HDC MTCT cap tinh nam hoc 2012 2013 mon Toan GDTX

vien lam cdclt khdc hoac n6i each sit dung true tiep tren may tinh klt qud dung vdn cho dilm I/i da ..[r]

mrosc DAN CHAM

mt CHiNH THU'C

KY TID CHQN HQC VIEN GI(~)IcAl>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 eM )

Ngay thi : Ngay l? thang 01 nam 2013

Chu y: Huang dan cham g6m co 03 trang

so GIAoDVC vAnAoT~o

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Quyuac: Khi tinh gdn clung chi /dy kit qua vai 4 chit s6 thdp phdn, rieng s6 do goc thi /dy

tlin s6 nguyen gidy.

Bai 1 : (5 diem ) Tinh g~n dung nghiem (dQ, phut, giay) cua phirong trinh 2sin2x +Ssin'x = 1

Chuyen phirong trinh da eho thanh phirong trinh bac Xl ~ 11042' 3" +k 1800 2.5 nhat d6i voi sin2x va eos2x X2 ~ 129038' 21" +k1800 2.5 Giai phirong trinh maio

Bai 2 : ( 5 tliim) Tinh gk dung nghiem cua h~ phuong trinh

Bat u =3x ,v = 2Y thay van duoc h~ phuong trinh X ~ 0,5635 2.5

Bai 3 : ( 5 tliim)

Tinh g~n dung gia tri IOn nhdt va gia trinho cua ham 86: y= I(x) =3x-4+J5-2x 2

Tim t~p xac dinh cua ham 86

Tinh dao ham va tinh nghiem cua dao ham max I(x) ~ 1,2440 2.5 Tinh gia tri cua ham s6 tai hai d~u rmit cua t~p min I(x) ~ - 8,7434 2.5 xac dinh va tai nghiem cua dao ham

So sanh cac gia tri vira tinh diroc rbi k~t luan

Bai 4: (5didm) Tinh gan dung gia tri cua a va b n~u duong thang y = ax+b di qua diem

M(4; 1)va la tiep tuyen cua elip - +- =1.

Duong thang y =ax+b di qua di~m M nen b=1- 4a {a1 ~ 1,4~04 2.5 Duong thang ax - y + 1- 4a =0 la ti~p tuyen cua elip b, ~-4, 7616

- +- = 1 1va ell

9a 2 +4(-1)2 =(1-4ai b 2 ~ 2,1902 2.5 Tir do, ta tlnh duoc a va sau do tinh duqe b.

Bai 5 (5diim )

Cho dirong tron x2+ l +ax +by+e di qua 3 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 ?

Cach giai

Thay toa dO cac diem da:vao phtrong trinh duong tron: a ~ - 45,1425

x2 +y2+ax +by +e =0 ta duoc 3 phirong trinh b~e b ~ 13,8267

nhftt 3 An giai h~ phuong trinh ta duoc cac h~ s6 a,b,c c ~ 76,6226 2.5

( r ( )'

tam 1=(-2;-2) va ban kmh R=~ -2 + -"2 -c 1=( 22,5713; - 6,9134)

Bai 6 : ( 5diim) Tinh a, b, c n~u dbthi ham s3 y=x3 +ax2+bx +c di qua ba di~m

A = (.J5;l);B =( /6;2);C =(7;.J3)

Thay toa do cua ba di~m A, B, C vao phirong trinh cua a = - 12,6815 2.5 ham s3, ta duoc h~ 3 phuong trinh b~c nhftt cua a, b, e b~ 47,6281 2.5 Giai h~ phirong trinh do, ta tinh diroc a, b, c e = -53,2726

Bai 7 ( 5 diim) Tinh gan dung th~ tich kh3i chop S.ABCD n~u day ABCD la hlnh blnh h' han , canhSA vuong goc VO'l, d'ay, AB =7dm, AC =9dm, SD = lId m, goe' ABC =80°

Tinh BC theo AB, AC va goc ABC

Tinh SA theo SD va AD =Be

Tinh SABeDtheo AB, BC va goc ABC V = 136,4968 drrr' 5.0 Tinh V theo SABCDva SA

Bili 8 ( 5 diim) Tim nghiem gAndung cua phuong trinh sau : 2" +3"+5"-=11 X

Ta c6 f(O» 0 va f(1) < 0 nen c6 1nghiem x 0 E ( 0; 1 )

Bili 9 (5 ilidm)

{UO =1;u 1 =5 Cho day {un}diroc xac dinh boi cong thirc - 3 _ 7

Tfnh gia tri cua U20va 820 (Tang cua 20 86hang dAucua day un)

voi VxeN

Gan D=1 ( bien dem ); A = 1 ; B = 1 (sohang ) ; C= 6

D= D+l: A=3B-7A: C= C+A: D = D+l: B =3A-7B:

An ===lien ti€p den khi D=20 ta co Uzo ;820 8zo =402.550.666

Bili 10 (5 ilidm)

Cho ham s6 f (x) = 32 sin 2x +3 cos 2x + 2x Tinh [(1[/7) va 1'(Jr/7)

86i don vi sang Ra dian gan x =1t17

Thuc hien phep toan ghi tren man hinh bi~u thirc tren 1(1[/7) = 31.6479 2.5

Luu y :Hoc vien lam cdclt khdc hoac n6i each sit dung true tiep tren may tinh klt qud

- II~T