[VO CVJLJTBZOOGBSLOCVMVOV[ LFOBSOFOLTBLFOBSEBOLBÀDNV[VOPMEVôVOVCV- MVOV[ ·ÀHFOJOLFOBSMBSL L L kk 10k = 30 L+L+L= 54 &L=UÑS + = 30 & L–L=L=p=DNPMVS 37 21 63 63 LJTF - = 21 –CVMVOVS 37 1. 36 2. 15 7 4. 12 3. 3

www.aydinyayinlari.com.tr ORAN VE ORANTI 6. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 5 %m/*m ;FISB)BONhOFWJOEFCVMVOBO¿BNBõSNBLJOFTJOJOJML öLJWFZBEBIBGB[MBPSBOCVMVOEVSBOPSBOUMBSB Ð¿ QSPHSBNOO ZLBNB TÐSFMFSJ TSBTZMB WF JMF CJMFõJLPSBOUEFOJS PSBOUM LVSVUNB NBLJOFTJOJO JML Ð¿ QSPHSBNOO LVSVU- NBTÐSFMFSJJTF WFJMFPSBOUMES BTBZTCJMFEPóSV DJMFUFSTPSBOUMJTF ¥BNBõSNBLJOFTJQSPHSBNEBLJLB LVSVUNBNBLJ- a · c = k õFLMJOEFHËTUFSJMJS OFTJJTFQSPHSBNEBLJLBEBUBNBNMZPS b ;FISB )BON ¿BNBõSMBS QSPHSBNOEB ZLBZQ QSPHSBNOEBLVSVUVZPS ÖRNEK 7 #VOBHÌSF ZLBNBTÑSFTJOJOLVSVUNBTÑSFTJOFPSB- OOCVMVOV[ BmTBZT C+JMFUFST DJMFEPóSVPSBOUMES a = C=JLFOD=PMEVôVOBHÌSFB= D= 3 4 1. 2. 3. 1. 2. 3. JLFOCEFôFSJOJCVMVOV[ ÇZ KZ 2k 3k 4k 3x 5x 6x L= = 5x ^ a – 1 h^ b + 1 h =k & 12 · 4 =6=k L== x 3 8 c ^ 5 – 1 h^ b + 1 h =6& 4·^b+1h =6& b=5 Ç^ 2 h 3.k k 15 3 ^ 3 4 h3 4 4PSVMBO K^ 1 h = 3.x = x = 20 = 4 CVMVOVS ÖRNEK 6 ÖRNEK 8 WFJMFPSBOUMJLJTBZOOLÐQMFSJUPQMBNEJS DJWDJWHÑOEFHSZFNZFEJôJOFHÌSF DJWDJWJO #VOBHÌSF CVTBZMBSOLBSFMFSJGBSLLBÀPMBCJMJS HÑOEFLBÀHSZFNZFEJôJOJCVMVOV[ 4BZMBSLWFLPMTVO 100 2 · 3 L 3 + L 3 =L3 =&L3 =&L= 2 = & Y & YHS L 2 - L 2 =L2 x 3·5 WFZB L 2 - L 2 = -L2 PMVQPMBCJMJS 3 6. 11 7. 5 5. 4

·/÷7&34÷5&:&)\";*3-*, 6. MODÜL ORAN VE ORANTI www.aydinyayinlari.com.tr \"SJUNFUJL0SUBMBNB (FPNFUSJL0SUBMBNB TANIM TANIM a B B BnHJCJOUBOFTBZOOBSJUNFUJL a B B BnHJCJOUBOFTBZOOHFPNFU- PSUBMBNBT SJLPSUBMBNBT A = a1 + a2 + a3 + . . . + an EJS G = n a1 · a2 · a3 · . . . · an EJS n a = x PSBOUTO TBóMBZBO Y QP[JUJG HFS¿FL BJMFCOJOBSJUNFUJLPSUBMBNBT a + b EJS xb 2 TBZTOB B JMF C TBZTOO HFPNFUSJL PSUBT WFZBPSUBPSBOUMTEFOJS ÖRNEK 9 x = a·b #JSËóSFODJNBUFNBUJLTOBWMBSOOJMLJLJTJOEFOWF ÖRNEK 12 BMNõUS #VÌôSFODJ TOBWEBOLBÀBMNBMLJOPUPSUBMBNB- JMFOJOPSUBPSBOUMTOCVMVOV[ TPMTVO x = 8 · 50 S +S +S 123 = 50 3 20 + 60 + S 3 & = 50 & S = 70 PMNBM 33 ÖRNEK 10 ÖRNEK 13 ËóSFODJOJOZBõPSUBMBNBTUJS 8 + 2 15 JMF 8 - 2 15 TBZMBSOOHFPNFUSJLPSUB- #VHSVCBZBöMBSPMBOLBÀÌôSFODJEBIBLBUMSTB MBNBTOCVMVOV[ ZBöPSUBMBNBTPMVS 8 + 2 15 = 5 + 3 WF 8 - 2 15 = 5 - 3 Yaﬂlar toplam› = ^ 5 + 3 h·^ 5 – 3 h = 5 - 3 = 2 #BöMBOHÀUB 6 = 15 JTFZBöMBSUPQMBN CVMVOVS 90 + 10x = 13 &YY x+6 & 3x = 12 &YÌôSFODJ ÖRNEK 11 ÖRNEK 14 #JSPLVMEBLJËóSFUNFOJOZBõPSUBMBNBTËóSFO- YJMFTBZTOOBSJUNFUJLPSUBMBNBT ZJMFTBZTOO DJOJOZBõPSUBMBNBTUJS #VOB HÌSF PLVMEBLJ ÌôSFUNFO WF ÌôSFODJMFSJO ZBö HFPNFUSJLPSUBMBNBTEVS PSUBMBNBTOCVMVOV[ #VOBHÌSF x PSBOOCVMVOV[ y 20 · 35 + 80 · 15 1900 x+ 5 = = 19 = 4 & x = 3, y · 3 = 9 & y = 27 20 + 80 100 2 x31 y = 27 = 9 9. 4 11. 19 12 12. 13. 2 1 14. 9

