Upload
math-ellinas
View
245
Download
2
Embed Size (px)
DESCRIPTION
Â
Citation preview
ΜΑΘΗΜΑΤΙΚΑA΄ Γυμνασίου B΄ Tεύχος
ΠΑΙ∆ΑΓΩΓΙΚΟ ΙΝΣΤΙΤΟΥΤΟΥΠΗΡΕΣΙΑ ΑΝΑΠΤΥΞΗΣ ΠΡΟΓΡΑΜΜΑΤΩΝ
YΠΟΥΡΓΕΙΟ ΠΑΙ∆ΕΙΑΣ ΚΑΙ ΠΟΛΙΤΙΣΜΟΥ
ΜΑΘΗΜΑΤΙΚΑ
A΄ Γ
YΜΝΑΣΙΟΥ B
΄ TΕΥΧΟΣ
Αναθεωρημένη Έκδοση
C
M
Y
CM
MY
CY
CMY
K
MATH COVERS.A-A&B.ai 2 15/04/2014 12:55 μ.μ.MATH COVERS.A-A&B.ai 2 15/04/2014 12:55 μ.μ.
Μαθηματικά
A΄ Γυμνασίου, B΄ Τεύχος
Συγγραφή:
Αθανασίου Ανδρέας
Αντωνιάδης Μάριος
Γιασουμής Νικόλας
Έλληνα Αγγέλα
Ιωάννου Ιωάννης
Ματθαίου Κυριάκος
Μουσουλίδου – Νικολαΐδου Μαριλένα
Παπαγιάννης Κωνσταντίνος
Τιμοθέου Σάββας
Φιλίππου Ανδρέας
Συντονιστής: Χρίστου Κωνσταντίνος, Καθηγητής Πανεπιστημίου Κύπρου
Εποπτεία:
Θεοφίλου Στέλιος, Επιθεωρητής Μέσης Εκπαίδευσης
Κωστή Αντώνιος, Επιθεωρητής Μέσης Εκπαίδευσης
Παντελή Παντελής, Επιθεωρητής Μέσης Εκπαίδευσης
Παπαγιάννη Όλγα, Επιθεωρήτρια Μέσης Εκπαίδευσης
Γλωσσική επιμέλεια: Κατσουρά Ευφροσύνη, Λειτουργός Υπηρεσίας Ανάπτυξης Προγραμμάτων
Παλάτου – Χριστόφια Μαριάννα, Λειτουργός Υπηρεσίας Ανάπτυξης
Προγραμμάτων
Σχεδιασμός εξωφύλλου: Σιαμμάς Χρύσης, Λειτουργός Υπηρεσίας Ανάπτυξης Προγραμμάτων
Συντονισμός έκδοσης: Παρπούνας Χρίστος, Συντονιστής Υπηρεσίας Ανάπτυξης Προγραμμάτων
Α΄ έκδοση 2012
Β΄ έκδοση 2014
Εκτύπωση: Ariagraf & ΣΙΑ ΕΕ
© ΥΠΟΥΡΓΕΙΟ ΠΑΙΔΕΙΑΣ ΚΑΙ ΠΟΛΙΤΙΣΜΟΥ
ΠΑΙΔΑΓΩΓΙΚΟ ΙΝΣΤΙΤΟΥΤΟ ΚΥΠΡΟΥ
ΥΠΗΡΕΣΙΑ ΑΝΑΠΤΥΞΗΣ ΠΡΟΓΡΑΜΜΑΤΩΝ
ISBN: 978-9963-0-4727-7
Στο εξώφυλλο χρησιμοποιήθηκε ανακυκλωμένο χαρτί σε ποσοστό τουλάχιστον 50%, προερχόμενο από
διαχείριση απορριμμάτων χαρτιού. Το υπόλοιπο ποσοστό προέρχεται από υπεύθυνη διαχείριση δασών.
5.
8 13
– 20 – –
26
35
6.
