UBND riNu rnAr NcUYEN
so crAo DUC vA o.lo rAo
on cnixn rHrrc
THI TUynN srNH vAo Ldp 10 THpr cnuy0x
NAU Hec: 2ot7 - 2ol8
nn6x rHr: roAN Hec
(Dinh cho thi sinh thi viro chuy6n Tin)
Thli gian lim biri: 180 phrrit (khingkA thdi gian giao di)
CAu 1(1,0 di6m). Kh6ng dtng m6y tfnh cAm tay hay rut gsn: A = (rJi. G)G-3J3.
Cfiu 2(1,5 di6m). Giei he phuong trinh sau:
l'Y*45Y=4*z
),J
|.y'* 95y+6=7x2 +5r
Ciu 3(1,5 di6m). Cho phucrng trinh: x'+Z(+Ji-f r)x +57 -24Jr= 0. Gei xr;xr tdhai
nghiQm ph6n biQt cria phuong fiinh. Kh6ng gi6i phuong trinh h6y tfnh gi6 tri cria bi+5u thric:
r =,ffi+.tx*1.
Ciu 4(1,5 tli6m). Tim t6t cb circnghiQm nguy€n (*,y) cria phuong trinh:
2x' -2xY = 5x - Y -19 '
Cfiu 5(1,0 ili6m). Tai mQt hQi ngh! c6 100 dpi bi€u, trong sO OO c6 15 ngudi Ph6p (m6i
ngudi quen it ntrdt ZO tlai bi6u) vd 85 nguli Dric (m6i ngudi quen kh6ng qu6 10 itai biilu).
Bii5t rang nguoi cilng quiSc tich c6 th€ kh6ng quen nhau. Hg du-o. c phdn vdo dn 2l phdng.
Chung t6 rdng c6 mQt phdng ndo d6 khdng chfta mQt cflp ndo quen nhau.
CAu 6(1,0 ili6m). Cho hai tludrng trdn tdm O, vir O, nimngoii nhau. DoAn tharg QO, cfut
dudmg trdn(Q) tpi diem A, cfutduong tron (q) @i B. Dung dudmg trdn tdm O ti6p xfc
ngodi vdi tl6ng thoi ctuong trdn (O,) tqi D vddudrng tron (q) @i C (di6m O kh6ng nim
tr6n do4n OrOr). Chimg minh rdng c6c iti6m A,B,C,D cting nim tr6n mQt dudrng trdn.
CiuT(2,5 ili6m). Cho dudmg trdn tdm O vd ddy cung AB cO einn khdng di qua tdm O clua
dudmg trdn. C,D li hai tli€m di <lQng tr6n cung rcn 7i sao cho AD vir BC lu6n song
song vdi nhau. Gqi M li giao cti6m ctn AC vir BD. Ctrung minh r6ng:
a.Tir gi6c AOMB nQi ti6p dugc trong dudmg trdn.
b. Hai duong thang OM vir BC vudng g6c v6i ntau.
c. Khi C vd D di ilQng, tludmg thdng ili qua M songsong vdi AD lubncti qua mQt tlii5m cti
dinh.
ndt----