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- 1. BO GIAO DUC VA AO TAO E THI TUYEN SINH AI HOC NAM 2014 Mo但n: TOAN; Kho叩i D E CHNH THC Th担淡i gian la淡m ba淡i: 180 phu湛t, kho但ng ke奪 th担淡i gian pha湛t 単e Ca但u 1 (2,0 単ie奪m). Cho ha淡m so叩 y = x3 3x 2 (1). a) Kha短o sa湛t s旦誰 bie叩n thie但n va淡 ve探 単o th嘆 (C) cu短a ha淡m so叩 (1). b) T狸m to誰a 単o辰 単ie奪m M thuo辰c (C) sao cho tie叩p tuye叩n cu短a (C) ta誰i M co湛 he辰 so叩 go湛c ba竪ng 9. Ca但u 2 (1,0 単ie奪m). Cho so叩 ph旦湛c z tho短a ma探n 単ieu kie辰n (3z z)(1 + i) 5z = 8i 1. T鱈nh mo但単un cu短a z. Ca但u 3 (1,0 単ie奪m). T鱈nh t鱈ch pha但n I = 4 0 (x + 1) sin 2x dx. Ca但u 4 (1,0 単ie奪m). a) Gia短i ph旦担ng tr狸nh log 2(x 1) 2 log4(3x 2) + 2 = 0. b) Cho mo辰t 単a gia湛c 単eu n 単脱nh, n N va淡 n 3. T狸m n bie叩t ra竪ng 単a gia湛c 単a探 cho co湛 27 単旦担淡ng che湛o. Ca但u 5 (1,0 単ie奪m). Trong kho但ng gian v担湛i he辰 to誰a 単o辰 Oxyz, cho ma谷t pha炭ng (P) : 6x + 3y 2z 1 = 0 va淡 ma谷t cau (S) : x2 +y2 +z2 6x4y 2z11 = 0. Ch旦湛ng minh ma谷t pha炭ng (P) ca辿t ma谷t cau (S) theo giao tuye叩n la淡 mo辰t 単旦担淡ng tro淡n (C). T狸m to誰a 単o辰 ta但m cu短a (C). Ca但u 6 (1,0 単ie奪m). Cho h狸nh cho湛p S.ABC co湛 単a湛y ABC la淡 tam gia湛c vuo但ng ca但n ta誰i A, ma谷t be但n SBC la淡 tam gia湛c 単eu ca誰nh a va淡 ma谷t pha炭ng (SBC) vuo但ng go湛c v担湛i ma谷t 単a湛y. T鱈nh theo a the奪 t鱈ch cu短a kho叩i cho湛p S.ABC va淡 khoa短ng ca湛ch gi旦探a hai 単旦担淡ng tha炭ng SA, BC. Ca但u 7 (1,0 単ie奪m). Trong ma谷t pha炭ng v担湛i he辰 to誰a 単o辰 Oxy, cho tam gia湛c ABC co湛 cha但n 単旦担淡ng pha但n gia湛c trong cu短a go湛c A la淡 単ie奪m D(1; 1). 旦担淡ng tha炭ng AB co湛 ph旦担ng tr狸nh 3x + 2y 9 = 0, tie叩p tuye叩n ta誰i A cu短a 単旦担淡ng tro淡n ngoa誰i tie叩p tam gia湛c ABC co湛 ph旦担ng tr狸nh x + 2y 7 = 0. Vie叩t ph旦担ng tr狸nh 単旦担淡ng tha炭ng BC. Ca但u 8 (1,0 単ie奪m). Gia短i ba叩t ph旦担ng tr狸nh (x+1) x + 2+(x+6) x + 7 x2 +7x+12. Ca但u 9 (1,0 単ie奪m). Cho hai so叩 th旦誰c x, y tho短a ma探n ca湛c 単ieu kie辰n 1 x 2; 1 y 2. T狸m gia湛 tr嘆 nho短 nha叩t cu短a bie奪u th旦湛c P = x + 2y x2 + 3y + 5 + y + 2x y2 + 3x + 5 + 1 4(x + y 1) . He叩t Th鱈 sinh kho但ng 単旦担誰c s旦短 du誰ng ta淡i lie辰u. Ca湛n bo辰 coi thi kho但ng gia短i th鱈ch g狸 the但m. Ho誰 va淡 te但n th鱈 sinh: . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . ; So叩 ba湛o danh: . . . . . . . . . . . . . . . . .