1. The document provides information about a math exam, including the duration of 180 minutes. 2. It lists 7 questions on the exam covering topics like functions, derivatives, integrals, geometry, and inequalities. 3. The questions involve solving equations, finding maximum/minimum values, determining tangent lines, proving relationships between angles and lines, and optimizing expressions.

1. c DAI Hec vINH Dt o sAr cnAr tUqrrlc t 6p tz LAN r, NAwI zorr
T c THPT CrrurEX UOX: TOAX; Thdi gian I m bii: 180 phrtt
r. prrn c c cHo rAr cA rff suvn e,o a$m')
7CiuI.(2,04i6m1 Chohdms6 v= !*'-(2**l)x2+(m+2)t..,'+ cOd6th! (C^), m ldthams6.
'3
I . Khio s6t sy bi6n thi€n vi vE dd thi cua ham s5 d[ cho l<hi m = 2 .
2. Gpi A ld grao tti6m crla (C,) vdi trUc tung. Tm m sao cho ti6p tuy6n cua (C.) t1i A tAo vdi hai FUc
tga itQ mQt tam gi6c c6 diQn tfch Ui"g 1.3
yCAu trI" (2,S trfrenre) 1. Giei phuong trinh (x+ 4)' -6 = 13.
2. Gifliphuong tinh (2cosx- l)cotx = -l *
srn.r,
Ciu Itr. (1,0 Ci6m) Tfnh tfch phin / = dx.
Cf,u IV. (f,O ai6m) Cho hinh hQp ABCD.A'B'C'D'c6 ttQ Oai dt ci cdc cenh <tdu Uang a>0 vi
ZBAD=ZDAA'=LA'AB=600. Ggi M,N 6n luqt ld trung ttidm ctra AA',CD. Chfmg minh
MN ll(A'C'D) vi tffi cosin cta g6c t4o bdi hai tludng rhing MN vd B'C.
Clu V. (f,0 tli6m) Cho c6c s5 ttrgc E a, h, c. Tlm grd fri l6n nh6t cua bi6u th{rc
r
FCA
P_
a2 + bz + c2 +l (a'+ lxb + 1)(c + l)
n. G Tht sinh cht ituqc tdm mQt trong hai phdn $hin a, ho{c b)
agn
Cf,u VIa. (2,0 rf6n) 1. Trong mflt g vdi hQ W Ory, cho tti6m MQ;I) vi hai ttudng thing
dr:3x-y-5=0,d2:x+y-4=0. Vi6tphuongtinht6ngqu6tcfia<firdng thing d ttiqua M vdctt
dt, d2lin t4t A, B saocho 2IuIA-3MB =0.
2. Trong kh6ng gian vdi hg fiUc tga tlQ Oxyz, cho c6c di6m A(2;0i;0), H(l; l; l). Vi6t phuong tinh
mflt ph[ng (P) di qt;n A,.F/sao cho (P)
"ii(
q, Oa lhn hqt Cr B, C th6a mfln diQn tich cta tam
gi6c ABC Uing +G.
Clu VIIa. (1,0 di6m) Cho t$p A=10,1,2,3,4,5,,6,7). H6i tU t$p ,qWp tlugc bao nhi€u s5 tp nhiOn
chin gdm 4 cht s5 khdc nhau sao cho m5i s6 iffi ttAu l6n hon 2011.
b. Theo chuolg trlnh Nf,ng cao
Ctu VIb. (2,0 di6n) l. Trong m[t phlng vdi hQ W Ory, cho c6c Adm ;0; 2), B(4;3). Ilm tAa d0 didm
M soeho ZM4B= 1350 vdkhodnecdchtir M dhnttu0nethEne AB hAns
JiO .
gian vdi hQ truc tqa d0 Oryz, cho c6c tti6m C(0; 0; 2), K(6;-3; 0). Vi6t phuong tinh
di qua C, K sao cho (a) cfit Ox, q 4i A, B thlaman th6 tlch cria tf diQn OABC
[3t*'+3' = lo
'lt. 1.,
l;logr x' -logr y = g
lz
I. Brc sd trd bdi vdo alc ngdy 26, 27/03201I. Dd nhdn thrqc bdi thi, tht sinh phdi nQp lqi phiiiu dtt
thi cho BTC.
2. Kj lrhdo sdt chiit ttrong t,in 2 sd duqc t6 chftc vdo chiiu ngdy 16 vd ngdy 17/04/2011. Ddng ki du thi tqi
Vdn phdng Tr THPT ChuyAn t* nSdy 26/03/201 I.
Thi thử Đại học www.toanpt.net

