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D B 1 TUYN SINH I HC NM 2012 KHI A, A1 D B 1 THI TUYN SINH I HC NM 2012
Mn thi : TON; Khi A, A1 PHN CHUNG CHO TT C CC TH SINH (7,0 im) Cu I (2,0 im) Cho hm s 3 23 1y x x a. Kho st s bin thin v v th (C) ca hm s cho. b. Gi d l ng thng i qua 2;3M vi h s gc k. Tm k ng thng d ct th ti ba im phn bit sao cho cc tip tuyn ti ba giao im ct nhau to thnh tam gic vung. Cu II (2 im) 1. Gii phng trnh: 3 sin 2cos cos 2 1 0x x x
2. Gii bt phng trnh: 2 2 21 3 2 1 3 2 3 2 2 2x x x x x x
Cu III: (1,0 im) Tnh tch phn: 2
6
sin 2 cos 1 2 cos 1 lnsin ln
x x x x xI dx
x x x
Cu IV: (1,0 im) Cho hnh chp S.ABCD c y ABCD l hnh vung cnh a. Mt bn SAD l tam gic u v 2SB a . Gi E,F ln lt l trung im ca AD v AB. Gi H l giao im ca FC v EB. Chng minh ,SE EB CH SB v tnh th tch khi chp C.SEB. Cu V(1,0 im) Cho a,b,c l cc s thc khng m tha mn 1a b c . Tm gi tr nh nht ca biu thc 2P ab bc ca abc PHN RING (3 im): Th sinh ch c lm mt trong hai phn (phn A hoc phn B) A. Theo chng trnh Chun Cu VI.a (2,0 im) 1. Trong mt phng ta Oxy, cho im 4;3A . ng thng : 2 0d x y v ' : 4 0d x y ct nhau ti M. Tm B d v 'C d sao cho A l tm ng trn ngoi tip tam gic MBC. 2. Trong khng gian ta Oxyz, vit phng trnh ng thng i qua 3; 2; 4A , song song vi mt
phng : 3 2 3 7 0P x y z v ct ng thng 2 4 1:3 2 2
x y zd
Cu VII.a (1,0 im) Tm tp hp cc im biu din trong mt phng phc Oxy ca s phc
' 1 3 2z i z bit rng s phc z tha mn 1 2z . B. Theo chng trnh Nng cao Cu VI.b (2,0 im) 1. Trong mt phng ta Oxy, cho im 1; 1M v hai ng thng c phng trnh 1 : 1 0d x y ;
2 : 2 5 0d x y . Gi C l giao ca hai ng thng trn. Vit phng trnh ng thng d i qua M, ct hai ng thng trn ln lt ti A v B sao cho ABC l tam gic c 3BC AB
2. Trong khng gian ta Oxyz, cho ng thng 11 3 3:
1 2 3x y zd v ng thng
21 1 2:
1 2 1x y zd . Vit phng trnh mt cu c tm thuc 1d , bn knh bng 5, ng thi ct 2d to
thnh mt dy cung c di ln nht.
Cu VII.b (1 im) Trong khai trin nh thc Niutn 12n
x
, h s ca s hng cha 21x
gp i h s
ca s hng th hai. Tm h s ca s hng cha 41x
v tnh tng h s ca tt c cc s hng ca khai trin.
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