49 – 55
61
7.
81 – 88
97
8. –
– 111 116
121
9. –
– 133 138
– 150
10.1.
165
, .
,
.
.
8
5:
…
.
.
. ( ) x x
B
. x .
.
.
.
.
R .
.
9
5:
. . , . + .
, , .
T .
. , . =
= = ,= + .
==
=
+
10
5:
1.
.
--
.
-
, = .
2.
.
= 7 .
7 2 = 3,5 .3,5
,
.
11
5:
,
1.
2. 10 .
, . .
. . .
-
.
12
5:
3. = (5 10) = (3 2) .
4. 36 1
5. = 2 , = 21 = 3 + 1.
6. = = .
7. , ,
, , . .
. . .
;
13
5:
60 60
°.
= 90°
0° 90°.
0° < < 90°
90° 180°.
90° < < 180°
14
5:
, 32 50
.
. ».
.
15
5:
A A A A
0
A B =
180°.
AB = 180°
° A B
= 360°
180°.
180° 360°.
A
B
0 < < 180
A
B
180 < < 360
=
16
5:
A
B
1.
-0
50= 50°.
17
5:
1.
2.
3.
45 90 190 180 134 0 360 270
4.
18
5:
5. .
6. = 60°, = 90°, = 132°, = 230° = 270°
7.
8.
19
5:
9. = 23 = 36 .
10. , , ,
11. = 65°
12. 130° + 140° = 270° 20° + 175 = 195 160° + 150° = 310°
13. 3 00 12 00 6 30
A
20
5:
–
. . .
21
5:
=
90° , ,.
+ = 90
180° ,.
+ = 180
, ,
=
1.
+ = 180 , = 180+ = 180 , = 180 = .
22
5:
2.
-
.
- -
, -
.
3.
50°50° 2 = 25°. 25°..
23
5:
1. = 110°
2. 35°,
3.
42° 90 42 = 48° 180 42 = 138° 10° 27° 90° 110° 210°
33°
104°
4. .
10 .
.
24
5:
5.
6.
7.
25
5:
8.
9. = 32
,
. . .
10. .
26
5:
…
.
.
1 2
.
1
2
1
2
27
5:
«A_En5_Ap
,
.
,
, = = .
28
5:
.
A
.
1.
,
- .
-
-.
--
.
29
5:
--
.
-
-0-90°.
.
2.
, .
30
5:
-
.
-
-.
-. -
--
. .
31
5:
3. .
4. .
. .
. = 4,5 -.
32
5:
5.
.
1. , , … , , , … ,
- ,
-
33
5:
2. .
3.
.
4.
5. 2 .
34
5:
6.
7.
– –
– .
35
5:
( , ).
36
5:
1
«P02_A_DEC12/S01-01/index.html»,
6 ,
3
.
.
, .
,
37
5:
( ) = 2
AB . AMB ANB
= R,
< R > R
. yKx.
AB AB .
°°.
AB = 50
38
5:
d > . .
(To
d = R
d < R
1. ( , 4 ).
( , 4 ) 4 4 .
39
5:
1. 5 , 80 .
2. 2 28 .
3. ( , 6 ) . . . .
.
4. 60° .
5 6.
5. ( , 5 ) = 3 = 60° 45°.
40
5:
6.
.
7. ( , 4 ) = = 3 . . .
8. ( , 4 ) 3
9. , .
.
41
5:
1..
2. = 60 , = 100 = 200
3.
98° 270° 180° 181° 0° 90° 360° 117°
4.
5.
6. 20%
7. = 10
42
5:
8. .
/
/
/
,
/
. / ( , ) 2 . /
9. .
10. = 20° = 60° , .
43
5:
11. , , , , , ,
12.
44
5:
13. , , , , , , ,
14. , ,.
15. ( , )
.
45
5:
16. , ;
, ,
, 1 12.
46
5:
1.
