139679092 ΕΠΑΝΑΛΗΠΤΙΚΕΣ ΑΣΚΗΣΕΙΣ Α ΛΥΚΕΙΟΥ ΑΛΓΕΒΡΑ
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ΑΛΓΕΒΡΑ Α ΛΥΚΕΙΟΥ
Transcript of 139679092 ΕΠΑΝΑΛΗΠΤΙΚΕΣ ΑΣΚΗΣΕΙΣ Α ΛΥΚΕΙΟΥ ΑΛΓΕΒΡΑ
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1. .
3 ( ) 2 2 ( ) 1 0P A P B :
. 2( )3
P A 1
( )2
P B .
. .
. 1( )3
P A B , :
i. A B A B .
ii.
.
2. : 3
2
x 4.xf x
x 2.x
. f.
. f.
. f xx
yy.
. :3
2
2014 4 2014
2014 2 2014
.
3. () y = x + , 3
yy -1.
. , .
-
. .
. () ()
y = -2x + .
4. 4, x 1, 3x 11
( ) 1.
. x .
. 4 :
) 11
2 .
) 10 .
) 3
16 2 2 , 10 .
5. 2(2x 7x 15)(4x 4)
f (x)8x 12
. f
2f (x) x 4x 5 .
. x Cf xx;
. 3f (3) 8f (4)
5( 7 3)f (2) 3
.
6. : 2 2 6 9
3
x x x
x x
3 328 1 28 1 .
. 2 2 6 9
3
x x x
x x
0 3x
. 3 328 1 28 1 .
-
. 2 3 : 3 4 35
.
7. 3 5x , 1x , 3x . . x , ,
.
. 5x 17 ( 1 )
(5 ) .
8. 2
1
6 8f x
x x
.
. f .
. 2 24h x f x x
.
. 2
4
xh x
x
,
1 3x h 21
3x
h .
9. ) x2-4x+8=0.
.
) :
+3( -1)=
+ +2
10. f(x)=2x2+3x+1=0.
) f(x)
B) x f
. .
) f(x) 1
11. f(x)= 2x +8x+9 -24 .
;
-
12. x2-4x++1=0.
) ;
) x1,x2 , ,
1 2
2 1
x x
x x =2.
13. f(x)=4x-5, x
-
. : x2-2x-5=0, x1, x2.
:
) x1+x2 ) x1x2 ) x12x2+x1x2
2
17. 2( ) 4 3f x x x ( ) 1 2g x x
) ( )( )( )
f xh x
g x
) 1x h() .
18. 2
10( )
3 10f x
x x
) f(x) ,
) 9
(0) 110 1
f
,
) 2( 5) ( ) 1x f x .
19. . : 2 3 2 51
2 3 6
x x
. : 2( 2).( 2 5 3) 0x x x
20. . :
( ) 2f x x 2( ) 9g x x
. f.
-
. g.
. : 2 2[ ( )] [ ( )] 13f x g x .
21. (1,2) , (-1,-4) , (2,5) f(x)=+.
1. , , f(x)
2. =3 =-1
f(x)
3. =3 =-1 f(x)
.
22. f(x)=2x2+5x-3.
. f(x)
-
) :
1= 1
(0) 1f 2 = 1 (0)f .
25. 1( ) 2( ) 1 : 3 2 2y x
22 : 2 5y x , R .
. 1 2// .
. R , .
. 1 , 1( ) xx ,
2( ) yy .
26.
2 9
3
x
x
.
. x .
. .
. 3x , 5
27. 2 2 0x x (1) , R .
. (1)
.
. 1 , 2 (1) :
i. 1 2 1 2
1 2 .
ii.
. 1 2 2 6
2 // xx
-
28. :
2 2f (x) 2x 5x 3 , g(x) x 9 , h(x) 4x 12
. 2f (x) 2x 5x 3 .
. x
f (x) g(x)K(x)h(x)
.
. (x) .
29. 2( ) 2f x x x
A. .
. 1x :
. 2
( ) ( ) 3 2A x f x x x
. (x)=7-4x
30. f 2
2
4
6
xf x
x x
.
. f.
. 2
3
xf x
x
x
. 3 3f x x .
. 10 6f x x .
-
31. . 2 2
( 4)x 3 2 ,
d(x , ) < 5.
. 5
x 81x 0 ,
:1 1
1 1.
32. (2-7+6,-1-3), R.
) R, y.
) R, 2 .
) =2 :
1. y'y .
2. 1-3
, =.
33. 2
1 2x .
-1
-
. (1) -2 .
. 1 2
,x x (1) : 1 2
1 11
x x
35. 2 4 4 4x x 12 22 1
x
i. 2 4x 2 1x .
ii. . 3 .
. 1 0 .
36. 2( ) 1 2f x x x , .
. :
) ( )f x .
) ( )f x
) 2 21 2 1 2 1 24 4x x x x x x , 1 2,x x ( )f x .
. 4 ( ) 0f x .
37. = 1 2 2x x . =0
=-2.
38.
= 2 2
1 1x x , 1x
= 2 2 4a >0 >0.
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39.
. 4 32 2 2
. 4 84 3
. 33 2 42 2 2
V. 12 411 32 2
40. f(x) = 2
2 1x .
I. N .
II. f .
III. f(x) = 0
41. f(x) = 6
1 2
a
x x
I. N
II. , (5,8)
III. (4,11) f
IV. yy
42. 3x2-5x+1=0 x1,x2. N
) x1x2 2 + x1
2x2
) x12+x2
2
) x13+x2
3
) 1 2
2 1
x x
x x
) 1 2
1 21 1
x x
x x
-
43. x2-(1-2)x+3 2 0 (1). )
. ) x1,x2
(1) ()
1 2
1 1
x x .
44. f(x) =x2+(2-1)x+-3, 0. ) )
) = 1 f(x).
