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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