THI TOÁN 2010 (TT CHÙA BỘC HN)

Theo chuong trinh chudn CAu VIa 2,0 didm i.. Tim phuong trinh crja mat phing r Cau VIi.. Theo chuong trinh chudn Cau VIa iz,O Aidrn r.. Theo chuong trinh ning cao Cnu VIb 2,0 diim r.. l-

1 Khrio sdt su bidn rhi€n vi v6 dd rhi cria him sd khi m = Z.

2 Tim m dd didm cuc dai vh cu c tidu c,ria him sd li ddi xrlng nhau qua dudng y - x.

8'UI (2,0 ilid@

L Giai phuongtrinh: 3cos.r-3sinx -rgx.sinx+sin xtgzx =0

2 Tim m dd phuong trinh c6 nghi€m duy nhAt: 25' + (ry -t)S' + 2m + 3 = 0

CAu III (1,0 didd

'\ Trong mat pliing vdi ir€ toa

dO Oxy, cho tam giiic cdn dinh A Canh AB c6 phurrng trinh

x- y+ 6 = 0- Canh BCc6 phuongtrinh x +2y- 0 Tim phuong tr)nh,Cudngcaoha ttllcrjatam

gi6c.

2 Chc ninh i3p phuong ABCDA'B'C'D'canh a, goi M v) N lh trung didm cua BC v) CC, I li giaodidm cria CD'vd DC'.

Qua I vE mdt duong thing cit BN vi DM tai p vi e, rinh d6 dai doan pe

CAu VII.b (i,0 did@ Ciiii phu,rng tr)nh

(x + l)togl (x + z)+ 4(; + z) log (x + 2) = 1 6

h chiduoc lAm mOt trong 2 phdn (phdn A horic B)

Oxy, cho tam giiic ABC PhAn giric trong AD iI x+y+Z=O,

Canh AB di qua didm M( t; I ), dicn tich tam gi6c li

pHAN RIENG (3,0 didm): Thi sint

A Theo chuong trinh chudn

CAu VIa (2,0 didm)

i Trong mat ph&ng voi h€ toa d6

duorg cao BH ld 2x -y+ I = 0 .

Tim phuong trinh crja mat phing r

Cau VIi a(i,0 didd

Tim nghi€m nguy€n cila phuong t

t-cosl

L

E0 GrAo DUC vA sAo rAo

1 KhAo s6t vh ve dd thi him so vdi m: -l

;: Tt;";tg ao irrila; ro;i aiC* ,ii rq va tam giiic tao boi 3 didm cuc rri nhy c6 dien tich

qs

bang 32

CAu II (2,0 tliCm)

sin3z cos3c - ".34'

1 Giai phuong t.inf,' ffi.* ffi - ianr-2cosz(:f - r)

2 Tim m dd phucrng hinh sau c6 nghiOm

' Cho hinh'l[ng tn] xiOn ABC.A'B'C c6 A'4 = A'B = A'C = 3a D6y ABC li tam giiic cAn 6 A ndi

'-PHAN RIENG (S,O DIf,nfl: Thi sinh chi duo.c lirrn mOt.irong hai phAn ( Fhdn A hoec Fhdn B)

A Theo chuong trinh chudn

Cau VIa iz,O Aidrn)

r Trong mat phing tga dQ Oxy, cho tam gi6c ABC c6 toa d0 A(2, -3), B(3, -2) Tigng tAm G ctratam gidc ABC thuOc ciuong thing (d): 3x - y - 8 = 0 vh tam gi6c ABC c6 di0n tfch Uang

phuong trinh tham sd cria Canh BC

CAu VIIa (1,0 didm)

