I,tsND HUYEN THANH TRi
PHONG GIAo DUC vA DAo rAo ot, xrnu rRA Hec srmr NAxc xrufu
xArvrnec 2022-2023
M6n: To6n 8
Thdi gian: 120 phit
Ngdy ki6m tra:27 thing3 ndn2023
Bei f (3 di6m) Phin tich ciic tla thric sau thdnh nhan tri
a) (x2 + 1)2 + x2 -1
b) x4 + 2023x2 + 2022x + 2023
Bni 2 (4 ili6m)
^., cho xz +9v2-4xv=2xv-lx-3l.Tinh: E = - x'-25 , =!-2
b) Cho a, b, c li cric s6 ttrgc kh6c 0 thda m6n didu kiQn:
1*1*1=, rrl; 1+*+1=z e).
abc"'a'b'c'
Chung minh ring; a + b + c - abc
Bni 3 (s tri6m)
a) Giii phuong trinh: .r 3 -2x2 - 3.r + 10 = 0
b) Tim c6c sii nguyOn duong n sao cho M: na - 4n + 8 ld s6 chinh phuong.
BAi a (6 di6m)
Cho hinh thang ABCD, ttriy lon AB > 2CD. Qua dinh D k6 duong thnng
song song voi c4nh BC, c6t dudmg ch6o AC t4i M vd cit c4nh <16y AB t4i K. Qua
dinh C ke tfuong thlng song song vdi AD, cit duong ch6o BD t4i I vd cit caoh
AB t+i F.
a) Tim <ti6u kiQn cta hinh thang ABCD dd tt gi6c ADCF ld hinh thoi.
b) Chtmg minh MI song song vdi AB.
c) Qua F kd dudmg thing song song vdi AC, cit c4nh bdn BC tai P. Chung
minh ba tli6m M, I, P thdng hang.
d) Chrmg minh rang: DC2 = AB.luII .
Bni s (2 di6m)
Trong hinh vu6ng c6 canh b6ng I cho 33 di6m b6t ki. Chtmg minh rdng
trong c6c <ti6m tt6 cho bao gid ciing tim dugc ba di€m tao thanh mQt tarn gi6c c6
diQn tich kh6ng vuqt qu6 j.
HCt