[ COMBO ] BỒI DƯỠNG TOÁN 8 NÂNG CAO VÀ PHÁT TRIỂN (VŨ HỮU BÌNH-NXBGD) & TUYỂN TẬP ĐỀ THI HSG TOÁN 8 (NGUYỄN VĂN TÚ-THCS THANH MỸ)

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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 Bµi 5: (3.5®) Cho tam gi¸c ABC vu«ng t¹i A, gäi M lµ mét ®iÓm di ®éng trªn c¹nh AC, tõ C vÏ ®- êng th¼ng vu«ng gãc víi tia BM t¹i H, c¾t tia BA t¹i O. Chøng minh r»ng: a) OA.OB = OC.OH b) OHA cã sè ®o kh«ng ®æi. c) Tæng BM.BH + CM.CA kh«ng ®æi. Bµi 1: (1.5®) C©u a: (0.57®) BiÓu ®iÓm vµ ®¸p ¸n to¸n 8 = (x 2 - 9y 2 ) – (xz - 3yz) 0.25® = (x - 3y)(x + 3y) – z(x - 3y) 0.25® = (x - 3y)(x + 3y - z) 0.25® C©u b: (0.75®) = x(4x 3 + 4x 2 – x – 1) 0.25® [ ] = x 4x 2 ( x + 1) − ( x + 1) 0.25® = x(x + 1)(4x 2 - 1) = x(x + 1)(2x - 1)(2x + 1) 0.25® Bµi 2: (2.5®) C©u a: 1® P = ⎡ ⎢ ⎣( x 2 = = = x( x + 3) + + 9)( x + 3) x x + 3 : 2 x + 9 x + 3 . 2 x + 9 x + 3 x − 3 C©u b: (0.75®) P = x + 3 ⇔ x − 3 x 2 2 3 ⎤ ⎡ 1 6x ⎤ ⎥ : ⎢ − 2 ⎥ + 9 ⎦ ⎣ x − 3 ( x − 3)( x + 9) ⎦ + 9 − 6x 2 ( x − 3)( x + 9) 2 ( x − 3)( x + 9) ( x − 3) 2 0.25® 0.25® 0.25® 0.25® DIỄN ĐÀN TOÁN - LÍ - HÓA 1000B TRẦN HƯNG ĐẠO TP.QUY NHƠN Px - 3P = x + 3 0.25® (P – 1)x = 3(P + 1) www.facebook.com/daykem.quynhon http://daykemquynhon.blogspot.com Skype : live:daykemquynhonbusiness https://daykemquynhonofficial.wordpress.com/blog/ DẠY KÈM QUY NHƠN OFFICIAL ST&GT : Đ/C 1000B TRẦN HƯNG ĐẠO TP.QUY NHƠN Gv: Nguyễn Văn Tú Đóng góp PDF bởi GV. Nguyễn Thanh Tú 108 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 3 P + 1 x = P −1 Ta cã: x > 0 ⇔ ⎡⎧P + 1 > 0 ⎢⎨ ⎢⎩P −1 > 0 ⎡P > 1 ⇒ ⇒ ⎢ ⎢ ⎧P + 1 < 0 ⎣P < 1 ⎢⎨ ⎢⎣ ⎩P −1 < 0 ( P + 1) 3 x = P −1 ( ) P + 1 > 0 ⇒ > 0 P −1 VËy kh«ng nhËn gi¸ trÞ tõ -1 ®Õn 1. 0.25® C©u c: 0.75® §KX§: x ≠ ± 3 x + 3 x − 3 + 6 6 P = = = 1+ x − 3 x − 3 x − 3 P nhËn gi¸ trÞ nguyªn ⇔ x - 30∈¦ (6) = { ± 1 ; ± 2; ± 3; ± 6} Tõ ®ã t×m ®îc x { 4;2;5;1;6;0;9; −3} 0.25® ∈ 0.25® KÕt hîp víi §/C x ≠ ± 3; x ∈ z ta ®îc. x ∈ { 4;2;5;1;6;0;9 } 0.25® VËy x { 4;2;5;1;6;0;9 } ∈ th× P nguyªn. Bµi 3: Gii ph¬ng tr×nh (1.5®) C©u a: (0.75®) - §a ®îc vÒ d¹ng tÝch: (x + 1)(x - 2) 2 = 0 0.50® ⎡ x = 1 ⇒ ⎢ ⎣ x = 2 VËy ph¬ng tr×nh cã nghiÖm: x = 1; x = 2 0.25® C©u b: (0.75®) §K: x∈N *n - §a vÒ d¹ng 2 2 2 2 2 3 4 ( x + 1) 31 . . ... = 1.3 2.4 3.5 x( x + 2) 16 2( x + 1) 31 ⇔ = x + 2 16 Tõ ®ã ⇒ t×m ®îc x = 30 (t/m x∈N * ) 0.25® 0.25® VËy ph¬ng tr×nh cã nghiÖm: x = 30 0.25® DIỄN ĐÀN TOÁN - LÍ - HÓA 1000B TRẦN HƯNG ĐẠO TP.QUY NHƠN Bµi 4: (1®) Gi sö a(2 – b) > 1; b.(2 – c) >1; C(2 – a) > 1 ⇒ abc (2 – b)(2 – c)(2 – a) > 1 (1) 0.25® www.facebook.com/daykem.quynhon http://daykemquynhon.blogspot.com Skype : live:daykemquynhonbusiness https://daykemquynhonofficial.wordpress.com/blog/ DẠY KÈM QUY NHƠN OFFICIAL ST&GT : Đ/C 1000B TRẦN HƯNG ĐẠO TP.QUY NHƠN Gv: Nguyễn Văn Tú Đóng góp PDF bởi GV. Nguyễn Thanh Tú 109 Trường THCS Thanh Mỹ www.facebook.com/daykemquynhonofficial www.facebook.com/boiduonghoahocquynhonofficial
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[ COMBO ] BỒI DƯỠNG TOÁN 8 NÂNG CAO VÀ PHÁT TRIỂN (VŨ HỮU BÌNH-NXBGD) & TUYỂN TẬP ĐỀ THI HSG TOÁN 8 (NGUYỄN VĂN TÚ-THCS THANH MỸ)

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