'Dnr sd iiflii ,'tnaa mdn: (z + 2z)3 :8t

B Theo chuong trinh ning cao

Cnu VIb (2,0 diim)

r Tiong mat phing tga dQ Oxy, cho tam gi6c ABC Phuong trinh canh AB ld: x + y + I = 0 GqiM(2; 1) lI'trung didm AC vd N lh trung didm BC Tam gi6c NAB c6 diOn tfch bang qrt Tim toa dO

didm N

2 Tiong khOng gian v6i hQ tga dd Oxyz, cho tam gi6c ABC c6 A(1, 2, 5) Trung tuyOn BM c6phuong trinh: "-=t : ';u : + Trung tuydn CN c6 phuong trinh: ' ,n :u-:2 -';' l-qp

phuoiig trinh tham sd cria canh BC

oTimtoadodidmMtr€nddthihhmso:,:ffisaochokhoAngc6cht}A{ddndudrrgthing

C:3sl*A+7:Onh6nhat.

a* cIA* r*a,ic vA ar.E* i'au: c)€ TF{r 'FHdi BAI F*sC e4*N F*AH ,\Aft4 z*!# - sGT 3

TTEE)1iH THANG LONG Tizdi giun it)nt bdi l8A ohur, khdtt,q ke' rhoi gian phdr de

pHAN cFruFrG ci{o rdT cA cAC THf srNH (7,0 srdu}

Cau t i2.S dierni

CFro h}rn so: ,: $ tt,

r KhAo silt vh ve dd thi hZim sc (ii.

z Cho hai didm,4(-5,1): F{i.3) Tlm cdc rii€m 1,'ir€n do thi (Ci sao cho ram gi6c }rten vu6ng raiM

C*u E-l (2,0 rliem)

L" Gitti phuong trinh: 2 cos2r+sin2riScosr-r-sins+I:0

i Giai he phirong rrinh sau:

CAu rV (1,s clidm) Cho hinh ch6p trt gidc ddu S ABCD cd do dhi duong cao bang a vi g6c SB : a, a f 4Eo.

Tinh ihd tfch cfia hinh ch6p S.ABCD theo a, ct.

' C6:u V (l,Cr didm) Cho ba sd thuc a, b c th6a mfur n + b + t: r Chrrng rninh €ng

# - * * # tf{r'*o + 3b+c + 3"+o)

PHaN RIENG (3,0 DIEM): Thi sinh chi du-o.c lim mdr rrong hai phdn ( phdn .4 ho6c Fhdn B)

A Theo chuong trinh chudn

Crtu Wa (2,0 tlidm)

1 Tiong mat.phing foa dd lxy cho tam gi6c ABC cd A(4, -1), ducrng cao BE cd phuong trinh

2:t - 3y i L2 : O, duirng trung tuyen BM c5 phuong "trinh 2r: * Zy :0 Lap phuong trinh ba canh cIa tamgiric

2: Irong-hg tryc lOa_dQ 9lrt"rhotti4 chgp S ABC cd canh ben SA wong g6c v6i m4t d6y (ABC)

vi A(0, 0, 0), S(0, 0, 6) Gi6 sr? K(1, 2,0) h tam duong trdn ngoai riep tari lUr nef f-ap pfiuongEinh mat cdu ngoai tidp hinh ch6p S ABC .

CAu VIIa (1,0 iiidm) Tim sd phrlc z thda mdn lzl:S vd lz- Z+Ail:2.

B Theo chuong trinh n6ng cao

Cau VIb (2,0 ttidm)

l Tiong mat phing toa d0 Oxy cho elip (E) , '94 * n { : , LAp phucrng hinh duong rhang ({ di quaM(7,7) sao cho cilt @) tai hai didm A, B th6a mdn MA = MB

2 TlonghQ tnlc toadO Oxyzchomdtcdu (s)

'12+y2*22:2b, dubrngthing (A) ,? :+ 1",'

Try phTg (Q) ,, + y t z j 1 :0

I-+p phuong tri4 mat phing (P) song song vdi Ouong tfrang (-n), -4t

piri.ng.(P) vuOng g6cvlur mit ph&ng (8) vA (4 cilt mat cdu (S) theo giao ruydn lb dubng t6n

T'F.ildNiG TT{PT

n i r'r FrEt-qz .nii'

L2 i.Lj -r.-t LI i -l u

2 Giiri phuorrg trinh:

Ciu IEE" Tiirh:

i Kh6o s6t.s1r bi6n thi€n vi v6 d6 thi hdm s6 v6im:3.

