105279281 Διαγωνίσματα Μαθηματικών Α Γυμνασίου

2 0 0 7

: T: :

Copyright

Copyright 2007:

EKOTIKO OPANIMO IBANH ABE

98 106 80 A. T.: 210 3661200, Fax: 210 3617791

http://www.livanis.gr

A , , , , -

, , , , , -

. N 2121/1993 E.

: E O

ISBN 978-960-14-1481-2

7

.....................................................................................................................9

1: .......................................................................13 2: .................................................................................17

3: ....................................................................21

4: . ......................................25 5: ...........................29

6: .......................................................35

7: .............................................................41 8: ......................................................45

9: .....................................................................................53

10: - - ...................................59 11: ..................................65

12: ..................................71

1: .......................................................................77

2: .................................................................................81 3: ....................................................................85

4: . ......................................89

5: ...........................93 6: .......................................................99

7: ...........................................................105

8: ....................................................109 9: ...................................................................................115

10: - - .................................121

11: ................................125 12: ................................131

9

.

12 , 10 2 , - .

, , , - .

.

, . .

13

1

1

: 1

1 . :

1. .............

, .................. ................., ............................ , ............................ .............................., = ....... + .........., < ... .... . = 0 = .......... ........................ .

(1,7)

2. : 1 = ..... .

..... : = 0. : ..... . ............................ ........................... . .................................... . ......... . , ... (, ) = ......... . ............................................. ... (, ) = .............. .

(1,7)

14

. :

+

.

.............................

+ = .... + .... = .... ....

+ ( + ) = (.... + ....) + .... ( ) = ...........

+ 0 = ....... .... =

0 = ....

( + ) = ........ + ........ ( ) = ........ .....

(1,6)

2 . , -

: 2 5 4 + 4 = 2 2 5 4 + 4 = 6 7 3 + 8 0 = 0 5 + 7 : 4 3 = 0 9 + 9 : 9 + 1 = 3

(2,5)

. :

418 100 31 23 7 12 1

(2,5)

15

3 . :

1. , = 1, :

. 1 = 1 . = 1 1 . = 1 = 1 . = 0 = 1

2. : 7 104 + 3 102 + 1 :

. 7.301 . 731 . 70.301 . 73.100

3. ;

. 5 + 0 + 0 + 4 . (5 + 0) (0 + 4) . (5 0) + (0 + 4) . 5 0 0 4

4. : x+ x+ x x x x x :

. x3 4 x B. x3 x4 . 3 x 4 x . 3 x x4

5. : x x x x = 0 :

. 2 . 3 . 4 . 5

6. 10 30;

. 4 . 5 . 6 . 7

16

7. 5 : . 5, 6, 7, 8 . 0, 2, 4, 6 . 0, 1, 2, 3, 4, 5 . 0, 1, 2, 3, 4

8. ;

. 0 = 3 0+ 0 . 40 = 6 6+ 4 . 83 = 10 8+ 3 . 91 = 10 8+ 11

2,4(8x0,3)

.

, .

3_ 6 _ 2

_ 2 _1 3

9 6 _ _ 3, 10 _ 3 6 _ 5, 9 2_ _ 4 2, 3, 4

3 _ _ _ 2, 3, 4, 5, 9, 10 (2,6)

4 . :

x = (23 10) 2, y = 14 + 24 + 34 = (23 + 5 2) : 32 + (15 3 5)5. x+ y+ , .

(2,5)

. = ... (6, 8) = ... (45, 60, 75) -

: = ( + )3 = 3 + 3 2 + 3 2 + 3

(2,5)

17

2

2

: 1

1 . :

i)

........ = ........

................... . .................................. , ............................. .

ii) 4

> 7 7

,

1 1 <

iii)

................................. .....................................................

.................... ....... .

(2,6)

18

. () (), 0:

i.

+= +

ii.

=

iii. 2

2

=

iv. :

: =

v.

1

+ = +

vi.

... (,) 1=

2,4(6x0,4)

2 . :

5

6

2

25

7

8

5

12

+ 22

25

27

16

(2)

. :

22 = , 20 5

24= , 21

28 4= , 3x x

4 = ,

5 7

11 11< < , 1 2

5 5< <

3 (6x0,5)

19

3 :

1. 2

1 1

2 2+ :

. 1

8 .

1

2 .

3

4 . 1

2. 1

2 33 :

. 2 . 1 . 7 . 3

3.

3 5

4 31 1

2 6

++

:

. 12

5 .

29

8 .

15

8 .

8

11

4. 3 22 71 2007

02 17 86 2008 :

. 2007 . 2008 . 86 . 0

5. x 5

x 6

++ :

. < 1 . > 1 . = 1 . = 0

6. 2 (x 3)

2 x 6

+ + :

. < 1 . > 1 . = 1 . = 0

7. 3 1 7 2

:4 4 6 3

+ :

. 4

3 . 12 . = 1 .

5

4 5 (7x0,7)

20

4

. 2

3 18 .

.

(2,5)

. :

22 7 1 1 13 1 1 2 (1 ) : ( 2 ) :

7 5 2 2 15 5 5 5

= + = +

= .

(2,5)

21

3

3

: 1

1 . -

:

1. 123: = 1,23 2. 1.000 = 57,4

3. 75 = 0,075 4. 32: 0,01 =

5. 0,00475 106 = 6. : 104 = 0,0302

7. 70.034 = 7,0034 8. 5 = 0,5

9. 3

0,01210

= 10. 11.092 11,09210

=

2,5(10x0,25)

22

. :

17,024 17,02

2.749

0,9156

304,9999

724.058

476,302

5 104 + 3 102 + 2 10 + 5 2,5

2 . -

= 2 ( + ), .

1 3,2dm 8dm

2 20cm 160cm

3 5m 180dm

4 400mm 80cm m

2 (4x0,5)

. .

. 5,23m 0,703m 2,023m 2m 0,7003m 0,052m . 0,023km 12,3m 134dm 1004cm 11011mm

1 (2x0,5)

23

. . -

.

160

4

523

100

41

6

523

10000

6,83333.... 40 0,0523 5,23

0,8 (4x0,2)

. .

3

5

21

25

3

800

1,2 (6x0,2)

24

3 x y cm, :

x = 15 + 0,02 (4,6 + 5,4)3 y = 0,2 2 102 = (0,1 + 0,12 + 0,13) 103. .

5

4 = 2 , = 0,8 , = 0,5 , = 9,6 , = 0,01 , :

= 2 (3 : + 2 : ) = (3 ) + : (3 : 4)2 5

25

4

4 5 1.