www.aydinyayinlari.com.tr ORAN VE ORANTI 6. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 15 ÖRNEK 17 Y JMF Z OJO HFPNFUSJL PSUBMBNBT BSJUNFUJL PSUBMBNB- YWFZQP[JUJGUBNTBZPMNBLÐ[FSF Y+ZJMFY+ y TBZ- TUÐS MBSOOBSJUNFUJLWFHFPNFUSJLPSUBMBNBMBSFõJUUJS #VOBHÌSF Y2 + y2EFôFSJOJCVMVOV[ #VOBHÌSF Y+ZFOB[LBÀPMBCJMJS x · y = 3 &YpZ= 9 YZYZJTFZYJTFYZZZZJÀJO x+ y ZPMVSTBFOLÑÀÑLPMVS = 4 & x + y = ÖRNEK 18 2 x2 + 2xy + y2 = 64 & x2 + y2 = 64 – Y Z [QP[JUJGHFSÀFLTBZMBSPMNBLÑ[FSF YpZp[=JTF Yy +Zz + xz & x2 + y2 = 46 UPQMBNOOFOLÑÀÑLUBNTBZEFôFSJOJCVMVOV[ A.O ã G.O ÖRNEK 16 2 22 2x y + 4y z + xz B JMF C OJO IFN BSJUNFUJL IFN EF HFPNFUSJL PSUBMBNB- $3 22 2 TYFFõJUUJS 2·x ·y·4y ·z·x·z #VOBHÌSF B CWFYBSBTOEBLJCBôOUZCVMVOV[ 3 a+b ·y + 4y z + x·z x = WFY a · b 2·x $3 333 2 a+b 3 8·x ·y ·z = a·b &a+ b= 2 a·b pY2pZpZ2pY2[ãJTFFOLÑÀÑLUBNTBZEVS 2 a2 +BC+C2 =pBpC& a2 -BC+C2 = ÖRNEK 19 B-C 2 =JTFB=C:BOJB=C=YUJS YWFZQP[JUJGHFSÀFLTBZMBSJÀJO x · y + 28 x·y JGBEFTJOJOBMBCJMFDFôJFOLÑÀÑLUBNTBZEFôFSJOJCV- MVOV[ %m/*m 28 x·y + x·y a B B BnHJCJOUBOFTBZJ¿JO 28 $ x·y x·y 2 Aritmetik ortalama Geometrik ortalama 28 6 4 4 4 4(4A7.O)4 4 4 448 x·y + x·y $ 2 28 a1 + a2 + a3 + ... + an 6 4 4 4 4(4A7.O)4 4 4 448 $ n a1 · a2 · a3 ·...· an 28 n x·y + x·y $ 112 EJS FOLÑÀÑLUBNTBZEFôFSJOJBMS \"SJUNFUJLPSUBMBNB HFPNFUSJLPSUBMBNBEBOCÐ- ZÐLZBEBFõJUUJS\"0$(0 15. 46 16. BCY 13 17. 7 19. 11

TEST - 5 %PôSV0SBOU5FST0SBOU 1. WFJMFPSBOUMJLJTBZOOUPQMBNPMEV- 4. BTBZTC+JMFEPóSVC-JMFUFSTPSBOUMES ôVOBHÌSF CVTBZMBSOÀBSQNLBÀUS a =JÀJOC=PMEVôVOBHÌSF B=JÀJOC LBÀUS \" # $ % & \" 6 # 7 $ 8 % 9 & 5 5 55 2. Y+JMFZ-EPóSVPSBOUMES 5. BTBZTCWFDJMFEPóSV EOJOLBSFTJJMFUFST PSBOUMES x =JLFOZ=PMEVôVOBHÌSF Z=JLFOY a = b = 1 D=JLFOE=PMVZ PSTBPSBO- LBÀUS 4 A 1 # 1 $ 1 % UTBCJUJLBÀUS 8 4 2 & \" # $ % & 3. x +JMFZ-UFSTPSBOUMES 6. a = 3 C=D DE= x =JÀJOZ=PMEVôVOBHÌSF Z=JÀJOY b LBÀUS PMEVôVOBHÌSF BöBôEBLJMFSEFOIBOHJTJZBOMö- US \" # $ % & \" BJMFEUFSTPSBOUMES # CJMFEUFSTPSBOUMES $ BJMFDEPóSVPSBOUMES % CJMFDEPóSVPSBOUMES & BJMFCUFSTPSBOUMES 1. D 2. A 3. A 14 4. B 5. D 6. E

%PôSV0SBOU5FST0SBOU TEST - 6 1. N O LTBZMBSTSBTZMB TBZMBSJMF 4. #JSPLVMEBLJËóSFODJTBZTÐ¿CBTBNBLMCJSTBZES PSBOUMWFN+ n -L=PMEVôVOBHÌSF LLBÀ- #VPLVMEBLJFSLFLWFL[ËóSFODJTBZMBS WF US TBZMBSJMFPSBOUMES #VOBHÌSF ÌôSFODJTBZTFOB[LBÀPMBCJMJS \" # $ % & \" # $ % & 2. WFJMFUFSTPSBOUMPMBOÑÀTBZOOUPQ- 5. Y Z [TBZMBSTSBTZMB WFJMFPSBOUMES MBNPMEVôVOBHÌSF CVTBZMBSOFOLÑÀÑL \"ZO TBZMBS TSBTZMB BöBôEBLJMFSEFO IBOHJTJ PMBOLBÀUS JMFUFSTPSBOUMES \" # $ % & \" # $ % & 3. #JSÑÀHFOJOEöBÀMBSTSBTZMB TBZMB- 6. BTBZTCTBZTJMFUFST DTBZTJMFEPóSVPSBO- S JMF PSBOUM PMEVôVOB HÌSF JÀ BÀMBS TSBTZMB UMES IBOHJTBZMBSJMFPSBOUMES BTBZTB[BMUMQDTBZTBSUUSME- \" # $ ôOEBPSBOUTBCJUJOJOEFôJöNFNFTJJÀJOCEFLJ EFôJöJNOFPMNBMES % & \" BSUUSMNBMES # BSUUSMNBMES $ B[BMUMNBMES % B[BMUMNBMES & B[BMUMNBMES 1. C 2. B 3. D 15 4. E 5. E 6. B

TEST - 7 %PôSV0SBOU5FST0SBOU 1. CJOMJSBWFJMFEPôSVJMFUFSTPSBOUM 4. #JSËóSFODJOJOJMLJLJTOBWOPUMBSUPQMBNEVS PMBDBLCJÀJNEFQBSÀBZBBZSMSTB CÑZÑLQBS- #VÌôSFODJOJOÑÀTOBWTPOVOEBOPUPSUBMBNB- ÀBLBÀCJOMJSBPMVS TOO PMNBT JÀJO TPO TOBW OPUV LBÀ PMNBM- ES \" # $ % & \" # $ % & 2. #JS JõJ Jõ¿J HÐOEF TBBU ¿BMõBSBL HÐOEF ZB 5. FSLFLL[ËóSFODJOJOCVMVOEVóV CJSTOGUBLJ QBCJMNFLUFEJS L[MBSOCPZPSUBMBNBT DN FSLFLMFSJOCPZPS UBMBN BT DNEJS \"ZOLBQBTJUFEFJöÀJHÑOEFTBBUÀBMöBSBL CVJöJLBÀHÑOEFZBQBS #VOBHÌSF CVTOGUBLJUÑNÌôSFODJMFSJOCPZPS- UBMBNBTLBÀTBOUJNFUSFEJS \" # $ % & \" # $ % & 3. LJõJHÐOEFTBBU¿BMõBSBLHÐOEFLPMUVLZB 6. UBOFUBNTBZOOBSJUNFUJLPSUBMBNBTEJS\"Z- QBC JMNFLUFEJS SDBUBOFUBNTBZOOBSJUNFUJLPSUBMBNBTUÐS \"ZOOJUFMJLUFLJöJHÑOEFFSTBBUÀBMöBSBL #VOB HÌSF UÑN TBZMBSO BSJUNFUJL PSUBMBNBT LPMUVôVLBÀHÑOEFCJUJSJS LBÀUS \" # $ % & \" # $ % & 1. E 2. B 3. C 16 4. D 5. D 6. D

