CLê g c $ê Gx’ A &>

Một phần của tài liệu Đề thi toán singapore SMO từ năm 2005 đến năm 2013 (Trang 37 - 41)

-c $êGx’A&> Hv’’FeêA)> ОtẵCT’ ОtẵKU’ Оtẵ>P2’

cêA>’ƠkẪẵ ™žẵ Ẫž—ỀẼž™ẵ oỀẼẵcêAG’eê HêẪẵkẵ Ẫž—ỀẼž™#

hƠw™ẵeê7’ẼƠwẵ ẪỀĐẵ žxẵ tÊẼẪẵ ẪẵHW+C’q>7$ cêFHc+ F4ê fƠỀẪẵcêẪẵ wảw™$

cC’Ẫẵ kẵ Ẫž—ỀẼž™ẵ fƠỀẪẵ ẼƠwẵ k™ẪỈwẶẵ ẪẵC7’Ẫ™qwẵ Ẽẵ ẪẵAGR2’ >Q2 C™Ẫ5ẵ > >

SẼẵ qk™ẵ wkẪ—¾ẵ owẵ qƠwq’wtẵ ẼƠkẼẵ xẵ> ’C ’H(ê>7’kẶwẵ Ặwtẵ k™tẵG’H’K’O’P’FêkẶwẵ o—Ềw ẵ ẼƠw™ ẼƠwẶwẵ tžẵ ™žẼẵ w͐ẪẼẵˆ’‰’>A 5Ažxẵ ẼƠwẵ ẪkĐwẵ qž—žỀẶẵ ẪỀqƠẵẼƠkẼẵˆ’’‰’$ê>A A 5A ež›?@ẵ>>2

eỀââžẪwẵ ẼƠwẶwẵ w͐ẪẼẪẵ kẵ qž—žỀẶ™Êẵ xžẶẵ›ẵA> >’ẪỀqƠẵ ẼƠkẼẵ ẼƠwẶwẵ tžẵ ™žẼẵ w͐ẪẼẵˆ’‰’>A 5A

žxẵ ẼƠwẵ ẪkĐwẵ qž—žỀẶẵ ẪỀqƠẵ ẼƠkẼẵˆ’$ꉒ$ê>A 5A fƠw™ẵ>’HêĐỀẪẼẵ owẵ žxẵ kẵ t}wẶw™Ẽẵ qž—žỀẶ xẶžĐẵG2’fƠỀẪẵ Ẫk¾ẵ >’k™tẵHêkẶwẵ Ặwtẵ k™tẵG’Ẫẵ o—Ềwẵ e™qwẵP’$ê>’’>’ H'êP’ĐỀẪẼẵ ẼƠw™ẵ ow o—Ềwẵ [žỈẵC’qG’$êG’AP’Ẫžẵ ẼƠkẼẵC’Ẫẵ Ặwtẵ k™tẵ Ơw™qwẵH’ ’A>’$ê>’$êC’Ẫẵ o—Ềwẵ IỀẼ

>>’MêG’$êH’$êH’Hê$ê>’$ê>’kẵ qž™ẼẶktqẼž™#

>R2 C™Ẫ=ẵ G

fƠwẵ ™wđỀk—Ẽ¾ẵ qk™ẵ owẵ ẼẶk™ẪxžẶĐwtẵ Ẽžẵ

G7C‰’ CK‚‰’

C77’'A C77’2’

·Ìwẵ €ẶẪẼẵ ™wwtẵ Ẽžẵ ẼƠwẵ А™ĐỀĐẵ âžẪẼảwẵ ™ẼwÊwẶẵ‰’ẪỀqƠẵ ẼƠkẼẵ ẼƠwẵ ™ẼwẶảk—ẵ’

qž™Ẽk™Ẫẵ k™ẵ ™ẼwÊwẶ#ẵ fƠẪẵ А™ĐỀĐẵ ảk—Ềwẵ žxẵ‰’ẪẵC2’ hƠw™ẵ‰’AC’ẼƠẪẵ ™ẼwẶảk— qž™Ẽk™Ẫẵ ž™—¾ẵ ž™wẵ ™ẼwÊwẶẵ ẼƠkẼẵ ẪẵG/’fƠỀẪẵ ẼƠwẵ k™ẪỈwẶẵ ẪẵG/’

