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MODÜL MATEMATİK - 1 Alt bölümlerin KARMA TEST - 5 ,ÌLMÑ4BZMBS Karma Testler EDĜOñNODUñQñL©HULU ÜSLÜ VE KÖKLÜ SAYILAR Modülün sonunda ³ ÜSLÜ SAYILAR 1. x = 7 + 3 ve y = 2 - 1PMEVôVOBHÌSF 5. x = 5 - 24 4PMEVôVOBHÌSF tüm alt bölümleri y = 5 + 24 L©HUHQNDUPDWHVWOHU 14 – 3 + 3 2 - 7 \\HUDOñU x-y JGBEFTJOJOYWFZDJOTJOEFOEFôFSJBöBôEBLJMFS- yx JöMFNJOJOTPOVDVLBÀUS EFOIBOHJTJEJS ³ Üslü Sayı t 2 A) x + y B) 2x - y xy A) - 5 6 B) - 4 6 C) - 3 6 C) 2 D) x.y E) x - y D) - 2 6 E) - 6 ³ Üslü Sayının Özellikleri t 2 ³ Toplama - Çıkarma İşlemi t 8 ³ Bölme İşlemi t 8 6ñQñIð©LðĜOH\\LĜ 6. 1 10 + 19 - 10 - 19 ³ Bilimsel Gösterim t 10·/÷7&34÷5&:&)\";*3-*, 3. MODÜL ÜSLÜ VE KÖKLÜ SAYILAR www.aydinyayinlari.com.tr %XE¸O¾PGHNL¸UQHN 2. 8 + 2 15 - 8 - 2 15 VRUXODUñQ©¸]¾POHULQH JöMFNJOJOTPOVDVLBÀUS DNñOOñWDKWDX\\JXODPDVñQGDQ ÜSLÜ SAYILAR - I XODĜDELOLUVLQL] JöMFNJOJOTPOVDVLBÀUS ·TMÑ4BZMBSO²[FMMJLMFSJ ³ Üslü Denklemler t 15 $OW%¸O¾P7HVWOHUL,ÌLMÑ4BZMBS A) 5 + 3 B) 2 3 C) 5 - 3 2 2 ·TMÑ4BZ E) – 5 - 3 A) B) D)2 E) 6 Her alt bölümün D) 2 5 C) 1 D) 2 E) 2 2 VRQXQGDRE¸O¾POHLOJLOL 4 2 WHVWOHU\\HUDOñU ³ Üslü Sayılarda S7aı$r`1a,Rl0avemn%a`m/Z*+tmolm2a0k üzere, 7$1,0%m/*m C) 2 - 3 2 a ` R - {0} ve n ` Z olsun. E) 3 an ifadesine üslü ifade denir. a–n = f 1 n 1 ,c a –n b n p= m =f p an = 1a4.4a2.a.4.4.a3 n Z üs, a Z taban a an b a n tane <HQL1HVLO6RUXODU a, b ` R, m, n ` Z olsun. 3. 11+ 2 24 – 10 – 2 16 7. A =( 7 +1) (4 7 +1) (8 7 +1) (16 7 +1) (32 7 +1) ³ Karma Testlae`r R t- {02} ,4n ` Z+ olsun. JöMFNJOJOTPOVDVLBÀ,UÌSLMÑ4BZMBS 0RG¾O¾QJHQHOLQGH\\RUXP r am . an = am + n <(1m1(6m/6258/$5 PMEVôVOBHÌSF 32 7 OJO\"UÑSÑOEFOFöJUJLBÀ- \\DSPDDQDOL]HWPHYE r a0 = 1 (00 belirsizdir.) US EHFHULOHUL¸O©HQNXUJXOX r an. an = ( a . b )n VRUXODUD\\HUYHULOPLĜWLU ³ Yeni Nesil Sor rua1la=ra t 32 $\\UñFDPRG¾OVRQXQGD r ( an )m = ( am ) n = am.n dir. A) 3 1B.) ô2F-LJM1EF CJS BNCC)VMB3OT+O L2B[B TPOSBTOEAB) HJAEF+C6JMF- A+4 C) A + 1 WDPDPñ\\HQLQHVLOVRUXODUGDQ r ( -1 )2n = 1 , ( -1 )2n-1 = -1 D) 3 - 2 DFóJIBTUBEO)F1MFSFPMBOV[BLMóHËTUFSJMNJõUJS A 3B. ) A 2A ROXĜDQWHVWOHUEXOXQXU a ` R- , n ` Z olsun. D) A LNEL AA B E) LN ÖRNEK 2 2A – 1 A+6 r n tek ise an < 0 , ( -2 )3 < 0 LN r n çift ise an > 0 , ( -2 )4 > 0 \"öBôEBWFSJMFOJöMFNMFSJOTPOVDVOVCVMBMN B LN LN LN -24á -2 )4 1 2 –2 -3 –1 p + 2–2 + f p a) f 4 LN 5 LN C 32 \"WF#EVSBLMBSOBTSBTZMB 75 LNWF 48 LN b) ( 5-3 . 54 ) –2 4. Y>PMNBLÑ[FSF A 3 LN 3LN8. 1 V[BLMLUB CVMVOBO CJS PUPCÑT ZPMDVTV \" EVSB- (1+ 3) (1+ 4 3) . (1+ 8ô3O)B._ 11+4176L3NiV[BLMLUBCVMVOBOWF 5 3 LNEL ^ –2 –2 h x – 2 + 2 x – 3 + x – 2 – 4x – 12 = 6 LN 16 TBCJU I[MB IBSFLFU FEFO PUPCÑTF BöBôEB WFSJ- c) JöMFNJOJOTPOVDVLBÀUMFSOZÌOWFI[MBSEBOIBOHJTJJMFIBSFLFUFEFSTF ÖRNEK 1 d) ^ 0, 3 hx.91–x.27x–1 PMEVôVOBHÌSF x + 4 + x - 3 LBÀUS E C16JO3FC–JM1JS D A) 16 3 - 1 B) a) \"öBôEB WFSJMFO ÀBSQNMBS ÑTMÑ JGBEF öFLMJOEF e) ( 0,0002 ) –2 . ( 0,08 )2 C) 1– 3 ZB[BMN A) 4 B) 5 C) 6 D) 7 E) 8 A) \"2ZËOÐOEF2 3 LNI[MB f) ( -a2 ) . ( -a )7 . ( -a3 )2 5SBGJLZPôVOMVôVTBCJULBCVMFEJMEJôJOEFBNCVD-) 3 - 1 B) #ZËOÐEO)EF3 3 LNI[MB MBOTOHJUNFTJHFSFLFOFOZBLOIBTUBOFBöBô- 2 r 5.5.5.5 = C)\"ZËOÐOEF 3 LNI[MB g) 22. 32. 42... 102 EBLJMFSEFOIBOHJTJPMVS TEST - 16 r ( -3 ).( -3 ).( -3 ).( -3 ).( -3 ) = 1. D 2. B A3). AC 4. D B) B C) C 58D) D E) E 5. B 6. B D)7.#AZË8O.ÐBOEF 3 LNI[MB ( 32 )5 ^ 2 5 h 2 3 3 a2x ax = a10 h) . r f 2 p.f 2 p.f 2 p =1. 5. 3 - 2 2 + 3 + 2 2 E) \"ZËOÐOEF 5 3 LNI[MB 3 3 3 2 UPQMBNOOTPOVDVLBÀUS PMEVôVOBHÌSF YLBÀUS A) 9 B) 10 C) 12 D) 14 E) 15 A) 2 B) 2 2 C) 3 b) \"öBôEBWFSJMFOJöMFNMFSJOTPOVDVOVCVMBMN 4. \"õBóEBWFSJMFO\"WF#NBLJOFMFSJOFBUMBOCJSBTB- r 25 - 33 - 190 = ZTOO ÐSÐO PMBSBL LBSõMLMBS TSBTZMB a - 1 WF a + 1 EJS #VOB HËSF IFS JLJ NBLJOFZF EF EFO r ( -2 )6 - ( -2 )5 + ( -24 ) = ZFLBEBS EBIJM UBNTBZMBSBUMZPSWFFMEF FEJMFOUÐNÐSÐOMFS¿BSQMBSBLCJS\"TBZTFMEFFEJMJ- r ( -1 )100 - ( -1 102) + ( -1 )103 = ZPS r [ ( -5)10 ] 0 - (-20190 )100 = 6. 1 + 2 BB 3 - 2 2 6 + 32 0 2. a2 3 a a4 = ab AB iöMFNJOJOTPOVDVLBÀUS r ^ - 8 h1 + f 2 p - ^ - 1 h1001 2. N EBOLпÐLCJSEPóBMTBZPMNBLÐ[FSF 5m2 + 4 9 PMEVôVOBHÌSF CLBÀUS (a > 0) Bm B JGBEFTJCJSUBNTBZZBFõJUUJS 3 4 5 3 A) -1 B) –2 2 #VOBHÌSF NOJOLBÀGBSLMEFôFSJWBSES 2 32 11 1 1. a) 54, (–3)5, d 2 3 A) 1 B) C) D) E) 1 1 e) 204 f) a15 Dg))0(10!)2 h) 342 A) 2 B) 3 C) 4 D) 5 E) 6 #VOB HÌSF \" TBZT JMF JMHJMJ BöBôEBLJMFSEFO n b) 4, 80, 1, 0, –6 2. a6) 6 b) 245 c) d) IBOHJTJEPôSVEVS 3 2 3 A) &OCÐZÐLBTBM¿BSQBOEJS B) 4POEBOCBTBNBóTGSES 3. a D R+ olmak üzere; C) EJS D) UBOFGBSLMBTBM¿BSQBOWBSES E) 361 JMFCËMÐNÐOEFOLBMBOEJS 1 3 a8 a5 4 1 7. a ` R+ olmak üzere, 63 a2 a12 3+a-2 a+2 =4 PMEVôVOBHÌSF BLBÀUS 1. C 2. B 3. B 4. B JöMFNJOJOTPOVDVBöBôEBLJMFSEFOIBOHJTJEJS A) 21 B) 23 C) 25 D) 27 E) 29 A) a B) a a C) a2 a a E) a D) a 8. 7 + 4 3 . 7 - 48 4. 3 2x + 6 . 3 2x = 128 JöMFNJOJOTPOVDVLBÀUS PMEVôVOBHÌSF YLBÀUS A) -1 B) 1 C) 2 3 E) 3 + 4 A) 12 B) 18 C) 20 D) 24 E) 32 D) 4 1. C 2. B 3. E 4. A 52 5. B 6. E 7. B 8. B
ÜNwİwVwE.ayRdinSyaİyTinlaEri.YcoEm.trHAZIRLIK ·/÷7&34÷5&:&)\";*3-*, MATEMATİK - 1 3. MODÜL ÜSLÜ VE KÖKLÜ SAYILAR ³ ÜSLÜ SAYILAR ³ Üslü Sayı t 2 ³ Üslü Sayının Özellikleri t 2 ³ Üslü Sayılarda Toplama - Çıkarma İşlemleri t 8 ³ Üslü Sayılarda Bölme İşlemi t 8 ³ Bilimsel Gösterim t 10 ³ Üslü Denklemler t 15 ³ Üslü Sayılarda Sıralama t 20 ³ Karma Testler t 24 ³ Yeni Nesil Sorular t 32 1
·/÷7&34÷5&:&)\";*3-*, 3. MODÜL ÜSLÜ VE KÖKLÜ SAYILAR www.aydinyayinlari.com.tr ÜSLÜ SAYILAR - I ·TMÑ4BZ ·TMÑ4BZMBSO²[FMMJLMFSJ 7$1,0%m/*m 7$1,0%m/*m a ` R ve n ` Z+ olmak üzere, a ` R - {0} ve n ` Z olsun. an ifadesine üslü ifade denir. an = 1a4.4a2.a.4.4.a3 n Z üs, a Z taban a–n = f 1 n 1 ,c a –n b n n tane p= m =f p a an b a a ` R - {0} , n ` Z+ olsun. r a0 = 1 (00 belirsizdir.) a, b ` R, m, n ` Z olsun. r a1 = a r ( -1 )2n = 1 , ( -1 )2n-1 = -1 r am . an = am + n a ` R- , n ` Z olsun. r n tek ise an < 0 , ( -2 )3 < 0 r an. bn = ( a . b )n r n çift ise an > 0 , ( -2 )4 > 0 r ( an )m = ( am ) n = am.n dir. -24á -2 )4 ÖRNEK 2 \"öBôEBWFSJMFOJöMFNMFSJOTPOVDVOVCVMBMN a) f 2 –2 + 2–2 + f -3 –1 p p 32 b) ( 5-3 . 54 ) –2 ^ –2 –2 h 16 c) ÖRNEK 1 d) ^ 0, 3 hx.91–x.27x–1 a) \"öBôEB WFSJMFO ÀBSQNMBS ÑTMÑ JGBEF öFLMJOEF e) ( 0,0002 ) –2 . ( 0,08 )2 ZB[BMN r 5.5.5.5 = 54 f) ( -a2 ) . ( -a )7 . ( -a3 )2 (–3)5 g) 22. 32. 42... 102 r ( -3 ).( -3 ).( -3 ).( -3 ).( -3 ) = ( 32 )5 ^ 2 5 h 3 d 2 3 h) . n 2 2 2 3 r f 3 p.f 3 p.f 3 p = 9 1 2 11 a) + - = 443 6 b) 56.5-8 = 5-2 = 1 25 b) \"öBôEBWFSJMFOJöMFNMFSJOTPOVDVOVCVMBMN 11 1 – = (24) – = 2–1 = r 25 - 33 - 190 = c) 16 4 4 2 4 r ( -2 )6 - ( -2 )5 + ( -24 ) = 80 d) 3–x.32.3-2x.33x.3-3 = 1 3 r ( -1 )100 - ( -1 102) + ( -1 )103 = 1 e) (2.10-4)-2 . (8.10-2)2 = 204 r [ ( -5)10 ] 0 - (-20190 )100 = 0 f) (-a2) . (-a7). a6 = a15 g) (10!)2 r ^ - 8 h1 + f 2 0 -6 h) 310.332 = 342 9 p - ^ - 1 h1001 1. a) 54, (–3)5, d 2 3 b) 4, 80, 1, 0, –6 2 11 1 1 1 e) 204 f) a15 g) (10!)2 h) 342 2. a) b) c) d) n 6 25 2 3 3
