tuyen tap 40 de thi hsg toan 8 co dap an

7/22/2019 Tuyen Tap 40 de Thi Hsg Toan 8 Co Dap An

1/47

Tuyn tp thi HSG Ton 8 Nm hc: 2011-2012 TH S! 1

"#u 1: (4,0 im)

Phn tch cc a thc sau thnh nhn t :

a) 3x2 7x + 2; b) a(x2 + 1) x(a2+ 1).

"#u 2: (5,0 im)Cho b!u thc :

2 2

2 2 3

2 " 2 3( ) : ( )

2 " 2 2

x x x x xA

x x x x x

+ =

+

a) #$% &'& * t ,-n b!u thc /

b) #$% , t0 ca x ! /

c) #nh , t0 ca ton, t45n, h6 : 8x 9 78 "."#u $: (5,0 im)

a) #$% xa %?n h4@n, t$nh sau :

Ax2+


2/47

Tuyn tp thi HSG Ton 8 Nm hc: 2011-2012 (x 9 a)(ax 9 1). 0,5

Bi 2: ,0a !,0

&'& :

2

2

2 3

2

" 2 2

33

2

x

x xx x

xx x

x x

+

1,0

2 2 2 2 2 2

2 2 3

2 " 2 3 (2 ) " (2 ) (2 )( ) : ( ) .2 " 2 2 (2 )(2 ) ( 3)

x x x x x x x x x xA

x x x x x x x x x

+ + + = = =

+ + 1,0

2" B (2 ).

(2 )(2 ) 3

x x x x

x x x

+ =

+ 0,5

2

" ( 2) (2 ) "(2 )(2 )( 3) 3

x x x x xx x x x

+ = = + 0,25

UV< DK 2 3x x x th$2"x

3A

x=

. 0,25

b ",0

UK2"

3 2 : 3

xx x x A

x > >

0,25

3 x > 0,253( )x T!"#! > 0,25

UV< DK x 3 th$ . 0,25c ",0

7 "7 "

7 "

xx

x

= = =

0,5

11( )

3( )

x T!"#!

x "T!"#!

= =

0,25

UK x 11 th$ 121

20,25

F 3 ,0a 2,

Ax2+


3/47

Tuyn tp thi HSG Ton 8 Nm hc: 2011-2012

#a cH : 21 ( ) 1x y z x y z

a b c a b c+ + = + + = 0,5

2 2 2

2 2 22( ) 1

x y z xy xz yz

a b c ab ac bc + + + + + = 0,5

2 2 2

2 2 2 2 1

x y z cxy bxz ayz

a b c abc

+ + + + + = 0,5

2 2 2

2 2 21( )

x y zd$cm

a b c + + = 0,25

F " #,0

O

F

E

K

H

C

A

D

B 0,25

a 2,0#a cH : FM C (,t); GN C (,t) FM [[ GN 0,5

Chn, %nh : ( )%&' !' g c g = 0,5 FM GN 0,25\u< a : # ,c : FMGN J h$nh b$nh hnh. 0,25

b 2,0#a cH: A% A! *% "!= = 0,5Chn, %nh : ( )%* !" g g : 1,0

. .)* )"

)* )! )" )%)% )!

= = 0,5

b ",$Chn, %nh : N ( )! A" g g : 0,25

N. .

A"A! A" A

A! A = = 0,25

Chn, %nh : ( )! A* g g : 0,25 A*

! A = 0,25

] : CG F . . A*

A% A* AA% A

= = 0,5

\u< a : F.S + F.S CN.C + N.C (CN + N)C C2

(^c%).0,25

S! 2

Gv: Nguyn Vn T Trng THCS Thanh M3


4/47

Tuyn tp thi HSG Ton 8 Nm hc: 2011-2012"#u1/

a. Phn tch cc a thc sau a thZa sQ:4x 4+

( ) ( ) ( ) ( )x 2 x 3 x 4 x 5 24+ + + + b. L_ h4@n, t$nh: 4 2x 30x 31x 30 0 + =

c. Cho a b c 1b c c a a b

+ + =+ + +

. Chn, %nh En,:2 2 2

a b c 0b c c a a b

+ + =+ + +

"#u2/ Cho b!u thc:2

2

x 2 1 10 xA : x 2

x 4 2 x x 2 x 2

= + + + + + a. `t ,-n b!u thc .b. #nh , t0 ca Ft |x|

1

2.

c. #$% , t0 ca x ! .

