Hsg Huyen 0708 Toan

  • July 2020
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Phßng GD – §T Tiªn du Kú thi HSG cÊp huyÖn N¨m häc 2007 - 2008 Bµi 1: 1, Cho A =

x+2 x +1 1 + + víi x ≠ 1, x≥ 0 x x −1 x + x +1 1 − x

Rót gän A vµ chøng tá A <

1 3

2, Rót gän biÓu thøc: 5 − 3 − 29 − 12 5 Bµi 2: 1. 2. a. b.

3 x 2 − 2 xy − y 2 = 0 Gi¶i hÖ pt sau:  2  x + 5y = 0 Cho pt Èn x: x 2 + 2(a − 1) x − (a + 1) = 0 gäi x1 x2 lµ nghiÖm Chøng tá pt cã nghiÖm víi mäi a. T×m a ®Ó pt cã nghiÖm x1 x2 tho¶ m·n x12 + x22 = 16 T×m a ®Ó pt cã nghiÖm tho¶ m·n x1 <1 < x2

Bµi 3: T×m gi¸ trÞ nhá nhÊt cu¶ A =

2 x2 + x −1 x2 − 2x + 2

Bµi 4: Gi¶i c¸c pt sau: a, x 2 + x + 12 x + 1 = 36 b, x 2 − x + 5 = 5 Bµi 5: Cho ®êng trßn t©m O. Tõ ®iÓm A bÊt kú bªn ngoµi ®êng trßn O kÎ c¸c tiÕp tuyÕn AB, AC víi (O) (B, C lµ c¸c tiÕp ®iÓm). I lµ 1 ®iÓm bÊt kú n»m gi÷a B vµ C. Mét ®õng th¼ng qua I vµ vu«ng gãc víi OI c¾t ®êng th¼ng AB t¹i E, c¾t AC t¹i F. AI c¾t (O) t¹i P, Q (P thuéc cung nhá BC) a. CMR I lµ trung ®iÓm cña EF vµ tø gi¸c AEOF néi tiÕp 1 ®êng trßn. b. KÎ ®êng th¼ng qua (O) vu«ng gãc víi OA c¾t c¸c ®êng th¼ng AB, AC lÇn lît ë M vµ N. X¸c ®Þnh vÞ trÝ cña A ®Ó diÖn tÝch ∆AMN nhá nhÊt.

c. KÎ 1 ®êng th¼ng bÊt kú song song víi AB, ®õng th¼ng nµy c¾t BP, BQ theo thø tù ë G, H. Chøng tá r»ngBC ®i qua trung ®iÓm cña GH.

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