Dya tr6n nguyOn tichoqt d6ng cria ba kim H,
M, S vira n6u tr6n, chring tahdy ctng nhau tli
tim hi6u mQt vdi bdi to6n d[c biQt sau.
\.*ffi6 ffi6
Bdri to6n 1
Thdi ifiAm -+V! tr{ (gdc) gifta hai kim. Thf dy. Hi€n nay la 2 gid'21 philt aO giay L.
l1
Hdy xdc dlnh gdc nhen tqo brti hai kim H vd M.
GidL (h.r)
12
I
Gii sri hic 2 gio 21 phrit 49 giety ' ; 11 kim H o
,4 vd kim M 0 B. Ta xdt g6c thoi gian li hic 2h00. Dc ti6n toi vi tfl, A thi kim H ph6i dich mQt cung tu sO Z -+ A: D[t cung ndY ld x (vong) thi kim M phii dich mOt cung tu s5
12 -+ B c6 d0 lon ld 12x (vdng). DQ lon ndy dugc mO ti o s5 phft cho trong bii. VQy :
21, 49, L _240' = !160, > l2x =ll 11 11 ll 11 11 Tri d6: 7B --tz, - * -l 6 (cung tu sO tz -+ s6 2 Uirg "6] vdng) _11 4 I 1 \ _rr.___=_ (VOnS). 11.12 6 6 '
Vay g6c gita kim H vi kim M o thoi itii5m
1^
zh2l'4g" j- a frE chin cung 7B *uti*
11 1 1 trdn: AOB:-x3600 =60o. 6 A - (vong).
* Cd thA fim tdt ldi gidi bdi todn ndy nha sau :
+ Quy sd phrit (dAu bdi cho) thanh s5 vdng mir
M dE dich chuy6n tu s6 12 d6n vi tri th<vi di6m
dang x6t, bing c6ch : L6y s6 phrit chia cho 60'.
+ Tinh d0 lon cung kho6ng c6ch gita H, M(AB), bing c6ch: LAy s6 vong tld dich cira (AB), bing c6ch: LAy s6 vong tld dich cira M, trt tli sd vong tucrng img dd dfch cria H,
tni di sO vdng vi tri ban iliu cira H, M (g6c). + Tinh g6c (H, M) bing c6ch : 78x360". Bhi todn 2
Vi tri @dc) gitra hai kim -+ Thdi diiim. Th{ rly. Ltic 15h00, ban Nguy€n ngii vao bdn giai todn. Khi gidi xong mQt bdi, Nguy€n rdt
ngqc nhiin tha,v kim H vd kim M cua d6ng ho
chua gdp nhau va cdn tqo vdi nhau Sa, I
8
vdng tron. Tha tinh xem lilc do ld miiy gid vd
ban Ngurin giai bdi todn dd trong bao ldu ?
GidL (h,2)
* Cd thA fim #it phaong phdp gidi bdi todn
ndy nhtr sau :
+ Tri s6 rto g6c = DO l6n khoing cSch gifia
H, M ( AB) do b[ng vdng.
+ Xem dO l6n g6c gifia H, M; so s6nh v6i
AB dC r:irt ra <10 dich chuy6n cira M tinh tu g6c s6 12. N6u'gi6tri ndy nh6 hon 1 thi s6
phrit md n6 chi o thdi di6m d6 bing s6 phrit n6 thlrc hiQn. N€u gi|trl ndy 16n hon 1, ta sE
dich H 16n 1 dcrn vf vi lugng phrit chi dugc lai
b6t di 60'.
Biri toin 3
V! tr{ gifta kim + Thdi diAm -+ Thdi gian.
Thi dqt. Luc rd'i nhd di hpc, Timg,thdy hon
1 gid. Khi to.i trudng, Tirng lqi thdy hai kim
(H vd M ddi vi trl cho nhau (trong khodng
thdi gian dd hai kim kh6ng g\p nhau lin
ndo). Hdi: Thcti di€m lilc Titng rdi nha, tcti
trtrdng t'd thdi gian Ti,mg dd di d€n tnrdng?
Gi,rtL $3)
t2 t2
Gii sit lfc d6 H 6 A, M o,B : (vdng).
I{inh 3
Goi cung dich chuy6n cira kim H (tu g6c
th00) toi vi tri ,4 (thdi di6m roi nhe) h
x (vdng), khi d6 cung dfch chuy6n cria M tu
sO tZ -+ B liL lzx (vdng).
