8/9/2019 DeToanDCt_DH_K2010

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B GIO DC V O TO

CHNH THC

THI TUYN SINH I HC NM 2010

Mn: TON; Khi: D

Thi gian lm bi: 180 pht, khng kthi gian pht

PHN CHUNG CHO TT C TH SINH (7,0 im)Cu I (2,0 im) Cho hm s .4 2 6y 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), bit tip tuyn vung gc vi ng thng 1 1

6y x= .

Cu II (2,0 im)1. Gii phng trnh s in 2 cos 2 3sin cos 1 0.x x x x + =2. Gii phng trnh 3 32 2 2 2 44 2 4 2 4x x x x x x+ + + + + + = + (xR).

Cu III (1,0 im) Tnh tch phn 1

3

2 ln

e

dI x xx

=

x .Cu IV (1,0 im) Cho hnh chp S.ABCD c yABCD l hnh vung cnh a, cnh bn SA=a ; hnh

chiu vung gc ca nh Strn mt phng (ABCD) l im Hthuc onAC,AH=4

C. Gi CMl ng

cao ca tam gic SAC. Chng minh Ml trung im ca SA v tnh th tch khi t din SMBCtheo a.

Cu V (1,0 im) Tm gi tr nh nht ca hm s 2 24 21 3 1y x x x x= + + + + 0 .

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

Cu VI.a (2,0 im)1. Trong mt phng toOxy, cho tam gicABCc nhA(3; 7), trc tm lH(3; 1), tm ng trnngoi tip lI(2; 0). Xc nh ta nh C, bit Cc honh dng.

2. Trong khng gian toOxyz, cho hai mt phng (P):x+y+z 3 = 0 v (Q):xy+z 1 = 0. Vitphng trnh mt phng (R) vung gc vi (P) v (Q) sao cho khong cch tOn (R) bng 2.

Cu VII.a (1,0 im) Tm s phc z tha mn: |z| = 2 v z2 l s thun o.B. Theo chng trnh Nng cao

Cu VI.b (2,0 im)1. Trong mt phng ta Oxy, cho imA(0; 2) v l ng thng i qua O. GiHl hnh chiu

vung gc ca A trn . Vit phng trnh ng thng , bit khong cch tHn trc honh

bng AH.

2. Trong khng gian toOxyz, cho hai ng thng 1:3 t

y t

z t

= +

= =

v 2:2 1

2 1 2

y = =

z. Xc

nh ta im Mthuc 1 sao cho khong cch tMn 2 bng 1.

Cu VII.b (1,0 im) Gii h phng trnh2

2 2

4 2 0

2log ( 2) log 0

x x y

x

+ + =

y =(x,yR).

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Th sinh khngc sdng ti liu. Cn b coi thi khng gii thch g thm.

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