C7/ C™Ẫ5ẵ G7HRR

VwẼẵ {ẵMê>O7’7A >P7’8A>Q7’9A >R72’ ^oẪwẶảwẵ ẼƠkẼẵ {ẵ >PKE’ >KD>PKD’' KD2’ VwẼ

ˆ’A>PKD#>CK2’fƠw™ {ẵAˆ#‚qqˆÊqq’X’ˆD(>7777’AˆD2’e™qw Ịẵ >PKD>CK’GO’ GO’

j™tẵ{# ˆ) >B’Y’ˆB’) >777* ˆ’# >\’8qCˆ’) >777>’ãvẵ Ơjảvẵ{’Aˆ’) >B6’fƠỀẪẼƠvẵ Џ™ĐỀĐẵ âžẪẼảvẵ ™ẼvÊvơẵԒẪỀsƠẵ ẼƠjẼẵÔB’A{’Ẫẵˆ% >’ >PKB’) >CO’8qG7HRR3’ ẼƠvẵ Џ™ĐỀĐẵ âžẪẼảvẵ ™ẼvÊvơẵԒẪỀsƠẵ ẼƠjẼẵÔB’A{’Ẫẵˆ% >’ >PKB’) >CO’8qG7HRR3’ C>2 C™Ẫ5ẵ >O

WvẼẵԒ’ ’C77KÔB88L’8q{ Ô Ô’+>’v’ãƠvơvẵ{ԒẪẵjẵ ➔¾™žĐj”ẵ žxẵÔ2’SxẵԒY’ >’

ãvẵ ƠjảvẵvY’>’’C’’ ’C77K’8qC77K’6A>77G0’^nẪvơảvẵ ẼƠjẼẵԒ’ ’C77KÔB88L’ẪtảẪn”vẵ n¾ẵԒ) >’xẵ j™tẵ ž™”¾ẵ xẵv’Y’C77K’6A >77G’Ẫẵ tảẪn”vẵ n¾ẵԒ, >2’fƠvẵ âơĐv tảẪn”vẵ n¾ẵԒ) >’xẵ j™tẵ ž™”¾ẵ xẵv’Y’C77K’6A >77G’Ẫẵ tảẪn”vẵ n¾ẵԒ, >2’fƠvẵ âơĐv xjsẼžơÒjẼž™ẵ žxẵv’Ẫẵv’Y’K’7AH7>’6A >P’7ACH5ê ežẵv’ƠjẪẵ ž™”¾ẵCJ’Y’ >O’xjsẼžơẪẵ fƠỀẪẵ ẼƠvơvẵ jơvẵ>O’âžẪẪn”vẵ âžẪẼảvẵ ™ẼvÊvơẪẵ1AẪỀsƠẵ ẼƠjẼẵԒ’ ’C77KÔB88L’Ẫẵ tảẪn”v n¾ẵÔ# >2’

CC0 C™Ẫ>ẵCH7OQ

Lž™Ẫtvơẵ ẼƠvẵẪvđỂv™svẵžxẵẼv™ẵ>’Ẫ ẵ fƠvơvẵjơvẵ v”vảv™ẵẪâjsvẪẵnvẼãvv™ẵẼãžẵ>’Ẫẵ žơẵnvxžơvẵ ẼƠvẵ ”vxẼОẪẼẵ>’žơẵ jxẼvơẵ ẼƠvẵ ơÊƠẼОẪẼẵ>0’Nžơẵ vjsƠẵ žxẵ ẼƠvẪvẵ ẪâjsvẪẵ ãvẵ sj™ẵ âỀẼẵ vẼƠvơ Ẽãžẵ _ẪẵtžỀn”vẵ _Ẫêžơẵ ž™”¾ẵ ž™vẵ7’Ẫ™Ê”vẵ73’ Sxẵ ẼƠvơvẵ jơvẵ vÍjsẼ”¾ẵ}’tžỀn”vẪẵ _Ẫ ẼƠv™ẵ ẼƠvơvẵ jơvẵ ž™”¾ẵ>7’#C}’Ẫ™Ê”vẵ _Ẫ ẵ fƠvẵ ™ỀĐnvơẵ žxẵ ãj¾Ẫẵ xžơẵ ẼƠẪẵ Ẽžẵ Ơjââv™ẵ Ẫ

