quan ddn bidu dien hinh hoc cria sd phfc.
Didu d5 chi dd minh hoa, gay hung thri vi
girip hoc sinh hidu 16 hon vd sd phrlc. Gi6o
viOn kh6ng nOn cho thOm ciic bdi toi{n di s0u vio ring dung cria sd phrlc trong hinh hoc.
Dd kdt thUc bai vidt ndy, ch[ng tOi xin n6u
mot nhdn x6t rdt d5ng ch0 ! trong vi6c thuc
hien chuong trinh vir SGK m6i, ld: c6 khOng
ft gi6ro vien v5n chua'ttl b6 duoc th6i quen gi6ng day theo noi dung cfia SGK CAi cSch Gi6o duc; hon nfra, nhi6u gi6o virOn yeu cdu
ki nang giai bai tdp cao qu5 m0c cdn thi6t,
vudt xa quy Clinh cfra chrlong trinh vir SGK
(c6 vd mrlc d0 kh6 l5n sd luong bai ta12p).
Ph6i chdng d6 c0ng ld mOt trong nhidunguy6n nh6n khidn du lu6n x5 hOi cho ring nguy6n nh6n khidn du lu6n x5 hOi cho ring chuong trinh vi SGK hi6n nay ld "qu6 t6i" ?
.JTORN H9C ^: __^ TORN H9C ^: __^ 50';*u,aE@8r (^Et-+l[ F. ! l.! v Jyl[V Y Jy Et.t: ! v ,lv Til d6 c5 Ndux>y>0thi Ndu0<x<ythi
VAy til (3) suy ra "rr = y. Thay vdo PT (1) ta c6
,ft =r-{ . ninn phuong hai vd duo. c \i xVx
2+! = o * !-4<+ x - 4 (thori man).
x x Jx
Viy hQ dd cho c6 nghiOm (x; y) = (4;4). J
Dd kdt thric bdi vidt xin mdi c6c b4n giii c6c
PT vd HPT sau: L il ^hx'? 1x4j--'E-=h)e -5x1*"{-*z a*a , trang 2) ) F;*-8.#, .F+.*,F,.i sffiu rlg,t<:... qidp DUNG (3) Et.:: ! v 'lv ,F+.*= 2. a) x3 -3x2 -8x+40:8\f 4x+4 ' ul Jxr +rz -r +.'lg+x2 +2 =3 . t. u1 j!:!=3aJr-"2 ' Vx -Vl-x 0.6c 1+"'l f 1xJ:Jz*' +2*+3+17 -x12
4. Gihi c6c hd phuong trinh sau.
,,|ffi* '['t:a[.,r*,. J*1=61 [.,r*,. J*1=61
o, {p * ^trzoot * )(y. Jroo. . y'
) = zoot
\"-* H ry'
rAf"r
$.\}{
6t gi6m ddc xi nghiOp mudn tuydn
chon mOt nhAn viOn mdi trong sd
hing tram ung cr} viOn. Ong ta ph6ng
vdn tirng ngudi m0t. Sau m5i cu6c ph6ng van
6ng ta c6 m6t vh chi m6t trong hai lua chon: 1. NhAn ngudi duoc ph6ng vdn vho llm viOc.
Cu6c ph6ng vdn cham drir, nhfrng ngudi xdp hing sau d6 dd du-o. c ph6ng vdn c6 thd ra vd.
2. Kh6ng nhAn ngudi du-o. c ph6ng vdn. Ngudi
ndy ra vd, khdng tr& lai nfia. Ngudi xdp hing lidn sau d5 tidp tuc duoc ph6ng vdn.
Chri i li 6ng ra kh6ng duoc thay ddi i kidn. C6i kh6 cira 6ng gir{m doc ld 6 ch6: Ndu chap nhdn ngudi dang ph6ng vdn, thi bidt dau se b6 qua
m6t ngudi khi{c sau d6 c6 kh6 ning tdt hon?