\"SJUNFUJLWF(FPNFUSJL0SUBMBNB TEST - 8 1. 6 - 4 2 ve 6 + 4 2 4. ¶¿UBOFQP[JUJGTBZOOHFPNFUSJLPSUBMBNBT 3 65 TBZMBSOO HFPNFUSJL PSUBT BöBôEBLJMFSEFO UJS IBOHJTJEJS #VOB HÌSF BSJUNFUJL PSUBMBNBTOO BMBCJMFDFôJ FOLÑÀÑLUBNTBZEFôFSJLBÀUS \" # $ % & 4 2 \" # $ % & 2. B C D TBZMBSOO JLJõFSMJ HFPNFUSJL PSUBMBNBMBS 5. YWFZQP[JUJGHFS¿FLTBZMBSJ¿JO x = 2 UÐS EVS y3 #VOBHÌSF #VOB HÌSF B C WF D TBZMBSOO HFPNFUSJL PS x + 17 UBMBNBTLBÀUS y \" 4 3 3 # $ 6 3 3 JGBEFTJOJOBMBCJMFDFôJFOLÑÀÑLUBNTBZEFôFSJ LBÀUS % & \" # $ % & 3. a JMF C OJOBSJUNFUJLPSUBMBNBT BJMFC 6. BWFCQP[JUJGUBNTBZMBSPMNBLÐ[FSF B+ JMF TBZMBSOOHFPNFUSJLPSUBMBNBTEVS C + TBZMBSOO BSJUNFUJL WF HFPNFUSJL PSUBMB- #VOBHÌSF a +COJOEFôFSJLBÀUS NBMBSFõJUUJS \" # $ % & #VOBHÌSF BpCOJOEFôFSJLBÀUS \" # $ % & 1. A 2. B 3. C 17 4. B 5. C 6. C

·/÷7&34÷5&:&)\";*3-*, 6. MODÜL ORAN VE ORANTI www.aydinyayinlari.com.tr ORAN VE ORANTI - III 0SBOm0SBOU1SPCMFNMFSJ %m/*m %m/*m &óFS¿PLMVLMBSUFSTPSBOUMJTF 0SBOUQSPCMFNMFSJOJ¿Ë[FSLFO ËODF¿PLMVLMBSO artar a D C B[BMS OBTMEFóJõUJóJOFCBLMS&óFS EPóSVPSBOUWBS- E sa; a D 5FST0SBOUBpD=CpE artar C artar E %PóSV0SBOUBpE=CpD ÖRNEK 4 ÖRNEK 1 #JSNBLJOFCJSÐSÐOÐEBLJLBEBÐSFUJZPS .BLJOFOJO ÀBMöNB I[ BSUSMSTB BZO ÑSÑOÑ 5P[ õFLFSJO HSBN Y TL ZF ZBSN LJMPHSBN LBÀEBLJLBEBÑSFUJS Y-TL ZFTBUMZPS #VOBHÌSF YJOEFôFSJOJCVMVOV[ L 60 L Y 300 gr Y ppY YEBLJLBCVMVOVS 500 gr Y- 3 YYmJTFYCVMVOVS ÖRNEK 2 ÖRNEK 5 )FS HS VO JÀJO HSBN öFLFS LVMMBOMBSBL ZBQMBO #JSBSBDOTBBUUFLNI[MBTBBUUFBMEôZPMV HSBNMLCJSLBSöNEBLBÀHSBNöFLFSWBSES TBBUUF HJUNFTJ JÀJO PSUBMBNB I[ TBBUUF LBÀ LN PM- NBMES LN TBBU TBBU 120 ·3 =p 36 gr HSBNöFLFS = 90 216 gr Y pY&Y ÖRNEK 3 ÖRNEK 6 #JSBSBÀNFUSFZJ 1 EBLJLBEBHJUUJôJOFHÌSF #JSHSVQJõ¿JCJSJõJHÐOEFCJUJSFCJMNFLUFEJS 3 &ôFS JöÀJ EBIB PMTBZE BZO JöJ HÑOEF CJUJSFCJM- EJLMFSJOFHÌSFCVHSVQUBCBöMBOHÀUBLBÀJöÀJWBSES NFUSFZJLBÀTBOJZFEFHJEFS NFUSF TO Y 16 NFUSF Y+ 2 12 TO pY Y Y 1. 9 2. 6 3. 80 18 4. 50 5. 90 6. 6

www.aydinyayinlari.com.tr ORAN VE ORANTI 6. MODÜL ·/÷7&34÷5&:&)\";*3-*, %m/*m ÖRNEK 10 #JSCJSJOFCBóMEJõMJ¿BSLMBSEBEFWJSTBZTJMFEJõ UBOF TBZOO BSJUNFUJL PSUBMBNBT UÐS #V TBZMBSB TBZTUFSTPSBOUMES BSEõL JLJ UFL TBZ EBIB FLMFOEJóJOEF UBOF TBZOO BSJUNFUJLPSUBMBNBTPMVZPS ÖRNEK 7 #VOB HÌSF FLMFOFO JLJ TBZEBO LÑÀÑL PMBOO CVMV- OV[ #JSCJSJOFCBóMÐ¿¿BSLUBOCÐZÐLPMBOUVSEËOEÐóÐOEF PSUBODBUVS LÐ¿ÐLPMBOJTFUVSEËONÐõUÐS ÷MLUPQMBN&p= ·ÀÀBSLUBLJUPQMBNEJöTBZTPMEVôVOBHÌSFCÑ- ZÑLPMBOÀBSLUBLBÀEJöPMEVôVOVCVMVOV[ YJMF Y+ & 48 + 2x + 2 = 6 & x = 17 4SBZMB JMFUFSTJTF WFJMFEPôSVPSBOUM- 14 ESL+L+L= 141 &L= 3 L=PMBSBLCVMVOVS ÖRNEK 11 ÖRNEK 8 :BõPSUBMBNBTPMBOCJSUPQMVMVLUBOËODFZBõPSUBMB- NBT PMBO JLJ LJõJ BZSMZPS 4POSB ZBõ PSUBMBNBT WF JMF UFST PSBOUM PMBO TBZMBS TSBZMB FO LÑ- PMBOLJõJLBUMZPSWFTPOEVSVNEBUPQMVMVóVOZBõPSUB- ÀÑL IBOHJ QP[JUJG UBN TBZMBSMB EPôSV PSBOUM PMEV- MBNBTPMVZPS ôVOVCVMVOV[ #VOBHÌSF CBöMBOHÀUBUPQMVMVôVOLBÀLJöJPMEVôV- OVCVMVOV[ WF\"&LPL\"EVS &,0, = YLJöJ\"JMLZBöUPQMBN\"Y 3x = 2y =[=j x = Z= [= 6 20x - 18·2 + 5·12 ÖRNEK 9 & = 18 x+ 3 #JS USBLUËSÐO ËO UFLFSMFóJO ¿FWSFTJOJO BSLB UFLFSMFóJO ¿FWSFTJOFPSBO 3 UJS &Y+ 24 =Y+ 54 & x = 15 5 ÖRNEK 12 5SBLUÌSJMFNFUSFMJLZPMHJEJMEJôJOEFLÑÀÑLUFLFS- MFL CÑZÑLUFO UVS GB[MB EÌOEÑôÑOF HÌSF LÑÀÑL UF- Y Z [LÐ¿ÐLUFOCÐZÐóFEPóSVTSBMBONõBSEõLÐ¿QP- LFSMFôJOÀFWSFTJLBÀNFUSFEJS [JUJG¿JGUTBZPMNBLÐ[FSF ZJMF[OJOHFPNFUSJLPSUBMBNB- T YJMFZOJOHFPNFUSJLPSUBMBNBTOO 6 LBUES ²O\"L \"SLB\"L LpY=Lp Y+ JTFY= 6 2 =Lp&L= 2 #VOB HÌSF Y Z WF [ OJO BSJUNFUJL PSUBMBNBTO CV- ,ÑÀÑLÀFWSF=L=p=CVMVOVS MVOV[ 66 y·z = x·y · & y·z = x·y · 24 3 &[=Yp & x =LWF[=L 2 Y Z [&L L+ L+JTFL+ 4 =L&L= 4 30 Y Z [& JTFPSUBMBNBT =EVS 3 7. WF 9. 6 19 17 11. 15 12.

