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-fRU'oNG rr-rpr EAo ouv rrj un Tnr rgtl D4.I HQC LAN lv (2710212011)
mON roAr'{ Hqc
xHOr a
Tttdi gian lam biti lB{) phitt; khong k€ thdi gian phdt di
PHAN cHUNG cHo rAr ca cAc rni SmH
Ciu I:
mx-4m-r3
Cho hirm'6 Y: x-m
1) Lrhao s5t vir vE d0 thi hdm s0 khi m= 2'
2),chf11;;; ;il;;; ili;
;1 "-ao t i .h'r.'? 1u6n di q"i lT di6m c0 dinh
g6c bang 1,5' Tinir
A va B.
diQn
Tri hai di6m A vi B hdy lap phucmg fiinh cua hai duong thangc6 hQ s6
tich hinh thang gi6i han bdi AB, hai dumrg thdng niry vd trlic Ox'
CAu il;
i; GiAi b6t phuong trinh:
2a{4*1ra <L
x
2) Giai phucrng trinh:
sinox+cosox i ^ 1
5 sin 2x 2 Ssin 2x
Ciu III:
Tinh tich phAn:
ft
? ,. '---rl+cosr
l= lln(l+srnx) &.
'0 'l + cosx 1
CAU IV:
Cho hinh chop S.ABCD, co da,v ABCD lA hinh vu6ng, dulng cao
SA' Gqi M lir trung
rli6m SC; N, P lan luqt nam tr€n SB va SD sao cho
-'^" = = ta, phang GvO-lP) chia hinh
* + 1
3 sB sD
chop thdnh hai ph6n. Tinh ti sO AC tich cuahal pUan dO'
Cfiu V:
Chimg t6 rang vsi mqi 916 ui cua tham s0 m, hQ phuong trinh sau lufin co nghiQm:
l*+*Y+Y=2m+1
i
1xY(x+ !)=m2 +m'
X6c dinh m ae ne cO ngtriem duY nhdt.
pHAN mtNC ( rgi SINH CHi LAIVI MQT TRONG HAI PHAN A HOAC B )

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A. Theo chuong trinh chuAn:
CAuVIa: _ j
' l) Tinh diQn tich tanr gi6c dAu nQi tii5p elip (E), ;+'r- = i. nhan dii5m A (u;2) la dinh
i,ir trpc turig lirm truc ddi xirng.
. ?)Trong kh6ng gian voi h0 uuc tga dQ oxyz, tim ba di6m M, N, P lan lugt thu0c c6c
rJucrng thing: (d,) +1 ='=' =+,
2 -)' "j/
(dr) + =*=+t
2 7 -1'
tor) i2=+=+
sao cho M'
1 i
N. P thang hAng, dOng thoi N lir trung di6m ciia doan flrang MP'
Ciu VII a:
.lnx1
Cho x > 0, x *1. Chimg minh rang:
,_l.G'
B" Theo chucrng trinh ning cao
Ciu VI b:
1) Tinh di€n rich tam gi6c dAu nQi ti0p paraboi (P): 1p
:2x, nhan dinh ctra parabol ldm
mQt dinh vir tryc hoanh Ox ldm trgc ddi ximg.'
2) Trong khOng gian voi h0 truc tga dQOxyz:
a) Tinh khoang crlch gita hai duong thdng:
I x =2-I
(o,l? =+:-i,^ o',
1r-::t*,
r
l.! -
b) Tinh goc gitadudrng therrg (dr)
r' +4 =+=+ -2
|
voi m{tphang (a):x+y-z+Z:0'
Cfru VII b:
Gi6su u1v. Chrmgminhring:u'-3u < v3-3v+4'
---------Gi6m thi coi thi khdng gi6i thich gi th6m-:

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TRCSTqG TEtrT SAG FUV T'EI
T'E{ANG Bstreg s'sgs sg{€t PAH E{Qa E"AN Hv G7
tfiztzw1l}
*Ap AN -
e{0lN , T'o6nu, umoi a
N$i dung cho
^ 2x-5 /--. 1- ,.,- I
m:2:) y=-- -,.) x-2-' Y - (x-2)'= , 0.
Khi
- x-Z "
TiQrn c$n dimg x = 2, tiQm cin ngang y :2'Ei0m dac Uiat ( J;O) ; O;|)
Phucrng hinh: xY - my = rnx - 4m + 3 ching Vre
e (x+ y-4)m+ 3 - xY = 0 dirng v6i Ym +1'
I lr=1
.ltoy-4=0 lx+y-4=o ltr=,
'[3-xY=g otr' -4x+3=o€lJ"=''
O<
LL'''=t
cO dinh lA A (1; 3); B (3; 1
- Phuong trinh dudng thing qua A c6 hg s0 g6c
t
i
-3 = 1G -l) e y - :x *;. (d t)
r =1r+1. rcrt
2-"' 2 2
- Fhuong trinh clubng thdng qua B c6 h0 sA gOc 1b
ld c
Orl- Giao diAm ciia (d1) vdi ox
(-1 ; 0), cria
y + =){r- 3) <+ , =1* -f,.
(d2) vdi ox ld D (1;o).
J
cao cta hinh thang
Khoang c6ch gita (d1), (d2) cfing ohinh ld chiAu

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Vpy, diQn tich hinh thang Phf,i tim li:
4n;5 20
5 =(AC +BDt=(Ji3.*'#= -.{lJ.=-=-'
3 J13 3
..:-
2
BiiII/I
1
1 Xdt hai trudrng hgP:
2a"[j; aaa <2x e
{zx-z> o
J1x' +x+4 <2x-2o l-r"'+x+4 > o I
0.5
f-:"t * x+4<(7x-2)'z=4x2 -Bx+4
(4
i"t
t4 lt'''=, is 4 .-..s 4
o1-1{x{; *1 s' o1.,=; (v t<1e27<28:duns-)
IJC>-
fzr'-0" r o lz
ong duong v6i:
2a'[4; a xa > 2x a't4r' + x + 4 > 2x -2'
0.5
Nh$n xdt rAng khi x < 0 thi 2x-2 < 0 n6n b6t phuortg toinh trOn sE tiring khi
-3x' + x+ 4>-0 <+ -1 = t 11.Vi
a
x < 0 :> -1 < x < 0'
J
r 0. (*). Vcyi tfi6u kiQn ndy, phucrng trinh ffiong ouong vo.t
bieu kign sin2x
l-2sin2xcos'x I coszx-l1€' ---2x - 5 coslx + I = o'
- o
< - '- cos'
=
z-""''" I 4
a
-sl"orzr=21lopi1 i
,-'l
o z
,nuu mdn (*) vi sin2x : xf * o 'l
f'orr' 1,
=
CAU
HI

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r = [t [(1 + cos x; in(l + s inx) - lrr(l + cos;r][dx
: .lo ",..
{i nrt+ s inx)d;r * [i ror r ln(l + sinx)d;c -
' Jo --"'- ""- / -:i- [i
Jo
fn(f + cos x)dx. Chri y ring nrSu
lr
AaTt:--x
'2
^Toro'no m{l + s inx)dx'
trri
fi lnlr + cos x)d:r = Ii t, + sin l)(-)dr = f
m{t + sin t)dt =
f
Y 4y, I= j'u lntr * lin*Vt' D?t t : l+5inx, ta c6:
"out
ln(l + s inx)dx = J tn{t + s inx).
Jcosx
d(l+sinx) :
llntdt = tlnt -t +c= (1 + sinx)ln(l+ s inx) - (1 + sinx) +c.
JJt =lnt.t - l r.L.a,
l+
:> I : (l+sinx)ln(l+sinx)-lsinxl =21n2-1.
t'
BAi XV
Gqi ffiacdi6md6i ximg cria C qua B vd qua D.
S
C
0r5
F
LEFC +A le trung ctiam cria EF*(MNP) di qua A. Theo da bdi' ta ph6i tinh ti 005
T/
-A
JU ' SAPMN
Vrou.,

