bộ đề học sinh giỏi toán 7

1234567689
76
7
75

!"#$%&'()"(*+",-.

/01235


1234567689
76
7
75

9:;<=;>?@

ABCDEFGCHICJKLELEMLKLNO EPLJFDEQRSTUVHWXCYZ
[\DZE]DEL^D_`]HabLLcD_HdD_HeDHPLOcZLKLEZfLELgLh
ijDLkDEHeLlD_LeDEmD_QnFEoFZEpO DEmD_HGZEF`]DEmD_
HICJKLEQRSqhrsLKLNO LeHabLDEmD_D_CdDZ]FQFtC[ufLE
LEM`FtLZEBO vE\M`]ZgEPLLwBOxDEhyEzD_Z^FZF{SZ|LJMkD
ZE\M }C~sDJKLErGZEFEPLJFDE_FoFZMKDq€Hs_FzSNO ExDE
CD_HabLDEmD_[]FZMKDEB~`]DEmD_HGZEFLeLEYZQabD_LwB
ZMKDqh
‚C~sDJKLED]~[BM_dO E]D_QMkZDEmD_HGZEFORFDEYZ
O]LEzD_Z^FLƒSDEƒZHabLZ„DEFGCD_CdDZ…jDZM]D}C†Lh‡fDE
SEu[F{DLwBDeDˆO ‰LEuLYCZ…zLHBkD_ŠSE‹D[uDEmD_
QCdD_vF{DZEŒLD‹D_LBMDEaD_DeHabLX‹~gD_Z„DEmD_vF{D
ZEŒLZMKDLJ‰hŽMHeŠZ…MD_vEF_F\F}C~{ZDEmD_HGZMKDHe
LEzD_Z^FL†_D_D_DEmD_vF{DZEŒLSEEbS`RFZ…xDEHcLwB

LKLNO QRSqŠZ„HeSEKZZ…FsDQIDQIDHsLKLNO LeHabLDEmD_
vF{DZEŒLD‹D_LBMEDh‡„HeLeZEsZF{SZECHabLDEmD_[]F
ZMKDOBD_ZfDELEYZZaC~Z…„CZabD_h
rs EPLZ†Z}C~sD JKLE D]~ŠZKL_F\ vEC~jD [kD DjD Le
DEmD_vF{DZEŒLL[\DLwBQRS‘`]QRSqHsZ„HeQ’DEEcFHabL
Z†ZEDhABCHeLeZEsZEBO vE\MEaRD_“D_F\F‰Z…MD_HGh
‚C~sDJKLEHabL…BHnFZ…jDZFDEZEID_FzSLEMLKLNO ZgEPLh
ŽMHeZ…MD_O”FHG[]FŠLEzD_Z^FHW[†Z…fD_B~SEIDEaRD_“D
_F\FhrFGCD]~_FzSLKLNOLeHabLDEmD_vF{DZEŒLZEfLEEbS`]
[F{ZHabLDEmD_SEIDLlD_DEaH†FLEF{CQkFDEmD_[]FLKLNO
HWQ]Oh
ŽMH‹~Q]OcZZ…MD_DEmD_Z]FQFtCSEKZZ…FsDHICZB~h•jD
ZKL_F\…YZOMD_DEƒDHabLJgSE\DEdFZfLELgLZ„SEfBHcL_F\h
–PF Jg HeD_ _eS XFD }C— `˜ _™F `G H˜B LEš NOBFQ›
}CMLZCBDJSœ_OBFQhLMOMžLLKL[kDLeZEsOCB[\DZ…gLZC~{D
D]~ZENMJ†HFtDZEMkF›ŸVŸh ‘qh¡¢£¢
!"#$%&'()"(*+",-.

