SO GD & DT HA I{OI DE THI THIJDAI HQC LAN ZNAru ZIII.IThoi gian litm bai: 180 phrtt, kh1ng ke thrli giun phcit cli Ciu I.. Tim ciic gi/a tri cira tham so m dii cfuLong ihing td: I=x+2mca
Trang 1SO GD & DT HA I{OI DE THI THIJDAI HQC LAN ZNAru ZIII.I
Thoi gian litm bai: 180 phrtt, kh1ng ke thrli giun phcit cli
Ciu I (2,0 itiefl
Cho hhm ro y, =
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i) Khdo sdt su bi€n rhi0n vi v€ d6 rh! crja hiirn sd ( 1).
' 7l Gqi I lh ,eiao di€m cua hai tifm can dd th! hnm s6 (l) Tim ciic gi/a tri cira tham so m dii cfuLong
ihing td): I=x+2mcat dd th! hhm sd (l) taihai di6m A, B phdn bigt Chrmg minh"dng khi cl6
ram .sidc L\B cdn tai I
,?
CAu ll (2,0 tfliml
l)Giiiphun,igtrinh:{tanx+cot2x)sin4x=2(cosx+2).-.
.';
huchphenI=J-sin?.{.e*h*dK-|
:
: m1tphan-e(SBC)u*gT.Xdcdinh tem#tinhbrinkfnhm4tciungbaiti€phinhcht5p$ABC.
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*t.1.,v+ 1): =.? nQrrti€p hinh vu6n-e ABCD, Biii I '
.-hinh tu0ng -.136P
l) Tmng.i.:hdng *s1an Oxlz cho cilc.di€m EtJ: l:0): F(0;f:0) vir Gt0;,g:-2) Vidq,pfriixg rrinh "'
maiphingtPJdiquaoEsaochokhoingcdchtir:cricdi6mF"r'hGnJ5q.ntirphing.(P)bin-.frrhau.,.
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linh $o' hiirl: - L- lim= : .x_+o
J*r+t_t :
Trang 2so Gp & ET HA:NQI
.TRU.OT-G'THP'[ LU.OI{G THE VINH
of rm ruu'o4l Hec lAru r nAm 2077
t) Khno s6t vi Y6 d6 th!hlm s6 t =ffi.
* i4p xi,c d!nh: D = R\{-1 }' :
- Chii, bi6n thi€n: t'=#,), > 0 Vxe D .
lim -+* Iim =€'
Di rhi (C) c6 tiQm cdn dtmg x = -1 vit tiQm c4n ngang v = I
thi€
t
-co
e do thi
t) Gtai ph""Ig tnqh (tan x + coi 2x) sin'lx = Z(cos :t + 2)'
Eiiuki€n: sinlx+0 o *+f
sinx- * to'2k)*ir,-rx = 2(cosx + 2) <+ ++ = Z(cosx + 2) Phuung uinh <+
1-cos r sin 2x sin 2x ecosll=cosx+f <+ 3cos2 x-cosK-3=0
3
€ cos* =i (loa) hoflg cosx=-l €] K=n+kn (kE Z) (thoamdn)
.1'-bie
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I rli€nt
0.15tt
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2) Tim cac gi6 11! cua thgrr,r sii m tI6 dutmg thnng (d): y = x * 2m cit ab th! .' """;"'
Phuong trinh hol,nh d0 graq 6i6rn; xj
=x+2m e g(x) = x2 + 2mx + 2m + 2=0 x+1
Duong thang td): y=xi2m qfi AO rhihhm sO (t) tqi hai di6m A, B phdn bi€t e phuong trinh
gix) =0 c6 i nghiemphanbiet x=-l c+
( Y +Y
-+
rf =-:-rrr
