De thi thu Toan THPT Thai Phien

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NOi du

l)Khio sit vi vc a6 tni hirm s5 -2x-3 x-2

1 TXD : R\{z}

2 Su biSn thi6n :

+ Gini hpn - TiQm cgn

+D6thi:

Gitii phu'o'ng trinh :

lim y =a6p ; hn-l_ ! =-q= d6 thi c6 ti6rn cf.1 dirng litx:2

x-+2-li+ y =2 = dd thi c6 tiQm cf.n ngang lity = 2

+ y' ' = J-< (*-2)' 0 Vx ;e 2 = hdrn sii nghich bi6n tr€n (- -; 2);( 2; +oo)

v

E? thigiao vdi trpc Oy tai di6m A(0;312);

D6 thi giao v6i fi'uc Ox t4i di6m B (3/2 ;0)

D6 thi nhdn Di6m I Q:2) lA giao cria 2 tiQm c6n lALrn tAm d6i xilng

2) co: M[",?;), xs * 2,y'(xo) =

6+

Phuong frinh ti6p ruyt5n A voi ( C) t4i M: t:y =-:! "(r-ro;+?&:1

l*o -2)- xo - z

To4 dq giao didm A, B cta (A) vd hai tidm cfln n(rje4)t Bea -z;z)

\ x\-z )

.Mdt khdc l(?;2) vit AIAB vu6ng t4i I n€n duorg h'dn ngo4i ti6p AIAB duoTrg tr-on cd b6n kinh R:AB/2

Md theo gt, diQn tich ducng trdn bdng 2x > R= Ji o AB =2Ji

f

<-." - tr' -l?; -,

).] = t -,* - t)' -

G+ =, * Ll

=', a M(t: t) vd M (3: 3)

cos2x+ssin(x+

=-z(1) Ekxd:

0,25 0,25 0,2s

,un[,-3n

2

-l.tanln+-l 6) l 3/

f sin(x - a

J cos(x - a lsin(x+,r Lcos( r + z

l6)*0 l6)*0 /3)*0 /3)*0

l'*

*]

l'*

r ktt

-+ - 62

r kr +

-2t

( zo.1^ ^ )

2 )=2eZcos'

4,25 0,25 4,25 0,25

I cosx=J ltoat) l r=-;+hZ|T

<+l r <+l '

L 2 L"=- : +kt/,

KOt hgp Ekxd phuo'ng trinh c6 ngiriQm :

(g

t-l^

[x + u

Cgc tri : kh6ng c6

+ Bing bi€n thi6n

(tt\(n\

ra c6 : t"[r-AJ ,*["*JJ=-l n6n (t)

x-5cosx-3=0

2r

3

l2x+9> 0

,-f 3-V9 +2x +0

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^ / .?

2x'13 + JS

+zx)-t -t2

r \2 (3-Je -2x)

bpte l -= <x+21

\3-J9+2x)

2x219 +6^19 a2* +9 +2x\

-T

<x+21

e18 +2x + 6.,1; 2 <2x + 42

Ktit h-op vdi di6u ki6n x6c dinh

x +21

a Jg+z* 4 er<i

2

ta c6 nghipm cta b6t phuong trinh ld : l <.r< lg j

-l1 la2

[,*o t- (

I - Jllxl,2'

0\

I

I, = [xe?'dx

0

lx*y=3 lt=3-x

?

-

z) fJ;r' + 3 * rly' *5 = n.' lJx' +: +

D[t /(x) =.,6t;+.ft-rt' * s =

-+)0.='l*r',d*-'l-L*

'14-x') i irl+_*?

Dat u = x,dy =e2t clx - tr=f

Ir

L='[+- oo, ,=t[4-] +at=P, x= 0=>r =z; x=1=>r=v5

o tf4-x'

^14-*/

2

+ r,=

le-f)at=f 4Ji

e2+l 16

+I=-:''*' 3Jj 43

lv{A,t = A,C,2 +C,Mt =7zo)t *("Ji)' =9a2;BC2 = AB2 + AC2 -zAB.AC3osl20" =7a2 i

BM2 = N +a,f =7d *(rJ t)' =tfr;48 =A4' +zE =(uJs)' +d =zti

Suy ra A,B' = MAr2 + MBz + MB L MAl.

