ДПА 2015 Збірник завдань з математики 9 клас

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1. IEieneza, -v-Ev-_-i ,r .VI ~ I . n-I-H - xx 322325 .ls ,73.; / If I I7 i ' :1I'%! '""'5"". """", " ,lgLI:. ; _i W 1'" ""' V L Jan.n3""?L-cue? Ln. " Bu-EC EFQEFZJO.C.|c'rep,O.B.priHapins:Qmcm Lsiilaae-: -/i>< I'i%*iC%5MOBPiX 5306: 3 ivxCiTeMCT! viK! 'i} A 2. YIIK.51(079.1) BBB.22.1si72I -4 I-89PeueH3eH'm:O. M. 1epacu. vzoeuI.MBTOJIMCT 3 Ma'reMa'rmm HMLI npnpoxmnqo-MaTeMaTuuHo'1' ocpi-rm i . exHonori171 IHIIO Ry iMeHi Bopnca Fpinqenxa.0.1. llpocrcypa,yxuxrenb BI/11110.1. xaweropii,ytmrem. -Me'ro; u4cT,3acT..-mpexwopa 3 HBP 3H3 . 2 9 O6OJIOHCbKOI0 paony M.Km-znaIcwep O. C.36ipHmc aarmanb 11.713 a'rec'ra11ix'IHIIx nncbmonnx po- 6iT 3 Ma1'eMa'rIucu :mm 3aIaJ'IbHO0CBiT.Harm.aaxn.: 9-I71 KJI./ O. C. Icrep,O. B. Cprina. Ruin :IeHe3a.2015. 32 c.: in. ISBN 978-966-1 1-0552- 1 . Hocinmc npxdanatxeno mm ninrowomm -ra n; um; z--:1 nepauannoi nizxcymxcoaoi a'rec'raui1 3 MaTeMa'rmcu 14 um LuKo. '1i.Bin MiCTH'l'b 12 Bapiawris arecmlziiiunx pofm.Icoxcni qo-mpn e OLIHOTHTIHI/ IMPI.3MiCT ycix aaanam,H1 nepxcasnnm BVIMOPEIM no pix! -{H 3a1*a. rILHoocBi'rHLo'1 n .yv-min :3 Ma'reMa'rmK co6o1o 3a q)opMo1o Ta pinuem cxnanaocwi.3M1C'I saananb KOJKHOFO 3 Bapiarrrin Binnoninae nepaxammm BnMoraM no pinxm 3a1"aJI1~. Ho0cBi'rHbo'1' ninIo1'oBxn ytmis 3 Ma'reMa'rmm. Hin Ixac mmopncwamm aipnmca Hemae no'rpe6u npyicynaru 6.namcn Binnonineii,ocxinmcu Icoacen 3 Bapiairrin e ninpisumu apxymem,mo Mi(: TllTb ne Jmme ymonn ncix sannaus,a 1'1 Micue mm nuecemm sinnosine no sannam.1-16. Owoxe,lcoalcen napianr onuov-Iacno c namcom ninnonineii,mmiui nicna aanonnenna i nmconannn po6o'm nin- Knanacnca no ocnonnoi poooni,T06l'0 no npourramnonarmx H8.B'Ia. TIblIKM samlanom i ninrmcamlx ylI-HIM}!aprcymin y mlirumcy,Ha mmx Bonn 38Ill'ICyl0Tb po3Ba3anHa sannam.17-19 (5160 17-21). IIIo0o odcxzy amecmauiimoi po6omu ma Macy Ha ii eurcortaumz. V'mi aaeaabuooceimuix rmacie eurcouyromb yci aaeauun 1-19 amecmaqilinoi nucbmoaoi po6omu. Y-mi rmacis 3 no2JLu.6JLeuuM sue-teruuun Mame/ namurcu yci saeaamm 1-21.lac Ha BPI11 aw 1r1eo11a1=111M11 3aBnaHHHMH 1-16. opMyJ11oBaHHs1 sannam.17-21 ytmi He nepenpxcg A ...