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.fac6: v"".," s,4.si/.sP 22 4 l/,u*u 2
/sANp
!auv' =Dtar)iv'Di ::-a-'3'sANl' -1.
/rnr,r- sl.sB.st 3'3 9 vrro,,,, 9
11) ')
=-,-.-
323
=
I
---Vrrr,, =l-Vrnrr,
- '- Vr^rr,, 9 Vrnur o -
Vdy, ti sO hai phdn trOn vd duOi bane j
(x=l'
-
DE th6y: ]- Id nghipnn cfia hQ v6iYm. Ngodi ra n6u (xo; Yo) 1d nghigm
ly =m
duy nhSt thi m =
cria hQ thi (ys; x6) ctng ld nghiQrn cria h6. vfly, da hQ c6 nghiQm
CAU
Vla
gi6c
Ggi B, C ld hai dinh cdn lai crla tam gi6c dAu thi B ( -m; n)' C (m; n)' Tam
ABC dAu nQi ti6p elip (E) khi vd chi khi:
l*' *!'
i16 4 =l ^ €j lntz
+4n' =16
l'- :
l4nt' nt'+n'-4n +4 l3m'=n'-4n+4
Tri he tr€n tim du-o.c : ,=-3 (n:2lopi vi A= B =C), tt d6 nz=J€ no*
16.,8 o -,"-^rr#-76BJt
(dl) c6 tqa d0 M (a+l ; 2"+2'-2"), N (2b+2 ; 2b ; -b+1), P (2c ; c ; c+l )'
Gii sir M thudc
Ba di6m M, N, P thing hdng khi m cing phucrng vot MP. Sir dgng gin thi5t N ld
11
trung diiim MP, tatim dugc M ( -14 ; -28 ; 30 ) ; N (-17 ; -1s ; ?) ;
'?," P ( -20 ; -10 ; -9 )'
X6t trudng hqp:
") x> 1: Bdtphuongtrinh ban dAu <+ fnt'f e f @)=lnx-Jx*f 'O'
(")
Ta c5: -f
I
'(x)=t--^---v
1 I -i=---------7-'
z zJi-x-r
x'/Jx 2 ZxJx
Theob6tdingthr?ccdsi: x+ i.>zJ;=.f '(x)<0 khix> 1'
: ) :) Bat d$ng thirc (*)
f(x) nghfch biiin trom [r;+o) + f(x) < f(1) 0 khi x 1

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*) 0 . x < 1: Bdt ddng thftc ban ddu
<> rnx ,#.e f (x):lnx-G*;;'0. (**)
Gi6ng tr6n ta c6 f '(x) =
2",[i -x-1 < 0 + Hdm s6 nghleh biiln tr6n ( o; 1):'
f(x) > f(l): 0:) eat dang th{rc (8+) tl6ng"
Cdu 2,0S
vIb
@ (n r 0 ) ld hai dinh con l4i cria tarngtilc otsc. Khi d6
tam gibcoBC d6u nQi ti6p (p) e tiuo'c ffi : 5, n : 2J1. I,00
I
It:. r::;:;rrim
T* d6 Soec: nJ.
Kho6ng c6ch gifra dr vd dz O** Gqi q ld goc gita d3 vi m$t phang @) ta
# 1,S0
2
t;
v/
co Slnq= .
3
C6u I,0s
vHb
Xdt hem s6 f(x): x'- 3x. :> f(x) =3x'- 3:0 € +1.
,.t
I a co bang Dlen mlen:
@,25
,f'{" +
----"+
Xetba trulng hgp:
*)u<-l
*v <-1.
-Vihdmf(x)ldd6ngbi6nh6n [-oo;-1) n6nf(u) <"f (v)'f(v) 14:] ut-3u'
'l^
v--Jv+4. U,75
*v>-1.
- Vi hdm f(x) c6 mQt cpe hi duy ntr6t tai x : I ndn: (v) > f (l) = -2, (u) < f (-1)
-L.
:>(u)-(v)<2-(-21:4.
*)-1.u(1:>v>-1.
5

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Vi hdm f(x) nghich bi*5n h6n [_t;t] nen f(u) . f (-1) :2' Ngodi ra tr6n khoang
(-1;+*) hdm sO c6 mQt cuc tri duy nh6t tai x : I ndn f(v) > f(1) : -2' VAy f(u) -
f(v)<2-{-21=4.
*) u >l=v>1.
-.Vi hdm f(x) d6ng bitfn fr€n [1;**; ndnrf(u) < f(v) + 4. =] u3 - 3u . o3 - 3v + 4.
,Ju,-JSr;: VrX f/"e;