30 ĐỀ ÔN THI CẤP TỐC VÀO LỚP 10
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Đề 1
A B= + − − = −
− +
!"#$%
&
'&()* &
+
,&
(-)*
.!"#$%&
''&(')*/012
34/!"#$%56,71,
8$.$"9:!)/%2;<="#>?!"#$%@
.56="#
*A"B!.$1.C3;=D$"96/
EDC/0F!GH$"98AIA.AJ=D4$J**;&KL
1;0.M/5N":O<KM$6P!L=4.1.
Q<RNS0N! $J<;F .TL.NU$AV
0F!GH5.<
+/."9$SW71W
X
5YTEZN
H/[..W\$<"9$SW
X
71W
X
\$<"9
$SWK"92WW
X
ZH[NA/Z"9$SW
X
N.
01]012&^[_W
X
$\H01L!;L^W/71H7Q5[]
8$<NH0?;`..H`)H]a`Tb"9c7Q
57FWZWNd/ZH]Ne01.^H71[]
HAW
X
e/H`dW01ML!
8HAd01%%fg%.
= 8E=6E!h^%W71%$SW
X
i.TE
Đề 2
[1/
I.
71
+
A
+ −
= −
− +
[1/*.6!"#$%
x y m
x y
+ = −
− =
012
6!"#$%7F)
8%656&;V@&
(;
)
[1/*Gải bài toán bằng cách lập phương trình hoặc hệ phương trình:
jM"9&iN!kHL[+Tdk[$B7lH"9
5m<7P2+Tn.7F0/7%7P;97lE#9*
!8E7P2&iN!TkHL[
[1+/."9$SW/=;[24[o71H=
M$<0F[..H[55"9.[`71
e^H[ZBA
$\H`AeML!
p
·
*
q*BAC =
/@;ET. kWLN[i.
$\"9cTr_H717Q57F`e0Q_
M24
=s5
·
ABD
ZeNj/ZHNss5
·
ACE
Z[`
Nt/ZH[Na8jtsa01%%f8N.f
[1/*.s)
q + - qxy x y x x y y− + + − + + +
s0Q="#7F$4&;
R∈
Đề 3
[13,0 điểm
H)
u −+
!"#
$%&
,+&')*
6!"#$%
−=+
=−
+
yx
yx
[11,5 điểm.s$.0s;)&
71"9c=;)&'
vgbs$.0s
v8%? $4^a"9c=71!$.0sTQ5
[11,5 điểmAQQY0TB11!2HL1!2[
**T7F7P2TQwgP2QQ0F#7P2QQ?
*Tn<QQL[$"FQQ?*!8E7P2^RQQ
$<
[1+3,5 điểm8$<"9$SW/.$"F/7b=;H[24TQ
=_WKj?Tx$<[H..j\.1"9$SW/kjTr
L!;Lj71j`7F"9$SW//`01L!
vWj`ML!
vj
)jHj[
vA01$=.NH[/]01.^`71WA
]0124Tj;w
[10,5 điểm.71012V@c
'
',-,-,
ab
'G)*
OP!!"#$%P5671
Đề 4
(2,0 điểm). 1) !"#$%
nG&
'&()* n&
+
'u&
(-)*
gF$41.1.^%J4^12;)&'u(71;)
&''ZNM$<$yf
(2,0 điểm) 1)
H
= +
+ +
.
*/
B x x
x
x x x
= + + − > ≠
÷ ÷
−
+ −
[ 8%^^&[)
(1,5 điểm). .6!"#$%
y x m
x y m
− = +
− = −
6!"#$%T)
8%$4^6!"#$%56&;..
s)&
';
N$4V?
