B GIO DC V O TO

THI CHNH THC

K THI TT NGHIP TRUNG HC PH THNG NM 2012 Mn thi: TON Gio dc thng xuyn

Thi gian lm bi: 150 pht, khng k thi gian giao

Cu 1. (3,0 im)

Cho hm s 2 1.1

xyx

+= 1) Kho st s bin thin v v th ( )C ca hm s cho. 2) Vit phng trnh tip tuyn ca th ( )C ti im c tung bng 5.

Cu 2. (2,0 im)

1) Tm gi tr ln nht v gi tr nh nht ca hm s ( ) 2 2 5f x x x= + trn on [ ]0 ; 3 . 2) Tnh tch phn ( )2 2

1

2 .I x xdx= Cu 3. (2,0 im)

Trong khng gian vi h ta ,Oxyz cho ng thng 2 2

: 14 2

x td y t

z t

= + = = + v

mt cu ( ) ( ) ( ) ( )2 2 2: 2 1 3 25.S x y z + + + = 1) Tm ta mt vect ch phng ca ng thng d. Tm ta tm v tnh bn knh ca mt cu ( ).S 2) Vit phng trnh mt phng vung gc vi ng thng d v tip xc vi mt cu ( ).S

Cu 4. (2,0 im) 1) Gii phng trnh ( )3 3 8 2.log x log x+ = 2) Tm phn thc, phn o v mun ca s phc ( )( )2 3 1 4 .z i i i= +

Cu 5. (1,0 im) Cho hnh chp .S ABCD c y ABCD l hnh ch nht, SA vung gc vi mt y. Bit 2,AB a BC a= = v n o60 .SCA = Tnh th tch khi chp .S ABCD theo .a

----------------- Ht ----------------- Th sinh khng c s dng ti liu. Gim th khng gii thch g thm.

H v tn th sinh:.............................................. S bo danh: ............................................. Ch k ca gim th 1: ...................................... Ch k ca gim th 2:.............................

B GIO DC V O TO

THI CHNH THC

K THI TT NGHIP TRUNG HC PH THNG NM 2013 Mn thi: TON Gio dc thng xuyn

Thi gian lm bi: 150 pht, khng k thi gian giao

Cu 1 (3,0 im) Cho hm s 3 22 3y x x= + + 1. 1) Kho st s bin thin v v th ( )C ca hm s cho. 2) Vit phng trnh tip tuyn ca ( )C ti im c honh bng 2.Cu 2 (2,0 im)

1) Tnh tch phn 1

3

0( 2 1)d .I x x= + x

2) Tm gi tr ln nht v gi tr nh nht ca hm s 92

y xx

= + + trn on [ ]1; 2 . Cu 3 (2,0 im) Trong khng gian vi h ta cho hai im ,Oxyz (1; 2; 1),A (0; 1; 0)B v mt phng

c phng trnh ( )P

2 7 0.+ + =x y z 1) Vit phng trnh tham s ca ng thng i qua hai im A v .B 2) Tm ta im l hnh chiu vung gc ca H A trn ( ).PCu 4 (2,0 im)

1) Gii phng trnh 25 26.5 25 0.x x + = 2) Tm s phc lin hp ca s phc ,z bit ( )5 1 2 (1 ).= + z i i i Cu 5 (1,0 im)

Cho hnh chp c y .S ABC ABC l tam gic vung cn ti ,B , 2AB a SB a= = v SA vung gc vi mt phng y. Tnh th tch khi chp theo .S ABC .a

--------------------Ht------------------ Th sinh khng c s dng ti liu. Gim th khng gii thch g thm.

H v tn th sinh: ............................................................................. S bo danh: ........................................................................

Ch k ca gim th 1: ................................................................... Ch k ca gim th 2: .................................................

B GIO DC V O TO

THI CHNH THC

K THI TT NGHIP TRUNG HC PH THNG NM 2014

Mn thi: TON Gio dc thng xuyn Thi gian lm bi: 120 pht, khng k thi gian giao

Cu 1 (3,0 im). Cho hm s 2 .1

xyx=

1) Kho st s bin thin v v th ( )C ca hm s cho. 2) Vit phng trnh tip tuyn ca ( )C ti im c tung bng 2.

