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Đề Kiểm Tra Chất Lượng Môn Toán Trường Chuyên Hà Nội Amsterdam

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Đề Kiểm Tra Chất Lượng Môn Toán Trường Chuyên Hà Nội Amsterdam

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Đề Kiểm Tra Chất Lượng Môn Toán Trường Chuyên Hà Nội Amsterdam

  1. 1. TRUONG PTTH HA NOI . AMSTERD}I : TO TOAN It) ,t ,? D0 KI6,MTRAcHAr LUQNG Mon Toin l,'?7 ( 1998- 1999) Thiri gianli'rmbiri : 90 Phtit Ilhil:(3didm) Chobiduthfc A=(18a- 86):(6a- 4) l. TinhsotriciraA biet| ^l=2 2.Tim aeZd€' AeZ 3.Tim aeQdd acU 4. Tirn a e Z ddA datgiritri nh6nhdt Bei2 : (2didm)Tronmlt phingtoact6xOycho3 didmA (l;3),B (-2.2) C (31-l).TinhdientichA ABC Bni 3 : (3didm)C5oA ABCcin taiA.Tilm6trJidmM bdtkj' trOncanhBC ctqngcludngthingvuongg6cv(riBC, catcdcdu$ngrhingAB I AC ' ii;, iu.nrai"p;e."Gqilt"r'5s lin h-rcnli tn-rngdidmcaccioanttiing pB;eC l. chrmg minh rang: MS songsongAB ; MR songsongAC 2;:Duinr! thringchfradudngcao AH criaA ABCcat cltrirng'lhingMR tai I. Chfng minh A ARI cdnvi BI = RS 3. Chfng minh rangkhi M chuydndQngtr€ncanh BC thi : a) Tdng do dii MP + MQ kh6ng cr6i b) Dud'ngrrungtrucctrarit S luon di quam6t'didmcd diilh Bii 4 : (2 didm)ChoA ABC cAncti g6c A = 140o,kd tia Cx thuOcnriam4t phing chfraA birBC saocht>g6c ACx = I l0o vi tia BA cit tia Cx iv D.Chfrngrninhring AD = BC
  2. 2. TRUONGPTHHHANOI. AMSTERDAM 16roAnl -,,t- 2.r1'+ 2y' +2x - 4v+22 Bli 1 (2.Sdidm):Cho.citcdathfc : . p(;r)= 7*o+r, -5x2 +5r+6 QG)=Z.ru-3;r3+4x2+6 a) Tim nghiOmcriadathrlc p(*) - eG) b) chring'mi'h rangvdi moi x kh0ngnh6 hon3 thi P(r) - Q(u) khOngnh6hcrn3r:3- 6;2 + 15 llii 2 (2.5didnrr: a) Biet .,* 1= j . Tinh .ru* f r -tu lr) BiCi x=by +cz; y=cz+ax; z=Ax+by v) x+ Chrhrgrninh riir I ,s:i."**t*fr=z Ilii 3 (1.5dieml: Tim cic sdnguyO'x , y saocho 2000 DEKldMTRAcHATLugNG(1eee-zooo) Mon: TOAN l6pT Thoigian: g0phut glli t4 tucmg rrrg cria :t + z.1o T datgiri tri ldn nhdt. Ilii 4 (3.5diim): ChoA ABC cfln dinhA (g6c .4< 60") , trennriamdtphing bd AC c6chfa B vEtiaAx saocho l.xAC= /.ACB,ldy didmC'saochoAx li trungtru.c cfiaCC'.NOiBC' cit tiaAx 6 D. a) Chfng minhrengA C'DA cin. b) Tim tr0nAx didmM saochochu vi A MBC datgid rri nh6nhat.Chung *tlh tlngqi. A* quayquanhdidmA thidolcrnio" znMC ruro"JJAil c) Ldy bdtk) didmE n€nc4nhAB vi didmF tr€n.*tt AC. Hay sos:inh,J0 dni AE + EF + FC v6i BC
