ΥΛΗ ΜΑΘΗΜΑΤΩΝ ΓΥΜΝΑΣΙΟΥ 2014 15
DESCRIPTION
ΥΛΗ ΜΑΘΗΜΑΤΙΚΩΝ ΓΥΜΝΑΣΙΟΥTRANSCRIPT
-
1
2014-2015
( 50/04-08-2014 ..)
2014-2015 :
. , , , .
. 1: 1.2 , 1.3 1.4 1.5 ... ...
. 2: 2.1 2.2 2.3 2.4 2.5 2.6 . 3: 3.1 , , , 3.3 . 4: 4.1 : x , x , x , x , : x
:x ( ). . 5: 5.1 5.2
-
2
. 6: 6.1 6.2 6.3 6.4 6.5 6.6 . 7: 7.1 ( ) 7.2 7.3 7.4 7.5 7.6 7.7
. 1: 1.1 1.2 1.3 ,
1.4 1.5 , 1.6 1.7 1.8 1.9 1.10 1.11 1.13 . 2: 2.1 2.2 2.3 2.4 2.5 2.6 . 3: 3.1 3.2 3.3 3.4
-
3
. 1, 2, 3 ( , , ) . , : 1. T 2. T
. : (..
, , ).
(.. , , ).
(.. , .).
(.. ), (.. 1 4.1), (.. 15 4.1, 3 1.1).
, , , 27 18. 1 ( 6 ) : . (. 3 6, 7 1.2). ( 2, 3, 4, 5, 8, 9 1.3).
( 6, 7, 11 12 1.3). , . ,
... ... .
2 ( 8 ) : , (
2.1, 1, 2, 3, . 36, 2, . 37 ).
( ,
, .. )
-
4
( 4 2.3 ).
, 10.
(..
2
5
3
8
2 3
5 8 ,
, , )
(, ) 3 ( 4 ) 3.2 . , 3.3 . 3.4 , 7.10. :
.
. , , 1, (..
2 32,52 (2,52) (2,52) ), , 1 (.. 2 30, 22 (0, 22) (0, 22) ). .
4 ( 2 ) . , . , . 4.1 ( 2 ) . ( ). ( 1, 2, 3 1, 2, 3), ( 4 7, 8) . 15 ' .
-
5
5 ( 3 ) . (.. , ...). 5.1 ( 1 ) ,
(.. 3
0,75 75%4 ,
10,33... 33,33...%
3 ).
. 5.2 ( 2 ) , ... . 6 ( 11 ) . , ( ) . 6.1 ( 1 ) 6.2 ( 2 ) 6.3 ( 2 ) ( ) (.. . 89, ...). 6.4 ( 2 ) , . , 3 4 . 6.5 ( 2 ) 1 . 6.6 ( 2 ) 7 ( 14 ) , ( .) . 7.1 ( 2 ) 7.2 ( 2 ) 2 2 , . , 0 ( ), ( ). , , . 7.3 ( 2 ) , : , , ( ).
-
6
7.4 ( 2 ) : (.. 2 ), (.. 3 ) (.. 3 8 ). . , (. 7.2). , . ( 8). ( ) . (. ) 7.5 ( 3 ) . , . . , 2 5
(2 5) 1 2 5 1 2 1 5 ( 2) ( 5) 2 5 , (.. ... ). , 1 , , 1 2 2 , 1 5 5 ... 7.6 ( 2 ) 7.7 ( 1 ) 7.8, 7.9 7.10 ( ). 1 ( 24 ) , ( ) . 1.1 ( 2 ) 1.2 ( 2 ) . , . . 2 . 1.3 ( 2 ) , , ( ), , (, ), , ,
-
7
. 1.4 ( 2 ) 5, 6, 7, 9, 10 11, . 8 , , . . 1.5 ( 2 ) , , . ( ) / , , ... () ( ). ( 1, 2 6) . , . , - (. 167) , . 1.6 ( 2 ) , , , . . (.. ), (.. , ), , . .. . , , . 1 (. 171) . 2, 3, 4, 5, 6, 7 . 1.7 ( 2 ) . . 1, 4 ( 3 2) 3 , . 1.8 ( 2 ) . 5 178. 1 2 .