. #$% cc , t0 n,u


5/47

+5

6

( "

,7

Tuyn tp thi HSG Ton 8 Nm hc: 2011-2012H&'NG ()N "H*+ TH H" SNH G '3 8

c/Xhn c_ 2 D ca:a b c

1b c c a a b

+ + =+ + +

DK a + b + c; t,-n c% (2 %i&'

"#u 2(# %i&'

F!u thc:2

2

x 2 1 10 xA : x 2

x 4 2 x x 2 x 2

= + + + + +

./`t ,-n 46c q:1

Ax 2

= (") %i&'

4/1

x2

= 1

x2

= horc1

x2

=

4A

3 = horc

4A

5=

(") %i&'c/A 0 x 2< > (") %i&'

. { }1

A Z Z ... x 1;3x 2

(") %i&'

"#u $(# %i&'

SU + L# + '

(" %i&'

./ Chn, %nh: AE FM DF= = AED DFC = c% (2 %i&'

4/ GM FN C] J ba 45n, cao ca EFC c% (2 %i&'c/ CH Chu D h$nh ch nhVt M]N 2a qhn, k

ME MF a + = qhn, kAEMF

S ME.MF = JKn nhjt ME MF= (M]N J h$nh Dun,)M J tun, !% ca FG. (" %i&'

"#u %:(2 %i&'

./#Z: a + b + c 1

1 b c1

a a a

1 a c1

b b b

1 a b1

c c c

= + + = + + = + +

1 1 1 a b a c b c3

a b c b a c a c b

3 2 2 2 9

+ + = + + + + + +

+ + + =

(" %i&'

Gv: Nguyn Vn T Trng THCS Thanh M


6/47

Tuyn tp thi HSG Ton 8 Nm hc: 2011-2012H&'NG ()N "H*+ TH H" SNH G '3 8

Gju bEn, x_< a a b c 13

4/(a21+ b21).(a+ b) 9 (a2+ b2).ab a22+ b22

(a+ b) ab 1 (a 1).(b 1) a 1 hoc b 1

U a 1 b2 b21 b 1 hoc b (Jov)U b 1 a2 a21 a 1 hoc a (Jov)Uw< a 1; b 1 a211+ b211 2

(" %i&'

thi S 3

Cu 1: (2 im) C! "#B1"7

""23

23

++

aaa

aaa

a) $%& ' "

b) *+m 'i, &- '/ ca a " 'i, &- '/

Cu 2: (2 im)

a) C' mi -' / &7' ca ai 8 '/ cia & c! 3 &+ &7' c,c


7/47

Tuyn tp thi HSG Ton 8 Nm hc: 2011-2012Cu 1: (2 )

a) (15) a3= 4a2= a > 4 # a( a2= 1 ) = 4(a2= 1 ) #( a2= 1)(a=4)

#(a=1)(a>1)(a=4) 05

a3=Ua2> 14a = V #( a3=V ) = Ua( a=2 ) #( a =2 )(a2> 2a > 4) = Ua( a=2 )

