b gymnasiou b tomos 14 15
DESCRIPTION
ÂTRANSCRIPT
B
B
–
–
©
B
4. –
9 15
18 23
– 29
5.
– 43 – 51
58 – 64
72
6. –
87 94
7. –
105 112
– 114
8.
127
– a
.
4
8 4: -
9
4: -
= {2 , } = {2, 4, 6, … }
= { , 3 4 = 4} = { , 3 4 = 3 + 4} = { , 3 4 = 3 4}
= { , ……………}
i. ( ) = ( )
ii. ( ) = ( )
iii. ( ) = ( )
10 4: -
=
.
0, = = .
2 = 4 = = 2 2.
= 0 0, = = .
0 = 3
. .
= 0 = 0 = =
.
0 = 0
. . 0 ( 2) = 0 0 3 = 0
= :
= 0 = 0 0 = 0 = 0
-
11
4: -
1. N =
=
= [5,10] = 10
.
=
,
. 6 (2 + 1) = 5 2 . 6 2 1 = 5 2 2 + 2 = 5 + 1 6 -
. 0 = 0 .
, , .
2. 3( 1) = 1
3( 1) = 1 3 3 = 1 3 = 3 1
(3 ) = 2
, - .
.
, -
.
(3 ) = 2, .
, (3 ) = 2 3 = 0 = 3
= 3
0 3 = 0, 0 ( 215) = 0,
.
-
, -
0 = 0
= 3 -0 = 2
12 4: -
1. 2 6 = 4 2 3 4 = 2 55( + 3) = 5 + 3 + =
2( + 4) 4 = 2(4 ) = 3 5 2.
3 + 15 = 4 3 3 + 5 = 3 3 + 8 2( + 2) 5 = 6 3( 1)
3 4 + = 7 + 4 2(2 1) + 5 = 11 4( + 1) + = 3.
0 = 0 0 = 3 3 = 0 10 = 0 0 = 10
4.
+ 3 = 0 = 0 = 3 = 2 = 2
( 5) = +3 = 0 = 3 = 5 = 5
0 = 3 + = 0 = 5 = 3 = 3
+ 3 = 2 3 = 0 = +1 = 1 = 2
13
4: -
5. ( 3) = 7 ( + 2) = 2014 4 = 3 3 + + 6 = 15 6
6.
. ( + 3) = 0 = 6 13 + 5 = 13 + 3 + = 3 1
7. .
( 4) + 1 = + 5 + = 5 + + 4
14 4: -
( ) ( ).
( ) ( )
= 1,8 + 32.
.
.
( ) ( .
(
, ,
.
= , = =
15
4: -
1. 42 7 10 3
:
= 2( + ).
( ), = 2( + ) ( ) .
= 2( + ) = 2 + 2
. 2 = 2 . 22 =
. , =
= 42
= 7 cm = 10 cm = 3 cm = =
=
=
= 14
= =
=
=
= 11
=
=
=
=
= 18
16 4: -
1.
i. = 3 ( ) ii. = ( )
iii. = 5 1 ( ) iv. = + ( )
v. 2 = 5 ( ) vi. = ( )vii. 2 5 = 1 ( ) viii. = ( )
2.
= .
=
= = = =
3. = 0,155 + 11
( = 0 6 180
(360
10 2 60 15 75 3
17
4: -
4. = ( ) .
60 8 12 .
5.
(2 + = i. == ii. = = iii. = 2 2( + ) = iv. = 2 2 3 + = 0 v. =
vi. =
vii. =
18 4: -
<
2.
100.
3.
2.
. 2.
100.
.
En Anisotites.ggb».
19
4: -
<, >, , , =.
< + < +
> + > + 5 > 3
5 5 + 5 = 10 3 + 5 = 8 10 > 8. .
4 5 + ( 4) = 1 3 + ( 4) = 1 1 > 1. .
,
.
< > 0 < > > 0 > < < 0 > > < 0 <
7 > 1
2 7 2 = 14 1 2 = 2 14 > 2.
.
20 4: -
8 > 6 8 = = 4 6 = = 3
4 < 3 .
1. > + 2 > + 2 > 5 3 ………… ………… > 2 ………… < 5 4 + 1 ……..…
> 2 ………….
> 5 3 > 5 3
3 > 2
3 3) . , .
-
3) . , .
> 2 < 2 2
. , .
< 5 4 < 4 5
4 + 1 < 20 + 1 4 + 1 < 21
4 1
. , .
> 2 1 > 2 1
<
<
1, -, 2 .
21
4: -
1. (>, <, =, , < 3 + 3 ……. 6 < 3 ……. > 5 3 ……. 2 6 ……. 2 2 2 ……. 4 < 4 ……. 6 < 7 3 ……. 21 4 ……. 2
2.