-
8
1.9 ( 2 ) . ( ) . 1.10 ( 2 ) 2, 3, 4, 5, 6, 7 . 1.11 ( 2 ) 2 3 1.12 , . 189. .. , (, . 189, , . 2). 1.13 ( 2 ) . 2 ( 12 ) 2 , ( , .) . 2.2 ( ) 2.1 ( ) . , , 1 ( , , , .), , , ( ). 2.5 ( ) 2.4 ( ) . 2.1 ( 2 ) 2.2 ( 2 ) 2.3 ( 2 ) 1, 2 5 1, 3, 4, 5, 7 9. 2.4 ( 2 ) 2.5 ( 2 )
1 , , , .
-
9
, , . 2.6 ( 2 ) , ., 1 2 ( ), . , 1 2 , , . 3 ( 8 ) 3.1 ( 2 ) , . , , . (.. , ). , , , , . , . . , ( ) , , . , , , .. . , ( ) , , . , , , , , 2 , , , . 3.2 ( 2 ) 180 , , . 1, 4, 5, 6, 7, 8 9. 10 . 3.3 ( 2 )
2 .
-
10
, . , 3.1. 3.4 ( 2 ) , , .
.
, , , : . 7: ( ) 7.8 7.9 7.10 , , , :
. 1: - 1.1 1.2 ' 1.4 1.5 ' . 2: 2.1 2.2 2.3 . 3: 3.1 3.2 ( 2
3 ). 3.3 y x 3.4 y x ( :
x y x y ).
3.5
yx
. 4: 4.1 : 4.2
-
11
4.3 4.5 ( :
)
. 1: 1.1 1.2 1.3 1.4 . 2: 2.1 2.2 ( 143).
2.4 30 , 45 60 . 3: 3.1 3.2 3.3 3.5 . 4: 4.1 4.2 4.3 4.4 4.6
.
7 ( 9 ) ( , , ) () (3 ) 7.8 ( 3 ) 7.9 ( 2 ) 7.10 ( 1 ) . 1 ( 12 ) 1.1 ( 2 ) , . 1.2 ( 3 )
-
12
, , . . , , , . , . , , 6, 7 9 ( ). 1.4 ( 4 ) 1.5 ( 3 ) , , , . , 7 ( ) ( ) . 2 ( 8 ) ( , , ...). 2.1 ( 3 ) 1.4 ( ) . 2.2 ( 3 ) , : ; 1; / ; 2.3 ( 2 ) 3 ( 13 ) , , ( , , , ) . 3.1 ( 2 ) . , ( ). 3.2 ( 3 ) "" y x
. 5, (4.5 ) . 2 ( ) 3 ( ), 3, 4 3, 5 6. 4 7
-
13
. , 4 8, 9 10. 3.3 ( 3 ) 1 2.1 (. 137) . 3.4 ( 3 ) x y x y .
( , , ). 8, 9 . 71, 5, 9, 10 . 78, 4, 5 82 (), . 3.5 ( 2 ) 4 ( 8 ) , , (, ). , . . 4.1 ( 2 ) 4.2 ( 2 ) 4.3 ( 2 ) 4.5 ( 2 ) 6, 7 8. 1 ( 14 ) 1.1 ( 3 ) . : ( )
(, , ...) . ()
(). ( ),
, .
-
14
() (.. )
.
. : , , (.. ) ., . , , , , 11 ( 1 6) 125 1.3 ( ). 3 115 . , 115 . 1.2 ( 2 ) . , , , ( 6 118), , , . 1.3 ( 6 ) . . . 3, : , . , .
. ( ) , ( ) ( )
.
.4 3 . , . 4 , , . (.. ) . , , .
-
15
(.. ). . applets , . 6 9 1.4 ( ). 11 ( 10) 15 ( ). 1.4 ( 3 ) 2.1 ( ). ( 1, 4, 5). 2 ( 5 ) 2.1 ( 2 ) 1 (. 137) , 3.3 . 2, 1/5, 1 5. 2.2 ( 2 )
, . 143 (
) 4,
. 3 146 , ( ). ( ), . 2,
3
5 3 5 .
2.4 ( 1 ) 1 3 153 3 4 154 ( , ). 2 . 5, 12 7, 5 12 . 3 ( 10 ) 3.1 ( 2 ) 1.12 ( , , ) , . 1, 3, 5, 6 7.
-
16
3.2 ( 2 ) , . 1), ), ), 2), ), ), 3), ), ), ) 1, . 3.3 ( 3 ) L L 3.3 ( y x ), . 1, 2 3 1, 3, 4, 5 7. 3.4 ( ), . , , 7 192 3 . 191. 3.4, , :
90 , 10 cm , 14
, 90 1
360 4
. 20 cm , 5 cm .
3.5 ( 3 ) ( 3, 4, 5). 3.6 ( ) . 3.6, , : 45 7 cm ,
1
8 ,
45 1
360 8
o
o .