www.aydinyayinlari.com.tr ÜSLÜ VE KÖKLÜ SAYILAR 3. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 3 ÖRNEK 7 274 . 323 = 6m . n , ( m, n ` Z ) 1– x FöJUMJôJOEFNOJOFOCÑZÑLUBNTBZEFôFSJLBÀUS 3 x =5 312. 215 = 612 . 8 jN= 12 PMEVôVOBHÌSF 3xJGBEFTJOJOEFôFSJLBÀUS 3 1 –1 = 5 & 3 1 = 15 x .3 x 15 3x = a 1/x k3x = 3 3 = 27 3 ÖRNEK 4 ÖRNEK 8 506 . 804 . 2503 x2 + 2x + 4 = 0 TBZTLBÀCBTBNBLMES = ( 52. 2 )6 . ( 24. 5 )4 . ( 53. 2 )3 = 525. 225 = 1025 jCBTBNBLMES PMEVôVOBHÌSF x–6 + c x –9 US 2 m JGBEFTJOJOEFôFSJLBÀ- ÖRNEK 5 (x – 2) (x2 + 2x + 4) = x3 - 8 = 0 j x3 = 8 9x + 1 = 25 x–6 + d x –9 = a 3 k–2 + 29.a 3 k–3 PMEVôVOBHÌSF x + 1JOEFôFSJLBÀUS n x x 2 = 8 –2 + 9 –3 = 65 2 .8 64 9x . 9 = 25 j x = 5 3 3 27x + 1 = 27x . 27 = d 5 3 n .27 = 125 3 ÖRNEK 6 ÖRNEK 9 4x = m , 25-x = n 5–x =PMEVôVOBHÌSF PMEVôVOBHÌSF xJONWFOUÑSÑOEFOFöJUJOF- EJS 25x + 1 + 1 - 9.52x – 1 25–x JGBEFTJOJOEFôFSJLBÀUS 25x. 25 + 25x - 9.25x. 1 5 d 64 x 16 x = ^ x h2 .25 –x =N2O 25x d 25 + 1 - 9 n = ^ x h2. 121 5 n =d n 4 55 100 25 =d 1 2 121 = 1 n. 11 5 5 3. 12 4. 26 5. 125 6. N2O 3 7. 27 65 1 8. 9. 64 5
·/÷7&34÷5&:&)\";*3-*, 3. MODÜL ÜSLÜ VE KÖKLÜ SAYILAR www.aydinyayinlari.com.tr ÖRNEK 10 ÖRNEK 14 BWFCZBOEBLJõFLJMJ¿JOEFLJIFS- IBOHJJLJTBZPMNBLÐ[FSF 2-x = m , 5x = n olmak üzere, 5 1600xJONWFOUÑSÑOEFOFöJUJOJCVMVOV[ –2 3 A = { x : x = ab } 1600x = (26.52)x = (2x)6. (5x)2 –3 –4 LÐNFTJUBONMBOZPS 2 1 2 n 2 = .n = 66 mm B = { m : m = x1 - x2, x1, x2 ` A } öFLMJOEF UBONMBOBO # LÑNFTJOJO FO CÑZÑL FMFNB- OLBÀUS ÖRNEK 11 2 N= x1 - x2 j x1 ZNBY Y2 ZNJO a+b =2 ve c b mx = 27 x1 = 35 = 243 x2 = (-4)5 = -1024 a-b a PMEVôVOBHÌSF YLBÀUS jN= x1 - x2 = 243 + 1024 = 1267 a + b = 2a - 2b j b1 = a 3 d 1 2/x = –2/x = 3 ÖRNEK 15 3 n 3 3 5n + 5–n = x PMEVôVOBHÌSF 25O + 25mOJGBEFTJOJOYUÑSÑOEFO 22 FöJUJOJCVMVOV[ - x = 3 & x =- 3 ( 5O)2 + ( 5-O)2 = ( 5O + 5-O) 2 - 2.5O.5-O = x2 - 2 ÖRNEK 12 YWFZUBNTBZPMNBLÐ[FSF xy =PMBDBLöFLJMEFLBÀGBSLM Y Z JLJMJTJWBSES 64 = 26 = (-2)6 = 43 = 82 = (-8)2 = 641 { ( 2, 6 ), ( -2, 6 ), ( 4, 3 ), ( 8, 2 ), ( -8, 2 ), ( 64, 1 ) } jBEFU ÖRNEK 13 ÖRNEK 16 Y EFOCÑZÑLQP[JUJGUBNTBZPMNBLÑ[FSF 2x = 3y a = ^ –x–2 h3 , b = ^ x–3 h3 , c = ^ –x3 h4 xy B C WF D TBZMBSO LÑÀÑLUFO CÑZÑôF EPôSV TSBMB- ZO[ PMEVôVOBHÌSF 8 y + 9 x JGBEFTJOJOEFôFSJLBÀUS xy 2y =3 , 3x =2 1 , b = 1 , c = x12 dx 3y 2 a =- 2y n d n + 3x = 33 + 22 = 31 69 xx jB C DEJS n2 2 12. 6 13. a < b < c 4 14. 1267 15. x2 – 2 16. 31 10. 11. - 6 3 m
www.aydinyayinlari.com.tr ÜSLÜ VE KÖKLÜ SAYILAR 3. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 17 ÖRNEK 19 5x =PMEVóVOBHËSF ôFLJMEFWFSJMFO\"WF#NBLJOFMFSJTSBTZMBBWFCCJSJN NBM[FNFZJTBCJUYCJSJNNBM[FNFJMFIBSNBOMBZBSBLBx x ve xbCJSJNFEËOÐõUÐSÐZPS – ax bx ^ 20 h 2x + 1 ifadeTJOJOEFôFSJLBÀUS x1 –– a 5 . 22 k 2x + 1 x 2x 2x + 1 = a .2 k AB 5 ax xb – 1 Yâ a 2x k 2x + 1 #VNBLJOFMFSEFOJLJGBSLMÐSFUJNEFOFOJZPS 2.2 = ÑSFUJN\"NBLJOFTJOFYCJSJNÐSÐOBUMBSBLFMEFFEJMFO ÐSÐOUFLSBS\"NBLJOFTJOFBUMZPS – 2x + 1 –1 1 =2 2x + 1 =2 = ÑSFUJN\"NBLJOFTJOFYCJSJNÐSÐOBUMBSBLFMEFFEJMFO ÐSÐOTPOSBTOEB#NBLJOFTJOFBUMZPS 2 4POV¿PMBSBLJLJÐSFUJNEFEFFMEFFEJMFOÐSÐONJLUBSOO ÖRNEK 18 FõJUPMEVóVHËSÐMÐZPS ôFLJMEF CJS GBCSJLBEB CVMVOBO \" # $ % & WF ' NBLJ- #VOBHÌSF YJOFOCÑZÑLEFôFSJJÀJO\"WF#NBLJOF- OFMFSJOJO CJS HÐOEF ÐSFUUJóJ ÐSÐO NJLUBSMBS NBLJOF Ð[F- MFSJOFCJSJNÑSÑOBUMSTBFMEFFEJMFOÑSÑONJLUBSMB- SJOEF WFSJMNJõUJS ¶SFUJMFO ÐSÐOMFSMF JMHJMJ BõBóEBLJ CJMHJ- SGBSLLBÀPMBCJMJS ler bilinmektedir. 2m 2O 2O b x x l x hx UBOF UBOF UBOF x = ^ x A B C j xx = x2JTFYFOCÑZÑLEJS \"NBLJOFTJj 52 =CJSJN #NBLJOFTJj 25 =CJSJN 7O 7L 7L 32 - 25 =CJSJN UBOF UBOF UBOF D E F r # JMF $ OJO CJS HÐOEF ÐSFUUJóJ ÐSÐOÐ \" UFL CBõOB üretebilmektedir. r %JMF&OJOCJSHÐOEFÐSFUUJóJÐSÐOÐ'UFLCBõOBÐSF- ÖRNEK 20 tebilmektedir. 75m - 2 = 15m #VOBHÌSF NmO . 6 + 7O-L . 12 UBOFÑSÑOUÑNNB- PMEVôVOBHÌSF N- 4JGBEFTJOJOEFôFSJLBÀUS LJOFMFSLVMMBOMBSBLWFHÑOEFOmL - 2N-O UBOF ÑSFUJMFSFLLBÀHÑOEFUBNBNMBOS 2N = 2O+ 1 + 2O+ 4 j 2N-O = 18 m–2 75 m = 15 7L+ 1 = 7O + 7L j 7O-L= 6 22 1– – & 75 m = 15 & 75.75 m = 15 2m –n.6 + 7n – k.12 18.6 + 6.12 30.6 2 m–4 = = = 5 gün j 5 = 75 m & 5 = 9 9.7n – k - 2m – n 9.6 - 18 9.4 1 18. 5 5 19. 7 20. 9 17. 2
TEST - 1 ·TMÑ4BZMBSWF²[FMMJLMFSJ 1. ( -a )5 . ( -a6) . ( a )-4 . ( -a )-7 5. a = 2b PMEVóVOBHËSF JGBEFTJOJOFöJUJBöBôE BLJMFSEFOIBOHJTJEJS 9a. 33 - 4b A) a B) -B $ % B–1 & -1 JGBEFTJOJOEFôFSJBöBôEBLJMFSE FOIBOHJTJEJS \" # $ % & 2. BQP[JUJGCJSTBZPMEVôVOBHÌSF BöBôEBLJMFS- –4 EFOIBOHJTJOFHBUJGUJS A) - ( -a–2 ) B) ( -a3 )2 $ B5 6. ;a ( –2) –2 –2 2( –2 –2 E ) k. % -a2 )3 & -( -a3 ) JöMFNJOJOTPOVDVLBÀUS A) 2-20 B) 2-16 $ -15 % -10 & -8 3. a =WFC= -2 PMEVôVOBHÌSF 7 a - ba – b 7. 90–3. (0, 01) –6. (0, 0081) 4 ab JöMFNJOJOTPOVDVLBÀUS JöMFNJOJOTPOVDVLBÀUS A) 3 . 102 # $ A) -32 B) -42 $ - % - & -64 & 2 . 10-2 % . 10-2 –2 a (- 2) –2 –3 1 p k (- 2) –2. (- 62) –1.f 8. –2 4. 3 a (- 42) –1 k (- 3–1) –1. 2–2 JöMFNJOJOTPOVDVLBÀUS JöMFNJOJOTPOVDVLBÀUS % 1 & 1 24 A) 2 B) 1 $ 1 % 1 & 1 \" # $ 3 2 6 12 24 1. E 2. D 3. D 4. D 6 5. D 6. C 7. A 8. E
·TMÑ4BZMBSWF²[FMMJLMFSJ TEST - 2 1. y D N+ için x-y CJS UBN TBZ PMEVóVOB HËSF 5. ôFLJMEFLJ LVUVMBSB ÐTMÐ TBZMBS LVWWFUMFSJOF HËSF x BöBôEBLJMFSE FOIBOHJTJPMBCJMJS Ð[FSJOEFCFMJSUJMEJóJHJCJBUMBDBLUS A) 0, 2 B) 0, 3 $ % & X X AB X2 X3 X4 2. 3x . 91 - x . 273 - x = 0, 3 CD E FõJUMJóJWFSJMJZPS #VOBHÌSF YLBÀUS ±SOFóJO % LVUVTVOB ÐTTÐ PMBO TBZMBS BUMBCJM- mektedir. \" # $ % & -2 #VOBHÌSF 81, 324 WF42TBZMBSOOBUMBCJ- MFDFôJUPQMBNLVUVTBZTLBÀUS \" # $ % & 3. f 0, 2 n 0, 5 n+1 3 n+1 0, 03 p ·f 2 p ·f 5 p 6. 2-0,017 = x JöMFNJOJOTPOVDVBöBôEBLJMFSEFOIBOHJTJEJS FõJUMJóJWFSJMJZPS A) 3 B) f 3 n $ f 2 n+1 #VOBHÌSF 22,051JOYUÑSÑOEFOFöJUJOFEJS 20 5 p 3 p A) 4 B) 2 $ - 4x– 3 x3 x3 % 3 & 2 2 5 % - 4x3 & - 2x3 4. a = (- 2) (32), b = (- 22) –3, c = (3) ((–1)9) 7. a ` R ve -2 < a < -1 olmak üzere, x = ( a + 2 )-1, y = ( a + 2 )2 ve z = ( a + 2 )3 TBZMBSWFSJMJZPS FõJUMJLMFSJWFSJMJZPS #VOB HÌSF BöBôEBLJ TSBMBNBMBSEBO IBOHJTJ #VOB HÌSF BöBôEBLJ TSBMBNBMBSEBO IBOHJTJ EPôSVEVS EPôSVEVS A) a < c < b B) c < a <C $ B< b < c % C< c <B & C< a < c A) x < y < z B) x < z <Z $ Z< x < z % [< x <Z & [< y < x 1. # 2. # 3. A 4. A 7 5. C 6. A 7. E
·/÷7&34÷5&:&)\";*3-*, 3. MODÜL ÜSLÜ VE KÖKLÜ SAYILAR www.aydinyayinlari.com.tr ÜSLÜ SAYILAR - II ·TMÑ4BZMBSEB5PQMBNB¦LBSNB÷öMFNJ ·TMÑ4BZMBSEB#ÌMNF÷öMFNJ 7$1,0%m/*m 7$1,0%m/*m )FNUBCBOIFNEFÐTTÐBZOPMBOÐTMÐTBZMBS a, b ` R - {0}, m, n ` Z olmak üzere, PSUBLQBSBOUF[FBMOBSBLUPQMBOSWFZB¿LBSMB- bilir. am = am.a–n = am – n dir. a.xO + b.xO - c.xO = ( a + b - c ) . xO dir. an an =c a n dir. bn b m ÖRNEK 1 ÖRNEK 2 \"öBôEBLJJGBEFMFSJOFöJUJOJCVMBMN \"öBôEBLJJöMFNMFSJOTPOVDVOVCVMVOV[ a) 10.3n - 2.3n+1 + 6.3n-1 a) 52x – 1 b) 62-x - 61-x + 5.6-x 251– x c) 2x – 2 + 3.2x + 1 b) 3x + y – 2.9x – y 22 + x + 2x –1 271+ x + y d) 43 – 2x - 1 - 2–4x + 5 x2.^ –x–2 h.^ –x h3 16x – 1 c) x = -2 için, e) 2x.2x.2x.2x x3.^ –x h4.x–2 2–x + 2–x + 2–x + 2–x d) 12x + 2.72 + x. 52x + 1 25x – 1. 21x + 2. 4x + 1 a) 3O(10 - 6 + 2) = 6.3O 2x – 1 5 4x – 3 a) = 5 2 – 2x 5 b) 6-x (36 - 6 + 5) = 35.6-x 3 x + y – 2 2x – 2y b) .3 3x – y – 2 – 3 – 3x – 3y 2xd 1 + 6 n = 3-4y - 5 4 25 3 + 3x + 3y =3 c) = 3 2x d 4 + 1 n 18 2 ^ - 2 h2.^ -^ - 2 h–2 h.^ 2 h3 1 c) = d) 4-2x (64 - 16 - 32) = 42 - 2x ^ - 2 h3.^ + 2 h4.^ - 2 h–2 4 ^ 2x h4 x x 2 2 x 2x 3 .4 .12 .7 .7 .5 .5 4.5 4x x–2 5x–2 d) = = 500 e) = 2 .2 = 2 –x x –1 x 2 x –1 4.2 25 .25 .21 .21 .4 .4 25 1. a) 6.3O b) 35.6–x c) 25 d) 42 – 2x e) 25x – 2 8 2. a) 54x – 3 b) 3–4y – 5 c) 1 d) 500 18 4
