TRUC'NG THPTCHUY6N NGUYEN I]UE l.
Trang 1TRUC'NG THPT
CHUY6N
NGUYEN I]UE
l<$ rm rnrl #4r F{qc lAw qrlU i*{HAr mAryr E{gc 201s - z01t
DE THr nrOru' roAN
xmox a,n
Thoi gian liun bdi: 180 phrit, khdng te thO'i gian giao d€
Cf;u tr: (2,8 di€,m) Cho hdm s6 ! : x3 - 3(n +7)x2 + 9x * m , v\i nt Id tham sO thuc.
l Kh6o s6t su bi6n thi6n vd ve AO tni cria hlm sO Aa cho irng voi nt:7.
2 Xic dinh nt dd hem sO Oa cho dat'cuc tri tqi rr,)r? sao c.iro lx, - rrl=2.
C6u X{: (.2,8 dihwe)
1 , Giai phuo'ng trinh:
2 Giai he phuong trinh:
'.'
I + 3 cosr; + cos 2x -2cos3x = 4sin x.sin 2x
f:-ra
].'t * t) + Y- * 1 :J:-r-l'
l.xy +:r +zv =1 (x' Ye R)
Csu EEE: (f,8 di\m) T\tn f :f ox
sinx.sinl
" -t
'
I
\ 4,/
C6u EV: (1,8 di6mc) Cho lang tru tain gi6c ABC.ATBTCT c6 tdt ch cdc canh bAng a g5c tao bdi canh bon rzd md'r phing d6y'oang 300 Flinh chieu H cira didin A tron mat ph&ng (ArBrCi) rhuOc dubng thing 8,C, Tinh thd tich khdi 16ng tru ABC.ATB'C, vd tfnh khoang c6ch gir-r'a hai dubng
thing AA, vlL B,C, theo a.
C6u V: (I,ff dihree) ){et circ sd thqc <lucrng a, b, c th6a mdn didu kiOn a + b +c = 1 Tim gi6 tri
nho nh6t eri.a :
r=
Ciiu VI y2,t) *i6rte'S
1 Trong mat phing v6i h0 toa dd Oxy cho hai duo'ng trdn :
, (lC1): x2 + f .:13 vi (C2): (x : 6)t + y2 :25 cit trirau tai A(Z:3).
Vi€t phuong trinh duo'ng th6ng di qua A va ldn luryt c5t (C'), (Cz) theo irai dAy cung phAn bi6t
c6 dQ ddi bdrrg nhau
2 Trong kh6ng gian vo'i hQ toa dQ Oxyz cho tam giac i,uong cdn ABC c6
A(5 ; 3 ; - 1), C (2 ;3 ; - ilvd B ld ditim nirn tr6n rndt phing co phucng trinh :
-^ -.;
lrm toa do cllern u.
CAU VII Q,A diAwt) Giii phuong trinh :
A (z-tog i-)iogn.3-; l- :- iog, x =l
F{Ct -Thf sinh kltong duqc sw dung tdi !f.€u Cd"n bc coi tlti kltong giai thich gi thenr
{r+-{+-)r:-l
BA : tsC Bi6t
.x+y-z-6=4.
Trang 2TR.IIONG TT{PT
CI{UYEN
NGUYEN HUE
IITI$NG NAX CTTANN rrU rgtl DAI HqC LAN g'rr{I ror{Ar
NAM FIQC 2010 - 20r 1
pg rril nnoN: ToAN KHoI A, ts
t
-6"t +9x_1.
-12"r'f9:3(;r -4x+3)
<0<=l<x<3.
=JX
Y6im=l tac6 y=a
* T4p xiic dinh: D = R
* Su bidn thiOn
n Chidu'bidn thi6n: y',
^ ["r3 laco v'>(l€l ' | , .1
L.^ uo do:
+ Him sd ddng bidn trOn m6i khoing ( ,1)
+ FIdm sd nghich bidn tre-1 khoring- (1, 3),
* Cuc tri: H)m sd dat cuc dai tai x:1 r,b
va (3, + *).
