SKKN toán 7 hay xếp loại B




A. 
I.  !"
 !"#$%&' ()*+,++ 
/#01+234+,+#$%5#"+)%
627/#8++$ $9+&&3:0&;<=
54 #&3:>3+?@8 A>+%1%B
!?C+D #E 6."2%D+C2)%15F, #
G1:0(E (>+ 6+H8&.&+:3)+I5
B#JKLMN"O2P)+AQ+&3R+2S2PT,
&+/1R#60%&R#6...2A3+/6
>30 #++U#5(+&3R1 +(1&A+"+V.
A+"+230+A#"+" V.%2V3%8B+(+(+*#
+I++C'&04+H1.2P%D+C#"+%&0
+A)+(+W5
$ #"+)+X#6&+$+!,B#5!,
B#%S#>3+$.U$82A3!"#$Y
Z5[+&#&82A3+$V+>3+YZG%D+C#6%1
8)G0,)*59!S+%2A3!+;#$%&'()*)+, /(
01$/,23,45016/(789():01;09<=0>?)@+$+>30>+ -+-8
0&+DG%S+D+.\0#=>+G0& :#G
0& :#,&#&+"V%D+C+V#40&%D+C5
3U 2/#&=#=]&+>+++3S+,
&S+,2A!+V.)...85D
)+*#&0& :#+9.&3#=.8'&0+*T&
10^1!S..%=.P0_&&4+SS+,%D+C@#
U&>+ 82A35
II. AB
1. .CDEFE9G/

60(.++4#A#^G%+D++C%&$S+$
+`S+&#+&&.8>+E (,=4%$!+P+V0)6%
)()+D65+"1Q9+GO2P)+A+6
+)++C#65I&V..++4+D!"#,A+
3:>3!6:+ .8+&3R02P.a.
)63:+(+D5
8)6+& $2P T,0:)*)V3
+B#JKLM)H&T& A+02P+&3R1..:+&3
R+2S2P65/12P 0.++4
V+C+23*++"4+H1.++4)6S.5
O2P+4%$I9+9++#+)G2PU
+$T& %/ ")'&+3$4+H1+IE (,
=+/%8B'&!8+U5`V3!=+:!60&!V
00^1G!bb)G+*3#"+U&D
%$+V+0(+V.+/#0^2:#>+,27D)3
++2++*#%D#++C5
 $.++4+/<3+$,5N=+:+H+c
/# #T/)6]&++3S+,5&+Y+Z/#
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+11!+; #$%&'()*)+, /(01$/,23,45016/(789():01;
09<=0>?)@
`V3 #+D41+4S+,2A!+V.)+
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2. .CD0,H30)I/J
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<}k qyyr
⇔
J
k−x
tlutL
& :#+C+;
;*#<!D+

L−x
t<uJ
0Q #0&;
D<tL
≥
K03&<tLt<uJ
D<tL}K03&Lt<t<uJ
qm)D+G%SC&+*#G%SP+4'&<r
9 #J;

L
−
x

u<•J
⇒
<tLu<•J9<tLut<tJ
`683/#%$<{++6G%S'&<27D%D+ VS#0&5
59>b<0c)&)/01$/,OQ<()*)+,:+_,)7d<OQ)06:/0$%&3,45789():
01;09<=0>?)e
Yf0,9<P0
;/,/(,g5;[8+H4#&D4#K++P0, ++3S+
,'&#"+0,&q& 0,+(r
hO++3S+,'&0,%$U# 1++3S+,'&0,U# 
0,,'&15
RT+; D
aaa =⇒≥ K
 D
aaa −=⇒< K
 D<t&≥Kuƒu<t&
 D<t&≤Kuƒu&t<
F/,3,80
 O++3S+,'&#0,G%$U#
RT+;
K≥a
)6#&∈„
 t &0,!@&9,&+*1++3S+,!@&)
 A&0,1++3S+,!@&+*- &0,!@&9
,&5
RT+;



−=

=
⇔=
ba
ba
ba
tF0,G 69!@,'&++3S+,'&1)h+
i9!@++3S+,'&15
RT+;
aaa ≤≤−
)
KwK ≥⇔=≤⇔=− aaaaaa
h&0,U#0,i+*1++3S+, 6
RT+; D
baba >⇒<< K
h&0,20,i+*1++3S+,i
RT+;D
baba <⇒<<K
hO++3S+,'&#"++!@+++3S+,5
RT+;
baba 55 =
hO++3S+,'&#"++!@+&++3S+,5
RT+;
b
a
b
a
=
hN*.'&++3S+,'&#"+0,!@!*.0,15
RT+;
J