www.aydinyayinlari.com.tr ÜSLÜ VE KÖKLÜ SAYILAR 3. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 3 ÖRNEK 6 A = 2 + 22 + 23 + ... + 230PMEVôVOBHÌSF 1 -1 24 + 25 + 26 + ... + 229 2–a - 1 1 - 2a JöMFNJOJOTPOVDVLBÀUS UPQMBNOO\"DJOTJOEFOEFôFSJOFEJS 11 ÷TUFOJMFOJGBEFYPMTVO - A = 2 (1 + 2 + 22 + 23 + 124444+2.x. .424293) 1 - 2a a A = 2^ 15 + x h & x = A - 30 1 - 2 2 a 2 a - 1 =-1 2 1 - a 2 ÖRNEK 4 ÖRNEK 7 5x = a 4 a = x3 , b = 4x , ba = 2162 2x = b PMEVôVOBHÌSF YJOBMBCJMFDFôJEFôFSMFSÀBSQNLBÀ- PMEVôVOBHÌSF . 10x + 5x - 2JöMFNJOJOBWFCUÑ- US SÑOEFOFöJUJOFEJS x d 2.2 x + 1 a.^ 50b + 1 h 3 x4 5 n= 4 25 25 ^ x hx 162 81 4 = = 2 = 4 x4 = 81 j x = ± 3 j -3.3 = -9 ÖRNEK 5 ÖRNEK 8 2–x + 2–x + 2–x = 81 A = 4 . 42. 43 . . . 410 PMEVôVOBHÌSe, 2220 + 2111 +UPQMBNOO\"DJOTJO- 6–x + 6–x + 6–x + 6–x 4 EFOEFôFSJOFEJS PMEVôVOBHÌSF x LBÀUS A = 41+2+ ... + 10 = 455 = 2110 2220 + 2111 + 1 = (2110 + 1)2 = (A + 1)2 –x 3.2 81 –x –x = 4.2 .3 4 x+1=4 jx=3 A - 30 a.^ 50b + 1 h 5. 3 9 6. –1 7. –9 8. (A + 1)2 3. 4. 2 25
·/÷7&34÷5&:&)\";*3-*, 3. MODÜL ÜSLÜ VE KÖKLÜ SAYILAR www.aydinyayinlari.com.tr ÖRNEK 9 ÖRNEK 11 y ve x y = 5200 \"öBôEBWFSJMFOTBZMBSOCJMJNTFMHÌTUFSJNMFSJOJCV- x= MVOV[ 4 PMEVôVOBHÌSF YLBÀUS a) 300000000 = 3.108 x h4 50 k4 b) 597.1011 = 5,97.1013 x 5 y = 4x j x4x = ^ = a xx = 550 = 52.25 = (25)25 j x = 25 c) 0,0000123 = 1,23.10-5 d) 72,5.10-23 = 7,25.10-22 ÖRNEK 10 ÖRNEK 12 BWFCJLJEPóBMTBZPMNBLÐ[FSF &SJõLJOCJSJOTBOEBZBLMBõLNJMZBSBEFUBMZVWBSIÐD- SFTJWBSES)FSIÐDSFOJOJ¿JOFEFNJMZPOBEFUPLTJ- aNb =BOOCEFGB¿BSQMNBTJMFPMVõBOTBZOOCOJO KFONPMFLÐMÐCBóMBZBOIFNPHMPCJONPMFLÐMÐZFSMFõUJSJM- a defa¿BSQMNBTJMFPMVõBOTBZZBPSBOõFLMJOEFUB- NJõUJS #VOB HÌSF JOTBO WÑDVEVOEBLJ UPQMBN IFNPHMPCJO ONMBOZPS 8 NPMFLÑMÑTBZTOOCJMJNTFMHÌTUFSJNJOJCVMVOV[ d 4N n NJMZBSNJMZPO #VOBHÌSF 2 N JGBEFTJOJOEFôFSJLBÀUS = 25.109 . 28.107 = 700.1016 = 7.1018 8 4 4N8 = 4 = 24 = 16 8 16 2N16 = 2 2 = 28 16 #JMJNTFM(ÌTUFSJN ÖRNEK 13 7$1,0%m/*m #JS ¿JUBOO TBBUUF PSUBMBNB LN I[B VMBõUó CJMJO- mektedir. #JMJNTFM HËTUFSJN ¿PL CÐZÐL WFZB ¿PL LпÐL TBZMBS HËTUFSNFL J¿JO LVMMBOMBO CJS TUBOEBSU- #VOB HÌSF ÀJUBOO EBLJLB JÀFSJTJOEF BMEô ZPMVO US DNDJOTJOEFOCJMJNTFMHÌTUFSJNJOFEJS | |a ` R ve 1 G a <PMBDBLõFLJMEF LN=DNTB a.10n ( n ` Z ) ifadesine CJMJNTFMHÌTUFSJNBE 12.10 6 5 verilir. = 60 ·3 = 6.10 cm/dk 9. 25 10. 28 10 11. a) 3.108 b) 5,97.1013 c) 1,23.10–5 d) 7,25.10–22 12. 7.1018 13. 6.105
www.aydinyayinlari.com.tr ÜSLÜ VE KÖKLÜ SAYILAR 3. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 14 ÖRNEK 17 *õLI[TBOJZFEF8NFUSFEJS(ÐOFõõóOOEÐOZB- .FSLÐS (F[FHFOJhOJO (ÐOFõhF PMBO V[BLMó ZBLMBõL ZBVMBõNBTJTF3 saniye sürmektedir. 57,9 milyar kilometredir. #VOBHÌSF HÑOFöJMFEÑOZBBSBTOEBLJV[BLMôONFU- #VOB HÌSF CV V[BLMôO NFUSF DJOTJOEFO CJMJNTFM SFDJOTJOEFOCJMJNTFMHÌTUFSJNJOJCVMVOV[ HÌTUFSJNJOJCVMVOV[ 3.108 . 5.103 = 15.1011 = 1,5.1012 57,9.109LN= 57,9.109.103N = 57, 9.1012N= 5,79.1013N ÖRNEK 15 ÖRNEK 18 öOTBO WÐDVEVOEBLJ IÐDSFMFSJO PSUBMBNB 12 tanesi (Ë[MFHËSÐMNFZFOLпÐLDBOMMBSOCPZMBSNJLSPOJMFËM- IFSBZEBCJSZFOJMFONFLUFEJS çülmektedir. #VOB HÌSF ZMEB CJS JOTBOO WÑDVEVOEB ZFOJMF- OFOIÑDSFTBZTOOCJMJNTFMHÌTUFSJNJOJCVMVOV[ 1000 mikron = 1 mm dir. 75.1012 . 35.2 = 70.75.1012 )FS CJSJ NJLSPO CPZVOEB U UBOF DBOMOO CPZMB- S UPQMBN N PMEVôVOB HÌSF U TBZTOO CJMJNTFM = 5250.1012 = 5,25.1015 HÌTUFSJNJOJCVMVOV[ N=NN =NJLSPO 15.10 6 5 6 t= 15.10 5.10 10 = = 1, ÖRNEK 16 ÖRNEK 19 #JSHÑOÑOTBOJZFDJOTJOEFOCJMJNTFMHÌTUFSJNJOJCV- #JS ZFUJõLJO JOTBOEB PSUBMBNB LÐUMFTJOJO 1 ü kadar MVOV[ 13 TO LBOCVMVONBLUBES#JSMJUSFLBOEB da 11.109 adet akyu- =TO= 8,64.104 WBSCVMVONBLUBES #VOB HÌSF LÑUMFTJ LH PMBO CJS JOTBOO LBOOEB CVMVOBO BLZVWBS TBZTOO CJMJNTFM HÌTUFSJNJOJ CV- MVOV[ 91 =7 13 7.11.109 = 77.109 = 7,7.1010 14. 1,5.1012 15. 5,25.1015 16. 8,64.104 11 17. 5,79.1013 18. 1,5.106 19. 7,7.1010
TEST - 3 ·TMÑ4BZMBSMB÷öMFNMFS 1. 2x + 2x + 2 + 3.2x + 1 = 44 0, 3.10–3 + 5.10–4 PMEVôVOBHÌSF YLBÀUS 5. \" # $ % & 0, 17.10–3 - 10.10–6 JöMFNJOJOTPOVDVLBÀUS \" # $ % 1 & 1 25 2. 3x - 2 + 3x - 1 + 3x + 3x + 1 + 3x + 2 = 121 6. 5n - 10n 5n + 1 - 2.5n - 3.10n PMEVôVOBHÌSF YLBÀUS JöMFNJOJOTPOVDVBöBôEBLJMFSEFOIBOHJTJEJS \" # $ % & A) - 2n + 5n B) 2n + 5n $ 2n - 5n 3 3 3 % - 1 & 1 3 3 3. 25x + 1 + 1 - 7.52x–1 = 123 7. 5x + 1 + 5x = 52x 25– x 125 5x –1 + 5x – 2 PMEVôVOBHÌSF YLBÀUS PMEVôVOBHÌSF YBöBôEBLJMFSEFOIBOHJTJE JS A) - # $ % & A) 1 B) 2 % 3 & 2 3 2 $ 8. 3x. 3x. 3x. 3x. 3x = 81 33x + 33x + 33x 4. 1616TBZTOOJLBÀUS PMEVôVOBHÌSF YLBÀUS A) 264 B) 262 $ 61 % 60 & 58 A) 5 B) - 5 $ % 3 & - 3 2 2 22 1. C 2. C 3. A 4. # 12 5. # 6. E 7. C 8. A
·TMÑ4BZMBSMB÷öMFNMFS TEST - 4 1. 4. 3 . 3n + 5 . 3n + 1 + 2 . 3n = 540 .BWJWFHSJLBSFMFSEFOFMEFFEJMNJõTÐTMFNFEF10 n tane mavi kare LVMMBOMNõUS #VOB HÌSF TÑTMFNFEF LVMMBOMBO HSJ LBSFMFSJO PMEVôVOBHÌSF n(n ) LBÀUS TBZTLBÀUS \" # $ % & A) 327 B) 39 $ 2 % 3 & 81 5. ( 0,0000005 )-1 TBZTOO CJMJNTFM HÌTUFSJNJ BöBôEBLJMFSEFO IBOHJTJEJS A) 5.107 B) 2.106 $ 6 % 5 & 7 2. YWFZUBNTBZMBS 6. #JS CBLUFSJ LÐMUÐSÐOEFLJ CBLUFSJ TBZT IFS HÐO CJS 2x – 2. 3y – x = 1 ËODFLJHÐOÐOLBUOB¿LNBLUBES 2y + 1. 32x + 1 HÑOÑO TPOVOEB NJMZBS CBLUFSJ PMEVôVOB PMEVôVOBHÌSF YZLBÀUS HÌSF CBöMBOHÀUBLJ CBLUFSJ TBZTOO CJMJNTFM HÌTUFSJNJBöBôEBLJMFSEFOIBOHJTJEJS \" # $ % & A) 36.105 B) 3,6.104 $ 6 % 6 & 4 7. öOTBOLBMCJEBLJLBEBPSUBMBNBLF[BUNBLUBES 3. xy – 1 + xy – 2 + xy – 3 = 16 #VOB HÌSF HÑO JÀJOEF CJS JOTBOO LBMCJOJO LBÀ LF[ BUUôOO CJMJNTFM HÌTUFSJNJ BöBôEBLJ- xy+1 + xy+2 + xy+3 MFSEFOIBOHJTJEJS PMEVôVOBHÌSF YLBÀPMBCJMJS A) 5184.103 B) 5,184.106 $ 5 A) -3 B) - 7 $ - 5 % - 1 & - 3 % 6 & 5 2 222 1. D 2. C 3. D 13 4. A 5. # 6. C 7. #
TEST - 5 ·TMÑ4BZMBSMB÷öMFNMFS 1. Y OTGSEBOGBSLMWFB EFOCÐZÐLUBNTBZMBS- 5. 124x 4. 22x f442x3 = 144x 4+444x2+ f4 4+444x3 y tan e 2y tan e ES OUBOFBxTBZTOOÀBSQNOOOUBOFBx sa- PMEVôVOBHÌSF YJOZUÑSÑOEFOFöJUJLBÀUS ZTOO UPQMBNOB PSBO BöBôEBLJMFSEFO IBOHJ- TJEJS y-2 y y+1 A) B) $ A) anx B) anx – x $ ax a y-4 y-2 y % ax + 1 n an – 1 y+3 2y + 1 & ax % & y-1 y+1 a–n n2 (- a) 4 . a–2 . (- a) –7 . (- a) 6 6. f ax + y 2 bx 2 ax 2 2. ay p .f bx + y p :f by p (- a) –3 . a5 . (- a) –5 . a4 JGBEFTJOJOFOTBEFöFLMJBöBôEBLJMFSEFOIBOHJ- JGBEFTJOJOTPOVDVBöBôEBLJMFSEFOIBOHJTJEJS TJEJS A) ax B) ax + y $ BC xy A) -1 B) -a2 $ % -B & B2 by bx – y & % bx + y ax 3. x2x - 4.xx = 27.xx - 108 FöJUMJôJOJ TBôMBZBO Y UBN TBZMBSOO UPQMBN 7. 1 1 11 LBÀUS + ++ \" # $ % & 3–1007 + 1 3–1006 + 1 31006 + 1 31007 + 1 JöMFNJOJOTPOVDVLBÀUS A) 31007 B) 31006 $ % & 4. x = 33 + 34 + 35 + …… + 327PMEVóVOBHËSF 3 + 32 + 33 + … + 328 JGBEFTJOJO Y DJOTJOEFO FöJUJ BöBôEBLJMFSEFO 8. 412 - 6.410 IBOHJTJEJS A) 2x + 17 B) 4x + $ Y+ 39 TBZTOOBöBôEBLJMFSEFOIBOHJTJEJS % Y+ & Y+ 53 A) 218 B) 219 $ 20 % 21 & 22 1. # 2. A 3. # 4. C 14 5. # 6. E 7. D 8. E