  3. 3. TP.UCNGPTTHHANOf- AtvtSTERDA&t:: TO TOAN b. Tim xdd A-(5x-t)l lfii 2 (l cliOnr): Clroa+b*c=2}oi vi I * 1,.* l =I Tf^h 5=-r-* b * 1*o b/t c+a lo b+c c.+a a+b lfrii 3 (2.5diim ) : i-1.Chfrrr_sminlrr.ir1_9x ll - x, + x t _ x + J> 0 b. Cho x.yeZvi 4x+5y=7. Timgidrrinhontratcira A _ 5lxl_ 3lyl Itai4 (3diOnr) : Cho AABC vu6ngcin tai B c6 AB = a.Tr€ncanh AC ldn luo-rla-r,cricdignr I' K saochog6c /rBK = 45o t | 1nmgita A, K). ve AACD vud'g carrr'li D sitoclroB vi D o vdhaiphfactia AC.ria nt cir canhAD tai lVI,riaBK cir ;l'*,:" tai N' Ke doarrBE*iong g6c'i biG gN-roochoE. A &cirngphiadoi a- chfnrgminhra'g bacti€mE, A, D thinghiurg. b- Ke BHj MN , ri'h ch* vi AMND uaaodniBH rheoa.c' chr?ngminhrangbadoarrAI, IK. KC c6 th€li bac+nhcuamorrnmgiiic vr-rong. Uni5 (2dieml- . cho AABCcin d A c6g6cA - 20".Chfn-eminhrarig:zBC<AB<3BC DeKfEMTRAcHAr LuqNG(2ooa. zao1) Mon: TOAN l6pT Thdigian: 120phut lliri I (1.5di€rn); ,. Wn- (2x- r)r- 2(2x- lX3+5x)+ (: +5x)2 V,xeQ k
  4. 4. t UO FA J .,8 .q1 O - -l -9 O C/) cg I o l .6. -'d E,7 ^{ t-rl v - .: ho a.t rp lcu v (-- l < ^ <0) o €)= OP H ll o 4 '< ..d ?LJ o0= Or <= "bPt< 'rCS .F l-' o , q R . r ) c v X ' = t t l*l -! ^- o?,= ?-A = l= U)EJ€ -{ bo,{ o (- (g E I< 'H ?< " "..9 S '.'9 bot O r * O t r v c-A Cii F< '!{ -/ C) -/ !+l 5 Inl g .-l tr .-l .a ,'rtl rl ,al 6J Fql€ pal)i 6d tl U ;^l&l tC! rc .O. "o ig ca U U-1 ltl m rQ) J4 a Ur hb J = r f i .:'-' '' -) ^ a ^ .:U S' nq cd - ^ F . J ?< O o.< E bo bo :.9 ,.8,,F.o g'] .o: Rk H E Fo;e 7 H,s-o n sn €'Ft :J .- t4 -;5 E.E g e3- FA k bJ) t < oL< {-l O -cl lo.r )g cil | ''J bO + e tr F { cclc{ E cl-o E +b0 -8l*- 'fiJ ll E o : + X trO + ** tl o?q) ''l oc T,S l - N OX oLO S! NT EJN (9 N i.,o' I Z go.'x j{ ..- O..Og O N X 5 _o) T I Y =z- ': + .'< c $ x ', ,,= C.$ x it .|- ;_ t7) il -:;. -A = E '...:', ,:. x {-, X q EP c Yr..tr E€Fr "€ ?U-l u F h r | 1 - C i 5 r - l ( J A - C + ' i , t + ' = q "H"P + ..-. ..fr 5 : rlcd'Y rlu ': trt Z o f; jqE,.8 T r :EF ?I tr = H tr tr "6 ,=E ".Dl ! . - t _ r L r _ oti'E z g e6 c,'-O F-{l Nl t 'Fl ,CUl F cai cal o ^ O N l l 1 - 1 O o bo rQ O U m o U '.G) ca eal .-l ,Cdl Fal t-( td cr)l.o l c g tl =- lco- l o + - lco'I,o + - l.o- l c d 'i, .5 f '
  5. 5. ,J + -c E + Ctr cO + o O + -o -o + +t ' : , J l-L (-; l r.. e ! E t l + r. i..^ l ,^ i --r v tir c c l u c { l c l .-, | -/ il ra l.-. o l o r bn c .r(l co r . (J l-u t l ol-o r- tl = l l l T v ,:-) -+ = . J "') i-.:'J I ci - l . - l , = l I v co C) o TC! O C O r J st -cv o - gF P.;ao-- rl) l- '$.= 6P r,5F = "{lJ = tltJ a
