DE THI HOC KI I MAỈE CUỈE

c Xdc dinh thidt di0n dc mat phing P di qua didm G; song song v6i SA ",rd AD, cit hinh chop tao nOn.. c Xdc dinh thidt diOn cria hinh ch6p khi cit b&i mp cr qua O, song song v6i BE vd SD

?.A[]C'I{G MARIE CURIE DE THI [Ioc tcV t nAnn Hoc 201r- zt]rz

MOn thi : Todn 1lEG - Thoi gian lhm bii : 90 phrit

Bei I (3 didm) : Gi6i cdc phuong trinh sau :

c) Ztanzx + Zcotzx + 3cotx - 3tanx -'3 = 0

Bni 2 (3 didrn) :

a) Tim n biet Ai + 2Cf;-2 -9vt

b) Tirn h0 sd cria sd hang chria xey3 trong khai tridn (x - 3y)tt

c) Nhd trudng c5 2 xe dua d6n hoc sinh hlng ngiy XAc sudt m6i xe bi h6ng trong m6i ngdy ldm'*ziOc ldn luot ld 0,3 vd 0,2

Tinh xdc sua't dd m6i ngdy c5 it nhat 1 xe di dua d6n duo c hoc srnh

Bni 3 (3,5 didm) : Cho hinh ch6p S.ABCD c6 d6y la hinh binh hdnh Gqi G ld trong tAm !*rn gidc

SAB ; N te I didm ndm tren doan AC sao cho g = 1.

AC3

a) CMR: N li trong tdm cira AABD.

b) CMR: cN // (SCD)

c) Xdc dinh thidt di0n dc mat phing (P) di qua didm G; song song v6i SA ",rd AD, cit

hinh chop tao nOn

d) Tinh chu vi ctra ttridt diOn n6i tr0n ndu AB = 6cm ; AD = 9cm TA't ch cilc canh bOn

b6ng nhau vi bang l}cm.

$ni 4 {0,5 didrn): Gi&i phudng trinh 5sinx - 2 - 3tanzx (1 - sinx)

TRIJCING MARIE CURIE pi rm Hqc xY r NAM *Ioc z{}Lt-?&Lz

1\{0n thi : ToAN l tIP - Thdi glan lirm bai : 90 phft

Bhi 1: Gtin cdc phudng trinh sau

a) Zsin2x- "o/12cos2x = 3 b) 5sin2x-r sinx + cosx + 5 = 0

c) 6sinx - 2cos3x - 5sin4x'i:osx

2cos2x Bii 2: a) Tim h0 sd xa trong khai tridn [ \ * i-'.l" 2x)

b) Tt 7 chfr sfj 0, 1, 2,3, 4,5, 6 ta cc' thd lAp duo c bao nhi0u sd chdn gdm 5 chfr sd dOi

m6t kh6c nhau

Bhi 3: Hai xa thfi doc lAp vdi nhau cing bin vlLo m6t tdm bia M6i ngudi bin mOt viOn X6c sua't

bin trung ctra xa thir thri nhat ld A,7 i crta xa thir thit Z le 0,8 Gqi X ih sd viOn dan trring bia L4p b6ng phAn bd x6c suAt cria X.

Bhi 4: Cho hinh ch6p S ABCD, d6y ABCD ld hinh thoi canh a, t6m O SA = SB = SC = SD = a"

M 1e 1 didm nam tren doan AO (cr) ld mat phing qua M, song song v6i AD vd SO

a) Tirn giao tuydn cfia2rn6t phing (SAB) vn (SCD)

b) Tim thiOt diOn ctra (cr) vd hinh ch6p SABCD.