www.aydinyayinlari.com.tr ÜSLÜ VE KÖKLÜ SAYLIAR 3. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÜSLÜ SAYILAR - III ·TMÑ%FOLMFNMFS ÖRNEK 4 TANIM a n {-1, 0, 1} , a ` R ve n, m ` R - {0} olmak Bâ-PMNBLÑ[FSF üzere, an = am ise n = m dir. 1 + 1 +...+ 1 = 144a +414. 444a2+ 14. .4. .44a44+ 13 a, b n {-1, 0, 1}, a, b ` R ve n ` Z - {0} ol- 12424–a4 4 42424–a2 4 4 4 4 4224–4a3 mak üzere, n tan e an = bnFõJUMJóJOEF i. n tek ise a = b dir. 8 tan e | | | |ii. n çift ise a = b dir. PMEVôVOBHÌSF OLBÀUS ÖRNEK 1 8.2a-2 = (4a+1)O 82n – 2 = 4n + 3 PMEVôVOBHÌSF OLBÀUS 2a+1 = 2(2a + O & a + 1 = 2a a + 1 k.n & n = 1 2 ( 23 ) O- 2 = (22)O+ 3 ÖRNEK 5 j 2O- 6 = 2O+ 6 jO- 6 =O+ 6 jO= 12 jO= 3 32a + 3a + 81a =a 3a + 2 + 9a + 1 + 34a + 2 27 PMEVôVOBHÌSF a LBÀUS ÖRNEK 2 a a 3a 2x + 1 + 2x - 2 + 2x = 26 PMEVôVOBHÌSF YLBÀUS 3 3 3 .a + 1 + k a = 27 a a 1 + a + 3a k 2x d 2 + 1 + 1 n = 26 9.3 3 3 4 a1 = &a=3 27 9 x 13 = 26 j 2x = 8 jx=3 2. 4 ÖRNEK 3 ÖRNEK 6 ( 0,125 ) x = ^ 0, 008 h 2 2 PMEVôVOBHÌSF YLBÀUS ( x - 1 )7 = ( 2x - 4 )7 3 PMEVôVOBHÌSF YLBÀUS . 10 x - 1 = 2x - 4 j x = 3 125 x 2 d n =d 8 n 3 2 1000 1000 .10 x 2 d 1 n =d 1 n 3 2 8 125 .10 –3x –3· 2 2 =5 3 2 & –3x 2 2 & x =- .10 2 =2 3 2 15 1 5. 3 6. 3 1. 3 2. 3 3. - 4. 2 3
·/÷7&34÷5&:&)\";*3-*, 3. MODÜL ÜSLÜ VE KÖKLÜ SAYLIAR www.aydinyayinlari.com.tr ÖRNEK 7 ÖRNEK 10 ( a + 2 )10 = ( a2 + 3 )5 x, y `;PMNBLÑ[FSF PMEVôVOBHÌSF BLBÀUS 23x – 6 = 35y – 25 (a2 + 4a + 4)5 = (a2 + 3)5 PMEVôVOBHÌSF YZLBÀUS a2 + 4a + 4 = a2+ 3 3x - 6 = 0 5y - 25 = 0 1 x=2 y=5 4a = -1 j a = - j x . y = 10 4 ÖRNEK 8 ÖRNEK 11 ( 2m - 1 )12 = ( 5 - m) 12 72a + 3b – 11 = 5b – 2a + 7 FöJUMJôJOJTBôMBZBONEFôFSMFSJOJOUPQMBNLBÀUS FöJUMJôJOEFBWFCUBNTBZPMEVôVOBHÌSF a LBÀ- N- 1 = 5 -NWFZBN-1 = -5 +NPMVQ b N=WFN= -CVMVOVS US O halde -4 + 2 = -CVMVOVS 2a + 3b - 11 = 0 b - 2a + 7 = 0 4b - 4 = 0 jb=1 j a=4 a =4 b ÖRNEK 9 ÖRNEK 12 ( 5x + 2 )4 = 28 ( x2 - 9 )x – 3 = 0 EFOLMFNJOJTBôMBZBOYEFôFSMFSJOJOÀBSQNLBÀUS PMEVôVOBHÌSF YLBÀUS ( 5x + 2 )4 = 44 5x + 2 = -4 x2 - 9 = 0 , x -â 5x + 2 = 4 5x = - 6 x = ±3 j x = -3 5x = 2 2 6 x= x =- 5 5 d 2 n·d - 6 n = - 12 5 5 25 1 12 16 10. 10 11. 4 12. –3 7. - 8. –2 9. - 4 25
·TMÑ%FOLMFNMFS TEST - 6 1. f 1 m 5. y = 4x ve (y.x–1) 2 = 128 a p = 3–81 m PMEVôVOBHÌSF NLBÀUS PMEVôVOBHÌSF BLBÀUS \" # $ % 1 & 1 A) 2 B) 4 $ 6 % & 9 81 7 7 7 2. f 1 3–2x 6. 2x .3y = 0, 3 ve 3x . 2y = 108 3 p . 9x–1 = 27x + 5 PMEVôVOBHÌSF YBöBôEBLJMFSEFOIBOH JTJEJS PMEVôVOBHÌSF x + y LBÀUS A) 5 B) 20 $ % & \" # $ 5 % & 4 7 2 x1 7. 7 . 99 + 89 - 63 . 98 = ( 0,5 )-3x 3. x x + y = 2 ve x x + y = 16 PMEVôVOBHÌSF YLBÀUS 1 PMEVôVOB HÌSF x 2 BöBôEBLJMFSEFO IBOHJT J EJS A) 1 B) 1 $ 1 % 1 & 1 A) -3 B) - $ 1 % & 16 8 6 42 3 4. 82x - 1 . 93x + 1 = 12x + 5 . 24x - 13 8. a3 = 4 ve ax = 1 FöJUMJôJOEFYBöBôEBLJMFSEFOIBOHJTJEJS ay 16 PMEVôVOBHÌSF x -ZLBÀUS A) 3 B) 2 $ 3 % 4 & 4 5 5 2 35 A) -12 B) - $ - % -6 &) -4 1. A 2. E 3. E 4. A 17 5. # 6. # 7. E 8. D
TEST - 7 ·TMÑ%FOLMFNMFS 1. ( x + 1 )14 = ( x2 + 4x + 1 )7 5. x+y a2x =f b 7 = 3 ve FöJUMJôJOEFYLBÀUS x-y b4y a p \" # $ % & PMEVôVOBHÌSF y BöBôEBLJMFSE FOIBOH JTJEJS A) - 3 B) - 5 $ - 3 % - 7 & - 5 2 4 442 2. 11a - 2 - 13b + 4 = 0 6. f 1 a–b 1 –b 1 a+b EFOLMFNJOJTBôMBZBOBWFCUBNTBZMBSJÀJO p .103b+2 - f p .f p . 25 = 0 a -CLBÀUS 8 125 2 A) -4 B) - $ % & PMEVôVOBHÌSF 7b -BLBÀUS A) -4 B) - $ - % & 2 7. 4x + y = 16 , 3x – y = 1 3x + y 4x – y 9 3. 2x – 1 = x3 PMEVôVOBHÌSF ZBöBôEBLJMFSEFOIBOH JTJEJS FöJUMJôJOJTBôMBZBOYUBNTBZEFôFSMFSJOJOUPQ- MBNLBÀUS A) - # $ % & A) 1 B) 2 $ % 4 & 3 2 3 32 4. x < 0 < y iken ( 2x - 3 )4 = ( 3y + 3 )4 8. x QPMNBLÑ[FSF PMEVôVOB HÌSF x BöBôEBLJMFSEFO IBOHJTJOF 1 y a. (45.x) x = (15.a x .x.y) x FöJUUJS PMEVôVOBHÌSF ZLBÀPMBCJMJS A) - 1 B) - 1 $ - 3 % - 2 & -1 \" # $ % & 2 3 23 1. A 2. E 3. D 4. C 18 5. D 6. # 7. C 8. C
www.aydinyayinlari.com.tr ÜSLÜ VE KÖKLÜ SAYILAR 3. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÜSLÜ SAYILAR - IV 7$1,0%m/*m ÖRNEK 4 ax = 1 denkleminde 3x = 8 ve 2y = 81 PMEVôVOBHÌSF YZLBÀUS i) BáWFY=ES ii) a = 1 ve x ` R olur. iii) a = -WFYCJS¿JGUUBNTBZES xn = ym 4 ise 3x = 23 x3 = xa = yb n = m dir. 34 = 2y ise 4y & x.y = 12 ab ÖRNEK 1 ÖRNEK 5 (x - 2) x = 1 5a = 80 PMEVôVOBHÌSF YJOBMBDBôEFôFSMFSJCVMVOV[ 4b = 50 x-2=1 jx=3 PMEVôVOBHÌSF BOOCUÑSÑOEFOFöJUJOJCVMVOV[ x - 2 = -1 j x = YâYÀJGUPMNBM x = 0, x -â ¦= {0, 3} ÖRNEK 2 5a -1 = 24 52 = 22b - 1 x2– 2x a-1 4 2b + 7 x =1 = &a= EFOLMFNJOJOÀÌ[ÑNLÑNFTJOJCVMVOV[ 2 2b - 1 2b - 1 |x| = 1 x2 - 2x = Yâ | x | = -1 j x = ±1 x=2 x2 - 2x jÀJGU ¦= {-1, 1, 2} ¦= q ÖRNEK 3 ÖRNEK 6 ( m + 3 )n - 2 2m + n = 125 JGBEFTJCFMJSTJ[PMEVôVOBHÌSF ONEFôFSJOJCVMVOV[ 52m - 2n = 32 N+ 3 = 0 jN= -3 22 O- 2 = 0 jO= 2 PMEVôVOBHÌSF 9m – n LBÀUS m –3 1 n =2 = 2N+O = 53 25 = 5N-O 8 j m+n = 3 5 2m - 2n N2 -O2) = 15 jN2 -O2 = 15 15 15 &9 2 =3 1 19 4. 12 2b + 7 6. 315 1. {0, 3} 2. {–1, 1, 2} 3. 5. 8 2b - 1
·/÷7&34÷5&:&)\";*3-*, 3. MODÜL ÜSLÜ VE KÖKLÜ SAYILAR www.aydinyayinlari.com.tr ·TMÑ4BZMBSEB4SBMBNB ÖRNEK 10 7$1,0%m/*m 4a = 50 9b = 95 x ` R, m, n ` R - {0} olmak üzere, 5c = 25 x > 1 ise xn < xm iken n < m dir. 0 < x < 1 ise xn < xm iken n > m dir. PMEVôVOBHÌSF B CWFDOJOLÑÀÑLUFOCÑZÑôFEPôSV TSBMBOöOCVMVOV[ ÖRNEK 7 16 < 4a < 64 j 2 < a < 3 a , 2,8 f 4 x+8 9 3x–1 81 < 9b < 729 j 2 < b < 3 b , 2,2 5c = 25 j c = 2 p <f p j c < b <BES 3 16 FöJUTJ[MJôJOJOÀÌ[ÑNLÑNFTJOJCVMVOV[ d 4 x+8 4 –6x + 2 j x + 8 < -6x + 2 n <d n 33 6 7x < -6 j x < - 7 Ç =d -3,- 6 n ÖRNEK 11 7 a = 44 , b = f 1 3 ve c = _ - 2 i12 8 p ÖRNEK 8 TBZMBSOO LÑÀÑLUFO CÑZÑôF EPôSV TSBMBOöO CV- MVOV[ f 4 3a + 1 125 a–7 p <f p 25 8 FöJUTJ[MJôJOJTBôMBZBOFOLÑÀÑLBUBNTBZTLBÀUS a = 28 b = 2-9 c = 212 j b < a <DEJS d 2 6a + 2 2 –3a + 21 n <d n 55 6a + 2 > -3a + 21 9a > 19 19 a> j a=3 9 ÖRNEK 9 ÖRNEK 12 1 = 64 a = -3-4 , b=f- 1 –3 , c=f- 1 –5 31– x PMEVóVOBHËSF YHFSÀFLTBZTOOLBSFTJOJOFOCÑZÑL p p UBNTBZEFôFSJLBÀUS 93 27 < 64 < 81 TBZMBSOO LÑÀÑLUFO CÑZÑôF EPôSV TSBMBOöO CV- 33 < 3x -1 < 34 MVOV[ 3<x-1<4 4<x<5 a = -3-4 b = -36 c = -35 j 16 < x2 <FOCÑZÑLY2 = 24 j b < c <BES 7. Ç = d - 3 , - 6 n 8. 3 9. 24 20 10. c < b < a 11. b < a < c 12. b < c < a 7
www.aydinyayinlari.com.tr ÜSLÜ VE KÖKLÜ SAYILAR 3. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 13 ÖRNEK 16 1 11 7x < 1 ve 3x > 1 – –– 49 240 a=3 2 , b=5 3 , c=2 4 FöJUTJ[MJLMFSJOJ TBôMBZBO LBÀ GBSLM Y UBN TBZ EFôF- SJWBSES TBZMBSOO LÑÀÑLUFO CÑZÑôF EPôSV TSBMBOöO CV- MVOV[ –6 4 – 3 – a = 3 12 , b = 12 , c = 2 12 7x < 7-2 3x > 1 1 5 > x < -2 1 11 j -4 < x < -2 240 243 EFôFSBMS a = a –6 k 12 . b = a –4 k 12 c = ^ –3 h 12 3x > 3-4 j x > -4 3 5 2 3-6 < 5-4 < 2-3 j a < b <DEJS j x = -3 ÖRNEK 14 ÖRNEK 17 x = 2150 , y = 3120 , z = 590 x–7 TBZMBSOO LÑÀÑLUFO CÑZÑôF EPôSV TSBMBOöO CV- MVOV[ 4 # 2 < 32 FöJUTJ[MJôJOJTBôMBZBOYUBNTBZMBSOOUPQMBNLBÀ- US 2 # |x - 7| < 5 2 # -x + 7 < 5 k30 k30 2#x-7<5 -5 # - x < -2 x = ^ 5 h30 , y = a 4 , z = a 3 9 # x < 12 2<x#5 2 3 5 25 < 34 < 53 ¦= {3, 4, 5, 9, 10. 11} j x < y <[EJS 5PQMBN= 42 ÖRNEK 15 ÖRNEK 18 a = 7-51 , b = 2-85 , c = 5-68 x = 5-5 TBZMBSOO LÑÀÑLUFO CÑZÑôF EPôSV TSBMBOöO CV- y = ( -5 )5 MVOV[ z = ( -5 )-5 TBZMBSOO LÑÀÑLUFO CÑZÑôF EPôSV TSBMBOöO CV- MVOV[ h17 h17 k17 1 y = -55 1 x= z =- a = ^ –3 , b = ^ –5 , c = a –4 5 5 7 2 5 5 5 j y < z <YEJS 5-4 < 7-3 < 2-5 j c < a <CEJS 13. a < b < c 14. x < y < z 15. c < a < b 21 16. 1 17. 42 18. y < z < x