;
2. Geogebra . ;
3. = = 4 ,
. 4. , , ,
.
5. , , ,
= .
6. (4,0) , (0,6) (0,0). .
48
:
49
:
10 x 10
-
-
:
(1)
(2)
«A_En6 ggb»
E
4 3
2
1
-
:
( , )
(2,4)2 4 (0,0)
4
12
34
-
-Descartes
52
:
(4, 1), (0, 3) ( 5, 2)
4352
(2,1), (1,2), (4, 2), ( 2, 1), (4,0), ( 4,0), (0,4) , 2
:
5
En6_syntetagmenes ggb»
( 2,5) (6,5)
54
:
( ) 1 2 3 4 5 ( ) ( , )
55
:
–
€3/
€2/
€1,50/
€3,00 1,5kg x €2,00/kg
56
:
(1)
€2,00/
)
) 1 2 3
( ) 5 2 3 (€) 10 6 18
1 1,5 3,25 5 3
6,5
2
6
10
5
57
:
(2)
«A_En6_michani_synartisis
6 ( ) ( )
58
:
( ) ( )
= 2 + 3 , = + 2 + 3
= + 4
= + 44
= 3
2 2 + 4 = +2 1 1 + 4 = 5 4 4 + 4 = 8
1 2
3 6 1
59
:
= 3
2 … 3 6 0 … 1 2 2 … 4 8
1 2 3 5
2
5
8
14
«……………………………………………………»
2 5 0 0,5
…
…
…
…
:
4
3, 0, 6 1, 4, 10
9
1 3 2 5 6
9 4 36 1 25
:
(1)
y = + 32 C y F
5 0 1 5 10 ( , )
62
:
_Synartisi
(2) 1650 2010
2000 1960
8 000 000 000
( , )
=
(
:
= +
= +
= 2 + 1
= 3
( , )
= 3
( , ) 2 3 ( 2) 6 ( 2, 6)0 3 (0) 0 (0,0)
3 ( ) , 2 3 (2) 6 (2,6)
64
:
2001
2001€24000 2003 €1975024000 19750 = 4250€12000 20052005 2006
( ) 3
( )= + 3
y
( , ) 4 1 ( 4, 1) 2 1 ( 2,1) 0 3 (0,3) 2 5 (2,5)
---
-
65
:
1. = 3 1
( , ) 2 1 0 1 2
( , )
2. ( ) ( )
3.
2 1 0 1 2 3 8 4 0 4 8 12
4.
= 2 = 2 + 3 y = + 1 = 3
66
:
5. ( , )
6. () 18
7
170
2 1 0 1 4 1 0 1
cm
67
:
7.
8.
6
66
6
68
:
9. ( ) ( )
10.
km
69
:
11. €8€40 30
€240
12. €3000
10
13. 100 80
2
80 6
:
( 3, 2) ( 3, 6) (5, 6) (5, 2)
, ,
0,2 500 250
=
2 3 1 5
:
1
,
2
y = 3 + 2
1 0 2 3
5 2 4 7
6 3 0 3
0 1 2 3
3 1 1 2 7 1 5 8
72
:
€4 ( ) 0, 1, 2 3
( ) 40
= y = y = 1 y = 2
:
3 €8 6 €2 1 €15 €
€200 €100
( )
€5 2
= + €13
74
:
( , ) (2 , 2 )
( , ) (3 , 3 )
( , ) ( , ) ( , ) ( , ) ( , ) ( , 1)
75
:
2,3 15 4,6 306,9 45 9,2 60
13,8
25
76
:
( ) ( )
( ) ( )
77
:
2 3 5 12 4 12 20 24
30 6 2003
78
:
= 220 – . = 208 0,7
80%
2003
80
7:
81
7:
N 1, 2, 3
« n7 paralliles.ggb»
82
7:
1 2 .
: , , , ,
3 3.
: , , , ,
3
:
–
,
.
=
« »
.