+(3,5 điểm) .H[55ML!"9$SWA
"9.[`71e^H[ZNAK"9c[`Z
"9$SWNs"9ceZ"9$SWN<a
$\
[e`01ML! AaA)AsA[
K"9c`e..7F"9csa
=K"9cWH01"9$$D^.Ncs
/*.&/;/z012DY;{&
';
'z
(;z(+&(
;
≥
,u
Đề 5
/l
8E
u +-− +
8E $4
( ) ( )
* *A = − +
/l.12;)(&('
gbJ4=^12T) 8%$4^J41
2JL
l 6!"#$%
x y
x y
+ =
− =
+/l
s"#$%&
(&()*56&
/&
8E$43)&
&
'&
&
'
jM!S!=D45*"9=D!/"T!5q*"9
=D<! T<<=@;L/R=@;! T<<ML|%7k^
8E2=@;L=D40h[L$\2=@;L0h$.!Sl#
*=@;L712L$<R=@;01\
l.H[7QNH/"9.HA8E7
H[L
H)A)
q/l.p"9$SW"9TEH[gbL!;LH&/[;
7F"9$SWO?;e$<p"9$S/_e7bL!;L7F"9$S
ZH&N`Z[;N
WH`eML!":"9$S
t2HZ[`N]e]..7FH`
Đề 6
/*
H -= +
( )
[ ' ,
, ,
=
÷
÷
7F
*/ */a b a b> > ≠
6!"#$%
&';)G
&,;)+
/*
.!"#$%
& ,, '+)*
/$.5012
7F!"#$%0Q56!6
&
/&
016^!"#$%8%
& '& *=
.12;)&'/$.5012
8%J412_H+gF$47k%":/
12JL;4L$<f
8%J412..7F"9c=5!"#$%
&';')*
/jM"9&iN!k4HL4[=1*Td
":$B0Nk[7lH"95m7P2<Tn<97lE#
901*!8E7P2^"9&iN!0kHL[
+/."9$SW/TE8kH<.1"9
$S/TrL!;LH[/H7F"9$S[/01L!8k[/Tr"9
c..7FHZ"9$SN``T[t2H`Z"9$SW
N01dt2[dZHN}
H[WML!"9$S
$\}
)}d}[
.
·
*
[H q*=
H/W/`c1
/*.2&/;/zV@
[ ]
&/;/z
&';'z
∈ −
=
$\
& '; 'z ≤
Đề 7
[1 6!"#$%
u
-
x y
x y
− =
+ =
.12;)&'8%71L$\J4^12@..
.7F"9c;),&'71_j
[1.!"#$%
+ *x m x m+ + + − =
012
!"#$%T),
$\!"#$%0Q56!67F
8%..!"#$%@.5<&
/&
V@6
*x x x x
+ + =
[1
jM ?%|P5l=1#l$Mq71%!"#M
=1"9>.?!0h78E=6E%|P
[1+."9$SW/7b=;[TQ_8$<2
^[0?;j?T%K"9c_jZ"9W0h0":N
t71st\|j71s..Wm<$.5sj8$<
Vts0?;H..Ht\HsA=;H[/HZts0h
0":N`71e
[`eML!
j[j)jtjs
[TEWHZtsNd
MK MB MC
>
[18%$4V?^
*x x
A
x
− +
=
7F&
≠
*
Đề 8
/.12
y f x x x= = + −
8E
f x
T
* x x= =
8%
x
L
f x f x= − = −
?!"#$%
+ qx x− > −
/.12P?
( )
( y m x m= + +
=
8%m12JL
8%mJ412=..7FJ412
y x= −
.6!"#$%
+ = −
− =
x y m
x y
8%$4^
m
656
( )
x y
..
+
x y
y
− −
=
+
/*A"9:_>#MQ1tLY01$.q
1;%&.Q76A"901Y$.1;%"9?
":;01Q76T/"901M%$.+/1;2
1;$"~|%.11Q76AVL01$<%R"9.11
Q765$..0
+/*."9$SW5"9TEH[71`7Q5
7F8$<.NcHW0?;jjTH71W8jZ"9$S
WN01tdrL!;L7F"9$SWNt8L!;L
1;Z"9c7Q57FH[NjBs
Wjts01ML!
tnnWs
d
Hj HW
=
8ETE^"9$S.NL!Wjt
i.
