Tap chi THT'[ vi ci{c nhi to6n hoc, chuyen viOn thu6c Vu Gi6o duc Trung hoc, Vi€n To6n hoc, Vi0n Chi6n lu-o. c vh Chuong trinh Gi6o duc
sE ra dd vi chdm thi.
Tap chi THTT cap giay chrlng nhAn cho ban doc doat giii.
COng ty cd phdn xuAt nhap khdu Le Minh, nhir phan phoi ddc quydn ciic sAn phdm SHARP hAn
Ngdy 17 th6ng 9 n[m 2004 HOi Todn hoc
Singlpore dd c6ng b,5 kdt qui cuOc thi Olympic.
to6n Singapore ngay 3.6.2004 (xem THTT sr5
326 thr{ng 8 nim 2004). Ngoii hqc sinhSingapore, c6 296 thi sinh tir 25 trudng cira 5 Singapore, c6 296 thi sinh tir 25 trudng cira 5
nudc Malaysia, An D6, Indonexia, Thrii Lan vh
Vi6t Nam tham gia o do tudi Junior, 346 thi
sinh ti 27 trulng c[ra 5 nu6c trcn tham gia 6 do
tudi Senior.
CuOc thi tai Viet Nam do HOi To6n hoc Hd NOi dang
"ui td cfr,i" vi hoc sinh Ha Noi du thi' M6i do ttrl cO tO cilutric nghicm vh 25 cAu phAi
vidt ldi gidLi bang tidng Anh, kh6ng duoc dilng
m6y tfnh.
Didm binh quan c[ra tdt ce 5 nudc li 6,8 ;
didm binh quAir ctra Vi€t Nam lh 11'2 (m5i cAu
dfng tinh ta t aidml & do tudi Junior. GiAi dring
t6 cau tr& lcn duoc Gi&i Vbng, tt 12 cldn 15 c0u
Junior Section (sinh sau 1.1.1990)
ltflr qUA C1IQC Tlll otYMPlC ToAN SINGAPgRE
i,oo4Md iroruc cuA Hoc slNH YIET NAM
Senior Section (sinh sau i.1.1988) I 2 J 4 5 6 7 8 9 10 11 T2 13 t4 15
Hulnh Trung Anh D5 Bd Khoa L€ Trung Hidu
Trdn Thi Minh Phuong Nguy6n I{uydn Anh Vuong Nhat Linh
Nguy0n Thi Hdng Hanh Nguy6n Thi Ngoc Trinh ThiHdng Ptruong Uong Ting LAm
Le 86 Cudng
Holng Thi Phucmg Thio
Pham Qu!'nh Trang
Trdn Dang Thu Hang
Trinh Thi HAi SOm
ilt
VO TTTU THUY
duoc Giii Bac, dr 10 ddn il cAu du-oc GiAi
Ddng vd 9 cdu dring duoc GiAi Khuydn khich (chidm ti l0 tuong fing l,4%o ; 6,4Vc; l0,87o vd 617o).
O do tudi Senior didm binh qudn ctra tdt cb c6,c
nudc th 6,8 ; cira ViOt Nam ld 17,4. GiAi dring til 22 cdu tr& len duoc Giii Ving, 16 dcn 2l ca.l
duoc GiAi Bac, 13 ddn 15 cau duo.c Giii Ddng, 12 cdu dring clu-o. c Giii Khuydn khfch (chidm ti lc
tuong rlng 5,5V0; I7,l7o ;6,57o;5,27o)
K6t qui Vi6t Nam dugc 2 Gi[i V]rng, 3 Giei Bac, 1 Cial Odng 6 do turji Junior tren tdng s6 9 hoc sinh du thi ; 2 Giai Vhng, 6 Giei Bac, 5 GiAi
Ddng, 2 Giei Khuydn khfch 6 do tudi Senior
trcn tring sO 20 hoc sinh du thi.
