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GII THI MN TON KHI A

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GII THI MN TON KHI A

K THI TUYN SINH H C NM 2009I. Phn chung cho tt c th sinh

Cu I: (2,0)

Cho hm s:

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

2. Vit phng trnh tip tuyn ca th hm s (1), bit tip tuyn ct trc honh, trc tung ln lt ti hai im phn bit A, B v tam gic OAB cn ti gc to O.

Bi gii

Bng bin thin

th:

bng bin thin ph

V th:

Nhn xt: th nhn giao im ca 2 tim cn l im lm tm i xng.

Cu II: (2,0 )

1. Gii phng trnh:

2. Gii phng trnh:

Bi gii

Cu III: (1,0 )

Cu IV: (1,0im)

Cho hnh chp S.ABCD c y ABCD l hnh thang vung ti A v D; AB = AD = 2a, CD = a, gc gia hai mt phng (SBC) v (ABCD) bng 600. Gi I l trung im ca cnh AD. Bit hai mt phng (SBI) v (SCI) cng vung gc vi mt phng (ABCD). Tnh th tch khi chp S.ABCD theo a.

Bi gii

Hnh thang ABCD.

Cu V: (1,0 im)

Chng minh rng vi mi s thc dng x, y, z tho mn x(x + y + z) = 3yz, ta c:

(x + y)3 + (x + z)3 + 3(x + y)(x + z)(y + z) ( 5(y + z)3.Bi gii

Phn ring (3,0)

A. Theo chng trnh chun

Cu VI.a (2.0 im)1. Trong mt phng vi h to Oxy, cho hnh ch nht ABCD c im I(6; 2) l giao im ca hai ng cho AC v BD. im M(1; 5) thuc ng thng AB v trung im E ca cnh CD thuc ng thng: (: x + y 5 = 0. Vit phng trnh ng thng AB.

2. Trong khng gian vi h to Oxyz, cho mt phng (P): 2x 2y z 4 = 0 v mt cu (S): x2 + y2 + z2 2x 4y 6z 11 = 0. Chng minh rng mt phng (P) ct mt cu (S) theo mt ng trn. Xc nh to tm v tnh bn knh ca ng trn .

Bi gii

Cu VII.a (1,0 im)

Gi z1 v z2 l hai nghim phc ca phng trnh z2 + 2z + 10 = 0. Tnh gi tr ca biu thc A = |z1|2 + |z2|2Bi gii

Cu VII.a (1,0 im)

Gi z1 v z2 l hai nghim phc ca phng trnh z2 + 2z + 10 = 0. Tnh gi tr ca biu thc A = |z1|2 + |z2|2

Bi gii

B. Theo chng trnh nng cao

Cu VI.b. (2.0 im)

1. Trong mt phng vi h to Oxy, cho ng trn (C): x2 + y2 + 4x + 4y + 6 = 0 v ng thng (: x + my 2m + 3 = 0, vi m l tham s thc. Gi ( l tm ca ng trn (C). Tm m ( ct (C) ti hai im phn bit A v B sao cho din tch tam gic IAB ln nht.

2. Trong khng gian vi h to Oxyz, cho mt phng (P): x 2y + 2z 1 = 0 v hai ng thng . Xc nh to im M thuc ng thng (1 sao cho khong cch t M n ng thng (2 v khong cch t M n mt phng (P) bng nhau. Bi gii

Cu VII.b (1,0 im)

Gii h phng trnh:

Bi gii

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