: ding thirc : tinh chdt
NGUYEN PHU HOANG LAN (Tradng DHKHTN, DHQG Hd N|i) eqnivalently ineqttality equali4t fact -... TOAN HQC JU -cludiff@
crAI oAr; cHi co 3 TrEP ruyBN cHUNG
lOi aa"g ffAn TH&TT s6 461, thting 11 ndm 2015) Phdn tich. IrI, =3Jj > R, + R = 6 n€n (C, ) vd (:Cr) 6 ngodi nhau, do d6 chring phdi c6 4 ti6p tuy6n chung. Sai l6m d loi gidi cua b4n YAn h b THz dA!
chgn ngay b = 4 md chua bi6t b c6 khdc 0 hay kh6ng. Sai 16m o lcri gi6i cira bpn Phong ld m6i x6t trudng hqp ti6p tuy6n c6 h6 s6 g6c, md chua x6t truoxg hqp tiaip tuy6n khong co he so g6c (ti6p hryi5n
r.u6ng g6c voi tmc hodnh). C6 r6t nhiAu crlch gi6i quy6t bdi todn ndy. sau d6y ld hai c6ch duoc c6i ti6n tu loi gi6i cria ban Y1n vdbqn Phong.
Ldi gidi drtng 1. (C,) c6 tilm I,(2;0) bdn kinhR, =3; (Cr) tim Ir(-4;3), brin kinh ld & =3. Gqi R, =3; (Cr) tim Ir(-4;3), brin kinh ld & =3. Gqi ti6ptuy6nchungc[ra (C,) vd (q) h A,:m+by+c=O,
a2+b2*0.Khid6
lattr.nl=Rr ^ l4a'+4ac+c2 =9a2 +9b2
l.lt 1.. al = n, - ll-+a + 3h + cl=lza + cl
.nlt, {4o, +4ar+c'2 =9a2 +91} ,_{+to, -4ac*c2 =0
l-4a+3b-rc:2a+c 'lb=?o
Niiu b=0 thi a=0, mduthu6nv6i a2 +b' +0. Dodo b* 0.Chon b=2 thi a=1vd O+4c-41=0 do b* 0.Chon b=2 thi a=1vd O+4c-41=0
ac=-2X3J5. Ta duoc hai ti6p tuy6n chung li
x +2y -2+3J5 = O.
,ur. [Oo'+4ac+c2 =9a2 +98
^!4ar+c2 =5a2 +98
'^*'
lla+3b+c'=-2a-c - llA=Za-2,(^ (^
- Neu b=0 thi )'=' €a=c. C6 thC
l4ac+c'=5a'
chgn a =c = 1, duoc ti6p tuy6n chung x+1 = 0.
-Niiu b +0, c6th6chon b=4 rhi
l4*'*r'' =5a2 +144 @6+c)c+C =5(6+c)2 +144
i <ii
la=6+c la=6+c
l36c+32+=0 lc=-9
[a=6+c [a=-3
Ta duoc ti6p tuy6n chutg 3x - 4y + 9 = 0.
Vpy c6 4 ti6p tuy€n chung gifta (C,) vd (q) h x+ 1 = 0, r +2y -2t3J5 = 0, 3x - 4y+9 = 0.
Lbi gidi drtng 2. (C,) c6 tdm Ir(2;0) b6n kinhRr = 3; (C) rdm Ir(4;3), b6n kinh ld R, = 3. Rr = 3; (C) rdm Ir(4;3), b6n kinh ld R, = 3. - Xdt tii5p tuytin chung A c6 d4ng A : x = xo.
llz-r"lA riep xrc (cL),(c,) A riep xrc (cL),(c,) ={a11''ai=! latr,,al=n *] , :'.- ll-+-"^l ' ll ul -1 Lt
€>x0 =-1 . YQy x +1 = 0 ld m6t ti6p tuy6n chung. - X6t titip tuy6n chung c6 d?ng L:y = 1ps + m . D6n ddy gi6i nhu cira lhong dugc 3 ti6p tuy6n chung
nta. Vfly c6 c6 4 ti6p tuy6n chung grfra (C, ) vd, (1Cr) .
NhQn xdt: Khen nggi cic b4n sau dd ph6t hiQn vd phdn tich
dfng sai Dm: Hir NQi: Nguydn Vdn Dfing, 10414, THPT Nggc T6o, Phirc Thg; Dinh Vdn Anh, l2Al. THPT Ho Xu6n Huong, s6 t Nguy6n Quf Eirc, Q. Thanh Xudn. Bic Ninh: Mal TiAn Thdnh,11A1, TI{PT qut' VO sO t, qrr6 Vo.
