DethiTOANkhoiDnam2014 - BO GIAO DUC VA AO TAO E CHNH THC E...

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BO˜ GIA°O DUˇC VA± ²A±O TAˇO ²E³ THI TUYE¯N SINH ²AˇI HOˇC NA˚M 2014 ---------- Mo´n: TOA°N; KhoÆi D °E± CH˝NH TH²³C Th°li gian lalm bali: 180 phuøt, kho±ng ke² th°li gian phaøt æe³ ------------------- Ca´u 1 (2,0 æie°m ). Cho halm soÆ y = x 3 - 3 x - 2 (1) . a) Khaûo saøt s´µ bieÆn thie¶n val veı æo· th¸ ( C ) cuûa halm soÆ (1) . b) T¹m toµa æoº æie»m M thuoºc ( C ) sao cho tieÆp tuyeÆn cuûa ( C ) taµi M coø heº soÆ goøc baLng 9 . Ca´u 2 (1,0 æie°m ). Cho soÆ ph´øc z thoûa maın æie·u kieºn (3 z - z )(1 + i ) - 5 z = 8 i - 1 . T¼nh mo¶æun cuûa z . Ca´u 3 (1,0 æie°m ). T¼nh t¼ch pha¶n I = π 4 integraldisplay 0 ( x + 1) sin 2 x dx. Ca´u 4 (1,0 æie°m ). a) Giaûi ph´½ng tr¹nh log 2 ( x - 1) - 2 log 4 (3 x - 2) + 2 = 0 . b) Cho moºt æa giaøc æe·u n æ¾nh, n N val n 3 . T¹m n bieÆt raLng æa giaøc æaı cho coø 27 æ´½lng cheøo. Ca´u 5 (1,0 æie°m ). Trong kho¶ng gian v½øi heº toµa æoº Oxyz , cho maºt phaoeng ( P ) : 6 x + 3 y - 2 z - 1 = 0 val maºt ca·u ( S ) : x 2 + y 2 + z 2 - 6 x - 4 y - 2 z - 11 = 0 . Ch´øng minh maºt phaoeng ( P ) caØt maºt ca·u ( S )
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