Tuyen Chon 25 de Thi Hoc Ky II Lop 10 Vip Nam 2013

7/26/2019 Tuyen Chon 25 de Thi Hoc Ky II Lop 10 Vip Nam 2013

1/16

http://trithuctoan.blogspot.com/B N TP KIM TRA HC K II MN TON 10 NM HC 2012 - 2013

1S IO !"C #$ $O T%O TPHCM

TR&'N THPT N KIM TRA HC K 2

M() T*+) ,. 10

Thi gian lm bi: 90 pht (khng k thi gian pht !

C/ 1( " im ! #i$i cc b%t ph&'ng trnh sau.a! ()*+!( ) + ,-) , ! 0

b! 0"

11++

+

++xx

xx

C/ 2( im !.Tm cc gi tr2 c3a m b%t ph&'ng trnh: )+4 m ) 4 "m * 0

C/ 3(5- im ! 6i7t cos 8 ( !. T;nh sin+


2/16

http://trithuctoan.blogspot.com/

! T;nh cc gi tr2 l&ng gic c3a gNc 5 bi7t sin 8 -

@

.

+

< ng minh r?ng: cot @tan 8 +cot+

C/ I#92;?6Trong mAt phBng 'xy cho hai im( H 0! )(*+ H 9!.

! Ii7t ph&'ng trnh tng Lut c3a &ng thBng i Lua hai im).

+! Ii7t ph&'ng trnh &ng trPn (*& cN tMm+(+ H 1! ti7p )c Gi &ng thBng .B6 PH7N RIN 93;?6(Th sinh hc chng trnh no th lm theo chng trnh )

1. Theo chng trnh c bn.

C/ #92;?6

! #i$i b%t ph&'ng trnh+ -.x c+ +( ! +( +! 0, x x m x m= + > 5 Gi .x R.

C/ #I91;?6

Tm tCa Q cc tiWu im5 cc nh H Q Ki trc lGn5 trc bj c3a Ulip (-&:

+ +@ +- 00.x y+ =

. !hng trnh n"ng c#o.

C/ #92;?6

! #i$i b%t ph&'ng trnh2 10 21 3. + < x x x

+! =ho ph&'ng trnh )+* +(m*!) , +m+* -m , " 8 0. Tm m ph&'ng trnh cN hai nghiOm K&'ng phMnbiOt.C/ #I91;?6

!Ii7t ph&'ng trnh ch;nh tc c3a hDpUbol (H&bi7t tMm sai U 8 +5 cc tiWu im c3a (H&trng Gi cc tiWu

im c3a Ulip (-&:

+ +

.+- x y+ =

+! Tm im.trWn (H&sao cho ++.F .F= .*************XYT************

3

!"$ 15 #i$i b%t ph&'ng trnh sau: a! +

( "! "

x

x x

+ + b! + + - @ "+ @x x x x + +

!"$ %#i$i cc ph&'ng trnh sau: a. ++ @ "x x x = + b. + +" + + @x x x x+ + = +

!"$ & :Tm iu kiOn c3a m b%t ph&'ng trnh sau : m)+4 +(m 4 + !) , m 4 9 0 cN nghiOm ng Gi mCi )thuQc .

!"$ ' : a! Tm cc gi tr2 l&ng gic c3a cung bi7t:

sin-

= +

< < .

b! t gCn biu th>c sau: 68+ + +sin +cos

cos sin cos sin

+

+

!"$ % =J : a! " "

cos sin sin cos sin @@

a a a a a = b!

( )+ "

"

cos sin

cot cot cot 5 .sin k!

+= + + +

c! + ++

sin sine e +

/in aa a

+ =

K! cos cos @cot

cos cos sin

x x x

x x x

+ =

+

!"$ 5 Trong mAt phBng Gi hO trc tCa Q )D5 cho F(H "! &ng thBng: K: ) 4 +D , @ 8 0

Trang 2
http://trithuctoan.blogspot.com/http://trithuctoan.blogspot.com/


3/16

http://trithuctoan.blogspot.com/a! Ii7t ph&'ng trnh tham s &ng thBng K.

b! Tm tCa Q im f trWn K sao cho tam gic Ff ung t\i F.c! Ii7t ph&'ng trnh &ng thBng K Lua F cch im 6(4 H -! mQt kho$ng cch l + .

