www.aydinyayinlari.com.tr ÷,÷/$÷%&3&$&%&/%&/,-&.-&31\"3\"#0-&õ÷54÷;-÷,-&3 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 5 ÖRNEK 8 Z= 3x2 - N- 2 ) x - 4 Z= 2x2 - 5x -N+ 1 QBSBCPMÐJMFZ= x -EPóSVTVOVOLFTJNOPLUBMBS\"WF #EJS QBSBCPMÑJMFZ= 3 -YEPôSVTVJLJOPLUBEBLFTJöUJôJ OFHÌSF NJOBMBCJMFDFôJFOLÑÀÑLUBNTBZEFôF [\"#]EPôSVQBSÀBTOOPSUBOPLUBTOOBQTJTJPMEV SJOJCVMVOV[ ôVOBHÌSF NLBÀUS 2x2 - 5x -N+ 1 = 3 - x 2x2 - 4x -N- 2 = 0 3x2 - N- 2 ) x -4 = x - 1 x2 - 2x -N- 1 = 0 3x2 - N- 1 ) x - 3 = 0 Ô>PMNBM x +x 4 + N+ 1 ) > 0 N> -8 12 N> -2 jNNJO = -CVMVOVS = 2 olmal› ÖRNEK 9 2 m-1 Z=NY2 - 2x +N QBSBCPMÑJMFZ= -NY+EPôSVTVOVOLFTJöNFNFTJ =2 JÀJONIBOHJBSBMLUBEFôFSBMNBMES 6 N- 1 = 12 NY2 - 2x +N= -NY+ 2 N=CVMVOVS NY2 + N- 2 )x +N- 2 = 0 ÖRNEK 6 Ô<PMNBM N- 2 )2 -N N- 2 ) < 0 Z= x2 - 4x +N- 1 QBSBCPMÑZ= 2x +EPôSVTVOBUFôFUPMEVôVOBHÌ N- 2 ) ( -N- 2 ) < 0 SF NLBÀUS 2 2 ß f - 3, - 2 p , ^ 2, 3 h x2 - 4x +N- 1 = 2x +1 – 3 x2 - 6x +N- 2 = 0 mß 3 Ô=PMNBM 36 - N- 2 ) = 0 –+ – 36 -N+ 8 = 0 ÖRNEK 10 ,PPSEJOBU EÑ[MF 11 NJOEFWFSJMFOQB N= 44 j m = y SBCPM WF EPôSV x HSBGJLMFSJOF HÌSF 3 –1 O 3 BLBÀUS 4 ÖRNEK 7 –4 y = ax + 2 Z= x2 - N- 1 ) x +N- 1 QBSBCPMÑOÑOYFLTFOJOFUFôFUPMBCJMNFTJJÀJONOJO 1BSBCPMÑOEFOLMFNJZ=N Y+ 1 ) ( x - 4 ) ve ( 0, - 4 ) BMBCJMFDFôJEFôFSMFSJCVMVOV[ EFOLMFNJTBôMBZBDBôOEBON=CVMVOVS Z= ( x + 1 ) ( x - QBSBCPMÑÑ[FSJOEFLJ - EPôSV Ô=PMNBM EFOLMFNJOJTBôMBS0IBMEF N- 1 )2 - N-1 ) = 0 -4 = a. 3 + 2 j a = -CVMVOVS N2 -N+ 2 ) = 0 N- N- 1 ) = 0 N=WFN=CVMVOVS 5. 13 11 49 8. –1 9. f - 3, - 2 p , ^ 2, 3 h 10. –2 6. 7. 1 ve 2 3 3
·/÷7&34÷5&:&)\";*3-*, 2. MODÜL ÷,÷/$÷%&3&$&%&/%&/,-&.-&31\"3\"#0-&õ÷54÷;-÷,-&3 www.aydinyayinlari.com.tr ÖRNEK 11 :BOEBLJHSBGJôFHÌSF ÖRNEK 13 BDLBÀUS y y = ax2 – 4x + c Z= x2 + 2x + 5 QBSBCPMÑÑ[FSJOEF Z= x +EPôSVTVOBFOZBLO OPLUBOOLPPSEJOBUMBSUPQMBNLBÀUS O2 4 x Z = x2 + 2x + QBSBCPMÑOF Z = x + EPôSVTVOB QB –2 SBMFM PMBDBL öFLJMEF WF \" Y0 Z0 OPLUBTOEBO HFÀFO %PôSVEFOLMFNJZ= x -EJS Z= x +DUFôFUJOJÀJ[FSTFL #VEPôSVJMFQBSBCPM - WF OPLUBMBS y = x2 + 2x + 5 LFTJöUJôJOEFO y = x + c 2 5 y = x + A(x0, y0) c = -2 ve a = CVMVOVS 4 5 #VSBEBO a.c = - EJS 2 x2 + 2x + 5 = x + c x2 + x + 5 - c = 0 EFOLMFNJOEFÔ=PMNBMES 1 - 4(5 - c) = 0 j c= 19 4 21 \" OPLUBTOO BQTJTJ x + x + = 0 EFOLMFNJOJO LÌLÑ 4 ÖRNEK 12 1 17 PMBO x = - EJS0SEJOBUJTF y = CVMVOVS Z= x2 - 3x - QBSBCPMÑOÑOIBOHJOPLUBTOEBLJUFôFUJZ= 5x - 30 24 EPôSVTVOBQBSBMFMEJS 1 17 15 Af - , pOPLUBTOOLPPSEJOBUMBSUPQMBN UÑS 24 4 Z= x2 - 3x -QBSBCPMÑOF Z= 5x-EPôSVTVOB ÖRNEK 14 QBSBMFMPMBDBLöFLJMEFWF\" Y0 Z0 OPLUBTOEBOHFÀFO Z= x2 - 2x - 2 Z= 5x +DUFôFUJOJÀJ[FSTFL QBSBCPMÑOÑO EFOLMFNJZ= 2x +PMBOLJSJöJOJOPSUB y = x2 –3x – 10 OPLUBTOOPSEJOBULBÀUS yy==55xx++c– 30 y = x2 –2x – 2 A(x0, y0) A(x 0, y 0) y = 2x + 3 x2 - 3x - 10 = 5x + c ,JSJöJO PSUB OPLUBT \" Y0 Z0 PMTVO \" OPLUBTOO BQTJTJ x2 - 8x - 10 - c = 0 PMBO Y0 BZO [BNBOEB QBSBCPM JMF EPôSVOVO PSUBL ÀÌ[Ñ NÑOÑOY=SEFôFSJOFFöJUUJS EFOLMFNJOEFÔ=PMNBMES x2 - 2x - 2 = 2x + 3 j x2 - 4x - 5 = 0 64 - 4 ( -10-c ) = 0 b EBOY0=EJS A(x0 Z0 OPLUBTBZO[B 0IBMEFr = - 64 + 40 + 4c = 0 2a c = -CVMVOVS NBOEBZ= 2x + 3 dPôSVTVÑ[FSJOEFPMEVôVOEBO\" Z0) \"OPLUBTOOBQTJTJY2 - 8x + 16 =EFOLMFNJOJOLÌ EFOLMFNJTBôMBSZ0= 4 + 3 jZ0 =CVMVOVS LÑPMBOY=UÑS 0SEJOBUJTFZ= -CVMVOVS 0IBMEF\" - ES 5 12. (4, –6) 50 15 14. 7 11. - 13. 2 4
www.aydinyayinlari.com.tr ÷,÷/$÷%&3&$&%&/%&/,-&.-&31\"3\"#0-&õ÷54÷;-÷,-&3 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÷LJ1BSBCPMÑO#JSCJSJOF(ÌSF%VSVNV d) Z= 2x2 - 2x - 5 Z= x2 - 4x - 7$1,0%m/*m 2x2 - 2x - 5 = x2 - 4x - 10 Z= ax2 + bx +DQBSBCPMÐJMFZ=LY2 +QY+S x2 + 2x + 5 = 0 QBSBCPMÐOÐOLFTJNOPLUBMBSCVMVOVSLFOCVJLJ EFOLMFNPSUBL¿Ë[ÐMÐS Ô= 4 - 20 = - 16 <PMEVôVOEBOSFFMLÌL ZPL0IBMEFJLJQBSBCPMLFTJöNF[ ÖRNEK 14 ÖRNEK 15 \"õBóEBLJQBSBCPMMFSJOCJSCJSJOFHËSFEVSVNMBSOJODFMF- Z= x2 - 8x +JMFZ= -x2 + x + 1 ZJOJ[7BSTBLFTJNOPLUBMBSOCVMVOV[ QBSBCPMMFSJOJO LFTJN OPLUBMBSOO BQTJTMFSJ UPQMBN LBÀUS a) Z= x2 - 5x + 2 Z= x2 - x - 6 x2 - 8x + 2 = -x2 + x + 1 2x2 - 9x + 1 = 0 j D = 73 > 0 x2 - 5x + 2 = x2 - x - 6 4x = 8 9 x=2 x +x = x = 2 jZ= -CVMVOVS 1 22 0IBMEFJLJQBSBCPM - OPLUBTOEBLFTJöJS ÖRNEK 16 b) Z= x2 - 4x + 1 Z= -x2 + 2x - 3 Z= 2x2 - 4x +WFZ= x2 - x +L- 1 QBSBCPMMFSJOJO GBSLM JLJ OPLUBEB LFTJöNFTJ JÀJO L x2 - 4x + 1 = -x2 + 2x - 3 IBOHJBSBMLUBPMNBMES 2x2 - 6x + 4 = 0 2x2 - 4x + 1 = x2 - x +L- 1 x2 - 3x + 2 = 0 x2 - 3x + 2 -L= 0 x = 2 ve x =EJS EFOLMFNJOEFÔ>PMNBM 9 - 4 ( 2 -L > 0 x = 2 jZ= -3 x = 1 jZ= -2 9 - 8 +L> 0 0IBMEFJLJQBSBCPM -3 ) ve ( 1, - OPLUBMBSOEBLF L> -1 TJöJS 1 c) Z= x2 - 2x + 3 k >- Z= -x2 + 6x - 5 12 x2 - 2x + 3 = -x2 + 6x - 5 2x2 - 8x + 8 = 0 ÖRNEK 17 x2 - 4x + 4 = 0 ( x - 2 )2 = UBNLBSF Z= -x2 + 3x -NWFZ= x2 - x +N-1 x = 2 jZ= 3 QBSBCPMMFSJOJOPSUBLOPLUBMBSOOCVMVONBNBTJÀJO 0IBMEFJLJQBSBCPM OPLUBTOEBCJSCJSJOFUFôFUUJS NIBOHJBSBMLUBPMNBMES -x2 + 3x -N= x2 - x +N- 1 2x2 - 4x +N- 1 = 0 EFOLMFNJOEFÔ<PMNBMES 16 - N- 1 ) < 0 16 -N+ 8 < 0 N> 24 N>CVMVOVS 14. B m C m m D EFUFôFU 51 9 16. d - 1 , 3 n 17. ( 1, R ) E LFTJöNF[15. 2 12
·/÷7&34÷5&:&)\";*3-*, 2. MODÜL ÷,÷/$÷%&3&$&%&/%&/,-&.-&31\"3\"#0-&õ÷54÷;-÷,-&3 www.aydinyayinlari.com.tr ÖRNEK 18 y = x2 + kx + p UYARI y = x2 + mx + n y Z= ax2 + bx +DQBSBCPMÐOFPSJKJOEFO¿J[JMFOUFóFU- MFSCJSCJSJOFEJLJTFÓ= -EJS –2 O 5x :VLBSEBLJHSBGJôFHÌSF m - k + n LBÀUS ÖRNEK 20 p Z= x2 -LY+ 2 1BSBCPMMFSJOLFTJöNFOPLUBT Y1 PMTVO Z= x2+NY+OQBSBCPMÑOÑOLÌLMFSUPQMBN QBSBCPMÑOFPSJKJOEFOÀJ[JMFOUFôFUMFSCJSCJSJOFEJLPM EVôVOBHÌSF QP[JUJGLHFSÀFLTBZTLBÀPMNBMES -2 + x1 = -N Z= x2 +LY+QQBSBCPMÑOÑOLÌLMFSUPQMBN Ô= -PMNBMES L2 - 4.1.2 = -1 jL2 j 7 x1 + 5 = -LES#VSBEBO k =\" 7 N-L=CVMVOVS LOJOQP[JUJGEFôFSJ 7 EJS #VJLJQBSBCPMÑOLÌLMFSÀBSQN x1. (-2 ) =O x1 . 5 =QPMEVôVOEBO n2 n 33 p = - 5 CVMVOVS#VSBEBOm - k + p = 5 UJS UYARI Z= ax2 + bx +DQBSBCPMÐOFYFLTFOJOJLFTUJóJOPL- UBMBSEBO ¿J[JMFO UFóFUMFS EJL LFTJõJZPSTB Ó = PM- NBMES ÖRNEK 19 y y = 2x2 – 3x + n Ox ÖRNEK 21 y = –x2 + mx + 2 Z= x2 +NY+ 12 QBSBCPMÑOÑOYFLTFOJOJLFTUJôJOPLUBMBSEBOÀJ[JMFO :VLBSEBLJHSBGJôFHÌSF N+OLBÀUS UFôFUMFS EJL LFTJöJZPSMBSTB N OJO BMBCJMFDFôJ QP[JUJG EFôFSLBÀUS 1BSBCPMMFSJOYFLTFOJOJLFTUJôJOPLUBMBSPMBO Y1, 0 ) ve ( x2 OPLUBMBSQBSBCPMMFSJOLFTJöJNOPLUBMBSES Ô=PMNBMES 0 IBMEF JLJ QBSBCPMÑO LÌLMFS UPQMBN JMF LÌLMFS ÀBSQ N2 - 4. 1.12 = 1 NCJSCJSJOFFöJUUJS N2 = 49 N= ± 7 3 NOJOQP[JUJGEFôFSJEJS x +x = =m 52 20. 7 21. 7 1 22 n x .x = = - 2 & n = - 4 12 2 35 #VSBEBOm + n = - 4 = - CVMVOVS 22 33 5 18. 19. - 5 2
