on rru rm rutlD4r HQC- IAN rvuON: roAN- BAN KHoA Ho.. Xdc ttinh m Oe ninn phing gidi han bdi C vi tryc hoanh c6 diEn tich phdn phfa tr€n vd phia dudi tryc hodnh bing nhau.
Trang 1on rru rm rutlD4r HQC- IAN rv
uON: roAN- BAN KHoA Ho c ryNnrcN
Thdigian: I80phfit Cdu l:
Cho hdm s5 y = xo -4x2 +m+2 (1)
l Kh6o srlt sg biiln thi€n vd vE AO tni (C) cua hdm sO (l) vdi m : 1.
2 Giast (C) cft Ox tai 4 di€m phen bi$t Xdc ttinh m Oe ninn phing gidi han
bdi (C) vi tryc hoanh c6 diEn tich phdn phfa tr€n vd phia dudi tryc hodnh
bing nhau
Cf,u 2:
l Giei phuong trinh: Q+c?tzx, -z- -+=ry.
tan x ' sint x cos" .r 9
2 Giaib6t phuong trinh: l' +.F+o > Jt'*' *" u.t' *12 .
Ciu 3: Cho hinh hQp dung ABCD.A'B'C'D' c6 <t6y li hinh thoi c4nh a, g6c AEc =60' G6c gita m{t phang (A'BD) vi mit phing elSy bing 60" Tinh theo a khoang cdch gifa tlulng thlog CD' vd mflt phAng (A'BD).
C0u 4:
TRrtoNG THPT r,E xoey
Niim hgc 2010-2011
1 Tinh tich phdn I = x.dx
!t7 -;;4
2 Cho x,y e R,x> 0 Tim gi6 tri lun nh6t cta biiiu thtic:
Jz
I
(xz +3y2)(x*JV *Wl
Ciu 5:
1 Trong m{t phAng v6i h€ trgc to4 dQ Oxy, cho tam gi6c ABC vu6ng t4i A Hai <liOrn A,B thuQc Ox Phuong trinh cgnh BC.ld: 4x + 3y - 16 : 0 Xric
<linh toa dQ trqng tem G cria tam gi6c ABC, bi€t b6n kinh itulng tron n$i titip tam gi6c ABC b6ng I ?
(x+l)2 +{y-t)2 +(z+l)2 =25 Lap phumg trinh ti+5p tuyiSn vdi m{t cdu bi€t titip tuyiin qua A(4; 0; 0) vi vuOng goc v6i Ox.
Cf,u 6:
Tim sd phrrc zbi€xl{=l vi rr 5 m$t acgum€n v grta -3-Mr( -1+i l-?J' 5'r)
Hg
Trang 2,f
st mrr rrtrlDAtrrgc - r.*N'rv
MON: rorix- BAI\I KHoA Hgc rf nmtx
Vdim = 1 Hfoir s6 tra.dranli y = x' - 4x2 +3 TXE: R
XCt sybitin thi€n:
lim u=+o: lirn v-+@
t-#t
'x-+<-y'= 4x3 -8x
lx=0 v'=0<)l
-' l, =+J2
Hnm s0 d6ng bi6n tcn {-f;0)v,i(J2;+"o)
Hnm s6 nghich bi6n tr€n ("*;-Ji)ua(o;f)
Hem S detctrc d4i ter.x = 0 -> lcs =3 Him s6 datcuc ti6u tdi "x = +Ji 4 l* ='l bi6n*riOn:
D6 thi:
Dths citOy tei di6m A(B 3) vnnhsn Oy hm trrrc d6i
xrmg-0,25
0,25
+-
+0-Xdt pt h"Atth tlQ grao tli€m crla (C) ve O:: xo'4x2 + m+2 = 0(2) (2) c6 4 ngliQrn phdn bi$t
o(=) pt t2 -4t +m+2= 0c6 2 nghiQm phin biQt duong
Trang 3o firo -4x2 +m+2)dr=A
0
cr 3Da -20b2 +6(m+ 2) = 913;
Me b h nghipm cria (2) n€n ba -4b2 + n+2=0(4)
1,, lo
lo =T
ru (3) vn (4)=+ 1 ,
l^ = ie(1;z>
f a'=4-m-z>o
I
<+{S=2>A e-2<m<2
lr=n+z>a
Ggi cto nghi$m cua (2).ln +a vi +b (0 < b.< a)
Do tinh tldi xfrng cria tl3 thi qua Oy r€n de tho6 m6n ycbt thi:
Jtr' - 4xz + m+Zft= -ttr' -4xz +m+z)&
Dap s6 * =?.