·/÷7&34÷5&:&)\";*3-*, 6. MODÜL ORAN VE ORANTI www.aydinyayinlari.com.tr ÖRNEK 13 ÖRNEK 15 #JSUFS[JBHÐOCPZVODBHÐOEFHËNMFL CHÐOCPZVO- ±óSFUNFOJ\"ZõFhZFTPSVEBOPMVõBOCJSQSPKFËEF- DBJTFHÐOEFHËNMFLEJLNJõUJS WJWFSNJõUJS\"ZõFIFSHÐOFõJUTBZEBTPSV¿Ë[FSFLËEF- WJOJCJUJSNFLJTUJZPS\"ZõFËEFWFCBõMBELUBOTPOSBLBMBO a HCPMNBLÑ[FSF UFS[JOJOHÑOMÑLPSUBMBNBEJLUJôJ TPSVMBSO[BNBOBHËSFEFóJõJNJBõBóEBLJEPóSVTBMHSB- HÌNMFLTBZTLBÀGBSLMUBNTBZEFôFSJBMS GJLUFWFSJMNJõUJS a =CPMVSTB 20 + 30 = 25 PMVS 4PSVTBZT 1200 2 300 a ãCJTFPSUBMBNBHÌNMFLTBZTJMFBSBTOEB EBIJM PMVS{ } \"GBSLMEFôFS ;BNBO HÐO BMS 6 \"ZöFÌEFWJOFQB[BSUFTJCBöMBEôOBHÌSFIBOHJHÑO CJUJSNJöUJS ÖRNEK 14 HÑOÑOTPOVOEBTPSVTVLBMNöJTFIFSHÑO TPSVÀÌ[NÑöUÑS#VOBHÌSFÌEFWJHÑOCJUNJöUJS ôFLJMEF CJS LFOBS CS PMBO LBSFMFS JMF CFMJSMJ CJS LVSBMB %PMBZTZMBQB[BSUFTJHÑOÑCJUFS HËSFPMVõUVSVMNVõBENMBSBTBIJQCJSËSÐOUÐWFSJMNJõUJS ÖRNEK 16 \"õBóEBLJEBJSFHSBGJLUFCJSFMNBMVOLVSBCJZFTJOJOZBQ- NOEBLVMMBOMBONBM[FNFMFSJOUPQMBNBóSMóOONBM[F- NF¿FõJEJOFHËSFEBóMNHËTUFSJMNJõUJS &MNB BEN BEN BEN :Bó 4ÐU 50° 6O 40° 140° \"INFUCJSLFOBSCSPMBOBEFULBSFMFWIBJMFõFLJMEF WFSJMFOLVSBMBHËSFIFSBENEBZFOJLBSFMFWIBMBSPMVõ- 100° UVSNVõUVS ôFLFS #VOBHÌSF \"INFUhJOPMVöUVSEVôVBENMBSOBMBOPS- UBMBNBMBSLBÀCS2EJS LBSFJMFBENPMVöUVSVMVS #JSLVUVLVSBCJZFZBQNOEBLVMMBOMBOVOWFZBóNJLUBS- MBSUPQMBNHSBNES 1. ad›mda 1 _ b #VOBHÌSF CJSLVUVLVSBCJZFZBQNOEBLBÀHSBNFM- b NBLVMMBOMNöUS 2. ad›mda 4 bb 1+ 4 + 9 + 16 + 25 55 = 11CS2 3. ad›mda 9 `\" = b5 5 4. ad›mda 16 b bb 5. ad›mda 25 a HS =HSBNFMNB 13. 5 14. 11 15. 1B[BSUFTJ 16.

0SBO0SBOU1SPCMFNMFSJ TEST - 9 1. 5VSHBZOZBõOO&SBZOZBõOBPSBO 2 &SBZO 4. #JSBSB¿5-MJLCFO[JOJMFLNZPMBMZPS 5 #VBSBÀLNMJLZPMVMJUSFCFO[JOJMFHJUUJôJOF ZBõOO$BOOZBõOBPSBO 3 UÐS HÌSFCFO[JOJOMJUSFGJZBULBÀ5-EJS 4 \" # $ % & #VOBHÌSF ÑÀÑOÑOZBöMBSUPQMBNOOUBNTBZ EFôFSJ FOB[LBÀUS \" # $ % & 2. MJSBZ \" # $ BSBTOEB ËZMF QBZMBõUSO[ LJ 5. ¶¿ LJõJ WF TBZMBS JMF PSBOUM PMBDBL õFLJM- \" #EFOMJSBGB[MBWF# $EFOMJSBGB[MBPM EFQBSBLPZBSBLCJSõJSLFULVSVZPS)FSZMTPOVOEB TVO PSUBLMBSTFSNBZFPSBOMBSOEBLºSQBZBMBDBLMBSES #VOBHÌSF B PSBOLBÀUS :MTPOVOEBFOB[LºSQBZOBTBIJQPSUBL5- BMNõUS C #VOB HÌSF ZM TPOVOEB öJSLFU UPQMBN LBÀ 5- L»SFUNJöUJS \" # $ % & \" # 6 $ 7 % 8 & 9 5 5 55 3. 'OEôO HSBN 5- PMEVôVOB HÌSF 6. #JSLPõVDVTBOJZFEFNFUSFLPõVZPS HSBNLBÀ5-EJS #VOB HÌSF LPöVDV NFUSFZJ LBÀ EBLJLBEB LPöBS \" # $ % & \" 9 # $ 5 % & 7 5 2 2 1. C 2. C 3. C 21 4. B 5. C 6. B

TEST - 10 0SBO0SBOU1SPCMFNMFSJ 1. #JSBóBDOCPZV NJLFOHËMHFTJOJOCPZV N 4. #JSCPZBDHÐOEFTBBU¿BMõBSBLCJSFWJHÐOEF EJS CPZVZPS #VBóBDOZBOOEBCVMVOBOCBõLBCJSBóBDOBZO &ôFSHÑOEFTBBUÀBMöTBZEBZOFWJOJLJLBU [BNBOEBËM¿ÐMFOHËMHFTJOJOCPZVTBOUJNFUSF- CÑZÑLMÑôÑOEFLJFWJLBÀHÑOEFCPZBSE EJS \" # $ % & #VOBHÌSF BôBDOCPZVLBÀNFUSFEJS \" # $ % & 2. 4BCJUI[MBHJEFOCJSBSBDOEFQPTVOEBLJZBLUIFS 5. #JSCJSJOJ ¿FWJSFCJMFO Ð¿ EJõMJ ¿BSLUBO CJSJODJTJ LF[ LNEFMJUSFB[BMNBLUBES EËOEÐóÐOEF JLJODJTJ LF[ Ð¿ÐODÐTÐ LF[ EËO NFLUFEJS %FQPTVOEBMJUSFZBLUCVMVOBOCJSBSBÀBZO ZPMEBBZOTBCJUI[MBLBÀLNZPMHJEFCJMJS ·ÀÀBSLUBLJUPQMBNEJöTBZTPMEVôVOBHÌ- SF JLJODJÀBSLUBLJEJöTBZTLBÀUS \" # $ % & \" # $ % & 3. )FSHSBN9NBEEFTJOFHSBN:NBEEFTJFLMF- 6. #JSUSBLUËSÐOËOUFLFSMFóJOJOZBS¿BQJMF BSLBUF OFSFLCJSLBSõNIB[SMBOZPS LFSMFóJOJO ZBS¿BQ JMF PSBOUMES 5SBLUËS r NFUSFZPMBMEóOEBËOUFLFSMFLBSLBUFLFSMFLUFO #VOB HÌSF HSBN LBSöNEB LBÀ HSBN : LF[GB[MBEËOÐZPS NBEEFTJWBSES #VOBHÌSF ÌOUFLFSMFôJOZBSÀBQLBÀNFUSFEJS \" # $ % & \" # $ 3 % & 1 2 2 1. D 2. D 3. C 22 4. B 5. D 6. C