‹êê;;*{ê~’ @8uB~’5êfƠẵỀẪẵ Ẽẵ vẵ j™Ẫãvơẵ -ẪẵƠẵ ẵ

L’ >>>>’)}’ * }’ >†’)C}’ Y’CH7OQ0’ * }’ >†’)C}’ Y’CH7OQ0’ ~[r’ CG2 C™Ẫ5ẵ >C VvẼẵ(Gˆ2’G¾ẵ sžẪ™vẵ ơỀ”v C>B’’CQB# >HB’ P’ >HB’GCQB,C>B’ >>’

sžàẵGY’ Mê Gê j™tẵ sžẪẵ]Y’

C>H CQ >O’

fƯỂẬẵ;>(qMê>HB’’PB#C>H P ’ Y’ Ȟẵ ẼˆjẼẵ<>8q

Cpžẵ -A A A #A B@S’ %A @A !A P’ =OQL9;>qMê B’ 8 C>H’ Q’

fƯỄẺẵ+ G +"%GY’+!#G'GẺăẵ ÉƯlẼẵ ÉưmẾԔvẵ)*GẸẵ ẪžẺsv”vẪ%ẵ fƠvơvxžơv&

#G C > Q

3AY’C’ Y’ -Y’>C0’

sžẪẵ G C’ P’

CH2 C™Ẫ;ẵQP

VvẼẵ ẼƠvẵ s‰êsỀĐs‰ês”vẵ žzẵNabd’ĐvvẼẵ ẼƠvẵ ”‰™vẵcd’kẼẵe.’fƠv™ẵe’a’b’d’kêvẵ sÁ™ạ s¾s”‰s#ẵ [žỈẵjc_a’k]ba’ jaed’ẪžẵẼƠkẼẵc’_’a’e’kêvẵk”Ẫžẵsž™s¾ s”‰sẵ fƠỀẪ

csB’ c_c]’X’caŽcb’ceŽcd’k™tẵdtB’X’dbŽd]’daŽd_’deŽdc0’

fƠvêvzžêvẵcsB’GdtB’X’ce’Ž’cd’qde’dc X’ce’Gde’Ž’cd’cdB0’Lž™ẪvằđỀv™Ẽ”¾ẵcd’X’ GOFB’X’QP0’ đỀv™Ẽ”¾ẵcd’X’ GOFB’X’QP0’

&A

2A

$A

CK3 C™Ẫ7ẵ :F

WvẼẵ *ẵ ovẵẼƠvẵsv™Ẽêvẵ žzẵẼƠvẵs‰ês”v ẵ N‰êẪ°ẵ Ỉvẵ ẪƠžỈẵẼƠkẼẵs’`’*ẵEUẵc’”‰vẵ ž™ẵkẵsžĐО™ s‰ês”v ẵ L”vkꔾẵs’_’*ẵc’kêvẵ sž™s¾ s”‰s#ẵ CẪẵj_sh;’ jf_a’X’ j_c1m’ F7‹’

➉™ẼẪẵs’_’Gc’kêvẵ k”Ẫžẵ sž™s¾s”‰sẵ fƠỀẪẵs’_’*ẵ ]Uẵc’k””ẵ ”‰vẵ ž™ẵ ẼƠvẵ s‰êsỀĐs‰ês”v

žzẵNs_c0’