: + = 180°
-
--
83
7:
« –
. : =
A = 25°, , ,
= = 25° + = 180° = 180° 25° = 155° = = 155° = = 25° + = 180°
= 180° = 180° 25° = 155° = = 155° ( – ) = = 25°
----
84
7:
A= 68°
= = 68° = = 68° – = = 68° + = 180°
= 180° = 180° 68° = 112°
= 360° 255° = 105° , : + = 75° + 105° = 180°
85
7:
86
7:
40° °
87
7:
A= 15° = 24°, . = 120°
= 60° + . .
88
7:
, ,
,
= 90°
> 90°
.
< 90° < 90° < 90°
89
7:
=
.
= =
«A_En7_Athrisma_Exxoteriki_Trig.ggb»,
90
7:
,
,
= =
,
= = , = =
91
7:
180°.
: + + = 180
90°.
= 90°: + = 90°
+ + = 180 = =
+ + = + + + + = 180180°.
= +
180° --
360°.+ + + = 360
92
7:
= 30° , = ( + 30)° = (2 )°
N
+ + = 180° 30° + + 30° + 2 = 180° 3 + 60° = 180° 3 = 180° 60° 3 = 120° = 120° 3 = 40°
= + 30° = 40 + 30 = 70° = 2 = 2 · 40° = 80°
= + 123° = 40° + = 123° 40° = 83° = = 83° + = 180° + 123° = 180 = 57 = + ( = 40° + 57° = 97°
93
7:
: :
I
94
7:
( = 90)
95
7:
,
+ 80° + 50° = 180°
96
7:
= 60° = 100° = 20°
,
97
7:
«A En7 DeyterevontaStoixeiaTrig.ggb».
98
7:
1B
=
=
=
-
99
7:
= , , =
--
100
7:
=
3 + 4 = + 8 3 = 8 4 2 = 4 = 4 2 = 2
101
7:
,
,
102
7:
= , , =
= = 5 = 120°
, , , , , , , ,
= 40° = 60°.
= , , ,
103
7:
60° 60° 36° 54°
70° 100°
60°
= = =
=
104
7:
= 125° =
5
(1,1), (4,1) (4,4).
105
7:
,
= 28°, = 224° = 31°
106
7:
, , = 3 5 = + 1 = 2 2 = 4 . ,
= 0. ( 1, 2), (3, 1) (1, 6).
.
107
7:
, = 77° .
,
108
7:
,
> = ( )
AZ = = = =, = 10°
o
-
:
110
: -
111
: -
-
90 16800 750 30 17000 1500
45 5000 600
112
: -
6 9 4 7
.
.
12 10 12 10
50 800
( ) ( ) = = 16
113
: -
=
=
, ,
= 3 12 9 4 3 4 9 12
1889
300 6 =
300 165 =
300 18 =
--
-300 .
114
: -
10 2
2 = 2 100 000 = 200 000 = = 1 20 000
2 6
10 15
6 8
-
--
115
: -
, , , , , ,
= .… = .…
= …. = …...
1 220
1 160
1 87
1 64
1 48
1 30
20 40
116
: -
1, 3, 4, 12
= A
…… = ……
B …… = ……
…… = ……
…… = ……
N
117
: -
i. = =
= 2 6 = 3 4
ii. = =
= =
=
=
6 = 2 3 6 = 6 = 1
118
: -
6,6 8 1 6
= , = 6 = 1 6,6
6 = 6,6 = 6,6 6 = 1,1
= 6 = 1 8
6 = 8 = 8 6
= 1,33 7 5 40.
= = 40
= =
= = = = 20
= 20 = 140
= 20 = 100
119
: -
= = = = 45 1 100 000
1 200 0005
6 8
12 = + = 64
250 1 2 0,05
€150
12 10 8
360 50
120
: -
€16006 8 €720
1
1,5 9
– Denis Guedj
= = = + = + 2560 .146,6 3800 138,8
121
: -
100
Donella MeadowsThe Global Citizen 1990
7 000 000 000 100 37 15 11 14
74 65 17 15 21
Sources: -
- Green
2011
122
: -
%
.