2. : 1

1 () : .

1. x + = . x = :

2. x = . x = 3. x = . x = 4. x = . x = 5. x : = . x = :

6. : x = . x = +

1 2 3 4 5 6

2,5

26

.

1. x 4

03

= . 3

2. x 12

120

+ = . 4 3. 2(x 3) = 8 .

4. 12 2x = 7x 15 .

5. x 1 4

15 5

+ = . 7 6. 3 : x = 1:3 . 9

7. (7 7)x = 0 . 2

8. (4 3 1)x = 2 . 8

A 1 2 3 4 5 6 7 8 B

2,5

2 () .

60 cm.

1. : . x2 + 2x = 60 B. x 2x = 60 . x + 2x + x + 2x = 60 . (1 + 2 + 1)x = 60

27

2. . 3. . 4. .

2,5

. = 30 2 5, = (22 + 2) 5 = (23 22)3 : 22 + 2 17

: ( + + ) x = 2 + 2 + 2 .

2,5

3 () :

1. 31,4% :

. 31,4

100 B.

31,4

10 .

314

100 .

314

1000

2. 200% 200 :

. 200 . 400 . 4000 . 40000

3. 4

5 :

. 40% . 50% . 60% . 80%

4. % :

.

100

+ . 100

. : 100

.

:100

5. 3% 1m :

. 3m B. 3dm . 3 cm . 3 mm

6. 50 80 : . 30% . 40% . 50% . 60%

7. 32 14 -

: . 40% . 43,75% . 42,15% . 49,12%

5 (7x0,7)

28

4 () 500. 12 10% 12 8%. - 10% + 8% = 18%; .

5

29

5

6

: 1 30

1 . : x y x , y ................................... .

x y .............................................. ........................................ .

x y .................................... .

(x, y) ................. .................... .

(2,5)

. x y ; 1.

x 10 20 30

y 60 120 180

30

2.

3. . 4. . 5. y = x

6. y = 3

7 x

7. y = 3

x

8. 9.

10.

2,5 (10x0,25)

x 6 15

y 4 12

31

2 . : x y x y ........................... .

.............................. x y ............................ .

(x,y) ........................................... ...................................... .

2,5(5x0,5)

. : x y

......

yx

= . - .

1,1

. x y ; 1. . 2. 12 cm2. 3. 4.

x 1 2 3 4

y 6 3 2 1,5

32

5. y x = 1000

6. y = 2

3

x

7. y = 0,01

x

1,4 (7x0,2)

3 :

= 10,5 x y , : ) :

(2)

) x y; .

(2)

x = 2 3 4

y = 6 10,5

33

) (x,y) ) , x y.

(1)

4 120 50 . ) 40

;

(2,5)

) ( 120 . ) -

1 ;

(2,5)

35

6

7

: 1 30

1 . : , ..... - , .

, .. .. .

..... .

....... , .. . . .

. .

1,8 (9x0,2)

. : 1.

;

36

2. ; 3. .

.

1,2 (3x0,4)

. .

:

1. 0 .

2. -

.

3. -

.

1 2 3

1

. :

-

. , , :

1.

2. x =

3.

4.

> 0

5.

1 (5x0,2)

37

2 . :

+ 12,64

+ 104,23 16

3

0

2 (4x0,5)

.

:

1. ( + 2) + ( 3) ( + 3) 2. (2) (3) + ( + 3) 3. ( + 2) ( + 3) + (3) 4. (2 + 3 + 3) 5. (2 + 3 3) 6. + ( 2 + 3 3)

. 2 3 3 . 2 + 3 + 3 . 2 3 3 . 2 + 3 + 3 . 2 + 3 3 . 2 3 + 3

1 2 3 4 5 6

3 (6x0,5)

3 . : 1. = 2, :

. + 2 . 2 . + 2 2 .

38

2. = 3, : . + 3 . 3 . + 3 3 .

3. :

. 8,64 < 3

2 < 1000 < 0 < 1

5 < + 4 < 100

. 1000 < 8,64 < 3

2 < 0 < 1

5 < + 4 < 100

. 1000 < 3

2 < 8,64 < 0 < 1

5 < + 4 < 100

. 1000 < 3

2 < 8,64 < 1

5 < 0 < + 4 < 100

4. 3

5 :

. 5

3 . 5+

3 .

3

5 . 3+

5

5. , = :

. = . > . + = 0 . = 1 6. 5

39

4 . :

1) ( 8) (2) ( 1) = + 16

2) [( 5) ( 3)] : [( + 1) ( 1)] = 15

3) ( 4) ( 5) = +

4) ( + 3) ( 1) 5 = 0

5) 5 8 + 2 = 20

6) (7 10) = 12

7) : (2

3 ) =5

2,1 (7x0,3)

B. 1. N :

4 4 3 4 10,2 3 10,2

3 3( 1)( 3)( 4)

6

18

4 ( 10)

= + + + + = = +

1,2 (3x0,4)

2. , -

: ( 2)

( ) ( 2)

+= 1

3. :

: x=, , , .

0,7

41

7

7

: 1 30

1 . : 1. , > 1, -

... . 2 .. . .. .

2. 1 = . = ., 0 = , 0

3. > 0 ..0 < 0 < 0 < 0 > 0

4. = .. 5. : = , 0 6. = .

42

7. ..... .

8. .....

........

......

= 9. . ..... .

10. ( ) .......... ........ = 2,5 (10x0,25)

. , -

.

1. x5 : x3 = x2

2. x5 = x5

3. x3 x4 = x12

4. (x3)2 = x5

5. (x)4 = x4

2,5 (5x0,5)

2 . N : 1. , ( + )2008 :

. 1 . + . 0 . 2008

2. ( )3 < 0, : . , . , . , . = = 0

3. =( 1)0 + ( 1)1 + ( 1)2 + ( 1)3 :

. 0 . 1 . 2 . 3

43

4. x : 1014 = 1010 : . 102 . 102 . 1014 . 1024

5. : 0,00001 x = 107 :

. 1011 . 1012 . 1013 . 1014

2,5 (5x0,5)

.

