ĐỀ THI HỌC SINH GIỎI CẤP TRƯỜNG NĂM HỌC Môn Toán 8 2009-2010 TRƯỜNG THCS XUÂN LAM

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ĐỀ THI HỌC SINH GIỎI CẤP TRƯỜNG NĂM HỌC Môn Toán 8 2009-2010 TRƯỜNG THCS XUÂN LAM

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Tài liệu tham khảo dành cho giáo viên, học sinh THCS chuyên môn toán học - ĐỀ THI HỌC SINH GIỎI CẤP TRƯỜNG NĂM HỌC Môn Toán 8 2009-2010 TRƯỜNG THCS XUÂN LAM.

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Nội dung Text: ĐỀ THI HỌC SINH GIỎI CẤP TRƯỜNG NĂM HỌC Môn Toán 8 2009-2010 TRƯỜNG THCS XUÂN LAM

  1. trêng THCS     k× thi häc sinh giái cÊp trêng n¨m häc 2009-2010 xu©n lam M«n : To¸n 8 (Thêi gian : 120 phót) Hä tªn häc sinh : ............................................................................................................................................................................................ ... Líp ................................ Sè b¸o Gi¸m Sè ph¸ch danh thÞ ..................................................................................................................................................................................... ...................................................................................................................................................................................................... ....................... ------------------------------------------------------------------------------------------------- §iÓm b»ng sè §iÓm b»ng ch÷ Sè ph¸ch ................................................................................................................................................................... ... Bµi 1: (6 ®iÓm) Ph©n tÝch ®a thøc sau ®©y thµnh nh©n tö: 1. x 2 + 7 x + 6 2. x32 - 1 3. Chøng tá r»ng A = (x - 3)(x - 5) + 4 > 0 víi mäi gi¸ trÞ cña x. Bµi 2: (2 ®iÓm) a/ T×m a ®Ó ®a thøc x5 + 32 chia hÕt cho ®a thøc x + a b/ T×m sè d trong phÐp chia cña biÓu thøc ( x + 2 ) ( x + 4 ) ( x + 6 ) ( x + 8 ) + 2008 cho ®a thøc x 2 + 10 x + 21 Bµi 3: (4 ®iÓm) a/ Chøng minh ®¼ng thøc sau:  x2 + y2 1  x 2 y 2  x + y  −  +  : 2 = x− y  xy x+ y y  x  x − y 2  x y z b/ Cho = = chøng minh r»ng: a + 2b + c 2a + b − c 4a − 4b + c a b c = = víi abc # 0 vµ c¸c mÉu sè kh¸c 0 x + 2 y + z 2x + y − z 4x − 4 y + z Bµi 4: (6 ®iÓm) Cho tam gi¸c ABC. ë phÝa ngoµi cña tam gi¸c vÏ c¸c tam gi¸c vu«ng c©n t¹i A lµ AEC, ABD vµ h×nh b×nh hµnh ADIE. Chøng minh a/ IA = BC b/ IA ⊥ BC c/ Gäi M, N theo thø tù lµ trung ®iÓm cña ®o¹n th¼ng BD, CE. Tam gi¸c ABC ph¶i cã ®iÒu kiÖn g× ®Ó ba ®iÓm M, A, N th¼ng hµng. Bµi 5: (2 ®iÓm) a) Cho x, y lµ hai sè d¬ng tho· m·n x2+y2-xy = 8 T×m GTNN, GTLN cña M=x2+y2 5 x 2 − 30 x + 53 b) T×m gi¸ trÞ lín nhÊt cña biÓu thøc: A = x 2 − 6 x + 10 Bµi lµm --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
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