De thi thu lan 3 NKSPHN nam 2012

<span class='text_page_counter'>(1)</span><div class='page_container' data-page=1>

TRU'ONC

DIISP I'iA NQI

TRU'cr.,rc

THPTcrquv0ru

-

flHsi)

Dtr

TFII.rrNti DAI F{ec

r-AN

trtI

zuenq

zorz

M6rr

thi

:

TOAN

Thdi

gian

titru biri

;

lB0

plnit,

khong ke thc)'i gicrn

phil

cli

tri

nAo c&a

m,

dLLo'ng

thang

_{)'= -}

x

*

n't

CAtr

l.

(2,0 di?ut

)

2x-1

t

Cho

hAm

so

y: ;1

L

l(hao

sdt

str bi6n thi€n vd v0 dd th! (C)

cfra

hdm

s6.

2.

Coi

1ld

giao

didm

hai

clLro'ng

ti$rn

c6n

cira

(C).

Vd'i

gid

cit

(C) tai hai

di6rl

pli6n

biet

A,B

vh

tanr

gi6c

_IAB

d€u.

C6u

2.

(2,0 dient)

l.

Ciai

phLlong

trinh

_{;h -}

( cosx + sinx.tan

j

₎

=

./rr\.fi

srnlx-;/+

cos

(;-

*.1

2.

Tim

citc

grhtri

cira thanr

s6

o

d6

phLrong

trinh

sau

c6 dilng hai nghi6m phdn bi6t

:

.. a f:-'--;

log3x"

-n.l

togzxu+a+

l:0.

C6u

3.

_{},0

dietn

_}

-n

2sin2

rI

_-

x)

j'inhticir

_ohdn

_{t: fo --+}

_4"

'

;

t.)

_coszx

Cdu .1, (1,0

iliitn

)

Tf'cliQn

ABCDc6c4nh

AB:6,canhCD:Svdc6ccanhconlai

bing..174.HsytinlrdiOntich

nrdt

cAu

ngo4i

titip

tri'diQn ABCD.

C6u

5.

(t,0

diAnt

₎

Clioc6cs6cluro'ng

a,b,c,m,n,p

thdamdn

ctf

nr:b+

n:c+

_P:k

Clrirng nrinh

ring

:

an-r

htrt

*

cm

<

k2.

Cdu

6.

(2,0 diAm)

I

.

Cho cli6m.M(0;

2)

vd hyperbol

_@

, +

-+ :1.

Lap

phuro'rrg

trinh

duLong

thing

(r/)

cli qua

5-di€n

A4

cht

(m

tai

hai cli6m

phAn

biQt

A,

B

sao

cho

MA:;Mtr.

2.

Trorrgkh6ng

gianOxyz,chorn{tcAu

(.},

x'+

y2

+22

+6x-2y-22- l4:0.

- ', !

Vi6t

phu'o'ng

trinh m{t

phdng

(P)

chfi'a truc Oz

vdr

cht nrdt cdu theo mdt

dLrirng

tron co

bdn
l<inh

r

:

4.

Cf,u 7.

(t,0

diim

)

Ciai

he

b6t

phLlo'ng

trinh

COSX

-''-13'

't

'

4il(i[{,$d5r:r,.,'&

@

/a-:"r

(

tog{z

_-

xz)

<

0

1

lx6

+

4(t

_-

*213

;'

1

r

tf

H6t..

</div>
<span class='text_page_counter'>(2)</span><div class='page_container' data-page=2>

rlAp

Ax

-

TFIAI{G

B}BM

nur

tnU

BH LAN

tll

-

nAtvq

zorz

.

N6ua+

l=0

<+

u=-

r+ttrltrothdnh

tt

-2t=0*

_[l=

_!

troail

.

N6u

a+-

I,khi

d6r=0kh6ngldnghigmcia(l).DCpt(l)cirdtngniQtnghiQmcluongthi

*)Trrdng hfp

L

Pt(l)

c62 nghi$mtr6i diu <+

a+ I <0

e

a<

_-

l'

t) )q

il )i

l.

(1,0

aliini.

Hoc sinh ttr

2. (1,0 dilm) .7int m ...

I

Q

ttidni

t-tJ,O

aiim),

Giai Phuottgtrinh ...

Didu ki0n

:

cosx 10, cc,s

j

# 0 .

r

sinx.sinl.
l)hrxrnc trinh dd cho

e --;

( cosx +

--#

)

=

.. _cos.x LU5;

1 _^ ?X.