c) Thidt diOn trOn lA hinh gi? Chfng rninh

d) Dat AM : k Tim k dd rhitit die.n tr0n c6 thd ngoai tidp duoc 1 dudng trbn

AO

TRUONG MARIE GURIE

GiAi c6c phudng trinh sau :

a) cos2x + sinx = 0

DE THI HOC KY { NAM HOC 2006 2047

b) 2sin2x + 2sin2x - 4cos2x = 1 c) cos3x - sin3x = cos2x

Bai 1

Bai 2

Bai 3

Bai 4

a) CMR trong AABC ta c6 : cosA + cosB + cosC = t + 4sin*rio|rm$

222 b) Ba sd c6 tdng bEng 26 l6p thlnh mQt cdp sd nh6n, Ndu giLt nguy6n sd hang thf n!dt, th6m 2 vio sd hang ing nai vir sd hqng th0 ba b6t di 4 thi ta duoc ba sd m6i theo thf tu d6 i?p ihdnh cdp sd cQng Tim ba sd e6

cho hinh ch6p SABC c6AIABC vu6ng c6ntqi B;AB = a vi SAI (ABC ); SR =ali

a) chfng minh c6c m{t b6n c[ra hinh ch6p ld c6c tam gi6rc vu6ng

b) Goi H la hinh chi6u cfra A tr€n SB

Ch0ng minh : (AHC) I (SBC)

c) -' Goi N tirtrung didm SC;M li mQtdidmtr6ncqnhABsaochoAM =x(0<x< a) ;Gqi (c) lamdt

;#;n na" niru vi vu6ns g6c v6i mit phSng (SAB)

1 X6c dinh thidt di6n tao b6i mdt phSng (a) vir hinh ch6p SABC Thidt diQn lA hinh gi ?

2 Tinh di6n tich thidt di6n

Cho MBC cMR : 3cosA + 2(cosB + cosc) <

f DBng thfc xiy ra khi nio ?

TRI.IONG MARIE CURIE EE THr HQC KY I NAM HQC 2010_ 20tt

M6n thi : Toan 1lEG - Thoi gian lim biri : 90 phirt

Bni 1 (3 didm) : Gi6i c6c phucrng tdnh sau :

a) 2sin2x + 3cosx = 0 b) 4sin2x * 5sinxcosx - cos2x = 1

c) sin2 x + sin2 2x = cos23* + ror'4*

Bdi 2 (2,5 didm) :

a) Tt c6c chf sd 0, 1, 2, 3, 4,5, 6 ldp duo c bao nhi6u sO tu nhien chdn gdm 4 chfr s6 kh6c

nhau

b) Bidt h0 sd cfia xn-2 trong khai tridn [ - 3)"oirg ? Tim n vi tim h€ sd cira s6 hang

chfa x2 trong khai tridn tren

BAri 3 (1,5 didm) : C5 ba hdm, m6i hbm chrla 5 tam th6 d6nh so tt 1 ddn 5 Rrit ng6u nhi€n tir m6i

hbm m6t tdm th6 Tfnh xdc sudt dd tdng c5c sd ghi trdn ba tdm th6 rdt ra bang 6

Bed 4 (3 didm) : cho hinh ch6p S.ABCD c6 ddy ABCD ti hinh rhang (AD ll BC ; AD > BC)

Goi M, N, E ldn luE ld rrung didm ctra AB, CD, SA

a) fim giao tuyOn ctra c6c mat phing (SAB) ve (SCD) ; (SAD) vn (SBC)

b) Chfne minh (MNE) // (sBC).

c) Xdc dinh thidt diOn cria hinh ch6p khi cit b&i mp (cr) qua O, song song v6i BE vd SD

(trongd6O=ACnBD)

TRUOI.{G MARIE CURIE DE THr HgC rt r NAnn HQC 2010- 2011

Mdn thi : Toan l1EG - Thli gian lirm biri : 90 phrit Bii 1 (3 didm) : Gi6i c6c phuong trinh sau:

a) 2sin2x + 3cosx = 0 b) 4sin2x - 5sinxcosx - cos2x = 1

c) sinz x + sin2 2x = cos23" +

"or24*

Bni 2 (2,5 didm) :

a) Tt c6c chfr sd 0, 1,2, 3, 4, 5,6 l4p duo c bao nhiOu sd tU nhien chdn gdm 4 chfr sd kh6c

nhau

b) Bidt h€ s0 cfia xn-2trong khai tridn [- \' - ]l"oe"g s/ ? Tnn n vd tim h€ sd ctra sd hang

chrla x2 trong khai tridn tr€n

Bni 3 (1,5 didm) : C6 ba hdm, m6i hbm chfa 5 tdm th6 d6nh sef til 1 den 5 Rrit ng6u nhiOn ti m6i

hdm mdt tdm th6 Tinh xdc sudt dd tdng c6c sd ghi trOn ba tdm th6 nit ra bang 6

Bei 4 (3 didm) : Cho hinh ch6p S.ABCD c6 ddy ABCD le hinh thang (AD ll BC ; AD > BC)

