Bài tập ôn học kì 2 môn đại số lớp 10 pdf

¤n tËp häc k× 2
BÀI TẬP : ĐẠI SỐ
Phần I: Bất Đẳng Thức
Bài 1:
 ≥ba











+
≥
+ baba





bababa ++
≥
+
Bài 2:
cba ≥≥




 cbacba +−≥+−

ababcba 

≤+≤++

Bài 3:


≥−−++ acabcba
Bài 4: !"#$





ba
baba
a −
≥
++









cba
aacc
c
cbcb
b
baba
a ++
≥
++
+
++
+
++
Bài 5: !"#$


%%

cbaab
abcba
++
≤
++

abc
abcacabccbabcba
%%%%

≤
++

+
++
+
++
Bài 6:

%
<<
x
&'(&))*

% xxxf −=


>
x
&'(&))*



x
xxf +=

%
<<
x
&'(&+)*
%

xxxf −=

Bài 7: !"#$,-

.%%% ≥






+






+






+
a
c
c
b
b
a


/ ≥






+






+






+
a
c
c
b
b
a
Bài 8:




=++
>
%

cba
cba
,-

0%
%
%
%
%
%
≥






+







+






+
cba

.
%%%
%%%
≥
−−−
+++
cba
cba
Bài 9:



=+
>
%

ba
ba


&'(&+)*12

ba
ab
+
By: BÙI NGỌC HOÀNG
1
&'(&))*12








+
ba
%%
Bài 10:



=++
>
%

cba
cba
&'(&))*12


cba ++
&'(&+)*12

/// +++++ cba
&'(&))*12
%
%
%
%
%
%
+
+
+
+
+ cba
"&'(&+)*12
%%% +
+
+
+
+ c
c
b
b
a
a
&'(&))*12
accbba +

+
+
+
+ 
%

%

%
Bài 11:



≤+
>
%

ba
ba
&'(&))*12
ba
ba
+++
%%
&'(&))*12
ab
ab
+
%
Bài 12:






=++
>
%
%%%

cba
cba
&'(&+)*12
accbba +
+
+
+
+ 
%

%

%
Bài 13:34567"89:8,-;#$' 2
<=


=+++++− cabcabxcbax
>:8?
Bài 14: !"#$,-




cba
ac
c
cc
b
ba
a ++
≥
+
+
+
+
+



≥
+
+
+
+
+ ba
c
ac
b
cb
a


%
%
%





≥
+
+
+
+
+
ab
ab
b
ba
a
"
cba
b
ca
a
bc
c
ab
++≥++
@









cba
ac
c
cb
b
ba
a ++
≥
+
+
+
+
+
A

%%%
cbaa
c
c
b
b
a

++≥++
Bài 15: !"#$,-


acaccbcbbaba
a
c
c
b
b
a
+−++−++−≥++
Phần II: Bất Phương Trình, Hệ Bất Phương Trình
Bài 1:(B8=:2C5D&
%%

−++≥+ mmxxm
Bài 2:&'61=5D& 2=



≥−+
+−+≥+
%
%%

mx
xxxxx
Bài 3:&'615D& 2#$6#$
%%


−+≥+− xxxx
%

≤+
mx

By: BÙI NGỌC HOÀNG
2
Bài 4:(B35D& 2

%%

−−+−≥− xxxx

% <+−− xxx

E%

≥−− xx
"



%
%
<
+
−
− xx

@
0%

≥−−− xxx
A

0E
%

%

<
+−
−
− xxx

E

≤− xx
Bài 5:&'&FG*38 ! 2

%
%

%

−
−
−
=

x
x
y

0E
.


+−
−−−
=
xx
xxx
y
Bài 6:&'618 !>36H
Rx ∈

%%

++++= mxmmxy
Bài 7:&'61=5D& 2=




−+≤
≤+−
%
0/


mxmx
xx






≤+++−
≤+−
0
%/


mmxmx
xx
Bài 8:(B3D&85D& 2

0

=+−+ xxx



≥+−− xxx



≤+− xx
"

