Vivlio a gym b tefchos

ΜΑΘΗΜΑΤΙΚΑA΄ Γυμνασίου B΄ Tεύχος

ΠΑΙ∆ΑΓΩΓΙΚΟ ΙΝΣΤΙΤΟΥΤΟΥΠΗΡΕΣΙΑ ΑΝΑΠΤΥΞΗΣ ΠΡΟΓΡΑΜΜΑΤΩΝ

YΠΟΥΡΓΕΙΟ ΠΑΙ∆ΕΙΑΣ ΚΑΙ ΠΟΛΙΤΙΣΜΟΥ

ΜΑΘΗΜΑΤΙΚΑ

A΄ Γ

YΜΝΑΣΙΟΥ B

΄ TΕΥΧΟΣ

Αναθεωρημένη Έκδοση

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CM

MY

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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.

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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 ÷ =

Vivlio a gym b tefchos

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