HDC MTCT cap tinh nam hoc 2012 2013 mon Toan THPT

<span class='text_page_counter'>(1)</span>so GIAO Dl)C vA DAo T ';'0. cuoc. THI cAp TiNH GIAI ToAN TREN MAy TiNH CASIO, VINACAL NAM HQC 2012-2013. LAo CAl. rHPn. Mon fbi: Toan (Chuung trinh. HUONG nAN CHAM DE THI cHiNH THUC. Thai gian thi: 150 phut (kh6ng Ngay thi: 17/01/2013. Jed thoi gian giao ai thi).. Huang ddn chdm g6m co 10 cdu, 07trang, m6i cdu 05 iliim (Chu y: Thi sinh lam bai thi vaa ban ild thi nay). DIEM. B~ng. eVA BAI. s6. so PHAcH. Giam khao (Ky va ghi ro ho ten). THI. (Do Truong ban cham thi ghi). B~ng chii' 1........................................... . 2 ............................................ * Quy. dinh : Thi sinh trinh bay tom titt each giai, cong tlnrc ap dungjhoac quy trinh bam phim neu bai toan yeu cau) va diSn ket qua vao 0 liSn kS. Cac kSt qua tinh gftn dung, neu khong co chi dinh cu thS thi duoc lay chinh xac toi 4 chtr s&thap phan. 2. Bai 1 Cho ham s& f(x). =x. - 3~ + 1 .Tim g~n dung tea dQ cac diem x+. C1,IC. KETQUA. CACHGIAI. tri cua ham s&.. DIEM. 2. f'(x)=x +4x-7 (x+ 2)2. Taco:. f'(x)=O<=>XJ. ~1,3166;x2. (x;t:-2). ... ~-5,3166. 1.0 1.0. Kit qua: A(l, 3166; -0,3668) B( -5,3 J 66; -13, 6332). Bili 2: Cho da thirc P(x) b~c 4, h~ so cua P(x)chia ~+l, x+2, x-I, x-2 du -2,4, 1. (3.5 diemj'Iim da tlnrc P(x).. CACHGIAI ,. .,. .~. X4. 1.5 1.5. bang 1. -11, 6.. KETQUA. DIEM. , P(I)=-11,P(2)=6,. Tu gia thiet co. (. P -1)=-2,P(-2)=4. Xet da thtrc b~c b6n Q( x) thoa Q(I) = Q(2) Gia. = Q(3) = Q( 4) = O.. su P(x) = Q(x). ta co h~. +a.x3 +bx2 + ex + d,. 0.5.

<span class='text_page_counter'>(2)</span> -ll=a+b+c+d 6 = 8a + 4b + 2c + d. 0.5. t. -2=-a+b-c+d 4 = -8a + 4b - 2c + d. 2.0. ~276'. a ~ .?_;c·~ ~ 37. d=_3}j'. 3. 6. Kdt (lud: 2. P ( x) = (x 23 +-x 6. 2. -. 37 --x-6. 2. 1)(x. -. 4) + % x. 3. 0.5. 31 3. .. 2. (1.5 diemj'I'inh : P(20) - P(1 0) .. ~. KETQUA. CACHGIAI. P(20) = 172737 P(10) = 11482 P(20) - P(10) = 161255. Bili 3: Giiii h~ phuong trinh : {. :3. + ( - xy = 6 x +y +x+y=5. KETQuA. {(x+ y)[ (x+ y)' -3xy ] ~ 6+ xy (x + y)2 -. 0.5. co h~ f'-3PS~6+P S2 +S-2P. 0.5. =5. S3 + 4S2 - 14S + 7 = 0. • Giai phuong trinh t2. (SJ; Pi) tren ta. DIEM. 2xy + x + y::; 5. f)~t S = x + y; p ::;xy ta ¢::>. 0.5 0.5 0.5. (I). CACHGIAI (I)~. DIEM. dUQ'C. -. 0.5. Sf + P = 0 'u'ng voi cac e~p SI ~ ~6,3702;~ ~ 14,6046. cac nghiem cua h~. S2 ~ 1,7379;Pz ~ -0,1209. 1,5. S3 ~ 0, 6323; ~ ~ -1,9839. {x ~ 1,8049 {x ~ -0,0670 y ~ -0,0670'. Y ~ 1,8049 '. 2.0. {X~-1'1274 {X~I,7597 y~I,7597 Ul. BAi 4: Cho day s6:. = 1;». = -2 _. { U + n 2. ' y~-1,1274. -. 1. 2un+1. -. 3un. 1. ViSt quy trinh bfim phim tinh. V6i n>O;nEN Un;. Sn (T6ng cua n. s6 hang. d~u cua day un). 2.