#( a =2 )(a2

= 5a > 4) # (a=2)(a=1)(a=4) 05 W/ XYZX : a ";2;1 aa 025

$%& ' "#2

1

+

a

a 025

b) (05) "#2

31

2

32

+=

+

aa

a; &a & " '/ Qi a=2 [c ca 3

m \(3)#{ }3;3;1;1 025

*] ? &+m Oc a { }n;3;1 025

Cu 2: (2)a)(1) Bi 2 8 i &+m a b &a c? a>b cia & c! 3 . 025

*a c? a3>b3#(a>b)(a2=ab>b2)#(a>b) abbaba 3)2( 22 ++ #

#(a>b) abba 3)( 2 + 05

^+ a>b cia & c! 3 (a>b)2=3ab cia & c! 3 ;

D! (a>b) abba 3)( 2 + cia & c! 9 025

b) (1) "#(x=1)(x>6)(x>2)(x>3)#(x2>5x=6)(x2>5x>6)#(x2>5x)2=36 05

*a & (x2>5x)20 "#(x2>5x)2=36 =36 025

D! ? Mi "#=36 Qi (x2>5x)2#0

*] ? &a &+m Oc x#0 !_c x#=5 &+ Mi "#=36 025

Cu 3: (2)

a) (1) x2>9x>20 #(x>4)(x>5) ;

x2>11x>30 #(x>6)(x>5) ;

x2>13x>42 #(x>6)(x>U) ; 025

XYZX : 7;;n;" xxxx 025

"


8/47

Tuyn tp thi HSG Ton 8 Nm hc: 2011-2012(x>13)(x=2)#0

*] ? &+m Oc x#=13; x#2; 025

b) (1) X_& b>c=a#x 0; c>a=b# 0; a>b=c# 0

*] ? 8/ -a a#2

;2

;2

yxc

zxb

zy +=+=+ ; 05

*a ! &a Oc A#

+++++=+++++ )()()(

2

1

222 y

z

z

y

x

z

z

x

y

x

x

y

z

yx

y

zx

x

zy 025

*] ? 8/ -a A )222(2

1 ++ a A 3 025

Cu 4: (3 )

a) (1)

*-!' &am 'i,c IDM &a c? : 1

112 ! =

^+ 2x #600 &a c? : 1

312 =

S/ -a 31 ! =

C' mi %! )& (1) 05

S/ -a)&

)

%

%! = &] ? ID.CE#IM.CM

^+ IM#CM#2

%) &a c? ID.CE#

"

2%) 05

b) (1) *] (1) 8/ -a&

!

)

%! = m IM#CM &a c?

&

!

%

%! =

C' mi %! &! 05

*] ? 8/ -a 21 !! = R! ? DM &ia P 'i,c ca '?c IDE

C' mi &


9/47

Tuyn tp thi HSG Ton 8 Nm hc: 2011-2012(>2)2#(x>=2)2 8/ -a >2 # x>=2 025

#x>=4 ; &a ! (1) &a Oc :

x#2(x>>x>=4)

x=4x=4#=V

(x=4)(=4)#V#1.V#2.4 025 *] ? &a &+m Oc c,c 'i, &- ca x :

(x#5#12#13) ; (x#12#5#13) ;

(x#6#V#10) ; (x#V#6#10) 025

E THI SO 4Cau1( !"#"ag &[c a &hdc 8a/ &a ag &h

( ) ( ) ( ) ( )1 3 7 1A a a a a= + + + + +

Cau ( !"#^jdi 'iad &-k a! c/a a a b &l a &hdc:

( ) ( )1 1x a x +

ag &[c &a &[c c/a m!& a &hdc bac a@& c!d cadc 8!@ '/g

Cau $( 1 !"#&lm cadc 8!@ '/g a a b n a &hdc A(x) # " 33x x ax b + + cia

@& c! a

&hdc 2( ) 3 "% x x x= +

Cau 4( $ !"# C! &am 'iadc AIC hj' ca! Ae] ag 'iadc ex c/a '!dcAeI a ag 'iadc e c/a '!dc AeC. Y AD /!g' '!dc jdi ex AE /!g'

'!dc e.

