De thi thu Toan THPT Thai Phien

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NOi du

oAp

Ax vA

BIEU DIEM

THI

THITE

C

LAN

II

_-

KIIOI

A

-2011

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-

x-+2-li+

y =2

₌

dd thi c6 tiQm cf.n ngang

lity

= 2

+

y'

'

_=--J-<

0 Vx ;e 2

₌

hdrn sii nghich bi6n tr€n

(-

_-;

2);( 2; +oo)

(*-2)'

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

|

-, (z*-z r'?l

,

[x^=1

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

z\

(

r\

-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^ ^

)

e

costx

+5srnIrc*

2

)=2eZcos'

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

r

^

,, ., ;

2r

I

cosx=J

ltoat)

l

r=-;+hZ|T

<+l

r

<+l '

I cosr

=--

I

2n

L

2

_{L"=- :}

+kt/,

KOt hgp Ekxd phuo'ng trinh c6 ngiriQm :

(g

lx>--e{

2

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

1

,-f

3-V9

+2x

+0

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^ /
--.?

2x'13 + JS

+zx)-t

-t2
r

--\2

(3-Je

-2x)



13+Je+zx)-.

2x2

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

_-

_lxl,2'

Jl
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=+

l(r 1

. - A. I

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

tt, , X X-3

:.:,=:-:

.J

x'

+3

./1:

-

x;'? + s

.f

'(x)=6a;"nf4afi

=(3-DJx'1

+3

o{"-'=t

l2x"

+I\x-27

=0

Phuong trinh thft hai

c6

A,=81+54=135=9.15,

vd hai nghiQm:

_,r=2Y.

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

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VIa
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

_.Ctngd6

th6y

tyif

_Q)=

co _,Tir. d6 suy ra: h€

x>2)

khi vd chi khi

*>"G

*J7

.

-4a-l -a+I

2

.( 2 2\

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 :

MAz +IvB2 =2742

*AB2

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

l---z:]--=r^4=4

(i)

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

Ydy z

_=1-i

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).

I

z

_=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; _-t1c J u ah

nin

n

₌_Je

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

</div>

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