tổng hợp 40 đề luyện thi toán 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**;&KL1;0.M/5N":O<KM$6
P!L=4.1.Q<RNS0N! $J<;F .TL.N
U$AV0F!GH5.<
+/."9$SW71W
X
5YTEZNH/[..
W\$<"9$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"9c7Q57FWZW
Nd/ZH]Ne01.^H71[]HAW
X
e/H`dW
01ML!
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"95m<7P2
+Tn.7F0/7%7P;97lE#9*!8E7P2&iN!TkHL[
[1+/."9$SW/=;[24[o71H=M$<0F[.
.H[55"9.[`71e^H[ZBA
$\H`AeML!
p
·
*
q*BAC =
/@;ET. kWLN[i.
$\"9cTr_H717Q57F`e0Q_M24
=s5
·
ABD
ZeNj/ZHNss5
·
ACE
Z[`Nt/ZH[Na
8jtsa01%%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[**T7F7P
2TQwgP2QQ0F#7P2QQ?*Tn<QQL[$"FQQ
?*!8E7P2^RQQ$<
[1+3,5 điểm8$<"9$SW/.$"F/7b=;H[24TQ=_WKj?Tx
$<[H..j\.1"9$SW/kjTrL!;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$41.1.^%J4^12;)&'u(71;)&''Z
NM$<$yf
(2,0 điểm) 1)
H
= +
+ +
.
*/
B x x
x
x x x
= + + − > ≠
÷ ÷
−
+ −
[ 8%^^&[)
(1,5 điểm). .6!"#$%
y x m
x y m
− = +
− = −
6!"#$%T)
8%$4^6!"#$%56&;..s)&
';
N$4
V?
+(3,5 điểm) .H[55ML!"9$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%$4^J412JL
l 6!"#$%
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.HA8E7H[L
H)A)
q/l.p"9$SW"9TEH[gbL!;LH&/[;7F"9$SW
O?;e$<p"9$S/_e7bL!;L7F"9$SZH&N`Z[;N
WH`eML!":"9$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[7l
H"95m7P2<Tn<97lE#901*!8E7P2^"9
&iN!0kHL[
+/."9$SW/TE8kH<.1"9$S/TrL!;LH[/
H7F"9$S[/01L!8k[/Tr"9c..7FHZ"9$SN``
T[t2H`Z"9$SWN01dt2[dZHN}
H[WML!"9$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":Nt71st\|j71s..W
m<$.5sj8$<Vts0?;H..Ht\HsA=;
H[/HZts0h0":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%$4^
m
656
( )
x y
..
+
x y
y
− −
=
+
/*A"9:_>#MQ1tLY01$.q1;%&.Q76
A"901Y$.1;%"9?":;01Q76T/"9
01M%$.+/1;21;$"~|%.11Q76AVL01$<%R"9
.11Q765$..0
+/*."9$SW5"9TEH[71`7Q57F8$<.N
cHW0?;jjTH71W8jZ"9$SWN01tdrL!;L
7F"9$SWNt8L!;L1;Z"9c7Q57FH[NjBs
Wjts01ML!
tnnWs
d
Hj HW
=
8ETE^"9$S.NL!Wjti.
/*.2
/ /x y z
. @
* / / x y z< ≤
71
x y z+ + =
8%$4V?^
H)
x y z
z x y
− − −
+ +
Đề 9
(2,5 điểm)
( )
+qG +=A
?!"#$%&,*o*
6!"#$%
=−
=+
yx
yx
(2,0 điểm)
!"#$%&
,&')*
8%$42!"#$%&
(,&',)*5<!6&
&
V@lT6&
,&
)+
(1,5 điểm) jM"9&iN!kHL[7F7P2TQwdk[LH"95m
7P2<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"9
cH[Nt pA01.^H[71jW
jt}AML!"9$S
$\W}AJ=N7FWjt/k5;$W}Wt)
•pWj)/jH[l
(1,0 điểm). .&/;012DV@lT6
xxyyyx
−−=−−
8%$4V?^
-
+−−+= yyxyxS
Đề 10
[1*.