www.aydinyayinlari.com.tr ÷,÷/$÷%&3&$&%&/%&/,-&.-&31\"3\"#0-&õ÷54÷;-÷,-&3 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 22 ÖRNEK 25 Z=G Y = 3x2 + 5x +GPOLTJZPOVWFSJMJZPS YFLTFOJOFUFôFUWFY-Z+ 6 =EPôSVTVZMBFL TFOMFSÑ[FSJOEFLFTJöFOQBSBCPMÑOEFOLMFNJOFEJS f ( x +L GPOLTJZPOVOVOHSBGJôJZFLTFOJOFHÌSFTJ NFUSJLPMEVôVOBHÌSF LLBÀUS x = 0 jZ= 2 f ( x ) = 3x2 + 5x + 11 Z= 0 j x = -6 5 QBSBCPMYFLTFOJOF - OPLUBTOEBUFôFUPMNBM0IBM QBSBCPMÑOÑOUFQFOPLUBTOOBQTJTJ - ES de f ( x ) = a ( x + 6 )2 + 0 6 5 OPLUBTEFOLMFNJTBôMBS f ( x +L GPOLTJZPOVOVOUFQFOPLUBT - - k = 0 PM 2 = 2 & a= 1 6 a.6 18 NBMES 5 #VSBEBOk = - CVMVOVS 6 f^ x h = 1 ^ x + 6 h2 CVMVOVS 18 ÖRNEK 23 Z= 3x2 - x -WFZ= x2 - 4x + 8 QBSBCPMMFSJOJOLFTJNOPLUBMBSOEBOWFPSJKJOEFOHF ÀFOQBSBCPMÑOEFOLMFNJOJCVMVOV[ 0SJKJOEFOHFÀFOQBSBCPMMFSZ= ax2 +CYCJÀJNJOEFEJS 8/ 2 + 5/ y = 3x - x - 5 y = 2 - 4x + 8 x Z= 29x2 - 28x #VSBEBOZ- 29x2 + 28x =CVMVOVS ÖRNEK 26 Z= - (x -S 2 +LWFZ= 3x2 r2 PSBOLBÀUS QBSBCPMMFSJUFôFUPMEVôVOBHÌSF, k ÖRNEK 24 0SUBLÀÌ[ÑNZBQMSTB -x2 +SY-S2 +L= 3x2 G Y = 2x2 +GPOLTJZPOVWFSJMJZPS 4x2 -SY+S2 -L= 0 Z=G Y- 3 ) + 1 D =PMNBM GPOLTJZPOVOVOBMBCJMFDFôJNJOJNVNEFôFSLBÀUS S2 - S2 -L = 0 S2 -S2 +L= 0 f( x ) = 2x2 + QBSBCPMÑOÑO UFQF OPLUBT 5 OPLUB S2 =L TES Z= 2f ( x - 3 ) +GPOLTJZPOVOVOUFQFOPLUBT 2 T ( 3, 2f ( 0 ) + PMEVôVOEBO5 CVMVOVS #VSBEBOGPOLTJZPOVOVOBMBCJMFDFôJFOLÑÀÑLEFôFSUÑS r4 = CVMVOVS k3 5 23. ZmY2 + 28x = 0 24. 3 53 25. y = 1 ^ x + 6 h2 4 22. - 26. 18 3 6
TEST - 19 1BSBCPM%PôSV 1BSBCPM1BSBCPM\"SBTOEBLJ÷MJöLJ 1. Z= x2 - 2x + 2 4. Z= 2x2 - 3x +N-1 QBSBCPMÑJMFZ= 4 -YEPôSVTVOVOLFTJNOPL QBSBCPMÑZ= 2 -YEPôSVTVOBUFôFUPMEVôV OBHÌSF NLBÀUS | |UBMBS\"WF#PMEVôVOBHÌSF \"# LBÀUS A) 3 2 B) 11 C) 10 25 5 C) - 9 D) 3 E) 2 2 A) B) 16 16 8 E) - 7 16 D) - 1 2 2. Z= 3x2 - x + 1 QBSBCPMÑJMFZ= 5x +EPôSVTVOVOLFTJNOPL 5. G Y = 3x2 - 2x -N- 1 UBMBS\"WF#PMEVôVOBHÌSF [\"#]EPôSVQBSÀB QBSBCPMÑJMFZ= 2 -YEPôSVTVJLJOPLUBEBLF TJöUJôJOFHÌSF NOJOBMBCJMFDFôJFOLÑÀÑLUBN TOOPSUBOPLUBTBöBôEBLJMFSEFOIBOHJTJEJS TBZEFôFSJLBÀUS A) ( -3, -8 ) B) ( -2, -3 ) C) ( 1, 2 ) % & A) - # $ % & 6. Z= x2 - 2x +WFZ= -2x2 + x -L+ 1 3. Z= 2x2 - N- 2 ) x - 1 QBSBCPMMFSJOJOJLJOPLUBEBLFTJöNFTJJÀJOLOF PMNBMES QBSBCPMÑ JMF Z = NY + N EPôSVTVOVO LFTJN OPLUBMBSOOBQTJTMFSJUPQMBN-PMEVôVOBHÌ A)L< - 5 # L> 5 SF NLBÀUS 8 8 C) - 5 <L< 5 D) -2 <L< 2 88 \" # $ % -1 E) -2 & L< -2 1. A 2. & 3. D 54 4. A 5. $ 6. A
1BSBCPM%PôSV 1BSBCPM1BSBCPM\"SBTOEBLJ÷MJöLJ TEST - 20 1. y 4. ôFLJMEFZ= x2 - 4x -QBSBCPMÐWFSJMNJõUJS y –3 4x O x O y = –x2 + kx + p A B y = –x2 + mx + n :VLBSEBLJ HSBGJôF HÌSF (m - k) . n PSBO LBÀ US p \"#0YPMEVôVOBHÌSF \"WF#OPLUBMBSOOBQ TJTMFSJUPQMBNLBÀUS A) 21 B) 11 C) 6 25 13 4 2 D) E) A) 8 B) 7 C) 6 D) 5 E) 4 42 2. Z= 2x - 1 5. Z= x2 - 4 EPôSVTVOVO G Y = x2 - LY + QBSBCPMÑOÑ QBSBCPMÑOFEöOEBLJ\" - OPLUBTOEBOÀJ \" O OPLUBTOB HÌSF TJNFUSJL JLJ OPLUBEB [JMFOUFôFUMFSJOFôJNMFSJÀBSQNLBÀUS LFTNFTJJÀJOLOFPMNBMES \" # $ % & A) -4 B) -2 C) 2 D) 4 E) 6 3. y = x2 - 3 x + 2 6. G Y = x2 - 4x +L 2 QBSBCPMÑJMFZ= 2x +EPôSVTVOVOLFTJNOPL UBMBSOOPSEJOBUMBSUPQMBNLBÀUS QBSBCPMÑOÑOZ= -2x +EPôSVTVOBEJLUFôF \" # $ % & UJOJOEFOLMFNJOFEJS \" Z= x + # Z= x -$ Z= 1 x + 1 2 D) Z= 1 x - 1 E) Z= 1 x + 2 2 2 1. A 2. D 3. $ 55 4. & 5. D 6. D
·/÷7&34÷5&:&)\";*3-*, 2. MODÜL ÷,÷/$÷%&3&$&%&/%&/,-&.-&31\"3\"#0-&õ÷54÷;-÷,-&3 www.aydinyayinlari.com.tr &õ÷54÷;-÷,-&3* ÷LJODJ%FSFDFEFO#JS#JMJONFZFOMJ D y = x2 - 4x + 2 &öJUTJ[MJLMFSJO¦Ì[ÑN,ÑNFTJ TANIM D = (- 2 - 4.1.2 = 8 x 2– 2 2+ 2 x2 – 4x + 2 + –+ y = ax2 + bx + c üç terimlisinde x= 4-2 2 =2- 2 EVSVN 12 x= 4+2 2 =2+ 2 D > 0 ise 22 x –R x1 x2 +R BOO BOO BOO Z BY2 + bx + c JõBSFUJ JõBSFUJOJO JõBSFUJ JMFBZO JMFBZO UFSTJ (KökleriO BSBT B OO JõBSFUJOJO UFSTJ LÌLMFSJO E y = -x2 + 2x - 1 EõBOOJõBSFUJOJOBZOTES EVSVN D = 0 ise -(x2 - 2x + = 0 x 1 -(x - 2 = 0 x2 + 4x + 2 –– x mÞ x1 Y2 Þ x1 = x2 = 1 Z BY2 + bx + c BOO BOO JõBSFUJ JõBSFUJ JMFBZO JMFBZO (x1 = x2OJOEõOEB IFSCÌMHFBOOJõBSFUJOJO BZOTES EVSVN D < 0 ise +R F y = x2 - x + 3 x –R Z BY2 + bx + c BOOJõBSFUJJMFBZO D = (- 2 - 4.1.3 = -11 < 0 x –ß +ß 3FFMLÌLZPLUVS )FSZFSBOOJõBSFUJOJOBZOTES x2 – x + 3 + + + + + + ÖRNEK 1 \"öBôEBLJÑÀUFSJNMJMFSJOJöBSFUMFSJOJJODFMFZJOJ[ B y = x2 - 4x + 3 x2 - 4x + 3 = 0 x 13 G y = -x2 + 2x - 10 (x - Y- = 0 x2 – 3x + 3 + –+ x1 = 1, x2= 3 D = 22 - 4 ( - - x –ß +ß C y = -x2 + 5x - 6 = - 36 < 0 –x2 + 2x – 10 – – – – – – 3FFMLÌLZPLUVS -(x2 - 5x + = 0 x 23 -(x - Y- = 0 –x2 – 4x + 6 – +– x1 = 2 , x2= 3 56
www.aydinyayinlari.com.tr ÷,÷/$÷%&3&$&%&/%&/,-&.-&31\"3\"#0-&õ÷54÷;-÷,-&3 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 2 G x2 - 2x + 6 > 0 \"öBôEBLJ FöJUTJ[MJLMFSJO FO HFOJö ÀÌ[ÑN BSBMôO D = (- 2 - 4.1.6 x –ß +ß CVMVOV[ = -20 < 0 x2 – 2x + 6 + + + + + + B x2 - x - 2 > 0 3FFMLÌLZPLUVS ¦,=3 x –1 2 (x - Y+ > 0 x2 – x – 2 + –+ x1= -1, x2= 2 ¦,= (-ß - b ß C -x2 - 3x # 0 H x2 - 3x + 12 < 0 D = (- 2 - 4.1.12 x –ß +ß = -39 x –3 0 -x(x + # 0 x2 – 3x + 12 + + + + + + –x2 – 3x – +– 3FFMLÌLZPLUVS x1= -3, x = 0 ¦,= q 2 ¦,= (-ß -3] b [ ß D x2 - x < 6 x –2 3 x2 - x - 6 < 0 ÖRNEK 3 x2 – x – 6 + –+ (x - Y+ < 0 x1= -2, x2= 3 N O`3+PMNBLÑ[FSF x2 + ( m - n ) x - mn < 0 ¦,= (- FöJUTJ[MJôJOJO ÀÌ[ÑN LÑNFTJ N - O - PMEV E x2 - 2x + 1 > 0 ôVOBHÌSF N+OUPQMBNLBÀUS? x + 1 (x - 2 > 0 x2 + N-O Y-NO< 0 x2 – 2x + 1 + x1= x2 = 1 (x +N Y-O < 0 x –ß –m n +ß + ¦,=3- {1} x2 NmO YmæNO + – mN O Nmæ Omæ F -x2 + 4x $ 4 -N=N- O=O- 6 N= O= 6 -(x2 - 4x + $ 0 N+O=CVMVOVS -(x - 2 $ 0 x 2 –x2 + 4x – 4 –– x1 = x2 = 2 ¦,= {2} 2. B mß m b ß C mß m>b< ß D m 57 G 3H q 3. 15 E 3m\\^ F \\^
