www.VNMATH.com TRNG THPT CHUYN VNH PHC K THI TH I HC LN 1 NM HC 2013-2014

Mn: Ton 12. Khi A, A1, B.

Thi gian lm bi: 180 pht (Khng k thi gian giao )

A.PHN CHUNG CHO TT C TH SINH (8,0 im)Cu 1. (2,5 im). Chohms 3 2y mx ( 2m 1)x m 1 ( Cm ) .

1) Khostsbinthinvvthcahmskhi m 1 .2) Tmttcccgitrcathams m 0 saochotiptuyncathtigiaoimcanvi

trctungtovihaitrctomttamgiccdintchbng4.Cu 2. (1,25 im) . Giiphngtrnh:

3 33 1 3 cos 2x 3 1 3 sin 2x 8 sin x cos x 3 sin x cos x 3 3 3 .

Cu 3. (1,25 im) .Giihphngtrnh: 2 1 xx y

x y x, y

5y 1 x y 1

.

Cu 4. (1,0 im). Tnhgiihn:3 4

x 2

x 6 7x 2L lim

x 2

Cu 5. (1,0 im). Chohnhchp S.ABCD cylhnhvungvicnh 2a ,mtbn SAB nm

trongmtphngvunggcvimtphng ABCD v SA a ,SB a 3 .Hytnhthtchcahnhchp S.ABCD vkhongcchgiahaingthng AC v SB theo a .Cu 6. (1,0 im).Xtccsthcdng , ,a b c thomn 7ab bc ca abc .Tmgitrnhnht

cabiuthc:4 5 6

2 2 2

8 1 108 1 16 1a b cP

a b c

B. PHN RING(2,0 im). Th sinh ch c lm mt trong hai phn (phn 1 hoc 2)1.Theo chng trnh Chun Cu 7A. (1,0 im).TrongmtphngvihtrctoOxy ,chohnhbnhhnh ABCD c A 2;0

,B 3;0 vdintchbng 4 .Bitrnggiaoimcahaingcho AC v BD nmtrnngthng y x ,hytmtocaccnh C,D.

Cu 8A (1,0im).Tnhtng: 2 1 2 2 2 3 2 20131 2013 2013 2013 2013S 1 .C 2 .C 3 .C 2013 .C

2.Theo chng trnh nng cao. Cu 7B (2,0 im).TrongmtphngvihtaOxychotamgic ABC cngcaokt B vphngictrongkt A lnltcphngtrnh: 3x 4 y 10 0 v x y 1 0 .Bitrngim

M 0;2 nmtrnngthng AB v MC 2 ,tmtoccnhcatamgic.

Cu 8 B (1,0 im). Tnhtng:0 1 2 20132013 2013 2013 2013

2

C C C CS

1 2 3 2014

----------HT----------

Th sinh khng c s dng ti liu. Cn b coi thi khng gii thch g thm.

H v tn th sinh:; S bo danh:

chnh thc(thigm01trang)

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SGD-TVNHPHC THI KHSCL LN I NM HC 2013 2014 TRNGTHPTCHUYN HNG DN CHM TON 12 A,B,A1 Hng dn chung.

- Mimtbitoncthcnhiucchgii,trongHDCnychtrnhbyslcmtcch

gii.Hcsinhcthgiitheonhiucchkhcnhau,nuvchoktqung,gimkho

vnchoimtiacaphn.

- Cu(Hnhhckhnggian),nuhcsinhvhnhsaihockhngvhnhchnhcabiton,

thkhngchoim;cu(Hnhhcgiitch)khngnhtthitphivhnh.

- imtonbichmchititn0.25,khnglmtrn.

- HDCnyc04trang.

Cu Ni dung trnh by im

1. Khi 31:y x 3 2m x

+TX:

+Sbinthin: 23 3 3 1 1 , 0 1y x x x y x 0.25

0 1 1y x x suyrahmsngbintrncckhong ; 1 , 1; ;

0 1 1y x suyrahmsnghchbintrn 1;1 .

Hmstcciti 1, 1 4;cdx y y hmstcctiuti 1, 1 0.ctx y y 0.25

3 3

2 3 2 3

3 2 3 2lim lim 1 ; lim lim 1x x x x

y x y xx x x x

y

y'

x

0

4 +

++

+

00

1 1

0.25

+th

0. 50

1

2. th 3( ) : (2 1) 1mC y mx m x m cttrctungti (0; 1)M m . 0.25

- GiaoOx: 2;0 , 1;0

;

- GiaoOy: 0;2

;

- imun: 0;2I

suyra

thtxngqua 0;2I

4

2

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23 (2 1) y 0 2 1y mx m m T,khi 0,m tiptuyn mt ca ( )mC tiMcphngtrnh

(2 1) 1y m x m 0.25

Do ( )mt tovihaitrctamttamgiccdintchbng4nntach

2

11

22

11 8 1 8 2 1

2 1

mm

mm m m

m

0. 50

Giih,thuc 7 56m v 9 72. ichiuiukinvktlun 0.25

+rng 2 3sin 2 1 (sin cos ) ;sin 3 4sin 3sinx x x x x x v 3cos3 4 cos 3cosx x x

nnphngtrnhcvitvdng

(sin cos )( 3 sin 3 cos 3 ) 0x x x x

0. 5

+Giiphngtrnh sin cos 0x x tachnghim ,4

x k k

0.25

+Giiphngtrnh 3 sin 3 cos3 0x x tachnghim ,6

x

0.25

2

+Ktlunnghim 0.25

iukin1

0,5

x y

Tphngtrnhthnhtcahsuyrahoc 2y x hoc 1xy 0.25

+Nu 1xy th 0x y vphngtrnhthhaitrthnh1

5 1 1yy

Phngtrnhnytngngvi 22

15 1

2 1 2 5

yy y y

y y y

Do 1y nnhphngtrnhnyvnghim.