J
aa =
hR&++3S+,'&&0, $ 69!@++3S+
,'&&0,2>!@<83&%)m%&0,a2>5
RT+;
baba +≥+
)
K5 ≥⇔+=+ bababa
ViUBjk
U!BlmJ
d/([;
kA (x) =
q1pq<r !4+CC&<% #"+0,+6r
Cách gii ;
tD%}K+*%$1+'&<+8#Q‚+Cq`*++3S+,
'&#0,G%$U#r
tD%uK+*+&1
KrqKrq =⇒= xAxA
- N u k > 0 thì ta có: ế



−=
=
⇒=
kxA
kxA
kxA
rq
rq

rq
UQ)0b+ ;*#<!D+;
&r
MlJ =−x
!r
KJ
M
l
=− x
r
k
L
l
L
−=+x
2r
Z
Y
LJ
M
k
=+− x
O8
&r
MlJ =−x
⇔
J<luM9J<lutM
• J<luM
⇔
<uMl

• J<lutM
⇔
<uKl
`V3+V.S#'&.+* ;
uvKlwMlx
!r
KJ
M
l
=−
x

⇔
KJ
M
l
=− x

⇔
J<u

⇔
<uKcJl
`V3+V.S#'&.+* ;
uvKcJlx
r`*
l
L
+x
0

%$1+'&<+i&#Q5
2r
Z
Y
LJ
M
k
=+−
x
Z
Y
M
k
LJ
−=+
x
Z
L
LJ
−=+
x
`*
LJ
+
x
≥ 0
%$1+'&<+i&
#Q5
!+V.++(;
UQ)[;*#<!D+;

&r
J
L
kJJ =−x
!r
lMJlklY −=−− x
r
LlJYlk
Ll
M
−−=−−+x
UQ)a;*#<!D+;
&r
lLLkJ =+−x
!r
kL
J
=−
x
r
lk
J
L
l
J
=++− x
2r
l
L
J

k
L
=−x
UQ)N;*#<!D+;
&r
€l
M
k
M
L
=−+x
!r
M
l
M
L
J
k
J
−
=−− x
r
M
Y
M
k
l
M
J
k

=−+ x
2r
c
l
k
l
J
L
M
k
lM =+− x
UQ)R;*#<!D+;
&r 
J
k
L
;
M
…
lc
=+−
x
    !r 
J
Y
l
L
M;
J
k

M
LL
=−+
x
  r
k
J
L
M
k
;lJ
M
Ll
=+− x
    2r
c
k
J
M
;k
l
JL
=−+
x
d/(a;
B(x)A(x) =
q1pq<r)Nq<r &!4+CC&<r
Cách gii;
`V2P+>+;




−=
=
⇔=
ba
ba
ba
+&1;



−=
=
⇒=
rqrq
rqrq
rqrq
xBxA
xBxA
xBxA
N+V.;*#<!D+;
&r
JMl +=− xx
yl<tMu<•J
l<t<uJ•M
M<uc
<uLl
`V3<uLlw<u
yl<tMut<tJ

l<•<utJ•M
c<uJ
<u
N+V.++(;
UQ) [;*#<!D+;
&r
LM
J
L
J
k
−=+ xx
!r
K
l
k
Z
l
J
Y
M
l
=+−− xx
r
M
L
k
M
k
J

l
Y
−=+ xx
2r
Kl
J
L
c
l
Z
Y
=+−+ xx
d/(Ne
B(x)A(x) =
q1pq<r)Nq<r &!4+CC&<r
Cách 1;&+>3DNq<r}K+*%$1+'&<+8#Q)*+
+3S+,'&#0,G%$U#5f)V3+&80&;
rqrq xBxA
=
qLr
G%S;Nq<r
K≥
qyr
qLr?+



−=
=
⇒=

rqrq
rqrq
rqrq
xBxA
xBxA
xBxA
q,D+<+*#)6G
%Sqyrr
Cách 2;&%8<{+G%S!i2>++3S+,;
D
aaa =⇒≥ K
D
aaa −=⇒< K
&80&;
rqrq xBxA =
qLr
yDpq<r
K
≥
+*qLr+?+;pq<ruNq<rq,D+<+*#)6
G%Sr
yDpq<r}K+*qLr+?+;tpq<ruNq<rq,D+<+*#
)6G%Sr
N+V.;
O8;*#<∈†!D+uJ<
yz{+<•≥K+&1<•uJ<
yz{+<•}K+&1<•utJ<
!+V.++(;
UQ)[;*#<!D+;
&r

xx Jk
J
L
−=
!r
JkL +=− xx
r
LJl
−=
xx
2r
LlY +=− xx
UQ)a;*#<!D+;
&r
xx J… =+
!r
Jkl =− xx
r
xx J…c =−+
2r
JLkJ =+− xx
UQ) N;*#<!D+;
&r
xx MJM
−=+
!r
xx =+− JLk
r
xx kLLl
=++