!"$ *%Trong mAt phBng Gi hO trc tCa Q )D5 cho F6= Gi F(H +!5 6(+H 4"!5 =("H -!. a! Ii7t ph&'ng trnh &ng trPn tMm 6 ti7p )c Gi &ng thBng F=. b! Ii7t ph&'ng trnh &ng thBng ung gNc Gi F6 t\o Gi + trc to\ Q mQt tam gic cN KiOn t;chb?ng 0.

!"$ +% Ii7t ph&'ng trnh ch;nh tc c3a Ulip( )-

bi7t (V! cN tiWu c l e 5 tMm sai

+=

!"$ ,5Trong mAt phBng Gi hO tCa Q )D5 cho EF6= Gi 6(+H *1!5 ph&'ng trnh &ng cao FF: ") , D , 80 H ph&'ng trnh trung tuD7n =J : ) , +D , 1 8 0 . Ii7t ph&'ng trnh tng Lut c3a &ng thBng F6 F=.

!"$ 1- %Ii7t pt &ng trPn i Lua im F(H"! ti7p )c Gi hai &ng thBng : ) , +D , + 8 0 +: +) 4 D, 9 8 0

!"$ 15#i$i cc b%t ph&'ng trnh hO b%t ph&'ng trnh sau :

a! + ++ -

- @ 1 0x x x xng minh biu th>c J 8 cos) , +sin) , sin@).cos+) , @sin+).cos+) 4 sin+) khng ph thuQc o ).!"$ 5 =h>ng minh cc Bng th>c sau:

a! + + sin + tan sin cos tan x x

x x x+ +=

b! " "sin ( cot ! cos ( tan ! sin cosx x x x x x+ + + = +

c! +"

cos sin sin @

x x x + =

K! @ +cos@ ecos ecos a a a= +

!"$ 5 Trong mAt phBng Gi hO trc tCa Q )D5 cho tam gic F6= cN F(5@!5 6(@5!5 =(15"

+!

a! =h>ng minh r?ng tam gic F6= ung t\i 6b! Ii7t ph&'ng trnh &ng trPn (=! ngo\i ti7p tam gic F6=.c! Ii7t ph&'ng trnh ti7p tuD7n c3a &ng trPn (=! t\i 6.

!"$ *5 a!=ho &ng thBng 2: + " 0x y+ = . Tm to\ Q im J thuQc trc honh sao cho kho$ng cch t^ J 7n

2b?ng @. b! Ii7t ph&'ng trnh &ng trPn tMm (+H 0! ti7p )c Gi trc tung.

!"$ +5Ii7t ph&'ng trnh &ng thBng (K! Lua F( H +! t\o Gi &ng thBng (q!:) , " D -

8 +

mQt gNc @-0.

!"$ ,5 Trong mAt phBng Gi hO trc tCa Q )D5 cho Ulip (-!: 9)+, D+8 @@. XD )c 2nh Q Ki trc lGn5 trc

nh5 tiWu c5 tMm sai5 tCa Q cc tiWu im tCa Q cc nh c3a (V!.!"$ 1- % Ii7t ph&'ng trnh &ng thBng (K! Lua J (H "! cch u hai im F(H*+!5 6("H!.

!"$ 1: #i$i ph&'ng trnh : a! " 4 -) , ++ ++xx 8 0 b!+ ++0 9 " 0 +x x x x = + +

!"$ : #i$i b%t ph&'ng trnh : a!+

+ " " "x x x < b! +" 1 @ +( !x x x + c!+

+ x x x + !"$ &: Tm m ph&'ng trnh : ( )+ + + " 0x m x m+ + = cN + nghiOm cng K&'ng phMn biOt.

