Ttr giac BMCS la hinh binh hanh rna P la trung di~m cua Be nen S, P, M thang hang ~ OP lit dirong trung binh cua tam giac SAM ~ OP = OC.[r]
(1)sa GD vA DAD TAO LAD CAl eeoc THI GIAI ToAN TREN MTCT cAp TiNH LOP THCS - NAM , HOC 2012-2013 MonTOAN Thai gian: 150 phut (khong k~ thai gian giao dS) Ngay thi: 17/01/2013 Huang d~n cham gbm co c~u, trang HUONGDANCIIAM DE CHiNH THUC ° A-HU'o-ng dIu cham: , an - Thi sinh phai vi@tdti quy trinh fin phim Trong mQt quy trinh phim n@u cac buoc tnroc lam dung, buoc sau lam sai thi cham diSm cac buoc dung N@ucac buoc truce lam sai, buoc sau lam dung thi khong cham diem buoc dung lam sau NSu HS vi@tdung quy trinh theo each khac v~n cho diem t6i da - Bai cham theo thang diem 50, diem cua bai thi la tang cQng cua cac diem phan - DiSm bai thi lam tron d@n0,5 diem N@u bai khong yeu cAu lam tron rna lam tron thi m6i diu trir 0,5 diem va ngiroc lai B- Bi~u di~m cham: (Dung cho hai loai may fx-500MS, fx-570MS, fx-570 vue) can Noi dung a) A = 0, 326401257 b) B~ 0,44586 a) UCLN(a,b,c)=170113 BCNN(a,b,c)= 214342380 b) co c~p s6 (x, y) la (-1; -3), (1; 3), (2; 3), (4; 21) a) U1= 1, U2= 5, U3= 16, U4= 45, U5= 121, Di~m 2,5 2,5 1,5 1,5 2,0 1,5 U6= 320 b) L~p cong thirc troy h6i tinh Un+2 theo Un+1 va Un Gia su cong thirc troy h6i co dang Un+2 = aUn+1 + bl.I, +c Theo k@tqua,phftn a, ta co h~ phirong trinh : Sa+b { +c;::::16 16a + 5b + C = 45 4Sa + 16b + C = 121 1,0 0,5 Sir dung MTCT -viSt qui trinh Giai h~ phuong trinh tren MTCT ta diroc a = 3, b = - 1, c = V~y cong tlurc truy h6i co dang Un+2 = 3Un+1 - U, +2 c) Vi@tdung qui trinh 1~A, ~B An phim theo ghi A 1,0 each ghi = 3B-A+2: B = 3A-B+2 0,5 (2) KQ: U2o=228 826 125, U22=1568397605 a) Ta co' a = 3e + 3k + 1= k • k 0,5 + 3k + 3k + 1- k = (k + Ii - e = !_ _ k3.(k+l)3 (e+k)3 k3.(k+1)3 k~ (k+1i 1,0 Do voi k=1,2,3, , 2013 thi S = at + a2+ a3+···+a2012+a2013 ;3 S=(113 - )+(2\ - 3\ )+"'+(20~23 - 20~33)+(20~33 - 20~4~) = 1- = 8169178743 20143 8169178744 b) {ao,at,a2,.' ,an} ={32,1,3,1,94,1,5,3,3} A=31+ 54216 =32+ 30127 1+ 1,5 2,5 1 3+ 1+ 94+ -:- 1+ 5+1 3+3 a) GiM phuong trinh sau, tinh x theo a va b (v6i a>0, b>O) ~a+b.Jl-"X (voi =l+~a-b~ X:$; 1) <=> ~ a + b J1 - x - ~ a - b Jl- x =1 Binh phuong v~ phirong trinh ta diroc: - 2~r-a:-2 -:b 2-:-(1-_-X-) = a + b J1- x + a - b~ <=> 2a -1 = 2~a - b (1- x) <=> a2 -b2(1-x) = (2a-l)2 ., <=> 1- x = (a2 _ (2a _1)2 ) b2 ee x= = 4a -1 4b2 4b2 -4a+1 1,5 1,0 2,5 4b2 Ap dung tinh x ta duoc k~t qua: x = 0,999994186 b) S6 d.n tim hi 4167 a) Ap dung cong tlnrc: T= a(l+m%).