2 Gie su dd th! him'so cit tryc hoinh qi b6n didm ph6n bigt Hay tim m d€

cho hinh phinq gidi hsn mi ao thi ham.s6 vd tryc hoanh c6 diQn ffi;hA;

pliia trdn vd phAn phia du6i tryc hoinh bing nhau

CAu II"

1 GiAi hp phuong trinh:

(l=90u), AB: AC - a h44t bdn qua canh huydn BC u:6ng g6c vdi m{t ddy,Irai mgt bOn con lai d3u hsp vc'i tu4* doi, cac g6c aiE'aoll iintt thc tf;h c;;

Cfiu V" I{4c <iinli m de hq sa-u c6 ngiriQm: /

ft

)x" - 5x+4 <0

l^

l3*'' -tnxrlx+i6=0

"-i TZi FF-^ - l-i-A !.'1^ , ra -i

\-Ad"& \,r rru.uB zurdr1g giarr vdi itO toa dO D,A c6c.rudng goc Oxyz cho hai di€m

A'(t;2;1), B(3; -I;2) iho dodrug thing id) va mat phini'(p) o cac phuo*g hir.h

, _ k I I /*\

nJrir sau: (d) = "- = ; (P l: 2x- J' l- zi 1 = 0

i:" Tim tga iio diOm C ddi;ririig.r,6'i ciidin A qua (F)

2" vidi ohuorig trinh dirong tiring (n) ai qua A, cit (d; vd song song ,rdi (p).

tim ioa aO"oieni l,zl thu-5c €t;t; f.- ta"g f.froaiug ,ach Ir{A + Iv{B dpt gid tri nh6 nhAt

CAu VXn Tim gi6 tri ion iih6t vd gi6 trinh6 nhat cira him sd:

oAp Aru - TI{ANG uldm f {

Hhm so khOng c6 ti6m cAn Dd thi cdt Ox tai fx=-l

Bing bien th

x

/:

Xric dinh tam-va Uan liintr*

ro4 dQ cr{c ditim s(ooa); ,(;+,,,,); r(ooo)

phuong trinh kh6ng cd nghi€m x< 0.

0,2s

VIa

(2,0

drem)

l Cho tam siiic ABC

Goi N li didm doi

C phii nam ue f'ai pt iu cua

n€n chi co C,(::-6) li rhich hon

AD0,25VIa

2 (1,0 die"d 'Iim mat phing

P :2(x - :).:[r * :)-'(,- ;J = 2x + 3y - 6z +]= o

0,25

CAu Ddp :in Didm

* = (;, o(, - t),-

; +) / /(:,, - r,

; - +) 7D=( or-t'.-aY.a\"( 1 v 1)

Po2 = r,' *4a2 *a'

VIIb.

(1,0

diem)

2 (1,0 died Giai phuons trinh

DAt u = log,,(x + 2), phuong rinh thlnh (x *3)u'+ 4(:r + 2\u -16 = 0 4,25

L

^ I 16l4-Lt

sAp Arq - rrrANG ndpr L

+ H)'nr sd ddng bidn tion (-v?, e ve (r,tr, *m); hdm s6 nghich bidn rren (-*, -rt) vit (g,.t/i)

+ Cuc dai tai x = 0; y = 2 CLrc tidu tai hai didm *: _@.