249 cm , 249
8
cm .
4 5 1, 3, 4 6 . 197 198. 4 ( 11 ) . , , ( ). , , , . , . , . , ,
-
17
, , , , . . 4.1 ( 2 ) 4.2 ( 3 ) , .. , . ( 4, 6, 9). 4.3 ( 2 ) , . , . , . . . 4.4 ( 2 ) 4.6 ( 2 )
.
, , , , . . 1: 1.1 ( )
. . .
1.2 . .
1.3 1.4 1.5 [ : )
]
-
18
1.6 [( : ) ) )
2 ( )x x ]. 1.8 ... ... 1.9 1.10
. .
. 2: - 2.2
. . (
) 2.3 2.4 2.5 '
. . . '
. 3: 3.1 3.2 3.3 . 4: 4.1 2y x 0 . 5 : 5.1 ( : , 2)) 5.2 ( :
)). 5.3 ( :
) . 1: 1.1 1.2 1.5
. . ( 220).
1.6 . 2: 2.1 0 180
-
19
2.2 2.3 2.4 v
.
1 ( 29 ) . 1.1 ( 2 ) . . 8, 9, 10, 11. 1.1 ( 1 ) . 1.1 ( 2 ) , 1 (
2 ), 3 (
) 6 8. , 2), 3 7. [ 1, 2), ), ), 9, 10, 11]. 1.2 ( 1 ) ( 5, 6, 7). 1.2 ( 1 ) 1), ), ), 2), ), ), 3), ), ), 5, 6. 1.3 ( 2 ) 3, [ 1) 9]. 2, 4, 5 (, , ), 7 10. 1.4 ( 2 ) 1, 2, 3), 7, 8. 4, 5, 6. 1.5 ( 6 )
2 2 3 3- ( ) 2 2 3 3 ( ) ( ). 4 ( ) 7 ( Lagrange) 9 10. 11, 12, 13, 14, 15 17 () . Pascal , , . 1.6 ( 6 ) 2 ( )x x . 6, 7, 10, 11
-
20
12, 13, 14, 19, 20 21. , . 1-5, 7-16, 22 23 . / / , 1.7 . , (1.5 1.6) , . . 1.8 ( 1 ) ... ... . 1.9 ( 2 ) 2) 3), 4, 5). 1.10 ( 1 ) 3), ) 4). , . 1.10 ( 2 ) 2), 4), 6 7. ( ): . . , . 2 ( 13 ) 1 . 2x 2 . . 2.1 . 1 2 . 2.2 ( 2 ) 2 0x x 2 0x . 2 0x x , 4 , x . : 2 15 16 0x x
2 16 16 0x x x ( 1) 16( 1) 0x x x ( 1)( 16) 0x x 1 6, . 7. 2.2 ( 3 ) ) .
, ( ) .
) 2 ( 7 8). ) 3 . 95. 2.3 ( 2 )
-
21
2.4 ( 3 ) 5. , . 6 , , , , . 2.5 ( 3 ) 6 12 , , . 3 ( 8 ) . : ) , ) . ( ) . 3.1 ( 2 ) , : y 2 3 5x y y x , . . 2 2 6 ( ). 3.2 ( 2 ) 3 4 . 3.3 ( 3 ) . , 8 . , 14 1, 2, 3, 5. 4, 6 12. 4 ( 4 ) , . 4.1 ( 3 ) 1 ( ) 5 6. 1, , . 5 ( 6 ) . ( ). 5.1 ( 2 ) , 2, 2), 2), 3, 4, 5 6, 7, 8 9. 5.2 ( 2 ) . 8 6. 5.3 ( 2 )
-
22
, 2, 4, 5 9, 10, 11, 12, 13. 1 ( 17 ) 1.1 ( 5 ) ( , , , ). , , (.. , .) 1, 2, 3, 4, 7, 8, 10, 11, 12, 16, 17 21. . 7) (.. ), 7) (.. ). 4 9 . 1.2 ( 2 ) 1.5 ( 4 ) 1.5 ( 2 ) 2 215 ( ). 1, 2, 3 6. 4 5 , , . 1.5. ( 2 ) (. 220, ) . , . 3. 1.6 ( 2 ) : . . , . 2 ( 12 ) 2.1 ( 2 ) 2.2 ( 2 ) 2.3 ( 4 ) . , 5, 7, 9 10 . 2.4 ( 4 )
-
23
, 5, 8, 13 14. ( ), . 2 : .