0SBO0SBOU1SPCMFNMFSJ TEST - 11 1. LJõJHÐOZFUFDFLFS[BLJMFCJSLBNQUBCVMVO 4. %ËSULBSEFõJOCPZPSUBMBNBTDNEJS NBLUBES &O LTB LBSEFöJO CPZV DN PMEVôVOB HÌSF HÑOTPOSBLBNQUBOLJöJBZSMSTBLBMBOFS- EJôFSLBSEFöMFSJOCPZMBSUPQMBNLBÀNFUSFEJS [BL LBNQUBLBMBOLJöJMFSFLBÀHÑOZFUFS \" # $ % & \" # $ % & 2. TBZOOBSJUNFUJLPSUBMBNBTEJS#VTBZMBS 5. Y Z [ QP[JUJGUBNTBZMBSOOBSJUNFUJLPSUB- EBOÐIBSJ¿EJóFSTBZMBSOBSJUNFUJLPSUBMBNBT MBNBTEJS PMVZPS #VOBHÌSF Y ZWF[UBNTBZMBSOOBSJUNFUJLPS- #VOBHÌSF ÑÀTBZOOUPQMBN LBÀUS UBMBNBTLBÀUS \" # $ % & \" # $ % & 3. BUBOFQP[JUJGUBNTBZOOBSJUNFUJLPSUBMBNBTCEJS 6. \"MJHJSEJóJTPOTOBWEBOQVBOBMSTBUÐNTOBW- #V TBZMBSB BSJUNFUJL PSUBMBNBT B PMBO C UBOF MBSEBO BMEó QVBOMBSO PSUBMBNBT TPO TOBW- UBNTBZFLMFOJSTFZFOJTBZMBSOBSJUNFUJLPSUB- EBOQVBOBMSTBQVBOMBSOPSUBMBNBTPMBDBL- MBNBTBöBôEBLJMFSEFOIBOHJTJPMVS US \" a + b #VOBHÌSF TPOTOBWEBIJMPMNBLÑ[FSF\"MJLBÀ a.b TOBWBHJSNJöUJS # 2.a.b \" # $ % & a+b $ BJMFCOJOBSJUNFUJLPSUBMBNBT % BJMFCOJOHFPNFUSJLPSUBMBNBT & BJMFCOJOBSJUNFUJLPSUBMBNBT 1. A 2. C 3. B 23 4. B 5. B 6. B

TEST - 12 0SBO0SBOU1SPCMFNMFSJ 1. %ÌSUQP[JUJGHFSÀFLTBZOOBSJUNFUJLPSUBMBNBT 4. )BUJDFYHÐOCPZVODBHÐOEFTPSV ZHÐOCP- JTFHFPNFUSJLPSUBMBNBTFOÀPLLBÀPMVS ZVODBJTFHÐOEFTPSV¿Ë[NÐõUÐS x ã Z JTF )BUJDFhOJO HÑOEF ÀÌ[EÑôÑ PSUBMBNB \" # $ % & TPSVTBZTBöBôEBLJMFSEFOIBOHJTJPMBNB[ \" # $ % & 2. ·À QP[JUJG HFSÀFL TBZOO ÀBSQN PMEVôVOB 5. ·ÀGBSLMQP[JUJGSFFMTBZOOBSJUNFUJLPSUBMBNB- HÌSF UPQMBNMBSOO BMBCJMFDFôJ FO LÑÀÑL QP[JUJG TPMEVôVOBHÌSFCVTBZMBSOHFPNFUSJLPSUB- UBNTBZEFôFSJLBÀUS MBNBTBöBôEBLJMFSEFOIBOHJTJPMBNB[ \" # 11 $ 16 % 43 & 21 2 352 \" # $ % & 6. ôFLJMEFLJ EPóSVTBM HSBGJLMFSEFO CJSJODJTJ [BNBOB CBóM PMBSBL CJS PUPNPCJMJO BMEó ZPMV JLJODJTJ JTF [BNBOBCBóMPMBSBLPUPNPCJMJOEFQPTVOEBLJLBMBO ZBLUNJLUBSOHËTUFSNFLUFEJS 3. #JSHSVQUBLJFSLFLMFSJOZBõPSUBMBNBT LBEOMB- :PM LN :BLU MU 22 50 SOZBõPSUBMBNBTEVS 47 ,BEOMBSO TBZT FSLFLMFSJO TBZTOO JLJ LBU PMEVôVOBHÌSF HSVCVOZBöPSUBMBNBTLBÀUS 20 dakika 30 dakika \" # $ % & #VOB HÌSF PUPNPCJM ZBLUOO UBNBNO LVMMB- OBSBLLBÀLNZPMHJEFCJMJS \" # $ % & 1. C 2. C 3. B 24 4. E 5. E 6. D

0SBOWF0SBOU KARMA TEST - 1 1. a 0, 75 5. YTBZTZOJOLBU ZTBZTJTF[OJOLBUES = 0, 66 3, 3 #VOBHÌSF z JGBEFTJOJOEFôFSJLBÀUS x PMEVôVOBHÌSF BLBÀUS \" # $ % & \" 1 # 1 $ 1 % 1 & 1 3 6 9 18 20 2. x = 3 x+y 4 PMEVôVOBHÌSF x-y PSBOOOEFôFSJLBÀUS 6. B=CWF 1 + 1 = 1 x a b 28 PMEVôVOBHÌSF CLBÀUS \" # 2 $ 3 % 5 & 7 3 4 68 \" # $ % & 3. x = 4 PMEVôVOBHÌSF 7. \"ZõFJSNJLUBUMTOZBQBSLFOIFSHSVOJ¿JOHS y3 õFLFSWFHSJSNJLLVMMBONõUS 4x - 3y \"ZöFhOJO ZBQUô JSNJL UBUMT HS PMEVôVOB HÌSF \"ZöFLBÀHSBNöFLFSLVMMBONöUS x + 6y JGBEFTJOJOEFôFSJLBÀUS \" # $ % & \" 5 # 7 $ 5 % 7 & 8 8 10 12 22 27 4. YWFZQP[JUJGHFSÀFLTBZMBSJÀJO #JSUPSCBEBCVMVOBOLSN[WFCFZB[CJMZFMFSJOTB- x = 3WF x.y = 3 ZMBSTSBTZMB WF JMFPSBOUMES y4 PMEVôVOBHÌSF x +ZUPQMBNLBÀUS #VOBHÌSF UPSCBEBLJUPQMBNCJMZFTBZTBöBô- EBLJMFSEFOIBOHJTJPMBNB[ \" # $ 7 % 8 & 23 \" # $ % & 1. B 2. B 3. D 4. A 25 5. D 6. E 7. C D

