a GPi o ld tdm cria tluong trdn ngopi ti6p tam giitc ABC.. nF cit eo vit BCtan tuqt tqi M vdl/' chung minh dulng trdn ngopi titip tam g iirc AMNdi qua mQt tti6m co ointr.. b c6c ti6p tuy
Trang 1B0 ciAo DUC vA DAo r.lo
tAhr ilHrhlH
BAi 1 6 aiefi GiAi h9 phuong rrinh
I a*-y+zz =3
I *' - ,, -22 = -l (x,y, z e IR).
I o*, - 3y, - y _2zz =o Bni 2 (5 diad a) cho ddy s6 (a,,) xircdinh boi ao =rn(2n2+r)-rn(n2 +r+r), v6i
n =1,2, Chung minh chi c6 hiiu hpn s5 n sao cho {a, } < 1.
b) cho dfiy sti (b,) xirc dinh b,i b, =rn(zn'+r)+rn(nz+n +l), v6i n=r,2,,.chr?ng minh tdn tpi v6 h4n sd , sao cho {6,,}.+ a'
2016
Trong dd {x} ld ky higu phAn 16 cria s,5 rhuc ;r : {x} = *_[r].
Bni 3 $ diad cho tam gi6c ABC c6 B, ccti dlnh, A thayddi sao cho tam gi6c ABC
nhgn' Gqi D ld trung di6m cria BC vir E, F tuong ung ri hinh chi6u vu6ng g6c c1,a D lln AB, AC
a) GPi o ld tdm cria tluong trdn ngopi ti6p tam giitc ABC nF cit eo vit BCtan tuqt
tqi M vdl/' chung minh dulng trdn ngopi titip tam g iirc AMNdi qua mQt tti6m co ointr.
b) c6c ti6p tuy6n cta dulng trdn ngopi ti6p tam giitc AEF t4i E, F citnhau tai r Chring minh ZthuQc m6t dudng thing cd Ointr.
BAi 4 g di1m) Nguoi ta rr6ng hai loai cAy kh6c nhau tr€n mOt mi6ng tl6t hinh chfr nh0t
kfch thudc mxn 6 vu6ng lmoi o tr6ng mQr cdy) MQt c6ch tr6ng Ja, aon gui rit dn
tuqng n6u nhu:
i) Sti.luqng c6y rlugc *6ng cfia hai lopi c6y bing nhau;
ii) Sd lugng ch6nh lQch cria hai lopi c6y trOn m6i rrang kh6ng nh6 hon mQt n&a sri 6 cira
hang d6 vi si5 luqn8 ch€nh lQch cria hai lopi ciy tr6n ,,6i Jot r.no"g *i hon mQr nria sti 6 cria cQt d6.
a) Hay chi ra mQt crich tr6ng c6y Lntugng l$i m = n=2016.
b) chring minh n6u c6 mQt crich trdng cdy 6n tugrlg thi c6 m yit nrl6u li bQi cria 4.
Thf sinh khong ductc su hlng
tdi li€u vd ntdy tinh can tay.
Cdn bo coi thi khong gidi thich gi
thAm.
Ki THT CHqN HQC SINH GIOI QUoC GIA THPT
NAM 2016
M6n : TOAIY
Thoi gian : 180 phrit (khong kA thd.t gian giao di) Ngdy thi thri nh6t : 06t01/2016