€4,85 18%
385
18% €96,70 96,70 = 17,41 96,70 + 17,41 = 114,11
18%€100 €18. €118
0 – 120 €0,23 120 – 320 €0,24 320 400 €0,25 400 900 €0,26 900 €0,27
120 120 0,23 = 27,60 200 200 0,24 = 48,00 65 65 0,25 = 16,25 4,85
,
- ‰ -
.
123
: -
€) €) €)100 18 118 96,70 , = 100 = 118 96,70 = , = 114,11
25% 35% 480
€2300 4%
450 90 280 25%
€900 €990
€90000 €40000 35%
%
--
124
: -
25%
€640
3% 1%400
€400 €320 €250
50 20%
€17700
125
: -
€350
18%
€22000 1 €22880
35%
126
: -
= = = = 1 1003 5
=
180 144
5 4 20
18% €2478
1, 2, 3, 4, . . . ,100
127
: -
1: 100 2,20 1,10 65 65 1,20 0,75
€100 €5000
€20 €30 €50 €100
20%
€32,50
20 €240 10% 20%
€5625 20%
15 12 18
128
: -
€36000 300 350 550 20%
3000
85%. 60%
129
: -
10 16
2 31 410 4 4 2500
1 1903
23,4 6,1 6,7 1 6
130
: -
1
1 2
5 1,618 1
Leonardo Da Vi
= 20
-
:
132
9: –
133
9: –
–
7 916 18 20 25 30 31 0,5
116.7 111% 63% 154% 8, 9 23 8 9 22 25 30 31
0.5 8 12 24 31 11 22 2 9 ° 10 25 30
134
9: –
2011
2001
;
135
9: –
.
.
2011
136
9: –
18 B
, , , , , , , , , , , , , , , , ,
.
. .
. .
Km/h
43 1 WS 37 0 EAA 42 4 DHG 48 3 KBE 35 2 HKF 39 0 KFC 40 1 YW 27 3 ST 36 2
HTP 47 2
;
137
9: –
20
(%) *
/
4% 4% 6% 6% 10% 10%
9% 9% 13% 13% 19% 21%
15% 18% 21% 22% 29% 29% 17% 18% 20% 23% 28% 29%
51% 50% 47% 47% 44% 42%
42% 44% 43% 40% 37% 34%
30% 28% 26% 25% 17% 19% 32% 29% 24% 24% 16% 16%
* 1992 2001
138
9: –
2010 11 19199 97,5% 2,5% 9247 9952. 1985 86 39%.
2010 11
32118 22092 ..
139
9: –
20
1
140
9: –
2
--
---
-
---
141
9: –
8, 5, 6
8 5
6
5 6 8 3
142
9: –
22 5 1,50 1,60 .
143
9: –
20
3 360° = 54°
7 360° = 126°
4 360° = 72° 4 360° = 72°
2 360° = 36°
20 360°
= 35%.
3
7
4
4
2
02468
144
9: –
(mgr/cm40
0
2
4
6
8
10
12
14
16
1,60 1,70 1,80 1,80
16 24 69 47 23 22 43 27 49 48 12 32 49 38 42 27 31 50 38 21 36 42 28 31 28 25 45 12 57 51 22 23 24 25 24 65 43 25 74 51
(mgr/cm 10 20 3 20 30 15 30 40 6 40 50 9 50 60 4 60 70 2 70 80 1
H
-
- -50 50 60
10 20 30 40 50 60 70 80
145
9: –
1. ( ) 30
25 26 26 26 24 21 21 22 24 26 25 27 22 22 24 23 23 26 25 26 22 23 27 24 23 21 21 23 23 22
μ 23° ;
24° ; 24° ;
2.