!"$ ': Z2nh m b%t ph&'ng trnh : +( ! +( ! "( +! 0m x m x m + + > nghiOm

Trang 3


4/16

http://trithuctoan.blogspot.com/!"$ : a! =ho

"sin

" + +a a

= < c sau : J 8+ +

+ +

sin tan

cos cot

!"$ *5 a!=ho &ng thBng (K! :+ +

+

x t

y t

= = +

im F("H !. RSp ptrnh tng Lut c3a &ng thBng (! Lua F

(K!.b! T;nh gNc gia + &ng thBng sau : ( ! : + " 0x y + =

+( u! : ( !

x tt 1

y t

= + = +

c! Ii7t ph&'ng trnh ti7p tuD7n c3a &ng trPn (=! : + + @ + @ 0x y x y+ = bi7t ti7p tuD7n Lua F(* H +!

!"$ +%a! RSp ch;nh tc c3a Ulip (V!5 bi7t mQt tiWu im c3a (V! l v (4eH 0! im J(-H 4" " ! thuQc Ulip.

b! RSp ph&'ng trnh ch;nh tc c3a (V! cN tMm sai-

"= hnh ch nhSt c' s cN chu i l +0.

!"$ ,%Ii7t ph&'ng trnh &ng trPn (=! bi7t:a. (=! Lua F(05 +!H 6(*5 ! cN tMm n?m trWn &ng thBng +) , "D 8 0

b. (=! Lua F(-5 "! ti7p )c Gi &ng thBng K: ) , "D , + 8 0 t\i im J (5 *!.

!"$ 1- %Trong mAt phBng )D5 cho F( H*"! &ng thBng ( ! : + + 02 x y = . Tm tCa Q c3a 65 = trUn (K! saocho tam gic F6= ung cMn t\i 6

!"$ 1: #i$i ph&'ng trnh : a. +" +@ ++ + x x x+ + = + b. + +e + " " 9x x x x+ = +!"$ : #i$i b%t ph&'ng trnh sau:

a! + " + +x x x + < + b!+ "

" x x x

+ +c! + ++ " - + e x x x x

!"$ &: Z2nh m ph&'ng trnh : + ++( ! e - 0x m x m m + + + + = cN hai nghiOm cng Mm phMn biOt.

!"$ ': Z2nh m b%t ph&'ng trnh : +( ! + - 9 0m x mx m + nghiOm

!"$ : a! =ho a b l + gNc nhCn K&'ng tha iu kiOn: ( , tana! ( , tanb! 8 +. =h>ng minh: @a b

+ =

b! t gCn biu th>cF 8, +sin)cos)

(, tan)!(, cot)!

c! =h>ng minh biu th>c + +cos ( ! cos +cos .cos .cos( !* a x x a x a x= + + + Qc lSp i Gi )

!"$ %=h>ng minh Bng th>c sau :

a!cos cos" cos-

cot"sin sin" sin-

a a aa

a a a

+ +=

+ +b! cot tan tan + @ tan @ ecot @a a a a a =

c!

sin .sin .sin sin "

" " @

a a a a + =

K!+

cos cos+ cos"+cos

+cos cos

x x xx

x x

+ + +=

+ U! 9 " sin cos cos cos cos 9

@e @e +@ +

=

!"$ *5 Trong mAt phBng Gi hO to\ Q )D 5 cho &ng thBng (K! cN ph&'ng trnh :+ +

"

x t

y t

= + = +

mQt im F(0H

!.a. Ii7t wTTx c3a &ng thBng (K! Lua F song song Gi (K! .

b. Tm im J thuQc K sao cho FJ ngn nh%t.

!"$ +:Ii7t ph&'ng trnh ch;nh tc c3a Ulip (V! 5 bi7t Ulip (V! i Lua hai im" + 1

H H H+ + + +

. N

!"$ ,% a! Ii7t ph&'ng trnh ti7p tuD7n c3a &ng trPn (=!: + + +x y+ = bi7t ti7p tuD7n cN hO s gNc l

b! Ii7t ptrnh ti7p tuD7n c3a &ng trPn (=!: + +( ! +-x y+ = bi7t ti7p tuD7n ung gNc Gi &ng thBng ") 4@D , 8 0

Trang 4


5/16

http://trithuctoan.blogspot.com/!"$ 1- %

a! =ho &ng thBng (K!: ) 4 +D , - 8 0. Tm trWn (K! nhng im J ()J H DJ! sao cho )+J, D+Jnh nh%t***b! =ho &ng trPn (=!: + + + @ 0x y x y+ + = &ng thBng (K!: @) 4 "D , m 8 0. Tm m (K! ct (=! t\i +

im phMn biOt F5 6 sao cho 0+0+)= 5 Gi l tMm c3a &ng trPn (=! :

C/ 15 . #i$i 6wT hO 6wT sau: a. + 1 " +x x x + + < + b. ++ + @x x x + c.

