4'-TRUoNG rHPr LE xoev Ot 1'fff 1'fftl DAI HOC - f,AN fff
f::ryNurEN
Cf,u 1: Cho him s6 y = -r' + 3x2 -4 (l)
1 Khio s6t sU bii5n thi€n vi v€ <16 thi (C) cua him sO (t).
2 Chrmg minh r6ng: Mgi duong thqg qua I(l; -2).v6ihp s6 g6c k < 3 dAu cit gO thi (C) tei
ba di6m ph6n bigt trong d6 mQt diiAm h trung dii6m cria ttoan thAng n6i trai tti€m cdnl4i.
Ciu2z
l Giaiphuongtrinh: tanx.tan3x a3=-2 - .
I + cos2x
2 Giii phuong trinh: !* * x ,12-x' =2.
3 Giai bAt phuong trinh: logo (9' - l).log* ,?, = j
'22
Ciu 3: Tinh tich ph6n: f = Jd+sinr.*
0
Cffu 4: Cho hinh vu6ng ABCD c6 cenh ld ali L6y H thuQc do4n AC sao cho ATI: a/2
Kd Hx *Qng g6c vqr (ABCD) vi 6y <Ii6m S thuQc Hx sao cho g6c ,lSC Uing 45o Tinh b6n
kfnh mat cdu ngo4i ti€p S.ABCD ry,
Ciu 5:
ciai he phuong trinh: {f1 J7;)0 +
'[v' +t) =t
lzt' - yt +(l+3x212' +3x.22r * ! =2
CAU 6:
l Trong mat ph6ng vdi hq trgc to4 tlQ Oxy cho iludrng trdn (C): x ' + y' - 4x + 6y =36 .
Dudng thang A qua f(-2:.0) vi cit duong trdn t4i hai <li€m P, Q Vi6t phuong trinh cria A
sao cho doan PQ ngin nhdt
2 Trong kh6ng gian v6i hQ tryc to4 ttQ axyz Cho A (-5; -3; 2); B(-2;0; -$;C(1; 0; -1)
Lfp phucmg trinh mat phing qua OA vi chia tti di$n OABC thanh 2 ph,an c6 t1i s6 th€
tich bAng 2 (DiCm B thu$c ph6n c6 the tich lcm hon),
Trang 2L of rm rrffDAr oApAN + HQc- r,AN ur
rnrOr* itoii sAI'{ KiroA' HQc rV NrrrSN
!=-x3 +3xz -4
TXD: R
C6c gioi h4n:
limy @;limY=+o
'#6-
J-+4 Xdt sg bi€n thi€n:
Y'=-3xz +6x
[x=0 /'=0el*=Z
Hdm s6 idng Ui6n tren (0; 2) vd nghich bi6n tren (-*; 0) vi (2; +o)
\,/'\
Dths cit oy @l!lL tat 9X
Trang 30,25
qua I vdiTalild6c k:> Pt A: Y : k(x - 1) -2
Gqi A li tlulng th6ng qua I v0i he so goc l(:> pt a: y: K(x - r, - z
phuong trinh hoinh <tQ giao iti€m cira (C) ve A: - xl + 3r2 - 4 = k(x-l) - 2
{Z) [i=l
e (x-lXx' -2x + k -2)= 0 e
l*, _2, + k -2= 0 (3)
Xet(3)c6A: l+2-k=3'k
Th"y-;=lvdo(3)=>k=3
Vflyvoi k < 3 thi (2) c6 3 nghigm ph6n biQt kh6c l'
<=> (2) c6 3 nghiQm Phdn biQt l; xlx2
-> L cilt(C) tai 2 dilmphan biet A(xr;v');I$;a);B(xz;lz)
\* xz =2;!t = k(xt-1) - Z;Yz = k(xr-l)-2
) fr * lz = k(xt * xz -2) - 4 = 4
Viv I li trune <ti€m cria AB.