Cu thd nhu sau : TT Ho t,d tdn Trtdng 56'cdr.t dfinp Gidi I 2 3 4 5 6 Phan Dfc Toin Nguy6n Thuy Hmg
Cao Ngoc Bio Long
Nguy6n Trdn Bi{ch Dho Anh Duong
Ba.ch Thd Phons He NQi - Amsterdam L0 Qu,v DOn GiAng V6 Trmg Vucrng Ngo Si Li6n Hh NOi - Amsterdam 22 t6 t4 t4 13 11 Vdng Vdng B?c 'Bac Bac Ddng Ving Vbng B?c Bac Bac Bac B?c Bac D6ng Ddng Ddng Ddng Ddng Khuydn khich Khuvdn khich He NQi - Amsterdam He Nqi - Amsterdam He NQi - Amsterdam He NQi - Amsterdam Ha NQi - Amsterdam Trmg Vuong THPT Chu Van An Hh NOi - Amsterdam THPT Chu Van An Hh NOi - Amsterdam THPT Chu Van An Ha NQi - Amsterdam He NQi - Amsterdam Nguy6n Trudng T6 HA NOi - Amsterdam 27 24 20 t9 18 18 16 L6 15 15 t4 13 13 t2 l2 25
Gidi ddp :
srdu BlEr vi rHrl po -
cAc coru sd vn MANH ein
He NOi li kinh d6 nudc Vier rU nam 1010 Tohn thlnh phd Hh NOi r6ng 923kmz
C6 5 huyOn C6 9 quAn
C6 233 phudng, xa, rhi rrdn DAn sd thdnh pho 2930600 (ngubi)
Ddn so nOi thenh 1800000 (ngudi) Sdphd cta khu phd cti bio ton : 58 pho Chidu ddi sOng HOng phdn qua Hh NOi lA 30km.
Hd Tay r6ng 466 ha (4,66km2)
Nui cao nhat (Chan Chim, huydn Soc Son)
ld462m
'Iinh li xa nhdt c6ch H)- N6i 20g0km (Ci Mau)
Tinh li gdn nhdt citch Hh Noi tlkm (HhDOng, tinh H) Tay) DOng, tinh H) Tay)
Nam ra ddi trudng dai hoc ddu tien 1075 (euoc Tu Gi6m)
Ilhr1n.xlt; it ban tham gia lim bdi niy. Cd IE do chua chac chrin tram ve cAu tra ldi ncn khong giii.
_B4n Nguydn Chung. hoc iop l2Al, TrIpT Tri€u Son II.
Tridu Son, Thanh [I6a gidi rar 16r cau nay.
C6c ban kh5c c6 ldi gidi ddng : Tren euoc Toan. 1242,- I}IPT ].Jguyen Van Tr6i.-Can Loc.-Hh Tlnh,
Nstydn,Dut-Uy11S_.)U. THCS Le Quf Doir, Hodng DtLl
lang, 12A2, THPT Duong Xd. Gia Lam" Dilong f ii
Binh Mi*,1043, THPT ycn Hda. HA Noi ; D6 phtong Tluiy, llBl, THPT lr Quy Don, Di€n Bien; phum Vdi
Mitth.GY trudng TIIPT Carn Th&y II._Thanh Htia.
VU DO QUAN
QUA KH[I'VA TUC'NG L \I
Ban dang c6 trong tay sd brio 328, trdn 40
nf,m sau ngiy ra sd I Toiin hoc vi Tutii tr6
15.10.1964. Mudi nam nfra Toiin hoc i.i Tu(ii
tr6 trdn 50 tueii.
1. B1n bi€i nhftng gi vd td b6o sd 1 thring l0 y!ry l96a (c5 nhfrng bhi rhu6c chny€n mui gi, hinh thric vi sd trang, ...)
2. Ban hinh dung, ruOng ruong dOn 10.201.1td
Todn hoc vd Tu6i tr6 se nhu thd nlo ? (bao
nhi€u trang, c6 nhftng chuy€n muc nho ? hinh thtic ra sao ? ...)
3 Ban h6y vidt mQr bfc thu ngln (m6t rrang khd
A4) gfri cho ban tr6 doc tap chi TI{ff nam 2014.
So baio 330 thring 12.2A04 se dang giii drip i'i
ten cric ban duo. c qui t5ng.
BINH NAM HA
u lac bO
Kdi qud bdi :
GIAI PHTJONG TRINH LLIcNG GIAC
KHONG KHO !
(THTT s6'324, thtdrug 6 ndm 2004) Nguy0n nh0n chfnh d6n d6n sai ldm li ban d6 rtd kh6ng xdt trudng hop cos{ = 0 trudc khi
2
dat An phu ^ I = te{ "2 vI do d6 d6n ddn lhm mAt 26
mdt ho nghiOm cfia PT dd cho. Ta phii x6t hai
truong ho. p
a) Vdi cos{=0 o x - x + Zkn (k e Z) ta2 2
thay dAy th mOt ho nghiem cria PT.
