apantiseis mathimatikon
DESCRIPTION
apantiseis mathimatikon genikis pedias panelladikes 2015TRANSCRIPT
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. 11 -- -- 18532 -- . 210-4224752, 4223687
2015
1. . 31
2. . 27
3. . 86
4. ----
1. 23x 1 8x 6x 1 0 x 1/ 3, x 1/ 2, x 1/ 4
1 1 1
, ,4 3 2
2.
1
11 1
6
31 4 3.
1 1 1
2 4 4
4. 29x 3x 2 0 x 6 /18( ), x 2 / 3( )
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. 11 -- -- 18532 -- . 210-4224752, 4223687
2
3
. .
5
12
5 3 14
1 12 4 12
.
1.
1% = 10%
5% = 30%
3 = 3 360 3 =108
360 3 = 0,3
2% + 4% = 100% 1% 3% 5% 2% + 4% = 30% 2 + 4 = 0,3 (1)
: 1 2 3 4 59, 11, 13, 15, 17x x x x x
5
2 2 4
1
14 0,1 9 11 13 0,3 15 4 17 0,3 11 15 4,1 (2)
i ii
x x f f f f f
(1), (2) 2 0,1f 4 0,2f
2% 10f 4% 20f .
2.
52 2 2 2 2 2 2
1 1 2 2 3 3 4 4 5 5
1
2 2 2 2 2
( ) ( ) ( ) ( ) ( ) ( )
(9 14) 0,1 (11 14) 0,1 (13 14) 0,3 (15 14) 0,2 (17 14) 0,3 6,6
i i
i
s x x f x x f x x f x x f x x f x x f
2 6,6 2,57s s
2,570,184 0,1
14
sCV
x
.
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. 11 -- -- 18532 -- . 210-4224752, 4223687
3.
4
5 5
1 5 55
1780 17 1780 178014 14 17 14 17
1780 1780 178014 17 0.3 14 5.1 8,9 200
i i
i
x v x vv v
x fv v v v v
vv v v
4.
1i i
a a
aa
s s
99
10
a a
aa
s s
11a
a
s ss
1. ()=10 ()2+ ()2 =()2
22
2
x 100
( ) 100 x
.
0 2 0 x 10
2x 100 x
2.
2
2
2 2
2x 100 2xf x 100 x x
100 x 100 x
x 0
2f x 0 100 2x 0 x 5 2 x 5 2
f . 0,5 2 . 5 2, .
x 5 2 . 5 2
( ) 100 50 5 2 . .
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. 11 -- -- 18532 -- . 210-4224752, 4223687
3.
0 0
1 99 1 1 1lim lim 1
98 98 98x x
f x f x ff
x x
1 98 1
98 99 99 .
4. 2 20 1 99 100 100P A P A 0 1P A B
20,1
100
P A B
P A
20,1
100
P A
P A B
0,1 f
. .
2 2100 100
fP A B P Af f
P A P A B
2 2100 100
P A B P A
P A P A B
2 2100 100P A B P A B P A P A
0 1
0 1
P A
P Af P A B f P A P A B P A
.