<+ ---;- - ( co:i)i + _{Islll ;./}
-aoszx

*

l- r^.L-(l-2sin2I+

2sin?l)

=Vs.,un* <+ tan2x

_-

J3.tanx = 0

I

tanx=0

I

tanx = VJ

lx=kn

lx=i+t<,t

(kez).

So siinh vdi

diiu

kiQn. nghiQm cira phr'rongtrinh ld

:

x--2h, *

=I+

lm'keZ'

-/ft\-[

sinlx-;J+

srn

(;

+ xJ

-;;;-zsi n x.cosl

c osx

0,50

0.50

II

(2 ttiim)

S

khi phuo'ng trinh sau co hai nghiQm phdn

2x-1-

(

x+1

bi0t x1.x2

: l_f:-x*tn

<+

_[xr+

(f-nr)x*m-1=0

lzi trLrng di0nr ctia

'lIJ'

r(hi c1(r ;;, =

-

-r, + nt ( i

=

t'

2; vit

H(T,

#l.m

:

t

#' l-l'

7E (*'

-

x1 i xr

-

xz)

(lA=tB

(lA2=lBz

\/.-r8diu

*

trn

=E-AB

(=

\tu,

=1rc,

(**)

Tacd

141

:lN e

(x1 -x2)[x1

+x2-(m-l)] :0'

l)o.r, +

\2:

tl:

_-

I

r,On ding tl.rirc ndy clirng vdi moi rrr thoa min

(t)

Tac6

(+*)

* gY:t.t*r-xr)2 e

(nt

-3)2:3;(xr+ xz)2-4xrx:l:3[(nr

-

l)'?-4(n

-

l)l

a

t,r'

_-

6n+

3 = Q

e

nt:3 trG.

Citc

gi|tri

ndy cLran ddu thoamln (*)'

Dip sii

:

m

=3

!,,18.

Z-

W iiiml.

Tim gia tt"! eia tham sd a

"'"

Grtign

: log3x8:0

<+

_lxl>

l.

pT<+

_log3

_{xr+Za,flQlp +a+}

l=0.DAtt=Jtg,y"

Z0.Ptdacho,trothdnh

t2+2at+a+l=0 (l)

Nhanx6t:V6i

m6i

t>0,

pt

_v4f,-g.F=t

<+log3x2=t2e x2=3t'

(*

xr.z=+JAAthoaminxr lxz.

Suyra ptcldchoc6d0nghai nghifmphdnbi€tkhi vdchi khi pt( l)c6dfingmdtnghiEmkhongdm'

</div>
<span class='text_page_counter'>(3)</span><div class='page_container' data-page=3>

1

2/3/201

2

orrr..itrsttoTtzpt(,1.,,,'ri***n*-;-*[f:==.i,=9out'=0o{n,_i,__tr=s€,r=r:'(

' t _-'fi

l)apso:it.-l.a='t'.

III

(t

itidn)

L (1,0 di2ntl

.

'finh tich phdn

"I r-

cosl|-

zx;

.

_"I

r-

si.zx

,l

(cosx

_-

sirrx)2

l-aco

-

l--l-u

_r0

_cos2x

,''-

tlx=

_J0

le

'',"'""ilr=l-6-rlr

cos2x

-

'

J0

(cosx

_-

sinx)(cosx + sinx) '' 0,5u

. r:cosx-sinx

r:d(cosx+sinx)r

_,

_t--...

_rsinxllf

_:',.,G*t

t=Jo'.*-*.i,*ut=Jouffi= lnlcosx ,lo

z

0.50

IV

(t

tliim)

(1,0 diAm). Tinh diQn tich mdt cdu

Tlreo giti thidt DA

:

DB = CA = CB = ,[74, tarn gi6c ACB cdn n€rr tdm I cua
dLrorg tldn ngoqi ti6p AACB thuQc cludng cao CE. Ta c6 ACAB = ADAB do

d6

EC ₌ED

+

ACED cdn

+

ctuirng cao EF cria ACED lA du6ng vudng g6c

chuug ctia AB vd CD d6ng thdi ld trung t4rc crha AB,

CD.

Vdy tdm O hinh
cALr ngo4i titip t['diQn ABCD nim tr0n EF.

0,5u

Tac6

EF"= ED,_ DF" mir ED' = 74 _() = 65 =r E.F,=65

_

l6:49

₌₊EF =

Mat l<hic

tlF:

OE +

OF:

.l

pt

-

9 +

^/ n2

-

te .

7

Ciiii phurrn-e

trinh

./Rt

:

9 +,'l

R'

_=G

:

7 ra dugc R

:

5.
Do db clien tich m4t cAu

la

S = 4nR2 = l00n (dvdt).