(>, <, =
……. ……. ……. + ……. +
……. ……. 3 ……. 3 …….
3. < 16 < 16. < < . < 6, < 3. < 0 2 < . > 1 1 > .
22 4: -
4. (>, <, = < < 0 ……. + ……. + ……. + ……. + ……. …….
5.
> > 0 > < 0 > > 0 >
23
4: -
.
(€) 5,35 10,00
(€) 0,10 0,05
1
2
12
24 4: -
.
2 + 1 > 7
2 + 1 > 7 2 > 7 1 2 > 6 > 3 3 .
,
> 3
3.
3
3.
< 3
3.
3
To 3.
,
--
-
, -
,
- -
25
4: -
1. 2 4 4 + 7 .
2 4 4 + 7 2 4 7 + 4 . 2 +11 .
22 +112
5 12
, 2.
. , .
5 .
:
2. ( ) .
( )
( )
,
. 4( 4) 3( + 8) (4 5) . 4 16 3 + 24 4 + 5
. 4 3 + 4 24 + 5 + 16 . 5 45
9
- .
9.
: --
-
-
26 4: -
3. 3 5 + y > 4y + 3
3 5 + y > 4y + 3 3 + 4 > +3 + 5 0 > 8
. .
4. 3 5 + < 4 + 3
3 5 + < 4 + 3 3 + 4 < +3 + 5 0 < 8
.
5. €40€1,50.
, 1,50
,
1,5 > 40
> 40 1,5
> 26,67 , 27 ,
.
27
4: -
1. > 2.
2. 3 9 < 0
3. 2, 8, 0, , 5 , 6 3 < 15.
4. 7 < 21
5. { | 4}
6.
2 2 2 2
0 0 0 0
1 1 1 1 3 3 3 3
28 4: -
7. 3 4 > 2 2( 1) + 3 < 5 1 3( 2) 10 2( 1) 3 54 5( 2) 13 3( + 1) ( ) >
8. 48
2,5 / . 24
9. €700 8%
€2300
10.
= 3 2 = 20 5
29
4: -
–
.
20 20000 15 50000 .
. 9 5 .
. .
«B En Synalithefsi.ggb»,
.
-
-
30 4: -
>
.
( , + )
.
[ , + )
<
.
( , )
.
( , ]
.
[ , ]
< <
( , )
-
- -
-
1655 «Arithmetica infitorum»
-
.
31
4: -
<
.
[ , )
<
-.
( , ]
< < +
.
< : < > <
>
-. -.
. .
-
-
[3,5] . ( 1,5) . [0,9) .
32 4: -
1. 2 1 2 < 3.
2 1 2 2 1 2 1
< 3 + 6 < 9 < 9 6 < 3
{ | 1 < 3 } [ 1,3)
2. €500
€20. €2250 .
€1200.
33
4: -
O 500 + 20 , .
€1200, 1200 < 500 + 20
€2250, 500 + 20 2250
, 1200 < 500 + 20 2250
500 + 20 > 1200 20 > 1200 500 20 > 700 > > 35
500 + 20 2250 20 2250 500 20 1750 87,5
, , 35
88 .
1.
[ , )
34 4: -
2. «B En diastimata.ggb»
3.
(2,7) ( 3,3) [ 4,4] ( , 5) ( 3, 8] ( , ) ( , 5] ( 2 , + ) [ 2, 5)
4. 30000
33000 26000
5.
.
6. 3 4 2 2 + 3 < 13.
4
100
65
35
4: -
7.
1
8. < 5 2 < 3 1 2 7 5 > < 15
9. 2 5 < 1 5 + > 4 3(2 1) < 2(1 ) < 0 3( + 2) < 4 3 + 2 5 6 1 1 + ( )
10. 15 3. 323 310.
36 4: -
11. 3 < . 3 < [3, 2014). 3 < . > 3 < .
12. 4 €19,50 20
€35
37
4: -
1.
(6, )
2.
[ 1, 5] ( 2, ) ( , 1] ( 3, 1] [ 2, ) ( 9, + )
3.
4. N = 9 3(7 2 )
3 5 = 2 1 + 7 3(2 5) = 152( + 2) + = 6 + 3( 1) 4( 1) = 5 4( + 2) 2( 3 + 1) = 6( + 3) 12 3 4 + = 7 + 4 + = = + 1
38 4: -
5. 8 + 11 < 83 = { | > 9} = { | > 9} = { | < 9} = { | < 9}
6. = + = = = = 2( + ) = = =
7. + 2 > 1 3 < 9 6 < 28 1 2 2( 1) 3 < 4(1 + ) 1 2 5 > + 3
( ) ( ) 8.
< 0 + 3 2 + 5 < 0 + 1
9. 4
33 3 4333
12
x
x
x
x
39
4: -
10. 9 = 3( 3)
11. 6( 1) + = 10 12. 8 3( + 1) > 7y + 5 + 2. 13. 3 200 8
14.
