(rl
Lcri gitiiiltng. TXD: D=jr, ;ax+20151
rL)lr lr
VoiJ2x-l =0ex=: (thod mdn). Voix>= thi(*) <+ * (*) <+ *
"?, ,o*lrx<2015 ,,n"u *u",lur,
x -215
[.__ r
nghigm cua 1*.; \d: | " - 7 [s<*<zors
NhQn xit. C6c bdi giri vC <l6u ph6t hiQn tlugc sai ldm vir dua ra loi giii dfng. Tuy0n duong c6c ban sau dua ra c6 nhirng ph6n tich sai lAm x6c d6ng:
Nam Dinh: Ldm Vfr Tuiin, 12 Anh l; Trdn Thi Kim
Ngdn,12A1, THPT chuy6n LC H6ng Phong. Hi NQi:
Dinh Vdn Anh, l2Al, THPT H6 XuAn Huong, sd I
Nguy6n Quj Er?c, Q. Thanh Xudn. Hung YEn: Trin
Phuong Linh, l0 To6n 1, THPT chuyOn Hung YCn;
Duong Hing Son, 1OA9; Nguydn Thi Thanh Lan, 11.48; Tri€u Ninh Ngdn, 11A9, THPT Duong QuAng Hdm, V[n Giang. Thanh H6a: Vfr Hiru Timg, 11A1,
THPT Hoing H6a IV, Hoing H6a; DSng Quang Anh,
9A, THCS Nguy6n Chich, D6ng Son. NghO An:
Nguy€n Philng Thdi Cudng, llAl, THPT Th6i Hda,
TX. Th6i Hda. Vinh Long: Trucrng Ng6 Minh Bdo,
l0/1, THPT chuy6n Nguy6n Binh Khi6m.
KIHIVI
PHTIONG TRiNH LSGARIT C6 HAIB,{.rAN r
Trong gid bdi tflp To6n cria lop 12A1, thAy gi6o dua ra bdi to6n: Gidi phactng trinh
1.
jlog, tr +2)2 -3=logr (4-x)3 +log, (-r+6)3 (1).
nn
Sau mQt lfc suy nghT, bpn Binh xung phong 16n b6ng
lg+2), >0
siai nhu sau: DK : ] t+-xl' ro e] x + -2
" I l-6<x<4[tr+6)'>0 \ [tr+6)'>0 \ V6i DK tr6n, ta c6: 3 (1) <+ 1og, ((r + 2)2f - 3 = logr [ta - xl'.tr + 6)3 ] iq
<> log, (x + 2)3 -logr[{+ - r)t.{, + O)'
] = :
x+2 I
e ___:_ (4-r)(x+6) _ _r 4€> 4(x + Z) = (4 _ x)(x + 6)
e x2 +6x-16=0<>x : 2 (th6a m6n), x: -8 (loai).Vdy PT (1) c6 nghiQm duy nhdt x =2 . Vdy PT (1) c6 nghiQm duy nhdt x =2 .
Sau khi b4n Binh giii xong thi ban Phuctng drmg dQy
xung phong 16n b6ng ldm theo c5ch kh6c nhu sau: (-*-1
DK: ] ^ I ' . . Voi DK niry, (1) tucrng duong vcri
[-6<x<4
3log, lx+21-3log, 1=31sg, (4-x)+3log, (x+6)
4 4 ' 4 4
e log , (4lr + zl) = los r [(4 - xxx + o)]
l[-2.*.+e alx+zl=@- x)(x+6, *llo'::" -= t4-xxx+6) e alx+zl=@- x)(x+6, *llo'::" -= t4-xxx+6) l)'6<x<-2 ll-+tr+2t=(4-.rXx+6) l-2<r<-4 I 1l x=2 il- llx=-t{ l--o AI f-e <*<-z -Lr= l-.Ei {lx=t+J::il_ lfx=l-J33 Vfly PT (l) c6 2 nghiQm ld x =2 vd x = 1- J33 .
Theo cdc bgn thi bgn ndo gidi ilfing? 14 sao?