2. DAp AN of IsAo sAr cn,ir LUqNG nfip pLAN 1, NAM zorr
*fON: TOAN; Thiri gian lirm bhiz 180 phrit
Ddn dn
L; (1,0 itiam)
-5x2+ +*+!.a
J
0x+4.
f x <ll2
<0<+ll2<x<2 vd'Y'>0€l -
l*>2
khodng (a;lll) vil (2;+o), hAm nghich bi6n t€n
(rtz;2).
i C* 1,!: Hilm sd dpt clrc tl4i tpi x = | I 2, y"u = 5 I 4 vi tl4t cgc ti6u t?i x = 2, ltr = -t .
c. Ed thi: Ed thi cit tryc tung
tei A(0;rl3)
I.
(2'0
-.. I
olem,
2. fl,O ttidm
Ta c6 A(0;1/3) vdy'= 4x2 -2(2m+ l)x * m +2. Suy ra y'(0) - m +2.
Ti6p tuy6n cria tt6 thi tai A l d : y = (m + z)x +
1.
Euhng th[ng d cht Oxtai atfr ; ol'
l. (1,0 ili,
DiAu kiQn: x3 +3x 2 0 e x > 0.
Kl
1 *:Te :* li :9:::11* i:l:l f-:ff I ? :

3. Nhfln thdy .r = 0 kh6ng thda min n€n (l) tucmg duong v&r x +t *i-6trf,J = 0
Dil
f+1, =t,.t2ffi t^dugc t2 -6t+8=0<+t=2 holc t=4 (tntlk)
0,5'
+)Vdi t=2 tac6 x=l,r-3.
+)VOi t=4 tac6 r--8+ Jdi,tr=8-.fiT.
DiEu kiQn: sin.r * O,cosr*l hay x *kn .
vci ailu kign d6 phuang trlnh da cho tuong rhrongot
2cos2r-cos'r-3
smr
o (2cosr-lXcosx+l)
- 2sinx-
<+ (2cosx-3)sin2x= -2sin2 x
sinr cosr - I
0'5
AzcOsI-3= -Zecos x=l O!= t! +kt.
23 0'5
Tac6 I n &
(2'
I
I0
z',
Vdi r= 0:+ t =lrvdi r=l=+ t =2.
&=dt hay fo-gi2, -".*?3ln2' 3
0'5
=2'g,d, : I '( t _ I tKhi d6!=rnzlt''-zs
5rnzlr-5 t+sl
#(,"F - sr - hr, . rrl',,=#rn* .
0'5
+) Gqi 'f l*ffing di€m DC'. Vl NI// CC'
vil NI * I Cc'n€n NI - rhil'vil NI /l IV/4.'.
,2'
:
:
+) vt AI,B',C //A',D
nEn flC)*./(A'I, A'D) (r)
,"
-t
,"
,r' Dry---a--
0'5
0'5
t2 A' D2 + A'.C',2 DC',z 5a2 oJiSuyra AI'=T- , =7+A't=7.
Trong LA'"DI ta c6 cos
'/.DA'I
, A' D2-+.A'12 r DI,
= -3,:-<-i-
2A'D.A'I 2J5
*";:33.,5
Tt (l) ve (2)suy ra cps(IAf, B'C) = | cos /.DA'l I =
-:: =
-
_iN._____, _, r__ ,
ZJS l0
(2)
V.
(1'0
-.1orem
,f e
Ap uung;nrycosita c6
az +b' +cr +r>|to+el'* jtr+l)'> Ir"*b+c+l)2,
(a +lXb + l[c * g < ['
*lftl']' .
......-:...-.-..,.............: i ]fr