  6. 6. H'39jq ll '--r '- : 'ct c.,t'''aY-9 f?:o.x-J€tr - ^Y F( "h l< x v 3 'il:H 'E c-t o_ _ - (t '/ lr V ;rt.l '< :f + -q U -c,U N q'Fa fII (- )r rrr = c m E;.)' J C -- 'Ft F : E i =.( m :, -1 brr r''r'ft 7 .b ?a t6 c1- d ]"' 3 I E"i EE3iil( *, ,; -x v = ?rro c i-, .f, 'g 'yo _: 4 .E'U o ,<i Y r.= rr, lb 'i 'v ; EE ;- zk C)...K 5:R J i i ^'x.ils, g ^a:g.,S =E:SAiiirslgg 4!.8.9'5; l.s: b € T i l-1 Ei ?r : ? : .,1T, ,: i,, 3,,?,H':€ ?,-.ri-ooF: oo x E.{ J t H E's'E n; :p U€50F! il l>- E ;d.Fn'V I r c .5 .g +- rHr .Eelr6"co g', € E I u€-i-g 3i4+:::t51 Y €€"l9'- -,'. '; : 'l = '8 '8: u,'9 )lt 5 f4 ^x '€ g J, ,f .l::.E{ boc;.6 tIr] ;M?;: H B=€tr8;=A N | 'r' 'E' b,J I 9E EE € € q=f F i ?I?'=?6i,t"a :t :t :t :l ?:l ff:t ):t : El. El El Ele-El€;El€ElE
  7. 7. Derc€nrRAcnArLugNG(2oo4- zoos) M6n: TOANtapT( g0 ph0t) g aidm):Tirnx biet: a) 9,- -2)'+(2x-1).(x+2)=12' 4 / c) (x- 2)'-31*- Zl=Ob) 5x+1+ 52* = 50 BAi2 (3 didm):a)Tm.3 sdnguyOnli0nriiOntiepbiertichctiachringlir lapphurrngcua4,{ BaiZ (3 didm): a) mQtsdnguy€n. ; r ' b) Chungrninhring vriimoisotu nhi€nn lonhon2,tdn1xisdrunhigncon chffsdvl chiahetcho Snr.l Bii 3 (2 didrn): cho tamgi6cABD ,ldy didm o namgifraqB, rr6ntia dciicrjatiaoA lay didmC saochoo k"hongphii le trungdidmcfiaAC . Ndi CD.CB. a)ryIemgrdiiryruyy .Ctrdng*inhrang NA +NB+NC+ND > AC ino ( dine thfc xiy rakhi nloi)) b) GoiM Ii trungdidmAc. eua M v€iuun tt,ingFq il BDsao,choM li trungdidmPQvl PQ= Bb . Chungminhrin! ( p,f i .t* *. t ' AP+PC+Ce +eA < AB +BC+Cb +DA . - Baf 4 Q did'm):ChoAABCnhonvi M didmruyy rrongramgiric.A,: B, : c, lin lugtlh hinhclricuvuongg6cc&aM tr€nBC,AC,AB. a) Chtineminhrangn€u.tamgi'6cABCddurh)tdngMA, + MB, + MC, khr)ngph9th-uOcveiovi tri cuaM . nnn rdngdri. bt GirisutamgidcAlc khOngctdu.Xic dinhvi rrfcur M sa,chorringMA,+ MlB,* MC, dargidrrinh6nhCt. s-
  8. 8. rg cua on .:atra trt M .) Jr-rcyt -- TRUONG 'THPT CHUYCN TA !"IOI_ AMSTERDAM TOTOAN Dd xrinn TRA'HAT LugNG(z'od- 2006) , M6n:TOAN Wp| Thdi gian : 90pif,t i &ir: (3didrn) i Urinrxbidi lr, * ll=..* i b/Timxtiei fr, +..r-rlf=-yr_1.1.r i , c/Timx.y biei. r-- 0'-5 r'- 0-4 $ iJ = = 3J- vi 5'r- 3-i'=2,5,6 { -'- f y : (l _5di&n)Oro.unrgidcABCcr1g6cI =5C1.8=.20o,phingi:icrr.rngBE.Tr€n i BEli.vdi&nF saochogdcFAB= 20".Goi I fl $ cocEruc. v'v 6L'e'rD = zu-'uor I li trungdidmAF' Et cdrAB rqiM.1'fnh $ Aail : (2djCrn)Cho3rtidrnA. B,Cnamlrdnm( ' i n:'",BC=11",",or",i,u,;"-;;;H':ffii,ffifl::: "'r:j:":;l;i sddocric-do'n DA, DB rrtsdnguydn.Goi n rirsridochuvi rarngiiic