371

Μαθηματικά Α Γυμνασίου

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Το σχολικό βιβλίο της Α' Γυμνασίου του Υπουργείου Παιδείας και Πολιτισμού Κύπρου.Η πρώτη έκδοση είναι του 1999 και η δεύτερη του 2007 (προσαρμοσμένη στο ευρώ). Το βιβλίο δόθηκε για τελευταία χρονιά στα γυμνάσια το Σεπτέμβρη του 2010.

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v n o ' ' A N A T V H l ."!J , 1'1 , "'!J , " " - , :rJ , 2007 ' ' 1999 ' 1999 : 2001,2002,2003,2004,2005,2006 ' 2007: ' 2007: m : 2008,2009 ISBN 978-9963-0-4488-7 : . & . 1995 1997 r 1. .........................................1 2 . ............................................................ .7 1. ...........................................................7 2. ......................................................8 3. ...................................................9 4. .................................................................13 5. (i ={:::>{:::> {:::> 1. {:::>...... {:::>2. {:::> =........ . {:::>3. {:::> = ........ . = 5' {:::> 4.25+ =37{:::> =......... 25+ = 37 25+ = 25 + 12{:::> = 12 9. 12. 10 5' 2. 5 37 25 + 12. 25 35 3. 9 36 5. =........ . 72 94 23 ...... 12 16 ...... 175 50 ...... 15 8 ...... + 94+23=117175 + 50= 22594 23+ 117 175 50+ 225 12+ 16 = 2815+8=2312 16+ 28 15 8+ 23 r 94,23, 12,175,50, 15,8 117, 28, 225, 23 1586 + 342. 1586 + 342 =1928 1586 342+ 1928 = 87 =36 + ..... . + + 36 =123 87 36 . =16, =25 =43, 250++ 17 ++250++ 17 ++=250 + 16 + 17 + 25 + 43 =351 37 3. 38 4 18 23 9 18 + 23+ 9 = 50 50 1. 18 + 59 = 77 += 130= 60+ + 2. 42+ 26 584 + 49 3 + 16+ 184 58 + 30+ 79 7865+ 7 + 385 + 62 3. 48+ 500 42+ 620 670+ 105+ 3004 5 + 12 + 1820 4. =1 =23, + 5. = 25 + 7 =23, + 6. = 83, =42 = + + 7. = 12, = 30+ =+ 8, + + 8. = 5, = 15 =+ + +9. 20. 80 45. 10. 4.250. 1600. 900, 11. 480 4 1245 3 280 2 360 12. 4 (i). k 10203040 29302832 27322830 30293127 39 3. 5. 014 5 9 4+5=9 5 014 9 5+4=9 9. 4 5 16 + 12 = 12 + 16135 + 47 =47 + 135

i L .. _____ ._______J 3 4 3 5 12 (4+3)+ 5 = 7 + 5 = 12 4 3 5 12 4 + (3+ 5)= 4 + 8 =12 12. 3, 4 5 (23+ 17)+ 30=23+ (17 + 30) 152 + (56 + 38)= 152 + (38 + 56)= (152+ 38)+ 56 ++= ++=+: , i ! ++=+ += + + 3 +8+'3+1 t5 g+9+3-1-i+5 23+9+(3+1)+5 3. "__ "__ _____ __ ____ __________________ " _ __+. _________ ____0. ___". __ < , ------ '-1 ! ,_ j 102 ____ M:..:....-____ =3cm = r ' , , . = . : = => : = u ~ = , , El. ----- = = = 103 4-,.. q:,,

104 - q:'" 1 m. . =4 m. 4 m. - 3 cm. 4 cm. 9 cm. < ~ . . .~ . , . _____ : ~ __ , ==4 cm. - 4 cm 4 cm. 105 4. 1. _______________ ___________ 2. .....Q..,) 3. cm 35 dm 0,4 km 7,2 m 0,3 hm 4. 625 cm= ............ m 5420 mm =............ cm=............ dm =............ m 2,5 hm= ............ dam= ......... dm = ............ cm 0,03 km=......... hm =............ m =............ mm 5. m 4dam4m 8cm2dm 18 m3 dm3 mm 6. cm 4m 1 dm 12 mm 5m8dm 106 7. 0,2m,3,4dm,1,34cm,34mm,1,3m 8. 9. .. 10. 1000 ft 350 m. 11. ! 12. 3 cm 13. 4 cm - ------:71--------- -----;-- -- -' --I1 -.--- =--- ____107 4. 108 , . . . - . , , ' . , . , , . ' . ' , . , , . . . . . 02' ..n' t'arpCf.pfl

_. ..... 109 4. 11 . 3 =3a. 1 60 (60'). 60 (60'). 1 = 60' = 3600" l' =60" 1. 2. 3. , (1) ____(2)/ (1) (3)::--.....,. = 1270 111 4. u c ;(. . : . : = 400 = 500 r---"..JL 178 =900.

