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VMO Mock Test 3

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Minh Ngô Vũ
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262 views8 pages

VMO Mock Test 3

Uploaded by

Minh Ngô Vũ
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF or read online on Scribd
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1.2 Dé mock test sé 2 Dé thi Dé thi ngay nhét 1 4 Cin 8 Bai 1. V6i sé thyc a > 1, xét day s6 (un) xée dinh bai wy = “Te véin = 1,2,3,... 1. Chitng minh ring day sé (u,) tang ngat. 2. Gid sit tén tai 96 thue asao cho lim = 1a hitu han, khéc 0. Chimg minh ring a € (2;3). Bai 2. Cho day cung BC c6 dinh khéc dung kinh cita dudng tron (0) va xét diém A thay déi trén (O) sao cho tam giée ABC nhon, khong can. Goi AD, BE, CF la céc dung cao ciia tam giée ABC, trong dé D ¢ BC, E € CA, F.€ AB. Ve dutng kinh AA’ ciia dung tron (0) va dudng kinh A’A, cita dutng tron (A'EF). 1, Chitng minh ring dudng thing AH ludn di qua mét diém c6 dinh. 2. Dinh nghia tuong ty véi cdc diém B,C}. Ching minh ring AA;, BBy,CC, déng quy. Bai 3. Cho da thite P(x) = aq" + aq-12"71 + +++ + a2 + a c6 bac n > 3 vdi hé s6 hitu ty va cé n nghiém thyc phan biét lap thanh mot cAp s6 cong. 1. Chitng minh r&ng néu n = 4 thi céc nghiém cia da thite P’(z)-ciing lap thah cAp 86 cong. 2. Ching minh ring P(z) kha quy trén Q. 3. Hi cfc 86 ao, @1,2,---,@n 06 thé lap thanh cp s6 cong (theo thit ty d6) duge hay khong? Bai 4. Cho ho 2 gém m tap con phn biét, khac réng cita tap hgp {1,2,3,... 90}. Hai tap hgp trong © dugc goi la lien két néu giao cia ching cé ding 1 phan tit cdn hai tap hgp duge goi la than thiét néu giao ciia ching la mot day céc sé ty nhién lien tiép c6 it nt 2 phan tit 1. Biét ring trong ©, hai tép hop bt ky déu than thiét, chimg minh ring m < 2025. 2. Biét rling 6 thé xép c&c tap hgp cia ho Q thanh mot day lién tiép sao cho hai tap hop ké nhau déu lién két va méi bo hai sé nguyén (a,b) voil 1, xét day s6 (un) xdc dinh béi tn = voi n=1,2,3,... Ch-a@ ne 1. Chitng minh ring day s6 (vq) ting ng’. 2. Gia sit tan tai s6 thyc @ sao cho jin Ja hitu han, khée 0. Ching minh ring @ € (2;3). Lei gidi. 1) D8 théy-u =2n aj = SF 922-94 B=? minh ring v6i moi n> 2 thi uay > tp, tiie 1a >2-—a=u, nén ta cin chimg Chy=a _ Cinta =a we (n+1)° wanton _ g BBR os an tac dun vi chitag maioh ae ntl (n+? i (n+ 1"0R,— a(n 41)? < eA hg an? 4 (4n® + 2n? — (n-+1)°)CB, > (n +1) [an? — a(n +-1)’] . Ro rang vé phai luén 4m véi moi a > 0, cdn 4n + 2n? — (n +1)' = 3n3— nn? -3n—1>0,Vn >2 nén bit ding thité cudi 6 trén 18 ding. Do d6, day s6 (up) 18 ding bién. 2) Dé ching minh a € (2;3), ta sé chi ra ring © va.dé théy lim =0 nen ta chi cin 6 tim S =0. Ta i" nt00 4” n-too 4" Chi ¥ ring 3-5<4,5-7<6%,...,(2n—3)(2n— 1) < (2n—2)7 nén (2)- 19976? -+-(2n—- 1)? 2n—1 an 224262... (Qn)? 