+ Gi6i han,

,IT*U: *oo; ,IT_U: *m

+ Bing bidn thiOn:

'\t/"

o,$t

+ Hlrn sd cd 3 didm crc fi-i y! - 4r{r2 - l+rn):0 c6 3 nglrigrn phAn bi€t D:ip sd m < l

+ Toa d6 : aidm cqc rri A(0,2);

B(-+ Tiung didm qfia BC te H(0, 2 - (t - m)2) Oien tich ,9 :

)nC.nU _r,t= *.11 _ *y

+ .9 : 32 Giai ra duoc nz : -B (rh6t ;en)

u

t (1,0 didm)

+ Ureu klen: cos r * -I; sffi

+ Vdi didu ki0n trdn phuong trinh ruong vdi

sin r(I - cosz c)

- cos r(1 - sin2 r) 3n

t**t" * 1+tin;-=tanr+1+cos(f -2c)+ Phudng trinh; (sinr -t cosc)(cosr - 1) : Q

+ sinr;+CoS,x*: n tu O

J

+ cos;r : 1 [a dLr'o-c nghiOm r : n2r, n e Z (thoa rn6n (*))

+ LAp b6ng bi0n thi€n cria hd.rn sO /(t) :

#, t e [0,2].

+ Gi6 tri lon nhat cna /(t) Uang

f ; gid rri nh6 nhat bang 0.

+mcdn.tim:0( *=l?,

Cnu iII (l,O didm)

,{: I ; -: -l;d.It.l 7-. - s-dr: i _ -r_dt:_r i _ dr: It+ IZ.

6 (srnc*cost)z g (sinr*cosu)z 6 2cos2(r_it d 1+sin2c"

f)Jloa - rl tan(r- lar: -;uitncos(c- ;)ld : _t* t

vayr:-;-ry

4 cos2r

S [ 1*sin2rCAu IV (1,0 ttidm)

+ Tiong tam giric ABC v€ hai duong trung truc AM, d cria BC vi AB Goi I li giao didm cfra AM vi d,

suy ra I Ih tAm dubng trbn ngoai tidp tam gi6c ABC vi A'I vuOng g6c vdi mar phing (ABC).

+ Thm gidc vuong AMB: AB : \/AF -BW : ot/E

Di0n tfch tam gi6c ABC: 5a66r : t1,n

U.AC - a2\/8

i Mat thac s.a.,,c: g+#?, suy ra AI:

#

+ Tarr gidc vuong A' AI: A'I : \/TF -AF : o\ly v32

* V4, Bgg, B, : V4g6.a, B,Ct - V.a,, AaC

= A'I.Senc - !n't.So".

,) .' -' ttr c ^3 /6;

- -A I.l

jnnc: asJfr

"A

CAu V (1,0 didm)

lo,+ Didu ki€n: 0 1 r,A * 1; (" - Z)(a - i) > 0, (/) tV

+ PT: 13 -3x2 : y3 -3a- 2 tuong duong: (" - 1)t - 3(r - t)i g, - Jy, (II)

+ X6t him sd /(t) : t3 - 3t ddng bidn tr€n (1,+oo) vi nghich bien rr6n khoAng (-1,1)

+ Tit (I) suy ra n > 2; U ) t hoAc r <2; E < 7.

I I

I

I I

+ V6ri O < r K2; 0 < gi < t; f(t)nghich bidn tr6n (-1,1) va 0D: f(" _ t) : fd)suy ra y : s _ l

Y4ya:r-L

+Thayy:x-lvioPTcdnlaicriah0:("-3)3-.0.vayh€c5cipnghiOmduynhatx=3;y=2.

CAu VIa (2,0 tlidm)

+ Goi C(o,b), suy ra trong ram G(+,fff

+ 'gng tarn G e (d).: 3z - g - g : d, suy ral b

il : Jjac

- Szc' 2, -1); C(

Giii ta duoc 11 : -2; tz !'!ri ,,fr!^ sr.,

Phuorg trinh Lham sti BC: x ='l - t: y = z

+ Gi6i ta duo.c u = -2,i; u: -r/j I i., u - ,/Z + r.