2A

"A

e‰™svẵls’_o’X’R7Œ’so’‰Ẫẵ kẵ t‰kĐvẼvêẵ žzẵ ẼƠ‰Ẫẵ s‰ês”vẵ k™tẵso’X’ G:7B’ CO# fƠ‰Ẫẵ s‰ês”vẵ ‰Ẫẵ k”Ẫžẵ ẼƠvẵ s‰êsỀĐs‰ês”vẵ žzẵNs’_^</’fƠvêvzžêvẵ_i=’CO’Ẫ‰™ẵF7‹’X’ >F0’

!#"$* &&* "&'*

`zud“”pê VdÃvp‰dÃzidˆê [ˆă‰“zdlê `V[#ê

X‘mÀê^mfĐwŽÀ&ê ^‘mfwbĂê\Ž›Àjê^ŽĂ›ĐwŽÀ•ê

%q hwẵ ẪƠj””ẵ ẪƠžỈẵ ẼƠjẼẵ ‰™ẵ Êw™wêj”ẵ xžêẵ j™¾ẵԒAq-

*X Ô4;&/G ;&/G

Nžêẵ j™¾ẵ`q Aq Rq™žẼwẵ ẼƠjẼẵcqsPê ]q‰xẵ j™tẵ ž™”¾ẵ ‰xẵ]q‰Ẫẵ ẼƠwẵ ”jêÊwẪẼẵ ‰™ẼwÊwêẵ ẪỀsƠ ẼƠjẼẵ](`qGÔ3’ Sxẵi_qX’m%(` q)(`q q](`nqỈƠwêwẵ]q‰Ẫẵ ẼƠwẵ ”jêÊwẪẼẵ ‰™ẼwÊwêẵ ẪỀsƠẵ ẼƠjẼ

](`qGԒẼƠw™ẵ~êtSê HR_bpq C”Ẫžẵ ‰xẵ`qj™tẵ/Ajêwẵ t‰ẪẼ‰™sẼẵ ẪđỀjêwẵ xêwwẵ ‰™ẼwÊwêẪ ẼƠw™ẵR_q0ARheq Pw™swẵ

e‰™swẵ wảwê¾ẵ ‰™ẼwÊwêẵ sj™ẵ nwẵ Ề™‰đỀw”¾ẵ Ỉê‰ẼẼw™ẵ jẪẵ](`qỈƠwêwẵaq‰Ẫẵ ẪđỀjêwẵ xêwwẵ2:&/G

m%q.ẵ #' ẵqÔnq fƠ‰Ẫẵ sžĐâ”wẼwẪẵ ẼƠwẵ âꞞx#

.%ẵ N‰êẪẼẵ Ỉwẵ ™žẼwẵ ẼƠwẵ sw™Ẽ꞉tẵ t‰ả‰twẪẵ wjsƠẵ Đwt‰j™ẵ ‰™ẵ ẼƠwẵ êjẼ‰žẵ +>.%ẵ VwẼẵSqnwẵ ẼƠwẵ Љt➉™Ẽẵ žxẵ9<qj™tẵTqnwẵ ẼƠwẵ Љt➉™Ẽẵ žxẵ9:q fƠw™ẵSP#P<q SG#G:q

+#. ẵ ežẵ n¾ẵ JwảjẪẵ ẼƠwžêwĐẵSqC q>qjêwẵ sž””‰™wjê%ẵ V‰“wỈ‰Ẫwẵ> qd’Tqjêwẵ sž””‰™wjê fƠwêwxžêwẵ>Cq IHq :9qj™tẵCq‰Ẫẵ ẼƠwẵ Љt➉™Ẽẵ žxẵ<Tq e‰Đ‰”jꔾẵ>Fq JKq <9qj™tẵ ‰Ẫẵ ẼƠwẵ Љt➉™Ẽẵ žxẵ>TqfƠỀẪẵCFq HJq STq IHq <:q e‰™swẵ ẼƠwẵ sžêêwẪ➙t‰™Êẵ Ẫ‰twẪẵ jẨwẵ âjêj””w”ẵ ẼƠwẵ ẼỈžẵ Ẽê‰j™Ê”wẪẵ jêwẵ Ẫ‰Đ‰”jê ẵ

