iB0 phirt, kh6ng kA thdt giarc phit riA C6u tr.. ViOt phu:o'ng trintr tiOp tuydn cfra ii6 thi 'r'?. , bitit tiep tuydn cht citc truc Cx, Oy iAn luct iai A, B vi.'iani gi6c AOts cAa tai C
Trang 1TRU'CNG EHSP i{A NOI
TF,{{J'ONG T'i{PT', Ct+UVntE - &E{SF
Dtr T'ixx rr+riB4x i{qc n-,AN,i\/ r"iAtof ztlll
1,,10n thi : TGlt Fi
Thd'i gian ldnt bdi iB0 phirt, kh6ng kA thdt giarc phit riA
C6u tr (2,0 di\m )
a\)
uno naili so y: x- - x" + 1 t
f i{hio sd.i sii' bi0n thi6n va vd Cb ihi {'65 ctra hAm s0.
^ ,,,; , ,i i ,; ,, ,,^ , 'A ,A
7 ViOt phu:o'ng trintr tiOp tuydn cfra ii6 thi ('r'? , bitit tiep tuydn cht citc truc Cx, Oy iAn luct iai A, B vi.'iani gi6c AOts cAa tai C
CAu 2 (2,0 aii6nt)
1
L Giai phuong trirrli : Zi-ar,x+ coix =Zsin}x* ;_ .
sin2;<
2, T'irl cAo gi|tri
^ ,t ,, +-.1
LA:i J" \I,t-t
'lrcrn J
Tinh ticir irliAn
Cfiu 4" (1,0 diLm )
Trcirg i<ir*ng gian, cho r,ii;:rh chr5p S.ABCI) ca dA.y AEiCD iA hinh binh h.*.nh, AB : a1D" BC : a"7t
vi d0 di.i cd.c canir bOn bdng aV5 Cpi giao dirlm cira AC vd BD li H T{nh the ilch kiioi cAu ngoai tidp hinh tii'ciiOr"r Si-laB,
C6m 5 (i,0 iiiiru).
Cho cdc sO dLrong a, b, c tir6a rn6n a + b + c: l Chfiirg iniiri"l
cte n cie i,6 sau c6 nghi0nr : j ';
1x' - ittxv:,, -;- 12 = C
1,,["*-.*s;
'tl rl7
!o
-'tl cos3 x cix.
['.t,
i - r_
!c+ab
rX rr cr
J
L
C[r: 5 i.?,G tiie ui)
1 Trcng m6.t piririg Oxy, ciro dud'ng ti'on (C) : x2 + y2 - 5>t'+ 2y r- 6 = 0 vd digri p(i; 3).
Vi6t phuo-rrg'cririh c6c ti€p triy6n FE, PF crlie dLl'dng h:dn (C), vo:i E, F iA c6c ti€p di€in
Tinli cii6n ticii tam giirc FEF
2 Trong khOng giair Cxyz, cho tam giSc ABC vd'i di6rn h{(l; 0; 2) thuQc canir BC, duo.ng ph6n
gi6c ilo:rg g6c B vi dud'ng cao kd til'ctinh A IAn luo-i c6 prru'ong irjnh :
cit: *; :;= =-;-; dz.:
li- = 3: ,
Tinir itiioAng c6ch tir di,5r:r Ir4 d6n dLLdn[ thing AB
CSu ? {},i} cii€rn)
^ ,,
Tlnr so pl-rirc z ci., rricci',rn nho irh,At vd thoa nifin i iz -,i l i- l-11. /-tl.a 'l
'S"cr*0i r v."rPac^,
Hdt
,Dry ki6rc [ri,thi u56" fiigai isoc lfrm ilo{r 5 sd awp'c td cfufi,c vdo ngd3t 7.8/SiI$]
Trang 2*Ap Arq * ?r{AFiG *rarvt arxi g't+ii Bn r,.4,rrr rnrr sc,- mana e*lt
Fv
i^o -i., j^o
-Ndu xo = I ihi phu'ongtrinhti4p tu5,g1.' ), : x =+ O = A =ts (loaj).
)l6u x^ " = 3 =+ r,^ = -; 27 =r r,l:ricng iiinh ' .- ? "." - t,€n -"-;- tuvdli : / : ;r -:- - i tlri,a mAn )
Lj
ir$y ti6p tuy€r-r cAn iim lA : Zix*77y +- 32 = A.
n'l{
0,5#
Phiiorrg trlnh i,E cl-lo tucng duoiig v6i i:t : ta;iy, * coix + taux :
+ t^w; *Zsin1r- -:- = 0 <+ 1
a
t^l.'n- , -,/.-stit/-x r .-"*
bIili,K
sinx
I
it, /"
I
i
I
,{f
;
#"rcF12,t
€" I * 2sin'x -2sin12x= A <'+ I 1- 1 -.ccs2x - * cos-Z)() = 0
k e Z (thda mdn fl"<)
L'acd :<' 10x+!<g ++ i (:i! 9.
Sr-iy ra- hd c6 nghidrr er piluo'ng iiinh x2 - nrx-,& 1- 12:0 c6 ngiri6rr thudc doan i1; 9],
IfX+ t:-.G * 4 cf 1':r L-t.:r.:, *.,-/-a a-:.+r^:-^r- 1 ,3 J^ ^ *,4+i2
#a 1 L-'vx + ','=ri;3] I(hicr6piirontro'thdnh ia-n-,ti -,riz:0 <+ in=
# {dctf 0).
f4 t l')
-+i
Ta.c6iii):13,
rn,
tEli.tt r Jl -i +'/+\=-_-:_ vi fl(i)=0 (*i=r,f; c/1.?\'"- I \Ll t+ _ * \,r _,i.