:

1. 2 = 1

2. 2 = 1

4

3. ( 2) = 8 4. ( 2) = 16 5. (2)3 = 64

. = 2

. = 0

. = 2

. = 3

. = 4

1 2 3 4 5

2,5 (5x0,5)

3 N :

1 3

4

3

3

1

3 3 9

2 32 + ( 3)2 3 1 0

3 23 2 2 23 24

4 4 3

4 3

8 4

4 2 4 8 12

44

5 ( 3)0 1 1 3

6 4

2

3

81

16 16

81

81

16

7 (56)2 121

5

4

1

5

12

1

5

8 6 2

8

6 6

( 3)

2

6 28 68

9 3 3 3

1 3 4

2 2 3

27

64 1

64

27

10 ( 1) + 1

2 0 2

5 (10x0,5)

4 . :

x = 24 + 2 ( 3)2 [23 ( 3)3] : 7

B. -: = 9 xx + 1 2 x2 + 18 xx + 3

5 (2x2,5)

45

8

1

: 1 30

1 . : 1.

.

2. . . . .. . .

3. - . . . .

4. .... . . .

5. ... .

2,5 (5x0,5)

46

. -:

1.

2.

3. 4.

5.

6. 7.

8. 9.

10.

2,5 (10x0,25)

47

2 .

:

1.

.

2.

.

3.

.

4.

.

5.

.

48

6.

.

7.

.

8.

.

9.

.

1 2 3 4 5 6 7 8 9

1,8 (9x0,2)

49

B. N x : 1.

= 12cm

x = 2.

x= ....

3.

x= .... 4.

x= ....

3,2 (4x0,8)

3 A. N : 1. , -

:

. . . .

50

2. 3/10 : . 54 . 98 . 102 . 108

3. :

. l l . l . l . l l ,

4. ,

: . 45 . 65 . 90 . 120

5. 2/5 .

: . 8 . 18 . 72 . 108

2,5 (5x0,5)

. lxOy . , , .

2,5

4 . :

1. ....... .

2. . .

0,5 (2x0,25)

51

. :

1. 70

2.

0,5 (2x0,25)

. (,2cm). x

. :

x

. 2 cm

1

E

1

. x :

1.

x =

2.

x =

52

3.

x =

4.

x =

5.

x =

1,5 (5x0,3)

E. l = 50 , l lA . p ;

1,5

53

9

2 B

: 1 30

1 . : 1. , , ....... .

2. ........................... .................. .

............................... .

3. , ............... ................................................................... .

1,5 (3x0,5)

54

. :

2 1.

.

2. .

1

.

3,5

2 . (1,3), (2,0),

(0,4), M(4,4) :

2,5

lxOy (1,3)

(2,0)

(0,4)

M(4,4)

55

. 3 cm = 4cm. ( ). ) . ) ,

. ) ;

) pA = 40 lBOK . 2,5

3 . : 1. -

.............. .

1

2.

.............................. . .............................. . : ......., ....... ..., ......... .

// , =............. // , + = ............ = , ............. .

1

56

. . :

2

. :

1

4 . //. .

1,5

120

57

. l l l l, B, .

1,5

. // l . , , , .

2

59

10

3 B - -

: 1 30

1 . : 1. ......................................................

.................................................... .

2. ............ .

3. ............................. .

4. ...... ................. . ...................... .

......... .................................. .

5. ................... . ........... . .......................... ............ .

2 (5x0,4)

60

. :

1 . :

1. l l 2. l 90 3. l 90 = + 4. l l = +

2 (4x0,5)

2 . l l l, B, -

, .

l lB l

;

80 40 110 75 60 30

60 60 92 40 45 45

100 40 52 52

1,4

61

. x. 1.

x = .... 2.

x = .... 3.

x = .... 4.

x = ....

5.

x = ....

62

6.

x = ....

3,6 (6x0,6)

3 . l 2/5 lB

l . . 2,5

. . ,, .

2,5 .

.

. . . . .

2,5 (5x0,5)

63

. (,2cm) (,4cm). . , , , . ; .

2,5

65

11

: 2

1 . : 1. -

0 .................................. .

2. ................... . ........................................... .

3. ....................... .

4. .................. .

5. ........................................... ............................ .

6. ............................. ......................................... : = + .......... .

7. ............................. ......................................... : : = .

8. 0 ...................... ...................... . : = ....... .

2,4 (8x0,3)

66

. :

1.

;

2.

+ = ;

3.

++ = + ; 4.

; 5. -

;

6. ;

7. ; 8. ,

; 9.

; 10. -

o + ;

11. , , 2 = 2;

12. 12345 3, 5 9;

13. x = 4, |x 4| + |2 x| + |x + 2| = 6;

2,6 (13x0,2)

67

2 . : 1. , = 1 :

. = 1 = 1 . = 0,5 = 2 . 1 1= + = + 1 1= = .

2. 120 350 -

: 120 = 23 3 5 350 = 2 52 7

...(120,350) : . 2 5 . 23 3 5 . 22 3 52 . 23 3 5 7 ...(120,350) : . 2 5 . 23 3 5 . 22 3 52 . 23 3 52 7

3.

: . (12 5) 2 . 3 (4 5 6 : 7) . 2 (4 + 7 32) . 7 + (2 5)+(3 : 4)

4. 5cm. ,

(%) ; . 100% . 200% . 300% . 400%

5. 3 5

2 , :

+= . 3 . 5 . 8 . 11

6. , x

:

. x = 2 B. x = 3 . x = 4 . x = 5

68

7. 1;

. ( 1) ( 2) ( 3)

6

. 2 ( 1) ( 3)

( 3) 2 5

+ +

. 6 4 8

3 2 4

+ + . 25 4 5 30 : 15

8.

36 12, :

. = 2 = 12 . = 2 = 3 . = 1 = 3 . = 2 = 4

9. (2) (3) (+4) (2)> 0, : . > 0 . < 0 . = 0 . .

10. = 10 232

: . 10 2 9 8 9 72 = = . 210 6 10 36 26 = = . 10 2 9 10 18 8 = = . 2 2 2(10 2 3) (10 6) 4 16 = = =

2,4 (10x0,24)

B. 1. 5 -

. :

5 5 5 5 5

1,3

69

2. x :

15

2

3 -

7

3

4 25

1,3

3

. : + 7 2 5 5x = 4 y = (3 )3 3 4 2

x .

2

.

y2 : x2.

1

. 20 x%

, y

x . ( x y -

. ). : i. . ii. (%) .

2

70

4 // . -

: l 3 2 3 2A = (2 2 7) [(2 2 ) : 2 6] 5 . l l l , x .