€10,00 €2,00 €17,50 €1,50
».
15. 98 76, 86 92 5
B B
(92,100] (83,92] (73,83] (47,73] (0,47]
40 4: -
1. 2( 3) > 2 3 2 < 13 3 + 1 5( 1)
2. 5 < < 7 < < 14 < < < < < < 1 < < 1
3. < 0 0 0 < 0
4. | + 3| < 4 1 9
5. 1 < < 4 = 2 3 = 5 2
6. < < < .
7. = 5 1 + 3
5
:
(
( ) = +
42
5:
43
5:
–
36
24
1 2 3 4 5 6 7 8 9 10 11 12 13
53 57 60 65 70 73 76 78 79 80 81 82 83 84
44
5:
«B_En5_Dedomena.xlsx»
).
45
5:
.
–
.
.
.
= { 1, 0, 1, 2} = {1, 0, 4}.
,
{ 1, 0, 1, 2} {0, 1, 4}
---
. -
-
46
5:
= {( 1,1), (0,0), (1,1), (2,4)}.
=
( ) =
.
, , ( ).
1 0 1 2
1 0 1 4
{ 1, 0 , 1, 2} .
1 - 1.
( 1)= 1
1 1. 0
0. (0) = 0
0 0. 1
1. (1) = 1
1 1. 2
4. (2) = 4
2 4.
47
5:
:
, .
: {1, 5, 10} : {12, 7, 2000}
, 5)
4 7) .
,
.
: {1, 5, 10} : {7, 2000}
, 1)
.
48
5:
= 0 , , 1 , , 2
5 .
: ,
:
3 0 + 5 = 5
3 + 5 = 6 3 1 + 5 = 8 3 + 5 =
3 2 + 5 = 11
, {5, 6, 8, , 11}.
= (0,5) , , 6 , (1,8) , , , (2,11) .
: , = 1
, = 0 = 2.
,
.
= 1,
, (1,2) (1,0).
= 1 .
49
5:
A B
1
2
3
4
A B
1
2
3
4
A B
1
2
3
4
A B
1
2
3
4
= {( 2,3), (0,1), (1,2), (3,0), (4,1), (5, 1)}
€30
) 1 2 3 4 5 )
, »
50
5:
. –
51
5:
–
( ) ( ) ( ) = 2 + 1 ( ) =
( )
«B_En5_GrafikiParastasi.ggb»
o o ( 3,9) ( )
( ) =
( ) ( ) ( 3,9) ( 10,20)( )
( )
( )
52
5:
«B_En5_y x+b.ggb»
= +
= +
2 3 1 1000 1234
1 2 1 5 4 4,5= + = 2 + 1 . (0,1)
(0, ) = + , ).
53
5:
H = + , ( ) = + = + , ,
. = + .
= 2 1
, .
, = + .
( , ) = + .
( , ) = +
( 1,2) = 2 = 2 2 = 2 ( 1) 2 = 2
= + ( , ).
= 3 1
(0, 1).
-= +
-
,
-( ).
54
5:
( 1,1), (2,3) ( 2, 1) = 2 1.
:
.
. . ,
, .
,
.
= 2 1
.
) ,
.
( 1,1) = 1, = 1
= 2 1 1 = 2 ( 1) 1 1 = 3
= 2 1 ( , ) 0 = 2 0 1 1 (0, 1) 1 = 2 1 1 1 (1,1)
.
-
--
-
GeoGebra - -
-
--y = 2 1 -
ENTER». -
-
-
«ENTER».
55
5:
(2,3) = 2, = 3
= 2 1 3 = 2 2 1 3 = 3
( 2, 1) = 2, = 1
= 2 1 1 = 2 ( 2) 1 1 = 5
= 2 1, .
= 2 1
:
, = 0. = 0 2 1 = 0
2 = 1 = ,
( , 0).
, = 0.
= 0 = 2 0 1 = 1. , (0, 1).
.
(0,3) (1,5)
= + .
, .
(0,3) . , = 0 = 3 = +
3 = 0 + = 3
, = + 3.
56
5:
(1,5) . , = 1 = 5 = + 3
5 = 1 + 3 = 5 3 = 2
, = 2 + 3.
= + 3 = 2 = 3 2 + 3 = 1
( ) = 2 + 3 (1,3), (1,1), (4, 5),(6,11) 3
= ( 1, 3).
2
= 2 + ( 2, 6).
= 2 4 6 2 = 3
(0,1) (2,4) (0,4) ( 1,2)
2 0 2 4 1 5 9 13
57
5:
GeoGebra (0,3).