t.2
1.I
0,25 0,25 0,25
- lcosx * 0
Di0u ki9n: { ^
[cos3r + 0
Phucmg trinh: <+ tan x.tan 3x + 3 = I + tan2 x <+ tan x(tan 3x - tan x) + 2 = 0
sin2x 2sin2
<)tanx.- +2=0e -:- x +2=0el-cos2x+cos4x+cos2x=0
cos3xcosx cos3xcosx
e cos4x - -l <+ 4v = (2k +l)n e t =4** 42
B6i ctri6u itiAu ki€n th6y thoi mdn
,rTkr
D6p s0: x =;+-;
Giai b6t phuong trinh: I +
Dk: x .FJ1;J7)vax+o
D$ Jz-x'z = t;(/ > o)
ft I
l-.+ - =2
Taduoc: 'l { x t
lxz +t2 =2
0,25
0.25
<+ (logr(9' - 1))' - 4lo
ftog, (9' - 1) > 3
el
[log, (9' - l) < 1
[g'-r>8 [g'>g
le' -t<z L9' '3
DS : x e(0;/riv[;+o)
Di€u kiqn: 9' -l > 0 c+ x > 0
Bpt
elrog,ls' -t,{+)tor, ? =I*log,(e' -r)'[og,(e' -r) -tog, 16l> -3
Er(9'-1)+3>0
Trang 41.1
2tr 2"- [
/= J".G-;.ar= fisin tX ' - + cos' tX - + zsln-cos-.dr X X
2222
Det ' t= I+ 24 ?-+ ax =2dt
OOi c4n: xl 0 I 2n
t I rll4l 5ft/4
*:M'o;<;.?
- x x\
srn-+cos- I
2 2)
[l,intlat i'!r^0.)
5r/
/4
I =2J7 [lti"tlat =z
%
= rJt(- cos 4:/ * "o' tl'/') = 4Jl
a,25
0,25
0,25
0,25
IV
1it
Dung tryc d cira dudng trdn ngo?i ti6p hinh w6ng ABCD
(d qua tAm I cira hinh vudng vd vu6ng g6c voi (ABCD))
Vfly d song song vsi SH vi d thuQc m{t phdng (SAC)
Trong tam gi6c SAC, dYng dudmg thdng
trung truc .atttt 54 c6t d tai O
:> O litdm m{t c6u ngo4i ti€p S.ABCD
Ap dUttg dinh l)t sin trong t.gi6c SAC:
AC-
=2R+2p= r?o, = + R= all
sinlSC Sin45"
V$y mat cdu ngo4i tii5p S ABCD c6 ban kinh:
R= ali.
\l
l\ \\\
4,25
0,25 0,25
0,25
c.5
1d ^,2;1.^ [(r*Jr'*rX y*.{y+ *t1=t (1)
ulal ne: {
Lz" -.yt + (1 +3xz)23.+3x.22' - f =2 Q)
Nhan 2v6, cia(l) voi * *J *' *t + 0 tadusc: - (y +,[y\l) = x -'{ ; 1
Nhen 2vEctn(l)vdi y-Jfe+0 taducr.c: -(x+ ,!.\l)-y-,tfi
=) X: -y
Th6 vdo (2): 23' + x' + (1 + 3x2 )2' +3x22' * x = 2
e23' +3x.22'+3x22' +x'+ 2" +x=2
o(z'*r|*Q'**)-z=o
D{t r = 2' +x Ta c6:
t3+t-2=0et=l
Ydy 2'rx = I e2' =1-.r (3)
Vsi x = 0 thi thon m6n (3)
Voi x ) 0, x < 0 dAu kh6ng thoimdn (3) (vi I vii > 1, I vi5 < l)
VAv nehi€m cria h€ (0: 0)
0,25
0,25
0,25
0,25 c6.1
(C) c6 tam I(2; -3); ban kinh R=7
AI = Jre = 5 < R :) A nim trong (C)
Gqi H la hinh chiiSu cira I tr6n PQ
0,25
Trang 5c6 PQ=2PH =2Jm
=> PQ nhO nh6t khi IH ton nfr6t
Khi dri: H trung voi A => A qua Ặ2; 0) vd nhfn frg;_Z) lim rapr
ViY A c6 pt: 4(x + 2) - 3y:0 Hay 4x - 3y + g :0
0,25
4,25 0,25
Gii sri (o) h mp can tim (o)
Vnor,
-" ^ Soou,
ffi=2effi=z
BM
fr=2+ BM =2MC
Gii sri M(xoiloizo)
fxo +2 = 2(l- xo)
= Jro +o =2(o- yo)
[xo ++ =2(-l-xo)
=) M (0;0; -3)
oM(a;0;-3);oĂ-s;-3;2) 1
r_ _1
) n =lou,o,ll= (- l;rs;o) ,
n cirng phuong vor ir= (-3; 5; 0)
Mp (OAM) qua O vd nh6n i, ta- v6cto ph6p tuyi5n.