TEST - 8 ·TMÑ%FOLMFNMFS 1. 3x = 16 ve 2y = 81 5. x2y = 16 ve x3y = 3a - 2 PMEVôVOBHÌSF YZLBÀUS PMEVôVOB HÌSF B BöBôEBLJMFSEFO IBOHJTJ PMB- CJMJS \" # $ % & \" # $ % & 27x–1 = f 1 y _ b 3 p bb ` 6. 1– y b bb 2. 3a = 8 ve 3b = 32 f 1 p = 8x +1 4 a PMEVôVOBHÌSF a + b JGBEFTJOJOEFôFSJOFEJS PMEVôVOBHÌSF x BöBôEBLJMFSEFOIBOHJTJE JS a-b y A) - 1 B) – 1 $ -1 % - & -4 A) 1 B) 1 $ 1 % 1 & 1 4 2 24 18 12 8 4 3. 3a - b = 5 ve 5a + b = 243 7. (0, 25) m. 1 = 1 ve PMEVôVOBHÌSF a2 - b2 LBÀUS 2n + 6 ( 0, 2 )n - 1. ( 0, 2 )-m - 1 = 1 FöJUMJLMFSJOJTBôMBZBON+OUPQMBNLBÀUS \" # $ % & $ - 10 % & 3 A) -5 B) -3 2 8. 4x . 5y = 100 4. (x4 + 1) x – 1 = 1 2y . 25x = 1000 ve 4x2 - y2 = 10 PMEVôVOBHÌSF 2x - ZOJOEFôFSJLBÀUS PMEVôVOBHÌSF YJOBMBCJMFDFôJEFôFSMFSJOÀBS- A) -2 B) - $ % & QNOFEJS A) -2 B) - $ % & 1. A 2. E 3. D 4. C 22 5. # 6. A 7. C 8. D
·TMÑ4BZMBSEB4SBMBNB TEST - 9 1. 3n = 176 5. 2x = 30 , 3y = 85 , 5z = 130 PMEVôVOBHÌSF, 2OBöBôEBLJBSBMLMBSEBOIBO- PMEVôVOBHÌSF Y ZWF[TBZMBSOOEPôSVTSB- HJTJOEFCVMVOVS MBOöBöBôEBLJMFSEFOIBOHJTJEJS A) x < y < z B) y < x <[ $ Z< z < x \" # $ % [< y <Y & [< x < y % & 2. 0 < a < b olmak üzere, 6. m = 757 , n = 2133 , k = 395 c a –x + 5 b 2x + 1 TBZMBSOO CÑZÑLUFO LÑÀÑôF EPôSV TSBMBOö BöBôEBLJMFSEFOIBOHJTJEJS m <f p ba FöJUTJ[MJôJOJTBôMBZBOLBÀUBOFOFHBUJGYUBNTB- A) m > k > n B) n > k >N $ L> m > n ZTWBSES % N> n >L & L> n > m \" # $ % & 3. f 7 3x–10 9 –6 7. 1P[JUJGUBNTBZMBSLÐNFTJOEFUBONMCJSGD fonksi- p >f p 1 yonu D Z D D õFLMJOEFUBONMBOZPS 3 49 FöJUTJ[MJôJOJTBôMBZBOFOLÑÀÑLYUBNTBZEF- #VOB HÌSF G2, f3 WF G4 EFôFSMFSJOJO LÑÀÑLUFO ôFSJLBÀUS CÑZÑôFEPôSVTSBMBOöBöBôEBLJMFSEFOIBOHJ- TJEJS \" # $ % & A) f2 < f3 < f4 B) f2 = f4 < f3 $ G3 < f2 = f4 % G3 < f2 < f4 & G4 < f3 = f2 4. a = (-27)10 , b = -9-12 , c = a _ - 9 i2 –4 ve d = 3-20 8. 1 = 240 ve 5y - 1 = 24 k 34 – x PMEVôVOBHÌSF YWFZHFSÀFLTBZMBSOOÀBSQ- TBZMBSOOLÑÀÑLUFOCÑZÑôFTSBMBOöBöBôEB- NOOFOLÑÀÑLUBNTBZEFôFSJLBÀUS LJMFSEFOIBOHJTJEJS \" # $ % & A) a < b < c < d B) b < a < c < d $ C< c < d <B % C< d < c < a & C< a < d < c 1. A 2. # 3. # 4. D 23 5. D 6. A 7. # 8. #
KARMA TEST - 1 ·TMÑ4BZMBS 1. (-a2)3å . (a-3)2 . (a-1)-2 . (-a3)-1. (-a2) 5. YQP[JUJGCJSEPôBMTBZPMNBLÑ[FSF JGBEFTJOJOTPOVDVLBÀUS a 2x 2 + 4 2 A) a B) 1 $ - % - 1 & -a aa 10 + 1 k JGBEFTJOJO SBLBNMBS UPQMBN BöBôEBLJMFSEFO IBOHJTJEJS A) x2 + 2 B) x2 + $ Y % & 2. \"öBôEBLJFöJUMJLMFSEFOIBOHJTJ ZBOMöUS 6. 16a . 53a + 1 A) ( 23)–5 = 2–15 B) (-33 )2 = (-32 )3 TBZT CBTBNBLM CJS TBZ PMEVôVOB HÌSF B LBÀUS $ -56)2 = ( 52)6 % -23 )4 = 212 \" # $ % & & -54 )3 = -512 8x+ 1.f 1 1– x 4 p . (0, 5) x 7. = 64 45 – x. (0, 125) 2x + 1 :(- x) –3 D –2 . > 1 PMEVôVOBHÌSF YLBÀUS (- x8) 3. H A) -3 B) - $ - % & JGBEFTJOJOFOTBEFCJÀJNJBöBôEBLJMFSEFOIBO- giTJEJS A) -x4 B) x3 $ -x3 % Y2 & -x–2 8. B C Y ZTGSEBOGBSLMSFFMTBZMBSES I. ax . ay = axy II. ax x y =a ay 4. 3n + 2 + 3n - 3n + 1 + 3n III. ( ax ) y = ayx 3n –1 + 3n – 3 3n – 2 + 3n –1 IV. ax . bx = ( a . b )2x JöMFNJOJOTPOVDVLBÀUS V. ax = a \" # $ % bx b & FöJUMJLMFSJOEFOLBÀUBOFsi EBJNBEPôSVEVS \" # $ % & 1. E 2. # 3. E 4. A 24 5. D 6. # 7. D 8. A
·TMÑ4BZMBS KARMA TEST - 2 41231 5. 3-x = y 1. (- 1) 3 + (- 1) 7 - (- 1) 5 - (- 1) 5 + (- 1) 9 PMEVôV CJMJOEJôJOF HÌSF 33x - 3 JGBEFTJOJO Z JöMFNJOJOTPOVDVLBÀUS UÑSÑOEFOFöJUJBöBôEBLJMFSEFOIBOHJTJEJS \" # $ % - & -2 A) 1 B) 2 $ 2 y3 27y2 27y3 % 1 & 4 27y3 y3 2. x = -2 ve y = -3 veriliyor. 3 xy +å - yx + (-x ) (-x) p :32 - 24f JGBE FTJOJOFöJUJBöBôEBLJMFSEFOIBOHJTJEJS 6. f 3 1 p 10 22.103 A) 59 B) 85 $ 149 JöMFNJOJOTPOVDVBöBôE BLJMFSEFOIBOHJTJEJS 28 27 36 A) -7 . 10–3 B) -7 . 10–2 $ -10–4 % & % -10–3 & –4 7. ôFLJMEFCJSCJSJOFEõUBOUFóFU¿FNCFSMFSJOJ¿JOFCF- MJSMJCJSLVSBMBHËSFTBZMBSZB[MNõUS 3. aa = 224 35 PMEVôVCJMJOEJôJOFHÌSF BBöBôEBLJMFSEFOIBO- 32 34 HJTJOFFöJUUJS 3 3 33 \" # $ % & )FSBENEBÀFNCFSTBZTCJSBSUUôOBHÌSF BENEBLJFOCÑZÑLTBZLBÀUS A) 352 B) 353 $ 54 % 55 & 56 4. YWFZQP[JUJGCJSFSUBNTBZ YâZWFYy = yx _ 0, 03 i–1._ 0, 2 i–2 % 3 & 1 22 PMEVôVCJMJOEJôJOFHÌSe, ( x + y )2JGBEFTJBöBô- 8. EBLJMFSEFOIBOHJTJOFFöJUUUJS _ 0, 02 i–1._ 0, 3 i–2 JöMFNJOJOTPOVDVLBÀUS \" # $ % & A) 3 B) 5 $ 2 1. D 2. C 3. # 4. E 25 5. D 6. D 7. C 8. D
KARMA TEST - 3 ·TMÑ4BZMBS 1. 2x + 2x + 2x + 3.2x = 192 5. \"öBôEBLJTBZMBSEBOIBOHJTJFOCÑZÑLUÑS FöJUMJôJOJTBôMBZBOYEFôFSJLBÀUS A) 555 B) 555 $ 5 ) 5 & 55 \" # $ % & 5 % 5(5 ) 2. 21- 4x = A 6. 3x = 22 - x PMEVôVOB HÌSF x + 1 JGBEFTJOJO \" DJOTJOEFO 1 x + 2 FöJUJBöBôEBLJMFSEFOIBOHJTJEJS PMEVôVOBHÌSF 4 x + 6 LBÀUS A) 32 B) 16 $ 8 % 4 & 2 \" # $ % & A A A AA 3. 2x = a 3x = b 7. 3a = 5 a 5x = c PMEVôVOB HÌSF 15 a + 1 JGBEFTJ BöBôEBLJMFS- PMEVôVOBHÌSF xJOB CWFDUÑSÑOEFOde- EFOIBOHJTJOFFöJUUJS ôFSJLBÀUS \" # $ % & A) a2 b2 c B) a b c2 $ B2 b c2 % BC2 D & B2 b2 c2 4. OCJSUBNTBZPMNBLÑ[FSF 8. 24–3x . 8x + 1 = (32) 2 ( -1 )2n + 4 - ( -18n - 2 ) - 14n - 1 - (-1)13 - 2n 2 . 161– 4x JöMFNJOJOTPOVDVLBÀUS FöJUMJôJOJTBôMBZBOYEFôFSJLBÀUS A) -2 B) - $ % & A) 1 B) 1 $ 1 % 1 & 1 6 5 4 32 1. A 2. A 3. A 4. E 26 5. D 6. D 7. C 8. E
·TMÑ4BZMBS KARMA TEST - 4 1. f 2 x PMEVôVOBHÌSF 5. BCJSBTBMTBZPMEVôVOBHÌSF 224 - a . 523 UBN 3 p =a TBZT FOÀPLLBÀCBTBNBLMPMVS 3.2x + 1 - 5.2x – 1 \" # $ % & 2.3x + 1 + 4.3x – 1 JGBEFTJOJO B DJOT JOEFO EFôFSJ BöBôEBLJMFSEFO IBOHJTJEJS A) 17a B) 21a $ 19a % 35a & 72a 25 44 37 72 46 2. 5x = 7y (0, 00002) 2 . (8000) 3 xy 6. PMEVôVOBHÌSF 25 y + 49 x OJOFöJUJOFEJS (0, 016) 4 . 5000000 JöMFNJOJOTPOVDVLBÀUS \" # $ % & \" # $ % & 3. 35x - 1 = 5x + 1 7. 1 + 1 PMEVôVOBHÌSF xJOEFôFSJLBÀUS 1 + 3a 1 + 3–a JGBEFTJOJO TPOVDV BöBôEBLJMFSEFO IBOHJTJOF \" # $ % & FöJUUJS A) -3 B) - $ - % & 4. BWFCSFFMTBZMBSJÀJOa - 1 = 3a + 2 PMEVôV- 8. M = ( 5 + 1 ) ( 52 + 1 ) ( 54 + 1 ) ( 58 + 1 ) ( 516 + 1 ) OBHÌSF 3a + 2 + 3a.2b PMEVôVOBHÌSF 32 OJO.UÑSÑOEFOEFôFSJLBÀ- (2a + b) + 9.2a US A) 2M + 3 B) 5M + $ .- 4 JGBEFTJOJOEFôFSJBöBôEBLJMFSEFOIBOHJTJEJS % .- & .+ 1 A) 1 B) 1 $ 1 % 1 & 1 24 18 12 9 6 1. # 2. D 3. C 4. # 27 5. D 6. C 7. D 8. E
KARMA TEST - 5 ·TMÑ4BZMBS 1. y-a =PMEVôVOBHÌSF 5. BWFOCJSFSUBNTBZES y2a + y–a a2n - 9an + 20 = 1 ya + 1 a2n - 16 4 JöMFNJOJOTPOVDVBöBôEBLJMFSEFOIBOHJTJEJS PMEVôVOBHÌSF LBÀGBSLM B O JLJMJTJWBSES A) 21 B) 7 $ 12 % 24 & 17 \" # $ % & 10 3 7 53 2. a = 3n - 1 6. 5a - 1 = 7a - 1 b = 3n + 3 PMEVôVOBHÌSF -a OOEFôFSJBöBôEBLJMFSE FO IBOHJTJEJS PMEVôVOBHÌSF BTBZTCOJOLBÀLBUES $ 1 % 1 & 1 7 53 % 1 & 1 \" # 9 81 \" # $ 3. B C DCJSCJSJOEFOGBSLMQP[JUJGUBNTBZMBSES 7. a-x + 1 .16x = bx -1 ve a .b = 2 (ab)c = 256 PMEVôVOBHÌSF x BöBôEBLJMFSE FOIBOH JTJEJS PMEVôVOBHÌSF B+ b +DUPQMBNOOBMBCJMFD FôJ A) - 1 B) - 1 $ - 3 % - 5 & - 5 GBSLMEFôFSMFSJOUPQMBNLBÀUS 3 2 234 \" # $ % & 4. a = 22 + 25 + 27 PMEVôVOBHÌSF 8. 2x + 3 - 3y + 1 = 5 2 + 2 4 + 26 4x - 1 + 3y - 1 = 7 JGBEFTJOJOBUÑSÑOEFOEFôFSJOFEJS EFOLMFNMFSJOJTBôMBZBOYWFZTBZMBSJÀJOYZ LBÀUS A) a # B $ a % B & a \" # $ % - & -6 2 48 1. # 2. E 3. E 4. A 28 5. # 6. C 7. A 8. C
