KV THI KSCL TTII DAI Hq}C xAIvI IOTIL,AN rr*tI lXA

nn rnr u0n : ToAr\, KI{or AThdi gian ldm bdi; 180 phtit, kh6ng ka tha gian phat di

nA tni g6rn: 02 trang*.||','

'|. . ffi-r*6 fr€' . gh-".%

psAw cguNc cno TAT ce Tui swn ( 7,0 arcm 1Cdu I. 12,0 dihml:

1. Khio s6t sp bi6n thi6n vA v€ dO rhi (C) ctra hdm s6 y _2*+rl .x-12. X6c dfnh m d6 duong thEng: y = x -2mc6t (C) tai hai di6m phAn bier M, N sao cho MN:4112.

Cffu II. (2,0 iti6m)::1. Giai phucrng trinh: cos2x*5: Z(Z-cosx)(sinx-cosx)

2. Giai phuong trinh: x'- x * 1006..[+ 8048x = 1006

ciu trrl. (1,0 di€m): Tinh gi6i han : I : ,' **o - J 20L?I - -204ix+l X-l

c6u IV. (1,0 ctihm): cho hinh ch6p S,ABCD cir d6y ABCD ld hinh chfr nh6t v6i AB : a ,AD : 2a . Canh SA vu6ng g6c v6i mat ph&n g diry, c?nh b€n SB tao vcyi mat phang clay m6t

g6c 600. TrOn canh SA I6y di6m M sao cho AM :a.6 ,-X+ ^r.i*=:i, mat phang ( tsCM) c6t cpnh SD tpi

N . Tinh th€ tfch kh6i chop S.BCNMcf,uv. (1,0iti€m): chox,y, zldbasOthucthoam6n: x'-xy+y'=1.,Tim giitrildnnh6t

vd gi6 tri nho nhAt ctra bi6u thilc: p : xo + yo - 4. x. +y'_3

PHA|{ RIENG ( 3,0 tti,m)Th{ sinh cht itwgc ldm mpt trong hui phan ( phhn A hoqc B)

A.Theo chwons trinh ChudnC6u VIa. (2,0 ctiA@

1. Trong mdt phing vdi h€ toa d6 oxy, cho ducyng tron (c): x2 +yz -2x+6y -15 : 0. \ri6tphuong trinh ducmg thing A vu6ng goc v6i ducrng thing : 4x-3y+2:0 vd c6t duong rr-on(C) tpi A, B sao cho AB : 6.

2. "Irong m4t phdng v6i hd truc toa dO Oxy cho hinh chfr nh4t ABCD c6 di6n tich bing 12, vd,c6 tdm I ld giao di6m ctra dudng thing d, :x-y-3=0 vdi cl, :x +y-6:0. Trung di6m cuamQt cpnh li giao diiirn cria d1 vdi truc Ox. Tim toa c16 c6c dinh ctra hinh chfr nhat.cdu vlra . (1,0 di\n) : cho n ld so tq nhi6n l6n hcyn 2, tinht6ng :

S=Cl, +2.Ci+3.C] +a.Cl +...+n.Cil

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I

B,Theo chwons trinh Ndns cao

Cfiu VIb. (2,0 dihm):1. Trong m{t pheng vdi hQ to4 d$ Oxy, cho hinh binh hdnh ABCD c6 di€n tich bing +. Bi6tA(1;0), B(0;2) vd giao didm I cua hui c,ro'g chdo nim tr6n ducrng thil; y f ;. ffi;;;c6c dinh C vd D.