Chd' mi -a'&hd 'iadc ADeE a l /!g'

Cau %( !": Chd' mi -a'

2 2 " 2

1 1 1 1... 1

2 3 " 1+= + + + + p 10) > 1

1 1 1 1

( 1) 1 1) 1

mn m n

m n n

+ =

+ =l m '/g &a c!d: {{ 1 1 1 11 1 1 1m mn n- = = = =8/ -a a # 12 !a`c a #V

025 025

025 025

025 025 025

31

*a c!d:A(x) #I(x).(x2=1) > ( a p 3)x > b > 4

on ( ) ( )A x % xM &l {{ 3 3" "a ab b = =+ = =05 05

43

*hd 'iadc ADeE a l /!g'ex a ag 'iadc c/a '!dc SF ; e ag 'iadc c/a

'!dc SC ma SF a SC a ai '!dc Qq b/ gex a e /!g' '!dcea GSM # 90

0ma`& Qadc GS MS= # 900

Wg &hd 'iadc ADeE a l ch] a& ( 1)

D!

A"

2 2

A"

2 2

A*%A*!

A*A*&

A*! A*&

= = =

= = =

=

ea eA a ag 'iadc !*&(2)*h (1) a (2) &a c!d &hd 'iadc ADeE a l /!g'

025

025 025 025 025 05

05

025 025 025



11/47

Tuyn tp thi HSG Ton 8 Nm hc: 2011-201252 2 2 " 2

1 1 1 1...

2 3 " 11 1 1 1

...2.2 3.3 "." 1.11 1 1 1

...1.2 2.3 3." AA.1

1 1 1 1 11 ...

2 2 3 AA 11 AA

1 11 1

+= + + + +

= + + + +

< + + + +

= + + +

= = +a a D aa )1( 2 nYn aaa + )1)(2( 22 o H

aaa ++ 33)1)(2( 22

Gju x_< a qh D ch qh 1 =a 1=a 2

' 2,i E$ imF

a(1 !%)Chn, %nh 46c t ,c ]X J h$nh than, Chn, %nh 46c X] tZ H su< a t ,c ]X J h$nh than, cn

b(2!%)

#nh 46c G cm33" ; FG 2G cm3

3B

] =%!2

1cm

3

3"

#nh 46c X ] cm3

3"

GC FC cm3

3B ]X =!)2

1cm

3

3"

#nh 46c cm3

3B

F ( !%)

a (1 !%)

V JuVn ! cH%!

'!

A%

' = A)

')

A%

'N=

V JuVn ! cHA)

')

!%

'! =

Gv: Nguyn Vn T Trng THCS Thanh M1B

(

I

)

* C

,

O()

* C

,+


19/47


A%

'N

A%

'= |] |X

b (1 !%)

It A%! ! cHA!

!

A%

' = (1) xIt A!) ! cHA!

A

!)

' = (2)

#Z (1) D (2) |].()!A%

11 + ) 1==+

=A!

A!

A!

!A

Chn, %nh t4@n, t~ |X. 1)11

( =+)!A%

tZ H cH (|] + |X). 2)11

( =+)!A%

N)!A%

211 =+

b (2 !%)

'!

'%

>

>

A'!

A'% = '!

'%

>

>

!')

%') = =A'!

A'%

>

>

!')

%')

>

> A'!%')!')A'% >>>> .. =

Chn, %nh 46c %')A'! >> = 2)(. A'!!')A'% >>> =

#ha< sQ ! cH 2B2.2A2 (\|G)2 \|G 2B.2A

Go H \FCG 2B2 + 2.2B.2A + 2A2 (2B + 2A)2 "172(@n D0G#)

S! -

, i 1:

Cho x 2 2 2

2

b c a

bc

+ ; <

2 2

2 2

( )

( )

a b c

b c a

+

#nh , t0 P x + < + x eai &am 'i,c ADC

IEC c?:B?c C c/'.)! )A

)& )%= (eai &am 'i,c

/K' CDE CAI

n' R')

D! ? c%' Rn' R' (c.'.c).S/ -a: 13%&) A!)= = (+ &am 'i,c AeD /K' cP &i e&! 'i &i&).W "nA&% = R! ? &am 'i,c AIE /K' cP &i A. S/ -a:

2 2%& A% m= =

10

05

4.2*a c?:

1 1

2 2

% %& A!