16n2° Scanned with CamScanner oh DE thy tin 28—1 _ g nen theo nguyen If Hep th ip, gu' = 0+ MO theo lim ~S" =0. Mat kde, voi déch gid tung tt 2h P46 Pyovg (t= 2020) <(20— ta duge ‘nG3, )? _ 189958. (Qn— I'm wee 7 pita, tie a ee ae 2 a nt Ma in 3 = +00 nea tin BCs — oo hay tim = +00. ‘Teese dit tren, te thy rng gif te tha man d® bai phi thude (253). Nhan xét. Bang céch xét tinh dom dita va bi chin, ta chm ching minh dutge két Qu monk hou nb sau (te 1a eh ra gi tr} cy thé cia bog #6 @) BAi 2. Cho day cung BC cb dink khéc dung Kinh cia dung ton (0) va xét diém A thay di trfn (0) sao cho tam gide ABC nhgn, khdng eA, Goi AD, BE, CF la cée ding cao cia tam giic ABC, trong 46 De BC, E € CA, F € AB. Ve dung kinh AA’ ede dutng tron (0) vd dutng kink A'A, cin dung tron (4’EF). 1. Ching minh ring ding thing A\#T Iuon di qua mot diém o6 dinh, 2. Dinh nghia tuong ty wi ee diém B,C. Ching minh ring AA, BB, CO, dng quy. Li git. 31) Goi O, 1a diém di ximg vi O gun BC vA M,O; Ih trung diém BO, A'Ay. Tre bie shag BHC’ a ink inh Mah nen Af eng rung dé ein HA. Sy ra HOA‘O, ciing 14 binh tinh hash. Do d6, #70, | 04", m4 OA' = O ciing 06 HO,LEF. ALE nin te Se es Tip tho to ME = ME = 350 8 OE = C1 tO. ehh sng re ela EF, suy ra O,MLEF- Lal eb 0:40 1 dang trang binherong tera se ben Quit If Ay. Ti db oy re HALER. Witbnes eta wee dung thing AyH Toon di qua O, lA diém of anh, eet hang hay 2) Gi st ta MAY eft Wi (0) tl th Bing ich x ‘A dutag tro dng Linh ABC. a wa BOER Ant dine huong gia (0) Age BAX. Gel Aa ino did Whee 4 tn (a2) (Oy, ESET a OE IIS, Blng cfch xét tryc ding phuong cia ba duing tri (O),(A’EF) va duong tron, dutng kfoh AH, ta suy ro A'A, eng di qua X. Lai cb AAzLA’A2 vA AyAa 1 A'Ay (che dung kink) nén A, Ay, Az thing hang. Suy ra cée did A, D, Ay, X cing thuge ing ttn ddng kin AX. ‘Tu 46 suy ra AA; chink la truc ding phuong ciis hai dutug trdn (0) va (AXD). ‘Tug ty, goi V2 Thn lug Ba gan diém efa DF,AC va DE, AB th w cing ob BB), CC, chinh a truc ding phuong ciia (O) wii cée dviing trim (BYE),(CZF). Dé ¥ ring céc dung trdn (AX), (BYE), (CZF) ef ba tien thing bing (nk teen dug thing Gauss cin ti gise toan phin tso bat AX, BY.CZ) ding thoi c6 Paaxn) = HA-HD = Purovey = Pancen <0 nth ofc dung trbn uby ding tryc, goi tryc d6 I &, Gid sit (9 AAy = T thd 1d ring, ‘T e6 cing phuiong tich dén (O), (BYE), (CZF) nén cing phii thude BB,,CC;. Tw 6 suy ra che dutng thing AA), BB,,CC, dng quy. 2 ‘Nha xét. Bui toin o6 thé tiép c4n theo bung sit dung dinh ly Ceva sin dia ‘vE Oy 96 sin chic gée-vA bién adi kbd tu mhién. ia (2) = pagar! ++ baie t ao 06 bien > 3 voi aise opin ip it pan cp ee 1. Chitag minh ing néa n = 4 tht che nghitm ela da this P'(z) cing Ibp thinh efp 8 cong. 2 Chtag minh P(e) Kh quy trén Q. aq 06 thé lap thanh cfip sb eng (theo thit te dé) 3. Hoi che sb 09,01,02,--- dduge hay khéng” Scanned with CamScanner CHUONG 3. TUYEN EAP GAN ee Lai gia. TE mm 4d the Pe) 6 4 nei theta Bt 2 theo dinh Ig Rolle thi P(2) 28 c63 nghidm thye pita Bit Ths 1# Néu tren oot 1, ee 6 date ot eang phil dye 10xen RS 2) Xét cfc sb duge dién y3o mot bing con 3 x 3 nh béa duti. ni rately ath [e ‘Thoo gid thie eh beetdtgzbtctdtend (mod m) nen e= 9 (eed m). Twang ty a= & (Wd m). Ta cdg 6 atdtethabedt+e+g (adm) ntrathzb+g (mod m). — A. Tig ty thd e~ k Say mag = hod m) nen O-95C=k (mod m) 4 22% 2 (mod m) ( ‘Tird6 ta duye 2 Hin cia cb bin 3 bén gée vi didu dy ding voi ml ng 32 Te dy to

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