·TMÑ4BZMBS KARMA TEST - 6 1. ôFLJMEFNFUSFZÐLTFLMJóFTBIJQCJSLËQSÐWFSJMNJõUJS 4. 7x = 50 3m 5y = 24 3m 3z = 200 3m PMEVôVOB HÌSF BöBôEBLJ TSBMBNBMBSEBO IBO HJTJEPôSVEVS A) x < y < z B) x < z <Z $ Z< x < z % [< x <Z & Z< z < x 0UPCÐTÐO ZÐLTFLMJóJ f 1 3x–7 729 p metre olup oto- CÐTLËQSÐEFOHF¿FNFNFLUFEJS #VOBHÌSF YUBNTBZTFOÀPLLBÀUS 5. x = 3-300 , y = 5-200 , z = 7 -150 A) - # $ % & TBZMBSOO EPôSV TSBMBOö BöBôEBLJMFSEFO IBOHJTJEJS A) z < x < y B) y < z <Y $ [< y < x % Y< y <[ & Z< x < z 2. f 1 2x – 1 1 7–x p <f p 9 27 FöJUTJ[MJôJOJTBôMBZBOYJOFOLÑÀÑLUBNTBZde- 6. 3x . 9x . 27x … ( 2187 ) x = 384 ôFSJLBÀUS PMEVôVOBHÌSF YLBÀUS \" # $ % & \" # $ % & 3. a = 9x - 1 , b = 3x + 1 9x 3x PMEVôVOBHÌSF BJMFCBSBTOEBLJCBôOUOFEJS 7. 2.9x + 1 - 3x + 1 - 1 = 0 A) a = 2b - b2 B) a = b2 + 2b - 1 EFOLMFNJOJTBôMBZBOYJÀJOYx - x2JGBEFTJOJO b-1 EFôFSJLBÀUS $) a = b2 % a = b2 - 2b + 1 A) -2 B) - $ % & b-1 b+1 & a = b2 + 2b + 1 b-1 1. D 2. D 3. A 29 4. C 5. D 6. # 7. A
KARMA TEST - 7 ·TMÑ4BZMBS x – 4 ^ x + 1 h2 5. (0, 5) x – 3 = (0, 25) x – 4 1. ^ x - 2 h x2 + x + 1 = 1 8x + 1 PMEVôVOBHÌSF Y-2LBÀUS EFOLMFNJOJTBôMBZBOGBSLMYEFôFSMFSJOJOUPQ- MBNLBÀUS A) 1 B) 1 9 4 $ % & \" # $ % & ax + ay = m 6. a = 32b - 1 2. ax - ay = n 3a = 81b + 1 PMEVôVOBHÌSF B3x + a3yOJONWFOUÑSÑOEFO FöJUJOFEJS PMEVôVOBHÌSF COJOEFôFSJLBÀUS A) 3n2m + m3 B) mn2 + m2 A) -2 B) - $ % 3 & 4 4 2 $) n3 + 3nm2 % 3n2 + 2m2n 4 4 & n3 - 3.m2n 4 7. ( 0,250 ) x = 27 . 2x PMEVôVOBHÌSF 3. a = 2x + 2 ( 0, 25 )x - f 1 x b = 2-x - 4 2 p PMEVôVOBHÌSF COJOBUÑSÑOEFOEFôFSJLBÀUS JöMFNJOJOTPO VDVBöBôEBLJMFSEFOIBOHJTJEJS A) 4a + 1 B) 7 - 3a $ 4a - 7 \" # $ % & a-3 a+3 2-a % 9 - 4a & 4a + 9 a-2 3a + 1 4. x = 3-3 + 3-4 + 3-5 + 3-6 8. Y Z [CJSFSUBNTBZWF y = 3-5 + 3-6 + 3-7 + 3-8 22x + y - 3 = 3x -2y - 4 = 5z - 4 PME VôVOB HÌSF x - 2y JöMFNJOJO TPOVDV LBÀ- US z PMEVôVOBHÌSF YJOZUÑSÑOEFOFöJUJOFEJS y y & 1 \" # $ % & A) $ % Z y # Z 3 9 1. # 2. A 3. D 4. D 30 5. D 6. A 7. # 8. D
·TMÑ4BZMBS KARMA TEST - 8 1. _ 0, 3 i x + 2 = f 1 2–x 5. BWFCUBNTBZMBSES 81 p 72a + 3b - 7 = 5a - b - 6 PMEVôVOBHÌSF BCLBÀUS PMEVôVOBHÌSF YLBÀUS A) -5 B) - $ - % & A) 1 B) 2 $ 3 % 4 & 6 5 5 5 55 2. ( m - 1)4 = ( 2m - 5 )4 6. a, b `Z için, FöJUMJôJOJTBôMBZBONEFôFSMFSJOJOUPQMBNLBÀ- 1 + 1 =1 US 2a + b – 6 22a – b – 1 PMEVôVOBHÌSF BCÀBSQNLBÀUS \" # $ % & \" # $ % & 3. (x - 6) x2– 5x – 6 = 1 7. *õóO V[BZEB CJS ZMEB BMEó ZPMB õL ZM BE WF- SJMJS &WSFOTFM PMBSBL CJS õL ZM ZBLMBõL 11 LN EJS %ÐOZBhEBO FO ¿PL V[BLMBõBO OFTOF PMBO 7PZBHFS–VZEVTVZMMLCJSZPMDVMVóVOBSEOEBO õLZMZPMBMNõUS EFOLMFNJOJTBôMBZBOGBSLMYEFôFSMFSJOJOUPQ- #VOB HÌSF 7PZBHFS- VZEVTV %ÑOZBhEBO LBÀ MBNLBÀUS LNV[BLMBöNöUS A) 38.1012 B) 38.1013 $ 10 \" # $ % & % 11 & 9 8. 5x = 3 ve 5y = 81 PMEVôVOBHÌSF x+y PSBOLBÀUS 4. x `;PMNBLÑ[FSF x-y ( 3x + 8 ) 2x - 5 = 1 A) 3 B) - 3 $ 5 % - 5 & 2 EFOLMFNJOJTBôMBZBOLBÀGBSLMYEFô FSJWBSES 5 53 33 \" # $ % & 1. E 2. A 3. E 4. E 31 5. A 6. A 7. C 8. D
<(1m1(6m/6258/$5 ·TMÑ4BZMBS 1. ¥FNCFS ¿FWJSNF M ZMMBSO NFõIVS ¿PDVL 4. \"õBóEBCJS¿J¿FL¿JOJOFõTBLTMBSLVMMBOBSBLPMVõ- PZVOMBSOEBOCJSJEJSöLJ¿PDVL¿FWSFV[VOMVLMBS UVSEVóVLVMFMFSWFSJMNJõUJS4BLTMBSOIFSCJSJOJOCP- 16 br ve 25 - a CSPMBOJLJ¿FNCFSJBZOZPMCPZVO- ca biri 25UVS¿FWJSFSFLEJóFSJEFUVS¿FWJSFSFL yu 32 cm olVQпTBLTÐTUÐTUFLPOVMEVóVOEBPMV- õBOLVMFOJOCPyu 42 cm dir. tamamlayabiliyor. 42 cm 32 cm #VOBHÌSF BTBZTOOBMBCJMFDFôJEFôFSMFSÀBS- \"SUBSEBPMBOIFSJLJTBLTOOUBCBOMBSBSBTO- QNLBÀUS EBLJV[BLMLTBCJUPMEVôVOBHÌSF CPZV2DN PMBOCJSSBGJÀJOPMVöUVSVMBOLVMFJÀJOEFFOGB[MB A) -3 B) - $ % & LBÀUBOFTBLTCVMVOVS \" # $ % & 2. LJõJMJLCJSHSVQZBQUL- ! DİKKAT MBS BSBõUSNB TPOVDVOEB 5. NFUSFMJL EÐ[ CJS ZPMVO CBõMBOH¿ WF TPOVOEB MJUSF BUL ZBóO NJMZPO CVMVOBO JLJ LJõJEFO CJSJ CJSCJSMFSJOF EPóSV V[BLMó MJUSFJ¿NFTVZVOVLJSMFUUJóJ- NFUSFDJOTJOEFOÐOUBNTBZLVWWFUJPMBOOPLUB- MBSBLSN[SFOLMJEJSFLEJóFSJEFÐOUBNTBZLVW- Atık yağ ni farkederek bir proje WFUJPMBOOPLUBMBSBNBWJSFOLMJEJSFLZFSMFõUJSJZPS CBõMBUZPSMBS #VOBHÌSF GBSLMSFOLUFPMVQCJSCJSJOFFOZBLO (SVQUBLJIFSCJSLJöJ7MJUSFBULZBôUPQMBEôO- JLJEJSFLBSBTNFTBGFLBÀNFUSFEJS EB UFNJ[ LBMBO TVZVO MJUSF DJOTJOEFO CJMJNTFM HÌTUFSJNJBöBôEBLJMFSEFOIBOHJTJPMVS /PU%JSFLLBMOMôHÌ[BSEFEJMFDFLUJS A) 5.1011 B) 6,4.109 $ 13 \" # $ % & % 8 & 8 3. &HFCJSPZVOHFMJõUJSNFQSPHSBNOEBLBSFLUFSJOLP- 6. #JS MBCPSBUVWBSEB CBLUFSJMFS JMF ZBQMBO EFOFZEF OVNVOVYWFZEFóJõLFOMFSJOJLVMMBOBSBLYyõFLMJO- CBLUFSJZPóVOMVóVNJLSPOJMFJGBEFFEJMNFLUFEJS EFUBONMZPS#JSLBSBLUFSJOLPOVNVOVCFMJSMFSLFO UBCBOJMFÐTTÐOZFSJOJLBSõUSBSBL YJOZJODJLVWWF- 1 mikron ZPóVOMVLUBJTFZBLMBõLNJMZPOCBLUFSJ UJZFSJOFZOJOYJODJLVWWFUJOJBMNõUS CVMVONBLUBESUCJSJNTÐSFEF2t-1 mikSPOZPóVOMV- óBVMBõBOCBLUFSJLPMJOJTJOEFZBLMBõLNJMZPOCBL- #VIBUBZBSBôNFOLBSBLUFSJOLPOVNVEFôJöNF- UFSJPMEVóVUFTQJUFEJMNJõUJS EJôJOFHÌSF YâZJÀJOYZBöBôEBLJMFSEFOIBO- HJTJPMBCJMJS 3 #VOBHÌSF 6 t NJLSPOZPôVOMVôBVMBöBOCBL- UFSJLPMJOJTJOEFZBLMBöLLBÀNJMZPOCBLUFSJCV- MVOVS \" # $ % & \" # $ % & 1. A 2. C 3. D 32 4. C 5. A 6. D
·TMÑ4BZMBS <(1m1(6m/6258/$5 1. #JSLFOBSV[VOMVóV10CSPMBOLBSFLBSUPOBõBóEB #BõMBOH¿ WFSJMFOLFTJL¿J[HJMFSCPZVODBCFMJSUJMFOZËOEFTSB- A x 22 TJMFLBUMBOBSBLBSEõLõFLJMMFSPMVõNVõUVS B ôFLJMUFPMVõBOпHFOJOEJLLFOBSMBSOOPSUBOPL- UBMBSCFMJSMFOFSFLFMEFFEJMFOUBSBMпHFOLFTJMFSFL I : 2–3 BUMZPS C D x 42 II E : 4–2 III IV x 8–3 ôFLJM ôFLJM ôFLJM ôFLJM V #VOBHÌSF TPOöFLJMBÀMEôOEBPMVöBOöFLMJO :VLBSEB\" # $ %WF&CBMPODVLMBSOEBOPMVõBO BMBOLBÀCS2EJS WF BõBó ZËOMÐ ¿BMõBO CJS NFLBOJ[NB WFSJMNJõUJS #BõMBOH¿HJSJõJOFCSBLMBOCJSTBZ HF¿UJóJCBMPO- A) 224 - 218 B) 220 - 217 $ 22 - 219 DVLJ¿JOEFLJJõMFNZBQMBSBLZBCJSTPOSBLJCBMPODV- óBHJUNFLUFZBEB* ** *** *7WF7OPMVLVUVMBSBEÐõ- % 20 - 216 & 19 - 217 NFLUFEJS#BõMBOH¿HJSJõJOEFOTBZTNFLBOJ[NB J¿JOFCSBLMZPS WFTPSVMBSZVLBSEBWFSJMFOCJMHJMFSF HÌSFDFWBQMBZO[ 3. *7OPMVLVUVZBEÑöFOTBZBöBôEBLJMFSEFOIBO- HJTJPMBCJMJS A) 27 B) 28 $ 9 % 10 & 11 4. \"öBôEBLJMFSEFOIBOHJTJ LVUVMBSEBOCJSJOFEÑ- öFOTBZMBSEBOCJSJPMBNB[ A) 23 B) 27 $ 8 % 11 & 12 2. 5. )BOHJ LVUVZB EÑöFO TBZ EJôFSMFSJOEFO EBIB 42 LÑÀÑLUÑS 32 8 \" * # ** $ *** % *7 & 7 :VLBSEB WFSJMFO ÑÀHFOTFM ZBQ EFWBN FUUJSJMJS- 6. )FSIBOHJCJSLVUVEB12TBZTCVMVONVõUVS TFTBUSEBCVMVOBOTBZMBSOTBôEBOJLJODJTJ BöBôEBLJMFSEFOIBOHJTJPMVS #VOB HÌSF TBZT TSBTZMB BöBôEBLJ IBOHJ CBMPODVLMBSEBOHFÀNJöUJS A) 237 B) 240 $ 46 % 56 & 67 A) A - B -% # \"-$ $ \"-$-% % \"-# & \"-$-& 1. # 2. C 33 3. E 4. A 5. E 6. C
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³ KÖKLÜ SAYILAR ³ Köklü Sayı t 36 ³ Kökten Çıkarma - Kök İçine Alma t 41 ³ Köklü Sayıların Eşleniği t 45 ³ İç İçe Kökler t 50 ³ Karma Testler t 54 ³ Yeni Nesil Sorular t 61
