SO GIA.0 DUC VA DAO TAO BiNii PHu·o·c KY THI C!"f QN HQC SINH GIOI CAP TiNH · LOP NAM HQC 2020-2021 Mon: Toan BECHINH TH(J'C Thoi gian : 150 phut (kh6ng Ngay thi: 14/03/2021 (DJ thi c6 OJ trang) kJ thoi gian giao aJ) Can (5,0 di~m) Cho bi Su tht'.rc A = ( x + + x✓ x- I ✓x x +I+ ✓x +- l- J ✓-; - 1- ·✓ x 2✓ x • b Chfrng minh A < I a R~t g911 A I ~ 0110 (2x + ✓4x - +I )(3y + ,j9y +I)= 1.Tinh gia tr! biSu thuc: 8x + 27 y + 2021 - Cau (5,0 di~m) I I Giai phuang trinh: ✓2x +5x+12 + ✓2x +3x+2 =x+5 \ {3x + y2) ( +4.xy =8 Giai M phuong trinh sau: ( I x+y Cho Parabol ( P): y =x2 X +xy+2 ) =8 mdS (d) dt (P) t?i hai di Sm phan bi~t A, B thoa man V =mx + (m la tham s6 thvc) Tim AB = ✓ 10 va duong th~ng ( d): y (;~ 3~ (5,0 di~m) Cho nua duong tron tam duang kinh AB G9i C la m9t diSm nfun tren 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 (a'./ Chung minh ciJ = CBii ~ Chung minh CJH d6ng d?ng v&i HIB c G9i E la giao di€m cua HD va BL Chung minh HE.HD = HC d Xac dinh vi tri cua di€m C tren nua duang tron (0) d€ AH+ CH d?t gia tri 16n nhk Can (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 (3,0 di~m) s6 dtrang Cho cac X, y, z thoa man xy + yz + zx = Tim gia tri nho nhfit cua biSu tht'.rc: S ~ 4x - yz + + L!y - zx + +- 4z - > -y + lQ , - Tim tfrt cit cac nghi ~m nguyen x, y cUa :'hucmg trinh: x' = y ' ( x + y + HET • Thi sinh khong thwc sir d~mg tai li¢u Giam thf khong giai thich gi them -\ 'J' "- A 1- -\1(~ 1< ~o