NGUYEN TRAN HOU
(GV THPT Cit Huy CQn, Vfi Quang, Hd Tinh)
I l-2.*.-+llr'+6r-to=o llr'+6r-to=o el ) <> I J-6<x <-2 l\r'_z*-zz=o tsn.ror-ror, T?Eil,5EESq
a_
Iqp rhi lolil H0( vi IUdl mi
Illulhemuti$ und Youth [lluguzine
BAN CO VAN KHOA HOC cH{u raAcru NyI$y xuAT BAN
otir* *Cr**camrroAx *L*'J#:ii:t#li,**
xuAT nix ru'tso't
sd 462 {12.2015),
Tia soan : I 878, shd Giens U6, Hal Noi 0T BiAn lap: 04.35121607 0T - tax Phil henh, IIi su : 04'351 21 606 Email: l0anh0clu0ilreYielnam@gmail.c0m
HaacvANrl{g-N GS.TIKH-rnANvaNNntxc
rs. NcuyEN VAN VO. NG Tdng Gi6m d6c ki€m Tdng bi€n tdp
cs. ooeNQrrixtr NXB Gir4o_dgc-vi6tNam
uQr odxc nrux rtP
Tdng bian fip : TS.rnAN ntfu Nlu Thu ki Tba soan : ThS' nd Qualqc vrNn
rs. rnAN oNn csAu, rm. NcuvEN ANH DLING., rs' rnAN Neu o(xc' rs' Ncuv6u uws otlc' zs NcuvEN unqn sA' rs. NcuyEN vrgr r*i,';;.;^';lo"O.. ";., rfts. PHA.M ,ill- '^o, PGs' rs' vu rHANH xsr6r'
GS. TSKH.NCUyEN vAN MAU, Ong NGUYEN KHAC MINH, rS. PHAM THI BACH NGOC' PGS TS' NG( ',EN,^Dy:,:ry;
pcs. Ts. TA DUy rrUf5C, ari. *C,i sN rns rn+Cn, GS.TSKH.DANG HUNG rniNc' PGS' rS' pneN oOAN TH6AI' Ths VU
"r* it,in, pcs. rs. vO DUoNG rHVY, Gs' rsra'
NcO vryr rmNc'
TRONG SO NAY
@ oann cho Trung hgc Co sd
@ HrArrg d6n giii Od tfri chon hoc sinh gi6i 16p 9 @ ciai bei ki tnidc
Solutions to Preuious Problems For Lotter SecondarY School
Nguydn Anh Tudn - MQt ddu hiQu nhAn
bidt tia phAn gi6c cria mQt g6c.
tinh Vinh Phric, n5.m hoc 2O74 - 2075'
@ ciai tri ro6n hgc @ fiA.tgAnh qua c6c bii to6n - Bdi s6'3'
@ r,i"t sft To6n hgc
@ Hrarrg d6n giii 'Dd sd3.
@ fftrf sfic trridc ki thi'Dd s6'a. @ nit5n din d4y hgc To6n
@ Cft.rdn bi cho ki thi Trung hqc Phd
th6ng Qudc gia
TrdnVd.n DAc - MOt sdbei to6n td hgp x6c
sudt.
(p ooan Quinh - Thi tldu Qudc td ctra nhtng
nhd To6n hoc tr6 (ITYM).
@ UUtt dgc tim tdi
Pham Thi LiAn - Vd mdi li6n hO dac biQt cira ddy sd Fibonacci vd sd 11.
Anh Bia 1: Ct6c thdy, c6 giiio vii cdc em hoo sinh rrudng Tl-{cS Giang vo. Hd Noi doat giii trong Kjr thi IMS() (lnrenrational Mathcmatics rnd Science olympiad) (i,i ,rai q"ua phai): Hnng l- Mdn Toiin: Thiy Trinh Hodi Dmmg' an
Ngu1,€n NttQt Linhtucvl, ;;rr;;C;. al, iuc'bj,"'n Ph'irng'Nam 'qnn,(uco)'cm Pham Hd Phtrons (HCB)' crn Bir PhrumgNari(HCV),emPhamGiaKhanhrrrcol,.navViuqnhlulns,Hdng2-M6nKhoahgc:C6DqneTh!Thuy,Nga^
em pham eui, Htnt,tn,,rj. "- ir*r,*, Ldi iritijcsi, c, '\'gzrvt:ln Sri t-tirn (HCID)' cm Tran Hrtitng Thv
L'vdn (HCB)' cnr
rri, Ba,tknin,A $Cgl. cm Biti An Binh (HCB), cd Hoing Kim U"van'
Phi Phi - ChuYdn khaY b6nh.