·/÷7&34÷5&:&)\";*3-*, 2. MODÜL ÷,÷/$÷%&3&$&%&/%&/,-&.-&31\"3\"#0-&õ÷54÷;-÷,-&3 www.aydinyayinlari.com.tr ÖRNEK 4 ÖRNEK 7 BWFCCJSFSQP[JUJGUBNTBZPMNBLÑ[FSF x2 - 2x + a - 1 > 0 x2 - ( a + b ) x + a . b < 0 FöJUTJ[MJôJ UÑN Y HFSÀFL TBZMBS JÀJO TBôMBOZPSTB B FöJUTJ[MJôJOJTBôMBZBOYUBNTBZMBSOOUPQMBNPM OOFOHFOJöEFôFSBSBMôOFEJS EVôVOB HÌSF CV LPöVMV TBôMBZBO LBÀ GBSLM N O JLJMJTJWBSES D <PMNBM 4 -B+ 4 < 0 ( x -B Y-C < 0 8 <Bj 2 <B x =B Y= b BOOFOHFOJöEFôFSBSBMô ß CVMVOVS x ab + –+ x2 – (a + b)x + ab x ` B C PMEVôVOEBOYEFôFSMFSJOJOUPQMBNJTF ÖRNEK 8 10 + 11 =EFO WF 6 + 7 + 8 =EFO WF x2 + ( a - 1 ) x + 9 $ 0 GBSLMTSBMJLJMJWBSES FöJUTJ[MJôJOJO ÀÌ[ÑN LÑNFTJ UÑN HFSÀFL TBZMBS PM ÖRNEK 5 EVôVOBHÌSF BOOFOHFOJöEFôFSBSBMôOFEJS x2 - ax + a - 1 > 0 D #PMNBM B- 2 - 4.1.9 # 0 FöJUTJ[MJôJOJOÀÌ[ÑNLÑNFTJ3- {1}PMEVôVOBHÌSF B- 2 - 36 # 0 B2 -B- 35 # 0 BLBÀUS B- B+ # 0 D =PMNBM B2 - B- = 0 x –5 7 B- 2 = 0 + –– B=CVMVOVS a2 – 2a – 35 0IBMEFBOOFOHFOJöEFôFSBSBMô[-5, 7]CVMVOVS ÖRNEK 6 ÖRNEK 9 4x2 - mx + 1 > 0 -x2 + 6x + a + 3 > 0 FöJUTJ[MJôJOJO ÀÌ[ÑN LÑNFTJ R - * m - 7 4 PMEVôV FöJUTJ[MJôJOJOÀÌ[ÑNLÑNFTJCPöLÑNFPMEVôVOBHÌ 2 SF BOO FOHFOJöEFôFSBSBMôOFEJS OBHÌSF NLBÀUS D <PMNBM D =PMNBM 36 - 4 ( - B+ < 0 N2- 4.4.1 = 0 36 +B+ 12< 0 N+ N- = 0 B< -48 N= - N= 4 B< -12 N= -JÀJOY2 + 4x + 1 > 0 j (2x + 2 > 0 (-ß - CVMVOVS Ç .K = R - ( - 1 2PMEVôVOEBOTBôMBNB[ 2 N=JÀJOY2 - 4x + 1 > 0 j (2x - 2 > 0 ¦,= R - ( 1 2TBôMBS 2 0IBMEFN =CVMVOVS 4. 4 5. 2 6. 4 58 7. ß 8. <m > 9. mß m
÷LJODJ%FSFDFEFO#JS#JMJONFZFOMJ&öJUTJ[MJLMFSJO¦Ì[ÑN,ÑNFTJ TEST - 21 1. x2 - 3x - 10 # 0 5. x2 - 4x + 4 > 0 FöJUTJ[MJôJOJOÀÌ[ÑNLÑNFTJOFEJS FöJUTJ[MJôJOJOÀÌ[ÑNLÑNFTJOFEJS A) ( -2, 5 ) B) [ -2, 5 ] A) R B) R - { 2 } C) R - { -2 } C) R - [ -2, 5 ] D) R - [ -2, 5 ) D) q & Þ ) E) R 2. x2 - x - 20 < 0 6. x2 + 14x + 49 < 0 FöUJTJ[MJôJOJOÀÌ[ÑNLÑNFTJOFEJS FöJUTJ[MJôJOJOÀÌ[ÑNLÑNFTJOFEJS A) ( -4, 5 ) B) [ -4, 5 ] A) R B) R - { -7 } C) { -7 } C) R - ( -4, 5 ) D) q D) q E) ( -Þ -7 ) E) R 3. 2x2 # x2 + 3x - 2 7. 4x2 + 4x + 1 $ 0 FöJUTJ[MJôJOJ TBôMBZBO Y UBN TBZ EFôFSMFSJOJO FöJUTJ[MJôJOJOÀÌ[ÑNLÑNFTJOFEJS UPQMBNLBÀUS A) R B) R - * - 1 4 A) 1 B) 2 C) 3 D) 4 E) 5 C) * - 1 4 2 2 D) q E) ( -ß, -7 ) 4. B CWFDHFSÀFLTBZMBSWFB< 0 < b <DPMNBL Ñ[FSF ( ax + b ) ( bx + c ) $ 0 FöJUTJ[MJôJOJOÀÌ[ÑNLÑNFTJOFEJS 8. -x2 - 2x - 1 < 0 A) >- b , - c H B) f - b , - c p FöJUTJ[MJôJOJOÀÌ[ÑNLÑNFTJOFEJS ab ab A) R B) { -1 } C) R - { -1 } C) >- c , - b p D) f - c , - b p D) q E) ( - Þ ba ba E) >- c , - b H ba 1. # 2. \" 3. $ 4. & 59 5. # 6. D 7. \" 8. $
TEST - 22 ÷LJODJ%FSFDFEFO#JS#JMJONFZFOMJ&öJUTJ[MJLMFSJO¦Ì[ÑN,ÑNFTJ 1. x2 - mx + m + 8 > 0 5. NQP[JUJGCJSHFSÀFLTBZPMNBLÑ[FSF FöJUTJ[MJôJOJOÀÌ[ÑNLÑNFTJ3- { 4 }PMEVôVOB x2 - m < 0 HÌSF NLBÀUS FöJUTJ[MJôJOJOÀÌ[ÑNLÑNFTJ B- 2, b + PMEV ôVOBHÌSF B+CUPQMBNLBÀUS A) 16 B) 12 C) 8 D) 6 E) 3 A) -5 B) -3 C) -1 D) 3 E) 5 2. x2 + x + 3 < 0 6. x2 -Yâ-2 FöJUTJ[MJôJOJOÀÌ[ÑNLÑNFTJOFEJS FöJUTJ[MJôJOJTBôMBZBOYUBNTBZMBSOOUPQMBN LBÀUS A) ( 1, 3 ) B) ( -1, 3 ) C) R D) R - { 3 } E) q A) -1 B) 0 C) 1 D) 2 E) 3 3. x2 - 4x + m + 2 > 0 7. #JSTBZOOLBSFTJJMFLBUOOUPQMBNOOGB[ FöJUTJ[MJôJOJO ÀÌ[ÑN LÑNFTJ SFFM TBZMBS PMEV MBTQP[JUJGPMEVôVOBHÌSF CVTBZOOFOHFOJö ôVOBHÌSF NOJOEFôFSBSBMôOFEJS EFôFSBSBMôOFEJS A) ( -Þ # -Þ -2 ) C) R A) R B) ( -1, 4 ) C) ( 1, -4 ) % Þ & q D) q E) ( -Þ 4. x2 + (m + 1) x + 4 > 0 8. x2 # x + 3 FöJUTJ[MJôJOJO ÀÌ[ÑN LÑNFTJ SFFM TBZMBS PMEV 2 ôVOBHÌSF NOJOEFôFSBSBMôOFEJS FöJUTJ[MJôJOJ TBôMBZBO Y UBN TBZ EFôFSMFSJOJO UPQMBNLBÀUS A) ( -5, 3 ) B) ( -3, 5 ) C) ( -6, 6 ) A) -2 B) -1 C) 0 D) 1 E) 3 D) ( -3, 4 ) E) ( -Þ 1. $ 2. & 3. D 4. \" 60 5. # 6. & 7. \" 8. $
www.aydinyayinlari.com.tr ÷,÷/$÷%&3&$&%&/%&/,-&.-&31\"3\"#0-&õ÷54÷;-÷,-&3 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, &õ÷54÷;-÷,-&3** ¦BSQN WF #ÌMÑN õFLMJOEFLJ &öJUTJ[MJLMFSJO ÖRNEK 3 ¦Ì[ÑN,ÑNFTJ ( 9 - x2 ) ( x - 2 ) ( x2 + 2 ) < 0 %m/*m FöJUTJ[MJôJOJOÀÌ[ÑNLÑNFTJOFEJS #JSEFO ¿PL ¿BSQBOM FõJUTJ[MJLMFSJO ¿Ë[ÐN LÐ- ( 3 -Y +Y Y- Y2 + < 0 NFTJCVMVOVSLFO IFS¿BSQBOOLËLMFSJCVMVOVQ x = 3, x = -3, x = 2 UBCMPZB TSBTZMB ZFSMFõUJSJMJS ¥BSQN WFZB CË- MÐN EVSVNVOEB PMBO JGBEFMFSJO CBõ LBUTBZMB- x –ß –3 2 3 ß S BMOBSBL ¿BSQMS ¥LBO TPOVDVO JõBSFUJ TBó mY2) (x – 2) (x2+ 2) + – + – CBõUBLJBSBMóOJõBSFUJEJS%JóFSBSBMLMBSEBJõB- SFUEFóJõUJSJMFSFLZB[MS ¦,= (- b (3, Þ &óFS ¿BSQBOMBSEBO CJSJOJO ¿JGU LBU LËLÐ WBSTB ZBOJBZOLËLWFZBOJOLBULBEBSEFOLMF- NJTBóMZPSTB CVLËLÐOTBóOEBWFTPMVOEBLJ JõBSFUBZOPMVS ÖRNEK 1 ÖRNEK 4 ( x - 2 ) ( x2 - 2x - 3 ) < 0 ( x - 1 ) ( x2 - 4x + 4 ) ( x - 3 ) $ 0 FöJUTJ[MJôJOJOÀÌ[ÑNLÑNFTJOFEJS FöJUTJ[MJôJOJOÀÌ[ÑNLÑNFTJOFEJS (x - Y- Y+ < 0 (x - Y- 2 (x - $ 0 x = 2, x = 3, x = -1 x = 1, x =WFY=ÀJGULBUMLÌL x –ß –1 2 3 ß (x–2)(x2–2x–3) – + – + x –ß 1 2 3 ß – + ¦,= (-Þ, - b (x – 1) (x – 2)2 Ymæ + – ¦,= (-Þ, 1] b [3, Þ b {2} ÖRNEK 2 ÖRNEK 5 ( x2 + 2x - 15 ) ( 7 - x ) < 0 ( x - 3 ) ( x2 - 6x + 9 ) ( 25 - x2 ) < 0 FöJUTJ[MJôJOJOÀÌ[ÑNLÑNFTJOFEJS FöJUTJ[MJôJOJOÀÌ[ÑNLÑNFTJOFEJS (x + Y- -Y < 0 (x - Y- 2 (5 -Y +Y < 0 x = -5, x = 3, x = 7 3 7ß x = 3, x = -WFY= 5 x –ß –5 x –ß –5 3 5ß (x2+2x–15) (7–x) + – + – (x–3) (x2mæY mY2) + – + – ¦,= (- b (7, Þ ¦,= (- b (5, Þ 1. mÞ m b 2. m b (7, Þ 61 3. m b (3, Þ 4. mÞ >b [3, Þ b\\^ 5. m b (5, Þ
·/÷7&34÷5&:&)\";*3-*, 2. MODÜL ÷,÷/$÷%&3&$&%&/%&/,-&.-&31\"3\"#0-&õ÷54÷;-÷,-&3 www.aydinyayinlari.com.tr ÖRNEK 6 ÖRNEK 9 x-1 <0 x2 + 4 $ 0 x-4 3-x FöJUTJ[MJôJOJOÀÌ[ÑNLÑNFTJOFEJS FöJUTJ[MJôJOJOÀÌ[ÑNLÑNFTJOFEJS x=1,x=4 x=3 x –ß 1 4ß x –ß 3 ß x2 + 4 + – x–1 + – + mæY x–4 ¦,= ¦,= (-ß ÖRNEK 7 ÖRNEK 10 1 $1 x2 - 4x + 4 > 0 x-1 x2 + 1 FöJUTJ[MJôJOJOÀÌ[ÑNLÑNFTJOFEJS FöJUTJ[MJôJOJOÀÌ[ÑNLÑNFTJOFEJS 1 2-x ^ x - 2 h2 -1$0& $0 > 0 JTFY=ÀJGULBUMLÌLUÑS x-1 x-1 x2 + 1 x = 2, x = 1 x –ß 2 ß x –ß 1 2ß (x – 2)2 + + x2æ mæY – + – x–1 ¦,=3- {2} ¦,= (1, 2] ÖRNEK 8 ÖRNEK 11 x-3 #0 x3 - 3x2 + 2x < 0 4-x - 2x - 4 FöJUTJ[MJôJOJOÀÌ[ÑNLÑNFTJOFEJS FöJUTJ[MJôJOJOÀÌ[ÑNLÑNFTJOFEJS x = 3, x = 4 xa x2 - 3x + 2 k <0 j x^ x - 2 h^ x - 1 h <0 x –ß 3 4ß -2^ x + 2 h -2^ x + 2 h x–3 – + – x = 0, x = -2, x = 1, x = 2 mæY ¦,= (-Þ, 3] b (4, Þ x –ß –2 0 1 2ß =3- (3, 4] x3 – 3x2 + 2x – + – + – –2x – 4 ¦,= (-ß - b b (2, Þ 6. 7. > 8. 3m > 62 9. mß 10. 3m\\^11. mß m b b (2, Þ
www.aydinyayinlari.com.tr ÷,÷/$÷%&3&$&%&/%&/,-&.-&31\"3\"#0-&õ÷54÷;-÷,-&3 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 12 ÖRNEK 15 ( –x + 1) 2 (x2 - 4) 3 ^ 2x - 8 h.^ x2 - 2x + 1 h3 ≥0 ≤0 x-3 x2 - x - 6 FöJUTJ[MJôJOJOÀÌ[ÑNLÑNFTJOFEJS FöJUTJ[MJôJOJOÀÌ[ÑNLÑNFTJOFEJS x =ÀJGULBUMLÌL ^ 2x - 8 h^ x - 1 h6 x = -2, x = 2, x = 3 #0 x –ß –2 1 2 3ß ^ x - 3 h^ x + 2 h x =WFY= 1ÀJGULBUMLÌL (–x+1)2 (x2–4)3 – + + – + x = -UFLLBUMLÌL x–3 x –ß –2 1 3ß ¦,= [-2, 2] b (3, Þ (2x–8)(x–1)6 –++ + (x–3) (x+2) ¦,= (-Þ, - b {1} ÖRNEK 13 ÖRNEK 16 3x - 3 ≤ 3 - x ^ 1 - x h ^ x2 - 2x - 15 h x2 - 1 $0 FöJUTJ[MJôJOJOÀÌ[ÑNLÑNFTJOFEJS x2 - 1 FöJUTJ[MJôJOJOÀÌ[ÑNLÑNFTJOFEJS 3x - 3 +x-3#0 & x^ x - 2 h^ x - 1 h #0 ^ 1 - x h^ x - 5 h^ x + 3 h $0 x2 - 1 ^ x - 1 h^ x + 1 h ^ x - 1 h^ x + 1 h x = 0, x = -1, x = 2, x =ÀJGULBUMLÌL x = -3, x = -1, x =WFY=ÀJGULBUMLÌL x –ß –1 0 1 2ß x –ß –3 –1 1 5 ß x(x–2) (x–1) – + – – + (1–x) (x2–2x–15) + –+ +– (x–1) (x+1) x2 – 1 ¦,= (-Þ, - b [0, 2] - {1} ¦,= (-Þ, -3] b (-1, 5]- {1} ÖRNEK 14 ÖRNEK 17 x+1 > x+2 - 6 # - 1 FöJUTJ[MJôJOJOÀÌ[ÑNLÑNFTJOFEJS x-1 x-2 x2 + x FöJUTJ[MJôJOJOÀÌ[ÑNLÑNFTJOFEJS x+1 x+2 - 2x >0 2 - >0 & x-1 x-2 ^ x - 1 h^ x - 2 h x +x-6 #0 x = 0, x = 1, x = 2 2 x +x x = -1, x = 0, x = -3, x = 2 x –ß 0 1 2ß x –ß –3 –1 0 2 ß –2x + – +– (x–1) (x–2) x2 Ymæ + –+ –+ x2 + x ¦,= (-Þ b ¦,= [-3, - b (0, 2] 12. <m >b (3, Þ 13. mÞ m b< >m\\^ 63 15. mÞ m b\\^ 16. mÞ m>b m >m\\^ 17. <m m b > 14. mÞ b