<span class='text_page_counter'>(3)</span> CACHGIAI. DIEM. Gan: 1 -> A; -2 -> B ; -1 -> C (tong hai s5 hang dAu)2 - >D (bien dem) 1. = 2B --A:. D = D + 1:A. C = C + A:. 3. 1.0. 1. D = D + 1: B = 2A - - B : C = C + B. 3. 2.0. ?. KETQUA. CACH GIAI. Bai 5:. ,. 0 Tim. ::::. Sl5. = -12664,2542. ,. ,. I(x) f'(X)::::. 5,. x. 5,. 2 + ~4- 3x2. KETQUA. tren doan [-. DIEM 0.5. 2 . X'et h'am so;. T3. = 3x-2+..}4-3x' 0 <=> X. 1.0 1.0. = 3x -. gia tri 1611nhat, gia tri nho nhat cua ham so : f(x). CACHGIAI 2 BK : - Jj. DIEM. -5694,4751. Ul5. Jj;~]. =1. . Thuc hien tren may tinh. f'(x)=O<=>x=l. f(1). 0.5 1.0. = 2;. 1.0. 2. /(Jj) ~1,4641; f(-. 1.0. 2 v13) ~ -5,4641. Max/(x). = f(1)::::. 2. 1.0. [-}~J Min/(x). [_~;~]. Bai 6 : Cho tam giac MBC vuong tai A, AB = 13; ACE = 30° . Cac duong phan giac trong BM, CN cua tam giac MBC e~t nhau tai 1.. = /C-1):::: -5,4641 3 II.

<span class='text_page_counter'>(4)</span> 1. (3di~m)Tinh do dai BM, CN. CACHGIAI BC=. AB. sin C. =. 13. KETQUA. =213. sin 30°. AC::;::3 BM ='. BC. 2 AB+BC. ~AB.BC.p(p. ,. = 2.f3. AC=3. - AC). BM=2. 2. CN=. DIEM. CN ~ 3,1058. ~AC.BC.p(p-AB). 0.5 0.5 1.0 1.0. AC+BC. 2. (2 diemj'Ifnh dien tich tam giac MMN. CACHGIAI. KETQuA. DIEM. Do duong phan giac BM, CN cat nhau tai I nen l la tam duong trong ngoai tiep 2S. r=IM=IN=. r~ 0.6340 = 180°-15° -300. BIC=NIM. V?y. St;jMN. 0.5. AB+BC+AC. ---. -----. 0.5. = 135°. ~ LO.63402.sin 1350 2. =~IM.JN.sin(MIN). ~. 0,1421. 0.5 0.5. Bili 7: 1.(2 di~m) Tinh gia tri eua bi~u thirc. = ~ I + .l)1 +.l + ]_. 1+.l + .!_+ i.. .A. 2. 2. 3. 2. 3. 4. ''-1+-_-1-+-.!_-+-...-+-=---1 ~. 2. 3. 20 s:. CACHGIAI Gan A. ?. KETQUA. = 0, B ::;::0, C = 1. Khaibao:A=A+. A. K~t qua: 17667,9757. A • I Tinh tong : S=l 2 C12013+22 C22013--+3 r. 2. 2013. 3 1 2 C2013 -+ ... +2013 ( 2013 ). 2. 2013()n-I1 C2013 -2013. CACHGIAI Ta co: (l+xY . ¢::? ¢::?. n(l +xr-I n.x(l+xy-l. KETQUA. ... +nC:x"-1. =xC~ +2C;X2 + ... +nC;xn. 2c;xn-1. n(1 + xy-I + n(n -I)x.(l + xy-2 ",,}2C! + 22 C;x + ... + n. ~ hex). ~ S=f. = n(1 +xy-I (_1_) 2013 2013. +n(n-l)x.(l. DIEM. 0.5 0.5. =C~ +C~X+C;X2 + ... +C;xn. = c~+2C;x+. 1.0 1.0. _!_ :C,=C.JB. 1 :B=B+. ,. ¢::?. DIEM. +xy-2. =2013(1 +_1_)2012 +2013.2012.-1-(1 2013 2013. 0.5 0.5. +_1_)2011 2013. 0.5 4.