·/÷7&34÷5&:&)\";*3-*, 3. MODÜL ÜSLÜ VE KÖKLÜ SAYILAR www.aydinyayinlari.com.tr KÖKLÜ SAYILAR - I ,ÌLMÑ4BZ ÖRNEK 3 7$1,0%m/*m 3x - 1 - x - 3 6 - 2x + 3x + 5 n ` Z+ ve n $ 2 olmak üzere, xn =BFõJUMJóJOJ JGBEFTJCJSHFSÀFMTBZZBFöJUPMEVôVOBHÌSF CVTB- ZLBÀUS TBóMBZBOYTBZTOBBOOOEFSFDFEFOLÌLÑ x - 3 $ 0 ise x $ 3 denir. 6 - 2x $ 0 ise x # 3 #VEVSVNEBY=UÑS xn =BFõJUMJóJOEF 4 x = * na , n tek x =JÀJOJGBEFOJOFöJUJ EJS ±n a , n çift ve a $ 0 7 n a ifadesinde i) n çift ise a $ 0 ii) n tek ise a ` R dir. ÖRNEK 1 ÖRNEK 4 \"öBôEBWFSJMFOEFOLMFNMFSJOÀÌ[ÑNLÑNFTJOJCVMV- 3a - 4b + 13 + a + b + 2 = 0 FöJUMJôJOJ TBôMBZBO B WF C HFSÀFM TBZMBSOO ÀBSQN OV[ b) x5 = -32 LBÀUS a) x2 = 81 d) x7 + 1 = 0 c) x2 + 64 = 0 3a - 4b + 13 = 0 a+b-2=0 a) x2 = 81 j x = ± 9 j¦= {±9} a = -3, b = 1 j a.b = -3 b) x5 = -32 j x = -2 j¦= {-2} c) x2 + 64 = 0 j¦= q d) x7 + 1 = 0 j x = -1 j¦= {-1} ÖRNEK 2 ÖRNEK 5 A= 3 x+ x-2 M = 2018 15 - x + 2019 x - 15 4 5-x+2 2020 x + 1 PMEVôVOBHÌSF \"OOHFSÀFMTBZPMNBTJÀJOYJOBMB- JGBEFTJOJOCJSHFSÀFMTBZCFMJSUNFTJJÀJOYLBÀGBSLM caôUBNTBZEFôFSMFSJUPQMBNLBÀUS UBNTBZEFôFSJBMBCJMJS x-2$0 5-x$0 15 - x $ 0 j x # 15 x # -1 x$2 x#5 x+1$0 j j2#x#5 j -1 # x # 15 {2, 3, 4, 5} jUPQMBN {-1, 0, ..., 15} jUBOF 1. a) {± 9} b) {–2} , c) qFd) {–1} 2. 14 36 4 4. –3 5. 17 3. 7
www.aydinyayinlari.com.tr ÜSLÜ VE KÖKLÜ SAYILAR 3. MODÜL ·/÷7&34÷5&:&)\";*3-*, 7$1,0%m/*m ÖRNEK 8 n ` Z+ ve n $ 2 olmak üzere, \"öBôEB WFSJMFO JGBEFMFSJO ÑTMÑ JGBEF PMBSBL FöJUMFSJ- Her x ` R için, n xn = * x , x tek ise OJCVMVOV[ 2 a) 5 x2 = x , x çift ise x5 x ` R+ ve m, n ` Z+ olmak üzere, 7 13 13 n b) 2 3 = 2 21 m xn = x m dir. c) 53 = 3 d) 3 4–1 = 52 –1 43 ÖRNEK 6 \"öBôEBWFSJMFOLÌLMÑJGBEFMFSJOFöJUMFSJOJCVMVOV[ a) 3 64 = 33 ÖRNEK 9 4 =4 \"öBôEB WFSJMFO JGBEFMFSJO LÌLMÑ JGBEF PMBSBL FöJUMF- b) 5 - 32 = 5 ^ - 2 h5 = - 2 SJOJCVMVOV[ c) ( –4) 2. 3 (- 4) 3 = | -4 | . (-4) = -16 15 13 15 a) 2 13 = 2 1 4 –1 – 5 b) 5 4 = d) (1 - 2) 2 = 1 - 2 = 2 - 1 13 17 13 c) 3 17 = 3 e) 3-1+ f- 1 2 d- 1 3 1 =- 1 + 1 2 3 16 27 9 p=3 3 9 3 9 9 n+ 3 – 3 d) f 4 = p 11 2 =- + =- 39 9 ÖRNEK 7 ÖRNEK 10 x < 0 < y < z PMEVóVOBHËSF 3 4x = (0, 5) 2x + 1 PMEVôVOBHÌSF YLBÀUS (x - y) 2 + 3 (y - z) 3 - 4 (x - z) 4 2x –2x–1 2x - 2x - 1 JöMFNJOJOTPOVDVOVCVMVOV[ 2 3 =2 2 & = 32 = |x - y| + y - z - |x - z| 3 & x =- = -x + y + y - z + x - z = 2y - 2z 10 2/5 13/21 3/2 –1/3 8. a) x b) 2 c) 5 d) 4 2 37 6. a) 4, b) –2 c) –16 d) 2 - 1 e) - 7. 2y – 2z 13 15 4 –1 17 313 d) 3 2 b) 5 16/9 10. m 9 9. a) c)
·/÷7&34÷5&:&)\";*3-*, 3. MODÜL ÜSLÜ VE KÖKLÜ SAYILAR www.aydinyayinlari.com.tr ÖRNEK 11 7$1,0%m/*m 2 4x + 1 49 x ` R+ , m ` Z, n, k ` Z+ ve n $ 2 için, 3 f p= PMEVôVOBHÌSF YLBÀUS 74 n m n xm = n.k xm.k = k xk dir. 4x + 1 2 –2 x ` R+ ve m, n ` Z+ ve n $ 2 için, =d n _ n x im = n xm dir. d2n 3 77 4x + 1 =-2 j x = - 7 34 ÖRNEK 12 ÖRNEK 15 0 < x < 1 olmak üzere, \"öBôEBWFSJMFOJGBEFMFSJOFOTBEFIBMMFSJOJCVMVOV[ x2 + 1 + 2 - x2 + 1 - 2 x2 x2 JGBEFTJOJOFöJUJOJCVMVOV[ a) 21 27 = 7.3 3 = 7 3 3 = dx+ 1 2 dx- 1 2 n- n xx 1 1 11 b) 8 16 = 4.2 4 = 2 = x + x - x - x = x + x + x - x = 2x 2 ÖRNEK 13 c) 15 32 + 18 64 = 5.3 5 6.3 6 3 - 27 + 144 - _ - 3 i2 2+ 2 5 - 32 + 4 _ - 9 i2 - 3 - 125 JGBEFTJOJOFöJUJOJCVMVOV[ =3 2+3 2=23 2 3 ^ - 3 h3 + 122 - - 3 - 3 + 12 - 3 6 = = =1 ÖRNEK 16 -2 + 3 + 5 6 5 ^ - 2 h5 + 4 34 - 3 ^ - 5 h3 a = 2 , b = 3 5 , c = 4 13 ÖRNEK 14 TBZMBSOO LÑÀÑLUFO CÑZÑôF EPôSV TSBMBOöO CV- MVOV[ 1-3+9 16 10 25 12 6 , 12 4 , 12 3 3 1 + f 7 - 1 pf 1 + 7 + 49 p 20 20 400 a= 2 b= 5 c= 13 JGBEFTJOJOEFôFSJOJCVMVOV[ 26 < 54 < 133 j a < b <DEJS d 1 - 3 2 13 - 45 n 45 = 7 =1 20 3d 7 3 20 n -1+1 7 12. 2x 13. 1 14. 1 38 15. a) 7 3 b) 2 c) 2 3 2 16. a < b < c 11. - 4
,ÌLMÑ4BZWF²[FMMJLMFSJ TEST - 10 1. (- 3) 2 + 3 - 64 - 4 (- 16) 2 5. 3 4.33 + 2.33 + 2.33 JöMFNJOJOTPOVDVLBÀUS 42 + 42 + 42 + 42 A) -4 B) - $ - % - & -8 JöMFNJOJOTPOVDVLBÀUS A) 2 B) 1 $ 3 % & 5 3 2 2 2 6. a < 1 olmak üzere, 2. ( –5) 2 - 6 (- 8) 2 - 3 - 14 & a2 - 2a + 1 3 a - 1 . 3 a2 - 2a + 1 JöMFNJOJOTPOVDVLBÀUS A) -3 B) - $ % JGBEFTJOJOFöJUJBöBôEBLJMFSEFOIBOHJTJEJS A) - # $ B- 1 & B2 - 1 % -B 3. 3 64 - (- 16) 2 7. 3 - 0, 125 - 1, 21 + 6, 25 JöMFNJOJOTPOVDVLBÀUS JöMFNJOJOTPOVDVLBÀUS A) -2 B) - $ - % - & -6 \" # $ % & 4. 13 + 6 + 1 + 64 8. 3 . 1 + 7 - 5 . 1 + 24 + 2 . 1- 3 JöMFNJOJOTPOVDVLBÀUS 9 25 4 JöMFNJOJOTPO VDVLBÀUS \" # $ % & A) -5 B) - $ - % - & -1 1. # 2. C 3. A 4. D 39 5. C 6. A 7. E 8. D
TEST - 11 ,ÌLMÑ4BZWF²[FMMJLMFSJ 1. 0 < x < y olmak üzere, 5. m = 3 3 , n = 5 , k = 5 9 3 - x3 - _ x - y i2 + 4 _ y - x i4 TBZMBSOO EPôSV TSBMBOö BöBôEBLJMFSEFO IBOHJTJEJS JGBEFTJOJOFöJUJBöBôEBLJMFSEFOIBOHJTJEJS A) x B) -Z $ -x A) m < n < k B) m < k < n $ O< m <L % L< m < n % Z-Y & Z- 2x & L< n < m 2. 5 - x - 4 2x - 10 x -xx 6. 2a = 5 , 3b = 7 ve 5c = 1 JGBEFTJ CJS HFSÀFM TBZ CFMJSUUJôJOF HÌSF JGBEFTJOJOEFôFSJLBÀUS A) -5 B) - $ % & PMEVôVOB HÌSF B C WF D BSBTOEBLJ TSBMBNB BöBôEBLJMFSEFOIBOHJTJEJS A) a > b > c B) b > c >B $ D> b > a % C> a >D & B> c > b 3. ôFLJMEFIFSBENEBJLJõFSBSUBOCJSCJSJOFUFóFUË[- 7. m - 3 = 3 - 2 EFõ¿FNCFSMFSWFSJMNJõUJS FöJUMJôJOJTBôMBZBONHFSÀFMTBZTLBÀUS BEN A) 3 B) 3 4 + 3 $ 3 - 3 4 BEN % & 4 4 + 3 BEN )FSBENEBCVMVOBO¿FNCFSMFSJOTBZTOOLBSFLË- LÐ BMOBSBL P TBUSO JTNJ CFMJSMFOJZPS ±SOFóJO BENOJTNJ 6 ES #VOBHÌSF JTNJUBNTBZPMBOBENTBZTPM- EVôVOEBIFSIBOHJCJSBENEBFOGB[MBLBÀÀFN- CFSCVMVOVS \" # $ % & 4. 2x - 3y + 18 + 6 3x + y + 16 = 0 8. 22x + 1 . 3 2x + 1 . 4 2x – 1 = 64 FöJUMJôJOJTBôMBZBOYWFZHFSÀFMTBZMBSJÀJO x PMEVôVOBHÌSF x LBÀUS PSBOLBÀUS y A) 21 B) 65 $ 60 % 12 & 15 13 19 17 5 7 A) -4 B) - $ % & 1. C 2. A 3. D 4. # 40 5. # 6. A 7. # 8. #
www.aydinyayinlari.com.tr ÜSLÜ - KÖKLÜ SAYILAR 3. MODÜL ·/÷7&34÷5&:&)\";*3-*, KÖKLÜ SAYILAR - II ,ÌLUFO¦LBSNB,ÌL÷ÀJOF\"MNB ÖRNEK 3 7$1,0%m/*m \"öBôEBWFSJMFOJGBEFMFSJOFOTBEFHÌTUFSJNMFSJOJCV- MVOV[ a, b ` R+ ve n ` Z+ ve n $ 2 için, a n b = n an.b dir. a) 288 = 2 = 12 2 x ` R+ ve a, b, c ` R, n ` Z+ ve n $ 2 ol- mak üzere, 12 .2 a n x + b n x - c n x = _ a + b - c i n x tir. b) 3 192 = 3 3 = 4 3 3 4 .3 c) 3 3 ^ - 5 h3.2 = - 5 3 2 - 250 = ÖRNEK 1 d) 5 - 224 = 5 ^ - 2 h5.7 = - 2 5 7 \"öBôEB WFSJMFO JGBEFMFSJ UFL CJS LÌL I»MJOEF JGBEF e) 4 162.1010 = 4 4 82 = 300 4 200 FEJOJ[ 3 .2.10 .10 a) 2 3 3 = 3 24 ÖRNEK 4 b) x. 1 = x 4 83 - 5 37 - 21 - 3 - 64 x JGBEFTJOJOEFôFSJLBÀUS c) - 1 5 64 = 5 -2 4 83 - 5 37 - 21 - 3 64 = 3 2 –4 d) ^ 5 - 3 h 7 + 3 5 = -2 2 5 2 3 ÖRNEK 2 ÖRNEK 5 a=3 5 , b=2 7 , c=5 3 a= 2 , b= 3 , c= 5 TBZMBSOO LÑÀÑLUFO CÑZÑôF EPôSV TSBMBOöO CV- PMEVôVOBHÌSF 2400 TBZTOOB CWFDUÑSÑOEFO MVOV[ FöJUJOJCVMVOV[ 2 _ b a= 3 .5 = 45 bb 52 b= 22.7 = 28 ` & b < a < c EJS 2400 = 3.2 .5 = 4.5. 6 b 2 bb = 4.5. 2. 3 = 42 = 52 c= = 75 a 5 .3 a .c .a.b a .b.c 1. a) 3 24 , b) x , c) 5 - 2 , d) - 2 2 2. b < a < c 41 3. a) 12 2 b) 4 3 3 c) - 5 3 2 d) - 2 4 7 e) 300 4 200 4. 3 5. a5.b.c2
·/÷7&34÷5&:&)\";*3-*, 3. MODÜL ÜSLÜ - KÖKLÜ SAYILAR www.aydinyayinlari.com.tr ÖRNEK 6 ÖRNEK 10 2 , 1, 41 ve 3 , 1, 71PMEVóVOBHËSF 7 - 3 15 + 2 + 1 - 98 - 108 + 75 + 162 48 16 JöMFNJOJOTPOVDVLBÀUS JGBEFTJOJOZBLMBöLEFôFSJLBÀUS =- 2 .2 - 36.3 + 25.3 + 81.2 7 -3 15 2+ 11 + = 7 48 16 2 =-7 2-6 3+5 3+9 2 1 4 = + 2 2 - 3 = 2^ 1, 41 h - 1, 71 = 1, 11 3 2 3 2 ÖRNEK 7 ÖRNEK 11 4 243 + 3 81 + 3 192 - 4 1875 x, y, z ` R+ olmak üzere, JöMFNJOJOTPOVDVLBÀUS x y.z = 5 , y x.z = 15 ve z x.y = 12 PMEVôVOBHÌSF YZ[LBÀUS 4 35 - 3 4 + 3 4 3 - 4 4 3 .3 5 .3 =34 3+33 3+43 3-54 3 =73 3-24 3 _ x y.z = 5 b b y x.z = 15 ` UBSBGUBSBGBÀBSQBMN b b z x.y = 12 a 222 x.y.z x .y .z = 5.15.12 ÖRNEK 8 x2 . y2 . z2 = 5.15.12 j x.y.z = 30 7 3 16 - 2 3 128 + 5 3 54 ÖRNEK 12 JöMFNJOJOTPOVDVLBÀUS AB 14 3 2 - 8 3 2 + 15 3 2 = 21 3 2 \"JMF#BSBT 20 3 CSEJS\"JMF#OPLUBMBSOEBCVMVOBO ÖRNEK 9 LJõJMFS CJSCJSMFSJOF EPóSV TBCJU I[MB TSBTZMB EBLJLBEB a3 8 b23 JGBEFTJOJOFöJUJOJCVMVOV[ 12 br ve 27 CSI[MBZBLMBõNBLUBES b2 a13 #VOBHÌSF EBLJLBTPOSBBSBMBSOEBLJV[BLMLLBÀ CSPMVS 24 23 8 a .b 8 12 = 2 3 ZEBLZ 10.2 3 = 20 3 11 7 27 = 3 3 ZEBLZ 10.8 3 = 30 3 16 13 = 50 3 - 20 3 = 30 3 br a .b b .a 6. 1,11 7. 7 3 3 - 2 4 3 8. 21 3 2 8 11 7 42 1 11. 30 12. 30 3 10. 9. a .b 2
