pgAN cHUNG cHo r{r cA cAc rHi srNH T iridm CAu I.. Hay tf.nh thd tich c'ia khoi chdp dd chc... Hoc sinh tU li'rn z.
Trang 1DAI Hoc su PHAIv{ riA NOt nE fm THU DAI HOC z0l0-201r (LAN r) rm/ouc rHpr NGU-yeN rar rliANH b,{oN TOAN'_ KHdI A
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(lg? phfir, kh1ng ke thai gian pk6t d€i
I pgAN cHUNG cHo r{r cA cAc rHi srNH (T iridm)
CAu I 12 diiim) Cho him sd -22u = 1.t' - 3-.' + I
1 Khio sdt vd v€ dd thi (C) cria hdm s6
2 Tim hodnh do cdc didm A thuOc (C) dd tidp tuy€h cria dd thi (C) tai A giao v6i (C) tai 3 didm ph0n biet
fr (2 ilid@ l Giai phuong trinh :
*.r* = 8cosx.
2 Giaib{t phuong trinh: (0,25){-,' > (0,125):(zl'-rl-'}
CAu ffi (I ilidr4 Cho hinh ch6p trl gidc S.ABCD, hai rnit ch6o (SAC) r,i (SBD) cilng vu6ng gdc
vdi ddy, ddy ABCD la hinh chfr nhAt c5 AB = o, BC = oJJ, didm I thu6c canh ben SC sao cho
sI :2c{ vi th6a man Al l- sc Hay tf.nh thd tich c'ia khoi chdp dd chc
Cdu IV (2 ilidm)l Tim nguy€n him t - = J [ ]e sin 2x + 4sinx
2.Haisdduong;r,ythayd<iith6amSn x+2y-r-v:0,h6ytimgi6trinh6nhatcliabiduthrlc
P: ot * !' 4+8y 1+ "r
il'PHAN nfSNC {3 didm) Tht sinh cht iluoc ldm mot trongftai phdn Qth,6n A hodc B)
A" T'heo chuong trinh Chudn
C&u V"a (2 didm) 1 Trong mat phang tga d0 Oxy, cho tam gii{c ABC, bidt toa do didm A(1;-3),
phuctng trinh ducnig cao h4 t& B vi trung tuydn qua C ldn iuot ld
(d):2x + 5y -21 = A, {d'};2x - 7y +8 =0 Hdy tim tga dQ hai dinh B vi C
2 Trong khdng gian toa d0 Oxyz, cho tam gir{c ABC v6i A(- 1;l;2), 8(6; l; zl), C(t; l; -1) Hay lQp phucnrg trinh mlt cdu (S) c6 tdm I, bdn kinh bang 3 vi tiep xric v6i mat phing (ABC) tai C Ddng
thbi tinh rhd dch khdi tf dien IABC
CAu VI.a (1 didrnlTm rn dd phudng irinh sau c6 nghiOm r e [-t; t0]
1+ 1og, {*t + l) - log, (x2 + 4x+ rn) = g
-B Theo chucmg trinh NAng cao
CAu V.b (2 di€d 1 Trong mat phang toa dO Oxy, cho tam gidc ABC, bidt duong thing AB, AC ldn
luot c6 phuong trinh ld (d): 8x+ 3y +l = 0, {d'): 2x - y-5 =0 vd X};l) ld trung didm cria canh BC Hdy vidt phuong trinh ducrng thing tsC vd rinh di0n tich tam girdc ABC
2 Trongkh0nggian toad0oxyz,chomatcdu (s): xt + y'+zt -zx+4y+Zz+2 =0 r'ihai
didm A( 2;a;3), ry- 2;a;-1) Hey tim ioa d6 tidp didm M cria mar phing (p) di qua A, B vi riep xric v6i mdt cdu (S)
CAu VI.b (ldiim)Giii phucrng rrinh (x+2) logl{-r+l)+ 4{x+i)log.(x+t)-16 = 0
Het -Thi sinh khong duo'c sft dung tdi li|u.
Ho r,i tcn hoc sinh:
Trang 2Ciu 1:
1 Hoc sinh tU li'rn
z x6t di6m A I 1
Lu';"
tii5p tryi5n qua A: d : y: (zo'-eo|r-o)+lon /\t22 -lo'+l
giao di€m gifra (C) vir ti6p tuy6n qua A li nghiQm cia phuong tlinh
L*o -3*, *I:Qo' -oo\r-a) *Loo'-3o'*|t*l
E6 cho c6 3 giao cli6m thi (*) phii c6 3 nghiQm phdn biQt
(*) € G-u)t (*'+ Zax+3*-6F0
I L'f(x): a' -(3a'-6) > 0
I -Ji.o.Ji
t aa r^+l
I
Cflu 2:
1 DK x+t?}tez)
2
(PT) () 6cosx*sinx:8cos2xsinx<>J3"o*t+sinx:8sinr-8sin3-r
(} J3"o.o-" : 2sin3x o *io[i-r]:rir3t
[3 )
do o<l<t)
-
-r,'*i) (c)
<+ ,x:L+k,, (kez) (t/m ilk)
|
-'u*ou 122 2.Dk x2 -2x>*ae
ual
tBpr)€ (;)'* =[;)"''-'r-') <+
'{IE<zF-rl-THI {) r> 2=2,{r'-2v <2(x-l)- toJ:l -2r.*
f x>2 f x<0
(+ r,, -2,<2-3x " t fii!e_3,I
r(
-2
(lu6n el""g)
+ T$p nghi€m 5-(-o;o].-,{2}
Cflu 3:
ACnBC:0 I (SAC)n (SBD):SO
C6 , (SAC)I(ABCD)
(sBD) r-(ABCD)
AC:JBA' * BC' :2a * OA :OC:a
f t rl \
r ,t
F +*l r1
rl
.rl -i'-1
:{+
-f;
fr
**
,t
*
Trang 3DAt SA:h >0 + SC: _.-.-r_^-^SOt + oC2 :lht +a'