81'82'

= = = =8= = =90 90' = .... 4 -...,/ - . . (1) (1) (1) l. 18 (2) : (3) (4) t. (2)5 (2) (3) AL 5. . . Venn. = $). XLX'L 180 $.

1 2 === === = = = = = rIJ ........ 5. . . = = 6.= = J = =2 cm ----"", = 3 cm. = =2cm . =Or=3cm = 182 + 50"+ 40"=180" + 90"=180" =90" .

, t 1. Ar=8cm 10cm. 2. 12cm. ______"-?IB 3. 7 cm 8 cm 40. 4. 5 cm 8 cm. 5. 7 cm. 6. - AQr z/;$J" 7. . 183 5. - - 8. . .9. ;( ) - ( ) - ( ) - .10. . .11. ::0: , .184 .

. , r 1. . 60 60 60 6 cm, 7 cm, 6 cm 58 32 30 5 cm, 6 cm, 3 cm 150 1350 2. 185 5. - - 3.

1';2

4. 11 11 5. == 11 == 6.

11

7. 186 r t , ' 8. .9. ( , ) . . , .( ) ;( ) ( ) ( ) . 10. . = . fu ;i11. . . .12. = 420 = 860. l. .187 5. - - 13. 64 14. 15. 6 cm. 5 cm. l. l. 16. 17. 18. 35 19. 188 23 235 2 5 . 3 . 3 2 2 . 2 . 2 33 555 2 2 . 2 . 2 33 555 2 . 2 . 2 2 2. 24. . 3 . 3 3. 32. J2= 3 189 6. 3 . 3 . 3 . 3 . 3 = 35 'W'_ 5 XXXxxx=f - . w 6 ... = 190 5 . 5 . 5 5. 53. 555 ==53 53== 5 . . ... w- 56, 5 56. 6 56. >- >---- >-->- -> -> -->- -- -- ->------ -->-- -- - 51= 5. >6. 202 (38323) : 34. (38 . 32 . 3): 34=38 + 2+ 1 : 34 = 311:34 .= 37 . 4 8 . 32. 4. 8. 32 = 22. 23. 25: 6 o ~ y o ~ 4,8,32 -=22 + 3 + 5 . 4= 22,8 = 23,32 = 25. = 210 . 34. 93. 34 . 93=34 . (32)3 = 3432'3 = 34. 36 = 310 t"___ . ~ _____ .. _..0._------.----.-. , 9 . 9 = 32. . .t .. , , ,

23. 25. =215 = 215 3 + 5 += 15 =510 =510 5 =1 310: =37 =37 1- =7 = 203 6. - 1. 27. 25 53. 59 . 5 310: 35 (78)5 .

.

(52) 1 212:212 (50) 1 5: 56 f 353630 2.

(59: 54)3 (32339): 38 (26)3: 210 54 . 52 . (53)3 (565)7 (34}2:38 (23)0.(25) 1 . (26)2 : 3. 556 = 514 = 315

= 1 66= 66 = 2824 (38. : 34= 35 4. 25. 4 37. 3 39 43. 85. 2 35 : 27 162.(26)3 (94275): 32 5. . 26=221. 6. 28: < 3, 7. (58: 56)+ 40 - (312: 310) 204 8 90 - (54: 54)6+ (3+ 2) 1 (3274): (10-1)6 t , ' . ( ) =1, 2. ( ) = 2, 4. ( ) = 3, 8. ( ) = 1 , ; ;205 6. - 206 3 9. 3 . 3 = 9 3 9. J9 =3 9 3. = .= = . ,;,". 14 =2 22= 422=4 f16 =4 44= 1642=16 =1 1 . 1 =112=1 )900=30 3030 =900 302=900 8, 22=4 8. J8 t t 1, 4, 9,16, 25, 36,... J25 - 16. -/25-16= V9 =3