5

71

12

: 2

1 . x :

1. 2

3 x 37 = , x .....= 2. ( 1)( 2)( 3) x ( 1)( 2)( 3)( 5) 0 + + = ,

x .....=

3. (6 x) : 9 0 = , x .....= 4. (x 3) : 3 1 = , x .....=

5. x 5

53

= , x .....= 6. x

31

7

= , x .....=

7. x10 0,0001= , x .....= 8. 2 6 75 10 x 10 10 = , x .....=

9. 4

x

10 10 1

10 10

= , x .....= 10. 129 9x= , x .....= x .....=

2,6 (10x0,26)

72

. - :

1.

.

2. .

3. , .

4. . 5.

.

6. .

7. 180.

8. .

2,4 (8x0,3)

2 . -

l =40:

1. lAOB ...................................... . 2. o ................... 3. p = ....... . 4. p = ........... . 5. p o ......... ,

........................... .......................... ........................ .

1,5 (5x0,3)

73

. + :

/ +

1,5 (5x0,3)

. //.

: . . . . . , -

. . x.

2 (4x0,5)

3

l l = = 45 . cm 30:(x-2)=5, cm :

2 2y 2

1

2

= ... (2, 3, 10) + ... (2, 6, 10).

74

1. . 2. .

5 (22,5)

4 16 cm = x + 2

= x cm. p = 140.

1. .

2,8

2. , , , , , , , , , o o .

2,2

77

1

1 . 1.

, , , = + , < 0. = 0 = .

2. : 1 =

0 : = 0 : 0

- .

.

2.

... (, ) = 1.

... (, ) = .

78

.

+ = + =

+ ( + ) = ( + ) + ( ) = ( )

+ 0 = 0 1 = 0 = 0

( + )= + ( ) =

2 .

2 5 (4 + 4) = 2, : 2 5 8 = 10 8 = 2 2 (5 4) + 4 = 6, : 2 1 + 4 = 2 + 4 = 6 (7 3 + 8) 0 = 0, : (4 + 8) 0 = 12 0 = 0 (5 + 7) : 4 3 = 0, : 12 : 4 3 = 3 3 = 0 (9 + 9) : 9 + 1 = 3, : 18 : 9 + 1 = 2 + 1 = 3

.

418 162 100 31 23 8 13 7 12 15 1 4

1.

2. = 23 7 + 1 = 161 + 1 = 162

418 31

= 5 13 =

79

3. = + , < 100 = 12 + , <

3 .

1. 2. , 7 10.000 + 3 100 + 1 = 70.000 + 300 + 1 = 70.301. 3. , : ) 5 + 4 = 9, ) 5 4 = 20, ) 0 + 4 = 4, ) 0. 4. 5. , : x3 x = 0 x3 = x, = 3. 6. , : 11, 13, 17, 19, 23, 29. 7. , .

.

3062

6201

9600 4365 2004 3600

4 .

x = 13 2 = 26 y = 1 + 16 + 81 = 98 = (8 + 10) : 32 + (15 15)5 = 18 : 9 + 05 = 18 : 9 + 0 = 2 + 0 = 2 x + y + = 26 + 98 + 2 = 126 = 2 32 7

100 12

= 4 8 =

:

.

.

80

. 6 = 2 3, 8 = 23 ... (6, 8) = 3 23 = 3 8 = 24, = 24 45 = 32 5, 60 = 22 3 5, 75 = 3 52, ... (45, 60, 75) = 3 5 = 15, = 15 = (24 + 15)3 = 393 = 59.319 = 243 + 3 24 152 + 3 242 15 + 153 = 13.824 + 3 24 225+3 576 15 + 3.375 =

= 13.824 + 16.200 + 25.920 + 3.375 = 59.319 = .

81

2

1 .

i)

= .

-, .

ii) :

8 4

7 7> 1 1

4 3<

iii)

.

1 .

. i.

ii. iii. iv.

v. :

1 1

+ = + = + = + vi.

82

2 .

61

48

4

5

+ 41

24

1. (6,8) 245 7 5 4 7 3 20 21 41

6 8 6 4 8 3 24 24 24

= + = + = + = + =

2. 22 2 20 20 : 5 4

25 25 25 25 : 5 5

= = = =

3. (16,12) 4827 5 27 3 5 4 81 20 61

16 12 16 3 12 4 48 48 48

= = = = = .

1, 221

=

6, 20 20 : 4 524 24 : 4 6

= =

3, 21 21: 7 328 28 : 7 4

= =

43

, 4 3

x x 1 x3 4

= =

6 ,11

5 6 7

11 11 11< <

:

: 1 1 4 4

5 5 4 20

= = 2 2 4 8

,5 5 4 20

= =

:7

20.

83

3

1. : (2,4) 4

2

1 1 1 1 2 1 3

2 2 2 4 4 4 4

=+ = + = + =

2. : 1 7

2 3 3 73 3 = =

3. :

3 4

(4,3) 12

(2,6) 63

2

3 5 3 5 9 20 2929 6 294 3 4 3 12 12 12

1 1 3 1 4 12 4 81 12 6 6 6 62 6

=

=

+ + + = = = = =+ ++

4. 5. , x + 5 < x + 6 6. , 2 (x + 3) = 2x + 6 7. :

1

2

3 1 7 2:

4 4 6 3

3 1 7 2 2 3 1 7 4: :

4 4 6 3 2 4 4 6 6

3 1 3 3 1 1: :

4 4 6 4 4 2

3 1 2 3 2 5

4 4 1 4 4 4

+ = = + = + =

= + = + =

= + = + =

4 . 2/3 18 1/3 18 : 2 = 9

3/3 3 9 = 27 .

84

. 2 7 1 1 13

A [ (1 ) ] :7 5 2 2 15

= + = 2 7 2 1 1 13 2 7 1 1 13

[ ( ) ] : ( ) :7 5 2 2 2 15 7 5 2 2 15

= + = + = ...(5,4) 202 1 13 2 4 1 5 13

( ) : ( ) :5 4 15 5 4 4 5 15

= = + + = = 8 5 13

( ) :20 20 15

= + = 13 15 15 15 : 5 3

20 13 20 20 : 5 4= = = =

2 21 1 2 1 2 2 ( 2 ) : ( ) :

5 5 5 5 5 5= + = + =

3 4 3 5 3:

5 5 5 4 4= = =

= .

85

3

1 .

1. 123 : 100 = 1,23 2. 0,0574 1.000 = 57,4 3. 75 0,001 = 0,075 4. 32 : 0,01 = 3.200 5. 0,00475 1.000.000 = 4.750 6. 302 : 10.000 = 0,0302 7. 70.034 0,0001 = 7,0034 8. 5 : 10 = 0,5 9. 12 : 1.000 = 0,012 10. 11.092 : 103 = 11,092

.