++ - + 0

"0

x x

x

x

+ +

ng minh Bng th>c l&ng gic sau: +(tan + tan !(sin + tan ! tanx x x x x =

b. =h>ng minh biu th>c "cos cos cos cos" @ @

( x x x x = + + + +

khng ph thuQc o )

!"$ *%=ho tam gic F6=. =h>ng minh r?ng :"

cos cos cos+

) *+ +

!"$ +%Tm t%t c$ cc gi tr2 c3a m lm cho b%t ph&'ng trnh +( ! ( ! +( +! 0, x m x m x m= + + + > cN tSp nghiOmT= !"$ ,%Trong mAt phBng )D cho hai &ng thBng5 +( ! : + 0H( ! : + - 02 x y 2 x y + = + = im J(*H@!

a! Ii7t ph&'ng trnh &ng trPn (=! cN tMm J ti7p )c Gi &ng thBng (K!b! Ii7t ph&'ng trnh &ng thBng ( ! ct (K! H (K+! ldn l&t t\i F 6 sao cho J l trung im c3a o\n thBng

F6

!"$ 1-%=ho ph&'ng trnh:@ +

+ " + 0x mx m + = . Tm m ph&'ng trnh cho cN @ nghiOm phMn biOt D

!"$ 1%#i$i cc b%t ph&'ng trnh sau: a! ++ -

1 "

x

x x x

!"$ &%

a! Ii7t ph&'ng trnh &ng trPn i Lua hai im: ( H-!5 (H@! ) cN tMm n?m trWn &ng thBng: + 0x y + = .

b! Trong mAt phBng )D cho &ng trPn ( ) ( )+ +( ! : + @* x y + = im ( "H @! .XD i7t ph&'ng trnh ti7ptuD7n c3a ( !* i Lua .

!"$ '%a! #i$i b%t ph&'ng trnh: a! + +- + 0 -x x x x + > + b!+ @ 0x x x+ < c!

+ +" x x x x + +Trang 5


6/16

http://trithuctoan.blogspot.com/ b! =h>ng minh r?ng 5

( )+

+

cos cos +cot (sin 0!

sin sin

xxx x

x x

+ =

6

!"$ %=ho &ng trPn ( ) +: @ @ 02x* y x y+ + + = &ng thBng : ") 4 @D 4 + 8 0. Ii7t ph&'ng trnh &ng

thBng song song Gi ct ( )* t\i hai im phMn biOt F 6 sao cho + -)=

!"$ % a!=ho cota8

". T;nh

+ +

"

sin sin cos cos

a a a a=

b! =ho tan "= . T;nh gi tr2 biu th>c + +sin -cos = +

!"$ *%Trong mAt phBng xy5 cho F6= Gi F(H +!5 6(+H 4"!5 =("H -!.a! Ii7t ph&'ng trnh tng Lut c3a &ng cao k{ t^ F.

b! Ii7t ph&'ng trnh &ng trPn tMm 6 ti7p )c Gi &ng thBng F=.c! Ii7t ph&'ng trnh &ng thBng ung gNc Gi F6 t\o Gi + trc to\ Q mQt tam gic cN KiOn t;ch b?ng0.

!"$ +%RSp ch;nh tc c3a Ulip (V!5 bi7t mQt tiWu im c3a (V! l v (4eH 0! im J(-H 4" " ! thuQc Ulip.!"$ ,%Ii7t ph&'ng trnh &ng trPn i Lua hai im F(*H*+!5 6(+H! ti7p )c Gi &ng thBng (! : +) 4 D , +80!"$ 1-%Trong mp )D5 cho tam gic F6= cN F(0H+!5 6(*+H*+!H=(@H*+!. #Ci X l chMn g cao h\ t^ 6 J5 f ltrung im c3a F65 6=. Ii7t ph&'ng trnh &ng trPn Lua X5 J5 f

E KIM TRA HC K II6 NK5 2011 2012FTG)J THPT ng minh r?ng:tan( ! tan( ! tan( ! tan( !.tan( !.tan( ! ) * ) * ) * ) *+ + + + + = + + +PL) G


7/16


THI HC K II MN TON NM HC 2011-2012QP 10

Thi gian lm bi: 90 pht ( !hng !" thi gian ph4t $%&

c F cos(a b!.cos(a b!= + - .