+132= )62 + 82 =136 + 64 =v100 =10 -/9+ 16= V9+ ff6 v169 -144= v169 - v144 =f25=5 V9+ ff6 = 3 + 4= 7 "* 9 = 6, = 8. 100. 207 6. 208 J169 - 144= J25 = 5 J169- 1144=13 - 12 =1 ::F = 4 = 3, JX2- = R- J

- = R-

=J42-32 =J16-9 =fi =Jl6-J9 = 4-3 = 1 = fi = 1 ::F = 4, = 3. = 4, = 3. . J

- = R- = = 3. X::F 1. f25 J49 J10000 .fO 2. .[9 + 16 J100 - 64 110064 J64 J8T .)400 J4 25 3. = 10 =8, JX2 _f4. =3 =4, JX2 + 5. =13 =4, J

_ 6. =5 =12 13, + =R. 7. =5 =4, = J + 2=+ JX2 = JX2 = 209 6. - 1. 4 . 4 ...4 125 - - 248 1 2. 17 08 120 2531. 2530 [(46 + 18) : 64]20 (37 + 25 . 10 -15: 3)0 3. 23 6 8 23 9

++ . 3Q 4. (33)4 (35. 34 . 36 . 3): (32)4 5. (23.2=1): 25= 4 (25)0. 162 =21264

34.45)0 =112 30: 81=9 38:(34)0=1 525125 =50 6.

+ + =5 =3. + 10

= 2 =3. 7. 5 . 24+ 3 (42-50) -37: 35 (3+ 4)2-55: 53+ 3260 49 - 5 . 22+ 32 : (7 - 5)3+ (9 . 2 - 24 : 3). 102 43: 4 + (22)2 - 3 . 32 210 ":V: fnl .// \\\ -7-';;'-- 1/;,-- !\:-:,.! .\,!(.\,II{,.lj\fi1'\\' .' ,;)1;\\ /\\, \/1/\\:1',:::'\\, '\\ ,."". .. L--=::>',,i'L"='.' 1100 ,., 211 1 7. 10m .: 16m 1m + 16 m + 1m + 16 m = 52 m ,, 4m-----0-----'----- ----- ----- j 1 m: -;;,- -:- -------------- _-- 5m---0+ 30m 64m 212 1 m 4 m . 5 m =20m2. , . ,

, =30 + 45 + 64 + 40 =179 n=179m 179 m D'4m24m =24 + 14 + 24 + 14 =76=> =76m =12 + 12 + 12 = 36=> = 36 dm =8 + 8 + 14 + 3 + 3 =36=>n=36cm 12dm ! 213 7. 1. 16m 2. 32mm

26 mm 24mm 1 cm

3. 120 m 60 m. m 2; 214 2. t'-...V' r-... \/ ....... ....... 1\ 11\ , V 1\1 11 \\\......../ / V v 15 . (1) 15. (2) 9 1 . (3) 15 - 2 =13 215 7. 1. 2 ( ) ( ) .2. .216

7 7 3 3 / 1

l', V 2

3

7 V 4

/ "" 5 / '" / 6 '" 217 7. 1m 1 m 1 dm 1dm 1 cm 1 cm 1 mm 1 mm 1--+--+---+----1 4 cm 4cm 3cm 3cm 218 4. 1 1 m2. 1 dm 1 dm2. 1 cm 1 cm2. 1 mm 1 mm2 16 1 cm 1 cm2. 16 cm2 = 4cm . 4cm =16cm2 = 4cm+ 4cm+ 4cm+ 4cm =4. 4cm =16cm 3 cm = 3 cm . 3 cm =9cm2 " = 4. 3cm =12cm 2 cm =2 cm . 2 cm =4cm2 =4.2cm =8cm = =