17,024 17,02

2.749 2.750

0,9156 0,9

304,9999 305

724.058 724.100

476,302 476

50.325 50.000

86

2 . = 2 ( + )

= 2 + 2.

1 : = 2 (3,2+8) = 2 11,2 = 22,4dm 2 : = 20cm = 2( + ), : 160 = 2(20 + ) 160 : 2 = 20 + 80 = 20 + = 80 20 = 60cm 3 : = 180dm = 180:10 = 18 m = 2( + ), + = : 2, + = 18 : 2 = 9, + = 9 + 5 = 9, = 4 m. 4 : = 400mm = 400 : 1000 = 0,4m = 80cm = 80 : 100 = 0,8m = 2 (0,4 + 0,8) = 2 1,2 = 2,4m

1 3,2dm 8dm 22,4dm

2 20cm 60cm 160cm

3 4m 5m 180dm

4 400mm 80cm 2,4m B. . 0,052m < 0,7003m < 0,703m < 2m < 2,023m < 5,23m

. .. m :

0,023km = 0,023 1000 = 23m 12,3m = 12,3m

87

134dm = 134 : 10 = 13,4m 1004cm = 1004 : 100 = 10,04m 11011mm = 11011 : 1000 = 11,011m : 10,04m < 11,011m < 12,3m < 13,4m < 23m

1004cm < 11011mm < 12,3m < 134dm < 0,023km.

. .

.

() ()

160

4

523

100

41

6

523

10000

6,83333.... 40 0,0523 5,23

3

5 3 : 5 = 0,6

6

10

21

25 21 : 25 = 0,84

84

100

3

800 3 : 800 = 0,00375

375

100000

: 160

160 : 4 404

= = 523

523 : 100 5,23100

= = 41

41: 6 6,8333......6

= =

523523 : 10000

100000,0523

= ==

88

3 x = 15 + 0,02 103 = 15 + 0,02 1000 = 15 + 20 = 35 cm y = 0,2 2 100 = 0,4 100 = 40 cm = (0,1 + 0,01 + 0,001) 1000 = 0,111 1000 = 111 cm = (x + y) = 111 (40 + 35) = 111 75 = 36 cm.

4 = 9,62 (23 : 0,8 + 0,52 : 0,01) = 9,62 (8 : 0,8 + 0,25 : 0,01) = 9,62 (10 + 25) =

= 9,62 35 = 92,16 35 = 57,16.

= (23 0,8 0,5) 2+9,6:0,01 (23:24)2 = (8 0,8 0,5) 2+9,6:0,01 (8:16)2 = = (8 0,4) 2 + 9,6 : 0,01 0,52 = 7,6 2 + 9,6 : 0,01 0,25 = = 15,2 + 960 0,25 = 975,2 0,25 = 974,95.

89

4

1. 2.

1 . :

1 2 3 4 5 6

. 1. 0 0, :

x 4 = 0, x = 4. ().

2. 1 , : x + 12 = 20, x = 20 12 = 8. ().

3. : 2x 6 = 8 . 2x = 8 + 6 2x = 14 x = 14 : 2 = 7. ().

4. x = 3. x = 3 : 12 2 3 = 7 315 12 6 = 21 15 6 = 6 . ().

5. 2 : 2 1 4 1 4 5

1 , . 1 , . 15 5 5 5 5

+ = + = = , . ().

90

6. : 3 1

x 3= 1 x 3 3 = x 9= .

().

7. : 0x = 0 - . ().

8. 0x = 2, . ().

:

A 1 2 3 4 5 6 7 8

B

2 . 1. . -

. 2. 1 , :

6 x = 60 3. x = 60 : 6 = 10 cm. 10 cm 20 cm. 4. = 10 20 = 200 cm2. B.

= 30 10 = 20 = (4 + 2) 5 = 6 5 = 30 = (8 4)3 : 4 + 2 17 = 43 : 4 + 2 17 = 64 : 4 + 2 17 = 16 + 34 = 50

: + + = 20 + 30 + 50 = 100 2 + 2 + 2 = 400 + 900 + 2500 = 3800

: 100 x = 3800 x = 3800 : 100 = 38.

3

1. : 314 314 : 10 31,4

31,41000 1000 : 10 100

= = = %

91

2. : 200% 200 200

200 2 200 400100

= =

3. : 4 4 20 80

805 5 20 100

= = = % 4.

5. 1m = 100cm 3% 100cm 3

100 3100

= cm 6. 30 :

30 30 2 6060

50 50 2 100

= = = %

7. : 14 43,75

14 : 32 0,4375 43,7532 100

= = = = %

4

10 : 10 5000

500 50100 100 = = .

500 + 50 = 550. 12 8% 550 :

8 4400550 44

100 100 = = 550 + 44 = 594, . -

594 500 = 94.

: 94 94 : 5 18,8

18,8500 500 : 5 100

= = = % 18%.

93

5

1 . x y x , y .

x y .

x y y = x

(x, y) . .

1. , : 60 120 180

610 20 30

= = =

2. , : 4 12

6 15

3. , x ,

4x : 4

4

= = .

94

4. , x , -: 1, 2, 3, 4, ..., x2, -: 12 = 1, 22 = 4, 32 = 9, 42 = 16, ...

:

1 2 3 4 ...

1 4 9 16 ...

1 2 3 4 ...

5. , y = x . 6. , . 7. , y = x x y. 8. , x y -

. 9. , . 10. , .

2 . x y x y .

x y

yx

=

(x, y) - x, y.

95

. y x = 6, 6

yx

=

. 1. , 10 6

, 20 3 . 2. , = x y

= x y = 12 = .

96

:

x 12 6 4 3 2 1

y 1 2 3 4 6 12

E = x y 12 12 12 12 12 12 3. , . 4. , . 5. , x y 1000.

6. , x, y

y , 0x

= .

7. , x, y

y , 0x

= - .

3 ) x , y y = 3x.

x = 2 3 3,5 4 y = 6 9 10,5 12

) :

6 9 10,5 123, 3, 3, 3,

2 3 3,5 4= = = =

x y : y

3x= y = 3x.

97

) :

4 . ) x -

. 120+x . :

(./) 120 120 + x

() 50 40 A - :

40 (120 + x) = 50 120 4800 + 40x = 6000 40x = 6000 4800 40x = 1200 x = 1200 : 40 = 30

98

30 . 40 .

) :

(./) 120 120 x

() 50 60

60 (120 x) = 50 120 7200 60x = 6000 60x = 7200 6000 60x = 1200 x = 1200 : 60 x = 20

20 . .