(0, 1) = 3 1 1 = 5 = 1 + 3 2 + 5 = 1
(0,3) ( 1,0) (0, 2) ( 2,0) 15
3
58
5:
GeoGebra
)
= 3 = = 5 = 0,4 =
GeoGebra
)
= 3 + 1 = + 12 = 5 + 3 = 0,4 2 = + 5
«B_En5_y x+b.ggb». 0
59
5:
«B_En5_y x+b.ggb».
0
=
= « = + »« = »
=
=
.
= 2
.
60
5:
= > 0 < 0
1 2 4 y = y (0, ).
= 2 (0,2).
= ( , 0).
= 2 (2,0).
( ) y = 0.
(y) = 0.
H =
=
61
5:
= . ( 2,0). , = 2.
= . (0, 1). ,
= 1 (1,1)
:
, (0,0), = .
(1,1). ,
. , = 1 = 1 =
1 = 1 = 1
, = .
62
5:
= 2 = 2 = 3 : = 3 : = 4
(3,1) (0,0)(3,4) ( 1000,4) : = 14 : = 2014
y = 3 = 8
=
(1 , 2) i. = 1 ii. = 2 iii. = 1 iv. = 0,5 (2 ,1) i. = 1 ii. = 2 iii. = 1 iv. = 0,5 = 3
i. (1 , 3 ) ii. (0 , 3) iii. ( , 3) iv. (3 , )
i. (1 , 1 ) ii. (0 , 0) iii. ( , 1) iv. (0 , )
63
5:
280
, ,
= 3 = = 3 =
0,4 500 ( )
300
( 2,4) ( 2,4)
( 2,4)
64
5:
–
(skateboard
.
.
. .
O
2 4 6
4
2
3 2
3
65
5:
«B_En5_Klisi.ggb».
,
= 2 .
5
66
5:
.
. =
.
( , ) ( , ) = = .
= 2 + 1
= 5 1 = 4
= 2 0 = 2
, = = = 2.
= = .
= 2 = 0 = 2
= = = 0
=
= 2 = 2 = 0
= =
= 1
-
- 1
67
5:
= + , = .
= 2 + 1 = 2
> 0, > 0,
< 0, < 0,
= 3 2 = 4 1 = 2 = 3
>-
<
-
.
= 1 > 0
= 1 < 0
68
5:
= 3 3. , = 3.
= + 2 = 4 1 = = 2 , = 2. = 2, = 0 + 2. , = 0. = 3, .
3
: . ,
= .
3. , = 3.
= 3 .
= + .
= +
(0, ).
(0,2).
, = 2.
= + 2.
69
5:
= .
. = = = = 2
, = 2
= +
. (0,2) (1,0) = + 2 = 0 + = 2
= + 2 0 = 1 + 2+ 2 = 0 = 2
= 2 + 2.
= 3 + 1 = 2 = + 1 = 5 2 3 3 = 9 2 + = 4 = 4 = 1
70
5:
( 1 , 3) = 3 ( 0 ,0) = 1 ( 0 , 1) = 2 ( 0 , 0) ( 1 , 3)
= ( + 3)
5 = 2
71
5:
4
( ) ( ) = 0,75 150 ( ) = 5,35 + 0,45 ( )
( ) = 54000 230 ( ) 2000
( ) = 15 + 0,05 ( )
72
5:
--
-
73
5:
200 100
€1200
€ €
( ) ( )
( , )
, ( , )
, .
= 2 + 3+ = 6
, .
74
5:
( , )
= 2 + 3+ = 6
(1,5), , 5 = 2 1 + 3
1 + 5 = 6
( , ) ( , )
= 2 + 3+ = 6
: = 2 + 3 : = 6 .
(1,5). = 1, = 5.
( , ) .
2 = 1+ = 7
2 = 1 = 2 + 1
75
5:
2 + 1 + = 7 + (2 + 1) = 7 + 2 + 1 = 7 3 + 1 = 7 3 = 7 1 3 = 6 = 2
= 2 = 2 + 1
= 2 2 + 1 = 5
( , ) , -
= 2 = 5 ,
( , ) = (2,5).
: = + 1 : = + 3
= 0, = 1 = 1, = 2 = 2, = 1 = 1, = 4
: , , . 1 = 0 + 1 2 = 1 + 1.
, , , . 2 = 1 + 3, 1 = 2 + 3 4 = ( 1) + 3.
, .
76
5:
€30
:
+ = 30 = 2
2
+ = 30 2 + = 30 3 = 30 = 10
= 10 = 2 = 2 10 = 20
, €20 €10.
1.
= 3 + 6 2 = 5
= 3 = 1
= 3 = 4
= 1 = 3
= 1 = 9
: = 1 : = 4 + 2
= 1= 4 + 2
77
5:
= 3 + + 2 = 6
2 = 0 2 + = 3 3 + 2 = 5 3 = 9 3 = 0 + 2 = 15 + 5 = 18 3 + 2 = 41
+ = 5 + 3( + 1) = 10
«B_En5_Sistimata.ggb».