2. Trong m4t phing vdi hQ top d0 Oxy cho parabol (p): y : x2 -2x vitelip (E): ** r, :r.Chirng minh ring (P) giao @) tai b6n di6m phdn biQt cung nim tr6n m6t ducrng tron.

lVi6t phuong trinh ducrng trdn di qua 4 di6m d6.

cdu vlrb. (1,0 rtihm): cho n ld s6 ru nhi6n l6n hon 2, tittht6ng :

s = cl, * 2.C:+ 3.c] * 4.ci+... + (-l)"-'.n.ci'

-,t-________-H6t_-____-_-_ ,

:

(Thf sinh kh6ng dwqc sir &,mg tdi liQu. Cdn b6 coi thi kh6ng gidi thich gi th6m..) i

kang2 /2

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oAp Ax - BrEU ornvrCAU DAP AN DIEM

I(2"r9

ili6m)

1.(1,0 tli6m)+) Tap x6c tlinh : n \ {t}+) Su bi6n thi6n

- Chi6u bi6n thi6n ' y'= *h

< 0, Vx e (-"o;1) u (1;+*)0r25

Him s6 nghich bi6n tr€n c6c kho6ng Coo;l) vd (1;+oo)

-Hdm sii kh6ng c6 cpc tri-Gi6i han vh tiQm cpn :

lim v: lim y:2 : lim v = -oo vd lim v: *cox-++.o" x-+-"oJ ' x-+l-' x--+l*'

OO tfri hdm s5 c6 tiQm cin ngang:y:2 vi ti6m cfln dimg : x :,1 0,25BAng bi6n thi€n

0,25

+)E6 thi :

1pO ttri hdm sd clt trpc Oy tai di€m ( 0 ; -1 ), clrtruc Ox t4i di6m (-l ; O )2

Giao di6m cria hai tiQm cQn ld tdm dOi xring cua d6 thi.

0r25

2.0,0 tli6m)Dudng thdng Y = x -2mcat (C) tpi hai di6m phdn biet M, N e phuong trinh :

2x+lx-l

<>Phuong trinh r,' -(3 + 2m)x +2m-1 = 0 (*) .o 2 nghiOm phan biQt kh6c 10,25

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n(4,0

iIi6m)

1. (1.0 di6m

* [:::x-:1tr I rt t"u".,"-,'". : ;i; ;;;* ;';-,r'

= o ;-----

;.lz"i"ft.olj*'tu(":fr;:;i4

vdyphuong trinh dd cho c6 nghi€m : x: f+k2n;x =n +k2n (kez)

2. (t,0 tti6m

,_-,[o= (3 + 2^)' - 4(2- ft'-(:* 2m)t+2m

l4*' + 4m+ l3 > 0(+{[*3*0

m-1)>0

-1+0

thoA m6n VmER.

cqi ip; d6;iil iiidrn M "tN

i[i rraii,lil: i,")lrvt.;H:]*) . Khi ciit;;;*li hai nghiOm cria phuong trinh (*).

Theo gi6 thirit : MN - 4"lt

VOy: i\ , )l2i cfic gia tri cdn tim.

Ei6u kiQn x6c dinh cira phucrng trinh , >< t - 1

8048Phuong trinh :

D4t 1+ JG 8048x =2y, y > 1

tu d6 ta duoc :"/ 21+ 8048x = 4y' - 4y +1 <) yr - y - 2012x

Mdt kh6c, thay I + Ji+ 8048x = 2y vao (*) ta duoc : x, - x _2012y

[,n=-1e4m2+4m-3-oel 2

Itlm=-L2

0r25

4,25

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t (;t: ; = t0 itt-iii - .---- .. . . .' . 'VdytacohQ : {'t.

n- z-vL/'!

rrtr liictroiti" a"q;lGryjG;FioTli= o---- ".."-'-'.'..

€x=y (dox+y+2011>0)Thay vdo (2) ta duoc :

y' -2013y=Oo[t =:o'3 lo?inghiQmy: 0 ui vr1

LY=u r J 2voi'p2oitt"4",; :iiili#"r*,t - :--'

Vdy phuong trinh dd cho c6 nshiCm : x =201?