9q

:q >q 4G

+ N‰êẪẼ”¾ ẵ VqWqXqBẵ )ẵ Ẫ‰™qvẵ ‰x ẵ xžêẵ vÍjĐâ”v ẵXq 7q) ẵ ẼƠv™ẵVqqWq8q /qj™tẵVWq 7q 3q‰Đ┾ ẼƠjẼẵVq8q Wq8q +qjẵ qž™Ẽêjt‰qẼ‰ž™ẵ C”Ẫž ẵVqWqXqẪjẼ‰Ẫ€vẪẵj,q /j(qq3jq VWXq 7q) ẵ ‰v

j +(q 7qVWX\jqe‰™qvẵj +(q/ẵ )ẵ xžêẵ j””ẵjqỈvẵ Ẫvvẵ ẼƠjẼẵVqWqrjêvẵ j””ẵ žxẵ ẼƠvẵ ẪjĐv Ẫ‰Ê™ ẵ j™tẵ ẼƠỀẪẵVqWqXqA)ẵ jẪẵVqqWqqXq7q/

[žỈẵ ẼƠvẵ ÊêjâƠẵEG7q j,q /j(qq3j VWXqƠjẪẵ ẪẼjẼ‰ž™jê¾ẵ ➉™ẼẪẵ jẼẵjq8q %qj™tẵjq8q +

j™tẵ qỀẼẪẵ ẼƠvẵ Ịj͉Ẫẵ jẼẵjq8q VWXqẪžẵ ẼƠjẼẵVq Aq g% qWBq %+qj™tẵXq Aq +g

N‰™j””¾ ẵ ‰xẵXqA-qẼƠv™ẵVWq8q X +(qA%qẪžẵ ẼƠjẼẵVWqWYqVXqA%qq-Wqq%#W qFỀẼ

jqq%#jq‰Ẫẵ ‰™qêvjẪ‰™Êẵ xžêẵjqAq %qgqfƠỀẪẵ%qq-Wqq%#WqA3qjẵ qž™Ẽêjt‰qẼ‰ž™

.63@?5G B@=DC8@?G CẪẵ ‰™ẵ ẼƠvẵ €êẪẼẵ Ẫž”ỀẼ‰ž™ ẵVqWqj™tẵXqẪjẼ‰Ẫx¾ẵ ẼƠvẵ vđỀjẼ‰ž™ẵj,q /j(q 3j VWXq8q) ẵ žêẵjj +(q 7q VWXq eỀnẪẼ‰ẼỀẼvẵjq 7q XqẼžẵ ÊvẼẵXX +(q 7q VWXqžê

X +(q 7q VWq[žỈ ẵ jẪẪỀĐvẵXqG-qfƠ‰Ẫẵ ‰Đ┉vẪẵ ẼƠjẼẵVWq0ẵ + ẵ ỈƠ‰qƠẵ ‰™ẵ ẼỀê™ẵ ‰Đ┉vẪ

V qWqA )qả‰jẵ CZOZẵ fƠỀẪẵXqA -qjẵ qž™Ẽêjt‰qẼ‰ž™ẵ Pv™qvẵXqA -q hvẵ ÊvẼ

VWX8q XX +(qA-q XqA)qẪ‰™qvẵVqWqqXq7q /

Nžêẵ ẼƠvẵ vđỀjẼ‰ž™ẵZjq 7q VWXqỈƠvêvẵVWXqA-qZNq 7q) ẵZ%q 7q -q‰Đ┉vẪẵ ž™vẵ ꞞẼ nvẼỈvv™ẵ )ẵ j™tẵ%q Z%q -qZ+q 7q)ẵ ‰Đ┉vẪẵ ž™vẵ ꞞẼẵ nvẼỈvv™ẵ%qj™tẵ+q Z+q8q)

