Μαθηματικά Α' Γυμνασίου

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Το τελευταίο σχολικό βιβλίο για τα μαθηματικά της α' γυμνασίου, πριν την εφαρμογή των νέων αναλυτικών προγραμμάτων στην κύπρο.

Transcript of Μαθηματικά Α' Γυμνασίου

I ' i ' I A N A V H - ,1'1 " " 2007 1999 1999 2001,2002,2003,2004,2005, 2006 2007: 2007: 2008,2009 ISBN978-9963-0-4488-7 & 1995 1997 1. ... .. . .......... . ........................1 2. . ................. . . . ...... . .... .. . ..........................7 1. . .. ... . . ... . ............. ... . . . .. .. . .. . .. .. ........ .. . . .. ..7 2. .. ... . . . . ................................... .. ........8 3. ... . ......... .. . .. ... .... ... ... ..... . ..... . . . ... ...9 4. .. ". ".. . .. . . .... ..... . .. . ...... . ........ . .. ...... . "........ . . .13 5. ~............................. . .. ..... ...... ...............14 6. .. ...... .. . . ... . .. .. . . ..... ...... .. . .. . .......................14 7. ............ . . . . . ..... .... . . ................................19 3. . .. .. . . .. . .. ...... . . ... . .. .. ............29 1. . ... .. ..... ... ..... ........ ..... ...... ... .. . ....... . ........ . .. .. . . ..30 2. .. . ........... . ... . ..... . .....................31 3. .. .. . . . ..... ..... .. .. . .............. . .........31 4. ................. . ............ . ...............36 5. ..... . ............... . ....... .... . . . ................. .40 6. ....................................... . .............. .46 7. ......................................... . ............ .47 8. .. .... . ..... .. .......... ...51 9. .. ... ... .. .............. ...... . ....... .. ......55 10. .......................... . ................ . .. . .56 11. .... . . .. .............. . .. .. . . .. . . . ... . ........ . . ... . ....63 12. ... . ..... ... ......... .. .. .. ...... . ....... .. ... . .. . .. ...66 13. m . .. . . . . .. .. . ... . .. ... ..... . . . ..... . . . .... . .. . .. . .68 14. .... . . ...... .. ... . . .. .. . . .. ............. . .. . ... . .. .73 15. . .. .. ... . . . . .. ...... . . . ... . .. . . .. .... . . .. . .. .. ...... . ...... .. .. .. .. .76 16. . . . . . ... .. . ... ...... .. .. .. ...... . ... .. .......... ... ... .. .. .79 17. ... . ....... . . .. ... . .. .. ...... . . ... .. .83 4. . . .. ... ... .. . . ........ . .......... . ... . .. .. 90 1. , , . ..... . . . ... .. ... . ... ... ....... . . . .... . .. .. . . . .. .. . . . .. .92 2. . . .. ... . . ... .. .. .. ... ... . .. . ... . ..... .. . . . . . . . ........... . ....94 3. ..... . . .. ... . . . . .. .. ........ . ...... ".... .. ...97 4. ... .. .. .. . .... .... . .. . ... ... .. . . ..... . . . ... . .101 5. .... . ... .. . ..... . .. .. . . ... . .. . . . . . ... .. .. . ...... .103 6. .. . . . . . . .... . .... .. ..... . .. . . . . .... . .... .. . . .. . ... . .. . .104 7. .. .. . ... . . . . . . .. ....... . ... . .. .. . ... . . .... .. .... . . ... . .. .. ..... . . ... . .. 108 8. .. . . . .. ... .... . . .. . .. . . ... . ... .. 109 9. . .. . . ... . .. . . .. . .... .. . . ....... . ....... . . . . . .... . . . ... ... . . .. 11 1 . . . . . . .. .. . . . . . . . ... ..... . . . .. . . . . . . .. . . .. .113 11 . .. .. ...... .. . . ...... .. . .... . . .. . ... ... .. .. . . . . . .... .... ... .. 113 12. .......... ....... ................ . .. .... ... .. ........... .. .. .. ... 113 13. . ... . . .. .. . ... . .. .. ............ . .. ......... .. .. ... ..... . . .... 118 14. . .. . . .. ... . .. .. . . . . . ... . .. . .. .... . . . . . ... .119 15. .. . ... . .. . . .. .. .. . . .... .. .. ... .. .... . . .. . . ... . . .120 16. .. . ..... .. . . . .... . .. . ... . ... . ... ... . .. .. . . . . ..... . . ... . ... . . ... 122 17. . .. ...... ... ..... . . . ... . .. .. . .. . . .. . ...... ........ .. 123 18. . . ... . .... ... ....... .. ...... ... . .. ......... .. ........126 19. . .......... . ..... .. .. ... .... . ............. . . .. .. .. ... 127 20. .... ... .. . . ... . . .. .. .. . .... ... .. . . . .. . .. . .. .... . . .. 