* u : -2i, suy ra z :2i

*u: rt*z,suy raz:-+-t

Cdu VIIb (1,0 tlidm)

04d

oist

qi4d

I Goi I lA trung didinr <:ira AI3, suy ruI{_2,2); rt0 dni AB _= V?0 :,t\/llj

I;ul giac MAB vudng rai M.:-r Ml = j,- AII - v,ltj

r Hanr so diirrg bie'rre' ( c<-,, - 2) vit (-.2,,r-rn); hii'r so kh6ng co cLrc rri

Ci6i hurt: I+-'N .lirn y=2; lim g-2; l++m - t.* -2_' lirrr ,9:+_cx,; ' ," -2_ru -'lirn ?J:*oe

3i1l|l nT

:: ll'lii i

lyligllrins r : 2 ldrn ri€' can dfng vi e: 2 rirui ri€rn can ngang

1- I3;ing bien rhidn:

r- I'l12cusz t;* L)12n-ilrJ.cr-rsL;.1-8c6sc+.si1 :r-l-1 il +rsirrt,(2.r.:os,r I l) + 4 cc,sl rr J- 8 cos:r: l- 3 : 0

r i2 cos:ri + l)(sin r -i- 2 crrs 1 + 3) = 0

+ r;i r: 1-2crt.rsr: l 3 :-0 .++ si':r -r- 2cos:r;: - J 1vo ngrricrri vil', -",;,r a arrl

L

a25'

+ ;t t:r;; ., j- .i : 0 +-, cos:r .- +i r: - :1 'l1T-;* -f A:2tr, l,: w Z

n.1"8t

2 {},{} riisur).

+ ilrt !,{t;- i 1j = rt, ,,ii:':-;i1 : ,t)\

11 ir ) i_j slry tit,J:t:.+ ,1!

{- Giii hC ta duoc u : 3; tr : i vh 1t Ll,ri : 1g (loa')

Cau ItrI 11,{.} ttiern)

,,1.t , ,,: tr2 ,lr)2

r''firr*):,, - !' )::-, y

l) { , ^.b, ,+ 'In t:ri h€ lrhrrrnrg rri,rh: { G : u - '}

ll"t - 2u2 I 5r, -, 3r)

tl+ Dar f =- cosr t ; .[ et.(zt l- t)dt

+ Vdi u : .J; u : I ta duo.c cap nghiOni rJuy nhdt x ::') ,U = J

*f :i.'''"'' "; 2 1(sirr2.r:*sin:r:)dr 1f 2i' os"" (2crw'i-l).sinl:d:r = :iucos,i(2cori.i ao l1)dc.*1 &n" d

+ Dat ?.r : 2t + I ; rio : efdt, suy ra \!, : 2 ,tt -= ct

+ I-dy It4 Ih trung didm cira BC Dat

\ -r- Trong tam gidc vudng Sh{B: SM =

+ Tir (l), (2) suy ra:

+ Giii ta duoc: a;2 :

BIV : z ) 0, suv ra 1J,44 =

M B |an.r : l .) tarr i:r, ( i )

+ Tlong tarn giic vuorrg SHM: SM = F; fl ,rr,

* - + ruon nguo.c dau n€n: (, -t)(+ - *f =o

30 _qLJ_" *, {r) ruong tu,T, # r-

f; s # -;, (2) va

# * # ,,+ C0ng ciic ve cua ciic bet dang tlrfic (l), (2), (3) ra duo-c (*+,)

I i rirr \'Nrr (l,tI dit'riil

I

i _ ! tl,U S_enrl * @%

+ !)ieirn 13 li giar: diCrn cta BE vi BM Giiii ta dLruc: I3(_3, 2)

r- IllrLrong rrinh canh AB: 3r l T,g * fi: U

+ Pliurtng rr-)nh canh AC di qua A, vLr6ng girc ilE: J:t -y Zy l0 : 0

+ Qua I{ vd dudrrg th6ng d song song vcli SA, suy ra dr(A BC) hay r/ ld truc cfia ram giric ABC.

