Tài liệu ôn thi vào lớp 10 môn toán - Pdf 23

 
PHẦN MỘT: ĐẠI SỐ
§1.CÁC BÀI TOÁN VỀ PHÉP BIẾN ĐỔI ĐỒNG NHẤT CÁC BIỂU THỨC ĐẠI SỐ
A- :
:
Định nghĩa


 









Các phép tính
























 





 







!

!
!




"#$%








   








   






 




 =
"##(#)#*
#
"!
#
"

!
"
#

!


 ==
2345-6(#)#*

!

!

!

−=

−=
()*+,-."/01230.4 5+,*&'6

 




=









: !"#;
!! =

! !  =






!

!
=

!

!
! !

!
! !
! !
!
! !
≠≥≥

=
±
≠≥

=
±
>=
≠≥=





≥<−
≥≥
=
≥=




+
+
+ 

!

+

!


AB
>?78#'1.C6<-#*D
?9E? > +=− 
0B!
()*+,-."/01230.4 5+,*&'6

 
>:"#F<-#*


+
− 
::D$';<-#*.G8#'1.C6<-
#*0#!:D
!



515
21
714











+


:AB
> 7#H#I(#J(8#

9

K?
0B 
 @ ! +−
0B>
>?$';<-#*

999
>>>


9!
>@>!
++
++++
0B
+
3. B:
>6"#*'#



−=
−+ 
D:
>"#*'#.L'



!
++=







!
>
@
>!
−=












()*+,-."/01230.4 5+,*&'6
!
 
>:"#*'#
@KEKE =+−
4. CDE8= :
>6"#F







:

:











!
!

9

!
E> 

+−

+

+
+−+++

 



!
  

+−


+
+
−+


!

!

!!
! 
!
!
!



=

=

=

+− 9

"

 −
D
$';"
78#8#" DD
!


 +
"
 −
"
!
>"#F<-#*
P



!


+−
+
+

+ 


 


 ^
! +−
: ^
!
()*+,-."/01230.4 5+,*&'6
9
 
>:"#Fb


−−
−−−


7RMZ-0I6M<b'#_
78#b


$';b
OP b'#_








≠−
≥−−



 








!



b









±
:
  ≥−−− 

PFM
cbY-
!   >⇔>−⇔>−⇔>−− 

cbY-
!    <≤⇔<−≤⇔<−⇔<−− 
[Db





<=
<≤
>
:!d-'#
! d-
!
%

&
>FeJ<-#*
f










+
+

+

+−







!


!
>?
E

  

+−




U

!


+


U
()*+,-."/01230.4 5+,*&'6
?
 

E!!
!
9
<⇔<⇔<−⇔<

⇔ 


AY#T(MZ-0I




<≤
9


±

±
9
fhMST1'1.C:9:>: ?:9ER90#i'#jk2Ae2W#[1'1.C'-DWX
:>: ?:9E#R<-#*'1.C'-DW
()*+,-."/01230.4 5+,*&'6
>
 
C.BÀI TẬP TỰ LUYỆN:
>6:78#

9K
K

@K? 9@ −+−
 0B
!−












?>9?>9 −++
0B>

> 9> −++
0B?
>?$';1<-#*

?

?


+
+
 
>

K 

+
+

AB9 
K
?
>:7RY 
!! =+ 

!>! =
0B!> 99



+






−=+− 

7R'1.CX#56<-#*


+− 

AB<-#*


+− 
X#5X
!
9
0#
9


>HP##FO\f7R=Q'-DWM<<-#*
!



X=Qil#R
!−
X=QilW
!
9
−
0#i'#<X=Q'-DW
()*+,-."/01230.4 5+,*&'6
K
 



X=Q'-DW#R
!−
X'-DW[DM<
!
9
−
'-DW(#h
!−
(#hXS69
nm0#1#dFMC#'#_`[##R




≥



 +


−+ 9

7RMZ-0IM<O'#_
A#O'#_"#*'j'1.C6O0#i'(#p#-&F
OP 2Z-0IM<O'#_X


O

[D'1.C6O0#i'(#p#-&F#l(#p#-&F
>6J"#F<-#*
q










+






qU0#
 
9

 
!
+

=+
+





'1.C)
PF 
+
4Sr'W9

(#h)7RMST>
>66B&

>! ! =−++

@
? 
9


9
?>
+
+



'' +≥++ 
4MZ-4Sr'




++≥++
MZ-4Sr'
>60

!
! ! 
+
−+

! !K! !K ++−

"
?9>?9 −−+








$';A:
78#'1.C6A
!

