Cho nua duong tron tam 0 duang kinh AB.. Cho tam giac ABC vuong can t?i A, trung tuyJn AD.. Giam thf khong giai thich gi them.
Trang 1SO GIA.0 DUC VA DAO TAO
BiNii PHu·o ·c ·
B E CHINH TH(J'C
(DJ thi c6 OJ trang)
Can 1 (5,0 di~m)
KY THI C!"f QN HQC SINH GIOI CAP TiNH
LOP 9 NAM HQC 2020 -2 021
Mon: Toan
Thoi gian: 150 p ut (kh6n g kJ thoi gian g iao aJ)
Ngay thi: 14/03/2021
1 Cho bi Su tht'.rc A = ( x + 2 + ✓x +- l J ✓ -; -1
1 x✓x - I x +I+ ✓x 1- ·✓x • 2✓x
a R~t g911 A
I
b Chfrng minh A < I
3
~ 01 10 ( 2x + ✓4x2 + I )(3y + ,j9y2
+I)= 1.Tinh gia tr! biSu thuc: 8x3 + 27 y3 + 2021
-
-Cau 2 (5,0 di~m)
I
I Giai phuang trinh: ✓ 2x2
+5x+12 + ✓ 2x2 +3x+2 =x+5
\
+ y2 +4.xy =8
2 Giai M phuong trinh sau: ( ) ( 2 )
x+y X +xy+2 =8
3 Cho Parabol ( P): y = x 2 va duong th~ng ( d): y = mx + 1 (m la tham s6 thvc) Tim
m dS ( d) dt (P) t?i hai di Sm phan bi~t A, B thoa man AB = ✓10
(;~ 3~ (5,0 di~m) Cho nua duong tron tam 0 duang kinh AB G9i C la m9t diSm nfun tren
V m'ra duang tron (0) (C khac A, C khac B) G9i H la hinh chiJu vuong g6c cua C tren AB, D
la diSm d6i xung v&i A qua C, I la trung diSm cua CH, J la trung diSm cua DH
~ Chung minh 6 CJH d6ng d?ng v&i 6 HIB
c G9i E la giao di€m cua HD va BL Chung minh HE.HD = HC2
d Xac dinh vi tri cua di€m C tren nua duang tron (0) d€ AH+ CH d?t gia tri 16n nhk
Can 4 (2,0 di~m) Cho tam giac ABC vuong can t?i A, trung tuyJn AD Di~m M di d9ng
tren do:;in AD G9i N va P 1§.n luqt la hinh chiJu cua diSm M tren AB va AC Ve NH l PD
t:;ii H Xac dinh vi tri cua diSm M dS 6.AHB c6 di~n tich 16n nhfit
Cau 5 (3,0 di~m)
1 Cho cac s6 dtrang X, y, z thoa man xy + yz + zx = 1
Tim gia tri nho nhfit cua biSu tht'.rc: S
- 4x - yz + 2 Ly - zx + 2 4z - > -y + 2
~ -Tim tfrt cit cac n hi~m n uyen x , y cUa :'hucmg trinh: x' = y ' ( x + y 4 + l Q ,
HET
• Thi sinh khon g thwc s ir d ~mg t a i li¢ u Giam thf khong giai thich gi them -\ 'J' ~ o 1 <
"-A 1 \ 1 ( ~