ACD, rinhrringriri I ciicricsrfn ci th6'cr1. T :".':r lt:r, ChorarngiricnhqruABC.dnrrngcaoAE,rrv.cftrnt{. M'r d'rrrethfrng f diluaHc:dr2canhAB,ACririp,e sacrchoHp= tJe. EI= J1 tt Eki rlrolcftrtrngttringso'-E'.ngFe *i l z tiuAB,AC raiI. J.chfngrrrinrr b/ QuaI{ ki tlut'ng thilngrhr?h;rivut)nggricpe cit IIC r?iM. ChftrgnrinhMLrlrungdierncfiaBC. eAU: (J.5didrn) cliQntfclr,nt:rnvurin.q i ' ) n o " " 5 , t ( l,{ r '['inr cdr. sri canh h;ing rulrJy(lncfurilrgx. .v.z lhoii c(i sri do lr:irrgchu r.i hirrh fltun vil 4t' _1__cr._ J-3
  9. 9. TRUONGTHPTCHUYENHANOI- AMSTF.RDAM rd roAru r r 3 r ' DE KIEM TRA CrIAr LUqNG ( 2006- 2OO7) Mdn:TOAN l6p7 Thdigian : 90phrit Biril: (3didm)CtroA - 2l*- 2007|-*l* - 20091 a/Tinhgi6tri cuaA bidt x = 2008 b/TlmxddA-x-2olo c/ Tm x dCA nhangi6tri nh6nhat Bni2 : (2didm)Cho 3 = I - O (a;c*0;a* b;b* c). c D-c Chungminhrang,I *-! = - I -1 a a-b b-c c Bii 3 : (2didm) Ctrotam gr6cABCvu0ngd A c6AB < AC,duongcaoAH al BidtBH= 9 cm;CH= 16cm.Tinhci{ccanhcia tarngi6cABC b/ Tr€ncanhAC lay clidmE saochoAE = AB. GQiM lb trungdidmcfiaBE. Tirrhg6cMHC Bni 4 : (2 didm) Chorarngi{c ABC vu0ngt} A c(rAC = 2AB. Trongnta rn{t phf,ng bd AB cti chfa C dUngdo4nrhing tsDrnrOngg6cvdi AB vI UD= AB. DidrnE tu! f thuocdoanBI),kdducrngrhfrngvuOngg6cvdi AE c:itDCdvF.ChfrngminhAE = EF. BjiS : (l tliCm)Tlm sOnh6nhCtc.64 chfis0 abcdtlroiinrfin: abcd=7 xabx ad t l ' t i
  10. 10. TruongTHPTchuy€nHI noi - Amsrerdam TejTorin Mon:I'OAN lopZ Thdi gian: 90phrtt BiiI(2didm). Cho ciic da thuc f(x)= 2*' (x' -5x* 7)-3x(x' 8(x)= -xs Tinhh(x)= g(x)- l(x). Saud6r)mnghiOmcuah(x) Bei2 (z,Sdidm).Chohaitamgii{cvuOngcAnABCvDADCraiB vi D ( B;D l5u6c h1 nuam?tP.hingdoi nhaubdAC ), vdiAB = AD. LorydidmN ru!'f rr6ncanlr AB,tiaCNc5ttiaDA &E,ketiaCxvu6ngg6cvdi CE,Cx cflrriaigtai F.CoiM lhtrungdidmcuaEF a) ChungminhCE= CF b) Chungminh ncb: liCir c) Chrlngrninhring batlidrnl), [J,M cirngnf,mtrennrotcludngthirrg Bni3 ( 2 didnl). lliir a < h < c < tf.I-lfrysdpxepcfc sosauril lhil dcrrlt'rrr. x=(a+b)(c+cl) y=(a+c)(b+tl; 'r,=(l+d;1b+c) Bii 4 (2,,5didrl). Cholanrgiiic:ABCvuOngtaiC criBC< AC. Goi O l1gi16tli(:rrr badudngtrunglt'trc,I li)giaotliiln llaphAngiriclnlrs cuartarl giiic.lli6iljipg tirrrr gi6cBIO vuOrrg. a) Cht?ngrnirrhring riiil:90'r Di xrirvrrRAcHArLuqNG( 2007-200s) h) Dit doirliriciraAB = c, AC= b, IJC= a, p= tir I tlerrAIl. Clrrtngnrinhrirrg: r = p-(l ,trIsxr-rx2+6x- -t)(x'1+l) re) T) ru*h*c , t' lit kholing c:iiclr Bei 5 (l didnr).llmtatcric:iicsoc6 4ch[ sosaoc:horn6iso virulir bjrrlrphrnrrrtciju mQtsoviralr'tltipphutrlrgclianr6tsokh6c. /" /-. t " . l ) ./ _ .-