129 21. . . . .... . ... . .. .. .. . . . .. . . ... . .. .. . . . . .... . .. . . .. . ........ 131 22. . .. . . . . . .. .. . .. . . .... . .. .. . . . . . . .. .. . . . . . .. .. . . . .... . .. .. . ... .. . ......136 23. ... . . .... ... . .... . . .. .. . . . ... . . ........ . . ......... .. .. .. . .136 24. .... .. , . ". . ......... . ... .. . . .. . .. .... . .. ... .... . . . . .. .... ... .137 25. . . . ... . ... . . ... . . .. . ... . . . . . ..... . . .. . . . . .... .. . . . . .137 26. .... . . . . ...... . .. . . . . ... ..... . ....... . .. .. ..... . . . . . . ...... . .138 27. . . ... . ... . . . . . . . . . ... . . . . . . .. .. .. . .. . .. ... 138 28. . . . ..... . . ...... ... .... . . . ..................... .. .... ... ...... 139 29. ..... . .. .. . .. ... . . . . . ... .. .. . . . . .. . .. ..... . ......... 140 30. . . ..... . . . . . . .... . . ... . . . .. ......... .. .. .. . .144 5. , , . . .. . . .. .. .. .. . ... . . . . .... .150 1. ........ . .. ... . . ... ... . . .. ... . . ........ .. ......... 151 2. .. . . . . .. ... . . . . .... . .... .. ...... . . ...... . .. . . ... .151 3. ... ....... ... ..... .. ...... . .. . ... . . . . ......... .153 4. . ... .. . . . . .. . .. ... . .154 5. . ....... . . .. . . ... ... .. . ... ... ...... . . . . .. . . ...... . .... . .. . . .. . . ... .160 6. - ... . .... .... ... .. .. ... . . ... ... . . .... .. ... .. .161 7. .... . ... . . . . . . .. .. . ... ..... ...... . ... .. ...... .. . . ..... . .. . .... .161 8. . . .. . . .. . .. ..... . .... .. .. .... . . . . . . . . .. .. 163 9. . .. . . . . . .. . . ... . .. . . ....... .. ... .... .. . .166 1 . ... . . . .. ... .. . . . . . .... . .. . . .. . . . . . . . ..... . . . ... . . . .. 169 11 . ......... . ..... ... . ... . .. ..... .... ....... .171 12. ....... . .. . . . . . . . .............. . .. .. . . .. .. . . . . . . .. . ..... . .175 6. . ............. . .. .... 189 1. .......... .. ............ . ...... . .. .... 189 2. m .. ............................ . ................. .... . . .... 193 3. .. .. ..... .. ..... . .. ....... .. . ........ .. ........... 194 4. . ................. .... ..... . ... ..... ....... .. ......... 198 5. 1 .... .. ...... . ... .... .... ...... ... ... . .. ..... .200 6. .... . . .. ... ....... ...... .... .. . .............. .206 7. .. . . ....... . . .. ... ... ......... .... . ...... ... .211 1. ................ . ................................................ .212 2. . . ...... .................... ...... .... ........... .. ...... .215 3. . . . ...... ..... . ...... .. . . . .... .. ......... .217 4.~ o ... . . ... ... . ... ..... ...... .... ......... . ...... ... .218 5. ...... ..... ..... ... ...... ....... . . .... ....218 6. ........ ........ ... ........ ...... . .... . . . .222 7. . . .. . . . ... .... .. . ...... .. .... . .. . .230 8. .................... . .. ... ... .. ... .... . . . . .. . . . ........... .234 9. .... . .... .. ....... ...... . . . .. ......... . .. .. . ... . .. . .... .......... . ... .238 10. ....................... . , . . . .. . . . ......... . . . .238 11. . . ....... . . . . . . ... . .... ...... . .. ....................... .241 12. . ... . ................................. . . .......247 8. .............. .... ........... .... ..... . ..254 1. . . . ... ...... . ..... ... . . . . ..... . . ... .. . . . .. . ............ . ...255 2. .. . ......... .... . ... . . .... ........... ..... ... .. . .. . .... .256 3. . .. .. . . .. ........... . . . .. ......... ... ...... . .......... .257 4. . .. . ..... . .. . . . . .. .. .. .. . . ....... . ..... ... . . .. .. ... ... .259 5. . ... ... . .. . . . ........ . .. . . .... ... .... . .. ... ... .. . .266 6. .. .. . . ........... . .266 7. . . . . ..... . . . . ... ..... . . . . . .. .. . .. ... .267 8. . . . . . ... . .... .. .. , . . ...... . .. . .... . . .269 9. . . . . . . . . . ... . ... .. .. ... ... .. ......... . . . ... . ......... . .272 9. . . . . . . .. . .. .... . . .. . ... . . ....... .. . . ..... . .. . . ... .. .....278 1. . . ... . ... . ...... . .... . .... ... ..... .. ... . .......... ... . .279 2. . .... ... ... ... .... . ... . ... .. ........283 3. m ................... . ... . ...................... .284 4. .. . ....... . .. . ... . .......... . ............. . . . . . ..... . . . . .287 5. ...... . ...... . . . , . . . ....... . ... .. ... 