~ ;1111e B1ea3y1o'rb "ix HoMep. Hpan;- 1 .33a3aH1m sannamm 17 oI1iH1oe'rbcs1 B 4 6aJI11, a Ieoxenoro i3 aannanb 18-21 - --:5113.01111110 - - aaanaui.17-21 npononyemo 3ni11cmo1za'm 3a iepprrepisimn,Hanenenmvm 13 Ta6nm11Ta6JLul4J1 1Binnoninna liJ[blCic'l'L 6aJ1in 3a sannannn 1111 yv-ma - Ma1ecuMaJ1r.1Im"I1Ma1oc11Ma: u.n1ni 6a.11 6 61111 4 OTp111v1a15 111.: .u11.n1,uy ninnonins i uasia 1103119 o6rpy1-1'1~yBa111151rpO3B'H8aHH 6 61111113 4 6a. rmOrpnm-as up: -111m1;.11_v uiniloninh,ane B0]-Ia Henocwawnbo o61py11- Tonmm ao p03BH. "1a1111:1 rv1ic'1'Ir1T1>.He3H8'1'a'1'y,. . . . . .. .3 6aJm 2 Gama . __aoo B pea_v:11.-ran 3H;11j. ._,11r_>s nmue qacnmy I! pBl/ IJIBHOI B1n11oB1n1 Posnoqan po3sa3y3arr:rxpaeunbuo.ane 13 npoueci po3n:1ay- sauna np11nyc'1*1111c11 ucM11:1K14 B 3ac'1'ocyBaHHi He06X11IH010 263.7111 Tnepnxeewrmt qn 1po; J_{1j.1_1_1 r i 7 1 Gan Jlnnm ncusaa npanun-.1-1 po3Bs13y1sa'm aannamm a6o nonran uenpammsuo,ane um: -wynni e'ra1m po31s513y1-xauasi Bmeonan 16311E T Po3a;13a11H:1 He sinnoainae neonuomy 3 Haaeneimx Hume 1epn- 0 Baum 0 aniaTepiiaBnnpannenas 1 3a1epec. r1eHHa B oq)opM. v1eH11i po313:13aHH51 3aBnaHb 17-21, memo ix 3po6neHo a1eypa'rHo,He 1: r1inc'1'aBo1o nna 31111>1eeH1m o11iH1e11. Flpo Haseneni 1113an11s1.TO 11110110 5 e 11x)2y" --25x.Binoeiab:I. 5 2 4 3 4 m m m. = A) --;B) 4m4; B) -~; 2 4 4 6,m6 m:m 2 2m" in 'Poan sr3aHna. +~: ~--- U;.Bianosiab:A.8 2 8 " '5' 4 6. 06-IHCJIi'lb suaqemm Izmpaay 16] 19.n A) -5; B) 5; B) -20; I) 20. P0 3 B :1 3 a H H :1. l6[]9 = ]6/25 =2 16-:16 5 -20. 16 16 Is 4Binoeidb:B. 7. Binomo,mo m > n.Hrca 3 uepi1sH0c're'vi e upaswnanovo? A) m > n;B) 5n : - 5m;B) 4m < 4n:1) 4m < ~41).Bidnoeib:I. 8. (an) apnqamewnqna nporpecia,a,= 2; a2 2 7. 3HaI}iLi'X'b u. A) 97; B) 102; B) 107; I) imua Bizznosinb.PO3B5{3aHH. .d= (l2-a| "~72;5; a; a, v (1{lI"1.TO1[_'(I21:2 + 50311);am =102.Bidnoeidb:B. 9. Ha MBJIIOHKY upsmi a i h ~ uapa. ne. r1bHi,m ciqHa.3Haf'1,u, '1r1. Fpanycy Mipy v 6 9. 