Htmg YOn: TriQu Ninh Ngdn, Nguydn Vi€t Drbc, 11A9,
TF{PT Duong Quang Hdm, Vdn Giang; Vil Minh Thdnh, 12
Torin 1, THPT chuydn Hrmg YCn; T6 Minh Hi€u, 12A1,
TIIPT Tnmg Vuong, Vdn Ldm. Ch Mau: Hodng C6ng
Minh. I I Todn I . TH PT chuydn Phan Nggc Hien.
KIHIVI
BAI TOAN'ORO[ RA.C"
Bdi todn. Mil de thi Todn 6 mQt trudng THPT g6m 3
bai; Ifinh hoc, Eai sii vd Tii ho. p. C6 100 em tham gia
lq, thi. KA qud cho thiiy: 80 em gidi dwo'c bdi llinh, TO
em gidi daoc bdi Dqi, 50 em gidi dactc bdi fA na. p, SO
em gidi duoc cd hai bdi llinh vd Dqi, 50 em gidi daoc
cd bdi llinh vd T6 ho. p, 40 em gidi dactc bdi Dqi vd bdi fA no.p. C6 30 em gidi dwrc cd ba bdi. Hdi c6 bao nhiAu em gidi duoc it nhifu m\t bdil
Ldi gidi. Gqi ,4 ld tflp hSp c6c hgc sinh giii dugc bii
Hinh, .B le tap hqp c6c hgc sinh gi6i dugc bdi Dai, C le tap hqp c6c hgc sinh gidi ilugc bdi T6 hqp. Ta c6:
ltw nwcl= lal+lrl+ lcl-la nrl-lr ncl
-lc ael+lanancl
= 80 + 70 + 50- 60 -50 -40+ 30 = 80.
Nhu v6y c6 80 em gi6i rlugc it nh6t m6t bdi thi. Cdc bgn cd nhQn xit gi vA bdi todn tr1n ?
PHAMQUANGHI)NG (GV THPT chuyAn Thdi Binh)
Gq#
tpthi lolilH9(uuIUdl mi
Huftemutits und You* Itlugarine
xuir niN rtl Dot
sd 465 (3.2016)
Tda soan : 1 878, phd Gians Ud, Ha iloi
0T BiGn mP:04.35121607
0I - Fax Phet hanh, Tri s[ : 04.351 21 606 Email: l0anh0Glu0itreuielnam@Umail'c0m
a,q.I't c6 viN xuot ttoc
GS. TSKH.NcursN cANH roAN
GS. T sKH . rnAN vAN ml-rxc
rs. NctrvEllvaNvollccs.ooANQuixn cs.ooANQuixn
PGs. rs. rxAN vaN HAo
Tdns bian @p : TS.rnAN nUu N.q.l\t
ruot odNc atEN rtP
cHlu rnAcn NnruPt xuir nel
Chir tich HOi ddng Thhnh vi€n NXB Girio duc Vi6t Nam
u4.cvaNruryN
Tdng Gi6m d6c NXB Gi6o duc Vi6t Nam
GS. TS. \'IJ VAN HI-NG en6 tdng Gi6m ddc ki6m Tdng bion tdP
NXB Gi6o duc Vi0t Nam
rs. PHANxUANTHANH
ThukiTda soan: ThS.ffd QUa'NC VINH
rS. rn&N oiNs CHAU, rlS. NCUyEN eNn ltnlC, rS. rn-A.N NAM DLNG, rS. NCuvf'N MINH DUC, zs NctrvEN MINH HA'
rs. NcuyEN vrer Ha|';;;.-;;.';-a;d; sAN, rrs. pHAM vAN HUNG, PGs. rs. vo rHANH xsI6r'
Cr. .r"".'*"i r"ai
"o" iia"]o'r ro#o*-"r.i.ic MrNH, rs. rHAM rI{ BACH NGoc, PGs. rs. NctrviN oANc psAr'
pcs. rs. rA DI-IY r"U:,f", i^. iuiiit* i 16 rn+c*r, GS. rsKH. DANG HuNG mANc, PGs zs' pruN ooAN rsoar' rns vU KrM THUY, PGS. rS. Vo DtIoNG THUY, GS. rsra. Nco vrEr rRuNc'
TRONG SO NNY
@ ciai bai ki trtlac
Solutions to Preuious Problems @ oien ddn d4y hgc To6n
Dd,o Tam - C6c phrrong thrlc dinh hu6ng c6
cdn crl nhim tim tdi ldi giAi c6c bdi to6n 6
trudng phd thOng.
Nguy\n C*u Huy - NguY1n Dinh Minh 56'hodn hio vd rlng dung.