= 4 . 36 cm. AIiafj: = . =36cm 36cm =1296cm2 . =4 36cm =144cm = 36 cm 64 m2. 2cm 219 7. 220 =. 64 =8m =48m =32m = 64 m2 8 . 8 =64. 1. cm2. ( 1 cm2). ( )2. :( ) 52 cm. ( ) 8 dm. ( ) 12 km. ( ) 105 m. ( )3. :( ) 16 cm2 ( ) 25dm2 ( ) 49m2 ' ( ) 81km2 221 7. 222 6cm 4cm : . 24 . 1 cm 1 cm2. 24 cm2. u = 6 cm . 4 cm =24cm2 u = 2 (6 cm+ 4 cm) =20cm : u = 3 cm. 2 cm 2cm= 6cm2 u = 2 (3 cm+ 2 cm)= 2 . 5 cm 3cm=10cm : U =5 cm. 3 cm = 15 cm2 u = 2 (5 cm+ 3 cm) =2 8cm =16cm 5cm 3cm

, , ---.-- ----- ---------- ---------------1 ! =+ + + , = =2 + 64 32 53 12dm 14dm. = . 64 32 53 =12dm 14dm = 168dm2 = 12 dm = 14 dm 223 7. = 84 m2 0= 7m 224 = 2 += 2 (12dm + 14dm) = 226dm =52dm 84 m2 7 m. 84= = 84:7 =12 =12m 64 mm2. = = 64= 64=

=64:4

= 16 =4 =44 = 16 =16mm = 4mm = = = 64 mm2 4 mm. 4 . 4 mm. =8 . 3 = 24cm2 = 41 =4cm2 = - = 24-4 = 20cm2 24 dm. = 2 +24= 2 +2424 = 24:8 =3dm = = 3 . 3 = 9 dm = 9 dm . 3 dm = 27 dm2 3cm 8cm Q=3x 225 226 6 20 cm 5 cm, = . =20 . 5::::} =100 cm2 = =100 cm2 100 ::::} =10cm =4 10 ::::} =40 cm r r t ! 1. -..... .. ---:..... . 2. 1 cm2). !! 227 7. ( )( )( ) ( )3. 15 cm 24cm. 4. X i 350 dm2 50 dm. .5. 1200 m2 30 m. .6. 256 dm2. 32 dm. 7. 162 m2. , .8. 147 dm2. , .228 ' 9. 20 cm. , .10. . r 16m 9 m, .11. .( ) ( )4m 6m ( ) - 10m( ) 3m 8m 1 m 229 7. -- . 5 cm, = 3cm. (2). (2) (3). (4) (1) (2) (3) (4) / / / / / V / / 7 V / V = = = 15cm2 = = = + + += 2 + 230 18 cm 24 cm. = = 1824=:} = 432cm2 . . = 16 cm =24 cm. ==810=:} = 80cm2 = 8cm u=10cm. 10 cm'" 231 7. 72 dm2 6 dm. =72 =72: 6 =12dm #. = 72 dm2 = 6 dm. 1. cm2. /i/ V 1 cm 232 2. 6cm 9cm 7cm "".' : ........ ... 1.... : 14dm9 3. 12 cm 14 cm. 4. 88 dm2 11dm. 5. 224 m2 14 m. 6. 256 cm2. 7. 288 m2 233 7. 234 8, ) / v \, :.U '1'1 / / 1\ L \ / = = =t = 1 2 =_ .. . - -2- , _ U2 - -2-_ U3 - -2- = + + 18 cm 9 cm. _-2-189 2 _l?'.9 - 71 =81cm2 =18 cm =9 cm. 2 18 5dm: ... .0 ..... "--____..::.... 6dm

65 2 -b -=15 dm2 3 cm =6 dm = 5 dm. 2 6 235 7. = -2- _3ff2 -21- = 3 cm = 4 cm. =6cm2 . 1. cm2. 236 2. 10mm ,' : 15dm ",8m"" m 6cm 16 dm 3cm ............... '; " 4dm 13 cm, 14 cm3dm 3. 20 cm 3 cm. 4. 30 cm2 6 cm. 5. 48m2 16 m. 6. 128 dm2 237 7. 1dm 2dm: 0. ............ . 3 dm 1 dm __ __ 238 = = + =2 =2' = 2 = AJ, - ---2-- =

=

r---------------, :

- -2- ; =40 =

= 2 ' =-2- 12 m 16 m.

=12 m,

=16 m, =; = :=} =12 16:=} =96 m2 22 239 7. 240 8 cm 72 cm2. =

=>72==>72=4

=> 22 =>

= 72: 4=>

= 18 cm 25 m2.