=> pt (OAM) ld: -3x * 5y = g.
0,25
0,25 0,25
C\/
-a-tl
Trang 6\rnr-roNc THPT r'fl xoaY
^^-
NA- hgc 2010-2011
dudngthing !=x'
Ciu II
4k_"
Dt rrrr rHU DAr Hgg;l'AN rrl 7
Ban co oa"" t' n'roo inii 1oful
Thdi gian ldm bdi ttti pntii'r'0"erc thdi gian giaod€
Ciuf.
i fnao s6t vdvd dd thi him sO
*t +(m+Z)x-m co
2 Cho
! = x3 -6xz +9x '
AO tfri (c')vd duong tnAng d"v=-x'4'lfim
€lua
,, dC duong th6ng dvd
x+l
r dvir(c",)c6t nhau t4i hai di0m phdn
biet d6i ximg nhau
ar=L
ta x'e'
J-+
.)
{)
*fi
1 TinhtichPhdn/ = lG*z)' I#
2 Nhan dang
Mncbi6t: atan A + b tan B = lo +
b)tan:l-*[i]-@
3 Tinh gioi h4n J =lill
Ciu III
1 Giai Phuong trinh:
x-1
(.F *r)' *: i(r-'l
, )/
)r-q;;i, j
*+&'T]t z.chohQphuonu, {f7: F=o Tim ,, eC hQ
dd cho c6 nghiQmthgc'
"uotl rrong hg truc rou uo.rrryIlS?.* #:r Dubng thrngBcc6
phuong
trinhr- v - 4 =o ; dinh/gr6m.tr€n dudng thdngx+zv -3 =o'Di0mM(z;o) le trung
di.m cua Ac Tim to11O "* i* ro
^ yl.'^,!i6iolen tigh c11n6 bhne 2'
2 rrong mflt phing hefruc ;il' ;;' 'vi6t;;;;;i'ior' m[t phing (or) chira trvc oxvd t4o vdi m{t nr'a"e Wi tu o*1"9 :*n -f" * v +22 = am6t g6c oo0 '
3 Cho ttl di€.n lncp|rJno*9:* eiui z.a;,yg thang AB,CDbhng
d, g6c gifra
chirngb6nga'blftts=o'ci=l'ir"rtth€tichtirdiQnABCD'
-HCt -Hs vdt€n thi sinh: """"""""':"": """""'SO b6o danh:';"""""""
A;;O;;i thi khong gi6i thich gi th€m'
Trang 7iy*: fri l{'a cs K*{ t)
?6^?,
_p
fu'vt"ut = j rc
I
,tt-ll rc
7, , 5t>- lLt<+3
B{;t
ws i9 t";+ ( -*, 4) )
K> rrrg la l+tt
Re dd u) +, 1t, +);
fu-W'
h"q'fr 1^$7t)
(, u4,
a ,14 (s,c)
i rtFr** r; q;
t^.L * Lw+t)u _tr,
= _ rr_ v
r+,1
€ t LtL'+ (rr^+))r + +-tn a) (,t)
) t+-L r i r - , ,
(, nd' t^' )i I ,pb r'1-; fT a' u' ' i' f I "; + 't
'
J " = h' + Lu+ + rt r 7a \er
[*'; 'iiPrm
qT L*,* d ' A(k.tt yt) ) [t(',v
V -)
h,te G l{od I, <tt 4 1q+*u Z
'#f }( ry )'-w -u)=^F+t)'ry -+)
cz) :U$ ='+4-q' € m=4
+oo+
t2+ \r.u ,/.