99

6

1 . , , .

, .

- .

- , .

+. . 1.

. 2. . , . 3. :

- . - . - .

100

.

1 2 3

. 1. . .

2. . x = x = : =

3. . 4. . , . 5. .

2 .

+ 12,64 12,64 12,64 12,64

104,23 + 104,23 104,23 104,23

16

3 16+

3

16

3

16

3

0 0 0 0 . : . +, , -

+, ( ), .

. .

1. (+ 2) + ( 3) (+ 3) = 2 3 3 . 2. ( 2) ( 3) + (+ 3) = 2 + 3 + 3 . 3. (+ 2) (+ 3) + ( 3) = 2 3 3 . 4. ( 2 + 3 + 3) = 2 + 3 + 3 . 5. ( 2 + 3 3) = 2 3 + 3 . 6. + ( 2 + 3 3) = 2 + 3 3 .

101

1 2 3 4 5 6

3 1. . || = 2, = + 2 = 2. 2. .

, - .

3. . 3 1

1,5 0,22 5

= = .

4. . 3

5 5 ,

3 5

3 5

3+

5. . 0. 6. . 5 8, 6

7. : |x| = 6 x = + 6 x = 6 |x| = 7 x = + 7 x = 7. 4 : 6, + 6, 7, + 7.

. 1. = 5, = + 7

+ = ( 5) + (+ 7) = 5 + 7 = 2 = 5 (+ 7) = 5 7 = 12 = ( 5)(+ 7) = (5 7) = 35

: = ( 5) : (+ 7) = (5 : 7) = 5

7

2. 1 1

, 3 3

= = 1 1

( ) 03 3

+ = + = 1 1 1 1 2

( )3 3 3 3 3

= = + = 1 1 1 1 1

( ) ( )3 3 3 3 9

= = = 1 1 1 1

: : ( ) ( : ) 13 3 3 3

= = =

102

3. 1 1 1

( )2 2 2

= = + = +

4 4 4 ( )

3 3 3

= = + =

3 2

1 4 1 4 3 8 11 ( )

2 3 2 3 6 6 6+ = + = = =

3 2

1 4 1 4 3 8 5 ( )

2 3 2 3 6 6 6 = = + = + =

1 4 1 4 4 2 ( ) ( ) ( )

2 3 2 3 6 3 = = + = =

1 4 1 4 1 3 3 : ( ) : ( ) ( : )

2 3 2 3 2 4 8= = + = =

4 1. (+ 8)( 2)( 1) = + (8 2 1) = 16 2. [( 5)( 3)] : [(+ 1)( 1)] = (+ 15) : ( 1) = 15 3. ( 4) ( 5) = 4 + 5 = + 1 4. (+ 3) 0 ( 1) 5 = 0 5. 5 8 + 2 x = 7 8 x = 1 x

1 x = 20 x = 1 + 20 = 19 : 5 8 + 2 19 = 5 + 2 8 19 = 7 27 = 20

6. 7 10 = 3 3x = 12 x = ( 12) : ( 3) = + 4 : (7 10) 4 = 3 4 = 12

7. x: (2

3 ) = 5

x = 5 2 2 10

( ) (5 )3 3 3

= =

: 10 2 10 2 10 3 10

: : 53 3 3 3 3 2 2

= + = = =

103

.

1. = 4 4

3 4 10,2 3 10,23 3

+ + + = 3 3 + 4 = 6 + 4 = 2

( 1)( 3)( 4) 12

2 26 6

+ += = = + =

18 18 18 3 3

4 ( 10) 4 10 6

= = = = + = +

2. ( 2) 2 2( 2 2 3)

( ) ( 2) [2 ( 2)] ( 2 2 2)

+ + = = = 2 2( 2 6) 2 2 4 2 8 10 5

(2 2) ( 2 4) 4 ( 6) 24 24 12

+ = = = = =+ 3. : x = || | | | |

: x = |2| |+ 2| |+ 3| A : x = 223 A : x = 3

( )

5:x 3

12

5 5 5 1 5x : 3 :3

12 12 12 3 36

= = = = =

.

- .

105

7

1 . 1. , > 1,

, .

2 .

3.

2. 1 =

= 1, 0 =

1

, 0

3. > 0 > 0

< 0 < 0 . < 0 > 0 .

4. = + 5. : = , 0 6. = () 7. -

.

106

8.

=

9.

10. () =

. 1. x5 : x3 = x53 = x2

2. x5 = 5

1

x

3. x3 x4 = x3+4 = x7 4. (x3)2 = x32 = x6 5. ( x)4 = x4

2 . 1. . , + = 0 ( + )2008 = 02008 = 0 2. . , < 0.

. 3. . = ( 1)0 + ( 1)1 + ( 1)2 + ( 1)3 = 1 + ( 1) + 1 + ( 1) = 1 1 + 1 1 = 0 4. . x = 1010 1014 = 1010 + 14 = 1024 5. . 0,00001 x = 107

105 x = 107 x = 107 : 105 = 107 ( 5) = 107 + 5 = 1012 . 1. 2 = 1, = 0

2. 2 = 1

4

2 = 22, = 2

3. ( 2) = 8 ( 2) = ( 2)3, = 3

4. ( 2) = 16 ( 2) = 24 ( 2) = ( 2)4, = 4

107

5. (2)3 = 64 2 3 = 26 3 = 6 = 6 : 3 = 2

1 2 3 4 5

3

1. 3

4

3

3 . 334 = 31 =

1

3

2. 32 + (3)2 . 9 + 9 = 0

3. 23 2 . 23 21 = 23+1 = 24

4. 4 3

4 3

8 4

4 2 .

4 38 4

4 2

= 24 23 = 16 8 = 8

5. ( 3)0 . 1

6. 4

2

3

. 4 4

4

3 3 81

2 2 16

= =

7. (56)2 . 5(6) 2 = 512 =

12

1

5

8. 6 2

8

6 6

( 3)

.