%) %) A)= = (R! %&) A!) : )

m 2A! A*=

(&am 'i,c AeD /K' P &i e)

1 1 2

2 2 2

% A! A* %* %*

%) A) A) %&A%= = = = (R! A%* )%A : )

D! ? %* %&) : (c.'.c) 8/ -a: 13n "n%* %&) A*= = =

05

05

054.3 *am 'i,c AIE /K' cP &i A &ia AM cu P 'i,c

'?c IAC.

S/ -a:0% A%

0) A) = m

( ) ( )[[

A% &! A* *!

A%) !&) &! A*A) !) *) *)= = =:

05

D! ?:0% *! 0% *! 0% *!

0) *) 0% 0) *! *) %) A* *) = = =

+ + +05

Phn, LG } # hu


28/47


b)1"B 1A 1B 1AA

12 23 21 1A

x x x x + + + =

c) 2 3 nx + =

,i $( i83"# >i?i ;i t)1

2x= } " #1

2

Gv: Nguyn Vn T Trng THCS Thanh M2B


29/47


>)1

2x

= }" # 2

3 1

c) " # 2 3

2 n

x

x

#

21

x+

*a c?: 1 ,^ " , Qi

2

n,

x

x p 5 \(2) M \(2)# ~ =2; =1; 1; 2 x p 5 # =2 x # 3 (*MXY) x p 5 # =1 x # 4 (Y*MXY) x p 5 # 1 x # 6 (*MXY) x p 5 # 2 x # U (*MXY)Y: x

~3; 6; U &+ " 'i, &- '/. 1

R) " # 2 3

2 n

x

x

#

21

x+

025

*a c?: 1 0

X " 0 &+2

x 0 x p 5 0 x 5 05

^[i x 5 &+ " 0. 025,i #

a) 21n 1 1

1 123 " " 3 3

x

x x x x

= ++ +

( ) ( ) ( )

1 1 11 12

" 1 " 3 1

x

x x x x

= + + +

XY: "; 1x x

3.15x p 3(x > 4)(x p 1) # 3. 12(x =1) > 12(x > 4)}

3x.(x > 4) # 03x # 0 !_c x > 4 # 0

>) 3x # 0 # x # 0 (*MXY)>) x > 4 # 0 # x # =4 (Y*MXY) S # ~ 0 1

b)1"B 1A 1B 1AA

12 23 21 1A

x x x x + + + =

1"B 1A 1B 1AA1 2 3 "

2 23 21 1A

x x x x + + + =

(123 p x) 1 1 1 1

2 23 21 1A

+ + + # 0

Gv: Nguyn Vn T Trng THCS Thanh M2A


30/47


D!1 1 1 1

2 23 21 1A

+ + +

0

W 123 p x # 0 # x # 123 S # ~123 1

c)

2 3 nx + = *a c?: 2 x x # 2 3x + 0

2 3 2 3x x + = + "* Oc i& R[i R':

2 3 nx + =

2x # 5 p 3

2x # 2>) x = 2 # 2 # x # 4>) x = 2 # =2 # x # 0 S # ~0;41,i $( " Bi Q!' c,c 'iya A I x (Qm) (x 0)025 ^ &c Rd ca 'ti x 'L m, :

3( [ )

1 13

3

x x?m 6=

(320# ( )1

33

6 )

025^ &c ca 'ti i x 'L m, Qi &v' 5 Qmw :

( )3

[1

x?m 6+

025*! H bi &a c?