+
:
7R'1.CX#56A
OP 2Ae2
:: ≠≥≥ 
:A


+

:A
!
!> +
:
A



















$';s:
7R'8.C6M<s>
OP20M:
≠
2m
 : ≠<−== 
UUUUE
>6F)8=
n









()*+,-."/01230.4 5+,*&'6
E
 
$';n:
7R'8.C6M<n
OP20M



=≠≤


:9
n
9


<≤⇔>

⇔ 

>6G)8=








? ?@ −


9 E

E


E


E


@

=−=−
+
+≥−
+
++=
+
+−=
+
+
=





+
+



t+
\-D.t+



 =⇔+⇔ 

s$Mt
>6I)8=









+

()*+,-."/01230.4 5+,*&'6

 
OP20M
: ≠> 


 +−
!





=−≥−+ 



P5-uvhD.0##S'#R<-#*0#i'#Fh
k[D
>J)8=













E

: ≠≥ 
$';:
78#1'1.C6M<
OP
E

: ≠≥ 

! −
+




=⇔

>6)8=
S =






+








++
+
$';<-#*7:
78#'1.C670#
KK>> +−
OP





=
≠>


7
:
7
()*+,-."/01230.4 5+,*&'6

 
§2. CÁC BÀI TOÁN VỀ PHƯƠNG TRÌNH VÀ HỆ PHƯƠNG TRÌNH
KIẾN THỨC CẦN NHỚ




∆+−
:





∆−−
Y-

#R(#Sr'.R#'#I0J(







Y-

U#R(#Sr'.R#i'#I
Hệ thức Vi-ét và ứng dụng
()*%+Y-(#Sr'.R#[#



#'#IX


Y-#R






!05B&'8!>7DY-#=Q-3'-\8#-t#R-
X'#I6(#Sr'.R#[#

\tMZ-0I\

9t


PM&'Q%)*R2L15S 

T8STUJV6O1)WX8XYM>)
B&'B
Z%6[<1<7B&'B=2L15V6OWAB
t#Sr'(#1('h"#0#h`'M<('#I





=



=




fhR 



=∆



fhR
s5DF&RMSTa)-
()*+,-."/01230.4 5+,*&'6

 
Z%?
O\1<>)7B52L15V6OWAB]Q#
t#Sr'(#1('ht#'#I+'45-





>
≥∆










<
>
≥∆






-
,

fhR
QO\1<>)7B52L15V6OWAB1Q#
t#Sr'(#1('ht#'#I.145-



<<





<
<





-
,

fhR
O\1<>)7B52L15V6OWAB1Q#>ABQ2LW
1<,A'L
t#Sr'(#1('h
t#'#I.145-'#I)'1.C-DIMQX#r





>
<





-
,





,

()*+,-."/01230.4 5+,*&'6
!
 
Z%F05BA7B&'B=2L15V6OWABS
6
XS

)_B_
BM1)A&














S

U
6

2Z-0IM<(#Sr'.R##'#I




≥∆
w
fh#I!R



#DF 'h
R"#;#FhkMZ-0Iw
8O  0123  `  S
6

 T  S


 U  
. =−+⇔





U
, =−⇔ !
!
VGO'hR"#;#Fhkw
Z%G
OB12L15V6OaaWABBE1<7B&'
B
(#Sr'(#1('h7#*'#

≥∆
;'1.C6
8OB12L15V6OaaWAB$8ABE1<
7B&'B
(#Sr'(#1('h7#*'#
>∆
;'1.C6
OB12L15V6OaABBE1<7B&'B
(#Sr'(#1('h7#*'#

<∆
;'1.C6
B.b cd0eb+:
1. K2L1589#:
>6:fh1(#Sr'.R#=-
 

!

 ?: 


!





=
+
+
++
+

− 



AB

?
:
! +
:
 −
:4
!
:d20



:0B




=+
==
−=+=
!
 

 





,


-
 
7R1'1.C6M<#F#(#Sr'.R#.W8#5&'#I#-'
OPf;

X'#I#-'6#(#Sr'.R#:
7




:




=
=





h#(#Sr'.R#.a##



9!Ut#Sr'.R#i'#I
XF]


#DF



  h#(#Sr'.R#&'#I#-'X
[D X'1.CoR
>:"#F(#Sr'.R#

 !

!
"#*'#.L'(#Sr'.R#X-iX-i#'#I0##DM3

!!
−=
−−


:




=
+−

!!

