đề tự luyện THPT QG môn toán đề số 24


 
Thời gian làm bài: 180 phút
!"#
( )
2
( )
2
x
y x C
x
−
= =
+
a) 

( )
   y x∆ = +
!"#$$%&'()*$+,-./$&(
!"#$%
0 1$$)234:
$  5 6  $7x c x
+ = +
 )8!
z
90:$;<=$+
   > i z i+ − − =
,4)?!@0)8!
w zi z= − +

!"&#$ 'A. 1$$B)234

>
>
C   C   x x− + − ≤
!"$  1$$+)234:
>  
   
5 
    > 
y y x y xy
x y x y x x

+ + − − =


+ + + = − −



!"#$,-/$+-!4)$D$#E$


x
y
x
+
=
−
!!3F!G0.
!"'$4!H)I&(J!HK&(JC40D$KCDC&JL!!
I&'&JM$.<MH!D$0<LI&N&NJN

a 2
&JN(,-%-!!@0
=$!H)I&(J=!!$O00$I(J
!"($,3P)D$+G0.Q7K'!0$!&(/
D$(!"!!!#&('&C?CR#$ST0!
=
AM CN
($U3VSW5L 'AL!*
)*$!3!@0H!&CJ LWX:K4G0.!@0&(
!")#$,3=M$0D$+G0.Oxyz'!0$

 >

 > 
x y z− −
∆ = =
−



> 

Y 5 A
x y z− −
∆ = =
−
,4G0.$0$%!@0

∆



∆
$U)234P)Z0!


∆
C4!$U<<MH!!@0

∆
C[P)Z
!"*#$ 'A Một HYG!$!H[=!0<'3H!H0$G!$[C&(4
\U)]<$[HG!$H./G!,-7!<B0!0$G!$&
(48!#0<
!"$ x'yC0$^!90:$;<=$+
5
>
≥++ xyyx
,4$39B!@0$U<
8!
 A5>>

+−−+−+= xyxyyxyxP

__________XU__________

XG[-$____________I/0_________
O=`$__________O=`$_________
+,-./0123
 !" $m
$$4

$$5
#,a)7!
bc dD = −¡
e
( )

5
f '

y x D
x
−
= < ∀ ∈
+
e,$+!a0KNW4
C$ L C$ 
x x
y y
→−∞ →+∞
= − = −
e,$+!a87NW4
( ) ( )
 
C$ L C$
x x
y y
− +
→ − → −
= −∞ = +∞
e($U$[

6 
∞
7 8
∞
9  7 7
 7
7
∞
8
∞
7
X!$U3[W
∞
LW'WLg
∞

X=M!H!^!3
e$%P!$+
: ' 7 7  
  7& ;:.  
e
x
y
y=-1
x=-2
0
-2
1
2
-1

-3
-5
3
e1G$
( )

LM x y
C$U)$%
e

f  5 >L ff   5f x x x f x x= − + = −
e

ff   5 f x x x= ⇔ − = ⇔ =
eI<K30'
( )



>
y f= =
'

f  f f x f= = −
eZ234$U)<KU
( ) ( )

fy f x x x y= − +
'A
'A

'A
'A
'A
'A

( )
 6
 
> >
x x= − − + = − +
ehaK)234$U)<KU!?4C
6
>
y x= − +
'A
'A
$$4 <=<>1+?-@AB1
$  5 6  $7x c x
+ = +
($Ui$)234;/#
$7 5  
$7j5! 

!

vn
x
x
=



− = ⇔

=

hD$

!7 
 >
x k
π
π
= ⇔ = ± +
C)234!HG$+
 '
>
x k
π
π
= ± +
0,25
0,25
$$5
    )8! 
z
 90  :  $;<  =$+ 
   > i z i+ − − =
  ,4  )?    !@0    )8!
w zi z= − +
1$k

 ' z x yi x y z x yi= + ∈ ⇒ = −¡

,l$$U'0!H

    >    >

x
i x yi i x y x y i
y
=

+ − − − = = ⇔ + − + − − = ⇔

= −

I<K30
z i
= −

,0!H

    >  w i i i i i i i= − − + + = + − + = −
haK
m w = −
0,25
0,25
$&

x >
(Z,



>
>
C   C   x x⇔ − + − ≤
> > >
C   C    C    x x x x⇔ − + − ≤ ⇔ − − ≤

   >  >  x x x x− − ≤ ⇔ − − ≤



x⇔ − ≤ ≤
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(
]
LS =
0,25
0,25
$
<=<1C>1+?-@AB1
>  
   
5  
    >  
y y x y xy
x y x y x x

+ + − − =



+ + + = − −


($Ui$)0?<;/#

     

y
y y y x y
y x
=


− + + − = ⇔ = −


= −

,XhD$KN0K)

6 > Y x x+ + =
M$+
,XhD$KNj0K
> Y x x
+ = ⇒ = −
<K30$+7LKNjLj
0,25
0,25
0,25

0,25
,X>hD$
y x= −
0K
5   
  A
>      
  
x x x x vn+ + = ⇔ − + + + =
C+)234!H$+
 L   L x y = − −
$
D1.<C@D011B1>1E--<,<1F5G<HI@1J1K3LM


x
y
x
+
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