KARMA TEST - 2 0SBOWF0SBOU 1. a = 1 ve b = 1 5. #JSNJLUBSDFWJ[ WFJMFPSBOUMPMBSBLÐ¿¿PDV- b2 c5 óBEBóUMZPS PMEVôVOBHÌSF BTBZTDTBZTOOZÑ[EFLB- 5PQMBNDFWJ[TBZTEFOB[PMEVôVOBHÌSF ÀES QBZ FO B[ PMBO JLJ ÀPDVôVO QBZMBS UPQMBN FO ÀPLLBÀPMVS \" # $ % & \" # $ % & 2. B C DQP[JUJGUBNTBZPMNBLÑ[FSF 6. WFJMFUFSTPSBOUMJLJTBZOOUPQMBNJTF a + b = 3WF b + c = 4 CVJLJTBZOOÀBSQNLBÀUS bc \" # $ % & PMEVôVOBHÌSF B+C+DUPQMBNBöBôEBLJMFS- EFOIBOHJTJPMBCJMJS \" # $ % & 7. YZ[=PMEVôVOBHÌSF 2x + y z-x 3. TBZMBSOOEÌSEÑODÑPSBOUMTLBÀUS JGBEFTJOJOEFôFSJLBÀUS \" # $ % & \" 7 # 7 $ 5 % 3 & 21 2 3 22 4. BWFCTGSEBOGBSLMHFS¿FLTBZMBSPMNBLÐ[FSF WFJMFPSBOUMPMBOÑÀTBZTSBZMBIBOHJ a + 1 = 3WFb + 1 = 4PMEVóVOBHËSF UBNTBZMBSJMFUFSTPSBOUMES ba a2 + b2 \" # $ a.b % & JGBEFTJOJOEFôFSJLBÀUS \" # 25 $ 27 % 32 & 12 8 15 1. A 2. C 3. A 4. B 26 5. B 6. C 7. B D

0SBOWF0SBOU KARMA TEST - 3 1. A = 2 , B = 4 5. a = c = e = 2 C-E+G= B3C5 bd f 3 PMEVôVOBHÌSF \"#$PSBOLBÀUS WFB+F=PMEVôVOBHÌSF DLBÀUS \" # $ \" - # - $ % & % & 2. B C D E`3J¿JO a.b = - 5 _ b d.c = - 3 b ` b b=1 b 6. WFJMFPSBOUMJLJTBZOOLBSFMFSJGBSL c 3a PMEVôVOBHÌSF LBSFMFSJUPQMBNLBÀUS PMEVôVOBHÌSF d LBÀUS a \" # $ % & \" 1 # 1 $ % & 5 3 3. B C D` R+PMNBLÐ[FSF 7. Y+JMFZ-EPóSVPSBOUMES 3a = 5b = c x =JLFOZ=PMEVôVOBHÌSF Z=JLFn x 43 LBÀUS PMEVôVOBHÌSF BöBôEBLJTSBMBNBMBSOIBOHJTJ EPôSVEVS \" BCD # BDC $ CDB A 1 # 1 $ 1 % & 8 4 2 % DCB & CBD 4. m = n = k PMEVôVOBHÌSF x +JMFZ-UFSTPSBOUMES 3 25 x =JÀJOZ=PMEVôVOBHÌSF Z=JÀJOY 2m2 - nk + mk LBÀUS 3m2 + mn - k2 \" # $ % & PSBOLBÀUS 27 5. D 6. E 7. A A \" 11 # 23 $ 23 % 11 & 7 8 8 28 28 4 1. C 2. A 3. C 4. B

KARMA TEST - 4 0SBOWF0SBOU 1. 3 = 1 = 2 5. #JSJöZFSJOEFJöÀJTBZT 1 ÑOFJOEJSJMJQHÑOMÑL 4a 2b 3c 3 ÀBMöNBTÑSFTJLBUOBÀLBSMQ JöNJLUBSLB- PMEVôVOB HÌSF B C D OJO BSJUNFUJL PSUBMBNBT a OOLBÀLBUES UOBÀLBSMSTB JöJCJUJSNFTÑSFTJLBÀLBUBSUBS A 23 # 23 $ 23 % 23 & 23 \" # $ % & 27 25 21 9 3 2. y +TBZTY +JMFEPóSV [-JMFUFSTPSBO- 6. UBWVóBHÐOZFUFDFLLBEBSZFNWBSES UMESY= Z=JLFO [=UJS HÑOTPOSBUBWVLCBöLBLÑNFTFZFSMFöUJSJ- MJSTFLBMBOZFNLBMBOUBWVLMBSBLBÀHÑOZFUFS #VOBHÌSF Y=WF[=JLFOZLBÀUS \" # $ % & \" # $ % & 3. BC= b = 3 , c = 2 ve d = e 7. #JSJõJBZOLBQBTJUFEFJõ¿JCFSBCFS¿BMõBSBL c4 d 5 HÐOEFCJUJSJZPS FõJUMJLMFSJWFSJMJZPS \"ZOJöJOHÑOEFOEBIBB[CJS[BNBOEBCJUNF- #VOBHÌSF B C D E FTBZMBSJÀJOBöBôEBLJ- TJJÀJOBZOLBQBTJUFEFÀBMöBOFOB[LBÀJöÀJZF MFSEFOIBOHJTJEPôSVEVS EBIBJIUJZBÀWBSES \" BBSUBSLFODBSUBS # CB[BMSLFOFB[BMS \" # $ % & $ BBSUBSLFOEB[BMS % DB[BMSLFOFBSUBS & CBSUBSLFOEBSUBS 4. JöÀJQBSÀBJöJHÑOEFZBQZPSTB JöÀJ JöÀJOJOHÑOEFTBBUÀBMöBSBLHÑOEFCJUJS- QBSÀBJöJLBÀHÑOEFZBQBS EJôJCJSJöJOHÑOEFTBBUÀBMöBSBLHÑOEFOEB- IBB[TÑSFEFCJUJSFCJMNFTJJÀJOFOB[LBÀJöÀJZF \" # $ % & EBIBJIUJZBÀWBSES \" # $ % & 1. A 2. E 3. D 4. A 5. B 6. D 7. C B

