vien lam cdclt khdc hoac n6i each sit dung true tiep tren may tinh klt qud dung vdn cho dilm I/i da ..[r]
(1)so GIAoDVC vAnAo T ~o LAoCAl CHQN HQC VIEN GI(~)I cAl> TiNH LOP 12 BT THPT NAM HOC 2012 - 2013 Mon : mAl ToAN NHANH TREN MAY TINH CASIO Thoi gian : 150 phut ( khong ki thai gian giao mrosc DAN CHAM mt CHiNH KY TID THU'C eM ) Ngay thi : Ngay l? thang 01 nam 2013 Chu y: Huang dan cham g6m co 03 trang (~ ~'\.I, flJ ;.\~ \ \ • -.t· _ I ., _- Quyuac: Khi tinh gdn clung chi tlin s6 nguyen gidy /dy kit qua vai chit s6 thdp phdn, rieng s6 goc thi Bai : (5 diem ) Tinh g~n dung nghiem (dQ, phut, giay) cua phirong trinh 2sin2x + Ssin'x Cach giai Chuyen phirong trinh da eho phirong trinh bac nhat d6i voi sin2x va eos2x Giai phirong trinh maio Bai : ( tliim) K~t qua Xl ~ X2 ~ 11042' 3" + k 1800 129038' 21" + k1800 /dy = Diem tirng ph~n 2.5 2.5 Tinh gk dung nghiem cua h~ phuong trinh Cach giai Bat u = 3x , v = 2Y thay van duoc h~ phuong trinh rnoi giai h~ tim u,v suy X; y K~t qua 0,5635 Y ~ 1,6521 X~ Diem tung ph~n 2.5 2.5 Bai : ( tliim) Tinh g~n dung gia tri IOn nhdt va gia tri nho cua ham 86: y = I(x) = 3x-4+J5-2x2 Cach giai Tim t~p xac dinh cua ham 86 Tinh dao ham va tinh nghiem cua dao ham Tinh gia tri cua ham s6 tai hai d~u rmit cua t~p xac dinh va tai nghiem cua dao ham So sanh cac gia tri vira tinh diroc rbi k~t luan K~t qua max I(x) ~ 1,2440 I(x) ~ - 8,7434 Diem tirng ph§n 2.5 2.5 (2) Bai 4: (5didm) Tinh gan dung gia tri cua a va b n~u duong thang y , x2 y2 M(4; 1) va la tiep tuyen cua elip - +- K~t qua - phfuI 2.5 1,4~04 b, ~-4, 7616 1~ • +-Y = Diem tirng {a Duong thang y = ax + b di qua di~m M nen b = 1- 4a Duong thang ax - y + 1- 4a = la ti~p tuyen cua elip ax+b di qua diem = Cach giai X = khi1 va ell hi 9a2+4(-1)2 = (1-4ai { a2 b2 ~ ~ -0,2975 2,1902 2.5 Tir do, ta tlnh duoc a va sau tinh duqe b Bai ( 5diim ) Cho dirong tron x2 + + ax + by + e di qua di~m A(1 ;-3 ) ; B(2; 2/3); C(3/4;- 4,8) a) Tinh cac gia tri cua a.b,c ? b) Tim tam va ban kinh cua dtrong tron vira tim duoc ? l , " Cach giai Ket qua Thay toa dO cac diem da:vao phtrong trinh duong tron: x2 + y2 + ax + by + e = ta duoc phirong trinh b~e nhftt An giai h~ phuong trinh ta duoc cac h~ s6 a,b,c ~ ab ", tam 1=(-2;-2) va ban kmh R=~ Bai : ( diim) A ( r ( )' -2a + b -"2 -c Diem tung phftn a ~ - 45,1425 b ~ 13,8267 c ~ 76,6226 2.5 1=( 22,5713; - 6,9134) R ~ 21,9233 2.5 Tinh a, b, c n~u db thi ham s3 y = x3 + ax2 + bx + c di qua ba di~m = (.J5;l);B = ( /6;2);C Cach giai = (7;.J3) K€t qua a = - 12,6815 b~ 47,6281 e = - 53,2726 Thay toa cua ba di~m A, B, C vao phirong trinh cua ham s3, ta duoc h~ phuong trinh b~c nhftt cua a, b, e Giai h~ phirong trinh do, ta tinh diroc a, b, c Diem nrng phfm 2.5 2.5 Bai ( diim) Tinh gan dung th~ tich kh3i chop S.ABCD n~u day ABCD la hlnh blnh h'an h , can hSA vuong goc VO'l, d'ay, AB = 7d m, AC = 9d m, SD = lId m, goe ' ABC = 80° Cach giai Tinh Tinh Tinh Tinh BC theo AB, AC va goc ABC SA theo SD va AD = Be SABeDtheo AB, BC va goc ABC V theo SABCD va SA Ket qua V = 136,4968 drrr' Diem tirng ph~n 5.0 (3) Bili ( diim) Tim nghiem gAn dung cua phuong trinh sau : 2" + 3" + 5"- = 11 X Cach giai Ket qua Ta c6 f(O» va f(1) < nen c6 nghiem x X x X fut may log11(2 + + 5) bieu thirc thay x= Ans = = = +x = 0E ( Diem timg phAn 0; ) X = 0,9157 tinh 1= khai 5.0 Bili (5 ilidm) UO Cho day {un} diroc xac dinh boi cong thirc Tfnh gia tri cua U20 va 820 (Tang cua 20 { = 1;u1 = Un+2 86 hang - - Un+1 _ voi VxeN Un dAu cua day un) , Ket qua Cach giai Gan D=1 ( bien dem ); A = ; B = ( so hang ) ; C= (tang) Ghi tren man hinh D= D+l: A=3B-7A: C= C+A: D = D+l: B = 3A-7B: C=C+B An === lien ti€p den D = 20 ta co Uzo ; 820 Diem tung phAn 2.5 2.5 Uzo = 468.104.176 8zo = 402.550.666 Bili 10 (5 ilidm) Cho ham s6 f (x) = sin x + cos 2x + x Tinh [(1[/7) va 1'(Jr/7) K€t qua Cach giai Diem timg phAn 86i don vi sang Ra dian gan x = 1t 17 Thuc hien phep toan ghi tren man hinh bi~u thirc tren Ta diroc k€t qua Luu 1(1[/7) = 31.6479 f'(7r/7) = - 39.1957 2.5 2.5 y : Hoc vien lam cdclt khdc hoac n6i each sit dung true tiep tren may tinh klt qud dung vdn cho dilm I(/i da II~T (4)