= 2 1= + 3
= 3 1= + 1
= 3 1= 3 + 3 = 3 + 3= 3 + 3
€120€10
260 50 4 6 4 6
60
€10 €6 10
€260
= + (1,1) ( 1, 3)
78
5:
= {( 2,3), (0,1), (1,2), (3,0), (4,1), ( 2, 1)}
1 7 100 354 ( ) 5 3,52 1,2 0,02 123
–
)
A B
A B
79
5:
( 2, 1), (1,4), ( 1, 2) , ,
= 3 + 1 + = 3
= 3 + 1+ = 3
( )
: = (3 + 2) , (1,8) : = , ( 1, ) : y = ( 1) , (2, + 3) : = + 3, (1, 5)
7. = 3 = 2 = 12 = 0
80
5:
€8,50 €50
3 (0,1) (1,2)
81
5:
,
= (1, 2)
2 3 5 8 12 5 8 14 23 35
. : 2 + 3 = 6
(0, 2) .
82
5:
2 = 9= 7 2 3 = 22 + = 3 3 + 2 = 92 = 13 1 = 2 3 5( + 1) = 0
.
€ 12,50 €1,50
100 10 /
€20 €0,32
26 8 – 4 2
3 1 €7,255 2 €13,00
83
5:
6 10 92
20%
= =
55
«B_En5_PO_PT.ggb».
(2) (5).
( + 2) + ( 1) = 7
6 + 8 = 2013
84
5:
6 + 8 =
= 4000 400 = 3500 250
1 + 2 = 2 + ( 5) = 6
, : = 0 : 3 + 2 = 6 : 3 + 2 = 6
24
: = (3 2)( ) 1 3 2 4
–
6
:
86
6: -
87
6: -
,
88
6: -
(2)
( , )
8
1 2 3 4 5 6 7 8
2 4
36
60
89
6: -
,
=
, =
2 . , ( ) ( )
= 2 . = = = = 2
.
, ( ),
( ).
, ,
= , = = , =
90
6: -
0,9 1,2 1,8 3,3
3 4 6 11
: , = 0,3 , = 0,3 , = 0,3 , = 0,3
. , . 0,3.
20 80 30
: .
( ).
.
= 20 = 60 80 20 = 4800 = 240
240 .
20 80 2 30 = 60
91
6: -
40%
€360
: 40%
60% .
. .
: : = = 0,6 360 = 0,6 = 360 0,6
= 600
, €600.
6 90 5 7 9 21
12 45 10 28 12 28
T
2 3
15 6 90
14 56
3 5 8
92
6: -
€800 16 12
3 240 5,5
120 125 300
85 . 4 1,70
16 8 500 10
.
2 85
4 170
93
6: -
60% ( ) ( ) 1800
€1500
GBP 0,85 USD 1,30 JPY 100,30 CHF 1,21 CAD 1,34 AUD 1,42
RUB 45,15
CNY 9,25
94
6: -
95
6: -
«B_En_6 24 (0,0)
( , )
1 24
12 24
8 24 4 24
3 24
2 24
96
6: -
= ,
, = ,
6 . , ( )
( ) = 6
= 1 6 = 2 3 = 3 2 = 6 1
( )
, ( )
.
= , = , =
-
.
97
6: -
1 2 3 4 24 12 8 6
:
1 24 = 2 12 = 3 8 = 4 6 = 24
. , . 12 15 2
: ,
( ) , ( )
. , ( ).
12 15 12 2 = 10
10 = 12 15 10 = 180 = 18
18 .
98
6: -
( ) ( ) 4 ,
8 ,
2
1 2 12 40 8
1,5 1,5 2 1 2,5
6 90 12 30 6 18
18 45 36 10 9 27
99
6: -
, 90 / 30
, 25
3 30 5 (
)
100
6: -
1 2 4
4 12 20
2
80 / 100 /, 180
12 6
200 450
750
450 50 750 75
101
6: -
kg 58 71 56 68 m 1,60 1,65 1,62 1,72
3 , 4 36000 ,
, 60 000 30 0,06
1,76 30
30 1,80 55
30% €280. €80
. 2
10
1 3 20 90
.
102
6: -
(0,0) (2,10)
110 €171,60
100 80 100 130
1 3
20
-
7
:
104
7: -
105
7: -
1 10
4 2004
Carly Patterson, USA 9,80 9,75 9,80 9,75 9,75 9,80 Alexandra Eremia, ROM 9,70 9,70 9,70 9,70 9,65 9,70 Catalina Ponor, ROM 9,80 9,80 9,80 9,75 9,75 9,80
106
7: -
21
=
12, 15, 16, 19
= 12 + 15 + 16 + 194 = 624 = 15,5
107
7: -
–
12, 14, 15, 18 , 19 15 12, 14, 14, 18 , 19, 20 = 16
36, 37, 37, 38, 40, 40, 39, 36, 37, 38, 37, 39, 39, 40, 40
37 40
( ). , 37 40.