Goi M, I.{, E ldn luot li trung didm'ctra AB, CD, SA '1 '

a) Tim giao tuydn ctra c6c mat phing (SAB) vn (SCD) ; (SAD) vn (SBC)

b) Chung minh (MNE) / (SBC)

c) Xdc dinh thidt diOn ctra hinh ch6p khi cit boi mp (o) qua O, song song vdi BE vd SD

(trongd6O=ACnBD)

TRUONG MARIE CURIE

Bii 1 (3 didm) : Gi6i c6c phudng trinh sau :

a) or2^ - sin2x - JSsin2x = 1

oC rru Hec xY r NAM Hec zau-zort Mon thi : TOAN I IIP - Thli gian lirrn bhi : 90 phrir

b) sinx cosx - 6(sinx + cosx) + 6 = 0

b) sinx cosx -6(sinx + cosx) + 6 = 0

c) 9sinx + 6cosx - 3sin 2x + cos 2x = 8

Beri 2 (2 didm) : a) Til cdc sO 1,2,3, 4, 5,6,7 c6 thd lQp duo c bao nhi€u sd tu nhi€n giim 5 chfr sd

kh6c nhau trong d6 nhdt thiet phai c6 mdt chfr s6 5

b) Tirn c6c sO hang chrla x v6i sO mfr tU nhiOn trong khai tridn Niu ton ctra nhi thrlc : (^r l)16

li/x+-1

\ x/

Bei 3 (1 didm) : Ba hgc sinh A, B, C cirng tham dr1 1 k! thi hgc sinh gi6i to6n X6c sudt dd hq

duqc didm 10 ldn lug li 0,5 ; 0,6 ; 0,8 Tinh x6c sudt dd c6 it nhat I hoc sinh duo c didm 10 Bii 4 ( didm) : Cho hinh ch6p S ABCD c6 d6y ABCD li hinh binh hinh mm O Goi E 1)r trung

didm SB, I la trung didm OD

a) X6c dinh giao tuydn cria (SAB) vn (SCD)

b) X6c dinh giao didm cria DE vi (SAC).

c) Gqi (c) li mlt phing di qua I vi song song vdi (ACE) X6c dinh thi€t di€n tao boi (cr)

vdi hinh ch6p

d) Bidt tam gi6c ACE ddu vi AC = OD = a Tfnh diQn tich cria thidt di0n tr6n.

TRUONG MARIE CURIE

l\

DE THI HQC KY l NAM HQC 2010-2011

Mon thi : TOAN l lIP - Thdi gian lim biri : 90 phrit

Bei 1 (3 didm) : Giii c6c phudng trinh sau :

a)

"or2^ - sin2x - J-3rin2^ = 1

c) 9sinx + 6cosx - 3sin 2x + cos 2x= 8

Bni 2 (2 didm) : a) Tt c6c sd I,2, 3, 4, 5, 6,7 c6 thd,lQp duo c bao nhi0u sd t{ nhiOn gdm 5 chfr sd

kh6c nhau trong d6 nhdt thi0t phAi c6 mit chf s0 5

b) Tim c6c sd h4ng chrla x vdi s0 mf, tg nhi€n trong khai tridn Niu ton ctra nhi thrlc :

fffi*l)'u

\x/

Bii 3 (1 didm) : Ba hoc sinh A, B, C cing tham dU 1 k) thi hgc sinh gi6i todn X6c sudt dd h9

duo c didm 10 ldn lugt li 0,5 ; 0,6 ; 0,8 Tfnh x6c sudt dd c6 ft nhdt t hgc sinh duo c didm 10

Bei 4 (a didm) : Cho hinh ch6p S ABCD c6 ddy ABCD le hinh binh hhnh mm O Gqi E lh trung

didm SB, I la trung didm OD.