/01235


1234567689
76
7
75

žjŸ
89:;<>?@ABCD
EFGHIJKLMNOPQRQFSTU

VW[X[Y[Z\W[VX[Y[Z\W[X[VY[Z\W[X[Y[VZ
W
X
Y
Z
]^_R`aKbcO`dTKFefUgh YW[[ZX[ZX[[YW[YW[[ZX[ZX[[YW

89:?<>;@ABCDi
EFGj h WXY[XYW[YWXk
EFeQR_`QFbPQRjlFmQRnFo`pqMNfFrQFnFstQRk
89:u<>?@ABCD
gvKmKmfFwJKxyz{Q|}~`}QKNf€l_‚Fƒf„QRp…fz†
_vK ‡ˆ_aJfFwJKx|z{Qy}~`}QKNf‰Šl_‚Fk|`{KlFGoQR
fafFy|pq‰Šl_ }qgpqKbTQRz`d_ f‹Sy|kŒ`MSTlF`lFŽ`
FqQFOSGpTKF^mKmfafFg_vKlFGoQROPQR‚‘lFGoQRfafFKx
‡ˆ_aJz{Qgk
89:’<>?@ABCD
EFGKS_R`afy|Eƒ“pqz`d_QP_KbGQRKS_R`afk
” \•™[”
SkEFeQR_`QFbPQRU–—˜
™–—[”
™˜—
™–—[”
™˜—\›ššœ•™V }qK`S|“pqK`SnFQR`aff‹SR†f
Ok|`{K”
|kEFeQR_`QFbPQRU]`SE“pqK`SnFQR`aff‹SR†fEk
!"#$%&'()"(*+",-.

/01235

1234567689
76
7
75

789;<=>?;@ABCDE
GHIJKLMNOPHQNOPRINOKSTHUNOVSWKLMNOPHQNONXI
YINOYINOZGH[NO\]NHR^NO_`PNHaPVbNOVSWKLMNOPHQNO\X
OSVNHcNO]deVHfNOTHUNONHgHhNWiiZ
789j<=>?;@ABCDE
kH]VHh]VlNOmenPHeopqO]rIsVINYfVYtVnPeO]rIVuHe]
VINYfVYtVVvNO\wPxfVPHqK]y\PHazNHaPxXWnVeINHaPxXsWZ
VlVK]y\THlVxX{|}|~|ssZoxzuNOPNYpTHuNNO
aPH]N\]xI]K]y\NS]PRN`NHPNaPVe\]xI]K]y\
KSZ
P

ÔÔàảàãáạs

789><]PYKVHIKPK]sPeKLV_
ĂÂĂ
ĂĂĂ
ÊÔeVƠƯi PHq eÂÂVÂƠxfVKSÂ
ssssÂ}
Ă ăâê
ô
ơ
ÊÔeVƠÂi PHq ơươĂĂăăââêê
ơ

đ Ă ăâê

kH]KSPeVS_ÂsÊsÊsÊsÊÂ }Z
!"#$%&'()"(*+",-.

/01235


1234567689
76
7
75

:;<>?@ACDEFGHIJFK

T X MNOOUYNOVYWPYMNOOVYNOWYUPYMNOOWYNOUYVP
TXNNNMUYVYWP
TX QRSQMUYVYWP
Z[\]A^E^C_`aHbHA^E^C eaf

dc

ghijklCmeneaopq
rbHemA^E^CodeapstjkuHvikwxyz{Ck|Hk}k~Hvf
:;HAHv~HvyF`a\fF
8
HvI~HvuiuylIIFxy 7
tqt`f@HvCHvqikFvFAHik[HvI~HvixikHFH
i{CIDTNN XT XmiCk|HkxyikFvFAHCHi[of

UƯMROƯP
U XROXQ
ip RÔOĂƯUXROÂƯOUÊXĂÂNOQƯOUXROÂƯOUXMĂÂOƯP
NQOƯÂO
ƠO
ZzAjkFjkĐFkyHkevFik[uiuClCkgăijkHvEâHvqê`
jkHvClCkiôlIGHgf
:;<ơ?
A@FAưđCiiFf
^iđCDảàãá xyvDCHvyFHbHảàãá p ảạNYằN
^iưCDvDCqxyvDCHvyFHbH ằNXạẳYáạN
Z ảàãá pạẳYáạN^ảạN
!"#$%&'()"(*+",-.

/01235

9


1234567689
76
7
75

â
ơ
ê

= G@??H>B
89:;< =

BCDFBED
A

ư

ô

IJKC=DE L >BF@??H>BAG@??F>AB

MNOPQRSTUV

X Y

BFC>]
?F>
EWAGZ[??H D>FCWA GZ[??H\
@
?
^
_
^
` A A_
a
?
>
>
>
>
EWAG@??HBFACG@??HZ[?AHEGEA

bpqrtu
vwcxfyzRO<{|o}xklOJklxTJoxklOJklJklTUxfyz OdklTJlfeJefxklOJklOdklxklOJklxTJoIklx
TnelUTxkJRgh xUOkJwOTUlUTJklkJJk
VL9OxUlUTkJĂklfeTJÂklJklkJJko
pqrÊu
IklxfyzlJfÔJefzƠOOdƯkTneJefTkÂTĐTTUOJyghV
Lă
!"#$%&'()"(*+",-.