(3)= + i(',6)=+'sLiyra T= i(t)=rn:r.
Vfly,J5 i-r3 c6 ngiii0in thi T = ,.,-r
=
.f
I {.trcfit
i" t|,0 dia-n\ Floc sinh tii gidi
2 {,1,ft diilm} Vi€t phuo'ng trinh ti5p ruy6n .'
Gii sri'ti6p diOm li ll(x"; y") F:e sd gdc cria ti€p tuyCIn ld i< = y'(xo) = 3xo' -Zxo
Dli AAOB cAn tpi O thi hoEc tiilp tuydn vudng g6c v6'i Cuo'ng thdng y = x hodc vudng g6c v6i
duong.il',ing!:-x.
0,5{}
TI-i1 : Ti€p tuy6n vudng g6c vdi duo'ng thing y = x.
Suy ra k = - ! =+ 3xo2 -Zxo= - 1 Firr-Long trinh niy v6 nghidnr (loai) .
TH2:Ti6ptu),An vu6-og6cvd'iduorgfl:Engy=-:t Suyralt= 1 =+ 3xo2-2x"= 1 o l^o - ' ,
* ?q
:1 ( J,r! di1wtS GiAi phLrong trii.ii"l
n r4
0,50
Trang 3-11 1
-.ui - l^- u ccs'x
/ *-."r1-{ *t,r
TTT
'L di€m)
r\'/
$ sie*'*
1 di6m,\
t], {} Tinh i{ch phdn
^T .1 1-4^ 1: l5-*
Jo coszx
1t
:* I = Jo6 Vtanrx.d(tanx) = T Vtansx
-fI
Ta c6 ASAC vd ASBD ld cdc ram gif"c,cdn n0n SH I (ABCD),
SH2: SD2-Df{2: SA2 -AH2 + DH =AH =i AC: BD =+ T(LgiiicABCD lihinh ch* , :iit.
AC2 : AB2 + BCz : Ba2 ,+ AC = 2atl7, =+ ./ilj = a:12
SIl2 = SA2 - AH? : 3a2 =i SH = ar6.
a (0,50 diiwt)
Do AHAB vudng t4.i H, n€n tAin O c&a m{t cAu ngcai tirip
tri'diQn SI-LAB ld giao di€m cia iruc AHAB v6.i mdi phEng
il'urrg tru'c cira canh Si-l" i lli io 1a c6 :
4 !, 'tz) ,tzJ a.-a27a39Tta3
\/Av.V,-.:-aR.':+-: 3332
61;
VJ
5
{s^\2
i*l
\o/
- _L
-
'i.-e 1-c- '1/1r-a;1r-c; '
v'
&,50
#,58
ut-)it
r lJ"{J
Tn gi*
l-a nA
Turrng tq ta cfing c6 :
ra 0<a,b,c<1.
;-leblatt
\l i"-a-b + ab -r/{r-u){r-i) '
thi6t suy r;
IdU l.
1 c.{-alt
ca
_-+:
b +ca
ca
(1-aX1-c)
\; lT
di€nr'1
Tiieo BET C0si ta co :
i , I
Uorrg ve vor v0 cac bdi tr$n ta Ju'o-c iipcm
{,}"8 di6nz}.
ilui;'ng tron (C) c6 t6:ri i i3; - t ) ttb6n k-Gh
R-Cii sfr lvl(x; y) e (C) sao ciio pM lAtir5ptuy6n Taco prt= (x_ 1; :t _3.)vA ll.A
Khi d6 pfr t tpi e+ (x- i)( <-3)+(y-3Xy + i)=0 ++ x, +,.r, _ ttx_2y =A.
Ta c6 Ir€ phLLoug trilrlr :
a
=u (x'
i3)
A - l.x2
*'yt -oxf Ly-io
-.5:r*
_U
*2x-ar
{*' + y, * sx 4 z.y -,r
't^
={x-3;y+l)
Trang 4o f"t'-yz tx=2y*3 - 6x*Zy*d = 0 * tUOr*Zy_3=O 1x=Zy*3 =) Suy ra phuong irlr:ir duo.ng thEng EF : x_21r_ 3 : 0 Eat E(l; a
"U phrrong irinh liai ridpm
f r
- <
ty=3"t Ya ly=Z-3t,
{.1,8 ffi0nt} Tfrih khoAng cach
-figi Ir4:(;<; y; z) td Ut6'
Goi H Idir''lirgdi€n cfia&'iM'tiri Hthu6c d1,tac6 'ii(2+2t;l
-3i; 1 r-2t), vecio chiphirc.ngc.,ia drlit i(2: -3; Z) vd Mndix * 7; y; z_ Z) Tr) d,6 ra c6 ii6
:
{ i'rV.d = o
jx+l =4Jr4-t
I rr -:- !^l * 'l
/!-I Y /!-I U *- /-
- n,
l"-"-t '
^-^
:-' nen ,48.',sdr=0 cr:(i -2t)_ 2(1_3i)+(_l +2f) =g =+ B(2; i: 1)
vccto chi phuo*g c''ia AB id r 7.1146 = ?29: i; 5) ir6n AB c6 prrruong irinh :
i(hodrrg cdcir iii M d€n dud.irg thirng AB : , - i[B=M.uot']l ^trtn
lx
I
lx
L
d.lia
!],50
{},25
,3r58
i,0#
l|t*;i /sn
{.!,# didm}" Tinl s6 ptruc ,- _
&xetrEj
GiA s# z= x * yi; 1x,l:e nffi
Sui,pu irz-Zl: lt-2-ii <+
Dodd lzl=$3lp :{;A 44,, * r: Gtu+ 5, +1 > i y., p
Biirg thilc;<Ay ia khi