b) Vdi cos] +0, giii nhu c6ch d6 trinh bdy,
2
cu6i cDng ta k0t luAn PT ban ddu cd hai ho
nghiOmi x=T+Zkn(keZ);
x = Za + Znm (m e Z)(v6i tgo = 1 I
2'
NhAn x6t. Nhidu ban dd chi rtring ch6 thieu s6t trong lbi
Sil cfra b+n hqc sinh'c16, adng tnai'OJa G* *dt *.a.n giai kh6c ggn hon cho bi,i ruin. Narn ban sau c6 hrip rin tot
hotr ci : Nguyin Vdn Ngoc. l0 Li, THPT chuyen Bic Ninh,
Bdc Ninh : Bni Phi Anh, ll Li, THPT He N6i -
Amsterdam, Hn Ngi ;Trinh Qu6b &io,|LA4.TFIPT Hong Quang, TP. Hii Ducrng, H6i Duong : Ngut*6n Dtlrc Totiri.
l0t, TI-IPT Hi Huy T4p, TP Vinh, Ngh0 An ; Hd Xwn
Thiin Haong,l0T, TIIPTLuong ThdVinh. Ddng Nai.
,@ @
x
Gidi ddp :
CUNG RA GA
Bdi to;in h6i hai ban c6 bao nhi€u cdch cting
di, ydu cdu cfra bii toiin ld diilm bdt ddu duoc
tinh ti nhd Ting d khu Tdm. Vi khOng quay lai
nhi Nam n€n c6c doan dudng Khu T6m - Bdn
Thdc, Bdn ThSc - Nhh mdy xay, Bdn Th6c - Ga
N[ng Tinh diiu khOng duoc di. Vi kh6ng lap lai
bdt cr1 doan dudng nio n€n tat ci chi c6 4 cdch hai ban cirng di tI nhe TIng ra ga nhu sau :
. Khu T6m -+ B -+ E + C -+ D -+ Ga
oKhuT6m-+B+E-+F-+Ga
Nhdn xit.
1. Da sd c6c ban kh6ng doc ki ddLr bhi, lai tinh sd
cdch di til Bdn Th6c nOn c6 nhidu c6ch hon (!). C6 ban "tim ra" toi22cAch.
2. C6cban c6 lbi giii dring bhi niy :
Bdc Ninh : Nguydn Manh Nhdi, 10A1, THPI
ThuAn Thinh 1 ; Hii Duong z PhamTh€'Thinh,Doi
5, Tdng Budng, ThSi Thinh, Kinh MOn ; Hh NOi :
Trinh Trong Thanh, l0A, chuyOn Lf, DHKHTN ;
Hi Nam z Nguy€n Kim Chi, s6 2, ng6 8, Quy Luu,
TX Phfi Li ; Nam Dinh : Trdn Ttut Trang, 12C,
THPT Luong Thd Vinh, Vu Bin ; Thanh H6a :
Tnrong M! Hqnh,9C, THCS LC Hfu LAp, HAU L6c ;
Ngh€ An z NgO D{rc Cbng, 12A, THPI Thanh
Clruong I ; Quing NgAi : Ddng Dinlt Nhd:t,12Li,
THPT chuyOn Lc Khidt.
VU THUY
si quvfir rHANG cuOc
Hai ban Mdo vi Ddn cDng tham gia trb choi
to6n hoc sau :
TrOn bAng c5 vidt sdn hai da thfc bidn x ld P(.r) = axs + bxa + cx1 + dl + ex + f vitQ6)-x+9.
M6i ngudi ddn luot minh chi du-o. c thay mOt
trong ciic chfi a,b, c, d, e,f, g b&i rnOt s6 tiy
thich. Khi dd thay hdt cdc cht a, b, c, d, e, f, I bOi c6c so, ndu da thrlc P(x) chia hdt cho da thfc
0(r) thi ngudi di cu6i cirng th6ng cu6c, cbn n6u da thrlc P(x) khOng chia hdt cho da thfc O(x) thi ngudi di cu6i cirng thua cu6c. M6o lh ngudi di
trudc.
Ban hdy girip Mdo mot bi {uydt don giin dd
M6o ch6c ch6n thSng cuoc trong trd choi nly.
NGUYEN DUC TAN.
(TP Hd Chi Minh) o Khu T6m -+ A -+ o Khu T6m -+ A --> Bdn Th6c D-+ Ga C-+ F->Ga
6i tri to6n hoc
G AI DUNG AI SAI ?