·/÷7&34÷5&:&)\";*3-*, 2. MODÜL ÷,÷/$÷%&3&$&%&/%&/,-&.-&31\"3\"#0-&õ÷54÷;-÷,-&3 www.aydinyayinlari.com.tr %m/*m ÖRNEK 21 .VUMBL EFóFSMJ JGBEFMFS J¿FSFO FõJUTJ[MJLMFSEF 3x – 1. x2 + 2x – 3 > 0 ^ 3 – x h2017 | |f ( x ) $ PMEVóVOEBO NVUMBL EFóFSJO LËLÐ FöJUTJ[MJôJOJOÀÌ[ÑNLÑNFTJOFEJS TJTUFNJOJõBSFUJOFFULJFUNFZFDFóJOEFO¿JGULBU- MLËLHJCJEÐõÐOÐMFCJMJS x = 3, x = -WFY=ÀJGULBUMLÌL ÖRNEK 18 x –ß –3 13 ß + – x-2 3x–1.|x2+ 2x – 3| + + # 0 FöJUTJ[MJôJOJOÀÌ[ÑNLÑNFTJOFEJS (3–x)2017 3-x ¦,= (-ß - {-3, 1} x = 3, x =ÀJGULBUMLÌL x –ß 23 ß + – |x – 2| + 3–x ¦,= (3, Þ b {2} ÖRNEK 22 ÖRNEK 19 ^ x2 – 16 h . x – 1 ≤0 x -2 $ 0 FöJUTJ[MJôJOJOÀÌ[ÑNLÑNFTJOFEJS 1– x x+3 FöJUTJ[MJôJOJOÀÌ[ÑNLÑNFTJOFEJS x = -4, x = 4, x =ÀJGULBUMWF- x > 0 j 1 >YPM NBMES x –ß –4 1 4 ß x = -3, x = -2 , x = 2 (x2m ]Ymæ] + – – + x –ß –3 –2 2 ß mæY |x| – 2 – + – + x+3 ¦,= [- ¦,= (-3, -2] b [ ß ÖRNEK 20 ÖRNEK 23 x–1 –3 x2 – 2x – 15 <0 >0 x2 – 4x + 4 x–2 –1 FöJUTJ[MJôJOJTBôMBZBOLBÀUBOFYUBNTBZTWBSES FöJUTJ[MJôJOJ TBôMBZBO Y UBN TBZ EFôFSMFSJOJO UPQMB NLBÀUS x = 4, x = -2, x =ÀJGULBUMLÌL x2 - 2x - 15 > 0 j (x - Y+ > 0 ß x –ß –3 5 x –ß –2 24 ß (x – 5) (x + 3) + – + – + |x–1|–3 + – x2–4x+4 |x - 2| - 1 > 0 j |x - 2| >JTFY>WFY< 1 ¦,= {-1, 0, 1, 3}PMEVôVOEBOUBNTBZWBSES xUPQ = ... -7 -6 - 5 - 4 + 6 + 7 + 8 + ... xUPQ = -CVMVOVS 18. (3, Þ b\\^ 19. m m>b< ß 20. 4 64 21. mß m\\m ^ 22. <m 23. m
¦BSQNWF#ÌMÑNõFLMJOEFLJ&öJUTJ[MJLMFSJO¦Ì[ÑN,ÑNFTJ TEST - 23 1. 1 > 1 5. 2x.^ x2 + 1 h ≤ 0 x-2 -x2 - x - 1 FöJUTJ[MJôJOJOFOHFOJö ÀÌ[ÑNLÑNFTJ BöBôEB FöJUTJ[MJôJOJO ÀÌ[ÑN BSBMô BöBôEBLJMFSEFO LJMFSEFOIBOHJTJEJS IBOHJTJEJS \" # Þ $ B) R+ C) R- A) R D) ( 0, 1 ) E) ( 0, 2 ) D) R+ b { 0 } E) R- b { 0 } - 2x (x2 - 5x + 6) 6. a < 0 <CPMNBLÐ[FSF 2. > 0 (ax + 1) (bx + 2) $0 8 - 2x x2 - a FöJUTJ[MJôJOJOFOHFOJö ÀÌ[ÑNLÑNFTJ BöBôEB LJMFSEFOIBOHJTJEJS FöJUTJ[MJôJOJO ÀÌ[ÑN LÑNFTJ BöBôEBLJMFSEFO A) ( -Þ b ( 2, 3 ) IBOHJTJEJS B) ( -Þ b Þ C) ( 2, 3 ) b Þ A) f – 3, - 2 H , >- 1 , 3 p D) (-Þ b ( 2, 3 ) b Þ ba E) ( 0, 2 ) b ( 3, 4 ) b Þ B) >- 2 , - 1 H ba C) >- 1 , - 2 H ab D) f - 1 , a p , f a , - 2 p ab E) ^ - 3, a h , f - 2 , 3 p b (2 - x) 2 (x2 - 1) 5 3. ≤ 0 x2 - x + 3 FöJUTJ[MJôJOJOFOHFOJöÀÌ[ÑNBSBMôBöBôEBLJ 7. ( x - 4 ) ( x2 - ax + b ) $ 0 MFSEFOIBOHJTJEJS FöJUTJ[MJôJOJO ÀÌ[ÑN LÑNFTJ [ ß PMEVôVOB A) [ –1, 1 ] # mÞ m] b { 2 } HÌSF BCLBÀUS C) [ –1, 1 ] b { 2 } % mÞ m] b [1 , 2 ] A) 12 B) 24 C) 36 D) 48 E) 96 E) [ 1, 2 ] b { –1 } 4. x2 - 15 . ^ 49 - x2 h $ 0 (x - 2) 2 (4x + a) FöJUTJ[MJôJOJO ÀÌ[ÑN LÑNFTJOEF LBÀ UBOF UBN 8. ≤ 0 TBZWBSES 3x - b A) 4 B) 6 C) 8 D) 12 E) 16 FöJUTJ[MJôJOJOÀÌ[ÑNLÑNFTJ-3 < x #PMEVôV OBHÌSF B+CUPQMBNLBÀUS A) -12 B) -15 C) -29 D) 2 E) 27 1. \" 2. D 3. $ 4. $ 65 5. \" 6. # 7. D 8. $
TEST - 24 ¦BSQNWF#ÌMÑNõFLMJOEFLJ&öJUTJ[MJLMFSJO¦Ì[ÑN,ÑNFTJ 1. ( 3 - x ) . ( x2 -Y ã x - 1 ^ 2 - x h.5x FöJUTJ[MJôJOJO ÀÌ[ÑN LÑNFTJ BöBôEBLJMFSEFO 5. ≥ 0 IBOHJTJEJS x2 - 9 A) [ 0, 3 ] B) [ 3, R) C) [ 0, R ) FöJUTJ[MJôJOJOHFSÀFLTBZMBSEBLJÀÌ[ÑNLÑNFTJ BöBôEBLJMFSEFOIBOHJTJEJS D) ( -R, 3 ] E) ( -R, 0 ] b { 3 } A) ( – R, – 3 ) B) ( – R ,– 3 ) b { 1 } b [ 2, 3 ) C) [ 2, R ) – { 3 } D) ( – R, – 3 ) b ( 3, R ) E) R – [ 2, 3 ] 2. ( 2 - x ) 2012 . ( x + 1 ) 2013 > 0 6. B< 0 <CPMNBLÑ[FSF FöJUTJ[MJôJOJOFOHFOJöÀÌ[ÑNBSBMôBöBôEBLJ ax + b > 0 MFSEFOIBOHJTJEJS x-a FöJUTJ[MJôJOJO ÀÌ[ÑN BSBMô BöBôEBLJMFSEFO A) R - [ - 1, 2 ] B) ( -R, 2 ) IBOHJTJEJS C) ( - 1, R ) D) ( -1, R ) - { 2 } E) ( -R, 2 ) - {- 2 } A) f a , - b p B) ( -R , a ) C) f - b , 3 p a a D) R - >a , - b H b a E) f , a p a | |3. x + 2 . ( x 2 + 1 ) . ( x 2 + 6x + 9 ) . ( 1 - x ) > 0 FöJUTJ[MJôJOJOFOHFOJöÀÌ[ÑNBSBMôBöBôEBLJ _ x + 4 i._ x + 5 i2 MFSEFOIBOHJTJEJS 7. # 0 A) ( -R, 1] B) [-3, R ) x C) [1, R ) b { -3 } D) (- R ,1] b { -3, -2 } FöJUTJ[MJôJOJTBôMBZBOGBSLMUBNTBZMBSOUPQMB E) [1, R ) b { -3, -2 } NLBÀUS A) -15 B) -12 C) -10 D) -8 E) - 6 ^ 4 – x h.^ x + 1 h 8. 4 > 1 4. > 0 2-x FöJUTJ[MJôJOJO HFSÀFL TBZMBSEBLJ FO HFOJö ÀÌ x-7 FöJUTJ[MJôJOJTBôMBZBOGBSLMEPôBMTBZMBSOUPQ [ÑNBSBMôBöBôEBLJMFSEFOIBOHJTJEJS MBNLBÀUS A) ( -R, 2 ) B) ( -2, 2 ) C) ( -2, R ) A) 4 B) 7 C) 9 D) 11 E) 15 D) ( 2, R ) E) R - [ -2, 2 ] 1. & 2. D 3. D 4. D 66 5. # 6. \" 7. \" 8. #
www.aydinyayinlari.com.tr ÷,÷/$÷%&3&$&%&/%&/,-&.-&31\"3\"#0-&õ÷54÷;-÷,-&3 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, &õ÷54÷;-÷,-&3*** ÷LJODJ%FSDFEFO#JS#JMJONFZFOMJ&öJUTJ[MJL4JT ÖRNEK 4 UFNMFSJOJO¦Ì[ÑN,ÑNFTJ x2 - 1 ≤ 0 %m/*m x-4 x2 - 3x + 2 > 0 öLJWFZBEBIBGB[MBFõJUTJ[MJóJOCJSBSBEBCVMVO- EVóV FõJUTJ[MJL TJTUFNMFSJOEF ¿Ë[ÐN LÐNFTJ FöJUTJ[MJLTJTUFNJOJOÀÌ[ÑNLÑNFTJOFEJS CVMVOVSLFO UÐNFõJUTJ[MJLMFSJOPSUBL¿Ë[ÐNLÐ- NFTJPMVõUVSVMVS ^ x - 1 h^ x + 1 h # 0 ,ÌLMFSY= -1, x =WFY= 4 ÖRNEK 1 x-4 2x - 6 > 0 (x - Y- >,ÌLMFSY=WFY= 2 1-x<0 FöJUTJ[MJLTJTUFNJOJOÀÌ[ÑNLÑNFTJOFEJS x –ß –1 1 2 4ß (x–1) (x+1) – + – – + x–4 (x – 2) (x – 1) + + – + + 2x - 6 > 0 j x > 3 ¦,= (-Þ, -1] b 1 - x < 0 j x >PMEVôVOEBO ¦,= (3, Þ ÖRNEK 5 ÖRNEK 2 2 < x2 - x < 6 FöJUTJ[MJLTJTUFNJOJOÀÌ[ÑNLÑNFTJOFEJS x2 - x > 0 2x - 1 < 0 x2 - x - 2 > 0 j (x - Y+ > 0 FöJUTJ[MJLTJTUFNJOJOÀÌ[ÑNLÑNFTJOFEJS x2 - x - 6 < 0 j (x - Y+ < 0 x (x - > 0 1ß x –ß –2 –1 2 3 ß x mß 0 –+ (x – 2) (x + 1) + + – + + (x – 3) (x + 2) + – – – + x2 – x + ¦,= (-2, - b 1 2x - 1 < 0 j x < 2 ¦,= (-ß ÖRNEK 3 ÖRNEK 6 x2 - x # 2 |x – 2| < 3 x2 + x > 6 1 >1 FöJUTJ[MJLTJTUFNJOJOÀÌ[ÑNLÑNFTJOFEJS x (x - Y+ # 0 FöJUTJ[MJLTJTUFNJOJOÀÌ[ÑNLÑNFTJOFEJS x mß –1 2 ß |x - 2| < 3 j -3 < x - 2 < 3 j -1 < x < 5 (x–2)(x+1) + –+ 1 >1 & 1 -1>0& 1-x >0 x x x (x + Y- > 0 x mß 0 1ß x –3 2 mæY – + – x (x+3)(x–2) + – + ¦,= ¦,= q 1. (3, Þ 2. mß 3. q 67 4. mÞ m>b 5. m m b 6.