H)
+ **+ −
[)
−
−
+ −
[1
6!"#$%
& ;
& -; G
− =
+ =
.!"#$%P&
(&'()*
!"#$%T)+
8%!"#$%56&
&
V@
*
x x
x x
+
+ =
[1.12;)
+
&
gbJ4s^125
3471"9c=;)&'Z$yN5M\,71ZJ
4s5$<N5.1M\
[1+ +*.p"9$SW/"9TEH[01E|^
H[8$<2^[0?;`..`)[W`ZHNj8kH/TrHA7Q57F
W`AMW`HAZ`[Nt71Zp"9$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&;/.!$.0s;)&
71"9c=;)&'01
2
gb!$.0s $\=0QZsN!6
x x
01.1M.^s71=/%&
'&
)
[1+3,5 điểm."9$SW/"9TEH[)Km$<2^[H..[)
K`M"9$SW..[`)K"9c7Q57F[NZH`Nj
$\
8[j`01ML! H[H)H`Hj
`01L!;L^"9$SW
K"9$SWH[j1!h/E=6E!hH[j\
.1"9$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
"R02$Jm<;%2$.17"9bm<;AV7"91j$J
.<;Z! f
[1+/*."9$SW"9TEH[71M24$<TEWHTH
71W/j=M$<"9$SjTH/[ajTr"9c7Q57Fj/"9
c1;ZL!;LNH71[^"9$SW0h0":N`71e
Hj`71[je01ML!
`
⊥
e
8%74$E^j=6EH`e[V?
/*8%M2D&/;/z. @
( )
G q * *q
x y z x y z− + − + − + = + +
Đề 13
[1/*TQ":=Y;E
,8D6!>!E
( )
u +- − +
,8$ymB•
+
− + −
[1/
, !"#$%&
(&()*
,.6!"#$%012
& , ; )
,& ' ; )
6!"#$%T)
8%$4^6!"#$%56=;?
[1/*8$<YMU!cM/.!$.0s;)
2
x
2
71"9c=
y x= − +
[\!>!E/@;%M.^s71=
8%"9c=X;)&(L!&7F!$.0s
[1+/."9$SW$71"9TEH[/`7Q57F8$<V`[/
0?;ttT[71`j01.^t71H[
,W`tj01ML!
,Htj[)Hjt
,.`t)$e01.^Ht71`8Ei.$M=1.Ne`/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=;sa7Q57Fjt8N}Tj/
t$<Vts0?;ƒTt/st2j7FƒZsaNA
jƒ01!^5
sƒa∠
A}tƒML!
.^st7Fjƒ01ƒa7Fjt01ddnnsa
= 01"9$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$4
0F?^;01.<f
[1qA@;Z!&L!…20":i.Dm=h/ Ef
.+u
*
/u-
*
/.+
*
/+u
*
/.-u
*
[1u.55\+
*
K"9.MNTl7F551!h*71
8EN0F$.NS0N
[1-."9$SWTEWH71"9$S"9TEWH
3474$E"#2^"9$S
`;H`^"9$S0FZ"9$SVN$\H)`
[1G.H/[//01$<M"9$SH01L!;L^"9$SNH"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!&7FJ
4s
+*.!"#$%
2
x 2(m 1)x m 4 0 (1)− + + − =
012
!"#$%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$S5j
TH/[8$<pU!c9H[p"9$STrL!;LH&8[jZH&N}!
^5}HjZp"9$SNe71Z[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^!"#
$%56
/x x
. @
( )
+x x− =
/jM 7"9%|P5=6EG
[L0hl$M0F#l
=1-8ETE"F^%|P5
+.p"9$SW/"9TE[`0124M.NcW`
TW71`D"9c=7Q57F[N`/Zp"9$SWNH8$<
H0?;j?TxjTH71/[jZ"9c=Nd/jZ"9c
=NeK"9c[eZp"9$SWNttT[
`teML!