0SBOWF0SBOU KARMA TEST - 5 1. a + 1 = 2 5. aEBSBÀPMNBLÑ[FSF b UBOa +DPUa PMEVôVOBHÌSF b2 - ab PSBOOFEJS JGBEFTJOJO FO LÑÀÑL EFôFSJ BöBôEBLJMFSEFO (a - 1) 2 IBOHJTJEJS A B # C $ Bm \" # $ % & % C- & b - 1 a-1 6. Y WF Z UFST PSBOUM TBZMBS PMNBL Ð[FSF BõBóEBLJ UBCMPEBYWFZTBZMBSOBBJUCB[EFóFSMFSWFSJMNJõUJS 2. Y ZWF[OFHBUJGHFS¿FMTBZMBSPMNBLÐ[FSF xy xy = yz = xz C+ 12 8 6 a+4 FõJUMJóJWFSJMJZPS 2 #VOB HÌSF BöBôEBLJ TSBMBNBMBSEBO IBOHJTJ #VOBHÌSF B2 +C2OJOEFôFSJLBÀUS EPôSVEVS \" YZ[ # ZY[ $ [ZY % [YZ & Y[Z \" # $ % & 3. BCCDBD= 7. #JSUSBLUËSÐOBSLBUFLFSMFóJOJO¿FWSFTJ ËOUFLFSMF- PMEVôVOBHÌSF ab a PSBOOFEJS óJOJO¿FWSFTJOJOLBUES5SBLUËSCFMMJCJSZPMVBME- . óOEBËOUFLFSMFLBSLBUFLFSMFLUFOLF[GB[MBEË- OÐZPS c cb #VOB HÌSF CV ZPMEB ÌO UFLFSMFL LBÀ LF[ EÌO- \" 4 # 9 $ 4 % 3 & 2 NÑöUÑS 25 25 9 5 3 \" # $ % & 4. BQP[JUJGHFSÀFMTBZPMNBLÑ[FSF WFZBõMBSOEBLJJLJLBSEFõFCJSNJLUBSQBSBZBõ- 4.a2 + 16 MBSZMBUFSTPSBOUMPMBSBLQBZMBõUSMNBLJTUFOJZPS a2 ZMTPOSBBZOQBSB¿PDVLMBSOZBõMBSZMBUFSTPSBO- UMõFLJMEFQBZMBõUSMBDBLUS#ÐZÐL¿PDVLJMLEVSV- JGBEFTJOJOBMBCJMFDFôJFOLÑÀÑLEFôFSBöBôEB- NBHËSFMJSBGB[MBBMBDBLUS LJMFSEFOIBOHJTJEJS #VOB HÌSF QBZMBöUSMBDBL PMBO QBSB LBÀ MJSB- # 32 $ % 44 & ES 33 \" \" # $ % & 1. B 2. B 3. C 4. E 29 5. B 6. A 7. D E

KARMA TEST - 6 0SBOWF0SBOU 1. #JSNJLUBSQBSBZ\" # $LJõJMFSJTSBTZMB JMF 5. #JSÐ¿HFOJOEõB¿MBSTSBTZMB TBZMBSJMF EPóSVPSBOUMBZOQBSBZ% & 'LJõJMFSJ JMF PSBOUMES UFSTPSBOUMPMBSBLQBZMBõZPS #VOBHÌSF CVÑÀHFOEFFOV[VOLFOBS FOLTB #VOBHÌSF FOÀPLWFFOB[QBSBZTSBTZMBLJN- LFOBSOLBÀLBUES MFSBMNöUS # 3 \" 2 $ % & \" #JMF$ # $JMF' $ \"JMF% % $JMF& & #JMF' 2. LHMLIBNVSZBQNBLJ¿JOTV UV[WFVOTSBTZMB 6. 10 – 2 21 ve 10 + 2 21 WFJMFUFST JMFEPóSVPSBOUMõFLJMEFLBSõUSM- TBZMBSZMB PSUB PSBOUM PMBO TBZ BöBôEBLJMFS- ZPS EFOIBOHJTJEJS #VOBHÌSF LBÀHSBNVOLBSöUSMNöUS \" # $ % & \" 200 # 400 $ % & 33 7. BáPMNBLÐ[FSF BY +CY+D=EFOLMFNJOJO LËLMFSJ Y WF Y JTF LËLMFS UPQMBN x1 + x2 =- b a 3. :Bõ PSUBMBNBT PMBO LJõJMJL CJS HSVCB ZBõMB- LËLMFS ¿BSQN x1.x2 = c FõJUMJLMFSJZMF IFTBQMB- a SUPQMBNPMBOLJõJLBUMQ ZBõMBSOOBSJUNFUJL PSUBMBNBTPMBOLJõJHSVQUBOBZSMZPS OS #VOBHÌSF ZFOJPMVöBOHSVCVOZBöPSUBMBNBT 7FSJMFOCJMHJZFHÌSF Y2 -Y+ 16 =EFOLMF- LBÀUS NJOJO LÌLMFSJOJO BSJUNFUJL PSUBMBNBT HFPNFU- SJLPSUBMBNBTOEBOLBÀGB[MBES \" # $ % & \" # $ % & 4. #JSUPQMVMVLUBLJFSLFLMFSJOTBZT JMFCBZBOMBSO #JSËóSFODJOJOQVBOÐ[FSJOEFOEFóFSMFOEJSJMFO TBZT JMFPSBOUMES TOBWOOOPUPSUBMBNBTUJS #VOBHÌSF CVUPQMVMVLUBFOB[LBÀLJöJWBSES ²ôSFODJFOB[LBÀTOBWBEBIBHJSFSTFOPUPSUB- \" # $ % & MBNBTQVBOEBOGB[MBPMVS \" # $ % & 1. B 2. E 3. C 4. C 5. D 6. A 7. A E