·/÷7&34÷5&:&)\";*3-*, 2. MODÜL ÷,÷/$÷%&3&$&%&/%&/,-&.-&31\"3\"#0-&õ÷54÷;-÷,-&3 www.aydinyayinlari.com.tr ÖRNEK 7 JLJODJ%FSFDFEFO#JS#JMJONFZFOMJ%FOLMFNJO ,ÌLMFSJOJO÷öBSFUJ x2 + 4 > 0 x2 – 4 < 0 %m/*m 1 >1 ax2 + bx + c =EFOLMFNJOJOLËLMFSJOJCVMNB- x-2 EBO LËLMFSJOJO JõBSFUJOJ BõBóEBLJ UBCMPMBSEBO ZBSBSMBOBSBLCVMBCJMJSJ[ FöJUTJ[MJLTJTUFNJOJOÀÌ[ÑNLÑNFTJOFEJS x2 + 4 >EBJNBTBôMBOS c x1 < 0 < x2 x1.x2 = a < 0 x2 - 4 < 0 j (x - 2 Y+ < 0 –b x1+ x2 = a 1 3-x D>0 c > 0 j 0 < x1< x2 a x-2 -1>0& x-2 >0 x1 < x2 x1.x2 = >0 x –ß –2 2 3ß x1+ x2 = –b < 0 j x1< x2 < 0 a (x – 2) (x + 2) + –+ + –b > 0 j 0 = x1< x2 x1 + x2 = a c 3–x – –+– x1.x2 = a = 0 –b x–2 a x1 + x2 = < 0 j x1 < x2 = 0 ¦,= q x1 . x2 = c =0 j x1 = x2 = 0 a D=0 x1 + x2 = –b > 0 j x1 = x2 > 0 a c x1 . x2 = a >0 x1 + x2 = –b < 0 j x1 = x2 < 0 a ÖRNEK 8 ÖRNEK 9 4x > 0 \"öBôEBLJEFOLMFNMFSJOLÌLMFSJOJCVMNBEBOLÌLMFSJ 2 >1 OJOWBSMôOWFJöBSFUJOJJODFMFZJOJ[ x2 - x B 3x2 - 4x - 5 = 0 x3 > 1 FöJUTJ[MJLTJTUFNJOJOÀÌ[ÑNLÑNFTJOFEJS 4x > 0 j x > 0 D = (- 2 - 4.3 (- = 16 + 60 = 76 >PMEVôVOEBOCJS 2 -^ x - 2 h^ x + 1 h -1>0& >0 x2 - x x^ x - 1 h CJSJOEFOGBSLMJLJLÌLWBSES x mß –1 1 2 ß c5 – x1 . x2= a = - 3 < 0 PMEVôVOEBO LÌLMFS [U JöBSFU –(x–2) (x+1) + –+ MJEJS Y Ymæ x +x =- b4 > 0 PMEVôVOEBO = 12 a 3 x3 > 1 j x > 1 | |x 1 < 0 < x2WFY2 > x1 EJS ¦,= 7. q 8. 68 9. B x1 < 0 < x2WFY2 > |x1|
www.aydinyayinlari.com.tr ÷,÷/$÷%&3&$&%&/%&/,-&.-&31\"3\"#0-&õ÷54÷;-÷,-&3 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, C x2 - 4x + 1 = 0 ÖRNEK 10 D = (- 2 - 4.1.1 = 12 >PMEVôVOEBOCJSCJSJOEFOGBSL N>PMNBLÑ[FSF ( m + 1) x2 - 3 ( m + 3 ) x + m + 4 = 0 MJLJLÌLÑWBSES EFOLMFNJOJOLÌLMFSJOJOJöBSFUJOJJODFMFZJOJ[ c x .x = = 1 > 0 PMEVôVOEBOLÌLMFSBZOJöBSFUMJEJS 12 a b x1 + x2 =- a = 4 > 0 PMEVôVOEBO 0 < x1 < x2 EJS D = N2 +N+ - N2 +N+ =N2 +N+ 65 >PMEVôVOEBOGBSLMJLJLÌLWBS ES x .x = m+4 > 0 PMEVôVOEBOLÌLMFSBZOJöBSFUMJEJS D -2x2 - x + 2 = 0 1 2 m+1 x +x = 3^ m + 3 h > 0 PMEVôVOEBO 12 m+1 D = (- 2 - 4.(- = 17 >PMEVôVOEBOCJSCJSJOEFO 0 < x1 < x2EJS GBSLMJLJLÌLÑWBSES c x .x = = - 1 < 0 PMEVôVOEBOLÌLMFS[UJöBSFUMJEJS 12 a -b 1 x +x = = - < 0 PMEVôVOEBO 12 a 2 | |x1 <0 < x2WF x1 > x2EJS E -x2 + x - 3 = 0 ÖRNEK 11 D = 12 - 4(- - = -PMEVôVOEBOSFFMLÌLZPLUVS N<PMNBLÑ[FSF ÷öBSFUJODFMFOFNF[ ( m - 2 ) x2 - ( m - 1 ) x + 3 - m = 0 EFOLMFNJOJOLÌLMFSJOJOJöBSFUJOJJODFMFZJOJ[ F 4x2 - 2 x = 0 D = N2 -N+ - 4 (-N2 +N- =N2 -N+ 25 >PMEVôVOEBOGBSLMJLJLÌLWBS D = ^ - 2 h2 - 4.4.0 = 2 >PMEVôVOEBOGBSLMJLJLÌL ES WBSES x .x = 3-m < 0 PMEVôVOEBOLÌLMFS[UJöBSFUMJEJS 1 2 m-2 c x +x = m-1 > 0 PMEVôVOEBO x .x = a = 0 PMEVôVOEBOLÌLMFSEFOCJSJES 1 2 m-2 12 x +x = 2 > 0 PMEVôVOEBO= x1 < x2EJS | |x1 < 0 < x2WF x1 < x2 EJS 12 4 C Y1 < x D Y1 <0 < x2WF]Y1| > x 69 10. 0 < x1 < x2 11. x1 < 0 < x2WF]Y1 | < x2 2 2 E ÷öBSFUJJODFMFOFNF[F 0 = x1 < x2
·/÷7&34÷5&:&)\";*3-*, 2. MODÜL ÷,÷/$÷%&3&$&%&/%&/,-&.-&31\"3\"#0-&õ÷54÷;-÷,-&3 www.aydinyayinlari.com.tr 7$1,0%m/*m ÖRNEK 12 ax2 + bx + c = 0 denkleminde, ( m - 3 ) x2 - ( 2 – m ) x + 6 - 3m = 0 r 5FSTJõBSFUMJJLJLËLWBSTB Y1 < 0 < x2 ise ) EFOLMFNJOEF x1 < 0 < x2 PMEVôVOB HÌSF N IBOHJ BSBMLUBCVMVOVS x1 . x2 = c < 0ES a r 5FSTJõBSFUMJJLJLËLWBSWFNVUMBLEFóFSDF %FOLMFNJOUFSTJöBSFUMJJLJLÌLÑWBSPMEVôVOEBO CÐZÐLPMBOLËLQP[JUJGJTF Y1 < 0 < x2WF x .x <PMNBMES 12 | |x1 < x2 ise ) 6 - 3m < 0 & m = 2 ve m = 3 c a m-3 x1 . x2 = <0 x mß 2 3ß 6 – 3m – + – m–3 b x1 + x2 = - a > 0ES N` (-Þ b (3, Þ r 5FSTJõBSFUMJJLJLËLWBSWFNVUMBLEFóFSDF ÖRNEK 13 büyük PMBOLËLOFHBUJGJTF Y1 < 0 < x2WF ( m + 1 ) x2 - ( 3m + 1 ) x - m - 3 = 0 | |x1 > x2 ise) | | | |EFOLMFNJOEF Y1 < 0 < x2WF x1 < x2 PMEVôVOB x . x = c <0 a HÌSF NIBOHJBSBMLUBCVMVOVS 1 2 x +x =- b < 0ES a 12 x .x <WFY1 + x >PMNBMES /05 :VLBSEBLJ EVSVNMBSEB c < 0 JTF Ó 12 2 a -m - 3 < 0 ve 3m + 1 >0 PMBDBóOEBOÓOOJõBSFUJOFCBLNBZBHFSFLZPL- m+1 m+1 –ß –3 –1 ß –ß –1 – 1 ß 3 tur. –+ – +– + r \"ZOJõBSFUMJJLJLËLWBSTB Ó$ 0 N` (-Þ, - bd - 1 , 3 n 3 c x1 . x2 = a >0 r 1P[JUJGJLJLËLWBSTB ÖRNEK 14 Ó$ 0 mx2 + ( 2m + 1 ) x - m - 1 = 0 x .x = c >0 | | | |EFOLMFNJOEF x1 < 0 < x2WF x1 > x2 PMEVôVOB 12 a x +x = -b > 0 HÌSF NIBOHJBSBMLUBCVMVOVS 12 a r /FHBUJGJLJLËLWBSTB Ó$ 0 x1.x2 <WFY1 + x2 <PMNBMES -m - 1 - 2m - 1 m < 0 ve m <0 x .x = c >0 12 a –ß –1 0 ß –ß – 1 0ß 2 – x + x = - b < 0 d›r. 12 a –+ – – + N` (-Þ, - b(0, Þ 70 12. N` mÞ b(3,Þ 13. N` mÞ m bd - 1 , 3 n 3 14. N` mÞ m b(0, Þ
www.aydinyayinlari.com.tr ÷,÷/$÷%&3&$&%&/%&/,-&.-&31\"3\"#0-&õ÷54÷;-÷,-&3 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 15 7$1,0%m/*m x2 - ( m + 2 ) x + m + 1 = 0 ax2 + bx + c >FõJUTJ[MJóJr x `3J¿JOTBó- MBOZPSTB EFOLMFNJOEFBZOJöBSFUMJGBSLMJLJLÌLWBSTBNIBO HJBSBMLUBCVMVOVS Ô WFB ES ax2 + bx + c <FõJUTJ[MJóJr x `3J¿JOTBó- %FOLMFNJOBZOJöBSFUMJGBSLMJLJLÌLPMEVôVOEBO MBOZPSTB WFY1.x2 PMNBMES Ô WFB ES N+ 2 - N+ >WFN+ 1 > 0 ÖRNEK 18 N2 > WFN> -1 ( 3 - m ) x2 + 2 ( m - 2 ) x - m + 2 > 0 N` (- ß ={0} ÖRNEK 16 FöJUTJ[MJôJr x `3JÀJOTBôMBOZPSTBNIBOHJBSB MLUBCVMVOVS ( m - 1 ) x2 + 2mx + m - 3 = 0 D WFB PMNBMES EFOLMFNJOEF0 < x1 < x2PMEVôVOBHÌSF NIBOHJ N- 2 - 4 (3 -N -N+ < 0 jN- 8 < 0 BSBMLUBCVMVOVS jN 3 -N> 0 jN< 3 %FOLMFNJOGBSLMQP[JUGJLJLÌLÑPMEVôVOEBO jN` (-Þ D > 0, x1.x2 WFY1 + x2 PMNBMES ÖRNEK 19 N 2 - N- N- > 0 ( m - 2 ) x2 + 4x + m < 5 3 FöJUTJ[MJôJr x `3JÀJOTBôMBOZPSTBNIBOHJBSB N- 12 > 0 j m > MLUBCVMVOVS 4 m-3 - 2m > 0 >0 m-1 m-1 –ß 1 3 ß –ß 0 1ß +– + –+ – m !d 3 ,1 n D WFB PMNBMES –ß 1 6ß 4 16 - N- N- < 0 +– + N2 -N+ 6 > 0 ÖRNEK 17 N- N- > 0 ( m + 1) x2 + ( 4 - 2m ) x + m + 3 = 0 WFN- 2 < 0 jN<PMEVôVOEBON` (-Þ EFOLMFNJOEFY1 < x2 <PMEVôVOBHÌSF NIBOHJ BSBMLUBCVMVOVS %FOLMFNJOGBSLMOFHBUJGJLJLÌLÑPMEVôVOEBO ÖRNEK 20 D > 0, x1.x2 WFY1 + x2 PMNBMES mx2 -åY+Nâ (4 -N 2 - N+ N+ > 0 FöJUTJ[MJôJr x `3JÀJOTBôMBOZPSTBNIBOHJBSB -N+ 4 > 0 j m < 1 MLUBCVMVOVS m+3 8 2m - 4 <0 m+1 >0 m+1 D #WFB PMNBMES –ß –2 2ß –ß –3 –1 ß –ß –1 2 ß – 16 -N2 # 0 –+ +– + +– + 4 -N2 # 0 m ! d - 1, 1 n WFN<PMEVôVOEBON` (-Þ, -2] 8 15. N` m ß =\\^ 16. m ! d 3 , 1 n 17. m ! d - 1, 1 n 71 18. N` mÞ 19. N` mÞ 20. N` mÞ m> 48
TEST - 25 ÷LJODJ%FSFDFEFO#JS#JMJONFZFOMJ&öJUTJ[MJL4JTUFNMFSJOJO¦Ì[ÑN,ÑNFTJ 1. x +âY 2 < 4x 5. x2 - 4 ≥0 FöJUTJ[MJL TJTUFNJOJO ÀÌ[ÑN LÑNFTJ BöBôEBLJ x-3 MFSEFOIBOHJTJEJS x-1 ≤0 A) [ - 1, 4 ) x B) ( 0, 2 ] C) [ 2, 4 ) D) ( -1, 2 ] E) q FöJUTJ[MJL TJTUFNJOJO FO HFOJö ÀÌ[ÑN LÑNFTJ BöBôEBLJMFSEFOIBOHJTJEJS A) ( 0, 1 ] B) [-2, 0 ] C) [ 1, 2 ] D) ( 0, 2 ] E) [ 2, 3 ) 2. x 2 - 2x - 8 < 0 6. x_ x - 3 i ≤ 0 x2 - 4 > 0 x3 - x $ 0 x x+1 10 x2 - 9 FöJUTJ[MJL TJTUFNJOJO ÀÌ[ÑN LÑNFTJ BöBôEBLJ MFSEFOIBOHJTJEJS? A) ( -2, 4 ) B) ( -R, 0 ) FöJUTJ[MJL TJTUFNJOJO ÀÌ[ÑN LÑNFTJ BöBôEBLJ MFSEFOIBOHJTJEJS C) ( 0, 2 ) D) ( -2, 0 ) b ( 2, 4 ) E) ( -R, -2 ) b ( 2, 4 ) A) ( 0, 3 ) B) [ - > $ < Þ> D) ( -Þ -3 ) E) [ 1, 3 ) b { 0 } 3. 4 < x2 - 3x < 10 FöJUTJ[MJL TJTUFNJOJO FO HFOJö ÀÌ[ÑN LÑNFTJ 7. ( m - 4 ) x2 - mx - 2 + m = 0 OFEJS EFOLMFNJOEF Y1 < 0 < x2 PMEVôVOB HÌSF N A) ( -2, 5 ) B) ( -1, 4 ) C) ( -2, -1 ) JÀJOBöBôEBLJMFSEFOIBOHJTJEPôSVEVS A) 2 < m < 4 B) m > 2 C) m < 4 D) ( 4, 5 ) E) ( -2, -1) b ( 4, 5 ) D) m > 0 E) 0 < m < 4 4. x2 - 2x < 0 4 8. ( m - 1 ) x2 + ( 2m - 1 ) x - m = 0 x2 - 3x > 4 | |EFOLMFNJOEF x1 < 0 < x2WF x1 > x2 PMEVôV FöJUTJ[MJL TJTUFNJOJO FO HFOJö ÀÌ[ÑN LÑNFTJ OBHÌSF NOJOBMBCJMFDFôJEFôFSBSBMôOFEJS OFEJS 1 A) ( 0, 2 ) B) ( -1, 0 ) b ( 2, 4 ) A) f , 1 p B) R - [ 0, 1 ] 2 C) ( 2, 4 ) D) ( -Þ -1) b Þ C) > 1 , 1H D) (0, 4 + 2 2] 2 E) Ø E) ( – 3 , 4 - 2 2] , [4 + 2 2 , 3 ) 1. $ 2. D 3. & 4. & 72 5. \" 6. & 7. \" 8. #