.- ArJ
atd
Trang 84 oLu= r e-(( ,L+L)
, \/= -J- x_+L
14 zri
+
Jr, rL Q-
clL-' In - lun uHu
Zl t1
.Q- I tD
Lk_
Ll= lt L
=&
(+e)'
I = -_tc'aL
ln
u+) lL'
_0
= ; tLt
b 3
= a- +Q-t
$
olr** * Afu^g : q{ +b1 lr.^ N
/-"
ew A t^'4 + 9r' *$to*$ = (9,n A+e;ng ) ta'-&
t4
#;!
"!,,
L+A : )-9
J
4
e 9* A -9i,-U L gal - q^ B!
J+ >o coa| A,, a-4
/>
+
hreA "C4^ ry
@- t- lau'81 9",
I
L 9.u 4 -t9 ,
L *\cr*
i") t*A
7
2 "V *'rl ; 4Cul =o
= ,!,-* l tq -+("
ryzD
l-"
(-L)
g)
=4L2 I
a6-02lrf o> 4^
It+ 4
7L,
lr'- rI
3w'u
L\4 A
1t^,
Trang 9-t, TW t)rk /
Fr!.d-y fr k =)
\, t+ l'- t+f +4 ''o
=c \2ju)
L'd
e t '4- lVt)
€ (ry/^- L
I ?L = 4.,&, Lr'
w
) TX\D ;
5 tt), Lf
) ,1 z,,t
q u',ffi ) v - W ('',Vzra)
IP;i.&or4 ' iHrv,I
lurL-tv'=brv-t_
( *+ V = I
1 u-v=u? *
l-W V P"- {\, cui 'fr Y
$" l,a J /v 47ro +L f @ /*"t ,tv
Uv2 o
+12 4 42
(w {
+-we Lt, kl
L.
QX* Lt -, t, ca)
f
'ab-q4
qu{
e43
_ ,
ry4
6
Trang 10
*:;
uk ro ct* Ac' + Ắú oQ =!dt+c'2
Jl' Ăb-At t)
l Jco
?ti 3
vc) =- t dttult)Y
gbtrl= V"
; t=4 ?) 7
A=? rt)
L u=-s/s r-AIE,i)
e ụo;
A (1,,t7
/+(\ t e (-f ,I)
9,\a4 - ,l t*, B c) " l,c- =
f*: oo
cr.,- AC' ud, cft5r-a| d*e
w
7,
&t' t.I *+z o
í g* )a,'rr- tt -+ =u (14; )
<") l) t =- 'l t ' Lt
(t+)t= L,a
4, h( Lr t-+)'' ;* Bc'=L 'a 1t- b)
'vca\cl
>"b oirYb''
n?:: tt:;-l'^ri ,!rY:j,
.- b= ++B(+,0/
L t=L ] W-L/
fr!rr, 8,Y rct=rt vrI il^ = (0, 9,1
t *hó
,d
ry
tvt
W'"f" a
6 g" + lc 0c- - k' o
-ar ,^f bv X* ir-
[ ,!'rrtzo
,4 + )bzo
(,9)'r/6 ! -6 z'a
J'L =1t"clt^- 8-1V'c=4
LZ.Z ủ e*4 C'-,
Trang 11C'& lv.
b h.'.4,0; A4T.l,4 nrutrN FcFo ryy' ?
A gr-{)
U-z 4-(nor='ulle^4
l/o*r, f W
('
1.,
t3 I
l-'
Iro
Fl
1,,
r
I
)
7
llrl 'lrl
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