DE CUONG ON TAP K10CB


PHẦN ĐẠI SỐ
A. LÝ THUYẾT
 Kiến thức cơ bản:
1. Bất đẳng thức, bất phương trình

 ! "#$ %
&'&
⇒
& ()*
&
⇔
+&+ #','-
#./
01 &
⇔
& "2','-
#./
&1 &
⇔
0
&'&$
⇒
+&+$ #3

01401 &'&$
⇒
&$ "23

5
$6

&
⇔

77
++
<
nn
ba
"2',
8#89:
1&&
⇒

nn
ba
77
<
01 &
⇔
ba
<
;<',#

&
⇔
==
ba
<
7>$>?5!/
xxxxx

−>>>
441
axaax
≤≤−⇔≤
@01A
axax
−≤⇔≥
BC
ax ≥
bababa
+≤+≤−
=(DE.
A141@
7
≥≥
+
≤
ba
ba
ab

7
ba
ab
+
=
FG5 H
2. Bất phương trình và hệ bất phương trình một ẩn
Các phép biến đổi bất phương trình
;!I8JK>./LBGM !K6N@FA&

O@FA
PK#
",Q@FAF>?IN@FA&O@FA
⇔
@FA+Q@FA&O@FA+Q@FA
PK2
",Q@FA014
Dx
∈∀
N@FA&O@FA
⇔
@FAQ@FA&O@FAQ@FA
",Q@FA&14
Dx
∈∀
N@FA&O@FA
⇔
@FAQ@FA0O@FAQ@FA
PKNK6
",
1A@
≥
xP
'
1A@
≥
xQ
4
Dx
∈∀

N@FA&O@FA
A@A@
77
xQxP
<⇔

3. Dấu của nhị thức bậc nhất f(x) = ax + b
F
∞−

a
b
−

∞+


Q@FAHF+ >$'-13$'-
4. Bất phương trình bậc nhất
(R$SN%JK!K6N
A1@
77
≠+≤+
bacbyax

(-TUV
cbyax
=+∆
T


(-7TW5#R
∆∉
AX@
111
yxM
@8/BY#ZA
(-=T[B.>
11
byax
+
'-
(-\T;,8J
",
11
byax
+
&N]CK
∆

1
M
8!
cbyax
≤+

",
11
byax
+
0N]CK

∆
 D
1
M
8!

cbyax
≤+

5. Dấu của tam thức bậc hai
A1@A@
7
≠++=
acbxaxxf
•
1
<∆
N'-%
ℜ∈
x
4Q@FA^3$'-!./
•
1
=∆
NQ@FAH1'-
a
b
x
7
−=

4''-%
a
b
x
7
−≠
4Q@FA8D3$'-
!./
•
1
>∆
NQ@FA^7!

x
4
7
x
@

x
&
7
x
A'Q@FA>$'-!./'-
%F#
AX@

x
−∞
5

AX@
7
+∞
x

^RFP$J_K
1
>∆
.T
F
∞−


x

7
x
∞+

cbxaxxf
++=
7
A@
3$'-1>$'-13$'-
6. Các số đặt trưng
6.1. Số trung bình cộng (
x
)
• _KGK2/*./4*.

kkkk
xfxfxfnxnxnx
N
x
+++=+++=
A@

7777
B^
ii
fn 4
8*8_8*./4*.>?
i
x

"8>./8!/ @
Nnnn
k
=+++

7
A
• _KGK2/*./4*.PK8-K
kkkk
cfcfcfncncnc
N
x
+++=+++=
A@


7777
B^
iii
fnc 4
4
8*8_8>?Y$!4*./4*.8-K
"8>./8!/ @
Nnnn
k
=+++

7
A
6.2. Mốt (
1
M
)
BGK2/*./4>?^*./8-%8/`
'_ !
1
M

6.3. Số trung vị (
e
M
)
[)K.,KL>./8!/ $M5 DG@BC D
<AT
","8aN>?
7


+
N
_%8./'?

","bNN>?
7
N
'

7
+
N
8./'?
6.4. Phương sai (
7
x
S
)
• _KGK2/*./4*.

[ ]
77
77
7

77
77
7


7
A@A@A@A@A@A@

xxfxxfxxfxxnxxnxxn
N
S
kkkkx
−++−+−=−++−+−=
B^
ii
fn 4
8*8_8*./4*.>?
i
x
X"8>./8!/ @
Nnnn
k
=+++

7
AX
x
8./N#>./8!MB
• _KGK2/*./4*.PK8-K

[ ]
77
77
7


77
77
7

7
A@A@A@A@A@A@

xcfxcfxcfxcnxcnxcn
N
S
kkkkx
−++−+−=−++−+−=
B^
iii
fnc 44
8*8_8>?Y$!4*./4*.8-KX"8>
./8!/ @
Nnnn
k
=+++

7
AX
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6.5. Độ lệch chuẩn (
x
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7

xx
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=
II. Phương pháp giải các bài toán thường gặp
B. BÀI TẬP
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7=
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+
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7
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xxxf
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7
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
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7
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
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mx @7
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7
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7
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1\A=@A=@
7
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7
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
17=A7=@A@
7
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THỐNG KÊ
(TBJK_K>./8!/ .T
1XdX=X7X1XjX=XdX=XfXjXhXhX1X=X1
 WJKGK2/*./
 N>./N4/4./'?
 N#8!k
(7T/ ./>5B#>#]>5
$PK_BBG.@6'?TDA
77 71 h 7 71 7\ h i 77 7=
h i 71 7 77 7\ 7f 71 h 7=
71 j h 77 7\ 7= 7\ 7d 71 7
WJKGK2/*./4*.
./N#
K6.'#8!k

(=TBG./8!/ 
"<.8lm@YnA<hhi=o:"!pq'B
=1 =1 7d 7d =d \d \1 \1 =d \d =d
7d \d =1 =1 =1 \1 =1 7d \d \d
=d =d =1 \1 \1 \1 =d =d =d =d
M58JKGK2/*./4*.
./N#4./'?4/
#8!k
(\TBG./8!/ 

@KlAB#JKB>r%.8-K1(
714i 714j 7=4 714j 714h 714h 7=4h 74f
7d4= 74d 7=4i 714j 7=4= h4i 714h 714
74= 7\47 7741 7=4i 7\4 74 774i h4d
h4j 74h 747 7\47 7\4= 7747 7=4d 7=4h
774i 774d h4h 7=4i 7d41 774h 774i 774j
M58JKGK2/*./'*.PK8-K4'->8-K.T
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d47dXd47\Xd47\Xd47=Xd47=Xd477Xd477Xd47Xd47Xd471Xd471Xd4h
./N#
#8!k
(dT'./sIi1N4'_G*./E*
..T
W-K *./ *.
[ ]
1X
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71X
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=1X7

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\1X=
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d1X\
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f1Xd
d
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
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# "Hi1 
 >./'Bt/@Aq#*.
 UVRuN#*.
 UVRuK l*./
$ ./N#
(fTgB$v%8_a.6.Y#!B#*8S_
G./8!.T
%8_@ A [/gB^
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=d
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71
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4\Xi4=
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