÷LJODJ%FSFDFEFO#JS#JMJONFZFOMJ&öJUTJ[MJL4JTUFNMFSJOJO¦Ì[ÑN,ÑNFTJ TEST - 26 1. x2 - mx + m - 1 = 0 4. mx2 + 4x + m - 3 < 0 EFOLMFNJOJO LÌLMFSJ BZO JöBSFUMJ PMEVôVOB HÌ FöJUTJ[MJôJrx ` 3JÀJOTBôMBOZPSTBNOFEJS SF NOFEJS A) m > 1 B) m > 0 C) m < 0 A) m ` ( -1, 4 ) B) m ` ( -Þ -1 ) D) m < -1 E) -1 < m < 1 C) m ` ( -Þ D) m `( -4, -1 ) E) m ` ( -Þ -4 ) 2. mx2 + ( 2m + 2 ) x + m - 2 = 0 5. c >PMNBLÐ[FSF EFOLMFNJOEF 0 < x1 < x2PMEVôVOBHÌSF NOJO –4x2 + x + 3c = 0 BMBCJMFDFôJEFôFSBSBMôOFEJS EFOLMFNJOJOLËLMFSJY1WFY2 dir. A) ( -1, 0 ) B) ( 0, 1 ) C) ( 1, 2 ) E) f - 1 , 0 p #VOBHÌSF BöBôEBLJMFSEFOIBOHJTJEPôSVEVS D) f 0 , 1 p 4 A) x1 < x2 < 0 4 B) 0 < x1 < x2 | |C) x1 < 0 < x2WF x1 < x2 | |D) x1 < 0 < x2WF x2 < x1 | |E) x1 < 0 < x2WF x1 = x2 3. ( 2 - m ) x2 + 2 ( m - 1 ) x - m + 1 > 0 6. N>PMNBLÑ[FSF mx2 - 3 ( m + 2 ) x + m + 3 = 0 FöJUTJ[MJôJrx `3JÀJOTBôMBOZPSTBNOFEJS EFOLMFNJOJO LÌLMFSJ JÀJO BöBôEBLJMFSEFO IBO HJTJEPôSVEVS A) m < 0 B) m < 1 C) 0 < m < 1 D) m > 1 E) 1 < m < 2 A) x1 < 0, x2 < 0 B) x1 < 0 < x2 C) x1 + x2 = 0 D) x1 = x2 > 0 E) x1 > 0, x2 > 0 1. \" 2. & 3. # 73 4. # 5. $ 6. &
·/÷7&34÷5&:&)\";*3-*, 2. MODÜL ÷,÷/$÷%&3&$&%&/%&/,-&.-&31\"3\"#0-&õ÷54÷;-÷,-&3 www.aydinyayinlari.com.tr &õ÷54÷;-÷,-&3*7 ÷LJODJ%FSFDFEFO&öJUTJ[MJLMFSJO(SBüôJ C y # x2 TANIM y > ax2 + bx +DFõJUTJ[MJóJOJOHSBGJóJ y x y = ax2 + bx +DQBSBCPMÐOÐOÐTUCËMHFTJOEFLJ O OPLUBMBSES y y y Ox y = ax2 + bx + c a>0 D y # -2x2 Ox x O y = ax2 + bx + c a<0 6:\"3*Z$ ax2 +CY+DFõJUTJ[MJôJOJOHSBGJôJO- EF QBSBCPMÑO Ñ[FSJOEFLJ OPLUBMBS EB HSBGJôF EBIJMFEJMJS y < ax2 + bx +DFõJUTJ[MJóJOJOHSBGJóJ E y < -x2 + 2 y = ax2 + bx +DQBSBCPMÐOÐOBMUCËMHFTJOEFLJ OPLUBMBSES y y = ax2 + bx + c y y a>0 2 x O Ox O x y = ax2 + bx + c F y $ x2 - 1 a<0 y 6:\"3*Z# ax2 +CY+DFõJUTJ[MJôJOJOHSBGJôJO- Ox EF QBSBCPMÑO Ñ[FSJOEFLJ OPLUBMBSEB HSBGJôF –1 –1 EBIJMFEJMJS –1 ÖRNEK 1 G y # -x2 + 2x \"öBôEBLJFöJUTJ[MJLMFSJOHSBGJLMFSJOJÀJ[JOJ[ B y > x2 y y x O2 O 74
www.aydinyayinlari.com.tr ÷,÷/$÷%&3&$&%&/%&/,-&.-&31\"3\"#0-&õ÷54÷;-÷,-&3 2. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 2 F y < -x2 y>x-2 \"öBôEBLJFöJUTJ[MJLTJTUFNMFSJOJHFSÀFLMFZFOOPLUB x.y < 0 MBSLÑNFTJOJBOBMJUJLEÑ[MFNEFHÌTUFSJOJ[ B y # x y y=x–2 O2 x y > x2 –2 y = x2 y y = –x2 y=x x O G x2 - 2x < y # x2 + 4x y C y > -x O x y # -x2 –4 2 y ÖRNEK 3 Ox y :BOEBLJHSBGJôFHÌSF y = –x y = –x2 r& r% \" # $ % & ' OPLUBMB SOEBOIBOHJTJ 3 r\" r# D y # x + 1 r$ x + 1 #Z# -x2 + 2x + 3 y $ x2 - 2 –1 3 x FöJUTJ[MJôJOJTBôMBS y=x+1 r' y Z= x +EPôSVTVOVOÑTUÑOEFZ= -x2 + 2x +QBSB CPMÑOÑOBMUOEBPMBO#OPLUBTTBôMBS –1 1 x –2 O 2 y = x2–1 –2 ÖRNEK 4 5BSBM CÌMHFMFSJ FöJUTJ[ MJLMFS LVMMBOBSBL JGBEF y FEJOJ[ 16 E x . y < 0 –4 2 x y $ x2 - 1 –1 O 3 y –3 O x 1BSBCPMMFSJOEFOLMFNMFSJZB[MEôOEBZ= -2x2 - 4x + 16 –1 1 WFZ= x2 - 2x -CVMVOVS0IBMEFFöJUTJ[MJLMFS –1 x2- 2x - 3 #Z# -2x2 - 4x +WFYZ$CVMVOVS 75 3. # 4. x2mYm#Z#mY2mY WFYZ$ 0
TEST - 27 ÷LJODJ%FSFDFEFO&öJUTJ[MJLMFSJO(SBGJLMFSJ 1. y # x2 - 2x 3. y $ x2 - 2x 4 FöJUTJ[MJôJOJO HSBGJôJ BöBôEBLJMFSEFO IBOHJTJ y<x EJS FöJUTJ[MJL TJTUFNJOJO HSBGJôJ BöBôEBLJMFSEFO \" y # y IBOHJTJEJS \" y # y x x O 2 x O 2x –2 O O2 –2 –2 $ y % y $ y % y Ox O2 x –2 2 x O 2x –2 –2 O & y 2x & y 2x O O 2. y $ x2 - 1 4. y <- x2 + 1 4 FöJUTJ[MJôJOJO HSBGJôJ BöBôEBLJMFSEFO IBOHJTJ y+x $ 0 EJS FöJUTJ[MJL TJTUFNJOJO HSBGJôJ BöBôEBLJMFSEFO IBOHJTJEJS \" y # y \" y # y Ox Ox O x O x –1 1 –1 1 –1 1 –1 –1 $ y % y $ y % y 1 1 O1 O 1 –1 1 x –1 1 O x –1 1 x –1 O x & y & 1 Ox 1 x –1 1 –1 O –1 1. D 2. & 76 3. D 4. &
÷LJODJ%FSFDFEFO&öJUTJ[MJLMFSJO(SBGJLMFSJ TEST - 28 1. y $ x2 - 1 3. y :BOEBLJ HSBGJôF HÌSF y # -x2 + 1 # \" # $ % & OPLUBMB $ SOEBOIBOHJTJ x2 - x - 2 #Z # 2x - 2 FöJUTJ[MJL TJTUFNJOJO HSBGJôJ BöBôEBLJMFSEFO O1 x FöJUTJ[MJLTJTUFNJOJ –1 \" 2 IBOHJTJEJS \" y # y % TBôMBS –1 & 1 1 x A) A B) B C) C D) D E) E O –1 O 1 x –1 1 –1 $ y % y 4. y :BOEBLJöFLJMEFUBSBM 1 1 CÌMHFZJ JGBEF FEFO O –1 x –1 1x FöJUTJ[MJLTJTUFNJBöB O 1 ôEBLJMFSEFO IBOHJTJ EJS x O & y A) y $ x2 B) y > x2 C) y $ x2 y # x2 + 1 y < x2 + 1 y < x2 + 1 O x 1 x.y $ 0 x.y < 0 x.y $ 0 x2 _ D) y > x E) y $ x2 y # x2 y # x2 + 1 x<0 x.y # 0 2. y $ + 2x b ` x2 b y $ - 2x a FöJUTJ[MJL TJTUFNJOJO HSBGJôJ BöBôEBLJMFSEFO IBOHJTJEJS 5. y õFLJMEFLJUBSBMCÌMHF \" y # y O1 ZJ JGBEF FEFO FöJUTJ[ –2 –1 3 –2 2x MJL TJTUFNJ BöBôEBLJ O –1 MFSEFOIBOHJTJEJS x O x 2 $ y % y x A) y $ x2 - 2x - 3 B) y $ x2 - 2x - 3 2 y<x-1 y#x-1 –2 O x –2 O 2 & y C) 3y $ x2 - 2x - 3 D) 3y $ x2 - 2x - 3 y<x-1 y$x-1 –2 2x E) 3y < x2 - 2x - 3 O y$x-1 1. \" 2. D 77 3. \" 4. & 5. $
KARMA TEST - 1 ÷LJODJ%FSFDFEFO%FOLMFNMFS&öJUTJ[MJL1BSBCPM 1. x2 - 6x + 4 = 0 5. x2 + 2x + 12 = 7 EFOLMFNJOJO LÌLMFSJOEFO CJSJ BöBôEBLJMFSEFO x2 + 2x IBOHJTJEJS EFOLMFNJOJO LÌLMFSJOEFO CJSJ BöBôEBLJMFSEFO IBOHJTJEJS A) 2 - 5 B) 5 - 2 C) 3 - 5 A) -3 B) -2 C) 2 D) 3 E) 4 D) 5 - 3 E) 4 - 5 2. ( a2 + 2a )2 - 18 ( a2 + 2a ) + 45 = 0 6. x + 34 - x = 4 EFOLMFNJOJO FO CÑZÑL JMF FO LÑÀÑL LÌLÑOÑO EFOLMFNJOJO HFSÀFM TBZMBSEBLJ ÀÌ[ÑN LÑN FTJ UPQMBNLBÀUS BöBôEBLJMFSEFOIBOHJTJEJS A) -2 B) -1 C) 0 D) 1 E) 2 A) { -9 } B) { 2 } C) { –9, 2 } D) { 2, 9 } E) { 9 } 3. x + 4 x = 20 7. B`3PMNBLÑ[FSF EFOLMFNJOJO HFSÀFM TBZMBSEBLJ ÀÌ[ÑN LÑN FTJ a2 + 3a + a2 + 3a + 5 = 7 BöBôEBLJMFSEFOIBOHJTJEJS PMEVôVOBHÌSF B2 +B+ UPQMBNOOEFôFSJ A) { -5, 4 } B) { 4 } C) { 256, 625 } LBÀUS D) { 256 } E) { 625 } A) 4 B) 8 C) 9 D) 10 E) 12 4. 3 x2 - 6 3 x + 8 = 0 8. f x+2 2 x+2 p+3 = 0 EFOLMFNJOJOHFSÀFMLÌLMFSJOJOUPQMBNLBÀUS x-1 p - 4f x-1 A) 6 B) 8 C) 24 D) 64 E) 72 EFOLMFNJOJTBôMBZBOYEFôFSJLBÀUS A) 35 E) 7 B) 2 C) D) 3 2 22 1. $ 2. \" 3. D 4. & 78 5. \" 6. # 7. & 8. $
÷LJODJ%FSFDFEFO%FOLMFNMFS&öJUTJ[MJL1BSBCPM KARMA TEST - 2 1. x2 - 2x + 4 = 0 5. [1 = 2a - b +CJWF[2 = 4 - ( 3a - 6 ) i EFOLMFNJOJO LPNQMFLT TBZMBS LÑNFTJOEFLJ TBZMBSJÀJO[1 =[2PMEVôVOBHÌSF B+CEFôF LÌLMFSJOEFOCJSJBöBôEBLJMFSEFOIBOHJTJEJS SJLBÀUS A) 1 - 3 i B) i – 3 C) 2 + 3 i A) 0 B) 1 C) 2 D) 3 E) 4 D) 1+ 2 3 i E) 2i + 3 2. ^ x2 + x h2 + 2x2 + 2x – 3 = 0 6. [ - i ) + 3i - 4 = zi + 2i – 5 EFOLMFNJOJOSFFMPMNBZBOLÌLMFSJOJOÀÌ[ÑNLÑ NFTJBöBôEBLJMFSEFOIBOHJTJEJS A) * –1– 5i –1+ 5i 4 FöJUMJôJOJ TBôMBZBO [ TBZT BöBôEBLJMFSEFO , IBOHJTJEJS 22 B) * 1– 5i 1+ 5i 4 A) 1 + 3i B) 3 - i C) -5 + i , 22 D) -1 - 3i E) -3 - i C) * –1– 11 i –1+ 11 i 4 , 22 D) * 1– 11 i 1+ 11 i 4 , 22 E) * –1– 5 i –1– 11 i 4 x - yi 74 , 22 7. f p y + xi TBZTOOFöJUJBöBôEBLJMFSEFOIBOHJTJEJS 3. ,ÌLMFSJ J - WF J + PMBO JLJODJ EFSFDFEFO A) -1 B) -i C) i EFOLMFNBöBôEBLJMFSEFOIBOHJTJEJS D) 1 E) 1 + i A) x2 - (2 - i) x + 3i - 1 = 0 B) x2 - ix + 3 = 0 C) x2 - (2 - i) x + i - 3 = 0 D) x2 - 3ix + i - 3 = 0 E) x2 - 2ix + 3i - 3 = 0 8. J[2 -J[+ i - 2 = 0 4. ,ÌLMFSJOEFOCJSJJ-PMBOJLJODJEFSFDFEFOSF EFOLMFNJOJO ÀÌ[ÑN LÑNFTJ BöBôEBLJMFSEFO IBOHJTJEJS FM LBUTBZM EFOLMFN BöBôEBLJMFSEFO IBOHJTJ EJS A) { -i, 2 + i } B) { -i, 2 - i } A) x2 + 2x + 4 = 0 B) x2 + 2x - 8 = 0 C) { i, 2i - 1} D) {1 - i, 1 + i} C) x2 - 2x + 4 = 0 D) x2 - 2x + 8 = 0 E) {2 - i, 2 + i } E) x2 + 2x + 10 = 0 1. \" 2. $ 3. D 4. & 79 5. $ 6. D 7. \" 8. #