86 2 6 2 88

8 8 8

6 6 6 6 62

3 3 3 3

+ = = = =

9. 3 3 3

1 3 4

2 2 3

. 3 3

31 3 4 12 1 12 2 3 12

= = =

10. ( 1) + 1

. (1) = 1, , 1 = 1

: ( 1) + 1 = 1 + 1 = 2

108

4 . x = 24 + 2 ( 3)2 [23 ( 3)3] : 7 = 24 + 2 ( 3)2 [8 ( 27)] : 7 =

= 24 + 2 ( 3)2 (8 + 27) : 7 = 24 + 2 ( 3)2 35 : 7 = = 16 + 2 9 35 : 7 = = 16 + 18 5 = = 16 5 + 18 = = 21 + 18 = 3

x = 3 . = 9 xx+1 2 x2 + 18 xx+3 = 9 ( 3)3+1 2 ( 3)2 + 18 ( 3)3+3 =

= 9 ( 3)2 2 9 + 18 ( 3)0 =

= 2

19 18 18 1

( 3) + =

19 18 18 1

9 + =

,

,

.

109

8

1 . 1.

.

2. . . 90 180 .

3. - . .

4. - . - - .

5. .

. 1. , . 2. , , ,

.

110

3. :

, .

4. , x x :

5. ,

6. , 90, 90 -

.

7. , 180 180 .= = 8. , 90 180,

180. 9. , . 10. , .

111

2 .

1 2 3 4 5 6 7 8 9

. 1. , = = 12 : 2 = 6cm.

, = 6 : 2 = 3cm. = + = 3cm + 6cm = 9cm. x = 9cm.

2. x = 360 35 = 325. 3. x + x + 110 = 180

2x = 180 110 2x = 70 x = 70 : 2 = 35.

4. :

x + 5 = 70 x = 70 5 = 65.

3 . 1. , -

.

2. , o

o o3 1080360 10810 10

= =

3.

4. , 180 45 = 135, - 90 45 = 45. : 3 45 = 135.

5. , o

o o2 360180 72 .5 5 = = : 90 72 = 18.

112

.

lxy , 70= . , 70 - :

70 180

70 70 180

140 180

180 140 40 .

+ + =+ + =+ == =

70 : 70 .= - 70 : 180 70 110 .= =

4 . 1. . 2. . . 1. , :

p o 70 , 70= = p o .

2. .

113

.

x

.

1) 2 cm T 2

2) 2 cm E 1

3) 2 m E 0

1) 2) 3) .

1. p , x = 180. 2. p , x = 90. 3. p = 50 360. x = 360 50 = 310.

114

4. l l ( ) . . x = 40.

5. , , l = 90. x = 90 55 = 35.

.

l 50= . l = 50 : 2 = 25. l l : 180 l = 180 50 = 130. l l 130 : 2 65 .= = l : l l l = + =25o + 65o = 90o, .

p = 90.

115

9

1 . 1. , , .

2. - .

.

3. , .

.

2

1. -

.

2. . 1

.

1

1

.

116

3 .

1

.

2 2 -

-

. 1

2 2

. 1

4

2

2

.

1

. . 1 .

2 A.

(1,3) (7,5)

(2,0) (6,8)

(0,4) (8,4)

M(4,4) (4,4)

117

.

) = = 3cm, -

. ) ,

. = 2 = 2 3 = 6cm .

) , , = .

) lAO , 40. - lAO l , l = 40. l l l = + =40 + 40 = 80. l = 180 80 = 100 ( lAOB ).

(1,3) (3,1)

(2,0) (0,2)

(0,4) (4,0)

M(4,4) (4,4)

118

3 . 1. -

.

2. , . , . : , , . // = . // + = 180. , -.

.

1. : 180 120 60= = .

2. , 120= . 3. , 60= . 4. , 60= . 5. , 120= . 6. , : 60= . 7. -

, 180 60 120= = .

120 60 120 60 60 120 60 120

119

. 300 = 360 300 = 60. l : l + = 60 + 120 = 180. //.

4 . 50 : = 180 50 = 130.

140 : = 180 140 = 40. , : = = 40. x 50 360 x= = 360 50 = 310.

. 180 75 105= = . , 180 105 75= = . l 180+ = , l 180 75 105= = l l 180+ = , l 180 105 75= = .

. 72 : = 72. :

180 (90 ) 180 (90 72 ) 180 162 18= + = + = = . 18= .

121

10

- -

1 . 1. ,

, o .

2. 180 .

3. , 90.

4. 2 . .

.

5. . 60 . .

. .

. .

. 1) .

2) , 90. 3) ,

. 4) , , : l l 180 = .

122

2 . 180. -

:

;

80 40 60

110 75 ,

180.

60 90 30

60 60 60

92 40 48

45 45 90

40 100 40

52 76 52

. 1) 2x + 3x + 4x = 180, 9x = 180 x = 180 : 9 = 20. 2) :

x + x + 50 = 180, 2x = 180 50 = 130, x = 130 : 2 = 65. 3) T .

30 + 30 = 60, x = 180 60 = 120.

4) : x + 2x = 90 3x = 90 x = 90 : 3 = 30.

5) x : x = 40 + 70 = 110. ( : 180 (40 + 70 ) = 180 110 = 70. x 70 x = 180 70 = 110).

6) 72 + 48 = 120. 180 120 = 60. 2x = 60 x = 60 : 2 = 30.

123

3

. l

2 2 90 180 90 365 5 5

= = = = . l l l 180 , 180 36 144 + + = + = = - 144 : 4 : 144 : 4 36= = . l = . l 3 = = 3 36 = 108 > 90 - . . 70= 180 120 60= = 180 , 180 (70 60 ) 180 130 50+ + = = + = = = , 50 .=

4 .

()

()

. . . -

. .

.

: = = 2cm = = 4cm, - , -.

125

11

1 . 1. -

0 .

2. . .

3. .

4. .

5. .

6. - . = + ( )

7.

. : = 1

8. 0 1

. =

1

126

.

1. . -.

2. .

. :

= .

3. . .

:

++ = .

4. .

5. .

:

= .

6. . . .

7. . , -.

8. . . .. ( 2)4 = + 16.

9. . () = .

10. . + .

11. . 3 +3 , ( 3)2 = (+ 3)2 = 9.

12. . 12.345 3 1 + 2 + 3 + 4 + 5 = 15 3, 5 - 5, 9 15 9.

13. .

|x 4|+|2 x |+|x + 2|=

=|4 4|+|2 4|+|4 + 2|= 0 +| 2|+|6|= 0 + 2 + 6 = 8.

127

2 . 1. . : (+ 1) (+ 1) = 1 ( 1) ( 1) = 1 , -

= 1.

2. ... - : . ... : .

3. . 7+(2 5) + (3 : 4) = 7 + 2 5 + 3 : 4 = 7 + 10 + 0,75 = 17,75.

4. 5 cm 4 5 = 20 cm. 2 5 = 10 cm

4 10 = 40 cm. 40 40 5 200

200%20 20 5 100

= = = . .

