2014 2015 de thi tuyen sinh lop 10 mon toan chuyen

TRUING THPT NANG KHIELT
DAI HOC TAN TAO
BE CHINH THfiC

Id 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)

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.
Cu
a 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

a

Cau 5: (1,0 diem) Tim cac gta tri dia 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)

yz + _ zx
xy ,
-tz+xy x+yz y+zx

< 3—
2

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