KARMA TEST - 3 ÷LJODJ%FSFDFEFO%FOLMFNMFS&öJUTJ[MJL1BSBCPM 1. x2- 13x + 3m + 12 = 0 5. x2 - 3x - 5 = 0 EFOLMFNJOJOLËLMFSJY1WFY2 dir. EFOLMFNJOJOLËLMFSJY1WFY2 dir. x2 = 2x1 +PMEVôVOBHÌSF NLBÀUS A) 5 B) 6 C) 8 D) 9 E) 10 #VOBHÌSF x13 + x 3 UPQMBNLBÀUS 2 A) 48 B) 64 C) 72 D) 84 E) 96 2. x2 + mx - 2x =EFOLMFNJOJOLËLMFSJY1WFY2 dir. 6. x2 - 4x - 3 =EFOLMFNJOJOLËLMFSJY1WFY2 dir. #VOBHÌSF x21 - x22 JGBEFTJOJOEFôFSJLBÀUS x2 =2 x 2 A) 4 5 B) 8 5 C) 4 7 1 PMEVôVOBHÌSF NLBÀUS D) 8 7 E) 12 7 A) -4 B) -3 C) -2 D) 2 E) 3 3. x2 + 10x + 3m - 2 = 0 denklemi bir tam kare 7. x2 + mx + n = 0 belirtmektedir. x2 + ( m - n + 1) x - 16 = 0 denk- EFOLMFNJOJOÀÌ[ÑNLÑNFTJ{7, 11} PMEVôVOB MFNJOJOTJNFUSJLJLJLËLÐWBSES HÌSF Y+ 2 +N Y+ +O=EFOLMFNJ OJOÀÌ[ÑNLÑNFTJBöBôEBLJMFSEFOIBOHJTJEJS #VOBHÌSF N+OUPQMBNLBÀUS A) { 17, 25 } B) { 7, 11 } C) { 2, 4 } A) 13 B) 15 C) 16 D) 18 E) 19 D) { -2, -4 } E) { 6, 9 } 4. 3x2 - 4x + 1 = 0 8. ( a + b ) x2 - ( a - b ) x + a2 - b2 = 0 EFOLMFNJOJOLÌLMFSJY1WFY2PMEVôVOBHÌSF EFOLMFNJOJOLÌLMFSUPQMBN LÌLMFSÀBSQN-4 JTFBCLBÀUS x 2 + x22 UPQMBNLBÀUS 1 A) 3 B) 2 C) -1 D) -2 E) -3 10 11 4 13 A) 1 B) C) D) E) 9 93 9 1. $ 2. \" 3. & 4. # 80 5. $ 6. D 7. $ 8. &
÷LJODJ%FSFDFEFO%FOLMFNMFS&öJUTJ[MJL1BSBCPM KARMA TEST - 4 1. 3BTZPOFM LBUTBZM JLJODJ EFSFDF EFOLMFNJOJO x+y=2 CJS LÌLÑ 3 + 2 PMEVôVOB HÌSF CV EFOLMFN 5. (x - y) 2 - 2 (x - y) - 8 = 0 4 BöBôEBLJMFSEFOIBOH JTJEJS EFOLMFNTJTUFNJOJTBôMBZBOZEFôFSMFSJOJOUPQ MBNLBÀUS? A) x2 + 4x + 1 = 0 B) x2 - 4x + 1 = 0 A) -1 B) 0 C) 1 D) 2 E) 3 C) x2 - 4x + 2 = 0 D) x2 + x - 4 = 0 E) x2 + x + 1 = 0 2. ,ÌLMFSJBSBTOEB 6. y ôFLJMEF f ( x ) = ax 2 + bx + c 3x1 (x2 - 1) - x2 (x1 + 3) = 13 O x fonksiyonVOVOHSBGJóJ WFSJMNJõUJS x1 (x2 + 2) + 2x2 (x1 + 1) = 13 CBôOUMBSCVMVOBOEFSFDFEFOEFOLMFNBöB Z G Y ôEBLJMFSEFOIBOHJTJEJS A) x2 + x + 5 = 0 B) x2 + 2x - 5 = 0 #VOBHÌSF B C DOJOTSBTZMBJöBSFUMFSJBöBô EBLJMFSEFOIBOHJTJEJS C) x2 - x - 3 = 0 D) x2 - 2x - 5 = 0 E) x2 - 2x - 3 = 0 A) -, -, - B) +, -, - C) -, -, + D) -, +, + E) -, +, - 3. 3x2 - 2x - 3 = 0 7. y G Y BY2 + bx + c EFOLMFNJOJO LÌLMFSJ Y1 WF Y2 PMEVôVOB HÌSF 1x LÌLMFSJ 1 ve 1 PMBOJLJODJEFSFDF x1 - 1 x2 - 1 EFOEFOLMFNBöBôEBLJMFSEFOIBOHJTJEJS A) 2x2 - 4x - 3 = 0 B) x2 - 2x + 6 = 0 –2 T C) 4x2 - 3x + 1 = 0 D) x2 - 3x + 2 = 0 E) 2x2 - x - 3 = 0 õFLJMEFLJZ=G Y QBSBCPMÑOÑOUFQFOPLUBT 5 - PMEVôVOBHÌSF G EFôFSJLBÀUS A) 12 B) 14 C) 15 D) 16 E) 18 4. y = x2 - 6x + 4 4 y =-x+k TJTUFNJOJO ÀÌ[ÑN LÑNFTJ CJS FMFNBOM PMEVôV 8. f (x ) = x 2 - 3x - 10 OBHÌSF LLBÀUS QBSBCPMÑOÑO FLTFOMFSJ LFTUJôJ OPLUBMBS LÌöF LBCVMFEFOÑÀHFOJOBMBOLBÀCJSJNLBSFEJS B) - 9 C) - 11 D) -3 E) - 15 A) -2 44 4 A) 24 B) 27 C) 32 D) 34 E) 35 1. # 2. \" 3. \" 4. # 81 5. $ 6. & 7. D 8. &
KARMA TEST - 5 ÷LJODJ%FSFDFEFO%FOLMFNMFS&öJUTJ[MJL1BSBCPM 1. y = x2 - 2x 5. y = x2 + ( m + 2 ) x - 12 QBSBCPMÑJMFZ= x +NEPôSVTVGBSLMJLJOPLUB QBSBCPMÑOÑOUFQFOPLUBTOOBQTJTJPMEVôVOB EBLFTJöUJôJOFHÌSF NOJOBMBCJMFDFôJFOLÑÀÑL HÌSF UFQFOPLUBTOOPSEJOBULBÀUS UBNTBZEFôFSJLBÀUS A) -16 B) -12 C) -8 D) -4 E) 0 A) -5 B) -2 C) -1 D) 1 E) 3 2. BÀLBSBMôOEBUBONM 6. y = x2 + _ m + 1 ix + 9 f ( x ) = x 2 + 2x + 5 QBSBCPMÑ Y FLTFOJOF OFHBUJG UBSBGUB UFôFU PMEV ôVOBHÌSF NLBÀUS GPOLTJZPOVOVOBMBCJMFDFôJFOLÑÀÑL UBNTBZ EFôFSJLBÀUS A) -9 B) -7 C) -5 D) 5 E) 7 A) 4 B) 7 C) 11 D) 13 E) 14 3. y 7. % $ $ 15 – 3x \" B # C x O \" # 3x – 9 Z G Y I I\"#$%EJLEËSUHFO AB = 3x - 9 br I IAD = 15 - 3x br ôFLJMEFWFSJMFOy = f ( x ) parabolünün denklemi y = -x2 + mx + n dir. :VLBSEBLJWFSJMFSFHÌSF \" \"#$% FOÀPLLBÀ CS2PMVS 3|AO| = |OB| A) 9 B) 49 81 PMEVôVOBHÌSF B+CUPQMBNLBÀUS C) 16 D) E) 25 44 A) 1 B) 2 C) 3 D) 4 E) 5 4. f ( x ) = x2 - 8x + 3m + 1 8. y = x2 + kx - 4x - 16 GPOLTJZPOVOVO BMBCJMFDFôJ FO LÑÀÑL EFôFS -3 QBSBCPMÑOÑOTJNFUSJFLTFOJY+ 3 =EPôSVTV PMEVôVOBHÌSF NLBÀUS PMEVôVOBHÌSF LLBÀUS A) 2 B) 3 C) 4 D) 5 E) 6 A) 8 B) 9 C) 10 D) 12 E) 15 1. # 2. & 3. # 4. $ 82 5. \" 6. D 7. \" 8. $
÷LJODJ%FSFDFEFO%FOLMFNMFS&öJUTJ[MJL1BSBCPM KARMA TEST - 6 1. f ( x ) = x2 - 3x + 5 5. ôFLJMEFf ( x ) = x2 + 6x + p -QBSBCPMÐOÐOHSBGJ- QBSBCPMÑ Ñ[FSJOEF LPPSEJOBUMBS UPQMBN FO B[ óJWFSJMNJõUJS PMBOOPLUBOOLPPSEJOBUMBSUPQMBNLBÀUS y A) 1 B) 2 C) 3 D) 4 E) 5 G Y Y2 + 6x + p – 3 Ox \"# 2. ôFLJMEFf ( x ) = ax2 + bx +DQBSBCPMÐOÐOHSBGJóJ AB = 5 PMEVôVOBHÌSF QLBÀUS WFSJMNJõUJS y BO 6 A) -19 B) -16 C) -13 D) 13 E) 16 –1 3x O G Y BY2 + bx + c 6. ôFLJMEFf ( x ) = ax2 + bx + c QBSBCPMÐOÐOHSBGJóJWF- #VOBHÌSF G +B+ b +DUPQMBNLBÀUS SJMNJõUJS A) -6 B) -2 C) 2 D) 6 E) 18 y kT 3. ôFLJMEFf ( x ) = x2 + bx +DGPOLTJZPOVOVOHSBGJóJ \" 4 #x O WFSJMNJõUJS G Y BY2 + bx + c y #VQBSBCPMÐOUFQFOPLUBT5 L PMVQ QBSBCPMY G Y Y2+ bx + c FLTFOJOJ\"WF#OPLUBMBSOEBLFTNFLUFEJS O x #VOBHÌSF \"WF#OPLUBMBSOOBQTJTMFSJUPQMB –3 7 NLBÀUS #VOBHÌSF C-DGBSLLBÀUS A) -8 B) 0 C) 4 D) 8 E) 12 A) -29 B) -21 C) -8 D) 8 E) 13 4. ôFLJMEFf ( x ) = ax2 + bx +DQBSBCPMÐOÐOHSBGJóJ 7. y = x - 4 WFSJMNJõUJS #V QBSBCPMÐO UFQF OPLUBT 5 -72 ) EPôSVTV Z= x2 - 7x +NQBSBCPMÑOFUFôFUPM dir. EVôVOBHÌSF NLBÀUS A) 3 B) 6 C) 9 D) 12 E) 15 y G Y BY2 + bx + c O4 x 8. y = x2 - 9 –2 –72 QBSBCPMÑOÑO HSBGJôJ ÌODF Y FLTFOJOJO OFHBUJG T ZÌOÑOEF CJSJN TPOSB Z FLTFOJOJO QP[JUJG ZÌ OÑOEFCJSJNLBZESMSTBFMEFFEJMFOZFOJQBSB #VOBHÌSF B+ 2b +DUPQMBNLBÀUS CPMÑOEFOLMFNJBöBôEBLJMFSEFOIBOHJTJPMVS A) -64 B)-56 C) -48 D) -40 E) -32 A) y = x2 + 6x + 4 B) y = x2 - 6x + 4 C) y = x2 + 6x – 5 D) y = x2 - 6x – 5 E) y = x2 + 6x - 9 1. D 2. # 3. & 4. \" 83 5. $ 6. D 7. D 8. \"
KARMA TEST - 7 ÷LJODJ%FSFDFEFO%FOLMFNMFS&öJUTJ[MJL1BSBCPM 1. LCJSEFôJöLFOPMNBLÑ[FSF 5. x 2 - x < 6 y = x2 - 2kx + k2 - 4k - 8 FöJUTJ[MJôJOJTBôMBZBOLBÀGBSLMYUBNTBZTWBS ES QBSBCPMMFSJOJOUFQFOPLUBMBSOOHFPNFUSJLZFSJ OJOEFOLMFNJBöBôEBLJMFSEFOIBOHJTJEJS A) 2 B) 3 C) 4 D) 5 E) 6 A) y = 2x - 4 B) y = 4x - 8 C) y = 2x - 8 D) y = 4x - 4 E) y = - 4x - 8 y 6. x # 2x + 8 2. G Y Y2 Nm YmNm x FöJUTJ[MJôJOJTBôMBZBOGBSLMEPôBMTBZMBSOUPQ x \"# MBNLBÀUS A) 12 B) 10 C) 8 D) 7 E) 5 T :VLBSEB f_ x i = x2 + _ m - 4 ix - 3m - 13 parabo- MÐOÐO HSBGJóJ WFSJMNJõUJS 5 QBSBCPMÐO UFQF nokUBT PMVQ 5OPLUBTZFLTFOJÐ[FSJOEFEJS1BSBCPMYFL- TFOJOJ\"WF#OPLUBMBSOEBLFTNFLUFEJS #VOBHÌSF \"MBO \"5# LBÀCJSJNLBSFEJS A) 75 B) 80 C) 90 D) 100 E) 125 7. &SLBO#FZ LBSFCJ¿JNJOEFLJCBI¿FTJOJOCJSLFOBS- 3. f ( x ) = x2 + 6x - 40 OBFõJUBSBMLMBSMBBóB¿EJLJMFDFLUJS ÷LJ BôBÀ BSBTOEBLJ NFTBGF UPQMBN BôBÀ TBZ QBSBCPMÑOÑOZFLTFOJOFHÌSFTJNFUSJôJPMBOQB TOBFöJUWFCBöUBLJBôBÀJMFTPOEBLJBôBÀBSB SBCPMÑOEFOLMFNJBöBôEBLJMFSEFOIBOHJTJEJS TV[BLMLNPMEVôVOBHÌSF LBÀBôBÀEJLJM NJöUJS A) y = x2 + 6x + 40 B) y = x2 - 6x + 40 A) 9 B) 10 C) 11 D) 12 E) 13 C) y = x2 - 6x - 40 D) y = -x2 - 6x + 40 8. #JTJLMFUUVSVOB¿LBOCJSTQPSDVJLJGBSLMQBSLVSLVMB- E) y = -x2 - 6x - 40 OBDBLUS 4. f ( x ) = x2 - 5x + 4 #JSJODJ QBSLVS LN JLJODJ QBSLVS JTF LN V[VO- MVóVOEBES #JTJLMFUMJOJO QBSLVSV HF¿NF I[ QBSBCPMÐOÐOPSJKJOFHËSFTJNFUSJóJPMBOQBSBCPMFL- QBSLVSVHF¿NFI[OEBOLNTBEBIBGB[MBES TFOMFSJ\" #WF$OPLUBMBSOEBLFTNFLUFEJS #VQBSLVSMBSTBBUUFHFÀJMEJôJOFHÌSF QBS #VOBHÌSF \" \"#$ LBÀCS2EJS LVSEBLJI[LBÀLNTBUJS A) 4 B) 6 C) 8 D) 9 E) 12 A) 4 B) 5 C) 6 D) 8 E) 10 1. & 2. & 3. $ 4. # 84 5. $ 6. # 7. D 8. $