%% ≤+−+ xx
@
xxx −≥−+ %
A
%

+−≤− xxxx

% −=−−+ xxx



+≤−− xxx


E


≤
+
−
x
x
Bài 9:(B3D&85D&

%% =+−−++− xxxx

E%0

+≤−−− xxxx




≥−+−+ xxxx
"
%%

+−≥−++ xxxx
@
% <+++ xxxx
A
%
%E
%


++
≥++
xx
xx
Bài 10:
&'61;#$' 2=
%

=+−−− mxx
&'615D& 2=


≥+−+− mxxxx
&'615D& 2=6I>27C;>36H

%%

=+−−+−++− mxxxx
Bài 11:&'615D& 2=6I>
/

E
%


<
+−
++
≤−
xx
mxx
Bài 12:,->JK

0

>+−−−+ yxxyyx



≥++++− yxyxyyxyx



>−−−−+++ xyzxzxyzyx
By: BÙI NGỌC HOÀNG

3
BÀI TẬP :HÌNH HỌC
B i 1:à
LD&&MND&&O*"
1. "6P261,QRN&D
Q0u =
r
2. "6P261)QN&D&
 Q%n = −
r
3. "6P261D%QN= !
k = −
 "6P2614RQN5%Q
Bài 2:
L;#$'6#ST"
% "6P261*6#ST
% 
  %E   %  d x y d x y− − = − + =
86
P2614Q
 "6P261*6#ST
% 
 E   E   d x y d x y− + = − + =
8
 6#ST

  d x y− + =
 "6P261*6#ST
% 
  E     d x y d x y− + = − − =

8
2<6#ST

 / % d x y− − =
 GP24Q89U8

0

Bài 3
L;#$'6#STdLdV3OxOy9ABW#S
X; 2

EQM
:8261AB

OAB
∆
2<Y8dP2
 QN −


OAB
S
∆
=
8dP2

Q%

M

 
 ÷
 

"
0
OAB
S
∆
=
8d2<6#ST
Z   % d x y− + =
Bài 4:
ABC
∆
L4QRE5%QRQR
L;#$'[P23*
% 59345
 G#STP248  95
 &22JL4,86#S4\&'67Y6#S\
 G#S2]95
E G#S2'  945
0 G#S;Y34
Bài 5:
   N %Qd x y M− + =
% &'67'L2\*,:^"
 &'6761)6!>*,P2"
3. L;#$'6#ST
d
′

6!>*
d
P2
M

Bài 6:F_H`#$6!*3a;6#ST 28'61*I
L2

+ + = + − =
1 2
: 2 3 1 0 & : 4 5 6 0d x y d x y

− + = − + + =
3 4
: 4 2 0 & : 8 2 1 0d x y d x y
By: BÙI NGỌC HOÀNG
4


= +
− − =

= − +

5 6
5
: & : 2 11 0
3 2
x t
d d x y

y t
"

= +
+ − =

= −

7 8
5
: & : 5 0
1
x t
d d x y
y

@
= + − =
9 10
: 2 & : 2 4 0d x d x y
Bài 7: 6#ST
% 
    /       D x y D x my+ + = + − =

&'m61
%
 D
V

 D


% 
  b b D D

% 
   D D⊥
Bài 8:&;67
ABC
∆
L4%Q%5QRQR
% &`
ABC
S
∆

 &'6761,276#STx-2y-1=0 
%E
ABC
S
∆
=
Bài 9:6#ST
   x y∆ − − =

  . x y
′
∆ − + =
% &'^c>61,3
∆
7dB

 &`dB3e
∆
8
′
∆
Bài 10:
%
   x y∆ + + =

  0 x y∆ − + =
% &`e
%
∆
8

∆
 L;#$'6#ST6P24%Q8X;
%
∆


0

 L;#$'6#ST  
%
∆
8dB36L

∆


%
Bài 11:&;674%QR%5%Q%QR
% L;#$'6#STP24836f258
2. L;#$'6#ST
∆
P258dB3g6L
∆

Bài 12&'C;X;36136f26#ST
%
%
  0 x y∆ − + =
N

   x y∆ − − =


  0 x y∆ + + =
N

E % x∆ − =
;Y39h

∆
8

∆

Bài 13:6#ST
: 3 2 1 0x y∆ + − =

8
: 5 3 +2=0d x y−
% F_H`#$6!e6#ST^
 &`dB3g4EQ6L6#ST
∆
 L;#$'36#S;Y3*9h6#ST^
 &'61,27
∆
 dB3g,6L
"
E
E &'61)276#ST
1
( ) : 2 0x y∆ − =
 dB3g)6L
∆
:idB3g)6L
"

Bài 14    '  '  8 ABCD   Y 
QEI
 8    9    ^
%
  0 x y∆ + − =
8

  E % x y∆ − − =
L;#$'39j:9*'
'8
By: BÙI NGỌC HOÀNG

5