D6 thi chon hoc sinh gi6i 16p 9 tinh Binh
Dfnh, nim hoc 2014 - 2015. LA Qu6b Hd.n - Tdc
ngudn cim hirng kh6ng
c6c nhd sdhoc.
phdm Arithmetica,
bao gid vdi can cria
@ Oi6r, dirn phridng Ph6P giii to6n
LA Xud,n Dqi - Bii to6n tim hing sd tdt nhdt trong bdt tl&ng thirc.
@ s"i tAm 6 aaut
Gid,i ddp: Ldi siai d6 tron vqn?
Ng^rydn TYdn Hilu - Phriong trinh Iiga-rit c6
hai dap 6n?
@ ,a ra ki niry
Problems in This Issue
T I / 462, ..., T 12 I 462, Ll I 462, L2/ 462.
Nguydn Vdn Qu6ic Tuan - Stt dung phrrong pt ap aa"ft gia dd giAi hQ phriong trinh'
Tru&ng ban biin tSPzTlS ffiry,ptufrhdnh:NGUYET
NHA XUAT ts IAO DUc VIET.NAM
!.,:lW
:EtlG;rgC gi0p cho hgc sinh THCS hoc tdp t6t m6n ;rgC gi0p cho hgc sinh THCS hoc tdp t6t m6n
,"1f,I1s5n, chudn b! cho ki thi vao lop 10 THPT va
lRpf chuy6n, Nha xuAt bdn Gi6o duc Vi6t trtam
xu5t ban bo sSch '."Cdc chuy\n dO chon tgc ToAn
IHCS" g6m 8 cu6n :
Cdc chuydn dd chon loc Todn 6 ffep 1, TQp 2),
Cdc chuy$n dd chon toc Todn 7 ffep 1, TQp 2),
Cdc chuy€n dd chon loc Todn I (Tep 1, TQp 21,
Cdc chuyiln CIii chon loc Todn I (Tep 1, Tqp 2).
M6i cu6n s6ch d6u co c6c chuong tuong ung vdi
c6c chuong trong SGK To6n THCS. M6i chuong
gOm ba phAn: Kien thuc can nho, Mot so vi du vA
Bai tQp de nghi. Phltn Ki6n thwc cAn nho dua ra
nhirng ki6n thuc co bin vd b6 sung nh&ng kirln
thtlpc cAn thi6t dC hoc sinh co th6 gidi ducrc c6c bai tQp, cdc dang to6n trong chuyen d6. PhAn MQf
sO vi du dua ra nh0ng vi du minh hoa cho cdc
dqng to6n di6n hinh cria chuy6n dO. O d6y co
sr
.Eian tlec c6 th6 mua'rdchtg
nghi dwa ra nhCr.ng bdi
d\n gidi - Dap s6, hoc sinh s6 n5m rO hcyn c5ch giSi cho m6i dang todn, ddn ddn tqr minh co thQ
ldm duoc c6c bdito6n tuong tu. ,
C6c t5c gid c0a bo s6rch la nh0ng thAy
giao di co nhi6u kinh nghiOm tro gidng day, bOi du0ng hoc sinh gi6i
bOi du0ng hoc sinh thi Violympic To6rI
bQ s6ch le NGND TOn ThAn.
Hi vong rang b0 s6ch se d6p ung nhu cAu hgc tqp ngdy cang cao cia dong d6o cdc em hoc sinh vd la tdi lieu tham kh6o hiyu ich cho viec gidng dqy cia c6c thay c0 gido.
