Bộ đề luyện thi đại học môn toán

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− −
= =
e!-!7.R2Q2Q|z!-!K/"!N4;!-n 456!-/+!N4;!-
L
*+-
3456!-/+!7
 

P 
P  P 
I- I-
x
x x x x
Log x x x
+
+ +
+ =

121345671*52
*+-9
*/!-N4;!-(HDE5?!-/C!
 
 7 C x y+ =
25?!-;!-
  7 d x y m+ + =

*+
m
.
 C
^
 d
1#(QO!A(-1HI=!
!:

w
o

o
g


*/!-BW!--(!#=O(HDEX2(N4;!-7
]7DkEjXjl2}7DkEjXjl2t7DjEkXjl
#5?!-;!-

∆
7


−
−x
l

+y
l


z
3

∆
I-(0E !'(]#}
n 456!-/+!5?!-;!-Q#0W!--L#=t#^(5?!-;!-

∆
2

∆

*+-9 3:456!-/+!7I-
D
I-

V
D
kw
≤

,
*+=> ?&@+5 &'(

~*\4D&!7
{ }
i D = ¡
~*A!



{ 
 
y x D
x
−
= < ∀ ∈
−
<!-& !/"!B!-
 @−∞
#
@ +∞
~<BW!-L/&
~3=!

+
→
= +∞
x
lim y

x
Limy
−
→
= −∞

x
Lim y
→+∞

=


x
Lim y
→−∞
=
%&LO\!e!-7Dl2O\!!-(!-El
~!- !"!
D
−∞

+∞
E| 
E

+∞

−∞


~n$%&
8
8
8
8

~* 40E !'(.
 
 @    M x f x C∈

L456!-/+!

  
{    y f x x x f x= − +
<(E
 
  
     x x y x x+ − − + − =
~
~!-S.s@ ! 40E !~K!-



P

 

  
x
x
−
⇔ =
+ −

-5U!-O

x =
#

x =

~ 40E !Y!+7
 x y+ − =
#
8 x y+ − =
8
8
8
8
 ~ !•456!-/+!)56!-56!-#=

p


  !     9 
9
c x x c x
π
− + + + =

  8    
 9
c x c x
π π
⇔ + + + + =


    8    
9 9
c x c x
π π

⇔ + + + + =
35U

 
9 
c x
π
+ = −
#
  
9
c x
π
+ = −
I
~3

 
9 
c x
π
+ = −
5U!-O


x k
π
π
= +
#

8

9
x k
π
π
= − +
8
8
8
8

~ !•O56!-56!-#=
  
 
  
  
x xy x y
x y x xy

− = −


− − = −


~N€!4G


x xy u

x y v

− =


=


2(5UO



u v
v u

= −

− = −

~3O/"!5U!-O0@#I@#@
~*SL-5U!-OD@EI@#@
8
8
8
8
 ~NlD
*A!Ql!DQD2•\!Dl+l2
P
x
π

=
+


t =
*SL



 



I! I!t t
I dt dt
t t
= − =
∫ ∫
~N


I! @u t dv dt
t
= =

 
@du dt v
t t
⇒ = = −
Z0E/(





 
   
I! I! 
 

 
I t dt
t t t
= − + = − −
∫
~ F0

  I! 

I = − −

8
8
8
8
P ~n$+!
~3<I/0!-.2e!-!
 SH ABC⊥
~•&!‚!--L-,((N4;!-Z12Z1#=NEI



9SEH SFH= =
~T
HK SB⊥
2I\4I0\!0E/(-L-,((N4;!-Z1#Z
K!-
HKA

8
8

V

~[\4I0\!#A!5U1l1l(2


a
HA =
2


(! 9

a
SH HF= =
~*(-Z<#0W!-<L
  
   

KH a
HK HS HB

= + ⇒ =
~*(-1<#0W!-<L



(!