50
1 3
3 5 5 5
3. 30
2 5 6 1 2 5 4 3 2 5 1 3 5 4 1 3 2 6 5 4 1 2 6 2 4 3 1 6 4 5
4. 16 21 17 18 20 19 21 21 17 19 19 18 18 20 19 17 19
0 5 1 10 2 15 3 8 4 5 5 4 6 3
146
9: –
5. A1
B2
6. 600
7. 55%
55° 99° 180° 198°
8. 180
A1 B2
4 8
6 6 8 3
3 2 4 6
147
9: –
9.
10. 100
11.
148
9: –
12.
25%
149
9: –
13.
cm 135 140 4 140 145 11 145 150 9 150 155 6
140 135 150
14.
50
2 4 2 6
15.
2 2 4 4 6 12 6 8 98 10 4
150
9: –
–
1 €25 2 3 €10 4 €10
5 €100
1 2
3 4
5
.
151
9: –
5
«
152
9: –
= {1, 2 ,3 ,4 ,5 ,6}.
: , = {2, 4, 6} : 5, = {5, 6} : 2, = {2}
A , ,
= {5, 6}
( ( ) = 2
To
-
153
9: –
( ) = = ( )( )
= {2, 4, 6}
( ) = ( )( ) = 36 = 12 50%.
1
: 7 ( = {1, 2, 3, 4, 5, 6} )
( ) = = 1
0
: 7 ( = )
( ) = = 0
( ) .
154
9: –
;
12
, , , , , 6 2 4 .
= { , , }
( ) = = =
( ) = = ( ) = ( ) = = ( ) = 0.
8 8. 4 ( ) = =
155
9: –
30
= 30 30 = 15
= 30 = 10
30 (15 + 10) = 30 25 = 5
( ) = =
( ) = = =
120°
60°
180°
156
9: –
.
.
.
8.
».
7.
1 25 2 20
20 1 20
: : 5 : 1 2 : 12 : 21.
157
9: –
25 0,4
20%
6 9
25
0 1 2 3 4 5
3 9 7 3 2 1
3
2
2
: : : .
( 8) = 1 ( 3) = ( 4) = ( ) =
158
9: –
O 2
; 2
2 2 ;
2
0 2 1 12 2 20 3 16
159
9: –
10 15 , 11 , 10 , 10 , 14 , 16 19 , 18 , 13 , 17
40
3
;
1, 1, 3, 2, 2, 1, 4, 1, 1, 4, 3, 1, 1, 2, 1, 2, 3, 1, 2, 1, 2, 2, 3, 1, 2, 1, 1, 5, 4, 3, 2, 1, 1, 3, 1, 2, 1, 1, 1, 1
160
9: –
( 1) = 40% ( 8) = 10% ( 4) = ( 2) = 0,2
( ) = 1 ( ) = 0 0 < ( ) < 1 ( ) = ( ) ( ) > ( ) 50
161
9: –
720
: 6 : : : 5.
20 0,2 ;
,
2 + 20°40° A
162
9: –
3 6 2 6
50
2 3 4 5
2
2011
15
0 41 5 2 10 3 14 4 8 5 4 6 3 7 2
%
31044
26659
24376
19197
9744
8663
7350
7102
163
9: –
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
€65 €5 €10 €20 €5 €10 €20
164
9: –
4 1 1 5 1 5 320
2, 5, 8
3 2
2003 1998;
166 : B
A : 167
5:
11
1. =2. = 5 cm = 10 cm
= 20 cm = 7,5 cm3. = 4 , = 20 4. 21 m5. y = 20 = 40 . , = 61 .6. =7. =
17
1. ,
2. , , , ,3.
5. , , ,6. , , ,7. + + + = 360°8. > >9. = 59°12. 30° + 120° = 150°13. 90° 0°15°
–
2. = 145°
168 : B
3.