/01235


1234567689
76
7
75

79:;<9<;:
=9:;79<;<97;:
>9:;=9<;797;<9=;:?
@9:;>9<;=97;79=;<9>;:
A9:;@9<;>97;=9=;79>;<9B@;:
C9<;@97;>9=;=9>;79@;<
D97;@9=;>9>;=9@;7
:E9=;@9>;>9@;=

::9>;@9@;>
:<9@;@?
FGHIKLMNO P Q R S T U V W XY XX XP
Z[\KLM\O X P Q R S T S R Q P X
Z[\K]^_M`OPaVb SaTb VaQb XXaXb XQaWb XTaUb XQaWb XXaXb VaQb SaTb PaVb
cdefghijklmnAopqrstudvkwklxvhyzkd{ii|p:@}A~
BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB€iBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB

œžŸ<
‚ƒ…† ‡ˆrs‰smnz}Š}sŠp€iy‹klŒzŠ9sŠs9=zzs9DŠ
‚ƒŽ† ‡ˆrmnklhkxid‘vr’kŒ
z}“>xB7“”<
Š}“7x;:“•=
s}“=Bx“;‚ƒ–†‡ˆrlp‰iy—kd˜kd{is™zŠpqidšsŒ ›9“x“;“CBx“
!"#$%&'()"(*+",-.

/01235


1234567689
76
7
75

789;<>?@ABCDEFGHIHHIJJIKKKIGLHMJNOK
PQDRASDEFTMHHIUHIKKKIHLH

789V<WRXAYZE?[\]>W^AB_DEA_`@D]aKbc?defAB_DEg?hZ
\iYgXjDARkDE]a^>d\lA\jDR]WAj?mK

YKWRnDEZ?DR]WMJ]m
oKWRnDEZ?DRdmMGpU>m
qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqr@Aqqqqqqqqqqqqqqqqqqqqqqqqqqqqq

r‘tbm’tbd“d

789sI^t@_Z~AABXDE\[\€Y^o^\oCDELARH€\‚Dej?\ƒDE
oCDEL
I^t@_ \„J€Y^o^\…R[\LAR\R?YHw@\RXYo\AYgyz\
Yo\MJ}
I^PvYo\MJ}wfYoM\AYgyz\\HMJ}D†D\M}‡\Mq}
I^PvYo\MJ}wfo\MUYAYgyz\UYHMJ}D†DYMJ‡YMqJ
I^PvYo\MJ}wfYoMˆoAYgyz\ˆoHMJ}D†DoMH‡oMqH
q^t@_\M}ARYwfo\‰DEŠx_D†DYMJ^oMHRX‹\YMqJ^oMqH
q^t@_\Mq}ARYwfoAB[?Šx_D†DYMJoMqHRX‹\YMqJoMH
PŒZej?\ŒOo~€{Y^o^\|ARXZDof?AX[D
{L^L^L|‡{J^H^}|‡{qJ^qH^}|‡{J^qH^q}|‡{qJ^HKq}|
789Ž
YK{Gg|PY\Œo?@DgS?F
!"#$%&'()"(*+",-.

/01235


1234567689
76
7
75

89:;<8=>
@ABCDE;>=9:;<=>FGH9IJ
FGH9IJ
K L K MN9=:=M
OPFMIJQDRSOTUVIWTE
8<:XM8YZ[Y<:XMYZ\]^R<:XM=;Z FGH9IJ
_`UA<:XMYZ[Y:YM
_`UA<:XM=;Z[Y:=;9N<
abB:YM\]^R:=;9N<
FGH9IJ
RPFMIJQDRSOTUVIWTE
8Z;:8X>:[< FMJ
_Z;:cG[Y:dZ FGH>9IJ
FMJ=[YZ;:X>:[<[Y:[;MFe\]fghVIiJFGH>9IJ
_Z;:=G[Y:YZ FGH>9IJ
FMJ=[Y:;ZX>:[<=[Y:[jN<Fk]lTJFGH>9IJ
mnopqFMIJrstuVv8DXO8d8D8X8O8
QDRSOTUVIWTE
w[8:8X8x;:8c8:Xx;:8[x
yTVw[x=[Y:Fx;:JcGFGH>9IJ
_|{z€}c€~c~[YGd:dxFGH>9IJ