11
79 84 63 95 89 71 90 81 77 54 75
: =
= = = 78
78.
- -
-
--
108
7: -
54 , 63, 71, 75, 77 , 79, 81, 84, 89, 90, 95
(11). ,
( ), 79.
: , ,
1 7.
20 ,
10 11 . 10 11 2 2. , 2 .
0, 0, 1, 1 ,1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 5, 6
= 2
109
7: -
0, 1, 2, 2, 3, 3, 5, 6, 6, 6, 7 7
0, 1, 1, 2, 2, 2, 3, 4, 5 2
--
-
-
15 15 15 12 9 5 11 15 16 15 16 16 14 12 13 11
: 17, 16, 15
110
7: -
16 22, 24, 23, 25, 24, 22, 21, 20, 21, 22, 19, 21, 23, 22, 22, 20
3, 4, 5, 6, 11
95 93 91 95 100 99 92
6, 2, 5, 4, 3, 4, 1 2, 3, 7, 3, 8, 3, 2 3, 1, 2, 1, 3, 2, 2 4, 3, 4, 3, 4, 6, 4 8 172, 175, 183, 177, 190, 193, 189, 195.
172 .
197 . 195 198 .
111
7: -
10 7 9 5 13 10 7 14 8 11
9,5
15
15 14,5 15 14
0
1
2
3
4
5
1 2 14 15 16 17 18 20
112
7: -
B Insert
-
---
113
7: -
1. :
TIMSS
«B_En7_DATA » TIMSS
2. :
tt .mo . o . y ystat
1 2 11 3 12 4 12 5 14 6 17 7 15 8 14 9 13 10 14 11 10
-
13,2 14
13,5
114
7: -
–
( ) = ( )( ) = 36 = 12
…
( ) = = ( )( )
, = {2, 4, 6}
, 50%.
1
, :N , ( = {1, 2, 3, 4, 5, 6} )
( ) = = 1
0
, :N , ( = ) ( ) = = 0
( ) .
115
7: -
1 2
= { , , , }
, , … , …
( ) = 2 2 = 4
1 111111
116
7: -
:
. ,
, , , , , ,
. . . . . . .
, ,
3 + 3 + 3 + 3 + 3 + 3 = 18
= 18 .
117
7: -
6
:
.
, 36 .
1 2 3 4 5 6 1 (1,1) (1,2) (1,3) (1,4) (1,5) (1,6) 2 (2,1) (2,2) (2,3) (2,4) (2,5) (2,6) 3 (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) 4 (4,1) (4,2) (4,3) (4,4) (4,5) (4,6) 5 (5,1) (5,2) (5,3) (5,4) (5,5) (5,6) 6 (6,1) (6,2) (6,3) (6,4) (6,5) (6,6) ( ) = 36 ( ) = 6 6 ( )
(6 2 )
:
(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)
( ) = 6. ( ) = ( )( ) = 636 = 16
:
6
(1,6), (2,6), (3,6), (4,6), (5,6), (6,6) (6,1), (6,2), (6,3), (6,4), (6,5). ( ) = 11
( ) = ( )( ) = 1136
118
7: -
:
.
= { , , , }
( ) = =
( ) = =
. . ,
.
119
7: -
1.
2.
3. 6
4. , , 4
5. 2 7 9 1
120
7: -
6.
1 2 3 4 5 6 1 2 3 4 5 6
7.
5 7
8.
9. 2, 5, 8 : 3 : 2 :
121
7: -
2000 2007
6,45 6,60 6,85 6,99 7,97 8,77 9,82 10,21
2000 2007
15° 17° 20° 21° 19° 15° 15° 15° 10° 9°
8° 10° 14° 13° 15° 8° 11° 14° 17° 20°
122
7: -
17
17
55 0 13 4 5
8 5
4 5 2, 4, 6 8
0
1
2
3
4
5
10 11 13 14 15 16 17 18 19
123
7: -
6 5
4 :
6
7 7,5 8
2 6 5 8 4 7 5 9 2 10
124
7: -
5 15 15 13 15
1000
50 100 75 60 75 1000 90 100
18 1 2 34 5
;
: : : : :
125
7: -
1.
2.
3.
4. 0, 2, 4, 6, 8, 10 1, 3, 5, 7, 9,11
: : 8 : : 0 :
17, 18, 18, 16, 1, 15, 15, 17, 18, 15, 20, 14, 17, 2, 17 17, 18, 17, 17, 15, 17, 17, 17, 20, 17, 17, 20, 17, 17, 17
126
7: -
5. ( ) ( ).
