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7/27/2019 Diagonismata G' Gymnasiou
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'
1 ' 2010/2011
: 04/11/2010 :
:
1. , 4
4
,
= 60 = 70 = 50 = =
50
70
60
. 4
[2 ]
. ,
. ,
,. 1 () . 2 () . 3 ()
[1,5 ]
-
7/27/2019 Diagonismata G' Gymnasiou
2/19
---2---
'
'
. , ,
.
. 1.
. 2. 50
. 3. 70
[30,5=1,5 ]
2. ,
, ,
\ = \ = 40
1
2
40
40
. 1 2 ;
[2 ]
.
4
4
[3 ]
3. , ,
, , ,
=
-
7/27/2019 Diagonismata G' Gymnasiou
3/19
---3---
'
'
[ [.
[5 ]
4. ,
4
.
E
. 4
4
, ,
=
[3 ]
. 4
4
.
(: , , ).)
[2 ]
-
7/27/2019 Diagonismata G' Gymnasiou
4/19
'
2 ' 2010/2011
,
: 24/01/2011 :
:
1. . , , ,
,
.
) ( + )3 i) 2 2
) ( )3 ii) 3 32+ 32 3
) ( + )2 iii) 2 + 2+ 2
) ( + ) (
) iv) 3 + 32+ 32 + 3
[40,5=2 ]
. ,
( )2 = 2 2+ 2
[3 ]
2. , , ,
, ,
i) ( 4) ( + 4) ii) ( + 5)2 iii) (3 1)2
iv) (3 + 2)3 v) (2 2)3
[51=5 ]
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7/27/2019 Diagonismata G' Gymnasiou
5/19
---2---
'
'
3. ,
i) 2 + 22 ii) + 2 2 iii)1
2 36
iv) 2 6 + 9 v) ( ) + 4 ( )
[51=5 ]
4. ,
i) 2 11 ii) 22 ( 1) 6 ( 1)2
iii) 16 ( + 1)
2
25 ( 2)2
iv)
2
25 2 + 25v)
63 + 2
22
3 2
[51=5 ]
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7/27/2019 Diagonismata G' Gymnasiou
6/19
'
1
' 2011/2012
,
: 07/12/2011 : , 1
:
1. . , , ,
,
.
) ( + )3 i) 2 2+ 2
) ( )3 ii) 3 32+ 32 3
) ( + )2 iii) 2 + 2+ 2
) ( )2 iv) 3 + 32+ 32 + 3
[40,5=2 ]
. ,
( + ) ( ) = 2 2
[3 ]
2. ,
i) 5 20 2 8 ii)r14
5 r10
7 +r21
2 r14
3
iii) (2)4 63 iv) (2)2 (23)
v) (3)3 : 2
[51=5 ]
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7/27/2019 Diagonismata G' Gymnasiou
7/19
---2---
'
'
3. , , ,
, ,
i) ( 6) ( + 6) ii) ( + 2)2 iii) (3 1)2
iv) (3 + 2)3 v) (2 2)3
[51=5 ]
4. ,
( 2)2 + (2 + ) (2 ) ( 2)2 = 2 + 22
[5 ]
-
7/27/2019 Diagonismata G' Gymnasiou
8/19
'
1
' 2011/2012
,
: 07/12/2011 : , 2
:
1. . , , ,
,
.
) ( + )3 i) 2 + 2+ 2
) ( )3 ii) 3 + 32+ 32 + 3
) ( + )2 iii) 2 2+ 2
) ( )2 iv) 3 32+ 32 3
[40,5=2 ]
. ,
( + ) ( ) = 2 2
[3 ]
2. ,
i) 2 32 8 2 ii)r5
2 r5
8r3
7 r12
7
iii) (2)3 54 iv) (3)2 (44)
v) (2)3 : 2
[51=5 ]
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7/27/2019 Diagonismata G' Gymnasiou
9/19
---2---
'
'
3. , , ,
, ,
i) ( 3) ( + 3) ii) ( + 4)2 iii) (2 1)2
iv) (3+ 2)3 v) (2 2)3
[51=5 ]
4. ,
(2 )2 + (2+ ) (2 ) (2 )2 = 22 + 2
[5 ]
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7/27/2019 Diagonismata G' Gymnasiou
10/19
'
2 ' 2011 / 2012
: 19/01/2012 :
:
1. , 4
4
,
= = 60 = 70 = 50 =
50
60
70
60
. 4
[2 ]
. ,
. ,
,
. 1
() . 2
() . 3
()
[1,5 ]
-
7/27/2019 Diagonismata G' Gymnasiou
11/19
---2---
'
'
. , ,
.