/d71tc1
}01"9$S.NL![de$\}0Q\$<M
"9c24Tj;w
*/.2D="#&/;. @
( )
( )
+ + *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$SW71H..WH)8kH7bL!;LH[/HL
W7F[/01L!
n8E5HW[
n8kH7b;LHsaL"9$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"9
c`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`.R1;M5B7":?<M@
.11TL.NF#9_;41;71B<":*?AVi.TL.NM&i
B1L.<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$SW/"9TEH[)=
71=
01L!;L^"9$S
WNH71[}01$^WH71e01M"9$SWeTQ$Y7FH
71[K"9c=_e717Q57Fe}Z"9c=
71=
0h0":Nj/t
Hje}01ML!
et} e[}∠ = ∠
71
*
j}t G*∠ =
Hj[t)H}[}
+]01E|^H[TQe^"9$SWA@;E=6E^
j}ti.Te/}/]c1
[1g(0,5 điểm) gF&‚*/%$4V?^
j +& & *
+&
= − + +
Đề 22
[1/s)
(4 2 8 2). 2 8− + −
8%.NM.^J412
2
y x=
71
3 2y x= −
[1jMQ;7P lM2&i LT.1B?1dLT.1%5
&i4V<BL0":15/R&i! B<*/?.7F=D4hAV0
hQ;@lLT.1.<&i[L$\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"9$SW
TQ.A01"97Q5TrkWL"9c=/j01M;w$<
=jTQ$Y7FA8kjTrL!;LjH71j[7F"9$SH/[01L!`;
H[ZWAN}
W/H/[/A/jY\$<M"9$S
}A}W)}H}[
Tj;w$<=%E}H}[TQw
[18%$40F?^
2
4( 1) 3 2 1y x x x= − − + + −
7F(o&o
Đề 23
(2.0 điểm) 6!"#$%
& ; *
& ; *
− =
− + =
(1.5 điểm) .!"#$%&
(&'
()*&01€/012
!"#$%7F),
8%? $4^<!"#$%56!6
8% $4^!"#$%56&
/&
..ws)&
'&
N
$4V?
(1.5 điểm) jM%|Ph5.7\**[L$\lml=1^%
|P<*71ml$M<*%=6E%|Phm0<**
8El=1/l$M^%|Ph
+(2.0 điểm) .H[55/TQ01/H[oH71ML!"9
$SW/"9TE[e"9.H`71[d^H[ZNAK"9c
[dZ"9$SWN01]}01$^NH$\
8H]e01%
[A)W}71A2&7F]_"9cH
(2.0 điểm) .//012D="#V@lT6'')8%$40F?^
s)
+ +
+ + +
Đề 24
[1/*
n !"#$%&'(&'+)*
n 6!"#$%&,
y
)
&';)
[1a)
q
−
−
−
+
−
−
[1.!"#$%&
(&(
)*012
n !"#$%T)*
n8%!"#$%56&
&
T*71VlT6&
)+&
[1+/jM%|P57\-71R"9>.^55M=1*8%M
=1N^%|P5
[1/.lH[ML!"9$S"9TEH`j01M=M$<
VH[jTQ$Y7FH71[
n$\j`01"9!^5[j
n.H`)8E=6EH[`i.
nd01.^H[71j`/A01.^H`71j
$\"9cHj/[`/AdJ_;
Đề 25
[1 !"#$%716!"#$%
*x x− − =
u
+ -
x y
x y
+ =
− = −
+
q *x x+ − =
=
*x x+ + − =
[1/
gbJ4s^12
y x= −
71"9c`
y x= − −
$<YM6$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]7Q
57FHeMH[/]MH
$\HeA]01%|P71WH7Q57Fe]
K"9ce]Z"9$SWNs71ae\|s71]
Hs
)HeH[I;$HsA
}01.^d]71[}A
)}}`01
= `01.^sa71[d01.YH`71"9$SWdTH
He]d01MML!
Đề 26
/*.H)
( )
−
+
−
+
−
x
x
xxx
t<lT6&471$H 8$4^&H)
8%$40F?s)H,G
x
/*.!"#$%P&
('&'
'u)*012
!"#$%T)
8%!"#$%56&
/&
V@&
&
(&
'&
)+
/a@"9H[=1*TA&i;TB1YM0kHL[gP2
^&i;?0F#7P2^&i;01*Tn<&i;?L[$"F&i;
98E7P5^R&if
+/.H\.1"9$SW8kHTrL!;LH[/H71;LH`e
F"9$S[/01L!`\|H71eA01.^HW71[
$\H[W01ML!
$\HAHW)H`He
8L!;LN`^"9$SWZH[/Hi.DN}71daWTr"9c
7Q57FWHZH[Ns71ZHNa$\}s'da
≥
sa
Đề 27
[1K# H
q - +
+
+ + + +
=
+ +
.