,ÌLUFO¦LBSNB,ÌL÷ÀJOF\"MNB TEST - 12 1. 3 27 - 4 12 + 2 75 5. 4999 - 4997 + 4995 UPQMBNOOTPOVDVLBÀUS 4994 + 4998 - 4996 JöMFNJOJOTPOVDVLBÀUS A) 8 3 B) 9 3 $ 3 & 1 A) 2 2 B) 2 $ 2 % % 3 & 3 6. f ( x ) = xn- 1 ve f ^ 6 2 h = 15 2. 3 = a , 5 = b PMEVóVOBHËSF PMEVôVOBHÌSF OLBÀUS 180 JOBWFCDJOTJOEFOEFôFSJBöBôEBLJMFS- \" # $ % & EFOIBOHJTJEJS A) 2ab B) 2ab2 $ B2 b % BC & B2 b2 7. 25 + 2500 + 250000 25 + 0, 25 + 0, 0025 JöMFNJOJOTPOVDVLBÀUS \" # $ & 3. 2a = x ve 4 3a = y % PMEVôVOBHÌSF 12aOOYWFZUÑS ÑOEFOFöJUJ BöBôEBLJMFSEFOIBOHJTJEJS A) x2 y4 B) x4 y4 $ x y % YZ2 & Y2 y2 8. 2 + 4 + 6 + 8 + 10 + . . . + 22 = x 3 + 6 + 12 + 18 + 24 + . . . + 66 = y PMEVôVOBHÌSF ZJMFYBSBTOEBLJCBôOUBöBô- EBLJMFSEFOIBOH JTJEJS 4. 4. 9 m - 3. 9 n = 2. 9 m + 9 n A) 3 + x = y B) y = 3 x + 1 FöJUMJôJOFHÌSF 3 m LBÀUS $ y = 3 (x + 1) % y = x - 3 n % 1 & 1 & y = 3 (x - 1) 24 \" # $ 1. D 2. C 3. # 4. A 43 5. C 6. D 7. C 8. C
TEST - 13 ,ÌLUFO¦LBSNB,ÌL÷ÀJOF\"MNB 1. 12 - 27 + 48 - 75 4. 1! .2! .3! .4! = a b 32 FöJUMJôJOJTBôMBZBOFOLÑÀÑL a +CUPQMBNLBÀ- JöMFNJOJOTPOVDVLBÀUS US \" # $ % & A) –2 3 B) – 3 $ % 3 & 2 3 5. 6 5 – 2 . 3 5 – 2 . 5 – 2 JöMFNJOJOTPOVDVLBÀUS A) 5 - 2 B) 5 + 2 $ 2. a > -2 olmak üzere, % & 5 + 2 a + 3 32a + 28 TBZT SBTZPOFM CJS TBZ PMEVôVOB HÌSF B UBN TBZTOOLBÀGBSLMEFôFSJWBSES \" # $ % & 6. 6 25 , b = 5 34 , c = 4 53 a= TBZMBSOO TSBMBOö BöBôEBLJMFSEFO IBOHJTJ- EJS A) b < c < a B) a < b <D $ D< b < a % C< a <D & D< a < b 3. B CWFYEPóBMTBZPMNBLÐ[FSF D x = a2.b = b õFLMJOEFUBONMBOZPS ±SOFóJO 9 18 = 2 dir. 7. YWFZQP[JUJGTBZMBS #VOBHÌSF 9 9 63 + 9 43 JöMFNJOJOTPOVDV 8 56.34.x2 = y 9 162 PMEVôVOBHÌSF Y+ZOJOFOLÑÀÑLEFôFSJLBÀ- LBÀUS US \" # $ 43 % & 44 \" # $ % & 25 1. A 2. C 3. A 44 4. # 5. A 6. # 7. D
www.aydinyayinlari.com.tr ÜSLÜ VE KÖKLÜ SAYILAR 3. MODÜL ·/÷7&34÷5&:&)\";*3-*, ,ÌLMÑ4BZMBSO&öMFOJôJ KÖKLÜ SAYILAR - III ÖRNEK 3 7$1,0%m/*m n ` Z+ ve n $ 1 için ¥BSQNMBS SBTZPOFM PMBO JLJ HFS¿FL TBZEBO /n IFSCJSJOFCJSCJSJOJOFöMFOJôJBEWFSJMJS f_ k i = f_ 1 i + f_ 2 i + f_ 3 i + ... + f_ n i a + b OJOFõMFOJóJ a - b k=1 a + b OJOFõMFOJóJa - b õFLMJOEFUBONMBONBLUBES a OOFõMFOJóJ a 99 1 JGBEFTJOJOEFôFSJLBÀ- n am OOFõMFOJóJ n an – m dir. k+1+ k /#VOBHÌSF k=1 US /99 1 11 + ... + 1 =+ k=1 k+1+ k 2+1 3+ 2 100 + 99 ÖRNEK 1 ^ 2 - 1 h ^ 3 - 2 h . . . . ^ 100 - 99 h 7 - 6 + 10 _ 3- 2 5- 2 5 b JGBEFTJOJOEFôFSJLBÀUS 2-1 b 3- 2 b b 4- 3 ` b 100 - 1 = 10 - 1 = 9 hb b b 100 - 99 a 7 6 10 ÖRNEK 4 -+ 3- 2 5- 2 5 ^3+ 2h ^ 5+ 2h ^ 5h 7^ 3 + 2 h 6^ 5 + 2 h 10 5 =- + 5+1 7 35 :_ 3-1i =3+ 2-2 5-2 2+2 5 =3- 2 3 + 5 + 15 + 1 JGBEFTJOJOEFôFSJLBÀUS 5+1 5+1 11 = ·= 3^ 1 + 5 h + 5 + 1 ^ 5 + 1 h^ 1 + 3 h 3 - 1 2 ÖRNEK 2 ÖRNEK 5 3+ 2+ 6+1 A = 15 - 6 2+1 2 -1 5 JGBEFTJOJOEFôFSJLBÀUS PMEVôVOBHÌSF \"2TBZTOOEFôFSJLBÀUS 3^ 1 + 2 h + 1 + 2 ^ 1 + 2 h^ 3 + 1 h = = 3+1 2+1 1+ 2 A= 3^ 5- 2h 15 & 2 = 15 UJS =- A 2- 5 5 45 3. 9 4. 1 5. 15 1. 3 - 2 2. 3 + 1 2
·/÷7&34÷5&:&)\";*3-*, 3. MODÜL ÜSLÜ VE KÖKLÜ SAYILAR www.aydinyayinlari.com.tr ÖRNEK 6 7$1,0%m/*m 3+ 2+1 a, b ` R+ , n ` Z+ ve n $ 2 olmak üzere, 3- 2+1 n a . n b = n a.b dir. JGBEFTJOJOFöJUJLBÀUS n a = n a dir. nb b 3+ 2+1 = ^ 3 + 2 + 1 h2 3 + 1 - 2 ^ 3 + 1 h2 - ^ 2 h2 ^ 3+1+ 2h ÖRNEK 9 6 + 2 6 + 2 3 + 2 2 2 2^ 3 + 1 h+ 2 3^ 1 + 3 h == 2+2 3 2^ 3 + 1 h \"öBôEBWFSJMFOJGBEFMFSJOFöJUJOJCVMVOV[ ^ 3 + 1 h^ 2 2 + 2 3 h a) 3 2 . 3 4 2. 5 = = 3+ 2 b) 2^ 3 + 1 h 4 16 3.3 9 48 + 3 128 c) d) 5 27 3 54 + 27 ÖRNEK 7 e) 3 3 . 3 9 . 3 0, 027 0, 49 + 0, 09 f) 2x2 + 1 - 2x2 + 3 = a ise 0, 25 - 0, 01 2x2 + 1 + 2x2 + 3 JGBEFTJOJOBUÑSÑOEFOFöJUJOJCVMVOV[ a) 3 2 . 2 4 = 3 8 = 2 b) 2. 5 10 = 4 100 10 = = 4 16 4 16 16 2 2x2 + 1 - 2 + 3 = a 4 UBSBGUBSBGBÀBSQBMN 3.3 9 15 10 = 30 2x 2x2 + 1 + 2 + = c) 3 .9 30 17 2x 3 b 5 27 6 = 3 (2x2 + 1) - (2x2 + 3) = a.b 27 2 48 + 3 128 4 3 + 4 3 2 4 -2 = a.b j b = - a d) = = 3 54 + 27 3 3 2 + 3 3 3 e) 3 3 . 3 9 . 3 0, 027 = 3 3.9.27 9 = = 0, 9 1000 10 0, 49 + 0, 09 0, 7 + 0, 3 1 5 f) = = = 0, 25 - 0, 01 0, 5 - 0, 1 0, 4 2 ÖRNEK 8 ÖRNEK 10 YWFZQP[JUJGHFS¿FMTBZMBSJ¿JO 11 - 2 . 3 11 + 2 . 6 11 + 2 x-y = 1 JöMFNJOJOTPO VDVLBÀUS x y+y x x PMEVôVOBHÌSF x PSBOLBÀUS y x-y 1 a x + y ka x - y k == =1 x . ya x + y k x ya x+ yk x 6 ^ 11 - 2 h3.^ 11 + 2 h2.^ 11 + 2 h x - y = y & x = 2 y j y = 4 UÑS = ^ 11 - 2h^ 11 - 2 h3 = 6 3 9 =3 2 46 9. a) 2 b) 10 30 17 4 5 10. 3 7. - a c) 3 d) e) 0,9 f) 6. 3 + 2 8. 4 2 32
www.aydinyayinlari.com.tr ÜSLÜ VE KÖKLÜ SAYILAR 3. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 11 ÖRNEK 15 2, 88 3 0, 024 2, 56 _ 2 + 3 - 5 i_ 2 + 3 + 5 i +- JGBEFTJOJOFLTJôJOJOLBSFTJLBÀUS 0, 02 3 0, 003 0, 16 ^ 2 + 3 h2 - ^ 5 h2 = 7 + 4 3 - 5 = 2 + 4 3 JöMFNJOJOTPOVDVLBÀUS & ^ 2 + 4 3 - 2 h2 = 48 2, 88 0, 024 2, 56 = +3 - 0, 02 0, 003 0, 16 = 144 + 3 8 - 16 = 12 + 2 - 4 = 10 ÖRNEK 12 ÖRNEK 16 M =_8 5+1i_4 5+1i_ 5+1i 5 a3.b . 3 a.b2 JöMFNJOJOTPOVDVLBÀUS PMEVôVOBHÌSF 8 5 JO.UÑSÑOEFOFöJUJOFEJS 30 a28.b–4 ^ a3.b h6.^ a.b2 h10 = 30 28 26 a .b 30 30 30 =b = ^ 8 h^ 8 h ^ 4 5+1h^ 5 + 1 h = M^ 8 5 - 1 h 28 –4 28 –4 b 1 2 3 4 454-441 4 454+441 a .b a .b 1 4 4 4 44454–4142 4 4 4 4 4 4 443 1 4 4 4 4 4 4 4 454–4142 4 4 4 4 4 4 4 4 4 443 4 4 = ^ 3 5 - 1 h.Mj 8 5 = M + 4 ÖRNEK 17 M 5 0, 3 = 5 81 PMEVôVOBHÌSF YLBÀUS ÖRNEK 13 3 31–x 3 33x–6y 51 1 = 81PMEVôVOBHÌSF YLBÀUS 3 15 3 3 15 91–2y = = 5x–8 3 1–x 5–5x 3 3 3 3 6x – 12y 6 + 5x–8 4 6 = 6x – 12y – 6 12y = 81 3 – 6y 3 = 3 15 = 3 5 & x = 4 9 6 6x – 6 = x – 1 = 4 &x=5 3 3 3 ÖRNEK 14 ÖRNEK 18 A = 3 1- 3 , B = 6 4 + 2 3 f 3- 1 2 2 bPMEVôVOBHÌSF BCLBÀUS PMEVôVOBHÌSF \"#LBÀUS 6 p =a+ 6 ^ 1 - 3 h2.^ 4 + 2 3 h = 6 ^ 4 - 2 3 h ^ 4 + 2 3 h =6 4=3 2 ^ 3 2 - 1 h2 19 - 6 2 = = a+ 2b 66 19 j a = , b = - 1 & 6ab = - 19 6 11. 10 M+4 13. 5 14. 3 2 47 15. 48 16. b 17. 4 18. –19 12. 4
TEST - 14 ,ÌLMÑ4BZMBSMB÷öMFNMFS 1. 3 + 4 + 9 5. 6 - 3 3 48 27 6+ 3 JöMFNJOJOTPOVDVLBÀUS TBZTOOÀBSQNBJöMFNJOFHÌSFUFSTJLBÀUS 73 B) 5 3 $ 3 A) 3 - 1 B) 3 + 2 $ 3 + 1 A) 3 & 3 3 3 % 3 3 % 2 - 1 & 2 + 1 2. 15 - 3 + 15 + 5 3- 3 3+ 5 5 6. 3 2 - 1 + ^ 3 2 h2 JöMFNJOJOTPOVDVLBÀUS 3 2-1 $ 5 % 3 & JöMFNJOJOTPOVDVLBÀUS 35 \" # B) - 3 2 $ 3 4 & 3 2 + 1 A) –1 % 3. 3 27 - 3 7. 3 + 2 + 3 . - 3 + 2 + 3 . 3 + 1 16 3 + 3 ÀBSQ NOOTPOVDVLBÀUS 27 A) 3 B) 2 $ % - 2 & - 3 JöMFNJOJOTPOVDVLBÀUS A) 3 B) 3 $ 2 % & 4 2 3 4. 2 8. a > b olmak üzere, 3 25 + 3 15 + 3 9 JGBEFTJOJOFöJUJBöBôEBLJMFSE FOIBOHJTJEJS A) 3 5 + 3 3 B) 3 5 - 3 3 9a2 - 9b2 + 4a2 - 4b2 a+b % 3 5 - 3 3 JGBEFTJOJOEFôFSJBöBôEBLJMFSEFOIBOHJTJEJS 2 $ A) 5 ( a - b ) B) 5 a - b $ 5 a + b & 3 5 - 3 3 15 % B+C 5 a-b & a-b 1. A 2. E 3. E 4. # 48 5. D 6. A 7. # 8. #
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