V id song song vdi canh BC nc nd nhan B C= (1; 3) lam vcctd
Diem Irung binh cong ciia xa ihii la
1. (0.75 diem) Tim k de hC' bat phifofng trinh sau co n^hi^m...
II (1,5 (1,5 diem) 2 x - 5 > - 4 x + 31 (1) Xct he: < . [x- - ( k + l)x + k < ( ) (2)
Ta CO (!)<=> X > 6. Vay lap hdp nghicm ciia (1) la S = [6; + oo).
PhiMng irinh x^ - ( k + l)x + k = 0co hai nghicm la 1 vii k.
0,25
II
(1,5 diem) diem)
. k = 1: (2) irc) lhanh x^ - 2x + 1 < 0 <=> (x - 1)^ < 0 <=> x = 1. Dc lháy trong Iri/iing help nay he v6 nghicm. Dc lháy trong Iri/iing help nay he v6 nghicm.
• k < 1:(2) CO lap nghicm la doan |k ; 1). Khi do Irong trifdng h(tp nay he v6 nghicm. h(tp nay he v6 nghicm.
0,25
II
(1,5 diem) diem)
• k > 1: (2) CO lap nghicm la doan 11 ; k]. Khi do he co nghicm khi k> 6. V a y he bál phifdng Irinh da cho co nghicm khi khi k> 6. V a y he bál phifdng Irinh da cho co nghicm khi
k >6.
0,25
II
(1,5 diem) diem)
2. (0,75 diem) Tim ni de bát phifc/ng trinh sau v6 nghicm
II (1,5 (1,5 diem) Dal l ' ( x ) - ( m - 3 ) x - -(2m + l)x + m + 2 r(x) > 0 vo nghicm khi f(x) < 0, Vx e K. 0,25 II (1,5 diem)
• m 3 : Khi do < 0 <=> x > (khong ihoa man). 0,25
II (1,5 (1,5 diem) . m ^ 3: Khi do r(x) < 0, Vx e 1 o J ""^ ^ ^ [ A < O [ m < 3 [ m < 3 [(2m+ 1)^ - 4 ( m - 3 ) ( m + 2 ) < 0 [8m + 2 5 < 0 25 25 <=> m < Viiy l(x) > 0 v6 nghiem khi m <
X 8
0,25
III
(2,0 diem) diem)
1. (1,0 diem) Tim tpa do cua d'inh C, B. III III
(2,0 diem) diem)
Ta lháy Irung diem M ciia ca Ihring chifa canh AC va dUc^ng Ihring chifa canh AC va dUc^ng [ x + J cua M la nghiem cua he <
B
/ *A
nh AC la giao diem ciia dúcJng Irung Irifc cua AC, ncn loa do Irung Irifc cua AC, ncn loa do , - 3 = 0 fx = 0 o \> M((); 3). , + 3 = 0 [y = 3 0,5 III (2,0 diem) A M C 0,5
Do M la Irung diem cua canh AC ncn toa do cua dinh C la
y c - 2 y M - y A = 6 - 2 = 4 hay C( - 1 ; 4).
0,25
Mat khac do G la Irong lam cua lam giac ABC nen x,j = 3X(; - ( x ^ + x^.) = 3 - ( 1 - 1 ) = 3 x,j = 3X(; - ( x ^ + x^.) = 3 - ( 1 - 1 ) = 3
y H = - ^ y ( ; - < y A + y c ) = ' ^ - ( 2 + 4 ) = 3 hay 8(3; 3).
0,25
2. (1,0 diem) Viet phi/ifng trinh tong quat cua dirc/ng thang.
V _ 1 V - ' ' AB: = ^ — < : ^ x - 2 y + 3 = 0. AB: = ^ — < : ^ x - 2 y + 3 = 0. 3 - 1 3 - 2 0,5 X - 3 V - 3 BC: ^ - c ^ x + 4 y - 1 5 = (). - 1 - 3 4 - 3 0,5 IV (1,0 diím)
1. (0,5 diem) Tinh diem trung hinh cua xa thụ
Diem Irung binh cong ciia xa ihii la
X = ^ ( 4 . 6 + 3.7 + 8.8 + 9.9 + 6.10) * 8,3 (diem). 0,5
2. (0,5 diem) Tinh phifdng sai va do lech chuan.
2. (0,5 diem) Tinh phifdng sai va do lech chuan.
1. (1,0 diem) Tinh dp dai MN.
x2 y2
Elip (E) CO dang — + ^ = 1 (a > b > 0) a b" a b"
Trong do a- =5 [a = N/5 . / 2 .2 ,
va c = Va - b-" = 1. b-- =4 b = 2 b-- =4 b = 2
Suy ra (E)c6 lieu diem F , ( - l ; 0), F2(l; 0)
Toa do giao diem M , N cua d va (E) la nghicm cua he:
^ 4 . ^ = 1 5 4 5 4 X = I x = l y ^ = 4 ^6 0 5 x = l y = ±- 0,25 0,25 0,25 i i l l