Gid,i &ip: Chi c6 ba tiSP tuYdn chung' Pham Quang Hilng - Bdi to6n "rdi r4c"
@ oarrn cho Trung hgc Co sdFor Lower Second,a.ry School For Lower Second,a.ry School
Vfi Htru Chin - Quy trinh stt dUng m6v tinh
Casio v)" Vinacal dd g"iai bai to6n vd ddv sd
@ UriOng dAn giii Dd thi hoc sinh gi6i l6p 9 tinh D6ng Nai, ndm hoc 2073 - 201.4-
Chi Minh, n[m hoc 2075 - 2016.
O chudn bi cho ki' thi rrung hgc phd @ oit5" dirn phuong ph6p giii to6nO ,U thi tuydn sinh vdo l6p 10 chuvOn TP. Hd O ,U thi tuydn sinh vdo l6p 10 chuvOn TP. Hd
th6ng Qudc gia
In Tdi Thdne - Phrrong ph6p d6nh gi6 midn gi6 tri cria bidn sdtrong bdi to6n chirng minh bdt d&ne thfc.
@ ^l'thi chgn hoc sinh gi6i Qudc gia
Bdi dlch s6'a - fi5ng Anh qua c6c bdi to6n
@ urrAng ddn giii - Dd sd6. THPT, nhm 2016'M6n ToAn
@ fnr:, sfic trtt'dc kj' thi ' Dd sd 7.
@ TiSngAnh qua cdc bii to6n - Bd.i s6'6
@ *u" dgc trao ddi
Dfnh Ij'sin dang dai sd.
@ Sai ldm & dau?
@ ,a ra ki niry
Problems in This Issue
T U 465 ..., TI.2l 465, Lll 465, Lzl 465.
fu,TAPCHnTOAN HAcvAmffiffi
1 I M % oa* b?e,nq/ %*i, ilte* d,nq/ U4* da,
sn& ruvfN cHoN rHEo cHuvpx pi
cnuAru B! cHo ri rnr vAo rRUNG Hoc pud rnOmc mOru roAru
j{eo sirch gdm hai tAp tuydn chon theoPchuyen dd nhung bai vidt hay tr6n Tap Pchuyen dd nhung bai vidt hay tr6n Tap
fr rlarr va mot sd oai viSt th6m cria c6cnha giao c6 kinh nghiem nhdm girip c6c ban nha giao c6 kinh nghiem nhdm girip c6c ban HS THCS 6n tap va thi c6 hi6u qu6 vdo l6p 10 cac truong THPT vd THPT chuy6n. 86 sach c0ng ld tai li6u tham kh6o h0u ich cho cac thdy
cd gi6o vd cac bAc phu huynh HS.
31llliiLfii[;;"' 31ll,Xi3;[H]H;-"
G& snfrh ruYiNCHoNrHEo cHuynxoi
^)
CHUAU Bl CHO Ki THt 16r NcHrEp rHpr vA THt vAo DAt Hoc,
CAoDANcMONTOAN rerG
7Oo s6ch co hai tdp gdm 10 cl"rrfong vdi
Pnhidu chuy6n dd du'oe tuydn chon trr
cY.c biri viSt c0a c6c thi'y co gi6o gi6i chuy6nmon vi co klnh nghiAnr gi6ng day trong ci mon vi co klnh nghiAnr gi6ng day trong ci
nUdc, drtOc sfrp xdp theo ilung thrl td trong
e&'u truc dd thi tuy{ln sinh Dai hoc, Cao ding
cfra Bo Gido duc vd Oio tao,
Fhdn cudi rn6i eu6n gi6i thieu mot s6 C6'ttrluy6n vi eo hddng dtn gi6i. luy6n vi eo hddng dtn gi6i.
ruYaH ti.6H T*EF *$ti.;?*H EiE
tiiiliJtl ili;lt! !ii ii!