+ Ooi M la trLrrrg ciidrn cLja SA suy ra M(0, 0, 3) Qua M ke ciLrdng thdpg A ,ong ,onf u,ii AK, A c6r

rl Lri i rlii I ln rtrn cArr s(Opt[.t "

10 5

+ Ko rang dl(ong thang :t: : I khdng th6a rrarr biri ra.

_*1 9::5{ lr.,yg rhing qua M c6 he s0 g6c k: y _ 1- A(r; _ i) hay e: k.r _ k+r

+ Xdi he *ioo O,d,r.r

:i2 -t g(k:c*k+L)2:36 <+ (4+Ok2)r2 +18,t(1 -,k)r+9(1 *A)z -36:0 {*)

+ M(i, l) & tro'g (") ne" (r)

lrr0n crj hai nghi€m ph6n bi6: vdi moi k

+ I(hoiing c;iclr tir I derr {P) beng 3 ,re,,

# : i] c1,i, ra D l-;t'7tl *$.56

+ VAy cri hai phtrong trinh mdt phing (I') ' t; ,- 3t1 j,Zz l,3141== g .L

a,I#nCAu VIIb (1,0 didm)

+ Tt'it (1) cho (2): -Ztnr - 2tn :0 * *2n*@: + l) : 0 +> rir : 0 ho6c :r; : *] d.a6t

+ Vdi r = -1 thay vio (2): 4 f 2m,:OS+y ry: -2 (th6a min vi x = -l),

'r Vdi rrr:0 thay vio (2): (r t)t:0,!iiryi:r - 1, suy ra n1 :::0 (loai).

VAy chi c6 nt : *2 th6a rndn bbi ra.

a,2#l

T'R.{'ONG TE{P'{'DAO pUv rti - H.A NQX

Gidih4nvirtiem can: lim y- Iim (*o -q*t+3): nm *[t-4-+l:{oo.

D6 thi hAm sii bdc 4 khdng co ti€m cin

DO thi hdm s6 dd cho cit Ox t+i 4 diiim phdn bigt ++ {*) c6 4 nghigm phdn biQt

<+ (**) c6 2 nghi€m clwongphAn bif t

I nt - lAu:4-m>

Di€uki€nlA: ]S" -4>0 <+0(m(,$

A_0,25

D 0,5

heo hlnh vd b8n diQn tich phdn hinh phang grcn hen bol do

rivi Ox, phAn nim trdn Ox lir: \

i, : il *' (y - o)cix : f'*t y l" \

\lisn tici phin hinh pfting nim dudi Ox lir: \

t, : .f

i,'lylox + Ii'lrlo- : - [:,' vdx -.{,- ro^ xr

T'heo y6u cAu cria bdi to6n ta cin c6:

I u : I ++ Isinxl : I +l cosx: 0.€) x: a+ tr',.

Kti iui;z: Tip nghi0m cira phuong trinh lii S: i;.'"i

Tinii gidi han iim

gaiti6n u:1,[x12 <+v5: x*2+^:u5 -2;

Thay bi6n moita duoc:

Do (SBC) I (AEC) thec giao tuydn tsC

+ K-e SI I BC tiri SI I {ABC)

Trong (.{EC), kA iFi r AB }* (srrl

=+ I le trung di€m cira BC

jNrru vqy sI: JJm: .,6

im m aC h6 bAt phus-ng trinh c6 lem

Di€m c(a;b;c) ld di€m aoi xtmg v6'i A qua (P) <+

ViCt

ffi : (m - 1;-m; -5 +2m) ld v6cto chi phuong crla A

AK // (Pl.p AK r rf' o AK'"- : 0 {+ 2'(n-r-i)+(-i)'(-m)+x'(-5 * 2m): g

# m:'J !5

o6 thdy (2*o-y t, *ze+1)(2x, -ye *2, +t)> O

+ A, B 6'cirng phia v6'i nhau so v6i (P)

+ Tca d6 I IA nghigrn cua hg:

o Tim GTLN: Ta c6: y: sin5 x +.'6cosx < sina x *^6cosx

Ta chr?ng minh sina x +.6cosx < .6

Q) e#(t - cosx) -sin4 x ) 0 + ^6(r - cosx) -(r -.ort *)t

<+ (t - ror-){ 6 -(i - ccsx)(t +.o*x)2}> o

I

-aL

?

