phaic6loi gificlrat ch€.[r]
Trang 1Bii l (2,0 diAm)
+ft-h
l Tim di6u kiqn xiic c1!nh cira bi€u thirc A = Vx + I
l-l-2 Chung niinh ring g = i JZI * ^:-= ld so ngLn Cn.
Bni 2 Q,0 diAm)
cho bi6u thirc: P - *Ji'-s x-4
-1 Rft ggn P.
M6n: TOAN 9
1-lio'igiarr lam bai: 120 phut (khdni4 ke thii giun giuo di)
-t_.F vo'i x > 0 x+ 4.
lt't - 1)x -l
1 Tim m dC (0,) song sorrg vo'i (ci, ) .
2 Tim m de (d,) cat Ox rr A c5t O), i B (A vir B lihar- O) slo cho AB = 2.,,5.
(d,)'y =(12-5a)x+ a'-zrlil di qua clienr C
Bni 1 (3,0 diim)
Cho dud'ng tron tdm O, di0m S ninr b6n ngodi dr-rc'ng trun Kei chc tiOp tr-ry€n SA SB vo'i dr-ro'ng tron (A B ld ctic ti€p cli6m) Ki dirotrg liinh AOC Ggi l-t la giao cli6m cura SO vir AB.
1 Chimg minh b6n di6m S A O B ciurg tiru6c nr61 tl-rdrg tror-r.
2 Chu'ng minh Fi-A : HB vir tinh d9 ddi AB biOt -!* j== r
SA- AC-'3 Gqi K ld hinli chi6u vu6ng g6c cira B tr0n AC Chimg nrinh tam giirc SA0 dong clqng
vo'i tam gi6c BKC vd SC di clua trr-rrrg di€rl cua BK.
Bri 5 (0,5 diAm)
Tim b0 ba s6 1x y z) tl-roa rrdn:
x+y+z<9
v[- 1 + /"o - z + J;-+ -5r + 4y' + 3z=,\)] + \'z- -r xz t- I I
socrAo DUC VA DAO T4O
THAI EiNF]
- I-tE]'
Trang 2-socno oltc
rHAt
vA DAO T4O
niNH
xHAo sAr cuAr Ltr'oNc ugc xi t NArn HQC 20ie-2020
oAp Aru vA BIEU strnn nrox roAru q
(Gint ()-l tt'tut:<)
1.
(2,0)
I
(1,0)
Bieu thu'c A rAc dlrrh c> x+l>0
4-2x>0
VQy bi6u thfi'c A x6c dinh e -l < x <2 0,25
2
(t,01
B
tI /^:
-= - \/ 1 1
a v-
-J
+ 2- J1
4-3
1-r
= -.JVj
J 2- J1
=.'6* 2- J3 =2
(i ?i
0,2s
Do 2 la so ngtrv0rr n€n ts ii so ttgu; ert () ?5
)
(2,0)
1.
(t,25)
Vo'i x)0; x+4 taco: P= r"(-s
([-r) ,'i ':) 0.2-s
n?5
(ur -:)(Ji r:1
2.r -r 4."-[
(/,,-:)(Jx+:J
z"[("(r z) ) /
Vdy,voi r>0:x+4 tac0 Ii= n C- zv.\
-Vx -l
P = r[+3 c> J
t
f ,( / , 1 ,)1 -
-!.\fJ \.
Pr(z) e zJi = (Ji - z)(Jx +:)
0.2:5
a,25
2.