. 1.
. 2.
. 3.
[30,5=1,5 ]
2. , b
, . ,
b = 60,
=
P
B
A
O
y
x
2
1
. 1 2
[2 ]
. 4
4
[3 ]
3. , ,
, , ,
=
-
7/27/2019 Diagonismata G' Gymnasiou
12/19
-
7/27/2019 Diagonismata G' Gymnasiou
13/19
'
1 ' 2012/2013
,
: 12/11/2012 : , 1
:
1. . , , , ,
.
) ( + )3 i) 2 + 2+ 2
) ( )3 ii) 3 + 32+ 32 + 3
) ( + )2 iii) 2 2+ 2
) ( )2 iv) 3 32+ 32 3
[40,75=3 ]
. ,
( + ) ( ) = 2 2
[2 ]
2. , , , -
.
i) 7 + 7 = 7 ( + ) ii) 6 12 = 6 ( )iii) 2 25 = ( + ) ( ) iv) 2 6
+ 9 = ( )2
v) 72 + 14 = ( + 2)
[51=5 ]
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7/27/2019 Diagonismata G' Gymnasiou
14/19
---2---
'
'
3. , , ,
, ,
i) ( + 4)2 ii)
22 + 2
iii)
1
2
2
iv) (3 + 2)3 v) (2 2)3
[51=5 ]
4. . ,
1
2
+ (2 3) (2 + 3) + 82
=1
2 + 2
[3 ]
. ,
3 ( 1)2 2
1
+ 1
2 + 3 + 6
= ( 3)
32 + 2
[2 ]
-
7/27/2019 Diagonismata G' Gymnasiou
15/19
'
1 ' 2012/2013
,
: 12/11/2012 : , 2
:
1. . , , , ,
.
) ( )3 i) 2 2+ 2
) ( + )3 ii) 3 + 32+ 32 + 3
) ( )2 iii) 2 + 2+ 2
) ( + )2 iv) 3 32+ 32 3
[40,75=3 ]
. ,
( ) ( + ) = 2 2
[2 ]
2. , , , -
.
i) 5 + 5 = 5 ( + ) ii) 7 14 = 7 ( )iii) 2 16 = ( + ) ( ) iv) 2 4
+ 4 = ( )2
v) 62 + 12 = ( + 2)
[51=5 ]
-
7/27/2019 Diagonismata G' Gymnasiou
16/19
---2---
'
'
3. , , ,
, ,
i) ( + 3)2 ii)
22 + 2
iii)
1
2
2
iv) (3 + 2)3 v) (2 2)3
[51=5 ]
4. . ,
1
2
+ (2 3) (2 + 3) + 82
=1
2 + 2
[3 ]
. ,
3 ( 1)2 2
1
+ 1
2 + 3 + 6
= ( 3)
32 + 2
[2 ]
-
7/27/2019 Diagonismata G' Gymnasiou
17/19
'
2
' 2012/2013
, ,
: 24/01/2013 :
:
1. (), , (), .
. .
. .
. .
. .
. , , ,
.
[51=5 ]
2. ,
,
= = = = 3 q q q
x
y
3333
H
Z
O
A B
E
-
7/27/2019 Diagonismata G' Gymnasiou
18/19
---2---
'
'
, , , ,
.
.
........................
. Z ................. .
.
........................
. ...............
.................... .
. ...............................
[51=5 ]
3. ,
x
186
12
,
= 18 = 12 = 6
. .
[2 ]
. .
[1,5 ]
-
7/27/2019 Diagonismata G' Gymnasiou
19/19
---3---
'
'
. ,
(
)()
.
[1,5 ]
4. , = 90
. .
[3 ]
. , , ,
() =225
2013 () =
64
2013
, ,
[2 ]