Cdn ndu b6 qua ngudi dang ph6ng vdn, thi li0u
nhtng ngudi sau c5 ai bang du-o. c ngudi niy
kh6ng? Chon sdm qur{ c6 thd "hd", chon mu6n
qu6 c6 thd "tuot" ! Dirng lai o dAu li tdi uu?
Nam 1960 Martin Gardner dd dua ra bli to6n nly
ldn ddu tiOn nhu li mdt "trb choi to6n hoc".
Trong bdi toiin cira Gardner dua ra hdi d6, ndu
c6 100 png cri viOn, ngudi ta di chrlng t6 rang
nhd tuydn dung nOn b6 qua 37 trudng hqp ddu tiOn, md chi chon ung c& viOn dat yOu cdu ti
ngudi thrl 38 ffA di. Ngudi ra n5i rang, mOt ciich
tdng qudt, kich cd ctra m6u ddu
ti0n chidm fi le 037 cira tdng sd. Chri f rang I
0,3 7 = I (e ld co so cfia logarit ru nhien).
e
Tat nhien chidn thuAt rr0n thAt bai ndu dd lot
mdt ngudi sr4ng gi6 nhat nam ffong sd 37 ngudi
bi b6 roi. Nhung lim sao duoc, vi day li vdn dti "khA ning cao nhat dd tim ngudi si{ng gir{", chrl
khdng phii "bien phdp toi uu dd tim ngudi s6ng
gii4" trong sd 100 ngudi! C6 rdt nhidu gi6i phdp
d6 duoc dua ra, dac biOt gi6i phr4p trong d6
ngudi ta x6t ddn viOc tdi uu h6a su s6p xdp rrung binh cira fng c[r vidn.
Cdc nhi nghiOn criu Thqy Dien Kimmo
Eriksson vb Pontus Strimling de Vdsteras, cing
nhu Jonas Sjostrand & Stockholm d6 chri 1i ddn
trudng hop c5 nhi6u nhd tuydn chon vi cdc rlng
ctr vi€n c6 nhi6u lua chon c6c 6ng chir. Bang
cdch gi6n tidp, ho trinh biy bli todn du6i dang
h6n nhAn: Mdt s6 l6n nam vd nfr gap nhau tirrrg
c4p. HS chon nhau dd srinh d6i (nam, nt), ngudi
nhy chon ngudi kia dd tiep xric; hop thi thdnh
ddi, kh6ng thi b6 dd chon ngudi khiic. M6i
ngudi chi duoc chon ngudi khr{c I ldn. khdng
duoc chon di rdi chon lai. Gia su m5i ngudi chi
duo. c chon tdi da ld N ngudi. Kdt qui chinh thric du-o. c ciic nhi nghi€n crfu dua ra ld:
Neu N khii 16n, cric thdnh viOn h)nh d6ng khon
ngoan nhdt c6 thd duoc, vd kh6ng phdi hgp vdi
nhau (kh6ng cho nhau bidt f kidn cira mlnh vd ngudi kh6c), thi m6i ngudi co thd hi vong kdt
hdn v6i ngudi kh6c 6 lugt ngudi tiep x:i,c thfi m
vdi m * Jlf . fni du ndu sd ngudi c6 thd tidp xfc ld 50, thi hi vong cao nhdt tim duo. c y trung
nhAn 6 ngudi tidp xric thf 7.
Cdc tdc gii cho rang ndu ciic thdnh viOn c6 hop
tilc vi bhn bac vdi nhau thi con sd Jl/ c6 thd
6;-
rrit xuong thap hon thlnh
^/! V32N. Nhung khi
nang phdi ho.p nhau rdt kh5, vi c6 nhting quydn
loi ri6ng ddi choi
nhau, ai cflng
mudn tim ngudi
ung f nhdt, khdng
mudn ngudi khi{c
"ph5ng" tay tr6n...
Tic gih bli vidtndy cflng khong ndy cflng khong
hidu cdc nhi
nghi0n cfu ldy
G-
ci{c so J,v. ^l:-N
\32
& dAu, nhung
o dau, nhung
cflng thuAt lai dd ,i
vui cing ban doc.