?6 =h>ng minh r?ng:+

++

sin ) +tan )

sin )

+= +

-CY8 35=ho tam gic F6= cN F 8 00H F6 8 -5 F= 8 e. T;nh KiOn t;ch 5 &ng cao FX bn k;nh &ng trPnngo\i ti7p c3a F6=.

CY8 5Trong mAt phBng Gi hO to\ Q xy5 cho F6= Gi F( +H !5 6(@H "! =(H 1!.?6Ii7t ph&'ng trnh tng Lut c3a cc &ng thBng ch>a c\nh 6= &ng cao FX.

?6Ii7t ph&'ng trnh &ng trPn cN tMm l trCng tMm # c3a F6= ti7p )c Gi &ng thBng 6=

Trang 7


8/16

http://trithuctoan.blogspot.com/CY8 5Trong mAt phBng Gi hO to\ Q xy5 cho Ulip (V!: + +) 9D "+ = . Tm Q Ki cc trc5 to\ Q cc tiWuim c3a Ulip (V!.

********************/t*******************

12

CY8 15 #i$i cc b%t ph&'ng trnh sau:?6 +") @) 1 0- + + > ?6 ++

"+ ?6-"

+

+

+

+ x

x

x

CY8 25

?6IGi gi tr2 no c3a tham s m5 hm s +D ) m) m= - + cN tSp )c 2nh l

?6Tm m ph&'ng trnh sau cN + nghiOm K&'ng phMn biOt: +) +m m - 0x- - - = 6

CY8 35

?6=ho 0 0@

0-

cos va 90a = c: 6 8+ + +sin +cos

cos sin cos sin

- a a -+

a + a a - a

CY8 5Trong mAt phBng tCa Q )D cho F(-H@! hai &ng thBng : ") +D 0D + - = 5

: -) "D + 0D - + =

?6Ii7t ph&'ng trnh tng Lut &ng thBng Lua F ung gNc E?6Tm tSp hp im f thuQc &ng thBng K : ) +D 0- = sao cho kho$ng cch t^ f 7n D g%p i kho$ngcch t^ f 7n E.

CY8 5Trong mAt phBng Gi hO to\ Q xy5 cho &ng trPn (=!: + +) D @ D " 0x+ - + - = . Ii7t ph&'ngtrnh ti7p tuD7n c3a &ng trPn (=! t\i im

J(+H !.

********************/t*******************

1

CY8 15#i$i cc b%t ph&'ng trnh sau5

?6 0@1+ + xx ?6+) e) + )

" +) +

- + ->

-CY8 25 ti7t t hCc t\i nh trong tudn (ti7t/tudn! c3a +0 hCc sinh lGp 0 tr&ng TXwT F &c ghi nhSn nh&sau: 9 - + + 0 @ @ - " .T;nh ph&'ng sai Q lOch chu|n c3a gi tr2 nD.

CY8 35

?6=ho tam gic F6=5 ch>ng minh r?ng: sin +F sin +6 sin += @sin Fsin 6sin =+ + =?6t gCn biu th>c +

c +)w -

+c )

os

os

+= -

CY8 5=ho

++

"H

-

"cos


10/16

http://trithuctoan.blogspot.com/CY8 5 Trong mAt phBng Gi hO trc tCa Q )D5 cho cc im F( H "!5 6(H+!- - =( H!-?6Ii7t ph&'ng trnh tham s c3a &ng thBng ch>a c\nh 6=.?6Ii7t ph&'ng trnh tng Lut c3a &ng thBng D Lua im F song song Gi c\nh 6=?6Tm tCa Q im q trWn &ng thBng D sao cho t> gic F6=q l hnh bnh hnh.Z?6Ii7t ph&'ng trnh &ng trPn tMm F5 i Lua =.