7U

U

U>PFMU!UU>

9UU>
>:"#F(#Sr'.R#

  !z=QX
2C#M<(#Sr'.R#'#I
2C#M<(#Sr'.R##'#I




K
AX-[t#Sr'.R#'#I




>
K
2Z-0I


>
K
:


7#dF#I#*J







+

==
+
+
=+=


 @

!>
=−
+
+
+
+







>!@ K

K[DK#FhMZ-0I





−≥
−≠
>
K




OP
=−+−+=∆ >9 


9

99

9 9 ?
525 ==∆

t#Sr'.R##'#I(#)I

3
2
512
+=
++
m
m
:
2
2
512
−=
−+
m
m
t#Sr'.R##'#IMZ-)





−=++
=++
⇔=++⇔
)2( 10733
)1( 10733
10733
2
2
2
mm
mm
mm
fhMST
2
51
;
2
51
21
−−
=
+−
= mm
fh (#Sr'.R#i'#I[D
2
51 +−

 
 


7R(#Sr'.R#[#Mk
'1.CF6#R(#Sr'.R#[##'#I(#)IMZ-4Sr'
OP7/'h#YRMST








+
=+

+
=
2
)12(2
2
12
21
21
m
m
xx
m








>

+
=
>







+
=


++
=∆

9


!


:!


:! >−≤⇔ 
(
2<%.L' 





≥−≤




#F!




)
()*+,-."/01230.4 5+,*&'6
>
 
>F: "#F#=QDy !9
fh(#Sr'.R#y 9
7R'1.C#j#56#=Q
OP !9 9






+−
−−
321
321

[D (#Sr' .R#   Q
'#I
32
: ::
32


9
?
9
?

?
?−≥−




(433)1('
222
>+−=+−=+−−=∆ mmmmm
[D(X-iX-i'#I;
t#'#IMQ#-



=
<

0
0
S
P



=−
<−

0)1(2
03
m
m
1
1
3
=⇔


>I"#*'#.L'

X-iX-i'#I#S'0#i'#<#'#I
4Sr'
OP
0)1(4124)1(
222
≥−=−++=−+=∆ mmmmmm
tX-i'#I;
t
m
a
c
=
:\
)1( +−=− m
a
b


Y-U(#'#I.145-*X0#i'#<#'#I4Sr'

Y-#R\UW(#'#I)*X0#i'#<#'#I4Sr'

Y-#R(#'#I.145-[D;(X-i'#I#S'0#i'
#<#'#I4Sr'
>6J"#F(#Sr'.R# 

x! 
fh(#Sr'.R#

fh(#Sr'.R#0#>
7RM<(#Sr'.R##'#I(#)I
4RMSTa)-Y#I#*'}



M&X[(MQ
>6F"#F(#Sr'.R#

9 x9
7RM<(#Sr'.R##'#I



#FhkMZ-0I

x

K
7RM<<-#*

x



'1.C#j#5
7R#I#*XW#I'}#'#CW0#i'(#p#-&
>6G"#F(#Sr'.R#

x !9


M]'1.C#j#5
>6 "#F(#Sr'.R#z 

 
"#*'#.L';(#Sr'.R#Mk#FX-i'#I7RM<(#Sr'.R#Mk#F
&'#I 
7RM<h#'#I6(#Sr'.R#MZ-X=Q)
7RM<(#Sr'.R##'#I



#FhkMZ-0I


 


>f;#'#I6(#Sr'.R#

KX



OkDX[(&(#Sr'.R#[#
1'#IX


E
 
>F "#F(#Sr'.R#[#

   !
"#*'#.L'(#Sr'.R#X-iX-i'#I;'1.C6
7RM<(#Sr'.R#Mk#F#'#I



#Fhk9

9

 ?
>G "#F(#Sr'.R#

?>OkDX[(&(#Sr'.R#[#1'#IX3'
8#1'#I6(#Sr'.R#Mk#F
>H f;#'#I6(#Sr'.R#[#

!X



7R'1.C#j#56





'#IX

 

 
>6fh1(#Sr'.R#=-


 
!

!
 
! !

=++− 

 !9 

=+++− 
4!

 >>
d
>! 

=++− 
0B
!!:! −+


>9
9
=−+−
+−


0B
!: ±±
:
E
>

?::> −±−
4:!
>"#*'#.L'0##DM3#;MS|'#N' DX-iX-iMB-&M<Q
MC#
>?7R'1.C#j#56<-#*
O KU

+−
+−


(012020345*

n~'#I6#I(#Sr'.R#wX&m(=Q

D

MG'#|'#IM$'h#(#Sr'.R#
 
a) (_A2L15VfO82L:
$#FmD/&.F'#(#Sr'.R#6#I
7#D#FmD#dFD#FmF(#Sr'.R#0
fh(#Sr'.R#[#5zD#FmR'1.C6D#Fm.G#D'1.CDF&.F'
#(#Sr'.R#6#IM<R#FmD
b) (_A2L15VfO82LM%&':
L'(#J(YM3Sr'MSr'M<MMY&z+'Wa#(#Sr'.R##I=QL'#-Z
'1.C-DIMQ
"&'Y#dFYY-##I=QMMQ#-./YYY-##I=QML'#-
2S#IMk#FSr'MSr'#I'G&(#Sr'.R#6z&.F'#(#Sr'.R#6
#IMk#F
8>)A2L15
>6fh#I(#Sr'.R#