a) X6c dinh giao tuydn cfra (SAB) vn (SCD)

b) X6c dinh giao didm ctra DE vi (SAC).

c) Gqi (cr,) ld mat phing di qua I vi song song vdi (ACE) X6c dinh thidt di6n tao boi (cr)

vdi hinh ch6p

d) Bidt tam gi6c ACE ddu vd AC = OD = a Tinh di€n tfch cfia thi0t diOn trOn

TR,UOFIG MA,RIE CURIE nd u'rm F{ec N'V r roAna E{qc z0s9-2sr.s

Mfin fhi : 'IOAN i ttp - T'hdt gian lhrn bhi : 90 phrit Bei 1(4 di0m):Gidi phuong trinh:

a) cos2x - gcosx+5 : 0 b) sin2x - 3sinxcosx*2cos2x : 0

-t:

c) J3cos5x+sin5x=2cos3x d) 4cosxcos2xcos3x:cos6x

Bbi2 (ldi€rn) : MQt trii chila 16 vi0n bi trong di c6 7 vi€n bi tring, 6 vi€n bi den vi 3 vi€n bi d6 L6y

i , ,^ ^

ngdu nhi€n 3 vi€n bi trong trii

a) Tinh x6c su6t de duoc 3 vi€n bi dd

b) Tinh x6c su6t dd dugc 3 vi€n bi vdi 3 mdu kh6c nhau

'ang klfing ch*a x)

Bni 3 (ldiem): Trong khai tri6n cira (i.l+ -it) 't, hay tim s6 h?ng tg do (tac td sii h

x'' '

Bli 4 (4diem): Cho hinh hQp ABCD.A'B'C'D'.

a) Chring minh ring: ( D'AC) // (BA'C').

I

b) Chri'ng minh ring dudng ch6o B'D c6t mp( A'BC') tai di6m G sao cho B'G=l GD vi G ld trgng

t6m c0a M'BC' .

c) Gqi P, Q, R lin lugt ld c6c di6m dOi xtng cira di6m B' qua A, D' vi C Chrlng minh ring:

(PQRy(BA'C').

d) Chil'ng minh D Iir trgng tdm tri'diQn B'PQR

MOn thi : roAN t lEG - Thdi gian lhm bhi : 90 phiit Bei 1 (2,5 didm) : Gili c6c phuong trinh sau :

a) sin2x + 2sinx = 0 b) 2sin2x + Zsin1x- 4cos2x = I

' c) 2cosx cosZx = I + cos2x + cos3x

Bli ? (2 didm) : a) Lcrp 118 c6 20 hoc sinh trong d6 c6 Zhoc sinh nam Ldy ng6u nhien ra 3 hqc sinh

bqi X lh sd hoc sinh nam trong 3 hgc sinh dugc lay ra d6 Lap bAng phan bo x6c sudt cira X

b) Tim hc sd cfia s.d hang khong chrla X trong khai tridn : (Z*' *+'l'o '

I x'l

Bli 3 (1 Cidm) : C6 3 sd x ; y ; z theo thritu d6 lap thlnh cdp sdnhAn ; Ddng thb'i cdc sd2x ;2y + 6 ;

z + 8 theo thrl tu d6 lAp rhlnh m6r cdp sd cong Ci{.c so x - 2 : y + 3 ; z- I0 theo thrl tu d5 cflng l{p

thdnh mOt cip so PQng Tim x i Y i z

Bni 4 (a didm) : cho hinh ch6p S.ABCD c6 d6y lh hinh vuong canh a ; c6c canh bOn bang nhau vh blng

uJi Ggi G, ; G2ldn luot lh trong t1m tam gidc SAB vi tam gi6c ABC,

a) Chung minh rdng G1G2l (SCD)

b) Goi (cr) ld mdt phing qua G' , Gr r'I song song vdi

tqo bbi mat phing (a) vd hinh chSp S.ABCD

AB X6c clinh vd tinh cli€n tfch thiet di€n

c) Tfnh tj' ,d s-oto't v6i s ld di€n tich tam

giric-Sorr

Bni 5 (0,5 didm): Gili phuong trinh: *2 -L*co.sx-2sinx +2 =0

a) Giai cric phucrng kinh sau : 2 coszx+ 5 sinx _ 4 = 0

b) nl m dd phuong rrinh.u

"rn,?"i'1;:r-1,:l^:1:;i;;fl =,"