/*.2
/ /x y z
. @
* / / x y z< ≤
71
x y z+ + =
8%$4
V?^H)
x y z
z x y
− − −
+ +
Đề 9
(2,5 điểm)
( )
+qG +=A
? !"# $% &,
*o*
6!"#$%
=−
=+
yx
yx
(2,0 điểm)
!"#$%&
,&')*
8%$42!"#$%&
(,&',)*5
<!6&
&
V@lT6&
,&
)+
(1,5 điểm) jM"9&iN!kHL[7F7P2TQwdk[
LH"95m7P2<Tn.7F0/7%7P;97lE#
9*!E7P20kHL[/L_@"9H[=1*T
+(3,0 điểm) ."9$SW/j\.1WTrL!;LjHj[
7FWH[01L!drj&\|jW71jH71ZWN`}
01$`"9cW}Z"9cH[Nt pA01.^
H[71jW
jt}AML!"9$S
$\W}AJ=N7FWjt/k5;$
W}Wt)
•pWj)/jH[l
(1,0 điểm). . &/ ; 01 2 D V @ l T6
xxyyyx
−−=−−
8%$4V?^
-
+−−+= yyxyxS
Đề 10
[1*.
H)
+ **+ −
[)
−
−
+ −
[1
6!"#$%
& ;
& -; G
− =
+ =
.!"#$%P&
(&'()*
!"#$%T)+
8%!"#$%56&
&
V@
*
x x
x x
+
+ =
[1.12;)
+
&
gbJ4s^125
3471"9c=;)&'Z$yN5
M\,71ZJ4s5$<N5.1M\
[1++*.p"9$SW/"9TEH[01
E|^H[8$<2^[0?;`..`)[W`
ZHNj8kH/TrHA7Q57FW`AMW`HAZ`[Nt71
Zp"9$SW/Ne
jtA01ML!71W`..7Fe[
d01.^e71W`
CKD CEB
∆ = ∆
/I;$01
$^de
eAd7Q71jtnnH[
+8Ei.=6E%$S.NL!jtA
Đề 11
[12,0 điểm.
x
A
x
x x
−
= − −
−
+ −
7F
*/ x x≥ ≠
H 8E$4^HT&)
−
[12,0 điểm.6!"#$%
q
+ =
= −
mx 2y 18
x - y
012
8%6!"#$%56&;$.5&)
8%6!"#$%56=;?&;. @&';)G
[12,0 điểm8$.U!cMW&;/.!$.0s;)&
71"9
c=;)&'012
gb!$.0s $\=0Q ZsN
!6
x x
01.1M.^s71=/%&
'&
)
[1+3,5 điểm."9$SW/"9TEH[)Km$<2
^[H..[)K`M"9$SW..[`)K"9
c7Q57F[NZH`Nj
$\
8[j`01ML! H[H)H`Hj
`01L!;L^"9$SW
K"9$SWH[j1!h/E=6E!h
H[j\.1"9$SWi.
[10,5 điểm.//012TQ. @'')**q
$\
*
*
*
*
≤
−
++
−
++
−
+
ba
c
ac
b
cb
a
Đề 12
[1/*
H)
( )
+ −
[ )
− +
+ −
[L$\J4^12;)&,+_j8%
[1/*
!"#$%
*x x− + =
+
*x x+ =
.!"#$%
*x m x m− + + − =
7F&01€2
$\!"#$%0Q56!67F
6^!"#$%01&
/&
/Ei.$4^e)
( )
x m x m+ + + −
[1 1.\0P!6!"#$%t1j5M
7"9$J$Z! g"9":1l02R02Y
$JM2;Z! jE$\Lm<u02$"R02
$JE;%2;.17"9EG;/L 02"R
02$Jm<;%2$.17"9bm<;AV7"91
j$J.<;Z! f
[1+/*."9$SW"9TEH[71M24$<
TEWHTH71W/j=M$<"9$SjTH/[a
jTr"9c7Q57Fj/"9c1;ZL!;LNH71[
^"9$SW0h0":N`71e
Hj`71[je01ML!