31/47


^ &c Rd : ( )3.1n

"n [1

?m 6=

,i 4(') ^ + 'i B* Y %' 05

a) Bi 'ia! im 2 t' cs! ca + cy & AICD. " t' &-/' b+ ca &8m 'i,c CAM. AMww" & 'i,c AMDI + &a'.1b) D! AM wwID '?c IA # '?c MAE (n' )

*am 'i,c AI cP ` '?c IA # '?c AIBi f 'ia! im 2 t' cs! ca + cy & AEMF &+ &am'i,c AfE cP ` f '?c fAE # '?c fEA.

*] c' mi &- : c? '?c FEA # '?c AI R! ? EFwwAC (1)1M_& Q,c f" t' &-/' b+ ca &am 'i,c MAC f" ww AC (2)

*] (1) (2) 8/ -a ba im E F " &{' '.1

c) ( )A( !%A g g : ( A!

(A A%= QK' 7i. (1)

R) W/A

1

+!

+%= &+ A 1

A 1

+! +%? +! ? +% ? = = = =

W/ )+ %! &+ ( ) )+ +%)%! !)+ g g +! )+

=: 1

R! ? C"2# "I."Da (24)2# 9.16 Q2 # Q # 02"D # 9Q # 1V(cm)"I # 16Q # 32 (cm)05RID # 5 (cm)Cwm IC2# I".ID # 16

05R! ? IC # 4 (cm)


F

CG

|]

P

M

N


32/47

Tuyn tp thi HSG Ton 8 Nm hc: 2011-2012 CD # 3 (cm)05

,i %#a) *a c?: 2009200V> 20112010 # (2009200V> 1) > ( 20112010p 1)

^+ 2009

200V

> 1 # (2009 > 1)(2009

200U

= })# 2010.(}) cia & c! 2010 (1) 20112010= 1 # ( 2011 p 1)(20112009> }) # 2010.( }) cia & c! 2010 (2)1 *] (1) (2) &a c? cm.

b)2 2

1 1 2

1 1 1x y xy+

+ + + (1)

( )

( )( )( )

( )( )

( ) ( )

( ) ( )( ) ( )

2 2

2 2

2

2 2

1 1 1 1 1 1 1 1

1 1 1 1

1 2

1 1 1

x xy y xy

x y x y x y

x xy y xy

y x xy

x y xy

+ + + + +

+ + + + +

+ + +

^+ 1; 1x y # 1xy # 1 xy # IX* (2) %' # IX* (1) %' (R/ # x -a Qi x # )1

S! 1

,i 1:E$Fa) Phn tch a thc x3

x2

+ Bx " thnh nhn t b) #$% , t0 n,u


33/47

Tuyn tp thi HSG Ton 8 Nm hc: 2011-2012 b) L- | J ,ao !% ca 2 45n, chIo C D FG. L- J tun, !% MN. Chn, %nh | C thRn, hn,.,i %: E2FCho ta% ,c FC Dun, cn ty . Cc !% G M tho th t~ chu

a[ GM cH d nh> nhjtb[ # ,c FGMC cH in tch nh> nhjt.

HGng 7n ch3 F ;i8u i83,i 1: E$ imFa) ( 7) x3 9 x2 + Bx 9 " x3 9 "x2+ "x x2+ "x " (2) x( x2 "x + ") ( x2 "x + ") (2) ( x 1 ) ( x 2 ) 2 (2)

b) (7) It2 1x 7x n 7

nx "F 2x 3 2x 3

= = + +

(2)

UK x th$ F qh7

2 3x 7 ( 2x 3) (2)

] (7) { }1;1; 7;7 x ; 9 2; 2 ; 1 th$ F (2)

c) (1) Fn k 3 3x 3

,i %: Bii bi &!, 8a/ b' c,c


36/47

Tuyn tp thi HSG Ton 8 Nm hc: 2011-2012A #

B")2(")2(

)2(2).2(2.

