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Toan2009A - THI TUYN SINH I HC KHI A NM 2009 Mn thi TON(kha...

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Ð Ề THI TUYỂN SINH ĐẠI HỌC KHỐI A NĂM 2009 Môn thi : TOÁN (khóa ngày 4-7-2009) PH ẦN CHUNG CHO TẤT CẢ THÍ SINH Câu I (2 điểm). Cho haøm s y = x 2 2x 3 (1). 1. Khaûo saùt söï bieán thieân vaø veõ ñoà thò cuûa haøm soá (1) 2. Vieát phöông trình tieáp tuyeán cuûa ñoà thò haøm soá (1), bieát tieáp tuyeán ñoù caét truïc hoaønh, truïc tung laàn löôït taïi hai ñieåm phaân bieät A, B vaø tam giaùc OAB caân taïi goác toïa ñoä O. Caâu II (2,0 ñieåm) 1. Giaûi phöông trình (1 2sinx)cosx 3 (1 2sin x)(1 sin x) . 2. Giaûi phöông trình : 3 2 3x 2 3 6 5x 8 0 (x R) Caâu III (1,0 ñieåm) Tính tích phaân 2 3 2 0 I (cos x 1)cos xdx Caâu IV (1,0 ñieåm). Cho hình choùp S.ABCD coù ñaùy ABCD laø hình thang vuoâng taïi A vaø D; AB = AD = 2a; CD = a; goùc giöõa hai maët phaúng (SBC) vaø (ABCD) baèng 60 0 . Goïi I laø trung ñieåm cuûa caïnh AD. Bieát hai maët phaúng (SBI) vaø (SCI) cuøng vuoâng goùc vôùi maët phaúng (ABCD), tính theå tích khoái choùp S.ABCD theo a. Caâu V (1,0 ñieåm). Chöùng minh raèng vôùi moïi soá thöïc döông x, y, z thoûa maõn x(x+y+z) = 3yz, ta coù (x + y) 3 + (x + z) 3 + 3(x + y)(x + z)(y + z) 5(y + z) 3 . PHAÀN RIEÂNG (3,0 ñieåm): Thí sinh chæ ñöôïc laøm moät trong hai phaàn A hoaëc B A.Theo chöông trình Chuaån Caâu VI.a (2,0 ñieåm) 1. Trong maët phaúng vôùi heä toïa ñoä Oxy cho hình chöõ nhaät ABCD coù ñieåm I (6, 2) laø giao ñieåm cuûa 2 ñöôøng cheùo AC vaø BD. Ñieåm M (1; 5) thuoäc ñöôøng thaúng AB vaø trung ñieåm E cuûa caïnh CD thuoäc ñöôøng thaúng : x + y – 5 = 0. Vieát phöông trình ñöôøng thaúng AB. 2. Trong khoâng gian vôùi heä toïa ñoä Oxyz cho maët phaúng (P) : 2x – 2y – z – 4 = 0 vaø maët caàu (S) : x 2 + y 2 + z 2 – 2x – 4y – 6z – 11 = 0. Chöùng minh raèng: maët phaúng (P) caét maët caàu (S) theo moät ñöôøng troøn. Xaùc ñònh toïa ñoä taâm vaø tính baùn kính cuûa ñöôøng troøn ñoù. Caâu VII.a (1,0 ñieåm). Goïi z 1 vaø z 2 laø 2 nghieäm phöùc cuûa phöông trình: z 2 +2z+10=0.
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