Lugng thdi gian Titng di dtin trucrng bing s6
phrit md kim M qudt fu= y (vdng) d6ng
thoi kim H dich mQt cung GE:z (vdng).
,yTaco z-' vdvlz:l Taco z-' vdvlz:l t2 t2.. 1 > y =- (vong) ; z = 13 (vong).
VQy thdi gianTilng di hgc :
9160'-720' =55'23'L.t3 13 13 13
(Xem ti€p trang 44)
@dc.,s:an /4
1
AB =1 8
1
Lric 15h00 : H I M vd cung " I2-->3= 4'. (vong).
Gqi d0 dich chuyiSn cira H ld "r (vong) : tu s6 3 -+ A thi d9 dich chuy6n cira M h
12x (vdng) : tu sr5 12 -+ B. Ta c6: lt13 l+x-::lZx)x- _ ?lZx: _ (vong) 4 8 88 22' + sO phrit : 1r,60' =90' =8'10'19 22 11 11
Vfly ttroi diOm Nguy6n xem gid ld : 15h8'10'f
11
vlr Nguy6n gi6i bdi to6n tl6 trong 8'10'f .
ll
offi..
,-AAr?nta'
GEI rHrE-U GUgC rHl T0Ail HoG rHE QUoG rE lMG ?{,i14ITHE IlffERIIATIOl{At MAIHEMAIICS GOMPETIIII|ilI IMC 28141 ITHE IlffERIIATIOl{At MAIHEMAIICS GOMPETIIII|ilI IMC 28141
PHUI.r|G KIM DIJNG (GV THPT chuyen Ha N6. i-Amsfrerdam)
.:,
ii viet gioi thieu cuQc thi Todn h7c tr€ Qudc t€ (Intemational Mathematics Competition, vi6t tit: IMC) vd cc ttii IMC 2014.
IWYMIC (The Invitational World Youth
Mathematics InterciQ Competition hay The International [4/orld Youth Mathematics Competition) dn d0u ti6n vi l6n thri hai dugc
td chric n[m 1999 tpi Ddi Loan cho hqc sinh Trung hgc y6u thich to6n theo s6ng ki6n cira
Gi6o su Leou Hsian, trulng Eai hgc Qudc gia
Cao Hung (Kaohsiung National Normal
University). Cdc nu6c ldn luqt tO chfcI^WYMIC 1d: Philippines (2001, lin thri ba), I^WYMIC 1d: Philippines (2001, lin thri ba),
An DQ (2002,6n thri tu), Macau (2004, Dn
thri n[m), Dii Loan (2005, lin thri s6u),
Trung Qu6c (2006 , 2OO7,6n thri biy vd lAn
tht t6m), Th6i Lan (2008, Dn thri chin). NIm
2003 kh6ng t6 chfc vi dich crim SARS.
EMIC (The Elementary MathematicsIntemational Contest) hn OAu ti6n duqc tO chric Intemational Contest) hn OAu ti6n duqc tO chric
n[m 2003 tpi Th6i Lan cho hgc sinh Trung hgc
Co sO. C6c nu6c An DO (2004,16n thri hai), Philippines (2005, hn tht ba), Indonesia (2006,
lgn thi tu) vi H6Te K6nS (2007, mn tfli naml
16n luqtdlng cai t6 chric EMIC.
Ndm 2009 IWYMIC 6n thri mudi tlugc tO
chric tpi Nam Phi vd EMIC Dn thri b6y dugc
tO chric tpi Philippines.
IMC N[m 2008, ThAi Lan t6 chric EMIC Dn thri 6. B0 Gi6o dpc Th6i Lan dd quy6t einn
t5t trqp EMIC v6i IWYMIC vd ggi ld The
International Mathematics Competition, vi6t
tit h rMC.
C6c IMC ti6p theo 6n luqt dugc t6 chric tpi
Hdn Qu6c (2010, 6n thri 11), Indonesia
(20ll,lAn thf 12), EAi Loan (2012, 6n thri13), Bulgaria (2013, ldn thrl 14). CuQc thi 13), Bulgaria (2013, ldn thrl 14). CuQc thi
I}/rC 2014 (An thf 15) de dugc t6 chric tu
ngiry 2t.7.2014 diin 26.7.2014 tpithnnh ph6 Deajoun (Hdn QuOc).