)2(

)"2)("2(

2

")2(

2

1"(2

22

2

2

==+

+=

++

=+

=

+

xxxx

xxx

xx

xxx

xx

xx

xx

xx

Ii 3: (2 im)a) 2x2> 2x # 2x(x > 1) 0

2x 0 x > 1 0 x 0 x =1 (1 im)b) $%& ':

xxx

x

xx

x

2

)1(2

)1(

22

2

=+

+=

++

(05 im)

2

21

2

=== xx

x (025 im)

^+2

n&! m iH/ Qi ca ai &am 'i,c

2

n=x

(025 im)

,i 4: a) XiH/ Qi x,c : x 0; x 2

= Bii:)2(

2

)2(

2)9(x92)x(x

=

+

xxxx x2> 2x p x >2 # 2;

x# 0 (!i) !_c x # = 1. S # { }1

b) x2p 9 x2> 4x > U x2p x2p 4x U > 9 = 4x 16 x = 4^ 'im ca


37/47


Ae # 122n

n.2 = (cm)

Ie # A2n

1n.1n= (cm)

eC # IC p Ie # 25 p 9 # 16 (cm)

c) eM # IM p Ie # )(3A22

2 cm%*%)

==

SAeM#2

1Ae . eM #

2

1. 12. 35 # 21 (cm2)

= ^ %' +: A

I e MC

1

1

1

S! 21,i 1(. im): #$% x bt:

a) x2 "x + " 2

b) "1"

1x

1AB

21x

1AA

17x=

++

+

c) "x 12.2x + 32

,i 2(1,5 im): Cho x


38/47

Tuyn tp thi HSG Ton 8 Nm hc: 2011-2012 c) "x 12.2x+32 2x.2x ".2x B.2x+ ".B ( 2!% ) 2x(2x ") B(2x ") (2x B)(2x ") ( 2!% ) (2x 23)(2x22) 2x23 horc 2x22 ( 2!% ) 2x 23horc 2x 22 x 3; x 2 ( 2!% )

,i 2 (", %i&')/

=

1

=1 8 '/ &.

b I # 2223

2

23"

++++

n

nnnn

C? 'i, &- mG& 8 '/. c D# 5=>2 8 cT


40/47


Cu Ni dung bi gii im

C5u1(5i

m)

a (1im) A#3

=2

>=1#(2

>1)(=1) X A 8 '/ & &+ =1#1 #2 Qi? A#5

0505

05

050505

0505

05

05

b (2im) I#2>3=2n

22 +

I c? 'i, &- '/ 22>2 2>2 [c &d i ca 2 2>2#1 QK' c? 'i, &- &! me!_c 2>2#2 #0 ^[i #0 &+ I c? 'i, &-'/.c (2im) D#5=>2#(4=1)>2#(>1)(=1)(2>1)>2 #(=1)(>1)( ) n"2 +n >2# (=1)(>1)(=2)(>2)>5 (=1)(>1)>2 M (=1)(>1)(=2)(>25 (&ic 58 &di i &i) ^ 5 (=1)(>15 ^ D cia 5 R 2 D! ? 8 D c? & c' 2 !_c U D QK'i 8 cT b>c#0 a2

>b2

>c2

>2(ab>ac>bc)#0 a2>b2>c2# =2(ab>ac>bc) a4>b4>c4>2(a2b2>a2c2>b2c2)#4( a2b2>a2c2>b2c2)>Vabc(a>b>c) ^+ a>b>c#0 a4>b4>c4#2(a2b2>a2c2>b2c2) (1)M_& Q,c2(ab>ac>bc)2#2(a2b2>a2c2>b2c2)>4abc(a>b>c) .^+ a>b>c#0 2(ab>ac>bc)2#2(a2b2>a2c2>b2c2) (2)

*] (1)(2) a4>b4>c4#2(ab>ac>bc)2

Gv: Nguyn Vn T Trng THCS Thanh M"