`
⊥
e
8%74$E^j=6EH`e[V?
/*8%M2D&/;/z. @
( )
G q * *q
x y z x y z− + − + − + = + +
Đề 13
[1/*TQ":=Y;E
,8D6!>!E
( )
u +- − +
, 8$y m B •
+
− + −
[1/
, !"#$%&
(&()*
,.6!"#$%012
& , ; )
,& ' ; )
6!"#$%T)
8%$4^6!"#$%56=;?
[1/*8$<YMU!cM/.!$.0s;)
2
x
2
71"9
c=
y x= − +
[\!>!E/@;%M.^s71=
8%"9c=X;)&(L!&7F!$.0s
[1+ /."9$SW$71"9TEH[/`7Q57F
8$<V`[/0?;ttT[71`j01.^t71
H[
,W`tj01ML!
,Htj[)Hjt
,.`t)$e01.^Ht71`8Ei.$M=1.N
e`/e
Đề 14
( 2 điểm) .s"#$%&
,,&()*2
!"#$%T)
&
&
01
6^!"9$%8%
+x x+ =
( 2 điểm).
x
Q
x x x
= −
− −
7F&‚*71
x
≠
8a 8%$4^
x R
∈
..
G
x >
71a5$4
;<
(1,5điểm)."9c0
/0
/0
/ / l y x l y x l y mx= − = = +
8M.[^"9c0
710
8%"9c0
/0
/0
w_;
+ (1 điểm) .&/;2="#71
x y
+ =
?c
x y x y+ = − + −
( 3,5 điểm)."9$SW/"9TEjt71=;sa7Q5
7Fjt8N}Tj/t$<Vts0?;ƒTt/st2j7FƒZ
saNA
jƒ01!^5
sƒa∠
A}tƒML!
.^st7Fjƒ01ƒa7Fjt01ddnnsa
= 01"9$SML!
PKJV
Đề 15
[1H)
+ +
a a a
a
− +
−
/7F‚./
[1dQ=Y;Eh;/@; !"#$%G&
,q&,).
[1dQ=Y;Eh;/@; 6!"#$%
*& ;
*& *; *
− =
+ =
[1+.12P?;)„&)*&'*.&$4?T%&
/&
..&
o&
A@;„&
o„&
A12JL;4L$<f
[1aJ4^12;),*/u&
/@;.LT&mk,L+%
$4V?71$40F?^;01.<f
[1qA@;Z!&L!…20":i.Dm=h/ Ef
.+u
*
/u-
*
/.+
*
/+u
*
/.-u
*
[1u.55\+
*
K"9.MNTl7F551
!h*718EN0F$.NS0N
[1-."9$SWTEWH71"9$S"9TEWH
3474$E"#2^"9$S
`;H`^"9$S0FZ"9$SVN$\
H)`
[1G.H/[//01$<M"9$SH01L!;L^"9$SN
H"9c..7FHZH[Nj71ZHNt
$\H[Hj)HHt
Đề 16
8E$^H)
25 9+
[)
2
( 5 1) 5− −
s)
2
1
:
x y xy
x y x y
+ +
+ −
gF&‚*/;‚*71&
≠
;
8E$4^sN&)*71;)*
gb$<YM6$yM/J4^12;)&
71;)
&(8EM.^J%$<
8EM=1N^%|P/Ll=1#l
$M71M=1R"9>.^%|P01
8%!"#$&,
x
')*56!6
+."9$SW71H\.1"9$SgbL!
;LH[/H7F"9$S[/01|L!
H[W01ML!t<7bL!;LH[/H
[`01"9TE^"9$SW`nnHW
.HW)/ETE"9$SML!H[
8%2D<L'I)*/$.5I01w|
2^
Đề 17
/.
x 1 1 2
A : (x 0;x 1)
x 1
x 1 x x x 1
= + + > ≠
÷
÷
÷
−
− − +
H 8%$4^&..
