LINK BOX: https://app.box.com/s/mbtcdzkyknzu3tt5xnuv4suq80w4mafz LINK DOCS.GOOGLE: https://drive.google.com/file/d/11FC-7DtuqyevI5EnZE5oOGH8vX5YHhK-/view?usp=sharing
https://twitter.com/daykemquynhon plus.google.com/+DạyKèmQuyNhơn http://daykemquynhon.ucoz.com Nơi bồi dưỡng kiến thức Toán - Lý - Hóa cho học sinh cấp 2+3 / Diễn Đàn Toán - Lý - Hóa 1000B Trần Hưng Đạo Tp.Quy Nhơn Tỉnh Bình Định Tuyển tập đề thi HSG Toán 8 c. x¸c ®Þnh vÞ trÝ cña H ®Ó tam gi¸c EHF cã diÖn tÝch lín nhÊt? Bµi 5 (1®) Cho c¸c sè d−¬ng a, b, c cã tÝch b»ng 1 CMR: (a + 1) (b + 1)(c + 1) ≥ 8 §¸p ¸n Bµi 1 (2,5®) sau khi biÕn ®æi ta ®−îc; − 6 x + 2 A = × 0,5® ( x − 2 )( x + 2 ) 6 a. TX§ = { ∀x : x ≠ ± 2; x ≠ 0} 0,25® −1 1 Rót gän: A = = 0,25® x − 2 2 − x b. §Ó A = 2 ⇒ x =1, 5 (tho· m·n ®iÒu kiÖn cña x) 0,5® 1 c. §Ó A < 0 th× < 0 ⇒ 2 − x < 0 ⇒ x > 2 (Tho· m·n ®k cña x) 0,5® 2 − x d. §Ó A cã gi¸ trÞ nguyªn th× (2 - x) phi lµ −íc cña 2. Mµ ¦ (2) = { − 1; −2;1;2 } suy ra x = 0; x = 1; x = 3; x= 4. Nh−ng x = 0 kh«ng tho· m·n §K cña x 0,25® VËy x = 1; x =3.; x=4 0,25® Bµi 2 (2,5®) 4 3 x + x + x + 1 a. P = 1® 4 3 2 x − x + 2x − x + 1 Tö: x 4 + x 3 + x + 1 = (x+1) 2 (x 2 - x + 1) 0,25® MÉu: x 4 - x 3 + 2x 2 -x +1 = (x 2 + 1)(x 2 -x + 1) 0,25® Nªn mÉu sè (x 2 + 1)(x 2 -x + 1) kh¸c 0. Do ®ã kh«ng cÇn ®iÒu kiÖn cña x 0,25® VËy P = 2 2 ( x + 1) ( x − x + 1) 2 2 ( x + 1) ( x − x + 1) ( ) ( x + 1) = x 2 2 + 1` mäi x 0,25® Nªn P ≥ 0 ∀x 1 1 1 1 b. Gii PT: + + + 2 2 2 x + 5x + 6 x + 7x + 12 x + 9x + 20 x + 11x + 3 x 2 + 5x + 6 = (x + 2)(x + 3) x 2 + 7x + 12 = (x + 4)(x + 3) x 2 + 9x + 20 = (x + 4)(x + 5) x 2 + 11x + 30 = (x + 5)(x + 6) 1 1 1 1 Trong ®ã = = − 5 6 ( 2)( 3) ( 2) ( 3) ... 2 x + x + x + x + x + x + TX§ = { ∀x ; x ≠ −2; −3; −4; −5; −6} ph−¬ng tr×nh trë thµnh: 2 = www.facebook.com/daykem.quynhon http://daykemquynhon.blogspot.com v× tö = ( x + 1) 2 ≥ 0∀x vµ mÉu x 2 + 1 >0 víi DIỄN ĐÀN TOÁN - LÍ - HÓA 1000B TRẦN HƯNG ĐẠO TP.QUY NHƠN 1 8 Skype : live:daykemquynhonbusiness https://daykemquynhonofficial.wordpress.com/blog/ DẠY KÈM QUY NHƠN OFFICIAL ST> : Đ/C 1000B TRẦN HƯNG ĐẠO TP.QUY NHƠN Gv: Nguyễn Văn Tú Đóng góp PDF bởi GV. Nguyễn Thanh Tú 36 Trường THCS Thanh Mỹ www.facebook.com/daykemquynhonofficial www.facebook.com/boiduonghoahocquynhonofficial
