Tinh dien tich tam gide OAB theo m.. Ba duong tron nay tiep xuc ngodi doi mot ya ding tiep fie voi throng thang xy ttro:ng frng tai cac diem M, N, P ,nhu hinh ye.. Duemg thang qua B so
Trang 1Id THI TUYEN SINH LOP 10 NAM HOC 2014 — 2015
Mon thi: TOAN (CHUYEN) Ngay thi: 13-06-2014
Thei gian: 150 phut (khong ke theri gian phat de)
TRUING THPT NANG KHIELT
DAI HOC TAN TAO
BE CHINH THfiC
Can 1: (1,5 diem) Cho Neu thirc:
p ( 1 + AFc AFc
+ 3) x + 3A5
a) Rilt gon bieu thirc P
b) Tim x de P = 7
Cau 2: (2,0 diem) Cho Parabol (P): y = x2 ya duong thang d: y = mx + 2
a) Chang minh vat moi gta tri cua m, duong thang d luon di qua mot diem M co
dinh
b) Chung minh duong thang d luon cat Parabol (P) tai hai diem A, B phan biet Tinh dien tich tam gide OAB theo m
Cua 3: (1,0 diem) Giai phtrung trinh: x2 — 8x + 4 + 2-V2x + 4 = 0
Cau 4: (2,5 diem) Cho ba duong tam: (A, R); (B ,r); (C, x) Ba duong tron nay tiep
xuc ngodi doi mot ya ding tiep )(fie voi throng thang xy ttro:ng frng tai cac diem
M, N, P ,nhu hinh ye Duemg thang qua B song song Wei xy cat AM tai D GO E la trung diem ciia MN
a) Chimg minh: MN = 2V7r
b) Chirng minh: = +
c) Chimg minh to giac ADEB not tiep
d) Tinh dien tich tam gide ABC, biet
R = 9 yar=4
N
Cau 5: (1,0 diem) Tim cac gta tri dia a a phtrung trinh sau co nghiem nguyen:
x2 — (a2 + 2)x + a2 + 3 = 0
Cau 6: (1,0 diem) Cho x, y, z là cac s6 thirc duong thee: x + y + z = 1 Chimg minh: a) x + yz = (x + y)(x + z)
b) xy , -t- yz + _ zx < 3 —
Cau 7: (1,0 diem) Cho to giac ABCD va mot diem 0 6 ben trong to giac Goi S la dien tich to giac ABCD Chung minh rang : 0A2 + OB2 + 0C 2 + OD 2 2S