4. Ps 2
-
54
Suy ra
a+b+c+l (a+b+c+3)3
DAt t - a + b + c +l,t > I . Khi d6 ta c6 P <?--54 =
t (r+ 2)t
0'5
Xdt him f (t) =i @
hen (L + co). Ta c6
f, (t) = -3.# = 0 <+ st = (t +2)2 el"='., f, (t) >0 <+ I < t < 4
Suy ra BBT
DWa vdo BBT suy ra P <l . n6u ding thfc xiy ra khi vd chl khi
4
Vfly gi6 tri ltu nh6t cta P le 1, Uut dugc khi a - fi =c = I .
4'
r ' '
i
t'=4Qa=fi=c=l
_f'(t)
VIa.
(2,0
tti6m)
l, (1,0 itifimr
-xr)'
r-
lzttu=3ffiI
lzffi=-3ffi
3-xr)'
(1)
(2)
0'5
+) (1)e 2(xr-1; 3xr-6) -3(*r-l;3- xr)O{* =}
lx, -z
(
suy ra
^lit ;),
BQ;z) .Suy ra phucrns nlnh d : x - y- 0 .
*) (2)<+ 2(x, - 1; 3*r- 6) = -3(x , -li3 - xr)*
fi; =1
Suy ra A(l;-Z), B(L;3). Suy ra phuongfitnh d:x-l = 0.
0'5
2. (1,0 ilidrn)
Gid su
Suy ra
B(0; b; 0), C(0; 0; c) trong d6 bc * 0 (vt n6u bc: 0 thi tam
(P)'*+ 4*' =l . vi H e(P) non 1*1=
1
/ 2 b c --, -
b c 2
s,u" =+lrzl,frll=; (bc)z +(2c)t + (2b)' - 4J6 e b'c' +4b
gi6c ABC suy bi6n)
(l)
+4c2 =384 (2)
0'5
ii
OFI b + c = u, bc =y . Khi d6 tU (1), (2) ta c6
ll
;i -Zu) = 384
b-c=4
[r=8, y=16
<+l .
L, - -6,p = -12'
suY ra fi = -c --3 + Jn
S=-c--3- Jzl
Vpy c6 3 m+t phing (P) thda mdn li (4)'*+ 1*1=t hay 2x+ y
244 +z-4-0,

5. c
1tS,|*-+.:h=t hay 6x+(3 +Jn)y+(3-
^r7-t2=0"
e)';.#.;E=l hay 6x+(3 -Jily+(3+ JnJ,-rZ=o.
VfIa.
(1'0
tli6m)
Gii srl s6 thda mfln bdi todn li ab;A . Theo bdi ra ta c6 o. {2,3, 4, 5, e,l; d e {0,2,4,61 .
Xdt hai tudrng hqrp:
TH I: d = 0 . Khi cl6 a c6 6 cdch chgn, b c6 6 c6ch chgn, c c6 5 c6ch chgn.
$qv rq q6i 6x 6r |
=
t!9 tq6l
0'5
TIt 2: d . Q,4, 61. Khi d6 d c6 3 c6ch chgn, a c6 5 cdch chgn, D c6 6 c6ch chgn, c c6 5
c6ch chgn.
Suy ra c6: 3 x 5 x 6 x 5 = 450 (s5).
Vfy s5 c6c s6 thda mdn h 180 + 450 = 630.
0'5
vIb.
(2,0
tli6m)
l. (I,o itidm)
Gii su M(x; y). Ke MH L AB .
TU giethi6t suy ra MH=g ve LIyAH vu6ng c6n.
2
Suy ra AA,I = MHJ, =.,6.
l3 50
0'5
D[t u - x-1, v - ! -2. Khi d6 ta c6
(
-1, v=-z
-zrv-1
0'5
2. (1,0 iti6m)
(1)
fab=)
<+ sb -9<*l
Lob = -i
Gi[ su A(a;O; 0), 8(0; b;0). Vl Vonu" > 0 n€n ab *0.
Suyla @):I+ 4*1=r.vi Ke (a) n6n 9-l=r
'iiobzab
il
Oe,ACle fii diqn vudng t4i On€n Vouur=
*
OA.OB.OC =
* I ol.t b I -3
(2)
(3)
0'5
hw thi tn> 0,25 didm.
2x*2y+32-6=0
x+ 4y'-32+6=0 0r5
VIIb.
(1'0
--. I
otem)
EidukiQn: x*0,y>0.
iu"o
|rcCr*' -log,y= 0 <+ log, lx I = logr y elxl= y e
l:=:,
* Vdi x = y, thay vio phuong hinh tht ntr6t ta dugc 32*' +3' = 10 c+ x = 0 (ktm).
0'5
* v6i
vay n
= 10
0'5