293 6. ................ . ..... . . . ...... . . . ..... . . . .......... . ... .295 7. ...... . ....................... .. .. . ............ . ..... . . . .299 8. ............. . .................... . . . ....... . ... . ........ . .322 10. ............................... .......... . ... ..327 1. . .... . ........ . ...... . ..... . ..... . .......330 2. ... . ................... . ...... . .. . ........ . .. .331 3. .. . . . .. . . . ........... . .. . . . . .. . . .. .333 4. .................... . ........ . . .... .....334 5. .............. . .................. . ........ . ...... .334 6. . ... . . . .......... . ............. . .. . ......337 ......... . . . .. . ... .. .. . ..... . .......... . ... .341 m ... . . .. . ...... . . . .. . .... .349 . . ... . ...... .. . . .... . . .. .... . .... . .. .. ....... . .... . .....354 11 T l ; . m , . , . , , m . , , . , . , . . 1 + (12+ 4)-7 - (12-4)-7 (12.4)-7 (12+4)(12:4) 12-7 4 2 12345 1 1 =11 2 =21 3=31 4=41 5=5 1 =2 2 =4 =6 =82 5=10 3 1 =33 =6 =93 4=123 5=15 4 =84 3=124 4=164 5=20 5 1 =55 2 =105 3=155 =205 5=25 66 2 =126 3 =186 4=246 =30 7 1 =77 2 = 147 3=217 =287 5=35 8 1 =88 2=168 3=248 4=328 5=40 9 1 =99 2 = 189 3 =279 4=369 5=45 102 =20103=3010 4=40105=50 678910 1 6=61 =71 8=81 9=91 10=- 10 2 6=122 7 =142 8=162 9=18 10=20 3 6=183 7 =213 8=243 9 =273 10=30 4 6=244 7 =284 8=324 9=364 10=40 5 6=305 7=355 8=40 5 10=50 6 6=366 7 =42 6 9 =546 10=60 7 6=427 7 =49 7 10=70 8 6 =48 8 9 =728 10=80 9 7 =639 8=729 9=819 10=90 10 6= 6010 7 =70108=80109=9010 10=100 3 1. 1.38+ 12 2.12+ 5 + 107 3.26 4.56 43+ 65+ 5.107 6.3785 285 + 402+ 742 7.95 24-11.78 - 6 8.308 245-12.48 - 29 15.19.24 3 20.18 13 23.12: 4 27.86 24.72: 9 28.1554\ 37 31. 4 9.3775 1008-13. 157 - 48 17.39 10 21.157 52 25.36 : 12 29.340 10.4308 299-14.1004 - 98 18.125100 22.2030 308 26.250 : 10 30.38834\ 125 32.(250: 50)+ (125 - 25) 33. 974 97. 34. 458 206. 35. 1099 888; 36. 14 37. 45 15.525. 38. 3.440 600. 5.400. 39. 98. 33 40. 80.000. 18.000. 12.000; 41. 120 72 78 102 3348 42.24,543.10,00644.4,42 45.36,45 0,18 + 8,43- 8,5 46.4,08+ 12,347.0,84 - 0,0848.48 1,249.1,782: 0,03 50.42,18 151.13,8 10052.0,45 : 100053.83,24 : 1 5 1. 217 54.9"+ + 9" 31 58.54+ 4 51 62. 13 52 55.7- 7 3 59.9-25 63 5. 25 . 13' 26 66. 81 56. 2 60.5 64.1i:130 12 57.66 - 23 45 61.78 65. :12 67. 15m 130m. 68. D468 D4 96 D+ 8 104D3D4D2 D78D D6 F 9D 9- 61D4 D76D8 6 . . . = . . = . .0 1. 7 2. 8 ( 3525 < < " . . , , , , , , 3,5, 2 , , , , , . 2. . 3525, : ={3, 5, 2} ={ 3525} ={/ 3525} , : John Venn, . = {3, 5,2}, = 3 3. ={3, 5,2} = 3525} ={/ 3525} r.:\ \:2 ={1, 2, 3} = 4} = 2312} = / 2312} = 6 6} 9 2. 1 1 ={/ 15} = 16} = 4 15 = 1= 831158} ={1, 2, 3, 4,5, 6,7,8,9, 1 11 , 12,13, 14, 15} 11 , 13,15} ={4, 8, 12} ={8, 3, 1,5} =15 =8 =3 =4 =4 2 = = = 11 2. 12 1. = = 302 043} = = 2. = = 1,2,3, 4} 3. 14 4. = 1 23} = 230151} = 5 30} = 30} 5. 4. = = 896 5} = = }0 .. . } {}0. = = = = 13 2. 14 5. ,,: ={1 , 3, 5, 7, 9} . 5 5 5 4 4 ,,: 4 6. = 33142} = 5} . ={3, 1, 4, 2} ={1 , 2, 3, 4} = =. "" ={1, 2, 3,6} 8={1, 6, 8 2, 3 8. 8 c 8 = 8) = 83 83' c 83' = c 00 '" 15 2. 16 {} , = = = 06 ={1, 2, 3, 4, 5, 6,7,8} .6 = 6} = 8} ={1, 2, 3, 4, 5} 1,3,5 c c . 8 . . 1. ={2, 4, 5, 6, 10},= = 6 4 (l 12 (l =5 9 5 (l =5 ={} = ={} 56 =1 =1 2. ={5,1,3} = 1, 3, 5} ={5, 3,3. = 113555} = 103050} = 4. _' ={_, {3, _' _' 5, 7} ={1, 4, _,7,_} (2,5, _} ={5, _,_} 5. = 2. 6. = 2 20} = 3} = 4} = 12} 17 2. 18 7. .. .... ...c c.. .... .. . ........ . 8. ={2, 8,7} = 2278} ..: ,= , c . .. .. .. .. . {8} .... .. ... 00 00 2 .... .. ... 9 .. .. ..... . . .. .. .. ... 27 .... ..... 7. ={2, 4,6,8} ={1 , 2,3,4,5}, u u={1, 2, 3, 4, 5, 6, 8} u u u= u0=0u= 0 19 2. 20 ={2, 4, 6, 8} ={1 , 2,3,4, 5} ={2,4} = / = {1 , 2, 3, 4, 5, 6, 7, 8} ={2, 4, 6, 8} =={1 , 2, 3, 4, 5} = {1, 3, 5, 7} = {6, 7, 8} 1 = 3} = An n A n B' 21 2.