6.
128 B :
B : 129
4: -
1. 2 , 8, 4 , 106, 2017 3, 4, 5
2. < 3 3, , 0
3. 2, 0, , 64. = 26.
7. > 1 < 2 1 2 < 17
8. 48 19 12
B
1. = 2 = 1 =
2.
3.
4.
5. = 3 = 2 = 4 = 9
6. = 3 = 6 = 5 = 1
7. = 4= 2 = 5= 1
130 B :
9. €2000010. 4
1. [ 3, 1) [ 1, 2] ( , 6]3. 2 < < 7 3 < < 3 4 4
< 5 3 < 8 < 5 2 < 2 < 5
4. [26000, 33000]5. 65 100 [65, 100]6. 1< 5 = 1
, 2, , 3 = 4 [1,5)
7. < 3 3 < 1
8. [ 2,5) [2, 7 ( , 5)
9. ( 1,3) ( ,0) ( , 5) [ 2, )
10. 31811. 2 2014
4 412. 77,5 .
1. [ 6, 3) ( 1, 3) [ 5, 0] 2. 1 5 2 < < 1 3 < 1 2 < > 9
3. = 0 = 1
= = 22
B : 131
5:
– 9
1.
4. < 2
5.
6.
7. > 1 < 3 > 4 1 > 1 > 8 3
8. 5 < 0 < 0
9.
10. = 311. = 612.
13. 2514. 1615.
( 63..
0
1. (2,3]2.
3. = 0
4. 7 < < 1 3 1
5. 5 < < 5 3 < < 7
7. 3
132 B :
2.
3. ) 1 2 3 4 5
( ) 30 60 90 120 150 = 30
4.
6.
7.
–
2. = 2 + 53.
(0,3)(2, 1) ( 1,5)4. = 3 (0,0)(1, 3)5. = 26. (2,0) (0, 4)
7. (0, )8. = + 1 = 2 + 410.
11. i.( 1,0)(0, 1) ( 2,1)(1, 2)
(1,1) (1, 1) = 1
B : 133
ii. (0,0) (1,2)(2,4) (1,1)( 2, 2) = 2
12. = 3 + 3 = 2
13. = 0,03 + 15
:
1. : = 2 : = 4
: = : =3.
:: (3,4) ( 14, 2014)
4. (0,0)5. Ii iv i ii
6. 14
7.
: = : = 3 : = 3: =8. 200 ( ) = 0,4
750 9. = + 2 = 2 = 4 – 9
1. = = = = 12. = 3 = 2 = 34 = 2
= 3 = 4 = 0 : 3. = 3 + 6 =
= 2 + 1 = 34. = 1 = 12
= 2 = 2
5. = 2 = 5
134 B :
6.
1. To ( .
2. = 1= 2
3. = 0= 3 == = 3= 2
= 9= 3 = 1= 13 = 1= 24. i. ii.
iii. iv.
5. €70€50
6. 20 430 6
7. 45 158. 109. = 2 1
1.
2. : {1,2,3,4,5,6} : {9,10,12,13,15} 3. = 4
4.
5. : : ( 1, 2)
6. = 2 = 5 = 5 = 2
7.
8. = 8,5 + 50:
9. = 3 = 1 = 2 = 0
B : 135
1. 7 = 16 202. 660004. = 2, 1 2, = 16. = 12
= 24
7. 3 208. = 310. = + 811. > <
6: –
9
1.
11. : = 2 : = 2: = 3
12. = 213. = 3 1. = 3
(0, 1)14. = = + 4
( 3,0)(0, 2) = 9 . .
15. = 5= 1 = 1= 1 = 5= 3 = 1=
16.
17. 5 3
18. €2,75
136 B :
=2.
5 2 3 30 15 6 9 90
14 21 35 56
2 3 5 83.
4. €6005. 440 6. 312,57.
8. 259. = 0,6 1080
10. $ 5850 9
1.
2. 12 3.
1 2 5 1240 20 8 3
B : 137
4. 1,5 1,5 2 1 0,5 2.55. 18 /6. 18
100
1. 1 2 4 6 102 4 8 12 20
=
2. 2,4 3. 225 4. 85. 120 7506. 58 1,60 71 1,657. 58. 1,79 1,785 9. €400 €56 = 0,7
10. 1 4 3 18 5 20 15 90 5
138 B :
7: -
109
1. = = 162.
3. = 13= 14 = 15
4. = 21,94
10
1. 5.
= 5 1 3 45 15 20
2. 150
B : 139
5. 2, 46. 957. ( ).
8. 184,25 186 cm
186 189 cm185,67 cm 189 cm184,625 cm 186 cm9.