_|{z€}d€~d~[Y |{z€€dc~ i\Vve\]hghVFGH>9IJ
abBgTVw[xi\TGd:dxFGH>9IJ
mno‚qQDRSOTUVIWTE
!"#$%&'()"(*+",-.

/012356

1234567689
76
7
75

BC879:;D8797;D999D879:=;7
B C79:D797 D99979
D 7:=7
7
BC78:D7 D999:
D =;
BC779>?@
BC:@A=
7
7
77 7 7
7 7 7

FGHIJKLMN
PQRSTUVSQWXYZ[\]^
‹

Œ






Ž

_`VabcdefST]VgUPhdeiST
dXUTVjklPhkmnabc]opST
defSTqrSQ
sfteXWnauulhYv[w\]^
xeiSTdXUTVjknyakmzbc
defST]VgUk{Xk|SQynYTd^
UczhuunaYTd^

}~ShbcdefST]VgUk{Xya
sfteXWyhhaYZ^Yv[\]^
€rabcdefST]VgUk{XhP S~S haaPYw^Yv[\]^
sijSQYZ^‚cYw^dX]oƒkWyhhaaP
x„]…tfteXWyP†yhYv[w\]^
q‡YZ]^xeiSTdXUTVjknya[zhbc]opSTdefSTqrSQYdQˆiX^
hi]mdXkm]oƒkzh:7naYZ^Yv[w\]^
xeiSTdXUTVjklPh‰nabcŠopSTdefSTqrSQ
!"#$%&'()"(*+",-.

/012355


1234567689
76
7
75

89:<=>?:@>ABCDEFGHIJKILMNOK
PQRS:TIUKVWIJK<=>?:@OXY>ZHDE[ GHILMJNOK
\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\]^<\\\\\\\\\\\\\\\\\\\\\\\\\\\\\

˜™Pš›
`abcdefgh iTQj mn omlokl p
}
iTq:@rs:Ttu:@j {yzmn||lm||klxvwoknp
`abfd ecghd~r€s^`ab‚defghd~r „…ƒ O† s†‡<Tq> €…ˆVW<r@sS=Kp €D „„Š|}Fp
Kp€D E„Š|F}„p
`ab‹defghd~rŒMs^=K „Š} DNp
Kp IŒJKJDŽUp
>KpNŒNŒJDNL
`abde‚ghdiTQ‘ €GiV‡’:@>“:<”s€M~tQ:@OAC…GiMG]–€CMi—–€CMI]M—…€CKpiTq:@rs:T‘
B]—V‡’:@>“:p
\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\]^<\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
!"#$%&'()"(*+",-.

/012356


1234567689
76
7
75

˜™ši›œi›žŸž

9:;=> ?@AB GECGFCDFHDEC IJK

?@LMNAB GEHGFHDFHGEOOFGOOEFCIPK

\
E
G
F
O
O
X
[
?QIJKRSIPKTU YZGOFODVWHDE]

9:;^>?@AB_N`abcNd
eT GOEFHEOFGHFOGE]T hfEEOOGGOOFFg]
i`j@k_kAlmTUeT nh]
i`j @k_kATm TU eToJ]
9:;p> @K]eTJk srqh bteuvwxyzoPLS{|AA}@~]
?Qb€w@ABdzPTI‚Jƒ‚~K
„ zT… TU eT†
„ zT‡ TU eTP
„ zTJ TU eToˆ „ zTo… TU eTm
_K eT s‰O\ oP bteuvwxyzk…LS{|AA}@‡]
TUzk…TI‚Jƒ‚‡K
„ zToP TU eT~
„ zTˆ TU eToJ
„ zToˆ TU eToŠ
„ zToJm TU eTo…]
9:;‹>ŒxN@w{Žax‘RSN’NA“A‘x{”awyaxaS€w@b{A
@K] zT • x–—AoP
!"#$%&'()"(*+",-.

/012356


1234567689
76