5. 3 5 3 5

3 5 3 2 5 6 5 11

+ = + = + = + = + = . .

6. : x + 3 = 9 x,

x + x = 9 3, 2x = 6, x = 6:2 = 3. .

7. . 2 ( 1) ( 3) 2 3 1

1( 3) 2 5 6 5 1

+ += = = + + . = 6

16

= , = 2 + 2 + 2 = 2, = 25 20 2 = 3.

8. . 1 36

36 123 3 = = .

9. . 3 , . < 0.

10. . , .

. 1. : = + , < .

5 : 0, 1, 2, 3, 4. = 0, = 5 ( = ), = 5 5 + 0 = 25, = 1 = 5 = 5 5 + 1 = 25 + 1 = 26, ...

128

0 1 2 3 4

5 5 5 5 5

5 5 5 5 5

25 26 27 28 29 2. 1 :

A x x + 1 : x + x + 1 = 15 2x + 1 = 15 2x = 15 1, 2x = 14, x = 14 : 2 = 7. H x = 7.

2 : x :

2 7 7 2 95x , 5x , 5x , 5x 3 , x 3 : 5 0,6

3 3 3 3 3 = = + = = = = .

3 :

4 : x = 25 4 : x = 1 4 1

, , x 4 32 12832 x 32

= = = .

15

2x + 1 = 15 x = 7

-

2

3 -

7

3

5x 2 7

3 3= x = 0,6

4 25

4 : x = 1

32 x = 128

129

3 .

2 4

7 8 15x 5

3 3 3

5 3 5 5 6 5 5 1 5 2 3y ( ) ( )

4 1 2 4 2 2 4 2 4 4 4

=

= + = =

= = = = =

.

22 2 2 2

2 2

3 3 1 9 1 9 25 225y : x ( ) : 5 : :

4 4 5 16 25 16 1 16 = = = = =

.

i. 5% , 5 5 20 100

20 1100 100 100

= = = .

ii.

3y 3 1 3 3 5 154 15%x 5 4 5 20 20 5 100

= = = = = = .

4 2 2

o

A (8 14) [(8 4) : 2 6] 5 ( 6) [(8 4) : 2 6] 5

36 (4 : 2 6) 5 36 (2 6) 5 36 ( 4) 5

36 ( 20) 36 20 56

= = == = = == = + =

: 56 + B 180+ = , 180 56 124+ = = .

: ,= = l l 124 ,+ = l 2 124 ,= l 124 : 2 62= = . x lA //, lx = 56. l l //, l = 62. ( l l l, x, , - o180 l l l o x 180 ,+ + = l l o o ox 56 62 118+ = + = , l o o o 180 118 62= = ).

131

12

1 .

1. 2

3 x 3,7 = 2

7 x , .

7x

2=

2. ( 1)( 2)( 3) x ( 1)( 2)( 3)( 5) + , x= 5

3. 6x

0,9

= 6x 0, . x=0

4. x 3

1,3

= x= 1

5. 5 x= 3 6. x 0= 7. x 410 10= x 4= 8. -2 6 75 x 10 10 10 = -2 (-6) 7 -8 7 -7 85 x 10 10 , 5 x 10 10 , 5 x 10 : 10+ = = =

-7-(-8) -7 85x 10 , 5x 10 += = 15x 10=

5x 10= x 10 : 5 2= =

132

9. 1 4 5

x x

10 1 10 1 ,

10 10 10 10

+= =

x 510 10 10= , x 1 510 10 += , x 610 10= x 6=

10. x 9= : 1 2 12

9 19 9

9 9 = = =

x 9= ( )1 2 1

2 2

9 9 19 9

9 99

= = = =

B. 1. . .

2. .

3. . , 180.

4. . 60, , 90.

5. .

6. . , , , 180.

7. . :

l l ,, : l l 180 , 180 , 180 : l l l l (180 ) (180 ) (180 ) 3 180 ( ) 540 180 360 + + = + + = =

8. . .

2 .

1. lAOB . 2. o l 3. p = 40 , . 4. p = 140 o , -

: 180 40 = 140.

133

5. p o 40 , .

.

/ +

+ +

+ + + +

+ + + + + . . : , . . : .

. : l l l l . : l l , l l , l l , l l , l l , l l .

// : l , l l , l l .

. //, :

l x= = . l lZ =2x= .

l l 180+ + = , : 39 + x + 2x = 180 39 + 3x = 180 3x = 180 39 = 141 x = 141 : 3 = 47.

3 x = 8 30 : (8 2) = 30 : 6 = 5 .

134

: : 5 (x2) = 30 5x10 = 30 5x = 30+10 5x = 40 x = 40 : 5 = 8

= 8cm. ...(2,3,10) = 30 ...(2,6,10) = 2

: 2 2y 2

2

1

= 30 + 2 2 2y 22 = 32 2 4 2y = 32 8 2y = 32 2y = 32 : 8 2y = 4 y = 2,

= 2cm. 1. : l 45= = l //. l l 180 180 45 135= = = . 135= l l

.

2. l l , . 90 l 45= l 45= , . = = 2cm. = = 2cm. = = 8 2 2 = 4 cm. -, = 2cm.

4 1.

+ + + = x + 2 + x + x + 2 + x = 4x + 4.

135

16cm, 4x + 4 = 16 4x = 16 4 4x = 12 x = 12 : 4 = 3cm

= 3 + 2 = 5cm, = 5cm = 3cm, = 3cm.

2. - , 140 .= . , .= 180+ + =

180 180 140 40+ = = = 40 : 2 20 .= = =

// 20 .= 20 .= = ( 90 ),= 90 20 70 .= = 70 .= = = l l (-) : p o 140 .= = p o 180+ = () o p 180 180 140 40 .= = =

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/CreateJDFFile false /Description > /Namespace [ (Adobe) (Common) (1.0) ] /OtherNamespaces [ > /FormElements false /GenerateStructure false /IncludeBookmarks false /IncludeHyperlinks false /IncludeInteractive false /IncludeLayers false /IncludeProfiles false /MultimediaHandling /UseObjectSettings /Namespace [ (Adobe) (CreativeSuite) (2.0) ] /PDFXOutputIntentProfileSelector /DocumentCMYK /PreserveEditing true /UntaggedCMYKHandling /LeaveUntagged /UntaggedRGBHandling /UseDocumentProfile /UseDocumentBleed false >> ]>> setdistillerparams> setpagedevice

105279281 Διαγωνίσματα Μαθηματικών Α Γυμνασίου

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