Bdi2 (zdidm) :

a) Tir cdcsos 0 ; I ; 2 ; 3 : 4 c6 thdldp duoc bao nhieu s6 gdm 6 chfr so trong dd so 3 c6 mlr

dring 2 ldn, cdc sd kh6c c6 rndt dring 1 ldn

b) Cho binh chria 5 cdu xanh, 3 cdu c16: Tt binh cl6 lay ngdu nhi6n 3 cdir Tinh x6c su6't dd trorrg

3 qud ca'u d6 cd 2 mhu xanh vd d6

Bni3 (1 (x didm):Gi6suci{csd5x-y - 1)'ldp rhinh ;zx+3y;r +zyleprh}nhclpsdc6ng Cdcsd(y+ l)2;xy+ l;

cdp sd ntran Tinh

" ujy ^

Bni 4 : cho hlnh AA'C'C ldng tru tam vl BB;C'C.gi6c ABC.A'B'C' Ggi M lI trong tam ram gi6c ABC N ; p li tdm c6c hi'h binh

a) Chfng minh Np ll (ABC)

b) Xrfc dinh thidt di0n cria nrdt phing (lvlNp) vdi lang rru dd cho

c) Goi K ii giao didm cfia mit phing (MNp) c6t B1c' Tinh rf sd B,K : c,K.

TRUOfiG MARIE CURIE ns'rHr E{oc Kt 1 NAM Hgc 2008-200s

BAi 1 (3 didm) :

Mon thi :

-TOAN I r c - T'hdi gian llm bii : 90 phrir

TRUONG MI\RIE CtJRiE Dn rnr HQC rY r NAvr lrgc 2oo8_200e

MOn thi : ToAN nrp - Thdi gian lim bii : 90 phrir Bei 1 (2 didm) : Giii cr4c phucrng hinh sau :

a) cos22x + sintx = 1

Bii2:

a) Tim h0 sd cria

I't.y't trong khai tridn cria (2xi + xyr),' (r didm)

b) MOt trii dung 6 vien bi d6, 5 vi6n bi trdng va 4 vi6nbi xanh* cr,on ngau nhi6n 4 vi.n bi Tinh

xdc suat dri chon duo-c 4 vi€n bi c6 dri cil mhu: rr

iic,"j Bni 3 (1,5 didm) : Hdy tim 3 sdhang ddu ri€n cta mQt cd'p.so nhdn bidt rang rdng c&a ch[*g bang

93, ddng'thdi ci{c sd hang ci5 tucrng frng lh sd hang^thrl nhar, thri ba vi thf mu}i ba cira m6t

BAi 4 : Cho hinh ch6p sABCD c5 dr{y ii hinh binh hinh tdm o M ld trung didm cira canh sc.

1) Xr{c dinh giao clidm I cira AM vi mp (SBD) (l did;) vsr'r vv'

b) X6c dinh giao tuvdn cria mp (sAB) uoi *p iscu (r clidrn)

t)

Tt^!:)_t::lt phing qua AM vi song song vdi BD Xric dinh thidt di€n cria hinh ch6p khi

d) Goi E vi K ldn lyvt le giao didm cria mp (a) vcii sB, sD Ggi N la giao clidm cira ME vdi cB,

H ll giao didm cria MK vdi CD t'rqv *r'

Chrrng miph : N, A, H thing hirng vd t)m ri ,o , EK

NH (t dicm)

Bii 5(0,5didm):ChoAABC.CMR:Neu cot1,.o,f ; corg.tlr.othrltud6 lapthhnhmot

cap so cong thi sin A, 'sin B, sin C cfing theo rhfi ,u AO t4p tnanfr m6t cap so c6ng ,

d) chu Gii srl tdt ch cdc.canh cria ldng tru ABc.A'B'c' ddu bang 9 cm vd Fcc'= FCC,= 1200 Tfnh

vi cria thiet diOn 6 f b

b) 2sinx + cotx = 2sin2x + 1