\ TRTIONG THPT r,A XOay On rHr CnUyfN DE LOp rr r,AN 1
y6n: Torln- ruiii O
hoi gian: 180'(khdng kC thcri gian giao <IA)
Ciu Ị Cho b6t phucng trinh: J *2 - J
" I , r* -rr[;J + *
1 Ciai b6t phuong trinh vcri m:-2
2 fimm AC U6t phucmg trinh da cho c6 nghi6m
,
1 Giai phucrng trinh: 4cosr.ror[1-r).^"[I*r)-+"ọzx+3cosx-4 = 0 I
[3 / 3 )
lx' + x+3y =9
)
3 Tfnh gioi han sau: A = lim x' + sin(x - 1) - 1
x-+l 4lx -I
4 Tinh gi6 tri biCu thuc: A= 4Cloơ8c,fu +l2Cfoợ +200c,1jj.
Ciu IIỊ
Trong mat phang voi h0 toa dQ Oxy cho Elip (E) c6 ti6u diOm thri nhdt h F1(3;0) vd di qua di6m t[t'+)
"* xic itlnh chu vi cria hinh chfr nh6t co s6 cria Elip{E). i
t
Cho hinh ch6p S.ABC diy ld tam giric rl6u c$h alt, SA: 2avdSA vu6ng g6c voi m{t
dey (ABC) Gqi I td trung di6m cira BC
1 chrmg minh rnng mat phang (sAD vu6ng g6c v6i mat phrng (sBC).
2- Gqi G ld trgng tAm cria tam giiic d6u ABC Tfnh khoang c6ch tir G dtin mat ph6ng (SBC)
CAU V
Cho a,b,c > 0: abc = l Chring minh rdng:
lll
a+b+l - b-+c+l -.;;= '
Trang 2N6i du Gi6i bdt phucrng trinh vli m:-2
Ei6u kiQn: -r > z
t = J a a2 - J -zUatphucrng trinh c6 dpng:
t'-t+m<0(2)
Khi m:-2, ta c6: t2 -t -2 < 0 e -l <t <2 e t <2
l;.2-J.-2<2e x>2
trinh c6 nghiQm x,> Z
Tim m OC U6t phuong trinh d6 cho c6 nghiQm.
Bdt phuong trinh dd cho c6 nghiQm khi b
th6a mdn: 0 <t <2 .
Xdt hem sO f(t)=t2 -t,v t e(0;2)
2
(0
'1 ,4
0.25
0.25
4 cos3 x - 3 cos x - 4(2 cosz -r - 1) + 3 cos x - 4 = 0 <> 4 cosz x(cosx-2)={ <+ cos*=0
V4y phuong trinh c6 nghiQm
^ f(f - x)(zx +3y) = 14
Lt'-" +2x+3y =)
x'-x=7
2x+3y =)
x'-x=2
2x+3y =7
Vfly h0 phucmg trinh c6 nghi6m:
(*; v)= (-r; :), (2 rr,(*P, =#),
Trang 3Ciu Y NQi dung Di6m
Ta c6:(1+x)'oo = C$o +C,toox+ C?rr*' + +C]jfx'oo (l)
(t-r)'o = c$o -c]oox+ cr'oo*' -clor*t + +cfifx'oo (2) Ley Q)+Q) ta dusc:
(t + r)'oo + (1 - r)'oo :2clro +2clorx2 +2cl*xa + + 2clff xr00
L6y dao hdm hai v6 theo 6n x ta dugc
1 00 (1 * r)nn - 1 00 (1 - r)nn = 4Clrox+ 8C$ox3 + + 200C]ffx"
Thay x:l vdo
:) A =100.2ee = 4Cr'ro+ 8C,fo + + 200clff
0r25
0r25
0,25
0,25
-4 = lim
x-+1
x2 +sin(x-1)-l
= lim ("'-t)G[? +G +t)
?,1;
-r)Gl7 +.8 + 1)
+ lim _ 1 x_+r
A= lr (*' -r)(tr[P+J7+1) ^
r-=
, ,,^(llxt +Jx +l)sin(x-l)
rtth' x->l
.4 = lim
x >l
x-1
G +r)6,[7 + rE + 1)
x-+I x-l
^ t .-(11 x' + Jx + l)sin(x - I)
0.25
0.5
0.25
Gia sft FrC3;0) ,vi 2 tiou di6m cria Elip il6i ximg nhau qua g5c at d0 ncn ticu"d
cdn l4i c6 tga d0 Fz(3;0) Theo dinh nghia cria Elip tac6: MF, + MF2:2a:10;h6n a:S
Ta c6: b2: t c2 : 14,viiyb:4.
Chu vi cua hinh cht nh{t co sd cria Elip: C:2(2a+2b):f6 .
l.Ta c6 BC r SA, BC l_ AI n6n BC r (SAI)
vay (sAI) r (SBC).
2.Ha AH vudng g6c vdi SI suy ra AH .J- (SBC)
Ta c6: d(G;(SBC)) =1 33 af er(sBc)) =? ou
111146
- -: -;-r -; g .,l,r,Ia = _Lt
AH2 SAz' AI2 -
4a2' go, n n"'
5 YQy d(G;(sBQ) =la
5
0.5
0.5
0.5 0.5
0.5
0.5
Trang 4IV 1.0
Ta c6:
a * b = (.,6 V6XJT - V.b {6t)
+ a+b+r > 16(16.Vb)+r = r6b(16.Vo)*iffi = #o(16*Vb *16)
.l_{6f
Tucrnstutac6: 1
=4 =_8 _
!:' !s vv'
b+c+1 - {E($*Vu.S) - 1,1;*Vu *i6
rlvb c+a+l=6=6;6m
Cgtre v6 vdi vti ta suy ra dugc dpcm
Ddu bdng s6y ra khi a:b:c:l
0.25
0.25
0.25
0.2s -H
I
,I
I