= − − ≥
− − + −
P a a
a a a a
s71Vs
≥
*
[1.!"#$%P&
'&')*56&
&
A@;0P!M!"#$%
P56&
'71&
'
6!"#$%
+
+
+ =
−
− =
−
x y
x y
[1a@"9kHL[=1*TjM"9=D4&iN!kHL[7F7P2
TQwd":9/"9?;=k0N*!•j2L[9@4/"95
! m7P2<Tn$<_@"9S0N8E7P2h^"9&iN!
[1++.H[5571A01$Dgb%%1[A`K"9c
_`71..[Z"9cHANe
H/[//`/eYMM"9$S
BAE DAC
∠ = ∠
W01"9$S.NL!H[71j01$^[/"9cHjZ
WAN01$^H[
+ pW`)A@;EM=1"9$S.NL![Ai.
Đề 28
/*TQp=y;Eh;
u M = + −
+
a
N
a
a a
= +
÷
−
+ −
/7F‚*71
+a
≠
/ !"#$%TQp=y;Eh;
+ *x x− + =
x
x
+
=
+
/*
gbJ4=^12;),&'
8%$<=5.1M71M\
+/*&
/&
016^!"#$%&
'&,)*8E$4^
x x+
/Giải bài toán bằng cách lập hệ phương trình: 8E7^M%|P/L$\
LmRl^%|P<+%=6E^%|Pm<-*
L
l$M71ml=1%=6E%|P\=6Eh
q/*.H[`ML!p"9$SW"9TEH`A"9>.H71
[`ZNedr]e7Q57FH`]
∈
H`]
≠
W
8H[e]ML!":
8H01!^5[]
j01$^`ej`[)`]`W
Đề 29
2 điểm.
& , q
H ) , '
& ,
& , & '
÷
÷
8%&H5†
H
2 điểm.!"#$%
& ,&,&,,)*
/012
$\!"#$%0Q56!6
& &
7F$4^
8%$4^
s ) & ' & , & & ' & ' &
N$4V?
2 điểmjMQ&Q=SQkLHLL[Lq9/":=SQkL[7l
LHL-9gP2=S"FTQ;w
AV7P2^QT"F;<0U?!?;0h7P2=S"F ;f
tL $QM‡kLHLL[%L.<9f
+3 điểm
.H[7QNH71H[)*A01"9.TrkH
&2[[L$\A[)q/EM=1N;l[
.H[ML!"9$SW/A01$D^/HAZ"9$SWN`
`TH$\A[`
A@;<7b%7QH[`TL}^%7Q71j/t0h0":M
"9cH[/`[j/}/tTQc1
1 điểm 6!"#$%
& ; , &; , ) *
& ' ; ) & ;
Đề 30(A18†
8%"9c;)(&'..7F"9c;)&,
6!
=−
=+
+
yx
yx
/.s)
+
+
−
−
aaa
7F‚*/ˆ
s8%s‚n
8%M.^;)&
71;),&'
34!
& ,&',)*
56&
/
V@+
*
=+−+ xx
xx
+/8$<p"9$S"9TE[/0?;j/t..jM[tH
01.^[j71tA01.^[t71j
jHjAtML! j
∆
H[tJ=N
∆
At
8E$4^I)[j[H'tH
.//‚Gn+8%8tt^a)
−
+
−
+
− a
c
c
b
b
a
Đề 31
}/
n s8&
(&()*
n As8
=−
=+
*
u
yx
yx
nK#
-* −+=P
+n.L
≥≥−+−=+ bababa
')
}}/*.s$!.0;)&
s/71"9c;)(&'=/7F012
ngbJ4s
n7F$4^/!$!.0s71"9c=0QZN!
6
n8%$4^/s71=ZN5M;)
}}}/.W/="9TEH[)/01M$<"9$STH/[j01$
^V[
nHj01!^5[H
n.LH)8E[/j[
n p[ZHjBtjtjH)j
}g/*s)&
+
(&
'&
(&'
*
≥
/7F$4^&
Đề 32
[1( 1,5 điểm )
.2
)'
),
8E
'
6!"#$%
−=−
=+
nm
nm
[1( 1,5 điểm ) .[)
+
+
+
−
−
+
−
−
+ b
b
b
b
b
b
b
7F
*
≥
71
≠
+
[ 8E$4^[N)q'+
[1 ( 2,5 điểm ) .!"#$% &
(,&',)*7F012
!"#$%7F)
j!"#$%0Q56!67F
&
/&
016^!"#$%7#E&
o&
&
(&
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≥
*
[1+.