0,25
0,25
0,25
0.2s
2.1
lil Dk: Phuons sin2x trlnh: * 0 <> | 'cos2x.cosx\21160 1a-
L-*-\ sin 2x.sin.r ,/ sin' x cos' r 9
cosr 2 | 160
f 2sin2.r.cos.r'sin2x' cosox - g
ll160
A ' -f-=-sinlx costr 9
l-2sin2.r.cost.r 160
A-(sin x.cosx)" 9
D$t (sinx.cosx)z = r(r > 0)
Ta tlugc:
l-2t 160
-=- el60t2 t2g + l8r -9 = 0
<+ (l6r * 3Xl0r + 3) = 0
0,25
0,25
3
e.t=-l6
Vgy (sin-r.cosx)2 = 't6 3 o 4srn2 2x =3
e sin2r = tf
2
frkr
e -f, =
+-+-62
0,25
0,25
Trang 4Bpt c{ nglria v6i mqi x
3ts,:e3'"${o >Jmi,3-fr
DAt: 3' = *ali *6 = v ta duqc:
lu+v> 0
fr*u >mzr'
{u+v>0
[(u -v)' < o
:+ 3' = .,ffi € 32' 3' -6= 0 :+ (3' - 3X3' +T) = 0
0,25
'0,?5
0,25
0,25
0,25
0,25 0,25
mEiaAi€t'=> aABC.dou o4nh a
-> r.{,C = a
+ Gqi O ld giao'cua AC vi BD
BD - (ABCD) n@ nDl|
+ A()A' * 6ae.QDoA'eo =90")
CD' lt A'B + d(CD';Qt BD))
+
= d(C;(A' BD]I' =11tr;(A' BD.})'
(vi AO * CO) '
+ lrtrl: J{H vudng 96o v6i A'O (1)
c6
AA'L BD\+
BD L AH (z)
AO t BD)
Tir(il) v$ (2) a AE L(A'BD',
v0y:
d(CD";(A'BD)) = AII: AO-sin AOH
a "Ji "Jj
= jsrnou"=
Z.T=T
4,25
0,25 0,25
0,25
D$ t =\[7a 4 f = x' -l> t-dt = x&
t}OI CAn:
xlll.D
t l0l1
,:1sff*.='!;Hr;J[*-*]
= i[U' -rl-]rnpr tt) t; = ](t"t-Jr"o)
a I.I*L
I
!v'-z*qJx'-t
Trang 5!t= ry'
(xz +3y.\x*Jffi/y
Xdt y=0=>M=0
Xdt y *0+M =ry'U-Jxz +t2y2)
-(rTtryit} =
EItr=4nui(t>0)
M=f(t)=#
f'(t) = 2-t +z.rlt+t
6(t +4)2.J1+t
f'(t)=0<+r=8
Bing bi6n thi€n:
=} M dat GTLN ** =* lzy, x' =g c)i fzt'=3r'
[rt0
0,25
0,25
0,25
. ld
Gi& sri: A(a;0)
B e BC :4x +3y- 16 = gJ = rt+'01
la 1l
MBC vu6ngtei A; C e BC +c6;We1
=1b-4y =iv-q{r-+.;)
ela-41= <) la =l
4,25
0,25
4,25
Trang 60,23
a;25
4,25
FF66t(-t; t;-t); bin kinh R = 5
ii6p tuy6na cln cm c6 vtcp il =(a;b"c\;.* 6)
+A IOx o T.T = 0.Voi i = (l$;O}'= a = 0
+ U(5;-l|);u(0,b,c)
t- -l
V4,;l=(-c -b.-sc.sb)
+ I tifu xuc (S) <=> d(Ii A) = R
lF,;l
(+3=)
lrl
V$y A c6 pf:
b2
s[=
-1*
=4 tl
=*l
+a:
€ ,*l x=
yt
tld)
Gt * z*{{*rr*isine)
+ i =j (."r* -,'in e)= |tead- *t* isin(- p[
c6 -r*,=.tr(rer?.t'*?)
vay:*=#[{-o-f).,'*[
3* 5t
Gt=-e-{=-++2kn
+ e = !+kzn
) 7 =]trorf *i*il
Hay
t.
0,25
0,25
0,25 0,25
6
(1d)