0,25

tr'?5

IN(1,0tli€m)

v*_1

0r25

0,25

{},25

_:_--___,_--__-

0,25

II/

(1,"0

tti6m)

G

" *ff,_\ .7"k'\

A a : ,'.':B,

vl"-AD7/BC;fi ( BcM)il At-."y ;t.p( BcMt;ti.mpasADi ih;" sd;--tuy6n MN // AD , MN//BC, SA r (ABCD;= Se r eC, fecIABIaco: { =BCI(sar)=BCl_BM.LBC I SA

--.-----------------:-

rri giric BCMNithl"riiri*s il6;s ;6 BMUa.'t*e.;; :-&t'ithid[;hi6;ru6ng g6c ctra SB l6n (ABCD) do vdy g6c hcro bdi SB v6i (ABCD) ld ffiIa c5 SA : AB tan,ffi :AB tan60o : u.l!

l

i

/

II o,,u--f----

ITrang3/7

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MN-sM .MN sA-AM a\6'* z 4aIvil\ DIVI IVIN JA - AJVI I 7 4.n.T=:-(=)-=AD SA 2a SA u.,6 jBM:",ffi[AM'-+

{3

(^' '4a\secxrr,r - BC tMN BM : l'+l+ : ry*

[ , )r' tJiHp SH IBM ,vi BC I(SAB) =+ BC r SH.

-Y-?y_.$_H__+._LP_-CN\0 = .9"1{_ 1.?.4s.ge__'_eg. s_ye_l_+& sb_Qp _s_,F_c_NM

.^=;=; AM "-5 :-=: ^^n :a:: n ltunffiF =+=++Affi = 300 > m= 300, sB = 2a, SH =153 =uAB 3 's'vll-z"

Goi V 1A th€ tich ch6p S.BCNM ta c6 1sH.s".r, :ryTa c6 : x' -xy+y' -l g7 1+3xy=(x+y)' >0=xy=-]

JMiI |.h.fP.:g j 1

: x' - xy + y' = (* - y)' * xy ) xy

Cfrngtir : x' -xy+ y' =r= x' *y' =xy+l={*' +y' -3 =xy -2-

[xo *yo -4- -("y)' +2xy_3

suyra: P= (xY)'+2xY-3xy, -2

Xdt hdm so : f(t) --( :2:-3 r,6i tt*2. 3 -(t_ z\'f'(t)- \-:z'f'(t;="'' (-z)' )

Ta c6 bing bi6n thi6n :

0,25

0,25

t;VJt;VJ

. [-1,r-lL 3')

ft-z-oelIt-Z+

|vtalf(t) =f (r)=2,L-t"l

-f1€'t'

..5) = zJi -z|{iq r(t) = f (2 -L-;r j

I

V(1rorli6m)

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-/ *kTir d6 ta c6 :

MaxP =2 uri,[*=Y=1Ix=Y=-1

r r----E -- |

| *_Vt-lJi -"JJl-r,,_"17_:JI+J"r6_i il^-T't=T II_t

I*-Jz-rS*J.,6-i ,,_!t t"1-t-JFL I

MinP-zJj-z ru'il - 2 'r-T

I

| " = -Jz-rS -J.-6-r .._ -#-tT+JG{ l^ ^_l^ 2 't:T 1o3s/--Fr--=--i

| * _ -Vz-rJr +VJ:-i .._ -,lt -tJi -JS-r j

l^--,Y=f i

Wa(ro

1. (1,0 diE\,-:*

\:'t""tIi6m)

:-3-y__l_1,6__lrurr \ \.,, uu raril r( r;_J ); oan Klnn t(:).

=9g"lg b glu,s*-q-i o* 4P

/----:--thi AH=3 vd IH eAB suy ra IF{ = ./nt - ALII _ 4

-or-?5-0,25

0,25

0,25

vr ouCIng rhang A vu6ng g6c v6i dudng th6ng : 4x_3y+2:o "e"piiucrngiiinhcira A c6 dang : 3x*{y+g:g

, lc-el [c--114=IH= d(I; A)= t- -t <>1"- rr- { l^-to'-j-r-:--------- ---. ---- -- : ----------l-u-.-

t'V0y A : 3x*4y*)e:0 hodc l: :xi+v_i-i:0--*,. \rr\, rtttttl,

Ta c6: a, nO

Do vai trd A,B,G,D la nhu nhau n€n gi6 sri M rd trung di€m canh ADM = d, nox suy ra M( 3; o). Q --'- -'