∆
[`55"9.e71`]ZNA
j8[]AeML!":$.M"9$S
∆
[]e71
∆
[`J=N
drL!;Le;^"9$SW"9TE`Z[ANtjt01$^[A
.2="#&/;/z?c
>
+
+
+
+
+ yx
z
zx
y
zy
x
Đề 33
[1 8D6!>!E
G
'
q
!"#$%716!"#$%
&
(*&'Gq)*
& ; +*
& ;
+ =
− =
[1.12;)&
5J401s71"9c=;)&'
gbs71=$<YM6.NMW&;
[\!>!E@;%.NM.^s71=
8$.YM6.NMW&;.H+[,,71,H/[/
TQc1
j)
x
x −
'
x x
x x
−
−
7F&‚*71&
≠
[1ALQT8#%MQ&Q=SkLHLL[/NL
[•*!$J":=SkL[$B7lLHwM0198E7P2^QT"F
;<0U/L7P2^=S"F01Tn
[1+.p"9$SW"9TEH[jM24M.NcHW
TH71TWK"9c_717Q57FHWZp"9$S@.N`
8$<[`0?;j7FjT[71jT`8L!;L^p"9$S@.NjZ
"9c`Ne]01.^Hj71`
[]j01ML!"9$S
ej)e]
}01"9$S.NL!]`j`/}/[c1k5;$
5H[}52.TQwTj;w$<[`
[1*.!"#$%€&&
('&')*&
71&
016^!"#
$%@.8%$4^&
'&
5$4V?
Đề 34
[18E
- qM x x= − +
/N&)
[1
gbJ412$<YU!c.NM ;)&(+= ;),&'=X
g1%.NM.H^=71=X\ 6!"#$%
8%s;)&
_5.NM
[1
!"#$%&
'u&'*)*
!"#$%&
+
,&
'q)*
[1+
8El=171l$M^M%|P5|70171=6E01
.!"#$%&
('&'')*
8%? $4!"#$%56!6l0F#*/
[1."9$SW8kH.17bL!;LH[/H7F[/01L!
gb"9c=_717Q57FH[/=Z"9cH[NAZNe/71
Z"9cWHN`
$\AnnW[71W`
$\W[`01%.
j01$^e/L!;L^NeZ"9cHNdW/j/d
c1
Đề 35
/.
& & & &
s
& & &
− −
= +
+ + −
7F
& * 71 & ≥ ≠
s
8%&Ls)*
/.!"#$%
2
x x 2m 0− − =
7F012
!"#$%7F)
8%!"#$%$<56!6
1 2
x ; x
V@
2
1 1 2
x x x 2+ =
/* 6!"#$%
+
& ;
& +; ;
+ =
+ + =
+/*.p"9$SW"9TEH[KMp"9$SW[oH/
T[`01E|^H/e01.^H`71[
H[eN[
]01M"9cH..01$H]
·
·
EFA EBD.=
A01.^H71[`/eAZH[Nd/dZ.Ne]N}$\
8e}[dML!
HF EI EK
BC BI BK
= +
/* !"#$%
3 2
x 3x 2 3 2x x x x 1− + − = + + +
Đề 36
[1ns)
q
+
−
+
÷
÷
+ +
n s8
*x x x
− + =
[1.12;),-&
5J401s
n8%.NM^H/[$<J4s5.1M0h0":01,71
ngL!"#$%"9cH[
[1
n8%$4^&. @
+GG
*
q u q- u - - u x x x x
+ + + =
+ + + + +
n.&/;012TQ. @&';)+8%$4V?/$40F?^
s)
+ +
+ - qx y xy x y x y x y xy
+ + + − + + − +
[1++.H[`ML!"9$SW71H`01"9TE}01E|^
V["9cH}Z=;[71"9c`0h0":Ne/j"9c`}Z
=;[71"9cH[0h0":N]/t
nn}Ht71}`jJ=N
nnHtj`01ML!
nnc}e}H)}]}`
=nnW}7Q57Fjt
I"ht;‰tAY(8AIA.13A@