.''''' ''.'''''''''.''.'''''''''' ''''
lcn: Y(1) = 3; dat ti0u
4"25
n ){
n ?5
4,25
o ?5
n ?(
n-1
{1di6m)
(Idrem)
)cr:YG):-1-e Gi6i han: lirn ;r - -co, 'P : +oo
" BAng bidn thiOn:
Ta c6 yl; 3x2 * 6(y+ l)x +- 9,
Him sd dat cuc dai, cuc fid; di ;;, ;;; d,,*""g tii"r, t.= 0; i;";;hie* ;t ra
", , ",
e Ft xt -21nt+1)x+3:0 c6 hai nghi€m phin biOt ld x1, x2
l-'uT
.2 1\,= (m+ l)t - 3 > o +> | r/? > -r -f {r
(l) 1,, < -l -",,5
V, - *rl = 2 e (x, +x, )' - 4r,r, - 4 e 4(m +t)' -12 = +
T
a(nt+l)2: ,ol'n=-'
q2s
Trang 30 ?5
0,25
o)s
0 )s
0.25
n ?s
4,25
4,25
0.2 5
o ?i
4.25
o " ) ?5
<> 1 + 3cosx+ cos 2x *2cos(2r+ x) = 4sinx.sin2x
1 + 3cosx+ cos 2x - Z(cos x.cos 2r - sin x.sin 2x) =4sinx.sin 2x
| + 3 co_s:r r, 9os2x _ 2cpS,r : 0.<+^ ] + c,os x + c_os 2:: =
-0
fcos": o
2costr+cos.t-0e I I
I cosx = l2
P'f
[-_, ,
{-t-1-l/-l
Suv - ra I
[-r *.v -4 VO'i , i y -t thay vdo t2) duqc - r l- 2), =A
Tiry dusc (x;;r) : (1;0); (x,y-) : ( 1;7)
Vcvi :r * y = -{ thay vdo (2) duo'c -),2
*3),-Irhuong trinh ver nghi0m
H€ c6 2 nghiim (x;y) : (1;0); (x,),) : (-1,2)
f
l/T lx:-*Kn
lr
I "r': + + K2tr
L3
(t^)^t
lt'' +2x +J'-+ f =J- ")tl lr,'-+)'l'rJ' +2.rt.v =3 (l)
CQng (1) vd (2) theo vC duoc (;,: + -1,12 + 3("r r-.1') - 4 : 0
II-1
(1 tli6m)
{H
(1 eli6m)
f cot-r l
I .l / .ci^' 7T\ : Jt I
srnxsrnl"*,
J
cot -x
s inx (s inx + cos x)
dx
sin2x(1+cotx) r:rCotx+l-l
cot-r+1
gifra AA, r')r (A,B,C,), theo giA thiet thi gdc
AB
J7 (-
"ot :r + ln lcot x + rl) +C
Do AH L(A.B.C,) nOn g5c A,4,H llgdc
AA.H bang 30('.
EI-?
{n diem}
IV
Trang 4X6t tam gi6c vuOng AHArc6 AA, = a, g6c AA.H =30" =
'ABL,l,B,cr-3tttt"uA,Br, -tt 4 - U
AH:!
2
0 ?5
Xdt tam gi6c vuOng AHAr cd AA, = a, g6c AA,H=300 -> AtH :+ Do tam gi6c
ArBrCr l) tam gir4c ddu canh a, H thu6c B,C, r'd
Matkh6c AH J B,C, nen B{'t J (,4Afi)
I^'
AtI{ ,) :$ nen A,H vudng g6c v6i 8,C,
K6 du'dng cao HK- cfra tam g-1;l-c_ AA,H thi FIK cliinli ld khoing cdch gifr'a AA, rlh ts,C,
A, H.AH orll
Ta c6 AAI.HK = ATH.AH -) HK - "'' 1A, :
4
nhdn c6 :
(t +a)](t + c)
- ab)(r - bc)(t
_(r
'.; cQn
)
;il;g bi"h
.(
a-p) -l 'i.
At afig B
1-ab>7-(abc)2 trung binh
[(t + a)+
- ro)
015
0 ?5
gva {z+a+u)(z*o*h}
TuongtU c6: 1-bc>@
2.
(1 di6ma)
n
, ('1")J(!:Xl:b)
Suy ra
H,ra:
Goi giao di€m thri'hai cira duong thing tirn vdi (Cr) vd (Cz) 16n luot id M vd N
Ggi I\{(x: V)e (C,) = "'*-y2 :l j (1)
vi A le truns di6* ;d ffi;d N(4:;; 6 : tj
DoN e (Cr)+(2+ x)2 +(6-),)2:25 (2)
( z 2 ,^
lx +V :lJ
Tn(l)ra(2)tacohd I "
'ftz*x)2+(6-1'l:=25
Giai heladuoc(x:l:y:3)(loai vi trungA)va(x= ; ,V:] f Val M1
-555
oucms thilg.in rir" oi q;; A id M io pn".ig rrinrr : i - iy I i-: a
0 ?5
0 ?5
0?5
vr- 1
(1 tli6m)
6
^:)5
Trang 5AC : 3J2 suy ra BA: BC: 3
n ?q
a)5
0 75
0 ?5
o ?5
o ?{
4,25
+(2* x)2
tqidoBi['gt'i6-.iiinepii,,*'eiiilil'. [{"-s)' + (y -3)2 +(z+l)2 = 9
lfr -r>' + (.y -3\2 + (z + 4)2 = e
f"*, -z-6:0
[r"-sl;i6_i;l; ir,i i; =s '[r" -s;;;a;-;;;'
l,.l
':, ::"
VII.
(1 tli6m)