(0,75)
n a( v,L)
o (*-:J )+(rJ*-u)= 0 r.,/i(rf -:) rz(Ji :
€x=9
l=L)
0,25
0,25
o)5
^.,,(-B-' (."'i-l)' +(."tT :)
(.''T-z)(vT-z)
(i ?5
0,25
ThAyx=9(thoarndrr (l)) Vfly p= fi, 3 3 r=9
Trang 3fJ,25
0.25
l) 15
(dr) i/ (d:) € I
L
) I
<> r'r'r - I V?f iclrtir'1d:.) € ttt - i
2=ttrr+l rn=-l
Itt = i i
m*-l
intt=I
Im +-l
(tlr) cirt ()x tr A € ) : (.1 l'a cti lr i rrr-= () lI
')
V0t' A llt d
2
I
I
,:-/ r
i= oA=l-i / t- l
0.25
(dr) cAt Oy cr B e x:0 Ta c6 y: r'l'r V{r- B(il: rn) ' QB = lrli
0.25
DoA B+O = ln 10 Khi cloapdLrng.linh li llitaqo cho AAOB vttdng dOco
OOi ctri6Lr v6'i didu ki€rt nt I 0 ta co t.tl ='i-ri Val' rri : +4 lri cire giii rli cin tinr
0,25
V6.i m :2ta co (clr): y = 2x +2t (d:): ),:5x - i Hoirrh ci6 giao di6rn Cl ctra(clr) (rL) la nghi|rri ct'irt phLtrini: [t'itrir 1r i] = 5s-l
<+ 3x = I 13 r = I l:flc-cJii -u- = + V+)' C'( l; +)
Do (cl:) rli qua C(l:a) lr6n x = l; y = 4 lit-nghi0rn e Lia (cl;).'l'a c6 pitttotrg trinh
a'-5a+8-2Ja, =0 Dl(XD: a>2
o (u' - 6a +q)- (n -2 - 2'6-I+ r) -0 o (r-i)'-{,"t-i -,) =i,
(0,7 51
<:> a - 3 (thcia Infur cliiLr l<ieirt a ) 2) Viit' a'= -i it\ giii u'i cAn ti,r'
a-3=0
J;-:-r=o
0,5
Vj SA, SB ld hai ti6p tuy6n cua (O)tai ti6p didrl ,4 B
+ SAtoA SB_LoB = ilit = j6b = eo,,
0,5
= A, B nirtt tr€rt cluo'ng trtin clrtorg kinh SO
VAy adi6m S, A, O, [3 cilnglhiroc rtt0t dut)'ng tt'irrt
Ei6m
Bni
(0,7 5 )
0.25
0,25
2.
(t,0)
0,25
0,2s
4.
(3,0) (t,01
Trang 4Bni CAu DAp rin Di6m
2
(t,0)
Vi SA, SB ld hai ti€p tuy6n cua (O) tai ti6p diOni A B = SA = Sl3 vA SO la
+ SO ld duong trung truc cira AB VQy SOf AII tqi l-l va IlA: llll
Xdt ASAO vudng 6' A AH ld dtrd'rig cao dLrng licl tlrirc tt'ong tam gidrc
vu6ngtu.o - f= ='.-' AI.I' SA AO SA =', u-1-= AI'- 1 = All =l
I
Do HA = HB=:-AB = AB=21-lA =2 Va)' AB=2
2
4,25
0,25
0,25
0,75
(1,0)
Tac6 ee I
I,o AC) )) = ABC = 90" => AII I UCI N4l.r SO-L AB
=SOll BC + SOA=BCA=BCK i\45t khiic UKIAU = llK = 90"
Xdt ASA0 vA aBKC co I
I
SAO=BKC =90"
SA AO z\C
= BIi _ 2ClK.S.,,rAL
(l)
0,25
0,25
0,25
CgiN ldgiao cli6nr cua SC vcii BI( Do NI( /i SA (cirng vu0ttg girc viri ACI)
Ap dung h€ qLra dinh lf -falets to .o |\ = !l = p6 = !5!1 (l)
Til' ( l), (2) = BK = 2N K f/ay N ld trLrng cti&l cLra tll(.
0,25
5.
(),5)
0,25
x=ar+l 5,=br+2
)^
7=c-+J
(l)
tr-/
(3)
DKXD: x>l;y>2;z>3 (*)
f', .O n 'l
t
a + b+ c = albl-+ b'ct -r- c'ur'
Phuongtlirrli (l)cr l(a'+b-c:)=1(,,'bt +b u c'ar)
= (a2 * I'ri -cr)t -(r' + [r' +.'' )
€) at +ht +ca +Z(a +b+c)= (at + b' * t)'
\26'i a b, c > 0 Ap dung BDT (AM -CM) ta co:
aJ +)^ = :r4 r- A -r o ) -jVau = 3a'
-qt4(t-q
Tuong tr.r: ba + 2b > 3b2
c'+2c>3c2
0,x
Tir (3) vd (4) ta c6 ddu bdng xty ra:
a.b,c>0
ar+b'+c2=3
^"1 _ ^
a -a v a-b-c- |
b'=b
.l
Trang 5= 3 (thoa rndn ('r');
-1
z-) = l2:.1: .t) lzi bti ba so citt tinr
x=2
Khi do v
Luu y:
- Trdn ctiy Id c6c buo'c giai cu th€ cho tinrg ciiir.-turs i'ri bicir cliernr rLrr.ing [rrrg thi sinh
phaic6loi gificlrat ch€ chinh xac nrtii cOng rrhrin e lro rli.irn
- Thi sinh c6 czich giai khric dfrng cl6n c{.lu clro dient tlri)rih phin cl0n titi
- Bai 4, thf sirrh phtii t,'0 hinh chinh xfc vd nOi dung ehinrg rlinlr pirir hop r.6i hinh vE moi
duo-c cdng nhdn cho di6m
- Di€m toln bii thi lir t6ng ciic cli6m thiurh plran lam tlrrrr tien 0.5tl