42° 48° 138°10° 80° 170°27° 63° 153°90° 0° 90°110° ----------------- 70°210° ----------------- ---------------57° 33° 123°76° 14° 104°° (90 )° (180 )°4. 135° 70°45°5. = 60 = 17
= 30 = 25 = 120 = 24
6. = 44° = 49° = 80°= = 51°7. 90° 9. = 16° = 64° = 32°10. = 12 = 13
– –
1. 4.
6.
4. = 60° 6. = 144° = 288°8.
9. =
A : 169
41
1.
3.
98°270°180°181°0°90°360°117°5. = 72°6. = 30°8.
9. , ,
, , , ,
10. >11. = 55° = 20°= 25° = 40° = 22°= 35° = 45° = 20° = 75°
12.
170 : B
13. = 38°= 70° = 40° = 140° = 70° = 50°
14. = 29°, = 32°, = 119°15. = 30°, = 60° = 120°
46
1. =2. = =4.
6. (2,2) 6:
2. (0,0), (1,1), ( 100, 100), (2012,2012) , ( , ), …
3. ( 2,0) (0, 2)5. i. ( 5,4) ii. ( 3, 1)
iii. (4, 4) iv. ( 5, 3)
v. (2,3)
( 5, 3) ( 3, 5) (4, 4)(2, 2) ( 3, 1)
6. (2,5) (14,5)7.
(3,0) ( 3, 1) ( 3, 1)
8. ( ) 1 2 3 4 5 ( ) 3 6 9 12 15 ( , ) (1,3) (2,6) (3,9) (4,12) (5,15)
A : 171
9. x
y
(1,1) ( 1, 1)(1, 1) , ( 1,1) ( 1,0) (0, 1)
-
1.
= 3 = 2 2 5 3 6 0 3 1 2 2 1 4 8
2. 2 7 5 13 0 3 0,5 4
3. = 3 + 24. = + 45. = 2
= 186. =
65
1.
( 2, 7) ( 1, 4) (0, 1) (1,2) , (2,5)
172 : B
2.
40 = 4
0,5 2 1 4 1,1 4,4 2 8
3. = 4
4.
5. 2
6. 124 188
14 1 27. = 3 =
A : 173
= 2 = 2 + 2
8.
9. ( ) , ( ) , ( )
10. 160 320 100 1 15 160 3
11. €280 = 8 + 40
25
12. €250 €5500 12
13. = 100 2 : :
10 88
70
1.
2. ( 2, 4) (3,1) (5, 4) ( 4,3)
3. 100 1250 = 0,2
174 : B
4. 2 8 , 3 27 , 1 1 , , 5 125
5. (2,5) (3,1) (5,4)
( 2, 5) ( 3, 1) ( 5, 4) 3 (2, 10) (3, 2) (5, 8) 4
6. ( )
7. = 4
(0,0) (1,4) (2,8) (3,12)
8. 10 15
9. ( )
10.
11. = 200 + 100
12. = 2 + 500 400
A : 175
74
1.
( , ) (2 , 2 )
(2,2) (4,4) ( 2,2) ( 4,4)
( 1,1) ( 2,2)(0,2) (0,4) (1,1) (2,2)
(2,0) (4,0) ( 2,0) ( 4,0) ( 2, 1) ( 4, 2) (2, 1) (4, 2)
4 3 ( , ) ( + 4, + 3) 3 1 i. ( , ) ( 6, + 6) ii. ( , ) ( + 6, + 6) iii. ( , ) ( 4, 7) iv. ( , ) ( + 6, 7)
2. =
= 90
3.
12 14
184.
5. 1 C , D , 4
6.
7. 40 = 166,4 0,56
176 : B
7: II
85
1.
2. = = 80° , = 100° = = 110° , = 70° = = = 120° , = 60° = 62° , = 118°
3. = = 120° , = 60°4. = 31° , = 45°5. = 147° , = 47°
= 68°6. = 56° , = 90°7. = 112° , = 68°8. = 409.
= = = 140° , = = = = 40° , = = = 130° , = = = = 50° 10. = 39°12.