{(I+m%)n-l} VOi m=0,52%, a=300 000, n=144 KQ: 64 392 497 d b) a= (T.m%) :{( l+m%t+I-(I+m%)} KQ : 465 893 d a) Vi! d6 thi cua ba ham s6 tren, : m% 2,5 2,5 (3) Db thi ham s6 y=3x+5 Db thi ham s6 y= Db thi ham s6 y=-2x+3 la dirong thang di qua hai diSm (0; 5) va ( -35 ;0 ) ~ x-21a dirong thang di qua hai diSm (0; -2) va (3; 0) Ve dung db thi ham la dirong th~g di qua hai diSm (0; 3) va ( ~ ; 0) s6 0,5 1,0 b)T oa d0 d"" tern A l'a ng h·rem eua h"e PT{ 3x+5 =-x-2 A A ? {x =-3 <=> y=-4 y=3x+5 15 Toa diSm B la nghiem cua he pt{23x _ = -2x y=-2x+3 Toa diSm C la nghiem cua he Pt{- 2x +' = y=3x+5 j + <=> x = -3 Y=- 3x + <=> jx = -~ 19 y=- 1;) V~y toa de>eac diSm A(-3; -4), B( 1:; -43), C( -52 ~ 15 e) AB=~ ( 8+3 1,0 )2 +( 4-4"3)2 =5,85902823, BC- V AC 2)2 +(195+4"3)2 = 5,087054649, 15 ( 8+5 ( 52)2 + (195+4 )2 =8,221921916 ~ 3- Chu vi tam giac ABC ia: 19,16799739 SABe pep - a)(p -b)(p - c) =14,78748531 =-J R = abc = S= 4S 4,142962708 1i R2_7Z'r2 Ri ,r S = 1,542934821 p 0,5 0,5 46,44(em 1) KQ: n=127 thi a=149 n=151 thi a-15I 2) n = 169; x=1013 = 1,0 0,5 ) 2,5 A .r-.; D / 2,5 a)Do LB+C=180o LHAK+LC=180o (4) => LHAK=LB => AH=AB.sin B-20,87302678 (em) AK=AD.sinB 27,33630453 (em) b)SABCD=BC.AH-AD AB.sin B 0,5 0,5 0,5 0,5 SAHK = _!_ AK.AH.sin HAK = _!_ AH.AK.sinB 2 = _!_ AB.sinB.AD.sinB.sinB = _!_ AB.AD.sin3B 0,5 => SABeD = AD.AB.sinB _!_ AB.AD.sin B SAHK _ 1,0 0,5 sin B An tren MTCT ta duoc k~t qua: 3,91256184 e) Sr= SABCD-SAHK = AD AB.sin B _ ! AB.AD.sin3B AD.AB.sinB.(I2 An tren MTCT ta diroc k~t qua: 594,0934812(em2) a) ~ABH eo LH =>AH = => AH = ' sin B) 1,0 = 90 , LB1= 30 .! AB _!_ .38,7624= 19,3812 em 0,5 10 BH = AB Cosls = 38,7624.eos300 BH = 33,56922311 em HC = BH TanHBC = 33,56922311 tan 42° HC = 30,22586425 em AC = AH + HC = 49,60706425 (em) BC = JBH2 +HC2 =45,17184532 (em) c 0,5 0,5 0,5 b) 2AE = AB + AC - BC => AE = AB+A C-BC = 21,59880946 (em) BE BK = AB - AE = 38,7624 - 23,27048889 =17,16359054 (em) (tie tt eAt nhau) CK = BC - BK = 28,00825479 ( em) e) Vi I If!tam duong tron nQi ti~p tam giac ABC nen CI, BI If!2 ', '" eua tam giac , ta co, L IBC = LABe ; L ICB = LACB duong p h"an giac 2 Ma BK = IK eot (IBC); CK = IK eot ICB 0,5 0,5 (5) = BC = IK(cotIBC ~ BK + CK IK =r = BC cot LMI = AM = LABC + cot = LACB 45,17184533 =12,47007846 (em) cot 36° + cot 24° 2 LAI+ LB1= 36°+18° = 54° (goe ngoai cua tam giac ABM) AH = 19,3812 = 23 95648069 (em) sin M + cotIBC) sin 540 1,0 ' Ttr giac BMCS la hinh binh hanh rna P la trung di~m cua Be nen S, P, M thang hang ~ OP lit dirong trung binh cua tam giac SAM ~ OP = OC =R= _!_ AM = 11,97824034 ~r-O-'P2-+-p-C-2 (em) = 25,56564383 (em) 1,0 (6)