0. 5

3

+Nu 2 ,y x thayvophngtrnhthhai,tac 25 1 1 | |x x x .

Giiphngtrnh,c ( ; ) (1;1), ( 2;2), ( 7 41;7 41)x y

Ktlunnghim

0.5

3 4 3 4x 2 x 2

x 6 2 7 x 2 2 x 6 2 7 x 2 2L lim lim

x 2 x 2 x 2

0.25

4x 2 2 33x 6 8 7 x 2 16

L limx 2 7x 2 2 7x 2 4x 2 x 6 2 x 6 4

0.25

4

4x 2 2 331 7 1 7 13

L lim12 32 967x 2 2 7x 2 4x 6 2 x 6 4

0.5

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M

OB

A

C

D

S

H

+Tgithitsuyratamgic SAB vungtiSv3

2

aSH (HlhnhchiucaA trnAB).

T,do SAB ABCD nn3

.

1 2

3 3S ABCD

aV SH AB AD (.v.t.t)

0.25

5

+DoABCDlhnhvung,nn1

2ABC ADC ABCDS S S suyra

3

. .

1

2 3S ABC S ABCD

aV V (.v.t.t)

M .1

; sin ;6

S ABCV AC SB d AC SB AC SB nn

32 3;

sin ;

ad AC SB

AC SB AC SB

0.25

+GiO,Mtheothtltrungim , .AC SD Khi ; ;AC SB OA OM

p dng nh l c-sin cho tam gic AOM tnh c 6

cos4

AOM suy ra

10

sin ; sin4

AC SB AOM

0.25

Vy 2

;5

ad AC SB (.v..d) 0.25

Ch : Vibitonny(phntnhkhongcch),cnhiucchgii,chnghnhcsinhcthsdngvect,tahaydngonvunggcchung.Nucchgiingvchoktqung,gimkhovnchoimtiacaphn.CchgiitrongbitonnysdngktqucaBitp6(tr.26)SGKHnhhc12(CCT)

6 Vitligithitvdng

1 1 17

a b c 0.25

pdngbtngthcAM-GM,tac

2

2

3 3

2 2 2

4

2 2

1 18 4," "

2 2

2 2 2 154 54 10," "

9 9 9 3

1 1 116 3," "

4 4 2

A a aa

B b b bb b b

C c cc c

0.5

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T,vi

2 2 2

1 1 1

2 3 2D

a b c ,theobtngthcCauchyBunhiacopsky-Schwarz,th

21 1 1 1 1 1

4 10 3 24," " ,2 3 2 2 3

P A B C D a c ba b c

KL

0.25

GiIlgiaoimhaingchocahnhbnhhnh,thth ;I a a vialsthcno.

Suyra 2 2;2 , 2 3;2 .C a a D a a 0.25

T,dodintchcahnhbnhhnhbng4nn 2 4 2.a a 0.25

Vi 2 : 2;4 , 1;4a C D ;vi 2 : 6; 4 , 7; 4a C D 0.25

7a

Ktlun 0.25

Tnhtng: 2 1 2 2 2 3 2 20131 2013 2013 2013 2013S 1 .C 2 .C 3 .C 2013 .C

Shngtngqutcatngl 2 k kk 2013 2013a k C k. k 1 1 C k 1,2,...,2013 0.25

k kk 2013 2013

2013! 2013!a k. k 1 C kC k. k 1 k. k 1,2,...,2013

k ! 2013 k ! k ! 2013 k !

0.25

k 2 k 1k 2011 2012a 2012 2013C 2013C k 1,2,...,2013

0.25

8a

0 1 2011 0 1 20121 2011 2011 2011 2012 2012 2012S 2012 2013 C C C 2013 C C C

2011 2012 2011 2012 20111S 2012 2013 1 1 2013 1 1 2012 2013 2 2013 2 2013 2014 2

0.25

: 3 4 10 0, : 1 0b ah x y x y

+Do 0;2M AB nnim 1;1N ixngviMqua a nmtrn .AC 0.25

+SuyraAlgiaoimcangthngdquaN,vunggcvi bh vngthng .a T

4;5 .A 0.25

+BlgiaoimcangthngAMvi .bh T1

3;4

B

0.25

7b

+Do 2MC nn C lgiaoimcangtrntmMbnknh 2 vingthngd.

Suyra 1;1C hoc33 31

;25 25

C

0.25

Tnhtng:0 1 2 20132013 2013 2013 2013

2

C C C CS

1 2 3 2014

Shngtngqutcatnglk2013

k

Ca k 0,1,2,...,2013

k 1

0.25

k2013

k

C 2013! 1 2014!a k 0,1,2,...,2013

k 1 k 1 k ! 2013 k ! 2014 k 1 ! 2013 k !

0.25

Vytack 12014

k

Ca k 0,1,2,...,2013

2014

0.25

8b

2014

20141 2 2014 02 2014 2014 2014 2014

1 1 2 1S C C C 1 1 C

2014 2014 2014

0.25

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