<span class='text_page_counter'>(5)</span> I Sd0930,2233 I Bai 8: Cho hinh ch6p SABCD co day ABCD la hinh thoi canh a. = {j20. 13;. 0.5. BAD = 60° ;. SO .L (ABeD); SO = %a ; mat phang (a) chua AD va (a) vuong goc. voi (SBC).. s. c. 1.(1.5 di6m) Tinh. VSABCD. CACHGIAI. KETQUA. DIEM. a J3. 0.5. 2. SAEeD. =-.-. 2. 1. VSABCD = -SO,SABCD. 0.5. 3. 0.5 ,. 2. (3.5 diem) Thill dien tich thiet dien tao boi (a) va hinh ch6p SABeD.. KETQuA. CACHGIAI. DIEM. +. dung d qua 0 vuong goc voi BC cat BC, AD tai I;J + Til J ke JH .lS1; tir H ke EF IIBC c~t SB, SC tai E; F. Thi~t dien la tu giac AEFD. + Xet MOl: 01 = BO.sin60o + IJ = 201. + SI = +. 2. 01 = aJ3 . IJ = aJ3 4. = -.SO.lJ. + HI =. 2. ~IJ2. ;. '. 0.5. 2 1. S/l.)'1J. _HJ2. = -.JH.SI. Suy ra JH = SO. 2. HI. =. aJ3 =. suy ra EF a 3a. + SAF.FD = 2·(a+2)·4. = -3a 4. l..S1. =. 0.5 0.5. 2. 4. 1. 2. SI = aJ3. ~S02 +01 1. S/l.)lJ. 1.0. 1 -.BC=. a -. 2. 2. 0.5. 2. = 9a = 9(\12013)2 ;;:;]1.7940 16 16. 0.5. 5.

<span class='text_page_counter'>(6)</span> Bai 9: B6 ban A tang ban mot may tinh tri gia 5.000.000 d6ng bang each cho ban tien hang thang thea phirong thirc nhu sau: thang dftu tien ban nhan duoc 100.000 d6ng, cac thang ill thang thir hai tro di m6i thang nhan duoc 8<3tien han thang tnroc 20.000 d6ng. NSu ban muon co ngay may tinh d~ h9C bang phuong thirc tra gop hang thang bang s<3 tiSn b<3 cho voi 1ffi sudt 0,7%-1 thang, thi sau bao nhieu thang ban tra h~t n9'?(ViSt quy trinh b~m him). CACHGIAI. KETQUA. Thang thu nhat sau khi gop con no: A = 5.000.000 - 100.000 = 4.900.000(d6ng) Gan: A = 4.900.000 ; B = 100.000 Thi thang sau gop: B = B + 20.000(gia tri trong o nho B cong them 20.000), con no : A = A x 1.007 - B. DIEM 0.5 0.5 0.5. 2.0. 0.5 20 thang S6 tiSn tra thang cu6i cung 1a 85392 dong. 1.0. Bai 10 : Cho nr giac ABCD nQl tiep duong tron tarn 0 ban kinh R= 4,20cm, AB = 7,69cm , BC = 6,96cm , CD = 3,85cm . Tinh ti l~ phan tram dien tich giira phan to mau va phan khong to mau, (Xem hinh ve). c. 6.

<span class='text_page_counter'>(7)</span> CACH GIAI AOB-2-. Sin. COB-2 . -. SIn. CoD --. .. -I. .. -I. KETQUA. AoB. AB 2R. -. CB 2R. CoB. 2 SIn . -1 -CD. 2R. I. ="2R. 2. 1 32°3i49". R:. 111°54'16". -. DoA = 360° - Doc' - CoB - AoB SABeD. R:. -----. -----.. (sinAOB+sinBOC. ...---.. => Dien tich phdn to mau la S. T'1 l~ s; y. . -Shin. .--. +sinCOD+sin DOA). Im= lr.R2. - 25,8374 29,5803. -SABCIJ. R:. R:. CoD. R:. 54°33'33". i50A. R:. 60°59'22". 29,5803 em'. 25,8374 SABeD. . 100~ 0. S S. /mR:. 1m. s.;. R:. R:. 29,5803. 25,8374. DIEM. 0.5. 0.5 0.5 0.5. 1.0 1.0 1.0. 87 ,3466%. .. ---------------------------H1tll-----------------------------. 7.

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