Ho*
*/u 6!"#$%
2x y 2
1 2
x y 5
2 3
− = −
+ =
/ugbJ412s
2
1
y x
4
= −
8%"9c=;)&
'L!&7FJ4s
+*.!"#$%
2
x 2(m 1)x m 4 0 (1)− + + − =
012
!"#$%T)+
V$\/7F$4^!"#$%0Q56!
6
&
/&
016^!"#$%$\
1 2 2 1
B x (1 x ) x (1 x )= − + −
TQ!yM71.
*.p"9$SW"9TEH[71j?T%$<
p"9$S5jTH/[8$<pU!c9H[p"9$S
TrL!;LH&8[jZH&N}!^5}HjZp"9$S
Ne71Z[jN][eZHjNd
$\e]jd01ML!
[H]01
8[eZH&NA8HA]d01%%f
Đề 18
/*
8E
u ++ q−
8%$4^212P?;),&'JL
$<
/*
a a a
A
a a
+ −
= − × +
÷
÷
÷
+ −
/7F
≥
*
≠
6!"#$%
+
x y
x y
+ =
− = −
.!"#$%
+ *x x m− + + =
/7F0128%$4^
!"#$%56
/x x
. @
( )
+x x− =
/jM 7"9%|P5=6EG
[L0h
l$M0F#l=1-8ETE"F^%|P5
+.p"9$SW/"9TE[`0124
M.NcW`TW71`D"9c=7Q57F[N
`/Zp"9$SWNH8$<H0?;j?Txj
TH71/[jZ"9c=Nd/jZ"9c=N
eK"9c[eZp"9$SWNttT[
`teML!
/d71tc1
}01"9$S.NL![de$\}
0Q\$<M"9c24Tj;w
*/ . 2 D ="# &/ ; . @
( )
( )
+ + *x y xy x y x y x y x y+ − + + + − =
8%$4V?^j)&';
Đề 19
[1.12;),&(5J401"9c=
n8$.U!cMW&;@;7b"9c=
nA12;)&'5J401"9c=
X
8%71l
"9c=71=
X
..7F
[1 !"#$%716!"#$%
n&
'+&')* n
=
+ =
x - 2y 4
2x 3y 1
[1
nH)
( 32 3 18):2+
n[)
q q
− +
−
− +
[1++."9$SW71H..WH)8kH7b
L!;LH[/HLW7F[/01L!
n8E5HW[
n8kH7b;LHsaL"9$SW;LHsaTQ_
WA01$^sa[ZsaNd
n+W/A/[/HYMM"9$S
nHsHa)
n.WA)
R
/EM=1.NcAdi.
Đề 20
[1(2,0 điểm)."9c=;),&'71!$.0s;)&
gb=71s$<YM6$yM
[\J4@;&4M.^=71s
[1(2,0 điểm)
!"#$%&
(+&()*
6!"#$%
=+
−=−
+
yx
yx
[1(2,0 điểm).s)
+
-
x
xx
xx
−+
++
−
/7F&
≥
*
s
8%$4;<="#^&a)
P
P
−
P
$4;<
[1+(3,0 điểm).H[55[H)q*
*
/"9!$.^
5H[01[`71"9!$.^5H[01eZN}`
∈
H71e
∈
H[
He}`ML!":$.M"9$S
$\}`)}e
$\[H[e)[`[}
[1(1,0 điểm).%7QH[`aH7bM"9cZN
[Ne71Z"9c`N]$\
FA Α
+
Ε
=
ΑΒ
Đề 21
[1}(2,5 điểm).
& * &
H
&
& &
= − −
−
− +
gF
& */& ≥ ≠
H 8E$4^HT&)G
8%&
H
<
[1}}(2,5 điểm)Giải bài toán sau bằng cách lập phương trình hoặc hệ phương trình:
jMM&ii.TL.NBL+*?1$.M21;_;4`.R
1;M5B7":?<M@.11TL.NF#9
_;41;71B<":*?AVi.TL.NM&iB1L.