0SBOWF0SBOU <(1m1(6m/6258/$5 1. \"MJ NFUSF V[VOMVóVOEBLJ IPNPKFO ¿VCVóV DN 4. ôFLJMEFLJ CJSCJSJOJ ¿FWJSFO EJõMJ ¿BSLMBS CJS NBLJOF DJOTJOEFO UBN TBZ PMBO Ð¿ QBS¿BZB BZSZPS %B- NÐIFOEJTJOJOQSPKF¿BMõNBTOEBZFSBMBOCJSEÐ[F- IBTPOSBCVÐ¿QBS¿BZB¿VCVLMBBZOË[FMMJóFTB- OFLUFCVMVONBLUBES IJQQBS¿BMBSEBOFLMFNFMFSZBQBSBL ¿VCVLMBSOPS- UBOPLUBMBSOOZFSEFóJõUJSNFNJLUBSMBSOTSBZMB 1. 2. 3. DN DNWFDNPMBSBLËM¿ÐZPS ôFLJMEFWFSJMFO¿BSLMBSEBLJEJõTBZTTSBZMB #VOBHÌSF ÀVCVLMBSOCPZPSUBMBNBTFLMFNF- WF EJS #V ¿BSLMBSB FO I[M EËOFO ¿BSLUBO ZB- MFSTPOSBTOEBLBÀDNBSUNöUS WBõ FO ZBWBõ EËOFO ¿BSLUBO I[M PMBO EËSEÐODÐ CJS¿BSLFLMFOJZPS \" # $ % & #VOBHÌSF FLMFOFOÀBSLUBCVMVOBOEJöTBZT- 2. ,BSBZPMMBS (FOFM .ÐEÐSMÐóÐ V[NBOMBS ZBQBDBL- OOBMBCJMFDFôJFOCÑZÑLEFôFSJMFFOLÑÀÑLEF- ôFSJOUPQMBNLBÀUS MBSCJS¿FWSFZPMVOEBNFUSFHFOJõMJóJOEFWFLN V[VOMVóVOEB BTGBMU ZPM ZBQNBZ QMBOMZPS :PM ZB- \" # $ % & QNOEB ¿BMõBO Jõ¿JMFSJO ZBQUó IBUB TPOVDV BT- GBMUNBM[FNFTJOJOUBNBNLVMMBOMBSBLNFUSFHF- OJõMJóJOEFZPMZBQMZPS #VOB HÌSF TPO EVSVNEBLJ ZPMVO V[VOMVôV QMBOMBOBOZPMV[VOMVôVOEBOLBÀLNGB[MBES \" # $ % & 5. .JMMJ1JZBOHPJEBSFTJOJOZMCBõ¿FLJMJõJOEFCJMFUOV- NBSBMBS CFMJSMFOJSLFO Ð[FSJOEF GBSLM SBLBNMBSO ZB[M PMEVóV UPQVO CVMVOEVóV LVUVEBO TSBZMB SBTUHFMFUPQ¿FLJMJZPS 3. (Ë[EFhOJO UFMFGPO GBUVSBT 5- EJS (Ë[EF ZMO 95 JMLÐ¿BZOEBCVUBSJGFZJLVMMBOELUBOTPOSBJOUFSOFU ¥FLJMFO UPQMBS TSBZMB TBóEBO TPMB EPóSV ZB[MB- LVMMBONOO BSUNBT OFEFOJZMF ÐDSFUJ 5- PMBO SBL CJMFU OVNBSBT PMVõUVSVMVZPS #ÐZÐL JLSBNJZF- CJS ÐTU UBSJGFZF HF¿NJõUJS :MO BZOEB BCPOFTJ OJO¿FLJMJõJOEF¿FLJMFOJMLÐ¿UPQUBOJMLJOJOPMEVóV PMEVóV (4. PQFSBUËSÐ GJSNBTOEBO GBUVSBTOB FL CJMJOJZPS ËEFNFMJPMBSBLZFOJCJSUFMFGPOBMNõUS$JIB[CF- EFMJZMOTPOBMUBZOEBIFSBZ5-FLÐDSFUPMB- ,BMBOZFEJUPQVOOVNBSBMBSOOPSUBMBNBTUBN SBLGBUVSBZBZBOTUMBDBLUS TBZPMEVôVOBHÌSF ÀFLJMJöTPOVDVCJMFUOVNB- SBTBöBôEBLJMFSEFOIBOHJTJPMBCJMJS #VOB HÌSF (Ì[EFhOJO CV CJS ZMML LVMMBONMB- SEJLLBUFBMOEôOEBBZMLGBUVSBMBSOOPSUBMB- \" # $ NBTLBÀ5-EJS % & \" # $ % & 1. D 2. B 3. A 31 4. C 5. B

<(1m1(6m/6258/$5 0SBOWF0SBOU 1. #JS UBWVL ¿JGUMJóJOEF UBWVLMBS Lõ BZMBSOEB LÐNFT- 3. ¥FWSF WF ôFIJSDJMJL #BLBOMó OBZMPO QPõFU UÐLFUJ- UFO ¿LNBZQ CVóEBZ JMF CFTMFOJZPS :B[ WF CBIBS NJOJB[BMUNBLBNBDJMFZFOJCJSVZHVMBNBHFUJSNJõ- BZMBSOEB JTF ¿JGUMJLUFLJ HFOJõ ZBZMNB BMBOMBSOEB UJS#VVZHVMBNBEBBMõWFSJõMFSEFLVMMBOMBOQPõFU- ¿FõJUMJGBZEBMCJULJMFSJMFCFTMFOJZPS¥JGUMJLTBIJCJOJO MFSJOÐDSFUMJPMBDBóWF0DBLUBSJIJJUJCBSJJMF ZBQUóHË[MFNEF LõBZMBSOEBHÐOMÐLZVNVSUBTB- VZHVMBNBOOCBõMBZBDBó CBLBOMLUBSBGOEBOEV- ZTUBWVLTBZTOOZBSTJLFOZB[WFCBIBSBZMB- ZVSVMNVõUVS6ZHVMBNBEB JõMFUNFMFSJOQPõFUNBMJ- SOEB Lõ BZMBSOB HËSF HÐOMÐL ZVNVSUB TBZT 1 ZFUMFSJOJO CJS LTNOO EFWMFU UBSBGOEBO LBSõMBOB- DBó CFMJSUJMNJõUJS ,VMMBOBDBó QPõFUJO UBOFTJOJ 2 LVSVõBNBMFEFOCJSNBSLFUCVVZHVMBNBËODFTJO- PSBOOEBBSUUóOHËSÐZPS EF BZEB BEFU QPõFU LVMMBONõUS 6ZHVMBNB TPOSBTOEB JTF NBSLFUJO BZML QPõFU LVMMBON 1 #VOB HÌSF ÀJGUMJLUF CVMVOBO UBWVôVO ZB[ BZMBSOEBCJSIBGUBCPZVODBUPQMBNÑSFUUJôJZV- 5 NVSUBTBZTBöBôEBLJMFSEFOIBOHJTJEJS PSBOOEB B[BMNõUS \"ZML UPQMBN QPõFU NBMJZFUJ LVMMBONOO B[BMNBT WF EFWMFUJO EFTUFóJ JMF \" # $ % & PSBOOEBB[BMNõUS #VOBHÌSF EFWMFUCVVZHVMBNBEBNBSLFUFQP- öFUCBöOBLBÀLVSVöEFTUFLWFSNJöUJS \" # $ % & 2. \"INFU#FZõFLJMEFLJHJCJNBMBOBTBIJQEJL- 4. ôFLJMEFCJSZB[DEBCVMVOBOEËSUSFOLNÐSFLLFCJO EËSUHFOCJ¿JNJOEFLJBSTBTOOZBSTOFWWFZBõBN LBMBONJLUBSMBSOHËTUFSFOEËSUTÐUVOCVMVONBLUB- BMBO EJóFS ZBSTO JTF UBSNTBM BMBO PMBSBL JLJZF ES , LSN[ . NBWJ 43 TBSWF 4: JTFTJ- BZSNõUS ZBISFOLNÐSFLLFCJHËTUFSNFLUFEJS&õJULBQBTJUFMJ TÐUVOMBSEËSUFõCËMNFZFBZSMNõUS N N 5BSNTBM &WWFZBöBN BMBO BMBO N N K M SR SY 5BSNTBMBMBOFõQBSTFMFCËMÐQÐ¿ÐOFTSBZMBEP- õFLJMEFLJNÑSFLLFQTFWJZFMFSJOFTBIJQZB[DEB NBUFT TBMBUBMLWFCJCFSEJLNJõUJS,BMBOQBSTFMJ CVMVOBOLSN[NÑSFLLFQNJLUBSOOTJZBINÑ- JTFFõQBS¿BZBCËMNÐõWFQBS¿BMBSBTSBZMBNBZ- SFLLFQNJLUBSOBPSBOBöBôEBLJMFSEFOIBOHJTJ EBOP[ NBSVMWFOBOFFLNJõUJS PMBCJMJS \"INFU #FZhJO FLUJôJ NBZEBOP[ WF OBOF FLJN \" 8 & 10 BMBOMBS UPQMBNOO BSTBOO UBNBNOB PSBO 9 3 BöBôEBLJMFSEFOIBOHJTJEJS \" 5 # 5 $ 1 % 1 & 5 16 24 12 8 12 # $ % 1. D 2. C 32 3. C 4. C

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TYT Matematik Ders İşleyiş Modülleri 6. Modül Oran Orantı

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TYT Matematik Ders İşleyiş Modülleri 6. Modül Oran Orantı

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