Zq-q-q‰Đ┉vẪẵ ž™vẵ ꞞẼẵ nvẼỈvv™ẵ+qj™tẵ-

H0 VvẼẵs’aẵ nvẵjẵâj‰êẵžxẵ™v‰ÊƠnžỀêẪẵeỀââžẪvẵs’ƠjẪẵ`q™v‰ÊƠnžỀêẪẵỈƠžẵjêvẵ™žẼẵ™v‰ÊƠnžỀêẪ žxẵ aẵ j™tẵ aẵ ƠjẪẵ9G™v‰ÊƠnžỀêẪẵ ỈƠžẵ jêvẵ ™žẼẵ ™v‰ÊƠẼnžỀêẪẵ žxẵs’Ỉ‰ẼƠẵaqG 7G fƠv™ẵ n¾ Оả‰™Êẵs’Ẽžẵ jẵ ➉™Ẽẵ ảvê¾ẵ q”žẪvẵ Ẽžẵ aẵ ẼƠvẵ ™ỀĐnvêẵ žxẵ ™v‰ÊƠnžỀꉙÊẵ âj‰êẪẵ tžvẪẵ ™žẼ ‰™qêvjẪvẵ j™tẵ ẼƠvẵ ẪvẼẵ žxẵ ™v‰ÊƠnžỀêẪẵ žxẵs’j™tẵ aẵ qž‰™q‰tvẵ gƠỀẪẵ n¾ẵ êvâvjẼ‰™Êẵ ẼƠ‰Ẫ âêžqvtỀêv ẵ Ỉvẵ Ẫvvẵ ẼƠjẼẵ ẼƠvẵ Љ™‰ĐỀĐẵ ‰Ẫẵ jẼẼj‰™vtẵ ỈƠv™ẵ ẼƠvẵ ➉™ẼẪẵ jêvẵ t‰ả‰tvtẵ ‰™Ẽž

4A q”ỀẪẼvêẪ ẵ 4A G +. qẪỀqƠẵ ẼƠjẼẵ ẼỈžẵ ➉™ẼẪẵ jêvẵ ™v‰ÊƠnžỀêẪẵ ‰|ẵ ẼƠv¾ẵ jêvẵ ‰™ẵ ẼƠvẵ ẪjĐv q”ỀẪẼvêẵ fƠỀẪ ẵ ‰xÃÀẵ ‰Ẫẵ ẼƠvẵ ™ỀĐnvêẵ žxẵ ➉™ẼẪẵ ‰™ẵq”ỀẪẼvêẵ8GẼƠv™

fƠvẵ ”jẪẼẵ ‰™vđỀj”‰Ẽ¾ẵ xž””žỈẪẵ xêžĐẵ ẼƠvẵ xž””žỈ‰™Ê5ẵ Rxẵ ẼƠvẵ ”jêÊvẪẼẵ žxẵ ẼƠvẵËẵẪ ẵ Ẫj¾ẵVq‰Ẫ

A.2 qẼƠv™ẵ ẼƠvẵ ẪĐj””vẪẼ ẵ Ẫj¾ẵWq‰Ẫẵ Aẵ.1qj™tẵâêq(*G aK}êq%*ỈƠ‰qƠẵ qj™ nvẵ âêžảvtẵ n¾ẵ t‰êvqẼẵ qžĐâỀẼjẼ‰ž™ẵ gƠ‰Ẫẵ Љ™‰ĐỀĐẵ ‰Ẫẵ jẼẼj‰™vtẵ ỈƠv™ẵ ẼƠvêvẵ jêvẵ 13ẵ q”ỀẪẼvêẪ ẵ).qỈ‰ẼƠẵ.1q➉™ẼẪẵ j™tẵ ,)ẵ Ỉ‰ẼƠẵ.2q➉™ẼẪẵ

Một phần của tài liệu Đề thi toán singapore SMO từ năm 2005 đến năm 2013 (Trang 37 - 41)

Tải bản đầy đủ (PDF)

(41 trang)