0,50

V

(t

itidnl

t

(1,0 diim). Chting minh riing ....

l'a c6

:

k'

=(a+

mxb+

n)(c+

p)=

abc 1 mnp+ abp+ can + anp + bcnr + brnp

r

cmn.

M4tkhdc k(an + bp +

crn):

an(c+

p)+

bp(a+

m)+cm(b+

n):

abp+ can + anp + bcm + bmp+ 0n1n.

Vril

l<r= abc4 mnp+ k(an+

bp+cm)> k(an+bplS;r1)

<+

l<2 > an + bp + cnr (clpcm).

t,0{)

VI
Q rlidm)

l.

(1,0 diAm). Vidt phuons trinh dud'ng thdns .

Nh{nxdt:DuongthangdiquaM(0:2)songsongv6'itr,ucCrykh6ngcii(fl.-Khi d6 (d)

:

y

:

/.x + 2. Toa dd giao di6rn cria (d) voi

(f0

ld nghi€m c(ra h6 phrcrng rrinh :

ti =H.;4

+

14k2-

l)x2+

l6kx+20:o

(l).

De((iln(ff) =\A,.Bl<e(t)c6hainghiemphinbiet

,'

(4lcz

-

1+

0 (

t' +

+!

"

t

A,>

o

*+

_iro

_{_}

_,u,.rt,

_o*

.l

k++-

_-''o

(2)

tkt<l:

₂

0,50

l(hi d6 ( I) c6 hai nghiQm phdn biQt x1 . x2 lir hodnh dd cria zl

5.-

s

Titdi0uliicrn

ly'l=rMB *X'

=-x2,khi

cldtac6:

{1",*x,=-#u^f",--ah

_ 36

t2

J g"-t- 20

_{I, s^z:4krfl}

o1

_1xz-n[z-l

-t-

Lz-+Gkr-r)r:---tc+l(=+L(thoanrinl2))

Vdy c6 hai dudng thing thoa mdn bdi to6n : (dy) : y = x +

2,

_{(dz) y =}

_-x

₊_2.

(ra

lx.

*x.

vaiB,thoamin

_J

_::'^'

I tr.t,

=

4kr_1

0,sa

2

r,

</div>
<span class='text_page_counter'>(4)</span><div class='page_container' data-page=4>

12/3/2012

TII|aiil,,llii!

l'lttrotz

trinlt ntd!

pltattg

_"

vlr|6r',

(5);r5 t6'-r-r l,i

G

3l

lr

l)

vd bin l<inh R

:

5'

(iQi //(.r : b: o) lir hinlr chi0Lr cria

/

ldri mat plrfng (P). Mat phang

(/')

chila truc o-- n€rr o6 vcct0 phiip tr-ry0rr

..:.-

,,r,ra

ii=(-b;n;Q)

voi

a:r

br+0.

rt--lfr,OHl.trong

d6 i< (O: O:

l)

vd

oH (a: b; c)' SL''

-Suy ra phucrng trinh m[t phdng (P) co ci4ng

:

_-

bx + a)' '= 0'
VI

(2 rtiim)

ffin

c6 b6n kinh

r:

4

*

tH:

\f R2

-

12

:

i'

l3b + al_

= 3 <+ 9b2 + 6ab +

.f

=

91,t2 + 9a2
Nlrtr vdy khoang c6cli tir

i

den (P) bang J

€

ffi,

la=0

c+

8a2-6ab=oel-=11

Lu-

q"

V{r} c6 hai m4t plrdng(P)

lin

luotcir phuongtrinh

ld:

x=0

' 4x-3y:0'

(1,0 tliznt). G,"L!19

sl.

l.

+ 411

e [0;

':l<+lxl

voi

_lsls

dnh g(t) =

tl

).

z

+l=-;3

0<+2-x'

411

-

xrlt

f1x) tro th

tt_

-2

_{e l,_}

[r-:l<

xt'+

I

rhi

-0

Ta

cir

log' (2

_,,

-

x

Xdt ht\ur s6

tlx)

=

Dat

t=xt,0<t<

o'(tt=0 et?:4(

VII

Q,0 didnt)

_ra

_co

_g(f)

_=f

_.

_*tol

=

a,

g(r)

:

I'

Su1,rarzing(l)

=!+

ntinf(xf

=f

'Suyrabdtphuongtrinh

x
T6nr l4i : 1'4p nghiQm cua hQ b6t phucrng trinlr

ld

S

:

[-

l; l]'

6 ₊

4( I

_-

*'l'>

_i

nghiQm dirng

vx€

[-l;

l]'

</div>

<!--links-->