Hinlr ch6p MBAAT vd GABA, c6 chung d6y ld tam gi6c BAA, vd du6ng

cao birrg nhau n€n th6 tich bing nhau

v-t/ v = yMB,t,t, -r/ -l - i -.!a.za.sin:20"=ltJE

= yc'ae,t, = jA4'S^rr =:2atl 5' 2 3

^ a'JE

=d(A,(A,BM))=#=ffi:m=+

- A I

\-,f(:*1\s=,,

:.:,=:-:

.J x' +3 ./1: - x;'? + s

.f '(x)=6a;"nf4afi =(3-DJx'1 +3 o{"-'=t

l2x" +I\x-27 =0

hainghi€m ndy ddu bi loai vi nh6 hon 2 vfy, dg.o hiim cria hdm s6 kh6ng rhe d6i

O5 t<icm tra ring cd

d6u tr6n 12;.o) , rigodi

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r)

VIb

1)

ra f '(3) > 0 n6n .f '(*) > A,Yx2Z .

Do d6, gi6 tri nh6 nirdt ciia f (x) khix>2

phuong trinh d6 cho c6 nghi€m (vdi

liL f (2)=^11 +Je .Ctng d6 th6y tyif Q)= co , Tir d6 suy ra: h€ x>2) khi vd chi khi *>"G *J7 .

1 = _ €d= = ,[_: , _ j )

817

0 _+b

DoBC//(il.'+=+

A( 4a+2i a) suy ra

eUe+a-1;-a+1) Do AM LBH

M tdnunghek,q,c ,a" c(2,!\ l3'?

/

\' - /

:x+ y +3 =0 n1n:

Be (d):x+y+3=0 n€n B(b;-b-3)

e b=-4e B(-4;l)

e,Kr1f 4y-lf =17 +1o*y

<> ir - -2y -1* z=(-Zy -1) + yi

-(q

1'7 \

=BC I Y-n :1-+b l.

\3 '3 )

Gqi I ld trung ditSm AB suy ra I( 3 ;-1 ;1) Ap dgng hg thric trung ruy6n ftong tam gi6c MAB n6n ta c6 :

2 + MA2 + W2 nhdnhd e tufr nnl nndi e l,fr L (p)

ndn M ld hinh chi6u ctia i tr€n (p)

Gqi (d) ld duong thing vu6ng g6c v6'i (p) va di qua I suy ra phuong trinh cria (d) Id :

M ld giao di6m crla (d) va @) n6n ta c6 M(2;1;-1)

Ddt z =x+ yi(x,y e R)

li(x + yi)- :l =l(x + yi) - z- rl o l-y - 3 + xil=le - 2) + (y - \rl

x-3 y+1 z -1

-=_=_1aa

Acgumencio,M)gfLellcz:'-,,"' *" 4 Jz

t l -f- =r-4=-l {3)

l^lt-zy -1)' + y' a 'Jz

Ctng Q)vd (Z)cho ta y - -1, thi tai th1amdncd 1t1vd 1zy

Goi A(x;y)=B(x;-y) A,B phdn bi|tn€n y* 0 Ae(

Do C (2;0) n€n ACAB cdn rai C.

=ACAB ftieCA=AB €(z-x)t + t, =4x2 (2)

lx=-2 >y=0(loqi) Gi;ih€(DvA e)ta itdc: i to ' , iru

L^ - 13 -'Y -

6'76

n,,.n*^e r\ -,\(to tz) lto -tz)

ta co z dtem A,b can rm ta

l,'; n I "" lO; n )

0,25

0,25 0,25 0,25

0,25 0,25 0,25 0,25 0,25 0,25

0,25 4,25

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I Y: l-Lf

I

a, :

I I = -3 + 3r = (d, di qua M r(2; -3:0) c6 WCp ur(I; 3; t)

ra rttlu : ,41.M/14, =60 +0+ dr;drch/o nhau.Goi MN litfoqn vutng g6cchung cila d,;d,

rh1 Mdt ct cobenkinh nh| nh{t trcl rhe void,d, titmit ciu ahig tciin uw

M e d,+ M(4+3r;I-r;-5 -Zt) ; N e dr+ N(Z+ t,;-3 +3t,;r)

I tutY .^ =O l-tqr -2t'=lZ lr = -I

\m.r,=o o

\ ,r* rtt'=9o {r'=t +M(r;2;-3);N(3;0;1)

M{t ctu &to-ng ki;h MN cJ ftn r (2;1; -t1 c J u ah nin n = J e

P hndng rriih mdt c d7t t d : (x - 2)' + (y- 1)t + (z + I)2 = 6

TiQm cAn xi€n (A): y = x + m2 .

t,m

y =1 ;>0,Vx+1:>

(x -r)'

a

Y4y m:_Z

0,25

TU M(1; 5) e (A):+ m = 12.

*2 -2* +1-m

{t -1)2

<+A'<0 em<O

>OVx *Ie x2 -2x+1-m>0Y x +1

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