3p03o1Kimb 3ae0aHHn 20, 21 ma 38/TULU/ mb po3e3aHHn KO)KHO2O 3 no3HuM O5/'pyHmy8aHHFIM nocni0oeHocmi11o3iwHux Kp0Ki8 i diu.I1OCUJ7aHHFIMu Ha Mamemamutmi m86'p0)K6HHF-I ma qbaxmu,3 max eunnueae ITIOL7 uu iHwuL7 eucHoeoK.rauo nompi6Ho, npoimocmpyume pO36'3aHH cxeMaMu,apad)iKaMu,ma6nuunMu. / 20., I1oBe;1iTb, LL1o KOJIH x >0, y > 0, 2 >0, 'ro[1+ M1*> 8. x21. Ceperum ninin Tpaneuii ziopinmoe 4 cm,:1 xcywn npn onai 3 ocnon 20 i 70.3321171- 111 OCHOBH Tpaneuii,mcmo B1I[p130K,H10 cnonyqae "ix cepe,1uIHxI,zzopimnoe 1 CM. 10 13. piaaume,iM' Knac1.Bapiaur 23aeOaI-ms 112 Maromb no uomupu eapianmu aidnoeide,3 Hxux mi. I'IbKU OLIMH e I7PABl/1l7bHl/ IM.Oepimb i nos; -Iaume npaeunbnufl aapianm aidnoeidi 8 ma6nuui. Hrcy qac'ruHy npamorcyrnmca aamwpnxonano Ha MEUIIOHRY? CCCKU mi mg:mg:mg2 5 2. Ba 1,5 ron Mmm 3MOJIOB 10 U,3epHa.Crcinbxn qacy no'rpi6Ho,r1106 3Mo.71o'm 12 u,sepna,memo nponywrnanicmb MJIYIHEI e c'raJIo1o?A) 1,8 r011; B) 1.6 mg;B) 2 mix;1) 2,2 Io, z1. ,_ A E B I 3. Vuancrna puansmna,xopeuem mcoro e rmcno 6. 1 A) 5x =30; B) 5x =-30; B) 0x =-6; I) -5x =-30. 2 4. Cnpocrin.Bnpaa (a 3b)(a + 3b) a2.A) 2a2 9122; B) ~3b2; B) 9b2: 1) 9b.5 5. Bnxonare Aim 7/ +6 A) 8[;B) 14J;B) 21; r) N6.1 "7 1 5 9 6. O6 ' - .tmcnrrn.[3] (3) 10 A) 6; 1;) 9; B) -1; r) 1. 11 9 6 12 7. Po3B'5mci'rb Hepianicm x2 ~ 36 < 0. A) (-6; 6);B) [-6; 6];B) (-1; 6);1) (300: -6) v (6; +00)- 8. Y ammcy e 20 Kynxia,npoHyMepoBaHux Bin 1 no 20. Hrca I&MonipHic'rb 'I0I"O,mo HOMep Hanmamm Basrroro 3 mnmca xymca 6y, z[e Kparunm qncny 7? 3 1 1 1 A ;B ;B ;I .) 20 ) 8 ) 10 ) 20 9. l'Ip5IMi c i d napanenbni,a ciqna.Toni Z x = A) 45;B) 55;B) 65;I) 125.10. 3a naumvx Mamomcom 3Ha1'I11i'rb S1I1(1. A 8 17 A ;B ; 17 ) s 8 17 B) 3; P) 1-5. 15 17 C B11.3Ha17t11i'rb KOODIU/1H8.T1vI cepezmnn Bizxpiaxca AB,memo A(-6; 11),B(2; -5).A) (-2; -3):B) (-4; 6);B) (-2; 3);I) (2; -3)-l2.V KBaLLpa'r 3'1 CTODOHOIO 6 CM Brmcauo Kpyr.Bnaain.lmomy xcpyra. A) 161r CM2; B) 9 CM2; B) 97r CM2; F) 367: CM2.11 14. Bc1QioHr 2Poae; mrimb aaedamm 13-16 i aanuwimb eidnoeidb do KO)KHO2O y eideedeuuu dim uboao pndox. a3b a+3b) 412*13. Cnpocrim.Bnpas (g; az _ 30b '.9b2~a2'Binnoaima: 2x+5i173x14.3nax7mi'rL Hamenme nine anaqemm x,npu axomy pismma npoin 3 4e aiifemnoro. B11IIIOB11IB2 H,A -15. 