=−
=+
1823
52
yx
yx



−=
=
3
4
y
x
 







=
−=
3
2
4
3
y
x
>fh1#I(#Sr'.R#
()*+,-."/01230.4 5+,*&'6

 




y
y
x
x
y
y
x
x
0B



−=
=
4
1
y
x




−=
=
8
3
y
x
>2C#'1.C6#=QM<#I(#Sr'.R#=-i'#I


 

.F'M
: −≠∉ $

e1MC#M<#I(#Sr'.R#'#I'-DW
0B







+
=
+

=

!








•


0B



=
=



=
=
?
!

!
?









−=
−=





>Ffh#I(#Sr'.R#



=+
=+

!


0B





−=
−=
!



?(_8>)892L15
()*+,-."/01230.4 5+,*&'6

 
A. 82_8>)892L15:
6g92L15

=−+⇔ xx
\-D.

!:

?XF][D[Q6'S|M&
X!0…#
>n&#Y#-DZ0#a##/Y=i'\-?'| (#$i#]D/YM-3#dF
M-30C(#-DZ1#Y 0Oj[Q6#-DZY.L'i#]D###r#-DZ
 0…#V
OPf;[Q6#-DZX0…#MZ-0I[Q6iX 0…#
(
3
16
12
2020
=
+

xx



 9?

!:

?XF][D[Q6#-DZX!0…#
>n&o-#6D#]D.W&0#$=i'4@0"hMZ5@'| (#$78#[Q6
o-#6D0#SDWXm'Y.L'[Q64†'SX90…#

9?!>fh

 


4
3
XF]
[Qi0#SDWXm'X 0…#
()*+,-."/01230.4 5+,*&'6
!
 
Dạng 4: TOÁN NĂNG SUẤT:
Dạng 5: TOÁN VỀ SỰ THAY ĐỔI CÁC THỪA SỐ TÍCH:
>6n&(#†'#;(?#~'GPF(#hY(>>#~'G'S|0W#W4kD'#Y~
4kDY(#W #~78#=Q4kD'#YX$Mo-6(#†'#;(
OPf;=Q4kD'#YX$Mo-Xt
2
500
3
616
=−
+ xx



??K?:

 ?


@

XF]A@0'…
!
>0'…
!
Dạng 8: TOÁN VỀ TÌM THỜI GIAN MỖI ĐƠN VỊ LÀM MỘT MÌNH XONG CÔNG VIỆC:
>6Y-#†S+'#hDF&1<#R=-'|!(#$MoD<Y-a†#*#5#hD
.F'?(#$†#*##hD.F' (#$#RMoD
5
1
<OjY-~†#hD&R##R(#h
FX)-MoD<V
OPf;#|'†#*#5#hD&R#MoD<X8#L''|f;#|'†#*#
#hD&R#MoD<XDDD8#L''|7#I(







=+
=+
5
1
3
1
4
1

4
365
36
511
yx
yx




=
=

18
12
y
x
AX-['S|#*#5)D&R#.F' '|#RF'*S|'
'S|#*#)D&R#.F'@'|#RF'*S|'
§3. CÁC BÀI TOÁN VỀ HÀM SỐ VÀ ĐỒ THỊ
()*+,-."/01230.4 5+,*&'6
9
 
A. h:
1. .>B&'89#:
n&#=Q4]'D
0≠
MST';X#=Q[#5MQY
78##56#=Q[#5D





X&MS|'F'MB-'QF]M&‹';X(.FX#[.p‹D
X.pMQ*'2<‹';XMl#6(.FX
Y-#RMG#CL(#8.W.p#F#‹XM<#5(#56MG#C
Y-U#RMG#CL(#84S.p#F#‹XM<F#56MG#C
b cd0eb+\i.cP4j
6.>B&'89#
>6Y(#Sr'.R#6MS|'#N'#jk&.F'1MZ-0I=-
\F'=F'MS|'#N'D !MB-M<






3
4
;
3
1

()*+,-."/01230.4 5+,*&'6
?

U
O

D


Nhờ tải bản gốc

Tài liệu, ebook tham khảo khác

Music ♫

Copyright: Tài liệu đại học © DMCA.com Protection Status