- {1,2,3,...} C C 22 ={1 . 2,3,4, 5, 6, 7, 8, 9, 10, 11 , 12, 13} ={3, 6, 9,1':} {2,4,6,8, 1J,12} .13 .1 .5 ={2, 3, 4,6, 8, 9, 10, 12} ={6, 12} ={1, 2, 4, ::J,7, 8,1 11 , 13} ={1,3, 5, 7,1, 11,13} ={1,5,7, 1 , 13} ={1 , 5, 7,1,13} ={3, 9}

(i)(ii)(iii) (iv)(v),(vi)(vii ) 2 n = 9 =13 n =3 3 n =7 =12 n = 16 n =11 v(A n =4 =8 .8 .4 23 24 = 20 n = 6 vry n= 8 vry u= 4 4 = u =28 n=14 = = =

(]) (]) (]) ' 1. ={ } ={ } ={ } : ( ){ } ( ){ } ( ){ } ( ){ } 2. ={ } ={ ' } ={ } , ( )( )( ) ( )( )( ) 25 2. 26 3. = 1 16}, ={4, 8,12, 16} ={2, 6, 10, 14, 16}, u u4. = = = 5. = = = u 6. u n v(A n n u 7. = 5, = 8 n= { }, u 8. = 4, = 7 n = 2, u 9. = 7, = 5 u = 8, n 10. = = = .18 11. ={1,2, 3, 4, 5, 6, 7,8, 9, 10, 11,12,13,14, 15} {2, 4,6,8, 10,12} ={4, 8,12} ={3, 6,9,12} 27 2. r------------------- -- ----------, (1 (1 (1 (1 12 (1(1