Theo xu hufng hOi nhflp gi6o dpc vdi th6
gi6i, tlugc ph6p cira BQ Gi6o dgc vd Ddo tpo, cta Uy ban Nhdn d0n thdnh ptrO Ha NEi, blt
d0u tu ndm 2011, trulng Trung hgc Ph6
th6ng Hd NQi-Amsterdam dd cri dQi tuy6n
li6n tuc tham gia IMC vd do4t nhi6u gi6i
thucrng cao. Cp th6:
Indonesia IMC 2011. DQi THPT: Giii Bacl6ng ttQi, Gi6i Ba nh6m. Giii c6 nhdn: Bpc: cl6ng ttQi, Gi6i Ba nh6m. Giii c6 nhdn: Bpc:
Trdn NS6 Quang Ngoc, D6ng: Nguy€n
Phuong Linh, NguyAn ThA Anh. DQi THCS
A: Giii Nhi tl6ng dQi, ciai Ba nh6m; THCS
B: Giii Ba d6ng dQi. ciei c6 nhdn: Ving:
Philng Ddc Vfi Anh; Bqc: Trin Dqng ViQt
Anh; D6ng: Nguydn Phuong Anh, Nguydn
Qutic Anh; Khuytin khich: Trin Hd Minh,Nguydn Hd Trang, Hodng Minh TuQ, TriQu Nguydn Hd Trang, Hodng Minh TuQ, TriQu
Ngpc Vy.
Taiwan IMC 2012. DQi THPT A vi B: Gi6i
Nhi d6ng dQi, ciei Ba nh6m. Gi6i c6 nhdn:
EOng: NS"yA" Dinh Bdch, Cao Hdi Nam, Hodng Minh TuQ, Khuy6n khich: Philng Ddc
Vil Anh, LA Trung Hidu, Trin E*c LiAm, Trin
Thanh Nhdt, Tq Hd NguyAn; DQi THCS A: Gi6i Ba d6ng dQi, Gi6i Ba nh6m; DOi THCS
B: Gi6i Ba nh6m. Gi6i cr{ nhdn: D6ng:
Nguydn Dinh Bdch, Nguydn Quang Dting, Phqm Nam Khdnh, Trdn ViQt Quang; Khuyl5n
khich: Nguydn Vii Duc Anh, Dd Hodng Nam Hidu, LA Quang Minh.
Bulgaria IMC 2013. T[{PT: Giii c6 nh6n:
DOng: NS"ye" Einh Bdch, L€ Hing Hqnh,Phqm Quang Nam;Y:huy,5n khich: Phqm Minh Phqm Quang Nam;Y:huy,5n khich: Phqm Minh
D*c, Dinh Phrtc Hung, Phqm Hd W. D}i
THCS A: Gi6i Nh6t dOng dQi, ciai xl6t nnOm;
DQi THCS B: GiAi Nhi nh6m. Gi6i c6 nhdn:
Vang: Phan Minh Eirc, Phqm Nam Khdnh,
,A^
Le Quang Minh; Bry: HO Minh LAc,
Nguy€n Nam VieL D6ng: Mai ThiAn An,
Phqm Kim Anh; Khuy6n khi ch: LA fran Uodnh.
Korea Il{C 2014. Qu6 trinh tuy6n chqn dQi
tuy6n tham gia thi IMC 2014 g6m ba vdng:
Vong 1 ddnh cho t6t ci hqc sinh tu ttrOi O Oi5n
t<trOi tO c6 nguyQn vgng tham dU lcy thi IMC,
chgn ra 35 bpn. Sau d6, qua vdng loai 2, chon ra 25 bqn. Vd cu6i cing li vdng 3 di5 chgn ra
20 hgc sinh xu6t sic nhAt, chia ldm 5 dQi (2 dQi Junior vd 3 ilQi Senior). Tai IMC 2014, dodn hqc sinh ViQt Nam gidnh dugc gi6i cao
ntr6t vdi 3 huy chuong Vdng (mQt hoc sinh
dpt di6m tuyQt d6i 150/150),4 Huy chuong
Bpc, 8 Huy chucrng D6ng vir 4 giili Khuy6n knich (phin thi c6 nhdn).