PHAN THANH QUANG
(Tlteo Benoit Rittaud
trong Recherche s6 112005).
Yq,p,d,i 70fr71, W80 ,,,A ?Wfr'| ru,$
itf
"tl,**l,i*a, *-d U arrtj- kfarrr7,i*
xuAr BAr{ TrJ'1961
So'372(6.200s)
Ioa soan: I878, pho Giing Uo, Ha N0i
0I Bien tap:04.5121607 0T - Fax PhAt hanh, Iri sil: 04.5144272, 04,5121606
Email; !apchil0anh0s_lu0ilrB@yah00.c0m.rn
BAN CO VAN I{HOA HOC
GS. TSKH. NGLI'EN CANH TOAN
GS, TSKH. TRAN VAN NHUNG
7S. NGIIYEN VAN VONGGs. DoAN quixu Gs. DoAN quixu
PGS. 7S. TRANVAN }IAO
c*lu rnAcn uufitt xuAr nAx
Chri tich Hoi A6ng QuAn tri kiem
Tdng Gi6m
"d6'c \Xg Gi6o duc
NGO TRAN AI
ehO Tdng Gi6m ddc ki6m
Tdng bi6n tAp NXB Gi6o duc NGLnTN errirneo
ruot o6xc ntix rep
Tdng bian fip : PGS, IS, PHAN DOAN THOAI Plt6 Tdng bian fip: IS. PHAM THI BACH NGQC rs. rneN uiNu cHAu, ?fts. NCUysN aNH DUNG, rs .rnAN NRnr oUNc, rs. Nr;uveN MINH DUc, rs. NcuvpN MINH HA, rs. NcuvBN vrnr sAr, pcs. rs. lB eucjc uAN, ras. eHAM vAN uuNc,
pcs. rs. vU rHaNg NHtfir, GS. TSKH. NeuypN vaN lrAu, ong NGUyBN ru[c MrNH,
rs. rnAN Hw NAM, pcs. ?s. NGLTTEN DANG pri-{r, ?s. TA DLry pHuoN G, Ths. r'rcursN ruf rrucu,
GS. TSKH. DANG HUNG THANC, TNS. VU TIIVT TUUY, PGS.
"S. VU DIJONG THUY,
GS. TSKH. NcO vrpr TRUNG, rns. ud euANG\.rNH.
TRONG SO NAY
Dhnh cho Trung hoc Co s& - For Lower
Secondary Schools
LA Bd Hodrug - Ding bidu thirc ii6n hop vdo
grAi phttong trinh vd he phrrong trinh v6 ti.
Ldi gi6i d6 thi vdo 16p 10 Trtidng THPT chuy6n Phan BOi ChAu, NghO An, ndm
hoc 2007-2008.
Dd thi vdo 16p 10 chuy6n Trudng DHSP
TP. Hd Chi Minh, nam hoc 2OO7 - 2008.
Chudn bi thi vho dai hgc - University
Entrance Preparation
Dd,ng Thanh Hdi - MQt sd phriong ph6p
@ Giii rt6p thdc mdc
@ fieng Anh qua cdc biri toin vi ldi giii -
English through Math Probiems and Solutions
Vu The'KhOl - Unit 9.
@ foan hoc & doi snng - Math and Life
Phan Tharuh Quang - Chon ai, ai chon
bAy gid chon ai.
Bia 2. Todn hoc mu6n mhu - Multifarious
Mathematics
Bia 3. Cdu lac b0 - Math Club
Bia 4. Cudc thi vui Giii tri ngiy hb
(& Dien dirn day hoc to6n - Math Teaching
Forum
Nguydn Huy Eoan - MOt s6'didm cdn luu y khi day - hoc GiAi tidn L2 nAng cao.
@ ,O ra ki niry - Problems in This Issue T1,1372, ..., Tt21372, Lll372, L21372.
GiAi bdi ki trudc * Solutions to Previous
Problenrs.
Giii c6c bdi cria so'e6S.