(1 {} : '" .. . / .. . 12) c (1 28 11 ... - ..., - .. ., - .. ., - ... 1,2,3, 10,8,9,20, 25,100, ... 29 3. 30 1. LiDJ.. - ----- ----- ----"-r' 4 15 20 15 20 155 5 >8; 7 < 9 9 < 7; > > 3 10> 3 5 < 8 8 8 . 3=(6+ 2). 3 ==> . = . (1) 8 . 3 =(6+ 2). 3=>8 =6 + 2 . = . =>= (2) (1) (2) IV. 8 =6 + 2 =>8 : 2 =(6 + 2): 2 ==> = (1) 8 : 2 =(6+ 2): 2 =>8 =6 + 2 : = : =>= (2) (1) (2) *- 3 kg = = 34 = 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. l 9 J 36 5.72: 9 = 9 {::::}=........ . 94 23 ..... . 12 16 ...... 175 50 .... .. 15 8 ..... . + 94+23=117 175 + 50=225 94 23+ 117 12+16 =28 17515+ 8 =23 50+ 225 12 16+ 28 15 8+ 23 94,23,12, 175,50,15, 8 117, 28,225,23 1 1586 + 342. l 1586 + 342 =1928 1586 342+ 1928 2 =87 =36 + + =87+ 36 =123 87 36 . 3 = 16,= 25 =43, 250+ +17+ + 250+ +17+ + =250+ 16 + 17+ 25+ 43 =351 J 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 + + 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 10203040 29302832 27322830 30293127 (11) 39 3. 5. 4 5 9 4+5=9 5 4 9 5+4=9 - -..L- /1'11, " ,L )/)1 _-1-- li!\ 9. 40 Jl.jj} 4 5 3434 _5233 -12 - 12 _19 -12 =12 (- 192 )' 3 . 12 (3, 4)= 12. -- i) _ 12(169) - 24 - 24 - 24 = _ 9) _127 - 24 - 24 _5 - 24 5 - 1 =g 63 1 =2Q 63 =1+g Q 63 = 1 +4 Q 66 - 5 -6 6 i- :t 2012 1 +1 + 1_ 20+12+15 354- - 60--_47 - 60 147_6047 1 - 60- 60- 60 _13 - 66 309 9. 1. 52 - - -33816128 31-g 25 8 - - -253625 4 g- 23 15- 41 72 542 118 -15 2. 4105 8 - (2 - 1 7 1_( 21 - g) 243 3. 8 - - - + - 1( 13) 234 2 + (3 1_ 1 3) 824 11 -(3 - 1 4. J t 5. 6. 7. -k i 1 ',( 8. 5 t 3 9. 3 1 m, 190m 2 m. 4310 11. + = 21 - = !i 8226 111. e f2 152 .555_15 12 + 12+ 12 - 12 (1 ) ,.555_5 12+ 12+12- 123 (2) + 1_1 =L 2312 0+0+0=0 3 (1) (2) . - 311 9. 312 152 3 12 _5. 3 =1 1212 5 12 3 1 18 1 500 90 2 18 18=L 18=36=12 3333 3, 3_3 . 500_1500_ 100 500 100500- 1 00- 100 - 15 900 90 0 =. iO =18300=60 0 2 1.400. j 5 1 1.400 55 i .1400 =1{0Q=280 1400 - 280= 1. 120 1.120. 6 6 2 2. (1) .3636 5 ."'---- 6---..- 3 2 'ill 18 j ;>, 19 3618 (2) (1) (2) 25_10 36 -18 25 3 6 313 9. 314 1 3. 2. 4. J1i 57931 () 381 79"10 32_32_6 5' 7 -- 35 2 418_418_8 9 -- 31 114 ()381 1 7 ' 9 ' 1- 7 105 _14" 1 _4 - 105 2 + 26 7 21 6 3 "7 ="444 _9 - 16 (3,10)=30 3 5 , 9 ' ti' 13

