Đề giữa kỳ 1 Toán 12 năm 2023 - 2024 trường THPT Võ Văn Kiệt - Gia Lai

1

4 2 y x x = − 3 y x x = − 1 2 x y x

− = +

3 y x x = +

3 2 3 1 0 y x x y x x  = +  = +  ( ) y x =

( ) 2;+ ( ) 0;+ ( ) ;0 − ( ) 1;2 −

( ) 0 f x   ( ) 2; x  + ( ) 2;+

( ) = y f x

( ) 0;+ ( ) 1;+ ( ) 1;0 − ( ) 0;1

( ) y f x =

2

( ) 1;3 ( ) 3;1 ( ) 1; 1 −− ( ) 1; 1 −

( ) y f x =

( ) 1; 1 −−

( ) y f x =

( ) f x  ( ) f x

( ) y f x =

3 0 2 1

0 x = 0 y = ( ) 4 2 , , y ax bx c a b c = + + 

0 1 − 3 − 2

3

0 x = ( ) 0 1 f = −

( )

3 3 f x x x = −   3;3 −

18 18 − 2 − 2

( )

2 3 3 f x x  = −

( )    

1 3;3 0 1 3;3 x f x x = −−  =  = −  ( ) ( ) ( ) ( ) 3 18; 3 18; 1 2; 1 2 f f f f − = − = − = = −

  ( ) ( ) 3;3 min 3 18 f x f − = − = −

( ) y f x = M

m   1;3 −

M m −

[ 1;3] 3 M max y

− = =

[ 1;3] min 2 m y − = = −

5 M m − =

3 1 2 x y

x

− =

− 1 2 x = 2 x = − 3 x = 2 x =

2

3 1 lim 2 x

x x  →

−=  − 2 x =

( ) y f x =

4

1 x = − 3 x = − 1 x = 3 x =

1 lim x y + → = −

1 lim x y − → = +

1 x =

4 1 1 x y

x

− =

+ 4 y = − 1 y = 4 y = 1 y = −

4 1 lim lim 4 1 x x

x y

x → →

− = = + 4 y =

4 2 2 y x x = − + 3 2 3 y x x = − 3 2 3 1 y x x = − + + 4 2 2 1 y x x = − +

4 2 y ax bx c = + + 0, 0, 0 a b c   =

( ) y f x =

( ) 2 f x =

1 0 2 3

5

( ) y f x = 2 y =

( ) 2 f x =

6 10 12 11

  4;3

  4;3 4

3

  3;3 4 6 4   4;3 8 12 6   3;4 6 12 8   5;3 20 30 12   3;5 12 30 20

h B

V Bh = 1

3 V Bh = 1

6 V Bh = V Bh = 1

2

h B V Bh = 1

3 .S ABCD 4 ABCD 3

7 5 4 12

6

.

1 1 . . .4.3 4 3 3 S ABCD ABCD V h S = = =

3a

3 27a 3 3a 3 9a 3 a

3 3 (3 ) 27 V a a = =

4 2 2 y x x = − ( ) ;1 − ( ) 1;0 − ( ) ; 1 −− ( ) 1;+

3 4 4 y x x = −

3

0 0 4 4 0 1

1

x y x x x x

=   =  − =  =  = − 

4 2 2 y x x = − ( ) ; 1 −− ( ) 0;1

( ) y f x =

( ) y f x =

( ) 2;0 − ( ) ; 2 −− ( ) 0;2 ( ) 0;+

( ) 2;0 − ( ) 2;+

( ) 4 2 , , y ax bx c a b c = + + 

2; 4; 6

16 12 48 8

2.4.6 48. =

7

1 x = 1 x = − 2 x = − 0 x =

( ) f x ( ) f x 

4 1 2 3

( ) f x  1 x = − 1 x =

( ) f x

1 x = − 1 x =

M

4 2 2 3 y x x = − + 0; 3     9 M = 8 3 M = 1 M = 6 M =

( ) 3 2 4 4 4 1 y x x x x = − = −

0 y=  ( ) 2 4 1 0 x x − =

0 1

1( )

x x

x l

=    =  = −  ( ) 0 3 y = ( )1 2 y = ( ) 3 6 y =

4 2 2 3 y x x = − + 0; 3     ( ) 3 6 M y = =

, M m ( )

4 2 2 3 f x x x = − +

  0;2 M m +

11 14 5 13

D = ( )

3 4 4 f x x x  = −

8

( )

     

3

0 0;2

0 4 4 0 1 0;2

1 0;2

x

f x x x x

x

=    =  − =  = −  =   ( ) ( ) ( ) 0 3; 1 2; 2 11 f f f = = =

11 13 2 M M m m

=    + =  = 

( ) y f x =

4 1 3 2

lim 2 x y →−= 2 y  =

lim 5 x y →+= 5 y  =

1 lim

x

y − →

= + 1 x  =

3

2

9 3 x y x x + − = + 3 2 0 1

 )   9; \ 0; 1 D = − + −

( ) 1 lim x y + →− =

( ) 2 1

9 3 lim x

x

x x + →−

+ − + = +

( ) 1 lim x y − →− ( ) 2 1

9 3 lim x

x

x x − →−

+ − = + = −

 1 x = −

0 lim x y + → = 2 0

9 3 lim x

x

x x + →

+ − + ( )( ) 2 0 lim

9 3 x

x

x x x + → =

+ + + ( )( ) 0

1 lim

1 9 3 x x x + → =

+ + +

1 6 =

0 lim x y − → = 2 0

9 3 lim x

x

x x − →

+ − + ( )( ) 2 0 lim

9 3 x

x

x x x − → =

+ + + ( )( ) 0

1 lim

1 9 3 x x x − → =

+ + +

1 6 =

 0 = x

1