[r]
(1)S6'Giao due va Dao tao Tp.HCM
DE KIEM TRA L~I NA.M HQC 2011 - 2012 MON ToAN LOP 10
Thoi gian: 90 phut
CaD 1: (3 diem)
Giai cac b~t plurong trinh sau:
a) x -4x+3 <1 b) 3x2 -15x-21 >a
3-2x c) .J2x+1 <x-1
CaD2: (2 diem)
Cho b~t phirong trinh: (m-1)x2 +2x -1 ~a (mIatham s6) a) Giai b~t phirong trinh tren voi m= -1
b) Dinh md~ b~t phirong trinh nghiern dung voi moi XER
CaD3: (3 diem)
Trong h~ true toa dQOxy,cho dirong tron (C): (x_1)2 +(y - 2)2 =8 a) Xac dinh tam I va ban kinh R cua (C )
b) Viet phirong trinh dirong thang (A) qua I, song song voi dirong thang d:x - y - 1=a c) Viet phtrong trinh tiep tuyen cua (C ) vuong goc voi (~)
CaD4: (2 diem)
) Ch T' h , , b·~ hu A 2sina
a tan a= . In gia tn cua leu t ire : =
+ sina - cos a cos2 a
1
b) Cho a-b =; Tinh gia tri bieu thirc: B=(cosa-2cosb)2 +(sina-2sinb)2.
(2)DAp AN DE KIEM TRA L~I LOP 10 Call 1:
1)
2
) x -4x+3 x -2x
a <¢::> <
3-2x 3-2x
¢::>x(x - 2) <0 (0,2Sd)
3-2x
¢::>x E(0;%)U(2;-too) (O,Sd)
b) 3x2 -ISx - 21>0¢::>3x2 >ISx - 21 (O,2Sd)
¢::>(3x2 - Sx+2)(3x2 +5x - 2) >0 (O,2Sd)
¢::>x E(-OO;-2)U(±;~)U(1;-too) (O,Sd)
(O,2Sd)
lx;::::1
1 x;::::1 x>1
c) .J2x+l <x-I¢::> x;:::: ¢::>{ ¢::>{ - 0¢::>x>4 (O,2Sdx4)
2 x - 4x >0 x>4 vx < 2x+l «x-l)2
Call 2: Xet b~t phuong trinh: (m -1)x2 +2x-1::; (*) a) m= -1: (*) ¢::>_2x2 +2x-1::; 0¢::>'IIxER (O,Sd)
b) NSu m= thi (*)¢::>x::;! => m= khong thoa man (O,Sd)
2
• N~u m"*1 thi (*) dung voi 'IIxE R ¢::>{m,-1 < (O,Sd) ¢::>m ~ °(O,Sd)
Ll =1+m-l::;O
Call : Trong h~ true toa d9 Oxy,eho dirong trim (C): (x_1)2 +(y - 2)2 =8 a) Tam 1(1; 2) (O,Sd), ban kinh R = 2Ji (O,Sd)
b) ViSt phirong trinh dirong thang !lqua I, song song voi dirong thang d:x - y - 1= °
• !l//d nen phuong trinh !lco dang x - y+ C =0 (C"* -1) (O,2Sd)
• !ldi qua I nen co 1- + C =0¢::>C =1 (O,Sd) => PT zl :x - y +1= (O,2Sd) c) ViSt phirong trinh tiSp tuyen cua (C ) vuong goc voi !l
.TiSp tuyen L\vuong goc voi !lnen PTTT co dang x+y+D=0 (O,2Sd) va d(l,L\) =R¢::>11;2+ DI=J8(O,2Sd)
\'12 + 12 ¢::>(D + 3)2 =16¢::>[D =-7 (O,Sd)
D=l
V~y PT cac tiSp tuyen dn tim: x+y+l =0, x+ y-7 =O
Call 4:
) Ch T' h , , b· ;: h'A sina
a tan a = In gia tn eua leu t irc : = +
(3)2sina 2tana
A= + = + tan a+ (O,75d) = 16 (O,25d)
sina-2cosa cos2a tana-2
b) Cho a=b =; Tinh gia tri bi~u thirc: B =(cosa-2cosb)2 +(sina-2sinb)2
B =(cosa - 2cosb)2 + (sina - 2sinb)2 =5-4(cosacosb +sinasin b)(O,5d)
Tr