10. = 14,67= 17 = 17
11. 14, 16, 17, 13 14, 15, 15, 16 14, 15, 14, 16 14, 15, 14, 17
– 119
1.
2. ( ) = 183. = ( , 1), ( , 2), ( , 3), ( , 4), ( , 5), ( , 6),( , 1), ( , 2), ( , 3), ( , 4), ( , 5), ( , 6)
4. = ( , ), ( , ), ( , ), ( , ), ( , ), ( , ),( , ), ( , ), ( , ), ( , ), ( , ), ( , ) = {( , ), ( , ), ( , )} = {( , ), ( , )}
5. = {(1,5), (1,6), (1,7), (1,8), (2,5), (2,6), (2,7), (2,8),(3,5), (3,6), (3,7), (3,8), (4,5), (4,6), (4,7), (4,8)}
140 B :
6.
1 2 3 4 5 61 1 2 3 4 5 6 2 2 4 6 8 10 12 3 3 6 9 12 15 18 4 4 8 12 16 20 24 5 5 10 15 20 25 30 6 6 12 18 24 30 36
7. ( ) = ( ) = ( ) =
1 2 3 4 5 61 (1,1) (1,2) (1,3) (1,4) (1,5) (1,6)2 (2,1) (2,2) (2,3) (2,4) (2,5) (2,6)3 (3,1) (3,2) (3,3) (3,4) (3,5) (3,6)4 (4,1) (4,2) (4,3) (4,4) (4,5) (4,6)5 (5,1) (5,2) (5,3) (5,4) (5,5) (5,6)6 (6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
8.
9.
= {25, 52, 28, 82, 58, 85} ( ) = 0( ) =( ) = 1 1
1.6 . .3 . .18,12,
2. 20072000
2006 1,05
B : 141
7,962004,2005,2006,20073.
= 15,05= 16 = 18 47,05%.
5. 406. 40
7.
1 2 3 4 5 61 (1,1) (1,2) (1,3) (1,4) (1,5) (1,6)2 (2,1) (2,2) (2,3) (2,4) (2,5) (2,6)3 (3,1) (3,2) (3,3) (3,4) (3,5) (3,6)4 (4,1) (4,2) (4,3) (4,4) (4,5) (4,6)5 (5,1) (5,2) (5,3) (5,4) (5,5) (5,6)6 (6,1) (6,2) (6,3) (6,4) (6,5) (6,6)8.
= (3,1), (3,4), (3,6), (5,1), (5,4), (5,6),(7,1), (7,4), (7,6), (8,1), (8,4), (8,6)( ) =
9.
1 2 3 4 5 61 (1,1) (1,2) (1,3) (1,4) (1,5) (1,6)2 (2,1) (2,2) (2,3) (2,4) (2,5) (2,6)3 (3,1) (3,2) (3,3) (3,4) (3,5) (3,6)4 (4,1) (4,2) (4,3) (4,4) (4,5) (4,6)5 (5,1) (5,2) (5,3) (5,4) (5,5) (5,6)6 (6,1) (6,2) (6,3) (6,4) (6,5) (6,6)( ) = ( ) = ( ) = ( ) = ( ) =10. = 8,0611. 7
8 8
12. 13,13,15,15,1913.
14. = 2115.
( ) =( ) = ( ) =( ) =( ) =
142 B :
1
4. ( ) = 0( ) = 1( ) =( ) =( ) =
5. = { , , , } 6.
+ ++
{ } =
{1,2,3,4, . . . }
{0,1,2,3,4, . . . }
{0, ±1, ±2, ±3, ±4, . . . }
{1,2,3,4, . . . } { 1, 2, 3, 4, . . . }
{ / : ,
/
o
=
·
Ans
^
SHIFT 2nd F
AC
DEL
Abs
(-)
a b/c 23
S D a b/c
CLR
M+
M-
M
3 + 4 3+4 7 2,34 – 1,1 2.34 – 1.1 1.243 2 3 2 6 2 2 2 32 5 10 5 3 5 103 5000
3 4 2
2
2 3 4 4 4 2 5 5 25 2 (7 3) 2 (7 3) 8 2 (7 3) 2 8 2 ( 3) 2 ( 3) 5 | 3| | 3| 3 0,25
9 6 2
9 – 6 2 + 6
3 (9 6: 2) 6: (9 6: 2) 3 – 6 17
+ = 3 4
· – 2 3 4 1 · 1 =
3 x 2 =
2 5 =
5 P 3 =
3 a b/c 4 =
3 a b/c 4 =
SHIFT 23 2 3 4 =
2 a b/c 3 a b/c 4 =
4 =
5 X² =
= 3 – 7 ( x 2 )
x 2 = 3 – = 7 Ans
2 ( (-) 3 ) =–
= 3 (-) Abs
S D
a b/c SHIFT
= 2 ÷ 6 – 9
3 – 6 ÷ =