_12 - -1-=12 1. .?4 9 13 100 _ . , 10 (8)10 3 100 2. 2,;> 37 ,32 458 52 (8)- , 2 -125 3. 3(_1+ 423 1 - + - , 1.( 21 )1 532 _5_, 16 12 4.?6 3 21, 2 10 20,3 200, 1 16, 4 100 3 90, 5 18 43 1 , :3. 5' 446710100 58 31 , .? (21 8' 5 5- , --23774 31 , 2 14 3,1 + .? 423 + j423 1) 4. 1000 i 8 6 2 g 315 9. 5. 1 t 6. cm m . m 235 km. 7. 650 173 8. 1.920. 9. t 6 } 28 31 2' 420. 180 15 25 175 20 14. 8 m 16. 2 m 2 m 1S:Eva 240km 4 3 316 . 75 = = = 1 j8 8 757 535 1. 8 = L l! = = 1 8818 .= =1 ' 1. t i, 8 1 1 27 i 4130 i- 27 ='lf f-t 4130= 317 9. 172 ' =1 1'. =1 12 ] _ .= 1 12 7_ .12=1 127 1= 1 1 172 12 =j2 ' &.:i, 1. 1\ 1t 4 18 102. 183'=1 24 =1 51. =1 =1 22 125 1 2 100 1560 =1 22 36 =1 ------ ----------318 IV.

g 4'5 2- 3 ' 5 - 4 42 (1) = = (2) = 1. (1) (2) 1 : 5 3

5 1 8'4 2 .. 319 9. 320 3.7= 8_24 5. 857- 35 :5=.= 223 31 :=. =14=4 5.1 =54=5=21 8 ' 48122 1 = 2=5 37 = g 7 ' 3 = 3 72 =15=11 1414 2 =11 14 158 250 158 250 250: 158= 5. =250 18 250.= 5 =900 1.

2,4 5'7 5'15 6'18 9,27 25' 25 1 : 1 : 4 :

2.1' 1 3'5 : 1 3 : 1 : 5 : 1 4 :1 10: 19J,4 21'3 2 : 6 2.

3'1 +1 5'24 :

: + : 5 + : 1 :+ 1) 1.1:12+ 12:1.1 9):3. 1 136 2 5 1 4. 5 1 J 1 4 25. 273 6. 7 J, 7. 11, 8. 12 9. 60, 10. = = 1 = =11. 2 + 1 = 3 1 _1 = 1 ,1 324243 321 9. 322 8. 3 3. =4 4'75 7 5 3=! 24:=9 3. 24 3 7 5 J, 214 9 ~ t : 7 ' "8_ 7.3 3- 8' 5 . 5 _75 - 8'3" _35 - 24 : ~ ~ 7 . 5 ~ ~ 8 . 3. : 1 : 33 ( ):.( ).[ 25 "7 : 3 5_3 7_21 ( )"2- 5 ~- 10 1 323 9. 324 3 ( )Ji 5 3 _8 -5 3 8 5 _3 - 40 6 (y)l =~ 217 33 6 3 1 7 _18 - 7 2 5 = ~ 6=61 21= 7 33 2+ 1 + ~ 3 -- - -126 : 2+1_ 34 - 1 - 1 3 ~ - -126 1111 12_12 37 _2- - 35 121212 11. 12 1235 _11 - 35 . ko . 1. 2 3 5 52 -17 13 6 3 10 - 6-2. .1+35 1.:[ 10 (3 _2 - -g. 1-33 4 2 7 )2 21 2 _ (9 =- 3+ 1 . 2 42 7 - 51 2 - 9-2 - .. . . . ,:, . : .... '..'._ ..... , 1. +2 45 5 _1 92 5 . 18 625 2 +31 46 25_ 1 1 62 12 2. 1 . 345 9 - 511 412 2. cm m hm 3 km 1 i dam 3. = 1 63 1= 71_ = 2 23 +4.= 12 53 4. . 1 +2. 423 + {+: 254 2' .1+1 '48 5. 21 5 1 1_ 2 99 : 1t _J _ /115. 4 3-2.110=-J :32510 325 9. g + (1)2 + 7 ( 3_2 c----;-32 _ 21+ 1 42 6. 7. 350; 8. 45 80 i 75 9. 8 m 3 2 m 400 30 25 56 11. 12 12. 1200 40 30 i 13.0 5600 m2 1 i m2 326 1m ; , . . m . . . , (98,9), . . , ........ ~ 100EURO 327 10. 328 . . . . . : ( ) . ( ) , . ( ) . ( ) . ( ) . ( ) ( ) , . t 1971 ( 10 001 006) 1 30 cm 1,30 m.