ra c6 : AB:2rM=rtre?T =3Jj

rheo gia trri6t , Soncn:AB.AD =IZ=AD:+S" = 12 :t^6AB 3Jr-', "Vi I vd M cung thu6c duong thing dr 3 dr I ADDucrng thdng AD diqua M ( 3; 0) vd vu6ng g6c v6i cl1 n6n AD nhfln i(t;t)dm v6c to phdp tuytin. Phucrng trinh cua AD: x * y _ 3 = 0

f. _gf*-y-3=0

i;;:o€)1 : vov'(Z'ij' tv--

t"2I

.l

mr rang 5/'/

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ng thuQc AD n6n:di€m A, D

*y-3:0

[y:-x+3 [y:-x+3 l]:'-*c>l e], .j €)]lx-3:1 <)[(*-l)'*y2 =r - l(" -t)'*(3-x)2 -2*

ll,. ,: ,lL

Lai c6: MA:MD:$-O2

Toa d6 A, D ld nghiQm cua h€ :

Y-ey-.A( ?;.0..P( $ :_!)

fqong tu I cfing lir trung di€m cira BD n6n ta c6 B( 5; a)V0y toa d0 c6c dinh cua hinh cht nhdt ld: (Z; t ), (S; +), (

Hodnh dd giao di cua (E) vd (P) li nghi6m "t

i phucrnf t.inh .

-2x)2 =1c)9xa.36x3 +37x2-9:0 (x)

VA

Ix

lL!

t;(x-t)2 +rz

ll":'llu=tir.'ll": o

llv=-tL L"

0,25

X1*,*'

?ry_lt," !{y_itr_gs?!: {11911: ci p"C1,*,'.;.;t::1.;:-._" _._ _ ,-_

Chonx : 1 = n.(1 +1)'-' =Cl + 2Ci +...+.nCiVdy: S=n.2n-r

1. (1,0 di6mVIbQ$tIi6m) 3:-"-, S-:-tI-?)=AB = J5 ' Ph.'o''g trinh AB: z

I e (d) : y : x si(ilit. I itiffis A;ffi ;il AC ;tBit ;a;;---C(zt - 1 ; 2t), D (2t; Zt - Z)

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X6ti(;i=da_3o"5_h7;i:q;-ir"iiic"ir,.t'o"n"o'-r(riifi0i.0(0X(1) < 0,,(1X2) .0,

"(2X(3) < 0 suy ra (*) c6 4 nghiQm phdn bi€t,

D"ge -(Pl

q41-e) Bi-l_4ieql_p_b4s_b_iet _-_,_...__ ._i ------

" I Y=x2 -2xTop d6 giao di€m cua (E) ve (P) tho6 mdn h€ i *, ,

| -=-*Y2:1Ie

[8*t-t6x:8v . ^ ^<> {-; _ ";-

--' > 9x'+9yz -l6x-8y-9:0lx'+9y' :9

<+ x2 +y'-**-*y-t = O (**)' g g' \ /

(**) te phur:ng trinh <tuong hon c6 t6m r: [3,f ),

b6n kinh R : gDo d6 4 giao di€m cua (E) vd (P) cung nim tr6n ttudrng trdn c6 phuong trinh :

xz+y2-f"-fv-r:o

0,25

0,25

4,25

v'ub(1roili6m)

X6t khai tri6n: (1+ x)" = Cl + xCl + x'Cf, +... + x"Cl Ar25

Dao him hai vti ta dugc: n.(1+ ")n-t = Cl + 2xcl + ... + nxo-rCi 0'?5

Chgnx : : 1 + n.(l-1)"-t - Cl - ZCI+...+ (-l)".nCi 0,25

Vdv : S:0 0.25

Chri i : - Gi6m kh6o tru6c khi chAm thdng nh6t <hp An.- Thi sinh ldm theo c6ch khdc md dring vdn cho cti6m t5i cla.- Cdu V thi sinh c6 thti lam theo cdch x6t :

% "" - %.r.* - SM'SN - q'{-i-

%.*o \.u.o sA.sD sD- C6u VIIa vd Cdu VIIb thi sinh c6 th€ cti chimg minh,cOng thirc :

kcl = ncl-iSau d6 thay lAn lucrt k :1,2,3, . . ..,n

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