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

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. 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. 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
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?a t6 c1- d ]"'
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i-, .f, 'g 'yo
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l.s: b € T i l-1 Ei
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El. El El Ele-El€;El€ElE

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. 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. 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. 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. 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. 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--