  11. 11. TRUONGTHPTCHUYft,NHA NOI AMSTERDAM DErrdvr TRACHA1LUQNGt dp 7(200s-2009) Thdi gian 90 Phtit /-<----- t eei dedidm) Vro c6cbiduthrlc A - Qt *1)t - 4(x+lXx - 1)+3(x- y) g=(y -3)'-(v -4)' +x(x-s)-(x -I)'-Y 1/ Rtit gqn A vh B 2l nm i, YnguYonddA + 38= -1 6t7 Ngox,y ll cdcsdtUnhien,chrlngminhtichA'B ld sdchf,n ( nai * Q,sdidm) V 9 1 r^<-- +/^L *2A +-l ^J'.' hicrr thr{v Il Bi6tx+y =- 4v1 a+b= j,n6ttinhgi6trictrabiduthrlc: B = ox+ ay+ bx + bY+ x + Y+ 2009 2l Ctrobasdhtuti a;b;c saocho: 3a+4b-2c=108' Tim a;b; c bidt a) 6a= 5bvd7b= 4c a+5 b+'6 . b+4 c+7 b) u-.s=;vafi=;- Bni3:(2fffTi6c ABCcanraiAc6c+nhAB-=a; s6ck=20".-J*netrqrcry3canh AB c6tc*,h Ac t?i rur;rru"g i*" cfiacanhec_:} f+"tt AB t4i N; BM cit cN tal P' Gqi E, Q;F ldnlugt li tnrngOidmcfiac6cdo*n'PN,PB,C1yI. . || Tam grdcPBCthtamgi6cgi? 2l Chfng minhtam giilcEQFlDrtamgi6cddu 3l Chfng minhchuvi tam gikcEQFt! 4 Bii 4: (2didm) cho tam sL1cABCrnr6ng0 A c6 AB < AC. Gqi o le giaodidmbaduitngtntng rruc;I thgiaoOIdmbadubrngpfrangi6ctrongcfiatam gi6c' I|D4tdQdeicri.aAB=C,BC=a,CA=b,o=ry,r1ikhoangc6cht.il.I ddnBC.Chungminhr=P-o Zlqr,tui; minhrangnduram gifucIBOrm0ngthi chi c6thdvu6ng6I
  12. 12. I ITNUONG TIIPT CHUTIN HA NQI _ AMSTERDAIVI rOroAN on xrcnnrRAcnAr LUSI.[G: MdnToanlW 7 (2010- 2011) Thli gianlembii: 120phut a'il_7 (2diem) a) Thgchipnphdptinh: A - rfi*o+-[',s-6i.iJ .[-'#)q2*!-(,,-tl 6 6 3) b) Chobi6uthtc B - f - 72+ I32- 1,9'+ 252 3I2+ ..,. (gO- n s5hang) r-'--1 Co haykhdng c6 si5qunhi6nn dOsaukhi rut ggnta dugc B - 201220rt? Tai sao?/ J (r . tr. . ( naiz3 diem) - I . Wim s6xthoam6n:l}x+ 5l: 13x-2'. b) Tims6xthoamenil(x-1)'+ 1l+l(x- I)'-41:5. c) ChomQtddyn s5qunhienH€nti6pUEtAAutu s61.Ngudi tax6adi rngtsOttri ' -9 , / trungbinhcgngc6csdconlpibdngtO , .Hdytim sdtt u?s6b!x6a. , o . ' Biri 3; (3 di6m) Chotam giagABCco g6cA - 600.Di0mE tr6ncanhAC, di6mF tr6ncpnhAB saocho gocCBEbengg6cFCB vdbdng300.Do?nthdtteBE vACF cit nhautai di6mI. Oudpgthing rm6nggocv6i BC terC cit tia BE tpi K. ay'Ch'mgminh tam gi6cICK d6u. b) Chrmgminh ia"g tam giitcBlF biirg tam gi6cCKE. c;:ChtrngminhrengBF : FE: EC. Bei 4.(1diCm) Chotamgi6cABC cdn,dinhA. C6cdiOmK, L tr6nc?nhBC saocho: r: in . 1 KAL s ^ BAC.ChringrninhrdngKL <;BC 2L Bai 5.(1diCm) -2 Tim c6csOt.unhienc6hai cht sd abbiettaogt aabb- aa-+ bb- --Het--

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