Hai ban A, B hoc l6p 7 cirng giii bli todn dudi dav :
Tim cdc s6'x, y th6a mdn ddy t{ s6'sau :
" 5x+3 3y-B 5x+9y-21
95Bx
str dung tinh chdt cira ddy ti s6 bang phAn sd bon tri{i vi phAn sd bcn phii
5x+9y-21-(5x+3)
8x-9
Ban B cfrng str dung tinh chdt cira ddy ti so
bang nhau bidn drji
5x+3 _9y-24 _5x+3+9y-24 _5x+9y-21
9 15 9+15 8x
Ldy tit trir ttr vI mdu trir m6u ctta hai phAn sd ddu bcn phii duoc ddy ti sp
'f =D#=, ,
38
SUyrax= -; VaY=;..)J
Hai ban ddu cho rlng minh llm khong sai vh
tranh luAn mdi chua th6i. Ban c6 th6 lhm trong
tli phin xu girip khong ?
VANKHANH (Ha N2i) Ban A nhau x6t duo. c : 3v-8 5 _ 9y-24 8x-9
tir d6 c6 8x - 9 = 15 nOn x = 3, thay vdo ding
thrlc & dd bei auo. '95E = 3y-8 , suy ra y = 6.
Hmeffm fsoc w& Tx"td,r fre
dklafhe matias amd Vouth
uiw rHLr 1t
s6'328 fi0-20A4)
Ioa sogn : 187B, phdGidng V6, Ha Noi
DT-Fax:A4,5144272
Email : toa n hoctt@ya h oo, co m & Dhnh cho Trung hoc Co s6 - For Lower (B ,A ra ki niy - Probtems in This Issue
T1/328. ..., T72t 328, Ll, L2t 328
@ Clal bni ki trudc - Sotutlons to PreviousProtrlems. Protrlems.
Giai c6c bAi cria sd 324 vit Cu6c thi ki
ni6m 40 ndm THTT.
@ li"fr sir todn hoc - History of Math Nguydn Vd.n ThiAm. - B( mAt cira to6n hoc
Inia dd duoc khdm phd
@ tu chriic cuoc thi giii to6n tr6n m6y
tinh khoa hoc SIIARP qua tap chf To6n - r'.i ,
noc va -t'uor tre
Vir Kim Thiy - Ket qua cu6c thi
Olympic To6n Singapore 2004 md r6ng
cria hoc sinh Vi6t Nam
ffiffi ffi ffi
,,t,,,'.., Qhiu:trgik:,,rtlii jn;eu€t bd.n : *
i.Ctt tieh,,f, iq.ltleA ne.qi6rrl ddc.NXB Giiio duc
Ph6Tdng Ciem C&'tic* fdng bi6n tfp N)G Gi6o duc
VU DL,6NG THIJY
Thrr ki Tda soqn : Yt KIM,THtii.
'. Tr! st1,Ctr€'bdn ..v0ANHl :'NGtryENTHIoANH, ^,
TRONG SO NAY
Secondary Schools
Trd.n Quang Vinh - M6t bdt ding thrlc
c6 nhi6u itng dung
Hridng dAn giAi dd thi tot nghi6p THCS vd x6t tuydn v).o trddng THPT chuy6n
LO Quj'D6n, TP DA Ning ndm 2004
Dd thi tuydn sinh t6p 10 hO THPT
chuy6n trr.idng DHKHTN-DHQG Ha Ngi n[m 2004
Tim hiiu sAu th€m tofn hoc so cdp - Advanced Elementary Mathematics
Trdn TuyAt Than,h - Mgt bdi to6n v6 phAn hoach m6t tAp hop
Thri trl ban mtr6n ndi
Kdt qui cu6c thi giAi To6n vd VAt li
tr6n tap chi ToAn hoc vi. Tudi tr6 nam
hoc 2003-2004
Tinh to6n c6ch nio ? How to Calculate ?
Pham Dang Long - M6t thuAt to6n khai tri6n nhanh Lam thttc NewLon
@ Cau lac b6 - Math Club
Sai ldm 6 dau - Where's the \listake ?
@ GiAi tri toin hoc - Marh Recrearion
fdng bici tdp:,: "'
NGTIYENCANI{.ioAN
'f ntdns ban biin tdp..NGUYEN \/t$f fl{l
Bien rtip. HO QITANG vtNH.
Dai diirtphiaNant TRANCIti HlEu,231 Nguydnvdtrct.e.5.Tp.H6ctiMinh. DT:08.8309049
DON EQC THTT SCirZs fitt2t04)
o Danh siich cdc ban doat giAi CuOc thi Ki ni6m 40 n5m tap chi To6n hoc vi Tudi
tr6 vd ldi giAi tidp cdc bdi inJmlCs vi TFIpT