&Uru*iYng hgc & cdc dia phucrng,ho{c
,Ne,yn,.,r,
=r&r
nhOng nh6n,,lffiriY
v6 nhirng ki6n thpq nl
md hoc sinh cin luu y,
i r:ti,e:C&a h&ng, s6.h .*.
dsiri'
m@mffiffiw,ffimHffirmmH
so uAwt xAy DUNG vrrRuoNc ruf'Ntt
Dia chi: xi Tdn L6p, huy6n Y6n My, tinh Hung Y6n; 56 dign thoai: 03213.961.906
T'i l0 hqc sinh khdi 12 c0a nhd truong d6 tdt nghiQp trong ky thi THPT Qu6c gia 2015 la 98% vd ti lC ha! sinh co td hop
s6 didm cdc mOn x6t tuydn Dai hoc d0 dd vdo Dai hgc ld
55,44%; x6p thu 9 tr6n 37 truong THPT todn tlnh.
PhAt huy truydn th6ng 50 ndm qua, truong THPT Y6n My dang tr6n dd vuun l6n phat tr,i6n Od khing dinh minh xung dAng voi truong trung tf,m. Thdy.va tro nhd truong dang ra suc phdn ddu vd chudn bihanh trang ti6n toi kf niem 5511m
ngdy thdnh lAp truong viro nam 2020. ::'
i
ThS. NguyOn Ngoe Luin
Bi thu chi b0 - HiQu truong nhd truong
-zruong
THPT YOn MV dus.c thdnh lAp vdo th6ng B '(11ndm 1965, ddn nay vua tron 50 nim tudi. Truong
lr!-LrOuo.. ddu iu xAy dung 36 phong hoc ki6n c6 ca6
tdng,3 phong hgc Ngoai ng0, 6 phong B0 mOn voi c6ctrang
thi6t b! hiQn dai. KhuOn vi6n truong xanh sAch vd dep. Hi6n nay Truong co 78 c6n b0, giao vi6n, cOng nhAn vi6n, trong do co 12 Thac si, 66 C0 nhAn. Ban gi6m hi6u vd tQp thd giao
vi6n nhd truong ld nh0ng nguoi gidu nhiOt tinh, y6u ngh6, c6 trinh d0 chuy6n mOn v0ng vdng, dugc c6c cdp l6nh dao, chinh quy6n, nhAn dAn vd hQc sinh y6u mdn!
Mot trong nhfng nidm tu hdo lsn nhdt c0a nhd truong ld cdc
thd hO hoc sinh sau khi t6t nghiOp, dd ti6p tUc phdn ddu vd truong thdnh. Nhidu trong sd d0 la nh0ng c6n bo cdp cao c0a DAng, Nhd nuoc, QuAn dOi, l6nh d4o c6c 86, Ngdnh, Dodn
.$6 o Trung uong vA cAc eiia ohuong. Ho ld nh0ng nhd khoa hoc, nh0ng gido su, tidn si, nh'ing cdn b0 quAn l! tdi ndng, "rtnh0ng doanh nhAn ndng dOng vd thdnh dat, ..., ho chinh la
';l,:"nguy6n khi qu6c Eia" ma truong THPT Yen My "dAng tdng"
:,. cho qu6 huong ddt nuoc. rL:-
*flItong nh0ng ndm qua truong luon tich cgc tham gia cdc hoat
dQng chuy6n mOn vd hoat dQng phong trdo do Sd GD&DT Hung Y6n, tinh - huy$n dodn td chuc. Ndm hoc 2014 - 2015 hai thdy c0 gi6o ctia truong tham gia HQi thi giAo viOn thuc hdnh thi nghiem gi6i cdp tinh ddu dat giAi Ba. Hoc sinh nhd truong iham dU ky thi hQc sinh gi6i khu vuc Duy6n hAi vd ddng bang Bdc b0 dat 4 giAi (1 HCD va 3 giAi khuy6n khfch).
Oac biQt trong ndm hqc 2015 - 2016 co 18 hoc sinh nhd truung dqt giAi trong ky thi HSG cdp tinh do Sd GD&DT Hung
Yenld chuc voi 2 giAi Nhi, 10 gidi Ba va 6 giAi Khuy6n khich.
TQp thd gi6o vidn'Truong THPT YOn Mi
Tqp thd cdc Thdy C0 td Toan - Tin c0a nhd truong