PV - CuQc vAn d6ng Hoc sinh srl dung 1ai
SGK cu vd tlng SGK cho nhd trtidng cria
86 Gi6o duc vd Ddo tao.
Dang Xuan Son - Ki Lhi hoc srnh_ gi6r
THPT chuy6n khu vr]c Duy6n hdi Bac bo
ldn thrl nh{t, nam hoc 2007-2008. @
6@ @
, tim gi6 tri l6n nhdt vd gi6 tri nh6 nhdt.
s} Thu sric truoc ki thi
- Hrrong dAn si6i Dd sd Z.
-Ddsd+,
PhLrdng phrip gi:ii to6n-Math Problem Solving
Trdn DL?c Thi€n - Tfnh khoins c6ch tii
m6t diem dOn mat phing vd khJAng c6ch girla hai drrOng thang ch6o nhau.
aarrrr--r ---rrrl
,
Ban hi6u
NHU THE ruAOT
d0 thi cia hdm s6 c6 trong c6c
rong Toiin hoc, dtbng thdng lh kh6i
ni6m duoc x6c dinh b&i c6c tiOn dd;
drdng dai s6'biic n trong mat ptring toa
dO Id tap hop c6c didm c6 toa dO ("r ,' y) md
thoi m6n phuong trinh F(;r ; )) = 0, trong d6
F(x ; y) ld da thric bAc n cfia hai bien x, y; n6i
rtAng drrdng bidu di€n gi6 tri m6t hAm so goi ld
ffr'r:T"Iffiffi
nhu thd nhoQB4n-thay trm
cho nghla bonp"eta rllroyg ln ac oitg xI va nsl van rhi ngft, tuc ngfr, ca
xem dttrn7dii darrt
khdc bietihan nhu:
duong, tholds
chi
nghia c6ng
* Ngay 6.3.1946 tai Hh N6i, Hi6p dinh So b6
Phrip - Vi0t duoc ki kdt, cOng nhAn ViOt Nam ld mdt Quoc gia tu do trong Li6n bang DOng Duong thu6c khoi Li0n hiep Phrip. Ta
ki Hicp clinh nhy dd Ady quAn Tu6ng Gi6i
Thach ra khoi mi<in Bic Vi6t Nam.
* Ngay 8.3.1899 tai hai rhdnh pho Chicago vd
New York d Hoa Ki' da nd ra cu6c ddu
tranh cta nt cOng nhdn nginh d6t may dbi tdng luong, gi6m gid lhm.
Ngiry 26-27.8.1910 Dai h6i ldn thrl hai Phu
nfr Qu6c td hop tai COpenhagen, Dan Mach, dd quyet dinh lay ngAy 8.3 ldm ngdy Quoc
te Phu n[.
* Nghy 9.3.1945 NhAt drio chinh Ph6p tai
DOng Duorrg. Ding C6ng si'n DOng Duongra chi thi Nhdt Phdp bdn nhau vd hdnh ra chi thi Nhdt Phdp bdn nhau vd hdnh
d|ng cria chting ta, vach hudng cho c6c td
chric Vi0t Minh chuAn bi kh&i nghla giinh
Chinh quyen.
* NgAy 19.3.1950 khoing 300.000 d6ng bdo
Sdi Gdn bidu tinh chong M!, sau tro thdnh
Ngdy tohn quoc ch6ng My cho den khi
thong nhat dat nudc.
cia. dap: (uANa?A, nEr s6 sv Kil L{ctt sV(Dd iildng ffAn THTT sd 369, thdng 3.2008) (Dd iildng ffAn THTT sd 369, thdng 3.2008)
Nghy 19.3 cflng ld Ngdy truydn thong cua B0 d6i Ddc cdng tU 1967.