2. 3. 5.
6.
7. = 90° , = 60° , = 30°8. = 64°
= 60°9. = 120° , = 30°
A : 177
10. = 63
= 34 = 27
11. = 79 , = 56 , = 45 10. = 36
= 120 = 32 = 113
11.
12.
13. = 40°, = 72 , = 72 14. = 105 16. = 20
= 30° = 90° = 60° = = 30° = 120°
101
1. = 5, = 41°, = 90° 5. 1) 2) 3) 4)7. = 35° = 90° = 7 , = 42°
= = 45° , = 90° = 30° , = 3 8. = 80° 120°9. = 70° , = 110° , = 30° , = 30°
1.
2.
3.
= = = 35° , = = 145° , = = = 70° , = = 110° ,
178 : B
= = 75° 4. = 120° , = 120° = = 30° 5. = 20
= 206. = 328. = 55° = 33° = 92°10. 11.
12. = 20°, = 70 , = 45 13. = 82 14. = 77° 19.
= 3 < 0 < 0
21.
= = 76° , = 153° , = 27° , = 27° 108
5.
8: -
- 114
1. 1 1 1 2
2 3 1 1,5 2. 1 3
3 83. = 2 3 = 3 4,
4. = , = , = , =5. 6 28
36. 1 220
A : 179
7. 1 2 1 21 4
11
1. 28 13
9 4
2. 45
3. 104. 9 5. = 406. 0,08
1,25 7. €60, €50, €408. : 160 , : 200
: 200 , : 2509. 1810. 6
1. 192
2. €23923. 80% 70
21,9% 4. 10%5. €455006. €562,5 €550
€280 €5,25 7. €360 3 18. 20000
180 : B
9. 20%10 1010.
11. €296,61
12. 4%
1. = 1
= 9
= 14 = 6
2. 3 5
3.
4. 20%5. : 80 : 100
6. €21007. 10% 50%9. €1000, €1500, €250010. €2611. €633612. €1500, €1200, €180013. €1320014. 1530
1.
2. = 5, = 8 = 10, = 163. 200 300 50 4. 140,4 36,6 40,2
1 8
A : 181
9: –
-
1. 18
2.
3.
36 / 2 42 /
4.
5.
145
1.
21 422 523 624 425 326 627 2
i. 9 ii. 11 iii. 15
2. 45, 90% 12, 24%17, 34% 47, 94%4, 8%
182 : B
3.
1 52 63 44 55 66 4
4.
μ μ μ
17 318 319 520 221 3
5.
A : 183
6.100 200 150 100 50
7. 198°8. 309.
10.n
11.01234567
0 1 2 3 4km)
184 : B
12.
μ
6 3 3 2 6
,
25%
13.
2680%14. 5 2013
A : 185
–
1.
2.
3.
8.
3
7.
4.
5. ( ) = =
0
5
10
15
20
25
0 2 4 6 8 10
186 : B
( ) = =( ) = =( ) = 0( ) = = 16. 157.
1 206.
8. ( ) = = 9.
10. 2014( ) = , ( ) = , ( ) =11. 1,3,4,5,6,7
2.
100 3. 20 34
40%
2
12
20
16
0
5
10
15
20
25
0 1 2 3
A : 187
=
4.
5.
0 0
0
0
6. 1 20 2 10 3 6 4 3 5 1
(i (ii (iii 50%
8.
0 4%
1 24%
2 40%
3 32%
188 : B
9.
151210
+ 8- 5
A : 189
10. 0 45.
11. = 70
12. ( ) = ( ) = =( ) = = ( ) =
13. 414.
(i ii iii
15. 4
16. = = = =
17.
18. 27
1.
1 12 114 115 316 117 418 320 1
190 : B
15 117 1118 120 2
5.
6. .
7.
8. ( ) = 1 , ( ) = , ( ) =
{ } =
{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 ÷ =