-37 :-

+ y<J3vdiVxeiR * Y.ffy:Ji ex:k2n

o Lai c6 y : sin5 x+.6cosx > -sina x +.6cosx.

Ddnh gi6 tucrng i.r ta duoc min y : -.6 o x : n t k2n

=+ Fhuong trinh (+) v6 nghiQm trdn [-1;1]

+ y'(u) kh6ng aOiaAu h'€n [-l;1], ngodLi ra dC i le

a c6 bAng bi6n thi€n cria him s6 tr€n [-1;1].

Vcyisinx {0 tac6hAunsotro'aanh, y(u):-(t-ot)t +^6u ue [-l;l]

uong t.u nhtr CI c6 bang bidn thi€n crla him s6:

,ir hqp cd hai f,.ucmg ho.p

+ ue[- min t;tl-v(u): -Ji o u:

eiz Ydi: ier"sl'c,

Mon rhi: TOAN - Khdi: A

Tldi gian ltlnt bcii: IB0 phirt, khdng kd thdi gictn phdt cI6

pHAN cHUNG cHo rdT cA rsi srNH (7,0 didm)

Cnu I Q,0 ilidnl

Cho hlm s6 y = x' -3tnx2 * nt -l

' l Kh6o s6t su bidn thi€n vi v6 dd thi cria him sd khi m = l.

i ^2,, Tim m dd him sd li ddng bidn Vx < 0

Cau III (2,0 dihn)

y 'frong lihOng gian v6i hQ to4 dQ Oxyz cho hai duong thing

s_x-r_y-r z-J r _x+) y+/ z

' trt =-Z =

Z = | ot= 6 =-3 =,

1 Clirl:g rninh d, vi d" cit nhau Tim giao didm I cria chring.

'1 2 Tirn toa dO didm A e d,, B e d2 sag cho tam gi6c IAB cin tai I vh c6 di€n tich bdng

PHAN RiEI\s (3,0 didm): Thi sinh chi rtuoc lim mOr rrong 2 phdn (phdn A hoec B)

A Theo chr-rorrg trinh chudn

Cdu \/a (2,0 di&n)

1 Trcn:g mirt phing v6i h0 toa d0 oxy, cho aidm l(3cosa;0) va B(0;2sin o), o thay ddi Tim

{M} 'oo cho ZZii +SME =6.

2 Trong khOng gial"v6i h€ toa do oxyz cho didm MQ42) Tirn"phuong rrinh mdr phing qua M, cdr

Ox, O1r, az & 3 clidnr A, B, C c6 toa dd a, b, c > 0 Tim mat phing ad i,i aren OAI|C coit d tich'nli6

nhiit.

C:iu r/ia (1,0 dil"nl Gihi phu'or-q trinn VF = (" - 3)3 + 6

ts Theo chuong trinh ning cao

CAU Vb (2,0 didn)

r 1 Trong mat piiiirrg*v'di hd ,:4.d:.Oxy cho tam gi6c ABC

c6 phdn gi6c trong cira g6c A li

)c + y + 2 = 0 , riLr'bJg cao r'6 ril B la 2x - y + 1 = 0 Canh AB di qua oig* fr,l(f if ) Til phuong tr'inh canh AC i

fhi lnfr T9ne.d*." sir dung rii ri€u .u.;;;;T:fiil;"* siei rhich gi rhem.

Ho vh t€n thi sinh Sd b6o

cl-anh ,