********************/t*******************

1

CY8 15 #i$i cc b%t ph&'ng trnh sau:

?6 0@" + ++ xx ?6 ( ) ( )++ @+ xx +ng minh: ( + "

"cos sin

cot cot cot k 5 .sin

ka + a

= + a + a + a a ! p "a

CY8 5 =ho tam gic D F6= cN b 8@ 5- cm 5 gNc00 1-5"0 == *(

?6T;nh cc c\nh a5 c5 gNc ) .?6T;nh KiOn t;ch EF6=.?6T;nh Q Ki &ng cao 6X.CY8 5 Trong mAt phBng xy5 cho F6= Gi F(H +!5 6(+H 4"!5 =("H -!.

Trang 10


11/16

http://trithuctoan.blogspot.com/?6Ii7t ph&'ng trnh tng Lut c3a &ng cao k{ t^ F.?6Ii7t ph&'ng trnh &ng trPn tMm 6 ti7p )c Gi &ng thBng F=.?6Ii7t ph&'ng trnh &ng thBng ung gNc Gi F6 t\o Gi + trc to\ Q mQt tam gic cN KiOn t;ch b?ng0.

********************/t*******************

1D

CY8 15 #i$i cc b%t ph&'ng trnh sau:

?6 +( ) !() ) ! 0- + - > ?6 ) +

) + ") -

+#

+ -

CY8 25 =ho ph&'ng trnh: @ +) +m) "m + 0- + - = .

?6#i$i ph&'ng trnh khi m 8

-.

?6}c 2nh m ph&'ng trnh cN @ nghiOm phMn biOt

CY8 35

?6 Cho @tan =x 00 900 ng t r?ng F5 65 = l " nh c3a mQt tam gic.?6Ii7t ph&'ng trnh &ng thBng (K! i Lua F song song Gi 6=.?6Ii7t ph&'ng trnh &ng trung tuD7n FJ c3a F6=.

Z?6Tm tCa Q im f thuQc (E!:

+=

=

ty

tx

+

+sao cho f cch u F56

********************/t*******************

1E

CY8 15 #i$i cc b%t ph&'ng trnh sau:?6

+ +( @)! 0) ) - > - + ?6+

+) + @ )

) "9

x

x

- -$

--CY8 25 =ho ph&'ng trnh: +m) +(m !) @m 0- - + - = . Tm cc gi tr2 c3a m:?6wh&'ng trnh trWn cN nghiOm.?6wh&'ng trnh trWn cN hai nghiOm K&'ng phMn biOt.CY8 35

?6 Tm cc gi tr2 l&ng gic c3a cung a bi7t:

sin-

a = +

p


12/16

http://trithuctoan.blogspot.com/CY8 5 =ho tam gic F6= cN F 8 00H F6 8 -5 F= 8 e. T;nh KiOn t;ch 5 &ng cao FX bn k;nh &ng trPnngo\i ti7p c3a F6=.

CY8 5Trong mAt phBng tCa Q )D cho hai im5 im F(H @! !+

0H+( )

1?6=h>ng minh r?ng F6D ung t\i H2?6T;nh Q Ki i7t ph&'ng trnh &ng cao X c3a F6D H3?6=ho &ng trPn (= !: + +() ! (D +! e- + - =

?6}c 2nh tMm bn k;nh c3a (= !?6Ii7t ph&'ng trnh ti7p tuD7n c3a (= ! ung gNc Gi F6.

********************/t*******************

20

I - PH7N CH8N !$NH CHO T[T C\ CC TH] SINH(*0- im)C/ 1(0 $i"m&;

! =ho 0H 0a b> > . =h>ng minh r?ng : ( !( !( ! ea b b 3 3 a ab3+ + +

+! #i$i b%t ph&'ng trnh:

a. ( ) ( )+ +"

09 @

x

x x

+

+ b.x x2 3 1 > +

C/ 25 (8;0 $i"m& =hiu cao c3a @0 Sn Qng iWn bNng chuDn &c cho trong b$ng sau:

RGp chiu cao (cm! Tdn s e H 1+ ! 1+ H 1 ! 1 H e0 !

e0 H e@ ! e@ H ee ! ee H 9+

@@

@e@

=Qng @0

a! Tm mt5 s trung 2b! T;nh s trung bnh cQng5 ph&'ng sai~

C/ 3 (80 $i"m&; =ho tam gic F6= cN 6= 8 - H F= 8 e H% 00*= T;nh F65 KiOn t;ch tam gic F6= bn k;nh

&ng trPn ngo\i ti7p tam gic F6=C/ (


13/16

http://trithuctoan.blogspot.com/C/ (80 $i"m&; =ho Ulip (V ! :

+ +

9

x y+ = . }c 2nh tCa Q cc nh5 tCa Q tiWu im c3a5 Q Ki cc trc c3a

(V !26 TL^* L_)J XG`)L N/)J *5C/ (


14/16


C/ 25 =ho ph&'ng trnh: x m x m m2 22( 1 8 15 0 + + + + =a! =h>ng minh ph&'ng trnh lun cN nghiOm Gi mCi m.

b! Tm m ph&'ng trnh cN hai nghiOm tri K%u .

C/ 35 Trong mAt phBng xy5 cho F6= Gi F(H +!5 6(+H 4"!5 =("H -!.a! Ii7t ph&'ng trnh tng Lut c3a &ng cao k{ t^ F.

b! Ii7t ph&'ng trnh &ng trPn tMm 6 ti7p )c Gi &ng thBng F=.c! Ii7t ph&'ng trnh &ng thBng ung gNc Gi F6 t\o Gi + trc to\ Q mQt tam gic cN KiOn t;ch b?ng0.

C/ 5 Zim trung bnh kim tra c3a + nhNm hCc sinh lGp 0 &c cho nh& sau:fhNm : (9 hCc sinh! 5 +5 "5 -5 5 5 15 e5 9fhNm +: ( hCc sinh! 5 "5 "5 @5 @5 5 15 15 15 e5 0a! XD lSp cc b$ng phMn b tdn s tudn su%t ghjp lGp Gi cc lGp 5 @H -5 H

15 eH 95 0 c3a + nhNm.b! T;nh s trung bnh cQng5 ph&'ng sai5 Q lOch chu|n + b$ng phMn b.c! fWu nhSn )jt k7t Lu$ lm bi c3a hai nhNm.

K! I biu ` tdn su%t hnh cQt c3a + nhNm.

C/ 5

a! =h>ng minh: ( )k k2 33cos s'

1 co& co& co& ) .s'

+= + + +

b! t gCn biu th>c: A2

&a'2 co&2

1 co& 2

+=

+. au N t;nh gi tr2 c3a biu th>c khi

8

= .

23

C/ 15

! =ho a b 3 0 . =h>ng minh r?ng:a b b c c a

c a b6

+ + ++ +

+! #i$i cc b%t ph&'ng trnh sau:

a! x5 4 6 b! x x2 3 1 > +

C/ 25 Tm m biu th>c sau lun lun K&'ng: f x x m x m2( 3 ( 1 2 1= + +

C/ 35 =ho tam gic F6= cN F 8 00H F6 8 -5 F= 8 e. T;nh KiOn t;ch 5 &ng cao FX bn k;nh &ng trPn

ngo\i ti7p c3a F6=.

C/ 5 Trong mAt phBng xy5 cho tam gic cN F(H @!5 6(@H !5 C 37*

2

a! =h>ng minh r?ng tam gic F6= ung t\i 6b! Ii7t ph&'ng trnh &ng trPn &ng k;nh F=

C/ 5 Z kh$o st k7t Lu$ thi tuDn sinh mn Ton trong k thi tuDn sinh \i hCc n]m ^a Lua c3a tr&ng F5ng&i iu tra chCn mQt m_u g`m 00 hCc sinh tham gia k thi tuDn sinh N. Zim mn Ton (thang im0! c3a cc hCc sinh nD &c cho b$ng phMn b tdn s sau MD.

Zim 0 + " @ - 1 e 9 0Tdn s " - e " 9 +@ @ 0 + f800

a! XD lSp b$ng phMn b tdn su%t.