* Xgay 26.3.1931 FI6i nghi Ban Chdp hdnh
Trung uong Ding C6ng siLn DOng Duong ra
Nghi quyet thdnh IAp Dodn Thanh ni6nCOng sAn D6ng Duong. Sau ndy Doln dfii COng sAn D6ng Duong. Sau ndy Doln dfii t€n thdnh Dodn Thanh niOn Lao d6ng Vi€t
Nam, rdi thdnh Dodn Thanh ni6n COng sin
H0 Chi Minh. Ngdy 22.3.196i Dai h6iDodn Thanh rri€n Lao ddng Vi6t Nam quydt Dodn Thanh rri€n Lao ddng Vi6t Nam quydt
dinh ldy ngdy 26.3ldm ngdy ki ni6m thdnh
l6p Dodn.
Cdc ban c6 ftn sau dd trd loi tcit, duoc nhan
tdng pi11[1n;
1) Hodng Philc Nguy€n, 10 To6n - Tin, THPT
chuy€n LC Khidt, IP. Quing Ngai, Quring Ngai.
2) L€ Trung \tcirt, l2cl, THPT VAn Tudng,
Quing Ngai.
3) Nguy€nThi Loan,10A1, THPT DO Luong 2, D0 Luong, Ngh€ An.
4) Trdn Ngoc Clrung. 98. THCS Vinh 'fdn. TP.
Vinh, Ngh€ An.
VAN KHANH
mffi
vu,!
Dd !dm gi6 dd th6m cho ni,5t tdm t6n to c6 khung la hlnh thong cdn
ABCEIAB/ / CtS1, ngudito tOn ciung bon thonh siltco dO dai o, b, c, d
vd sE hdn ch0ng toi cdc didm P, A, P', C, Dvsi PA= a, PB= b, PC = c, PD = d
'rir,-" lrinh v6. M6t bon tr6 y6u tcdn nhln thcy c1;, 1d ngh i rn6t
phu'ong 6n ld hdn bdn thonh stit c6 do Ce,t r.lru tr6n thdnh nr6t t0 gidc soo cho bdn dinh cdo no ndm tr6n khung. Bcrn c6 thd vE hinh theo piru,rr',q dn do t<hdng? , ^ \ a
HOANG NGUYEN
Bdi 5 r<o ttvn tRAN?t N?lhu
Hoi Codn xe lha, m1i doan kao 30 toa gQp nhau toi m6t qudng dvong (nhv hinh vd) nd o d6 chi c6
m6tqudng duong ray rG nhanh co thd chva dA mOt dodn xe l1a v1i I 0 toa t...,li. Hai td phu trdch ddu m(ty da hai y,vai nhou cdch gidi quydt r6i sou do cd hoi dodn xe lOo tidp tuc dvsc cu6c honh trinh
ctia minh m6t cdch nguy)n ven. Cdc bon nghr xem hoi td phtl troch dd gioi quydt nhv thd noo?
THANH LOAN
Bdi 6 v an fing vian d,h knh fi ban
Trong m6t cu6c thi Morofhon, cdc vdn d6ng vi6n dong ki theo thO tu bot ddu tu sd I . M6t vdn d6ng vi6n
y6u todn do nhdn ro rdng t6ng cdc sddang ki nha hon sddong kicOo onh to bdng tdng cdc sddong krlon
hon sd dong ki cOo onh to vd ndu gdp dOi sd vdn d6ng vi6n thom du to duo. c rn6t sd chinh phuong.Bidt
rdng sdvdn d6ng vl6n thom gio ndm trong khodng ti I 00 ddn 500. Hdy x6c dinh sdvAn d6ng vi6n thom
gio vd sddOng kicOo ngudivdn d6ng vi6n y6u to6n do.
OATTRI tcAYHE
Cde bil,ildl,rilt thfrJ" ba bdi ddvwi : Oui fung 6Up tl,a:n],
hinl,aunrtgadBi&, sdx-e bunt ctuca? Lftut14 filff #
tAi?* tldp v 6rt, oi, betu ba bd, t d uw tli a i rr?a- ilq! gi
sbt z,frdp 6n, a;a cdL hi drfii frfu od Tda. soqn trljna ngfu
3UA/?D@rllri!
Bdi 4 TruO Tq6Truq