TRNG I HC VINH

TRNG I HC VINH

TRNG THPT CHUYN KHO ST CHT LNG LP 12, LN 1 - NM 2014

Mn: TON; Khi: A v A1; Thi gian lm bi: 180 pht

I. PHN CHUNG CHO TT C TH SINH (7,0 im)Cu 1 (2,0 im). Cho hm s

a) Kho st s bin thin v v th (H) ca hm s cho.

b) Tm m ng thng ct (H) ti hai im M, N sao cho tam gic vung ti im

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

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

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

Cu 5 (1,0 im). Cho hnh chp S.ABCD c y ABCD l hnh ch nht, mt bn SAD l tam gic vung ti S, hnh chiu vung gc ca S ln mt phng (ABCD) l im H thuc cnh AD sao cho Gi M l trung im ca AB. Bit rng v ng thng SC to vi y mt gc Tnh theo a th tch khi chp S.ABCD v khong cch t M n mt phng (SBC).Cu 6 (1,0 im). Gi s x, y, z l cc s thc khng m tha mn Tm gi tr ln nht ca biu thc

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

Cu 7.a (1,0 im). Trong mt phng vi h ta cho tam gic ABC c l trung im cnh AC, im l chn ng cao k t A, im thuc ng thng cha trung tuyn k t C. Tm ta im B bit im A thuc ng thng v im C c honh dng.Cu 8.a (1,0 im). Trong khng gian vi h ta cho ng thng v hai mt phng Vit phng trnh mt cu c tm thuc d, ng thi tip xc vi hai mt phng (P) v (Q).Cu 9.a (1,0 im). Cho tp hp Gi M l tp hp tt c cc s t nhin c t nht 3 ch s, cc ch s i mt khc nhau thuc E. Ly ngu nhin mt s thuc M. Tnh xc sut tng cc ch s ca s bng 10.

b. Theo chng trnh Nng caoCu 7.b (1,0 im). Trong mt phng vi h ta cho hai im v ng thng Vit phng trnh ng trn i qua A, B v ct ti C, D sao cho

Cu 8.b (1,0 im). Trong khng gian vi h ta cho im v hai ng thng Vit phng trnh mt phng (P) song song vi v ng thi cch M mt khong bng

Cu 9.b (1,0 im). Tm s nguyn dng n tha mn

EMBED Equation.DSMT4 ------------------ Ht ------------------Ghi ch: 1. BTC s tr bi vo cc ngy 22, 23/3/2014. nhn c bi thi, th sinh phi np li phiu d thi cho BTC.

2. K kho st cht lng ln 2 s c t chc vo chiu ngy 12 v ngy 13/4/2014. ng k d thi ti Vn phng Trng THPT Chuyn t ngy 22/3/2014.

TRNG I HC VINH

TRNG THPT CHUYN KHO ST CHT LNG LP 12, LN 1 - NM 2014

Mn: TON; Khi: B v D; Thi gian lm bi: 180 pht

I. PHN CHUNG CHO TT C TH SINH (7,0 im)Cu 1 (2,0 im). Cho hm s

a) Kho st s bin thin v v th (H) ca hm s cho.

b) Tm m ng thng ct (H) ti hai im M, N sao cho tam gic vung ti im

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

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

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

Cu 5 (1,0 im). Cho hnh lng tr tam gic u c ng thng to vi mt phng mt gc Tnh theo a th tch khi lng tr cho v khong cch gia hai ng thng v BC.

Cu 6 (1,0 im). Gi s x, y, z l cc s thc khng m v tha mn Tm gi tr ln nht ca biu thc

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

Cu 7.a (1,0 im). Trong mt phng vi h ta cho tam gic ABC c l trung im cnh AC, im l chn ng cao k t A, im thuc ng thng cha trung tuyn k t C. Tm ta im B bit im A thuc ng thng v im C c honh dng.

Cu 8.a (1,0 im). Trong khng gian vi h ta cho ng thng v hai mt phng Vit phng trnh mt cu c tm thuc d, ng thi tip xc vi hai mt phng (P) v (Q).

Cu 9.a (1,0 im). Cho tp hp Gi M l tp hp tt c cc s t nhin c t nht 3 ch s, cc ch s i mt khc nhau thuc E. Ly ngu nhin mt s thuc M. Tnh xc sut tng cc ch s ca s bng 10.

b. Theo chng trnh Nng caoCu 7.b (1,0 im). Trong mt phng vi h ta cho hai im v ng thng Vit phng trnh ng trn i qua A, B v ct ti C, D sao cho

Cu 8.b (1,0 im). Trong khng gian vi h ta cho im v hai ng thng Vit phng trnh mt phng (P) song song vi v ng thi cch M mt khong bng

Cu 9.b (1,0 im). Tm s nguyn dng n tha mn

EMBED Equation.DSMT4 ------------------ Ht ------------------

Ghi ch: 1. BTC s tr bi vo cc ngy 22, 23/3/2014. nhn c bi thi, th sinh phi np li phiu d thi cho BTC.

2. K kho st cht lng ln 2 s c t chc vo chiu ngy 12 v ngy 13/4/2014. ng k d thi ti Vn phng Trng THPT Chuyn t ngy 22/3/2014.

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