DapanTOANkhoiBnam2014 - BO GIAO DUC VA AO TAO E CHNH THC AP...

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BO˜ GIA°O DUˇC VA± ²A±O TAˇO ²A°P A°N - THANG ²IE¯M ---------- ²E³ THI TUYE¯N SINH ²AˇI HOˇC NA˚M 2014 °E± CH˝NH TH²³C Mo´n: TOA°N; KhoÆi B (°aøp aøn - Thang æie´m goµm 03 trang) ------------------- Ca°u ±aøp aøn ±ie²m 1 a) (1,0 æie´m) (2,0æ) V¶øi m = 1 , halm soÆ tr¶û thalnh: y = x 3 - 3 x + 1 . Ta·p xaøc æ¸nh: D = R . S¹º bieÆn thie»n: - Chieµu bieÆn thie»n: y prime = 3 x 2 - 3 ; y prime = 0 x = ± 1 . 0,25 Caøc khoaûng æoµng bieÆn: ( -∞ ; - 1) val (1; + ) ; khoaûng ngh¸ch bieÆn: ( - 1; 1) . - C¹ºc tr¸: Halm soÆ æaºt c¹ºc æaºi taºi x = - 1 , y = 3 ; æaºt c¹ºc tie´u taºi x = 1 , y CT = - 1 . - Gi¶øi haºn taºi vo» c¹ºc: lim x →-∞ y = -∞ ; lim x + y = + . 0,25 - Baûng bieÆn thie»n: x -∞ - 1 1 + y prime + 0 - 0 + y 3 + -∞ - 1 a16 a16 a16 a16 a16 a16 a49 a80 a80 a80 a80 a80 a80 a113 a16 a16 a16 a16 a16 a16 a49 0,25 °oµ th¸: x y 3 - 1 - 1 1 O 1 0,25 b) (1,0 æie´m) Ta coø y prime = 3 x 2 - 3 m . °oµ th¸ halm soÆ (1) coø hai æie´m c¹ºc tr¸ ph¹¶ng tr¼nh y prime = 0 coø hai nghie·m pha»n bie·t m > 0 . 0,25 Toºa æo· caøc æie´m c¹ºc tr¸ B, C lal B ( - m ; 2 m 3 + 1) , C ( m ; - 2 m 3 + 1) . Suy ra --→ BC = (2 m ; - 4 m 3 ) . 0,25 Goºi I lal trung æie´m cuûa BC , suy ra I (0; 1) . Ta coø tam giaøc ABC ca»n taºi A -→ AI.
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