.. ... ,,'" 10EURO 329 10. 330 1. . 0 ' 111 100'1000' ... 10, 0,1, 0,01 , 0,001... ... 10, 0,5, 0,04, 0,009, 0,18 .. . ... 135=4 _35 100100 4, 35. 15,70,036 , . 253=25 3 1' 327=327 100' ; ' 1660 =0,014 , ' : 237 =237 ,100 , . 2. . ; 2,32,302,300. :2 3 - 23 ,-10 2,30 2,300 _230_23 - 1-00- 10 _2300_23 - 1000- 10 :2,3= 2,30= 2,300. , . 1 ,100, 1000 .. . : 1 35 . 1=135. 1 ,100 _135 -10 =13,5 0,124 . 100=124. 100 1000 1,35 . . 0,124 . . _124 -10 . = 12,4 331 10. 332 2,45.1000=245. 1000 100 =245 10 = 2450 2,45 . . 10,100, 1000 ... . 1 ,100,1000 ... ,_1251 :12,5 : 10- 10 _125 - 100 =1,25 _3671 0,367 : 100- 1000. 100 367 100000 =0,00367 1 425:100=425100 _425 -100 =4,25 12, 5 . 10. . 0,367 . 100. . 425 . 100. . 10,100,1000 .. . . .. 1. 71523234515 10'10'100'100'-100 '1000 2. 0,51,215,40,250,025. 3. 2,50,415,650,060,07581,873 10 100 1000 4. 47,561,550,231,8237,8 10 100 1000 3. 3,27 + 2,5 + 2,5= + 25 10010 _327+ 250 - -- 100-_577 - 100 3,27 2,5 =5,77 3,27 2,5+ 5,77 333 10. 334 23,6 - 2,75. 23,60 2,75-20,85 . . . 4. 2,6' 0,19 ,_2619 :2,6 0,19- 10 ' 2,6 0,19 . . . _494 - 1000 =0,494 : 2,6 0,19 234 26+ 0,494 . . . , 2,6 0,19 . 0,494. 5. 64,88: 4 ' 64 884- 64881 64,88 :,:- --:roo' '4 . _1622 4 -- 100 . =16,22 . 64,884 24 08 16,22 45 : 8 45,0008 50 20 40 f----5,625 45= 45,0 = 45,00 = 45,000 = 45,000 ... 2,808 : 1,2 2,808 r- 10, 28,0812 402,34 48 335 10. ...... -,1 "

,..;:;; " 336 /.q -,' 17,6 : 3 17,63 265,8666 20 20 20 2 5,866 :6 ", 5,867 , , , 5,86 :66 ", 5,87 , , 5,8 :666 ", 5,9 , 2. 5,8666 5,867 5,8666 5,87. 5,8666 5,9. 5, 1 4, 3,2 4) 6. 1J =15: 8 15: 8. 158 70 60 40 1,875 = 1,875 = 4: 9 7 1, 4: 9. 409 40 40 4 0,444 ... 4 9 4 0,44 :::0,4 5' , 0,44: 4 '" 0,44 , 337 10. 338 11111111' 2' 3' 4' 5' 6' 7' 8' 9 =0,333...\ =0,166...\ =0,111...f t =0,142857142857 .. . 1_\ 2 - 0,5\ 1=25 f 4' J23=4,795831523 ... 1. 4,6 + 7,46 40,65-18,49 1,3 0,18 0,023 0,14 0,04: 0,2 25,44 + 11 ,6 + 12,78 14,6 - 11 ,35 3,148 0,15: 0,5 0,0018: 0,09 2. 15,6: 1,2 4,05: 3,6 5,616 : 1,8 3. 38,2: 1,2 130,4: 3,6 42: 12,5 4. 15,88:12 10,6: 0,27 9,2: 7 5. 3,468 + 12,84 8,19-3,8 (8)11,4 1,15 1 : 0,08 12: 0,04 82: 0,32 2,05: 9 6. f2 j 7. 2,5+ 3,14 (2,3)2+ (4,1)2 Jf + 5,48 8. =12,56 (12,6-3,15): 4,2+ 11,74 13,84:1,6+ 3,2 1,4 5 : 0,8+ 4,3 2,4 + 4,82 =8,96 339 10. 9. 4,80 120. 5 . 16; 10. 15 6 . 16 . 18 . ; 11. 9 m 4 m. ~m 0,6m. ; 340 1. ={1 , 2, 3, 4, 5, 6,7} ={1 , 3, 5} ={2, 3, 4, 6} . u u 2. u u 3. {4, 6,D.5,6, D }={D,1,4} D. u D. = , D. 4. 30: 6 + 4 + 5 8 (5+ 3 . 2). 2 - 1+ 8 : 4 5. +13 = 31 8+ 105+6 : (13 - 7) 15 + 7 . (8 - 5 +1) - 12 : (9 - 3) =26 = 36 2 =7 + 5 = 27 6. 360 15 240 120 7. 85 103 45. 341 8. 4.800. 1.200 120. 9. 35 84. 8 8,80; 10. ..1 ..1 =180 / / / / / 11. 12. ro.l =320. ___ 13. 14. 180 =400 342 16. 17. =: TLS /\J: 18. =400

=1200 19. 11 20. = =".".= =",," .. . . .. =..... . 21. 650 343 22. 11 23. 11 AB .l

24.

