S GD & T NG THP THI TH TUYN SINH I HC NM 2014 - LN 2 THPT Chuyn Nguyn Quang Diu Mn: TON; Khi A + A1 + B

Thi gian lm bi: 180 pht, khng k thi gian pht CHNH THC I. PHN CHUNG CHO TT C TH SINH (7,0 im)

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

1

mxy

x

(1) c th l ( mC ).

a) Kho st s bin thin v v th (C) ca hm s (1) khi 2m . b) Tm m trn th ( mC ) c hai im ,M N cng cch u hai im ( 3;6), (3;0)A B v to thnh

t gic AMBN c din tch bng 18 (vdt).

Cu 2 (1,0 im). Gii phng trnh sin 2 cos 2 4 2 sin( ) 3cos

4 1cos 1

x x x x

x

.

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

2 2

2 5 3 4

3 3 1 0

y y y x x

y x y x

( , )x y .

Cu 4 (1,0 im). Tnh tch phn 2

33

1 1ln

( 1) 1

x xI dx

x x

.

Cu 5 (1,0 im). Cho hnh chp S.ABC c y ABC l tam gic vung cn ti B, AB = BC = 3a ,

090SAB SCB v khong cch t A n mt phng (SBC) bng 2a . Tnh th tch khi chp S.ABC v din tch mt cu ngoi tip hnh chp .S ABC theo a .

Cu 6 (1,0 im). Cho cc s thc dng ,x y tha iu kin 4 42

3 3x y xyxy

. Tm gi tr ln nht

ca biu thc 2 22 2

16

2P x y

x y

.

II. PHN RING (3,0 im): Th sinh ch c lm mt trong hai phn (phn A hoc B) A. Theo chng trnh Chun

Cu 7.a (1.0 im). Trong mt phng ta Oxy cho tam gic ABC c trc tm 1;3H , tm ng trn ngoi

tip (3; 3)I v chn ng cao k t nh A l 1;1K . Tm ta ca cc nh A, B, C.

Cu 8.a (1.0 im). Trong khng gian vi h to Oxyz , cho im 5; 2;2 , (3; 2;6)A B . Tm to

im M thuc mt phng ( ) :P 2 5 0x y z sao cho MA MB v 045MAB .

Cu 9.a (1.0 im). Tm s phc z tha cc iu kin 1z i z v 2 4( 2 )z z i l s thc .

B. Theo chng trnh Nng cao

Cu 7.b (1.0 im). Trong mt phng vi h to Oxy cho tam gic ABC c nh 4;3A , ng phn

gic trong ca gc A c phng trnh 1 0x y v tm ng trn ngoi tip tam gic ABC l 3

2;2

I

.

Vit phng trnh cnh BC , bit din tch tam gic ABC bng 2 ln din tch tam gic IBC . Cu 8.b (1.0 im). Trong khng gian vi h to Oxyz cho im (1; 1;0)A , ng thng

x 2 y 1 z 1

:2 1 1

v mt phng ( ) : 2 0P x y z . Tm to im M thuc mt phng (P) bit

ng thng AM vung gc vi v khong cch t M n ng thng l nh nht. Cu 9.b (1.0 im). Trong mt hp c 50 vin bi c nh s t 1 n 50, chn ngu nhin 3 vin bi. Tnh xc sut tng ba s trn ba vin bi c chn l mt s chia ht cho 3. -------------- 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:..............................