Ving: Phan Minh D*c, Hodng Nguydn Minh
Phuong, Nguydn Nga Nhi.
Bqc: Ddo Vil Quang, Nguydn Ddng KhAi,Phqm Nam Khdnh, Chu Minh Hi€u. Phqm Nam Khdnh, Chu Minh Hi€u.
Eiing: Trinh Duc ViQt, Nguydn Tudn Hodng, LA Nhqt Quang, Phqm E*c,Long, Mai ThiAn
An, Dd Hodng Nam Hi€u, Hodng Titng,Hodng Anh Minh. Hodng Anh Minh.
Khuy6n khfch: NSuyAn NhQt Quang, Ui Uintt
L6c, Dinh Thanh Himg, Nguydn Nam Vi€t.
Do tinh chdt c{rc eC tni IMC c6 nhirng ili6m
lrtr6c biQt voi cdc CC ttri hoc sinh gioi o ViQt Nam, n6n viQc tuytin chqn dQi tuy€n cfing gip
nhi6u kh6 kh[n. Ldm th6 ndo iI€ chon duoc
c6c hoc sinh d6p img duoc dAy dt c6c ti6u chi cira lcj, thi li mQt bdi to6n vdi c6c thAy c6.
Quy6t tlinh chgn ba hgc sinh cria khOi O ctng
h di6u md c6c thAy c6 ph6i d6n do cdn nhic
r6t ntri6u vi hgc sinh lop 6 cdn chua dugc hgc nhiAu ki6n thric 16p tr6n, trong khi bdi thi c6
nhirng cdu phii sri dpng ki6n thric lW 7, 8.
M[c di vQy, c6c thAy cO dA tin tu0ng vdo tu
ch6t cira c6c em vd c6 vdo kinh nghiQm hu6n luyQn tlQi tuy6n. Vd ni6m tin tu&ng d6 dA
ctuqc khing dinh qua thenh tich rdt xu6t sic
cria tloin Vi_6t Nam tpi ki thi I}i.{C 2014. Dodn hoc sinh ViQt Nam trong bQ ddng phuc
trudng He N6i-Amsterdam vli rdt nhi6u dn
16n linh thuong (19 giei c6 nhdn, 7 cirp tl6ng
dQi, trong d6 c6 3 Huy chuong Ving vd mQt
Crip v6 dich), tt6 trrhing dinh chAt luqng cira
hgc sinh ViQt Nam n6i chung vd cira trudng Hd NQi-Amsterdam n6i ri6ng.
Thdnh tich ndy cfing th6 hiQn ch6t luqng hgc tpp t6t cira hgc sinh ViQt Nam. Ei5 d4t dugc
nhtng phin thu&ng cao qu;f ndy, ngodi su c5 ging h6t minh cria cdc gi6o vi6n t6 To6n vd hoc sinh trudng Trung hgc Ph6 th6ng Chuy6n
Hd NQi-Amsterdam, cflng c6n nhic d6n sg
quan t0m oba cdc c6p Hnh dpo, cira nhd
trudng, phu huynh, c6ng sric cria 10 th0y cd
gi5o tli ctng doin.
Dodn cflng tham gia nhi6u ho4t dQng: Thdm quan thdnh ph6 Daejeon, th[m vi6n bio ting
d6n t6c, b6o tdng khoa hgc, th[m quan nhd
, , A,.A
m6y ch6 bi6n crlc s6n phdm tu S6m, l6n th6p truy€n hinh ngim Seoul, gip Eai sri ctra ViQt
Nam tpi Hdn Qu6c, di c0ng vi6n Everland,
Cung diQn Gyeongbokgung, thlm quan dio
Nami noi quay BQ phim "BAn tinh ca mia
d6ng" nOi ti6ng... Dodn ViQt Nam cflng tham gia giao luu trong DOm VIn ho6 vd trinh di6n
tiiit mgc v[n ho6 ddn tQc v6i titSt muc Ddn ca ba midn th6 hien bin s6c ddn tQc Vi6t Nam do
c6c em trinh diSn r6t nhuan nhuy6n vd hAp
d6n. M[c dt chi v6n vgn c6 5 bu6i tdp, nhrmg
doin ViQt Nam thgc sp dd c6 mQt bei trinh
,.i !
olen oac sac.
Dodn ViQt Nam tai IMC 2014
Dfii ddy ld Di thi cd nhdn IMC 2014