2r
JlJ =+− xx
UQ)R;*#<!D+;
&r
LlJ +=− xx
!r
xx =−− LJk
r
LJYk +=− xx
2r
xx =+− LLJ
UQ)n;*#<!D+;
&r
xx
=+−
ll
!r
YY =−+ xx
r
xx kMMk
=+−
2r
xx JYJY =+−
d/(R;‚+CC&G2>++3S+,;
Cách gii :V.!8<{+G%S!i2>++3S+,;
mxCxBxA =++ rqrqrq
BC!8+<{++H%88!+q,DG%S+Cr
N+V.;*#<!D+@
1 3 2 1x x x− + − = −
qLr

Nhận xét;+-+&Q!DR!4+CC&2>++3S+,
+!4+C%$C&2>++3S+,5`V3+&0^!DR!4+C?
)D+'&‚+C+5H10^+*#<
O8
z{+<LuK
⇔
<uLw<L}K
⇔
<}Lw<LƒK
⇔
<ƒL
<tkuK
⇔
<ukw<k}K
⇔
<}kw<kƒK
⇔
<ƒk
&1!8<{+2>&+C<tL)<tk26U3;


z{+%8<}L+&1;qLr
⇔
qL<r•qk<ruJ<L

⇔
tJ<•MuJ<L

⇔
<u

5
4
q+3%$+"%8&<{+r
z{+%8L
≤
<
≤
k+&1;
qLr
⇔
q<Lr•qk<ruJ<L

⇔
JuJ<L

⇔
<u
3
2
q+3+"%8&<{+r
< Lk
<L tK• •
<k t tK•
z{+%8<ƒk+&1;qLr
⇔
q<Lr•q<kruJ<L

⇔
tMutLq`$ r
[D+ V;`V3<u

3
2
5
!+V.++(;
UQ)[;*#<!D+;
&r
LJkYlJLkM
=−+−−+−
xxxx
!r
l…klLJMk =−++−+−+ xxxx
r
JL
l
L
Z
l
L
l
L
J =+−+− xx
2r
xxx −=−++
l
L
J
J
L
k
J

L
kJ
UQ)a;*#<!D+;
&r
ZkcJ =++− xx
r
…kl =−++ xx
2r
JMkJ =−+−+− xxx
/r
ckJL =++−++ xxx
‡r
LLMJJ =−++ xx
UQ)N;*#<!D+;
&r
…ZJkJ =−+−+− xxx
!r
LJJJLk =+−+ xxxx
r
MJJkkL =−−−+− xxx
2r
xxx =−−+ JLl
/r
LkJ −=+− xxx
‡r
kL −+=−+ xxxx
UQ)R;*#<!D+;
&r
klJ =−+− xx
!r

Zlk =++− xx
r
MlJLJ =−+− xx
2r
LJMkk +=++− xxx
d/(n;z{+G%S!i2>++3S+, A+;
rD(xC(x)B(x)A(x) =++
qLr
G%S;fq<r
K≥
%{+/
KrqwKrqwKrq
≥≥≥
xCxBxA
f)V3qLr+?+;pq<r•Nq<r•q<rufq<r
N+V.;*#<!D+;

xxxx MkJL =+++++
qyr
G%S;M<|K
⇔
<|K
qyr+?+;<•L•<•J•<•ku<•M
⇔
J<utJ
⇔
<utL
!+V.++(;
UQ) [;
&r

LlMkJL −=+++++++ xxxxx
!r
xxxx M
J
L
l
k
J =+++++
UQ)a;*#<!D+;
&r
xxxxx LKL
LKL
LKK
555
LKL
k
LKL
J
LKL
L
=++++++++
!r
xxxxx LKK
LKK5……
L
555
M5k
L
k5J
L

J5L
L
=++++++++
r
xxxxx lK
……5…Y
L
555
Y5l
L
l5k
L
k5L
L
=++++++++
2r
xxxxx LKL
MKL5k…Y
L
555
Lk5…
L
…5l
L
l5L
L
=++++++++
d/(o;
0BA
=+