https://twitter.com/daykemquynhon plus.google.com/+DạyKèmQuyNhơn http://daykemquynhon.ucoz.com Nơi bồi dưỡng kiến thức Toán - Lý - Hóa cho học sinh cấp 2+3 / Diễn Đàn Toán - Lý - Hóa 1000B Trần Hưng Đạo Tp.Quy Nhơn Tỉnh Bình Định Tuyển tập đề thi HSG Toán 8 1 1 1 1 1 1 1 1 1 − + − + − + − = x + 2 x + 3 x + 3 x + 4 x + 4 x + 5 x + 5 x + 6 8 1 1 1 = − = x + 2 x + 6 8 = 8( x + 6 − x − 2) = ( x + 2)( x + 6) ⇔ = + + 2 32 x 8x 12 2 ⇒ x + x − = ⇒ x = x = − 8 20 0 2; 10 VËy PT ®· cho cã nghiÖm x =2; x = -10 Bµi 3 (1®) T×m gi¸ trÞ lín nhÊt, nhá nhÊt cña biÓu thøc 27 −12x A = 2 x + 9 ( ) ( ) 2 2 2 27 −12x x − 12x + 36 − x + 9 x − 6 A = = = −1 ≥ −1 2 2 2 x + 9 x + 9 x + 9 A ®¹t gi¸ trÞ nhá nhÊt lµ -1 ⇔ ( x − 6) 2 = 0 hay x = A = ( 4x 2 + 36) − ( 4x 2 + 12x + 9) ( 2x + 3) 2 27 −12x = = 4 − ≤ 4. A ®¹t GTLN lµ 4 2 2 2 x + 9 x + 9 x + 9 ( 2x + 3) 2 = 0 ⇒ x = − 3 2 Bµi 4 (3®) a.(0,75®) do E ®«ie xøng víi H qua AB nªn AB lµ ®−êng trung trùc cña ®oanh th¼ng EH vËy gãc EAH = gãcIAH (1) gãc FAD = gãcDAH (2) céng (1) vµ (2) ta cã : gãc EAH + gãc FAD = gãcDAH + gãcIAH = 90 0 theo gi thuyÕt hay gãcEAI + gßcAD + BAC = 90 0 + 90 0 = 180 0 . Do ®ã 3 ®iÓm E, A, F th¼ng hµng b. Tam gi¸c ABC vu«ng ë A nªn gãcABC + ACB = 90 0 (hai gãc nhän tam gi¸c vu«ng) Mµ gãcEBA = gãcABH (tÝnh chÊt ®èi xøng) gãcCA = gãcHCA (tÝnh chÊt ®èi xøng) suy ra gãc EBA + gãc FCA = 90 0 haygãc EBA + gãc FCA + gãc ABC + gãc ACB = 180 0 suy ra gãc EBC + gãc FBC = 180 0 (hai gãc trong cïng phÝa bï nhau) do ®ã BE song song CF. Vậy tø gi¸c BEFC lµ h×nh thang 0,75® Muèn BEFC lµ h×nh thang vu«ng th× phi cã gãc AHC = 90 0 ⌢ ⌢ 0 ( E = F = 90 ) vËy H phi lµ ch©n ®−êng cao thuéc c¹nh huyÒn cña tam gi¸c ABC Muèn BEFC lµ h×nh b×nh hµnh th× BE = CF suy ra BM = HC. VËy H phi lµ trung ®iÓm cña BC………….. 0,25® DIỄN ĐÀN TOÁN - LÍ - HÓA 1000B TRẦN HƯNG ĐẠO TP.QUY NHƠN 2 www.facebook.com/daykem.quynhon http://daykemquynhon.blogspot.com Skype : live:daykemquynhonbusiness https://daykemquynhonofficial.wordpress.com/blog/ DẠY KÈM QUY NHƠN OFFICIAL ST> : Đ/C 1000B TRẦN HƯNG ĐẠO TP.QUY NHƠN Gv: Nguyễn Văn Tú Đóng góp PDF bởi GV. Nguyễn Thanh Tú 37 Trường THCS Thanh Mỹ www.facebook.com/daykemquynhonofficial www.facebook.com/boiduonghoahocquynhonofficial
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