41/47


05

c (2im) , Rj' b& {' &c: x2>22x D/ b' Qi x#

c

a

c

b

b

a

c

b

b

a.2..2

2

2

2

2

=+ ;b

c

a

c

b

a

a

c

b

a.2..2

2

2

2

2

=+ ;

ab

cb

ac

cb

ac .2..22

2

2

2

=+

CG' &]' ba b& {' &c &- &a c?:

)a

b

b

c

c

a(2)

a

c

c

b

b

a(2

2

2

2

2

2

2

++++ a

b

b

c

c

a

a

c

c

b

b

a2

2

2

2

2

2

++++

C5u$(5im)

a (2im) B2

"

B"

132

B

21"=

+

+

xxx

)3

B2

"()2

B"

132()1

B

21"( =++ xxx

B2

3

B"

3

B

3=

+

+

xxx

(x=300) B2

1

B"

1

B

1=

++ x=300#0 x#300 ^ S #

{ }3

10

05

05

0505

05

05

05

05

b (2im) 2x(Vx=1)2(4x=1)#9 (64x2=16x>1)(Vx2=2x)#9 (64x2=16x>1)(64x2=16x)# U2X_&: 64x2=16x>05 #Q *a c?: (Q>05)(Q=05)#U2

Q2#U225 Q# V5^[i Q#V5 &ac? 9#0 (Vx=1)2>V#0 K 'im.

^ S #

"

1

2

1

c (1im) x2=2>2x=4=10 # 0 (x2>2x>1)=

(2>4>4)=U#0 (x>1)2=(>2)2#U (x==1)(x>>3) #U ^+x '/ R


42/47


C5u4(5im)

a(1im) ^+ AIwwCD S DAI#S CIA(c' , c' t' ca!) S DAI pSAI # S CIA= SAI

ea SAD # SIC

b (2im) ^+ EwwDC A)

A'

!)

&' = M_& Q,c AIwwDC

!)A%

A%

!)

&'

A)

A'

%)A%

A%

')A'

A'

%)A%

A%

')

A'

!)

A%

+==

+

+=

+=

&(A%!)&(!)A%

!)A%

!)A%

A%

!)

&( 2112

.2=+=

+

+=

c (2im) >Dd' &-/' &/ EM > Dd' EWwwMY (WDF) >Y t' &{' YW t' &{' i Rd'C' mi: SEDM#S EMF(1).Bi 'ia! ca EM YW f &+ SfYE#SfMW(cma) (2) *] (1) (2) SDEYW#SYFW.

1

1

1

+-M T.N /1 MNG V3T N1M/u4 5h6y 78 v 9n h;y 5 7h5 5hi gian %& %?7 9i gi@i 5hiAu au 7a 58i v h;y 5ri Dn

ngi %ng 5i EiAu ny 9Fng 77h


43/47

Tuyn tp thi HSG Ton 8 Nm hc: 2011-2012bt s n, %< tnh %dt cht. UV< th~c chjt ca Dic n< J Dic ,$ D J% nh4 th no/ zuf thO< c Dcc byn h?< -c b Dt ca t D nu cH hn, th th$ h?< b{t ta< Do cn, Dic n,a< th.

#hO< c ch{c ? n,h n,hTu n Dic q% tTn ua %yn,. Ch{c ch{n J cH. #u< nhYn tYn ntnthin na< cH nhTu tan, b q% tTn qhn, u< tn( H J nhn, tan, b n4Kc n,o nhn, tan, b t_ th Jao jt cao...). Xu J b n4Kc n,o th$chn, ta s ,r jt nhTu qhH qhn DT %rt n,n n, nhn, b t_ th Jao jt cao Tu qhn, u< tn chn,

ta h?< nhVn nhn, ,$ t4@n, xn, DK cn, Jao ca chn, ta H J s~ thVt. Uit Xa% tan, b thVt s~ u< tn H J : htt:[[I.t.Jin./com.c Ou b_n thn t cn, thj

tuyen tap 40 de thi hsg toan 8 co dap an

Documents