Cu 2 (2,5 im)

1) Cho s phc tha mn Xc nh phn thc, phn o v s phc lin hp ca

z ( ) (21 3 2 .z i z= )i.z

2) Tm gi tr ln nht v gi tr nh nht ca hm s trn on [

4 3 2( ) 2 5 1f x x x x= + +]1;2 .

Cu 3 (1,5 im). Tnh tch phn ( )221

1.

xI dx

x+=

Cu 4 (1,0 im). Cho hnh chp S.ABCD c y ABCD l hnh vung tm O v 2 .BD a= ng thng SA vung gc vi mt phng y, gc gia ng thng SO v mt phng y

bng 60 Tnh th tch ca khi chp S.ABCD theo a. .D

Cu 5 (2,0 im). Trong khng gian vi h ta Oxyz, cho im v ng

thng :

( 2;2;3A )

11 2

.

x ty tz t

= = + =

1) Vit phng trnh mt phng i qua A v vung gc vi . 2) Vit phng trnh mt cu i qua A, c tm l giao im ca v mt phng ( ).Oyz

------------------ Ht ------------------

Th sinh khng c s dng ti liu. Gim th khng gii thch g thm. H v tn th sinh: .. S bo danh: . Ch k ca gim th 1:. Ch k ca gim th 2:

I. PHN CHUNG CHO TT C TH SINH (7,0 im)

Cu 1. (3,0 im) Cho hm s ( ) 4 214

2y f x x x .= = 1) Kho st s bin thin v v th ( )C ca hm s cho. 2) Vit phng trnh tip tuyn ca th ( )C ti im c honh 0x , bit ( )0 1f " x .=

Cu 2. (3,0 im) 1) Gii phng trnh ( )2 4 33 2 3 2.log x log .log x + = 2) Tnh tch phn ( )2 2

01

lnx x .I e e dx=

3) Tm cc gi tr ca tham s m gi tr nh nht ca hm s ( ) 21xx m mf

x += + trn

on [ ]0;1 bng 2. Cu 3. (1,0 im) Cho hnh lng tr ng ABC.A B C c y ABC l tam gic vung ti B v BA BC a.= = Gc gia ng thng A B vi mt phng ( )ABC bng 60 .D Tnh th tch khi lng tr ABC.A B C theo a. II. PHN RING - PHN T CHN (3,0 im) Th sinh ch c lm mt trong hai phn (phn 1 hoc phn 2). 1. Theo chng trnh Chun

Cu 4.a. (2,0 im) Trong khng gian vi h ta Oxyz, cho cc im ( )2;2;1A , ( )0;2;5B v mt phng ( )P c phng trnh 2 5 0.x y + =

1) Vit phng trnh tham s ca ng thng i qua A v B.

2) Chng minh rng ( )P tip xc vi mt cu c ng knh AB. Cu 5.a. (1,0 im) Tm cc s phc 2z z+ v 25i ,

z bit 3 4 .z i=

2. Theo chng trnh Nng cao

Cu 4.b. (2,0 im) Trong khng gian vi h ta Oxyz, cho im ( )2;1;2A v ng thng c phng trnh 1 3

2 2 1x y z . = =

1) Vit phng trnh ca ng thng i qua O v A.

2) Vit phng trnh mt cu ( )S tm A v i qua O. Chng minh tip xc vi ( )S . Cu 5.b. (1,0 im) Tm cc cn bc hai ca s phc 1 9 5

1iz i.i

+= -------------- Ht --------------

Th sinh khng c s dng ti liu. Gim th khng gii thch g thm. H v tn th sinh: .................................................... S bo danh: .................................................. Ch k ca gim th 1: ............................................. Ch k ca gim th 2: ..................................

B GIO DC V O TO

THI CHNH THC

K THI TT NGHIP TRUNG HC PH THNG NM 2012 Mn thi: TON Gio dc trung hc ph thng

Thi gian lm bi: 150 pht, khng k thi gian giao

B GIO DC V O TO

THI CHNH THC

K THI TT NGHIP TRUNG HC PH THNG NM 2013 Mn thi: TON Gio dc trung hc ph thng

Thi gian lm bi: 150 pht, khng k thi gian giao I. PHN CHUNG CHO TT C TH SINH (7,0 im)

Cu 1 (3,0 im). Cho hm s 3 3 1y x x= .