<1;f
[1}}}(1,0 điểm) .s$.0s
; &=
71"9c=
; & G= − +
8%.NM.^s$.0s71"9c=T)
8%"9c=Zs$.0sN\7l!E^
$y
[1}g(3,5 điểm)."9$SW/"9TEH[)=
71=
01
L!;L^"9$SWNH71[}01$^WH71e01
M"9$SWeTQ$Y7FH71[K"9c=_e
717Q57Fe}Z"9c=
71=
0h0":Nj/t
Hje}01ML!
et} e[}∠ = ∠
71
*
j}t G*∠ =
Hj[t)H}[}
+]01E|^H[TQe^"9$SW
A@;E=6E^j}ti.Te/}/]c1
[1 g (0,5 điểm) gF & ‚ */ % $4 V ? ^
j +& & *
+&
= − + +
Đề 22
[1/s)
(4 2 8 2). 2 8− + −
8%.NM.^J412
2
y x=
71
3 2y x= −
[1jMQ;7P lM2&i LT.1B?1
dLT.1%5&i4V<BL0":15/R&i! B
<*/?.7F=D4hAV0hQ;@lLT.1.
<&i[L$\T20":1BBR&i01"
[1/.6!"#$%
( 1) 3 1
2 5
m x my m
x y m
− − = −
− = +
6!"#$%7F)
8%
m
6!"#$%56=;?
( ; )x y
..
2 2
4x y− <
[1+."9$SWTE71M"9c=24/=71
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WAN}
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Tj;w$<=%E}H}[TQw
[18%$40F?^
2
4( 1) 3 2 1y x x x= − − + + −
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Đề 23
(2.0 điểm) 6!"#$%
& ; *
& ; *
− =
− + =
(1.5 điểm) .!"#$%&
(&'
()*&01€/012
!"#$%7F),
8%? $4^<!"#$%56!6
8% $4^!"#$%56&
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N
$4V?
(1.5 điểm) jM%|Ph5.7\**[L$\l
ml=1^%|P<*71ml$M<*%=6
E%|Phm0<**
8El=1/l$M^%
|Ph
+(2.0 điểm) .H[55/TQ01/H[o
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01]}01$^NH$\
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(2.0 điểm) .//012D="#V@lT6'')
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+ +
+ + +
Đề 24
[1/*
n !"#$%&'(&'+)*
n 6!"#$%&,
y
)
&';)
[1a)
q
−
−
−
+
−
−
[1.!"#$%&
(&(
)*012
n !"#$%T)*
n8%!"#$%56&
&
T*71Vl
T6&
)+&
[1+/jM%|P57\-71R"9>.^55
M=1*8%M=1N^%|P5
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n$\j`01"9!^5[j
n.H`)8E=6EH[`i.
nd01.^H[71j`/A01.^H`71
j
$\"9cHj/[`/AdJ_;
Đề 25
[1 !"#$%716!"#$%
*x x− − =
u
+ -
x y
x y
+ =
− = −
+
q *x x+ − =
=
*x x+ + − =
[1/
gbJ4s^12
y x= −
71"9c`
y x= − −
$<Y
M6$y.NM
8%.NM.^s71`B$<\!>!E
[1/8
+ +
A
− +
= +
+ −
- + -
+ +
x x x x x
B
x x x x
− + − +
= − +
− − + −
*/ qx x≥ ≠
[1+/.!"#$%
+ *x mx m− − − =
&01€2
$\!"#$%0Q0Q567F
&
/&
016^!"#$%8%H)
x x x x+ −
N$4V?
[1/."9$SW5W/"9TE[O?;MH
$<"9$SW..H[‚H8kH/7bHA7Q57F[AM
[8kA/7bAe7Q57FH[71A]7Q57FHeMH[/]M
H
$\HeA]01%|P71WH7Q57Fe]
K"9ce]Z"9$SWNs71ae\|s71]
Hs
)HeH[I;$HsA
}01.^d]71[}A
)}}`01
= `01.^sa71[d01.YH`71"9$S
WdTHHe]d01MML!