Trang 14


15/16

http://trithuctoan.blogspot.com/b! Tm mt5 s trung 2.c! Tm s trung bnh5 ph&'ng sai Q lOch chu|n (ch;nh )c 7n hng phdn tr]m!.

C/ 5

a!T;nh gi tr2 cc biu th>c sau: A 11 25s' s'

3 4

= 5 B 13 21s' s'

6 4

=

b! =ho sina, cosa84

7

. T;nh sina.cosa

2

C/ 15 #i$i cc ph&'ng trnh b%t ph&'ng trnh sau:

a! x x x x2 25 4 6 5 + + b! x x x24 4 2 1 5+ +

C/ 25 Z2nh m b%t ph&'ng trnh sau ng Gi mCix:

mm x mx 2( 4 2 2 0 + +

C/ 35 t gCn biu th>c A

3 3cos s'1 s' cos

= + . au N t;nh gi tr2 biu th>c F khi 3

= .

C/ 5 =hiu cao c3a @0 Sn Qng iWn bNng chuDn &c cho trong b$ng sau:

RGp chiu cao (cm! Tdn s e H 1+ ! 1+ H 1 ! 1 H e0 ! e0 H e@ ! e@ H ee !

ee H 9+

@@

@e

@=Qng @0

a! XD lSp b$ng phMn b tdn su%t ghjp lGp ~b! fWu nhSn )jt chiu cao c3a @0 Sn Qng iWn bNng chuDn k trWn ~c! T;nh s trung bnh cQng5 ph&'ng sai5 Q lOch chu|n ~K! XD biu ` tdn su%t hnh cQt m t$ b$ng phMn b tdn su%t ghjp lGp lSp cMu a!.

C/ 5 Trong mAt phBng to\ Q xy5 cho F(4H +!5 6("H 4-!5 =(@H 1!.a!Ii7t ph&'ng trnh &ng ung gNc FX k{ t^ F 7n trung tuD7n 6 c3a tam gic F6=.

b! T;nh KiOn t;ch tam gic F6.c! Ii7t ph&'ng trnh &ng thBng Lua F chia tam gic thnh + phdn sao cho KiOn t;ch phdn ch>a 6 g%p +ldn KiOn t;ch phdn ch>a =.

K! Ii7t ph&'ng trnh &ng trPn ngo\i ti7p ABC . Tm tMm bn k;nh c3a &ng trPn nD

2

C/ 15

a! IGi gi tr2 no c3a tham s m5 hm s y x mx m2= + cN tSp )c 2nh l (4 * + !.

b! #i$i b%t ph&'ng trnh sau:x

x

3 133+


16/16

http://trithuctoan.blogspot.com/! t gCn biu th>c

= + +

A

3 3s' coss' cos

s' cos+! =ho F5 65 = l " gNc trong tam gic. =h>ng minh r?ng:

a! A B Cs'( s'+ = b!A B C

s' cos2 2

+=

.

"! T;nh gi tr2 biu th>c A 2 0 0 08s' 45 2(2co&30 3 3cos90= +

C/ 35 =N 00 hCc sinh tham K k[ thi hCc sinh gii mn ton5 k7t Lu$ &c cho trong b$ng sau: (thang im l+0!

Zim 9 0 + " @ - 1 e 9Tdn s " - e " 9 +@ @ 0 + f800

a! T;nh s trung bnh s trung 2.b! T;nh ph&'ng sai Q lOch chu|n.

C/ 5 =ho hai &ng thBng : x y3 2 1 0+ = : x y4 6 1 0 + = .

a! =h>ng minh r?ng ung gNc Gi b! T;nh kho$ng cch t^ im J(+H 4! 7n

C/ 5a!=ho tam gic F6= cN F("H !5 6(4"H @!5 =(+: 4! J l trung im c3a F6 . Ii7t ph&'ng trnh tham sc3a trung tuD7n =J.

b! RSp ph&'ng trnh ti7p tuD7n c3a &ng trPn (=!: x y x y2 2 4 6 3 0+ + = t\i J(+H !.

************************************** XYT **************************************

Documents

Tuyen Chon 25 de Thi Hoc Ky II Lop 10 Vip Nam 2013