2 0.x x + =

1) Kho st s bin thin v v th ( ca hm s cho. )C

2) Vit phng trnh tip tuyn ca bit h s gc ca tip tuyn bng 9. ( ),C

Cu 2 (3,0 im) 1) Gii phng trnh 3 3 1

2) Tnh tch phn ( )20

1 cos d .I x x

= + x 3) Tm gi tr ln nht v gi tr nh nht ca hm s 2 3 lny x x= + x trn on [ ]1; 2 . Cu 3 (1,0 im). Cho hnh chp c y l hnh vung cnh cnh bn vung gc vi mt phng y. ng thng to vi mt phng mt gc Tnh th tch ca khi chp theo

.S ABCD ABCD ,a SASD (SAB)

yz.

o30 ..S ABCD .a

II. PHN RING - PHN T CHN (3,0 im) Th sinh ch c lm mt trong hai phn (phn 1 hoc phn 2). 1. Theo chng trnh Chun Cu 4.a (2,0 im). Trong khng gian vi h ta Ox cho im v mt phng c phng trnh

, ( 1; 2; 1)M ( )P2 2 3 0x y z+ + =

1) Vit phng trnh tham s ca ng thng d i qua M v vung gc vi ( ).P

2) Vit phng trnh mt cu c tm l gc ta v tip xc vi ( )S ( ).PCu 5.a (1,0 im). Cho s phc tha mn (1z ) 2 4 0.i z i+ = Tm s phc lin hp ca .z 2. Theo chng trnh Nng cao Cu 4.b (2,0 im). Trong khng gian vi h ta cho im v ng

thng c phng trnh

,Oxyz ( 1; 1; 0)A d 1 1.

1 2 1x y z += =

1) Vit phng trnh mt phng i qua gc ta v vung gc vi ( )P .d

2) Tm ta im M thuc sao cho di on d AM bng 6 .

Cu 5.b (1,0 im). Gii phng trnh 2 (2 3 ) 5 3 0z i z i + + + = trn tp s phc. -------------------- Ht --------------------

Th sinh khng c s dng ti liu. Gim th khng gii thch g thm.

H v tn th sinh: . S bo danh: ...

Ch k ca gim th 1: Ch k ca gim th 2:

B GIO DC V O TO

THI CHNH THC

K THI TT NGHIP TRUNG HC PH THNG NM 2014Mn thi: TON Gio dc trung hc ph thng

Thi gian lm bi: 120 pht, khng k thi gian giao

Cu 1 (3,0 im). Cho hm s 2 3 .1

xyx

+= 1) Kho st s bin thin v v th (C) ca hm s cho. 2) Vit phng trnh tip tuyn ca (C) ti cc giao im ca (C) v ng thng 3.y x=

Cu 2 (2,5 im)

1) Gii phng trnh ( )22 2log 3log 2 1 0x x+ = trn tp hp s thc. 2) Tm gi tr ln nht v gi tr nh nht ca hm s ( ) 2 21 4 .

4f x x x x x=

Cu 3 (1,5 im). Tnh tch phn ( )10

1 .xI xe dx= Cu 4 (1,0 im). Cho hnh chp S.ABC c y ABC l tam gic vung cn ti A v 2 5SC a= .

).

Hnh chiu vung gc ca S trn mt phng (ABC) l trung im M ca cnh AB. Gc gia ng thng SC v (ABC) bng Tnh th tch khi chp S.ABC theo a. 60 .D

Cu 5 (2,0 im). Trong khng gian vi h to Oxyz, cho im v mt phng (P) c phng trnh

(1; 1;0A 2 2 1 0x y z + =

1) Vit phng trnh tham s ca ng thng i qua A v vung gc vi (P). 2) Tm to im M thuc (P) sao cho AM vung gc vi OA v di on AM bng ba ln khong cch t A n (P).

----------------- Ht -------------------- Th sinh khng c s dng ti liu. Gim th khng gii thch g thm.

H v tn th sinh: ....... S bo danh:

Ch k ca gim th 1: Ch k ca gim th 2:

Bookmarks from 2013pt.pdfI. PHN CHUNG CHO TT C TH SINH (7,0 im)