÷LJODJ%FSFDFEFO%FOLMFNMFS&öJUTJ[MJL1BSBCPM KARMA TEST - 8 1. - x 2 + 6x +NÑÀUFSJNMJTJrx `3JÀJOEBJNB 6. x 2 - 3mx + m - 3 = 0 EFOLÑÀÑLPMEVôVOBHÌSF NOJOBMBDBôFO EFOLMFNJOJOLËLMFSJY 1WFY 2 dir. CÑZÑLUBNTBZEFôFSJLBÀUS 1 + 1 >4 A) -5 B) -6 C) -7 D) -8 E) -9 x1 x2 2. ( m - 1) x 2 + 6x + 2 = 0 PMEVôVOB HÌSF N LBÀ GBSLM UBN TBZ EFôFSJ BMS EFOLMFNJOJO CJSCJSJOEFO GBSLM SFFM LÌLÑ WBS TBNOJOBMBCJMFDFôJLBÀQP[JUJGUBNTBZEFôF A) 5 B) 6 C) 8 D) 10 E) 11 SJWBSES A) 4 B) 5 C) 6 D) 7 E) 8 x-3 7. ( m + 1) x 2 - ( m + 2 ) x + m + 3 = 0 3. # 0 EFOLMFNJOJOLËLMFSJY 1WFY2 dir. x2 - 11x + 28 | |x 1 < 0 < x 2WF x 1 < x 2 iseNOJOBMBCJMFDF FöJUTJ[MJôJOJTBôMBZBOYUBNTBZMBSOOUPQMBN ôJEFôFSBSBMôBöBôEBLJMFSEFOIBOHJTJEJS LBÀUS A) (-R, -3 ) B) ( -3, -2 ) C) ( -1, R) D) (-3 , -1 ) E) ( -2, -1 ) A) 11 B) 14 C) 18 D) 21 E) 25 3x.^ 2 - x h2000.^ x + 1 h2002 8. ôFLJMEFZ=G Y GPOLTJZPOVOVOHSBGJóJWFSJMNJõUJS 4. > 0 y x2 + 2x - 15 FöJUTJ[MJôJOJO ÀÌ[ÑN LÑNFTJ BöBôEBLJMFSEFO IBOHJTJEJS A) (-ß, -5) B) (-Þ -5) b Þ x –2 1 $ Þ % -5, 3) Z G Y E) R - (-5, 3) _ x + 1 i. f_ x i ≤0 x-2 5. (1 - m ) x 2 + 4x + m 2 - 4 = 0 FöJUTJ[MJôJOJ TBôMBZBO BSBML BöBôEBLJMFSEFO EFOLMFNJOJOUFSTJöBSFUMJJLJLÌLÑWBSTBNOJO IBOHJTJEJS BMBCJMFDFôJFOLÑÀÑLUBNTBZEFôFSJLBÀUS A) ( -R, -2 ] B) ( -1, 2 ) A) -5 B) -3 C) - 2 D) -1 E) 1 C) [-1, 1] D) [-1, 1] b [ 2, R) E) [-1, 1] b {-2} b Þ 1. D 2. \" 3. D 4. # 5. D 85 6. $ 7. # 8. &
KARMA TEST - 9 ÷LJODJ%FSFDFEFO%FOLMFNMFS&öJUTJ[MJL1BSBCPM 1. ^ x2 - 2x - 8 h.^ x2 - 9x + 20 h # 0 32x. x + 5 . (x2 + x + 7) x2 - 3x - 4 5. # 0 FöJUTJ[MJôJOJTBôMBZBOLBÀUBOFUBNTBZWBSES ^x-2h x+1 ^x+3h A) 9 B) 8 C) 7 D) 6 E) 5 FöJUTJ[MJôJOJTBôMBZBOUBNTBZMBSOUPQMBNLBÀ US A) -6 B) -5 C) -3 D) -2 E) -1 2. ( 2x - 16 ) ( x2 + x - 6 ) # 0 6. ôFLJMEFy =G Y GPOLTJZPOVOVOHSBGJóJWFSJMNJõUJS FöJUTJ[MJôJOJO LBÀ UBOF QP[JUJG UBN TBZ EFôFSJ y Z G Y WBSES –1 O 2 x A) 4 B) 3 C) 2 D) 1 E) 0 5 (x2 - 4) 3 - x #VOBHÌSF f(x) . f(x+ 3) < 0 3. < 0 FöJUTJ[MJôJOJTBôMBZBOYUBNTBZEFôFSMFSJUPQMB x2 + x + 1 NLBÀUS EFOLMFNJOJTBôMBZBOLBÀUBOFYUBNTBZTWBS A) 3 B) 4 C) 5 D) 6 E) 7 ES A) 5 B) 4 C) 3 D) 2 E) 1 7. y õFLJMEF HÌTUFSJMFO UBSBM BMBO BöBô 23x. (x2 + x + 1) .^ 3 - x h EBLJ FöJUTJ[MJL TJT 4. $ 0 1 UFNMFSJOEFO IBO (x + 3) (x2 - 1) –1 O0 3 x HJTJOJO ÀÌ[ÑN LÑ FöJUTJ[MJôJOJ TBôMBZBO Y UBN TBZMBS LBÀ UBOF EJS NFTJEJS A) 0 B) 1 C) 2 D) 3 E) 4 –3 A) y # x 2 - 2x - 3 B) y $ x2 - 2x - 3 y#x+1 y#x+1 C) y # x2 + 2x - 3 D) y $ x2 - 2x - 3 y#x+1 y#x-1 E) y $ x2 - 2x - 3 y$x-1 1. D 2. # 3. $ 4. D 86 5. \" 6. \" 7. #
<(1m1(6m/6258/$5÷LJODJ%FSFDFEFO%FOLMFNMFS&öJUTJ[MJL1BSBCPM 1. \"INFU#FZõFLJMEFWFSJMFO BMBON2 olan dik- 4. (ÐOFõ )BONhO HJUNFTJ HFSFLFO ZPMVO CJS LTN EËSUHFO CJ¿JNJOEFLJ CPõ BSTBZB CJS LFOBS Y NFUSF BTGBMU CJSLTNUPQSBLUS\"TGBMUZPMLN UPQSBL PMBO LBSF CJ¿JNJOEF CJS FW ZBQUSNBL JTUJZPS :BQ- ZPMLNV[VOMVóVOEBES\"TGBMUZPMEBLJI[ UPQ- MBOFWJOпUBSBGOEBõFSNFUSFCJSUBSBGOEBN SBLZPMEBLJI[OEBOLNTBEBIBGB[MBES CPõMVLCSBLMNõUS :PMDVMVLUPQMBNTBBUTÑSEÑôÑOFHÌSF UPQSBL 20 m ZPMEBLJI[TBBUUFLBÀLNEJS 20 m x m 20 m A) 30 B) 25 C) 40 D) 45 E) 50 xm 35 m #VOBHÌSF FWJOCJSLFOBSV[VOMVôVLBÀNFUSF EJS A) 12 B) 15 C) 18 D) 20 E) 21 2. #JS PLVMVO TBUSBO¿ UBLNOB TF¿JMFO L[ WF FSLFL 5. #JS TPLBóO EPóSVTBM PMBO ZPMVOVO SFGÐKÐ Ð[FSJOF ËóSFODJMFSEFO PMVõUVSVMBO LJõJMJL HSVQUBLJ L[ FõJUBSBMLMBSMBBZEOMBUNBEJSFLMFSJEJLJMFDFLUJS ËóSFODJMFSJO TBZT JMF FSLFL ËóSFODJMFSJO TBZTOO ¿BSQNES \"SU BSEB EJLJMFO JLJ EJSFL BSBT NFTBGF UPQMBN EJSFL TBZTOB FöJU WF CBöUBLJ EJSFL JMF TPOEBLJ (SVQUBLJ FSLFL ÌôSFODJMFSJO TBZT EBIB GB[MB EJSFLBSBTV[BLMLNFUSFPMEVôVOBHÌSF EJ PMEVôVOBHÌSF HSVQUBLBÀL[ÌôSFODJWBSES LJMFOEJSFLTBZTLBÀUS A) 5 B) 6 C) 7 D) 8 E) 9 A) 11 B) 12 C) 13 D) 14 E) 15 3. #JS\"#$пHFOJOEF\"LËõFTJOEFO#$LFOBSOB¿J[J- 6. BY2 + bx +D=JLJODJEFSFDFEFOEFOLMFNEF | |len yükseklik BC kenaSOEBOCSEBIBLTBES I. D JTFEFOLMFNJOTBOBMJLJLËLÐWBSES II. C JTFEFOLMFNJOHFS¿FLJLJLËLÐWBSES | | \"#$ÑÀHFOJOJOBMBOCS2PMEVôVOBHÌSF #$ III. B WF D JTF EFOLMFNJO HFS¿FL JLJ LËLÐ LFOBSOBBJUZÑLTFLMJLLBÀCSEJS WBSES A) 3 B) 2 C) - 1 + 3 ZVLBSEBLJ JGBEFMFSEFO IBOHJMFSJ EBJNB EPôSV EVS D) 1 + 3 E) - 1 + 2 \" :BMO[* # :BMO[*** $ *WF** % *WF*** & * **WF*** 1. # 2. $ 3. $ 87 4. \" 5. $ 6. D
<(1m1(6m/6258/$5 ÷LJODJ%FSFDFEFO%FOLMFNMFS&öJUTJ[MJL1BSBCPM 1. I. 32x - 1= 16x + 2EFOLMFNJOJOLËLÐY1 dir. 3. Yerden j0 I[ZMB HZFS¿FLJNJWNFTJBMUOEBGSMB- II. ( 3x - 2 )3 = ( 2x + 1 )3EFOLMFNJOJOLËLÐY2 dir. UMBO CJS UPQVO Y TBOJZF TPOSB ZFSEFO ZÐLTFLMJóJOJ ***LWFNSFFMTBZMBSPMNBLÐ[FSF WFSFOJGBEF f_ x i = j0.x - 1 gx2 biçimindedir. x2- ( k - 9 ) x + m =EFOLMFNJOJOLËLMFSJY1WF 2 x2 dir. :VLBSEBWFSJMFOCJMHJMFSFHÌSFL+NUPQMBNOO EFôFSJLBÀUS ///////////////////////////////// A) 25 B) 30 C) 39 D) 48 E) 64 j0 =NTWFH=NT2PMEVôVOBHÌSF UP QVOÀLBCJMFDFôJNBLTJNVNZÑLTFLMJLLBÀNFU SFEJS A) 30 B) 35 C) 40 D) 45 E) 50 2. ôFLJMEFNPMP[UBõWFLFTNFUBõMBSMBQBSBCPMJLPMB- 4. #JSCBLLBMY5-ZFBMEóCJSÐSÐOÐZ5-ZFTBUNBL- SBLJOõBBFEJMNJõCJSLËQSÐWFSJMNJõUJS#VLËQSÐOÐO UBES UFQFOPLUBTOOZFSEFOZÐLTFLMJóJNFUSF BZBL- MBSOO J¿ LTNMBS BSBTOEBLJ NFTBGF NFUSF- Y JMF Z BSBTOEB Z = -x2 + 11x - CBôOUT dir. PMEVôVOBHÌSF CBLLBMOTBUöUBOFMEFFEFDFôJ L»SFOGB[MBLBÀ5-EJS A) 19 B) 17 C) 15 D) 13 E) 11 #VOBHÌSF ZVLBSEBLJHJCJNPEFMMFOFOQBSBCP 5. ôFLJM*EF¿FNCFSCJ¿JNJOEFWFSJMFOWF¿FWSFTJ MÑO EFOLMFNJ TJNFUSJ FLTFOJ Z PMBDBL öFLJMEF BöBôEBLJMFSEFOIBOHJTJEJS DNPMBOJQLVMMBOMBSBLôFLJM**EFLJHJCJEJLEËSU- HFOCJ¿JNJOFEËOÐõUÐSÐMNFLJTUFOJZPS A) y = 9 _ x2 - 400 i 50 ôFLJM* ôFLJM** B) y = 3 _ x2 - 100 i &MEFFEJMFOEJLEÌSUHFOTFMCÌMHFOJOBMBOFOÀPL 10 LBÀDN2EJS C) y = - 9 _ x2 - 50 i 50 D) y = - 9 _ x2 - 100 i 50 E) y = - 9 _ x2 - 400 i 50 A) 400 B) 300 C) 250 D) 200 E) 150 1. & 2. D 88 3. D 4. D 5. \"
CEVAP ANAHTARI (m.m1&m'(5(&('(1'(1./(03$5$%2/(6m76m=/m./(5 r Sayfa 30, Örnek 11 a r Sayfa 30, Örnek 11 b r Sayfa 74, Örnek 1 a r Sayfa 74, Örnek 1 b y y y y y = x2 Ox x x x O O O y = –2x2 r Sayfa 30, Örnek 11 c r Sayfa 30, Örnek 11 d r Sayfa 74, Örnek 1 c r Sayfa 74, Örnek 1 d y y = x2 –1 y y = 2x2 + 4 y y O 4 Ox 2 –1 1 x x x –1 O O r Sayfa 30, Örnek 11 e r Sayfa 30, Örnek 11 f r Sayfa 74, Örnek 1 e r Sayfa 74, Örnek 1 f y y = 2(x–1)2 + 4 y y y 3 –1 O –1 x O 2x –1 6 O x 4 –3 –2 –1 O1 x y = –3(x+2)2 + 3 r Sayfa 30, Örnek 11 g r Sayfa 30, Örnek 11 h r Sayfa 75, Örnek 2 a r Sayfa 75, Örnek 2 b y y = 2(x–2)2 y y = x2 – 3x + 2 y y = x2 y=x y 8 Ox O2 x 2 x x O1 2 O y = –x y = –x2 r 4BZGB ²SOFL r Sayfa 30, Örnek 31 i y y x O 4x r Sayfa 75, Örnek 2 c r Sayfa 75, Örnek 2 d y = 4x – x2 y=x+1 y y O1 3 –1 1 O –6 –2 O –1 1 y = –2x2 + 8x – 6 x –1 x 2 r Sayfa 56, Örnek 1 y = x2–1 –2 a) (-Þ b Þ BSBMóOEBQP[JUJG BSBMóOEB r Sayfa 75, Örnek 2 e r Sayfa 75, Örnek 2 f OFHBUJG y y b) (-Þ b Þ BSBMóOEBOFHBUJG BSBMóO- O2 y=x–2 EBQP[JUJG x c) (-Þ - b + Þ BSBMóOEBQP[JUJG –2 O 2 x _ 2 - 2, 2 + 2 iBSBMóOEBOFHBUJG –4 d) 3-{}BSBMóOEBOFHBUJG y = –x2 e) (-Þ Þ BSBMóOEBQP[JUJG f) (-Þ Þ BSBMóOEBOFHBUJG
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