(3,0
diem) Taco ^O^'^-^^^^'^ho
x 2 _ 6 x + 8 ( x - 2 ) ( x - 4 ) 0,25
<=> • x - 4
^ x/2 0,25
<=>xe|-2; 4)\{2}.
Vay tap nghiem cua BPT da cho la S = [-2; 4 ) . 0,5
2. (1,0 diem) Giai bfít phif(/ng trinh...
Dat I = J — > 0. Khi do BPT da cho trd thanh
2t - 3 > 0 <=> I < - i (loai) t>3 t>3 0,5 ^\ 1 X X X 0,25 < = > - - < x <0. 8 r 1 ^
Vay tap nghiem ciia BPT da cho la S= - - ; 0 • , .
[ 8 J - ,
0,25
3. (1,0 diem) Giai bát phtf(/ng trinh...
f2x + 5 > 7 - 4 x (1) Xet I . .... , Xet I . .... , 1 X < 2 X - 4 + X - 3 (2) . i Taco (l)<=>(2x + 5 r > ( 7 - 4 x r » (2x + 5 + 7 - 4x )(2x + 5 - 7 + 4 x ) > 0 o ( 1 2 - 2x)(6x - 2) > 0 < = > - < x < 6 . 3 0,25
Xet (2), vdi dieu kien ^ < x < 6 ihi x = x.
. Neu < X < 4 thi X - 4 < 0. Ta c6 (2) <=> x < -2(x - 4) + x - 3
<:> 2x < 5 <=> X < - •
2
Ket hdp dieu kien ta difrtc - < x < - • 3 2 3 2
0,25
. Neu 4 < x < 6 thi X - 4 > 0. Ta c6 (2) 0 x < 2(x - 4) + x - 3
« 2x > 11 <=> X > — •
2
Ket hrtp dieu kien ta dúdc y < x < 6.
0,25
Vay tap nghiem ciia he BPT da cho la ^ ~ 3' 2 Y ' ^ 0,25
II
(1,5 diem) diem)
Tim a de bát phifcJng trinh... II II
(1,5 diem) diem)
Dai r(x) = ( X -+ 4x + 3)(x-+ 4x + 6) Yeu cau bai toiin minflx) > a Yeu cau bai toiin minflx) > a
0,5 II II (1,5 diem) Ta CO r(x) = ((x + 2)- - l j ( ( x + 2r +2)==(x + 2)'*+(x + 2r - 2 . 0,5 II (1,5 diem)
Ta thiíy Rx) > -2 . Suy ra minr(x) = -2 0 x = - 2 . Dodo (*)<=> a < - 2 . Dodo (*)<=> a < - 2 .
lUyen tm J8 th^; sdc HQC kl mOn l o i n Idp 10 M3ng cao - Ph^m Trgng T h j
III
(2,0 diem) diem)
Tim t(.)a dp cac dinh ciia hinh vuong ABCD
Difclng iron (C) c6 lam 1(4; -3) va ban kinh R = 2. Ta CO A e d A( a ; 1 - a), a € K . Ta CO A e d A( a ; 1 - a), a € K .
Thco gia ihic'l 1 e d va hmh vuong ngosii tiep difdng tron nen
I A = V2R = 2N/^.
(a - 4)- + (4 - a)^ = 8 (a - 4)^ = 4 <=> a - 4 = 2 a - 4 = 2 a - 4 = 2
a - 4 = -2 a = 6 a = 2
Vdi a = 2 thi Ă2; - l ) n c n C ( 6 ; - 5 ) . Vdi a = 6 thi Ă6; - 5 ) n c n C ( 2 ; -1). Vdi a = 6 thi Ă6; - 5 ) n c n C ( 2 ; -1).
D
R
Mat ivhac, di/ftng thang BD qua I va vuong goc d c6 phiTcJng
trinh BD: x - y - 7 = 0, do do B(b; b - 7) Taco IB = 2 N ^ « ( b- 4 ) -+ ( b- 4) 2 = 8 c^ ( b- 4) 2 = 4 Taco IB = 2 N ^ « ( b- 4 ) -+ ( b- 4) 2 = 8 c^ ( b- 4) 2 = 4 b - 6 b=:2' b - 4 = 2o Vdi b = 2 thi B(2; - 5 ) n e n D ( 6 ; -1). Vdi b = 6 thi B(6; - l ) n c n D ( 2 ; - 5 ) .