Do SI : 2CI + IC : t.sc: 1
33 AAIC rrrdng tai I * AI: ,{AC' 1C' :!
3
c6 2S5a5A[.SC: SO.AC 4116;:17
3
(+ iu +za2lf -35aa:0€ (t, *1"=\lrt -5ot):g
<+ ft: oJ5 ( h>0, t/m h<aJ3s )
Vs^eco:i so.snec*+
,ns"'-t; pr n<a.€5)
CSU 4:
l y:[ 2d'; :[
d-r sin?-d-r+4sin.d-r J sin.r{cos-.:
DAtt:c6x * dt:-sinxdx
*I: -[ d' :[ d'
r (l-r'?Xr+2) J (r? -tXr+2)
LJIaSU_-;= - + - +
-(r'-l)(r+2) t-l r+l t+2
Ddng nh6t thuc ta duo- c t A: I
[ .:-l =
3
-l- ?\ {l:,cos2 x}(cos.r+2)
t't'tB
:,
-8+4t- t+4t 5-5
+ r:.1 [i|-!l!-*!l d, :!
6J t-l 2r t+l 3r t+2 6 "k - { - 1rr,lr + { +1n la + zl+ c
64"osx'+ { +1lol*r* + zl+ C
(x+2y)2
2 Vot x,y )0, d{t e x+2y > 0
Tri gin thii5t: x+2y
-2
{} rci*+r>8 (do t > 0)
I
P: t' *rt: t' *4Y'>
4+8y l+-:r 4+8y 4+4x
Deng thric xdy ra € x4; y:2
Vdv minP : E
)
2
1 Cffu Y.a,
ht +a
h2 +a2
8+4(x+2y)
Trang 4[r: t
* cho n vtcp 4':(0;1 ;O)*(dX y: I +t(r e
[z=-l
f,
Tt gi6 thitit c5 I e d vd IC:3 + I Ir: ::' -3
X6t F3 <+ I(1;4;-1) * (S): 1x-t;2 +1y+;2
Ir5+ r:-?d\ l(1 ).-1\* fS\' fv-l\ 2+(w+)\
/LVLL -Jt'^\rrk) Ltt -\J
2 B(xs;yu) * {: "ol , D _
lhangdiemAB e(d') lLx"+5t,r-21:0
3 {+
Jr.t*r, -7.-3*r', +8=o tBC2;5)
lz2
C6 i.nc :4or : (5;-2) > AC : 5x-21:-1 1 :'0.,
C[n, : 5x- 2-r' - I I : o e c(3;2)
f(d'), 2x -7 Y-Y$:g
ZJ(6t tludmg theng (d) vu6ng g6c voi (ABC) t?i C
ca<-2;0:3)
CB:(5;0;5)
)lpa,cE1:(0;25;0)
v,.or.=
1 IC seec-
| t QIc a; c e|: +( dvtt)
Cflu Vf.a.
DK: x2+4x*mX)
(PT) e5(xt+1;: 12 +4x*m € m:4x2-4x+5
X6t f(x):4x2-4x+5
d€ pt c6 nghiQm xe[-l;10] thi m phii thuQc t+p gi6 tr! cria {x) voi xe[-l;10]
f("): 8x-4; f (x):S {) 1:1
Bang biiin thi€n
l1
Tt BBT * 4s ms365
B CT ne.ng cao
Cf,u Vb.
l.B(xs;ys); C(xc;yc)
Ta c6
ft)j
+(z+1)?:9 2+(z+l'l2:9
Trang 58x" +3_r'o +1=0 2]: t,c -5:0
xu+x _ I *{r(-z;s)
-lrB +_1'a a
2
= l(l;-3)
(d'):2x-7y+$:g
B Tdrn I(1;-2;-1), R:2
in eg1
{ce1a.'; <+
[i iu ,r*g diem BC
*BC:4x+Jy-17:0
A:ABnAC*{4x., +3r', +l =o
L2*.0-r'.r-5=0
M le ti6p di€m gifra (P) r'd (S)
lw.u:a [{*-r)t-.-2)+(-r, +2)t;+(z+l)(z-3):g
) ]w.aE -o <> {-+(*-t)-a(z+t):s
[rn.1s) [fr-rl, +(_i,+ z\2 +(z+t)? :4
laa(t;o;-i)
*l'(;'#,*)
Cffu Vf.b.
DK: x> -l
*80
81
-2
t:
5y-21:0
d(A;BC) :#; BC:J+I * Soec:l4 (dvdt)
2, (S): (x-l)2+(y+2)2 +12+1)' 4
EAt ' {'::*t -., + (u + l) u'+ 4,rro -16:0 {+ (v+4)[(u+1)v-4] :0
[u:logr(x+t) -
\-v*4:0 s log(x+l):-4 o *:-#(ft dk)
(u + 1).v - 4-0 (} v (3"+ 1)==4
OE tfr6y VT la him il0ng bi6n vi cd v:l ld nghiCm
* nghi€m duy nh6t v:l {+ log (x + 1) : 1
C) x:2
vay