`V2P+>+%$U#'&++3S+,27D...!>+‚
+C5
yV<{+;R'&0,%$U# #"+0,%$U#)+R1!@K%
)m%0,A'&+Rh+!@K5
y8;
K
=+
BA

N6L;;
K
K
K
≥+⇒





≥
≥
BA
B
A
N6J;[‚;
K
=+
BA




=
=
⇔
K
K
B
A
N+V.;*#<3+8#Q;s<Js•s3YsuK
V<{+;s<Js|Kws3Ys|K
3&s<Js•s3YsuK%)m%<JuK)3YuK
⇔
<uJw3uY
!+V.++(
UQ)[;*#<3+8#Q;
&r
KlkMk =++− yx
!r
K
Jl
…
=++− yyx
r
KlMJk =++− yx
UQ)a;*#<3+8#Q;
&r
Kk
Y
J
M

k
l =−+− yx
!r
K
Lk
Jk
LY
LL
lL
M
k
J
L
k
J
=+−++− yx
r
KJKKZJKKY =−+− yx
UQ)N;*#<3+8#Q;
&r
KZcLl ≤−++ yx
!r
KkMJ ≤−++ yyx
r
KLJJ ≤+++− yyx
UQ)R;*#<3+8#Q;
&r
KlLLZLJ ≤−++ yx
!r
KLMJk ≤−++ yyx

r
KLKY ≤−+−+ xyyx
UQ)n;*#<3+8#Q‚+C;
&r
KkJ
=++−−
yyx
!r
KMk
JKKZJKKY
=++−
yyx
r
( )
KLJKKY
JKKc
=−++ yyx
 2r
( )
KkJKKYl
JKKZ
=−+−− yyx
UQ)o;*#<3+8#Q;
&r
( ) ( )
KkL
JJ
=++− yx
!r
( )

KYJllJ
l
M
=−+−
yx
r
( )
K
J
L
MJk
JKKM
=++− yyx
2r
K
J
L
JLk
JKKK
=






−+−+ yyx
UQ)p;*#<3+8#Q;
&r
KJKKZJKKY ≤−+− yx

!r
K
k
J
LKk
Y
l
≤++− yyx
r
K
Jl
c
l
M
JKKZ
JKKY
J
L
M
k
J
L
JKKc
≤++







− yx
2r
KMJKKZJJKKY
JKKYJKKZ
≤−+− yyx
d/( pe
BABA +=+
8;_2P+>+;
H1+&1;
K5 ≥⇔+=+ bababa
N+V.;*#<!D+;s<Js•sl<suk
O8;&1<J•l<uk
3&q<Jr5ql<r|K

⇔
Jˆ<ˆl
!+V.++(;
UQ)[;*#<!D+;
&r
Zkl =−++ xx
!r
klJ =−+− xx
r
cLklk =++− xx
2r
LLlJkJ =++− xx
/r
JkkJL −=−++ xxx
‡r
JMJlk =−+−+− xxx

UQ)a;*#<!D+;
&r
JcM =−+− xx
!r
MlL =+++ xx
r
LkJkYk =−++ xx
2r
xxx kMJkLl +=−++
/r
kLLkJ =−+−++ xxx
‡r
MYJ =−+− xx
U3 .:+*!3'&+$)G.: +3D+)#"+0,2A!+V.!8
)U&5$Q >33G342A3+4#? 6..PA)9!S+ ?
$+!h2b0i+Y5
&%2A3<3G+$+>3&0,/#=#4!5
/#%$I8#+>3  =%9.!++*#<C&2>++3S+
,&5‰~
[D++-3G+$Q&!+V.%4#+&Ll.-+0&;
&
r
M
Y
M
k
l
M
J
k

=−+ x
!r
KlkMk =++− yx
r
xxxx M
J
L
l
k
J =+++++
3G!&%1G%80+>+ !&:%D+T8+>+
%8T&5P+40&;
)\) ],: 19/(O$/, P9^Q_`%
k~Jc•LJ€ LK~Jc•kZl€ LL~Jc•MJ€ J~Jc•Yl€
J]AYj
[.2PG+C&3)82A30+$+>3
0 #2A+3&50%$I -+%9.
2A+35P+4;
t0%$I -+-)G...8+H A!5
tND+ (&8&. 5
t:D+0Q!D++*!3 89+^5
])P//(,;e
U3 #"+0,%S#'&+$+)S2A308#"+
2A+5$]%S#+*%$+4%$+%i+D01+):
&0X5$%#0(1.j'&>. QA)'&!A
hS.4!80%D+S5
$<U+8#Š
U3 0%D%S#'&!8+U+$)D++3S+,%$0&{.
"2'&%5
)D+;


[JUQ),M3_)/,/(,)=%;[CG+3+$-+&#"+0,!!8+U
+)S!h2b&:03D)0%ti0&;
- S+,%D+C!R+2A+0=.2A35
- S+,...!848 A+15
- [T++R.+H2A+H A!+V.5
- *#+I%&+0U%D+C0+:#)+ ‹G!+0=.<D.+/
+H A2A!4%2A3 /#=#)2A+5