a
AH
AK H
KH
a
= = =




AK H⇒ =

8
8
8
~ !•
 
   
a b c c
ab c ab b a a b
+ − −

= =
+ + − − − −
~*SL
  
        
c b a
VT
a b c a c b
− − −
= + +
− − − − − −
h(22Q56!-#(jjl!"!(220B!-@lv(22
Q56!-
~4QG!-:;!-eW(Q56!-(5U

  
  
        
c b a
VT
a b c a c b
− − −
≥
− − − − − −
l4
;!-eDE/(B#yB


a b c= = =
8

8
8
8
9(
~
∆
L456!-/+!(
 
 
x t
y t
= −


= − +

#L#4
 @u = −
ur
~10
∆

  @   A t t⇒ − − +

~*(L1@
∆
lP8




 @ 

c AB u⇔ =
uuuur ur





AB u
AB u
⇔ =
uuuur ur
ur


8 
9V 89 P8 
 
t t t t⇔ − − = ⇔ = ∨ = −
~.Y!+I
 
 P  
 @ 2  @ 
   
A A− −
8
8
8
8

9(
~QF0(

@ @M −
#L#4

@ @ u = − −
uur
Q|F0(

@@PM
#L#4

@@8u =
uur
~*(L
 
@  P@ p@Pu u O
 
= − − ≠
 
uur uur ur
2
 
@@PM M =
uuuuuuur
•ƒ
   
@  9 P u u M M
 

= − + =
 
uur uur uuuuuuur
Q#Q|%!-4;!-
~3]IN4;!-e(Q#Q|lv]L#4
@@ n = −
ur
#F0(
R

!"!L456!-/+!
  x y z+ − + =
~h„:E.R@@0o]2SL(L4
8
8
8
8
w( ~0BO!7Dv



~*<7DƒDlI!-O
~*<7Dƒ
x ≠
2 !•456!-/+!56!-56!-#=

  
 I- P   I- P  I- P 
x x x
x x x

+ =
+ + + + +
N
I-  
x
x t+ =
2(5U456!-/+!

  
  t t t
+ =
+ +
-5Ul#lg
~n=l
I-   
x
x⇒ + =
456!-/+!!E#W!-O
~n=lg

I-  

x
x⇒ + = −


 
P  x x⇔ + =
~
b\!:E


p
x =
I!-O'(~
b 0

p
x >
+n*~v
b 0

p
x <
+n*~…2#\E~L!-OQ0E!:

p
x =
~ I0\!7!-O'(456!-/+!)IDl#

p
x =
8
8
8
8
9 ~LfH@2!BA!tl
~Q^(.4f!O
 @  d O d⇔ <
~*(L
  

 ! !
  
OAB
S OAOB AOB AOB= = ≤
*SLQO!A(-1HI=!!:B#yB

VAOB =


 @ 

d I d⇔ =

m⇔ = ±
8
8
8
8
9
~

∆
L456!-/+!(
 


x t
y t
z t
= −



= − +


=

~

∆
L456!-/+!(

8 
x s
y s
z s
= +


= +


=

~3†
 
@d A d B∩∆ = ∩∆ =
  @  @ j@8j@A t t t⇒ − − +
~
  @ 9@  AB s t s t s t= + − + −

uuuur
2otL#4
@@ n = −
ur
8
8



~
  ‡d R AB n⊥ ⇔
uuuur ur
z!-456!-

  9 
  
s t s t s t+ − + −
⇔ = =
−


P
t⇒ =
~QF0(
  
 @ @ 
  p
A
#L#4
@@ n = −

ur
lvQL456!-/+!

 
p
 
  
z
x y
−
− −
= =
−
8
8
w
~0BO!7


I- V w 
V w 
x
x
x >


− >


− >


-5U
V
I- wx >
n+
V
I- wx >
v!"!4)56!-56!-#=


I- V w
x
x− ≤

V w 
x x
⇔ − ≤

 p
 V
x
x
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V
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8
8
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x
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lZ|l
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V V V V V V
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x y y z z x
P
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P  P x y x+ + − =
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P 
x t
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= +
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d
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ứng như trong đáp án ).
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x y x
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