iL' rliHtlir lil:il :i![ f Ii] I HUit{
jI iiji lllit llt1,,.1lll.;. tlitij iti'ilil r .i ,-ia, I -r-ni x I ivi L/l\ ;t/,t-ri\ rAP MoT Bf;t58.trym&ffiMIfll trt .,,,..,....,.-..,...,.,-,.,..,,,r1 260trang, Kh61l*24cm Gi6 bia: 46.000 ddng ruvix cx*x rxrs.cflulEfl oE fi{iJfin Il xt}0 i{t 1tlt
{fi *&gr*p txtlnr ttre piu mrne
ils }til r,gfl e&l iloe. rff! fiiilis
t a rixl r:=i, ai
rvit/i'.t iLr&+I\
.!:aP HAt
lrA$ire: r* |iB? - e&s u$ir. $*{m
;ri... ,,,,_
240trang, Kh617r2+cm Gi6 bia: 44.000 ddng
GO
Moi chi tidt xin ti6n h6: TAp CHi TOAN HgC vA fUdt fn*
1878, Giing V6, He NOi
NHA)ruffiBANqAore\nffiNAnn
%oa* tue,nq/ W t/rQ* Ua sa:e/,
cAc ri rur roAu Quoc tE DAI\H QHo rndu Hgc
YA TRUI\G HOC CO SO
d?o- au b0 sdch Cdc ki thi Todn Qudc td dann cno nq, sinh THCS vd THPT ditduo, c cdc gido vi6n vd
qScdc bqn hoc sinh hdro hung don nhdn, ch0ng tOi gioithiQu tiSp bQ.sdch tuong tqrddnh cho luatudi
ng nho hon, b0 sdch Cdc kithi Todn Qudc 6 denh cho hgc sinh Tidu hoc vd THCS. DU ki6n bdn tqp tifu c0a b0 sdch ndy nhu sau:
Tap 1. lnternational Kangaroo Mathematics Contest (IKMC) - Ki thi To6n Qudc td Kangaroo. Tap 2. Bebras ComputationalThinking Ckallenge (BCTC) - Thach thuc tu duy tinh todn Bebras.
Tap 3. lnternatianal Mathematicallssessment for Schoots (IMAS) - Ki thi danh giii ndng lqrc Todn hgc Qu6c t6.
fap 4. Math Otympiads for Elementary and Middte Schools(MOEMS) - Ki thi hgc sinh gi6i Todrn Hoa Ki ddnh cho hgc sinh Tidu hqc vii THCS.
ViQc tiSp cin voi cac ki thi qu6c t5, cdc dqng to6n moi la vii hdp d6n s6 c6 t6c dQng tich cr,rc ddn phong trdo hqc tap noi chung. Ben canh do, dAy c0ng sE ld mQt tdi lieu tham khAo h0u fch giup cdc em hqc sinh chudn bi t6t hon trong cdc ki thi hoc sinh gi6i md c6c em co co hQi tham dU. B0 sach duo:c thqc hiQn duoi sq ch0 bi6n c0a PGS.TS. Le Anh Vinh cung cdc tdc giA co nhidu kinh nghiQm trong viQc bdi duOng c0ng nhu dAn doan hgc sinh gi6i c0a Viqt Nam tham du cac ki thi Todn qu6c td vd khu vgtc.
TCp I cuc bo soch gicri thieu Ki thi Toon Qu6c td Kongoroo
(lnternotronol Kcngaroo Mcrthemotics Contest - IKMC)dugc t6 chuc ldn ddu ti6n toi Phop voo ncm 1991. Ddy dugc t6 chuc ldn ddu ti6n toi Phop voo ncm 1991. Ddy
ta li thi Toon hpc co s6 luqng thi sinh thom du 1on
nhdt tr6n the giorr, thu hut tr6n 6 000 000 thi sinh ddn tu
kho&ng 50 qu6c gio m5i ndm. Ki thi Ia moi hoqt dong
phi loa nhuon, nh&m thuc ddy phong trco dcy vcr hec
Tosn theo xu huong h0i nhQp quoc t6, tqo ro mot son
chsi md cho cac em hoc sinh Ti6u hoc vd Trung hoc cos6. Trung tam Nghi6n cuu vc 0rrg dqng khoo hoc Gioo s6. Trung tam Nghi6n cuu vc 0rrg dqng khoo hoc Gioo
duc (CEHA), Truo,ng DCIi hoc Gloo duc, Dor hoc Qu6cgio Ho NOi ic don vi dugc Uy bcrn Kongaroo qu6c te chi gio Ho NOi ic don vi dugc Uy bcrn Kongaroo qu6c te chi
dinh la di6u ph6i qudc gic toi ViOt Nam, dqi dien ph6i
hgp cung Trung tom Phot tridn Tu duy va I(i nong IEGt6 chuc Ki thi Tocrn Qu6c td Kangcroo toi Viet Nom. t6 chuc Ki thi Tocrn Qu6c td Kangcroo toi Viet Nom.
riAilsvrx| HoiN(N(tu&6
i5& lan va bih dthi
:hwtulldqe ilSdEfs(Gt$f|o
16tttiTo&lo,&Gl(dB.M
ffi
E.,^."^,,^" AoDU( v'rlAd
Li6n hQ mua s6ch: Phdng Kinh doanh - Cdng ty c6 ph0n Dich vB Xu6t hin Gi6o dgc Hn NQio Dia chi: 1878 Giaing V6, Qu$n DOng Da, Thinh phd Hn NQi o Dia chi: 1878 Giaing V6, Qu$n DOng Da, Thinh phd Hn NQi
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