3na1'mi'rL 05JI8C'lb anaqeab qryaxnii y =2x2 8x + 1.Bi11lIOBi; B: 16. Hpn mcnx auaqenns-Ix a Bewropn (2a; 6) i r7r. (3; a) 6yp; y'rb xonineapni? Binuoninsz __, _ , _Po3en)Kimb aasdamm 17-19 ma sanuwimb po3en3aHI-m KO)KHO2O 3 noeHuM O5I"pyHmy6aHHM nocnidoenocmi noaicmux Kpoxie i did,nocunaHHnMu Ha Mameuamukmi meepdxremm ma qaakmu,3 mcux eunnueae moa uu iuwua eucHosoK.nuo nompi6Ho. npoimocmpyme po3a'n3aHH. q cxeMaMu,apacpixamu,ma6nuL4nMu. 17. llna anromoini ozmottacno nnixann 3 omxoro MicTa B npyre.Innnxicn.nepmoro 6y. ua Ha 10 KM/ ron Ginbmoto 3a I1IBHJ1K1C1b npyroro,i 'roMy Bin Bwrparnn Ha secs numx Ba 1 rommy Menme,nixc npyrn.Bnazxi-M.mnnnxcicm.xcoxcnoro 3 aB'roMo6iJ1in.mcmo B1). ICTaI-lb M1.>! C Mic'raMn 560 mu. 18P .. .-'/ '9! /3"=3' .033 iI>K1'1b cncwemy DIBHJIHL 2y + xy + x :_2.19. Ky-rn napanenorpama aizxnocsrrscn ax 4: 5. 3Haiu1i'n.Kym Mine Imcommn napaJIe. no- rpama,npoaenennmn 3 nepnmzm Tynoro zcywa.3aedaHH2 20 me 21 euxouylomb nuwe yw-/ i Knacie 3 noanu6neHuM BUB-leHHM Mameuamuku. Poaemximb aaedamm 20, 21 ma aanuwimb po3e, q3aHHn K0)KHO2O 3 noeHuM o6rpyHmyeaHHnM nocnidoenocmi noeiwiux KpOKi8 i am,nocunammuu Ha Mameuamutmi meepd>KeHHn ma 1>aKmu,3 sutux eunnueae mod vu iHLuuD GUCHOSOK.v""; -r~: ;;i~ 'npoimocmpyflme po3e'n3aHHn cxeMaMu,epatpixamu,ma6m.3 . V 320.. E[one;1i'r1.,mo 1:01:14 .2 > O i y > 0, '10[1 + 5N1 ++ -1 9 3. y x21. Y Tpauenii Kyru npn ogmiifr 3 ocnoa zzopinmorors 40 i 50,a , n;on1-. Hcnonyqae cepezunm ocxoa,2 CM.Bnaiimi-rb ocnoan Tpaneuii.mcim v. .,. :,. ..'. ; . . . ... .ia nopinmoc 5 cm. 15. I'Ipi33Mu4e,iM 37 {Mac _ Bapiaur 33ae: j7aH, -4;;7--12 Mr-3OIT1b no L/ omupu enp/ aH/ nu 8.'. (3.'108/(! (l.3 HKLIX minbxu Ol/1H . ; /7PABI/1/7I: .'v'MM (Jri. ~:, ,i/ nu i nos-Hawm /7,r>ae1.'. n.5mJz1r eap: aHm ezdnoeidi 6 manuui. . Pu'. '; Li'Jt.~m; 'w._-_ :1 ,1.3 A) _ .1)) A_: la 1 I 2,: 6; IT ; 1:. B) :5) .,17 3 ( L--. ___. _;_>.1;; 11. 3Hai"1 '11:. - I u .n. s-n'm rz-; u'-, /Iumx ai, rm*I. ;mx 41.1 "1. 'n

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