Tac6 I(-l: 1).GsiE ldtrungcti6mcuaABthi l*e =jfl-=-*
= il-(-m+1; m-1)
lYe =*e +2m= m
._+J
Tir ua=(1:1) + IE'u4=0 <+ IErAB <+ ALA'B cdntail'
2) Gi[i bAt ptruung triirh: tog* 11r3 -3x+2)+log*13(i2 +x-2) > 5 '
Bit phuong uinh <+'log,-1(x-l)l(\ +2)+log.*'(x+ 2)(x -1) > 5'
Eiiuki*n: x>l:x=l
Bir phuong uinh <+ log*-1(x 1 1) + log.*2 (x - l) > ? '
1 fli6nt
0.25tI 0.2-i6
0;2Sal r*l
t>0
I ^ (r-l)r Dqr r=log*-1(x+?) = t+l > I e ::f>0 €+
Trang 3llog*-'(x+2t>0
I x>'l: x+z l(x -?)tx + 1,1> ()
fl
;
Tinh tich phAn I = I sin 2.r.e-''ntdx
I
0
D4t t = sinx thi dt = cosxdx vi x=0 =+t =0;
L
?l
Tac6 I =2isinx -sinx - cosxdx = 2 i te-tdt
00
D4t u = t + du = dt vit dv =e-tdt +
t, I
Khi d6 I =:(-te-'il
0
CAU IV
Xdc dinh tim vi tinh bdn kfnh m{t hinh chdp SABC
t:=
Gqi H h 1nm cua d:i-v ABC vd lvl lh trung didm BC Ha {K r Strl + AK I (SBC) ua eK = 9{P
l
0,25d
t1,256
-t
- e-'l i =2(l - -)
loe
r ngoqi Szt
D+t SA =.\ (x> 0) Trong tam siric S{t t111 SH'AII:IK.l]lvI (*)
Thav L\I = tJ3 AI{ = a{3 ' SH =,,1x: -f : S\t ='rl*= - 1- viio (*) tim ra
? ':-^ 3 ' - y'- 3 y +
r-rknh R=SH=T
uJ6
r\-a i
r - -a
m4t cdu ngoar tle
H li tim
0.25d
0.25ii
0.15.I
0.25it
' iir
Cho x lir sii thEc ducrng; Chring'minh r'Ing
ii
,-Bdt ding thiic <+
irrr+ = [*J' Dat >,= i:it= i in udt ding thfrc cin chung minh
uo' thiurh ] rn y' ,l:1 € f (v) = t" 1' - 4:,n 2 6'
I 4 - (v-1)- l0 Vy2l + tiy)d6ngbi$n Vy)l + f(y)>f(l)=O
laCO I (y)= - r 1 J-\ < r\r'lsvrre\vrvr'
Trang 4Ciu VI 2 di6m
t t ,f ,ec Oinn tqa dQ c6c ttinh A vlr C
Do AB di qua M(l : - 2,r nOn AB c6 phuong trinh:
Drrong trirn (C1c6 tim l(2' -l) vir R =Ji
= Ji=dil tr!;=-$la+bl :? a=b = phuongtrinh t- AB: x+Y+l =0
Gla su A(t; - I -t) Tu tl2 =2R2 =4 = (2-i)?'+rz =+
YFtl A(2;-3) = C(2:!t vir B(0; -l) + D(4;'-l)
4 Yiltphurng trinh m4t phing'(P)
Mat phing (P; di qua O n€n c6 phuong trinh Ax + By + C2.10 ' j_
Do (P) qua E(2: l; 0) n€n 2A+B=0 ++ B=-2A = phuqng trinh (P): At=ZAy *cz=Q
Ttu d(F (P)) = d(G (Ptr
Vdy phuong trinh (P):
ax+by-u*26=0
<+ lzal=lcl
:+t=0 (loai) hogc'l=2
-: :-Jsaz + c2 Jsnz + c2
K-Zy *22=A ho{c x -2Y -Zz=O
a2 +b2
I di€m 0,25d
$2,sd
0J5d
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I rti6m
$zsd
025dl
025d
0,2,5aI
1 cti€m
05d
05d
Cdu V,IIa
-.-. -.-Tinh gioi h4n:
Tac6 L= lim(2*2
'x-r0
.- 2*? cosl x - I
lr#
- -r-+o {*? +l -l