= E=25m2 2 =_1_2=>25=-- =>25= => 22 => =>x=5m

= =5 m

= =25 =>

=10 m , ' 1. 14 m 1 m. .2. 20 m 300 m2. .3. . 24 cm2. .4. 8 dm. .5. . 17 dm 20 dm. .6. 48 m 36 m. . , (582-500 . . ) . . , =900 ( ) . . . ( = 1 ) = 3 = 4 = 5 .241 7. 242 = 32= .. = 52= + = 32+ 42= 52 ,-----------------, ! + == .,_. __. __..___;> __._. ___. ____,,,._"._._" 1 5 cm 12 cm. = + = 52+ 122= 25+ 144= 169 = J169 =13cm 6 m 1 m. = + 102=62+ 100= 36+ =100 - 36 =64 =.f64 =8 cm 9 dm 15 dm. = =9 dm, = + = - =152 - 92 =225 - 81 =144 =J144 =12dm

108dm2 12cm 9dmL:SJ 243 7. 1. d 2. 9 cm 12 cm. 3. 16 dm 20 dm. 4. 244 = 13 m, = 12 m. = 5 m, = 3 m. = 5 m, = 13 m. = 8 m, = 15 m.

5. = = 13 cm =1 cm. 6. 3 m 5 m. 7. = 1 = 60 m = 80 m. 8. 24 m 7 m [ 9. 117 120 .8.12 ..... 10. 25 m. 24 m. . 11. 61m 60 m. 245 m. 20 m 113. ! ,! i !! , 17,15,8 6,9,14 13,16,19 \14. 1500 15. 8cm 'om150m .,__._ .__ .. __ _,,_,, __ _____ .> ____ '__ 29,21,20 90Km1'20Km 15cm , , , r , f 12. -L = =

=1 5 cm 13 cm. . =1L 13cm =5cm 5cm 247 7.

\j \i , = = + = =132 - 52 = 144 =1144 = 12cm =13 + 5 + 12 =30cm 2 = 30cm2 = 60= 1. 13 2120= 93cm 13 =>=13 ;;:1 1 4 t 3: 4 3: 4 = 3: 4. := J' ,.. ".. _.. __ .____ .__ .... __ .. _. ___ .. _._ .... ,____. 9. 284 =: * i==1:3,190==9:10,... ,,8 9. 4 7 1 4 7 4 7. l' 2 ==2: 1 ==r =1 =l'

Q=O = 5 : 5 =1 = 7. =7 =7: 3 - 7 - 3- 285 2 5: 8 12 : 13 1: 50 8 =12: 13 = 1 : 50=56 65= =6. 65 - 5 = 1. 2 : 5 1: 100 13: 100 25: 83 2. 40 16 1 55 11 3. =2 =15 286 1 2 36 253 + 1 = 1 - 2 = 16 J

J 4. Q=4 4. =7 =18 .213 + 1= 1 10 : I'--__________ 1 2 * . . *, 2 4 287 9. 11-___________--11 Br .. 2-3 3 I'-___ --L____'--__--II Br 2 - . 2 "3 :1i 1i i : i i i i 4 288 8 12 12 8 182 = 312 8 = 2 . 4 12= 3 . 4, =182' = : 4 4, 182' .. -' -.. = 182 182 4, 8:4,12: 4). f2. Q = Q..:.,\ ', 18_18: 3_6 24- 24: 3- 8' 18_18:6_3 24 - 24: 6- 4' i (3, 4)= 1 3, 4 289 9. 160' 310 =30 56=30 3 . 1= 5 . 6 = 30 %,! = 28. 4. 3_34 7-74 _12 - 28 290 12_12: 2 30- 30: 2 2. 6,12 015 30 _6 -15 _6:3 - 15: 3 3. _2 -s 2 5 2 (12,30)=6 12_12: 6_2 30- 30: 6- S

77=49 95=45 49*45 * 291 9. 292 t>< 8888 295 9. 296 , m . ~ , ~ : ~ , ~ . .35 4'6 . . . (4,6)= 12 192'~ ~ . ~ ~ 192' ~ g , ~ ~ .,53,35 : 6 > 4 4 < (3 01. , 4 . t . 6 . i . 1 i i i. 1 > 1 1 < 1 4664 % % > < 4664 1. 25 3' (3 2931 5' 4' 2 %, i2' 3,-151 2. ) 1113 60' 144 7315 8' 4' 16 25 8,3' 8 3 4 297 9. 3. (>,=,