1300. 11 = =480 26. 11 27. AH .l 344 23 28. 11 29. 1112' = =1250. l' l '

30. (12 - 3) 3: 3 - 1 +(16 - 8) 0- (9 - 7) 3 31. 24 20= 212

= (23) 4 = 20 (253)0 = 530 70= 1 76 : 70= 7 32. 34. 27 . 81 2 . 3. 33. = 3 = 2 = -= - +1, = +4+34. = 90 = 15 m = 25 m. 35. 18 m 8 m. 8 m. 36. = = 15 cm = 24 cm. 345 37. 52 cm 24 cm. . 38. 64 cm 32 cm. . 39. 25 m 20 m 60 m. . 40. : ( ) 75 0 2 ( ) 75 0 9 ( ) 15 0 2 3 ( ) 267 0 2 5 ( ) 8 0 30 1 9 ( ) 4 0 70 2 5 9 41. . . . . . . : ( )180,120,420 ( )200,80,2 352 ( )360, 108, 126 ( ) 24 . 3 . 52,2 . 33, 90 42. 400 ,300 200 . ( ) ; ( ) , ; 43. . 20 , 30 12 . 346 ( ) , ; ( ) ; 44. 350 400. 8 12 15 3. 45.

3412 (1; -5: 2 i (31)2 '2 - 3 46. =41 42 2 =136 5. - 1 12'- '2 3}- =2i :=16 2 + 1 =1324 47. ) 21 - - ( ---)2--331} - 1 - - - - -25 .1 6 ' 2 1): i )2 48. 49. 1.272. 1 % 50. 180 15 i 4 2 347 51. 5" 24 52. 240, 53. 54. = i = = 55. i ): +56. 3,56+ 5,2 . 3 4,8 + 157. + =5,8 0,231=100 58. 0,4 (2,6 + 5: 0,4 - 1 t 42,8:1,6 + 15,49 9 - (2,03+ 1,4) =72,5 =359. 50,5 14,5 20,5 30 18,5 20 60. 9 12 9 11 ,20 61. 360 5 3,80 66. 62. 9 m 32 m. 63. 40 m 12 m. 348 ......... ........ ...... ... ............... . .................... . .. ............ ... .... .. . 2 ....... .... ....... .. .. . .. .... .............. . ...... ................................. ........................ ........ ....... ............ . 15 12. 1 1. 5+13-(8-4):4= 2. 3. 1 + 4= 35 2 = 349 4. () 5. =90) =26 cm =24 cm. 7 =10 =9 5 =8 6. 58:=5 7. .. ... .... ... ..... .. ...... .. .... . ..... .... ...... .. ... ... ...... ... . 8. = =+20 =50 350 9. (--f---7 10. 12cm =12 m 96 m2. =13 cm =12 cm 20cm. 11. 71 9 10 3 1 9 5 2 8 0 2 3 5 12. . 8 - 2 1 . !i + (1_ 1)2 = 42' 62 13. 14. 1 + 24' 8= -

5 a, f 351 15. 120 m. 16 13.600 6 4. 2 1. 510 : 57 _ 38:27+ 23 : (32_ 23)4 = 2. f5 60 3. 30 25 20 352 4. 5. 6. = =60 0

= =10 m, AE=8m // 1. f, 353 134.2522 4 35.211 63.5 3 36. 4264. 3 4 1.50 2.124 37.3451 38.1,360 6523 3.69 66.26,408 m 4.121 39. 65 163 67. 50 5.392 40.110,OOO 6.492941.60 2 7.7142.24, 32 12 8.6343.1,5764.={10,11 ,12,13,14, 9.2767 44.37,57 15, 16, 17,18, 19, 20, 10.4009 45.40,5 21 , 22,23} 11.72 46.16,38 = 1, 2,3, 5} 12.19 47.0,76 = 5, 10, 15, 20, 25} 13.109 48.57,6 { 1, 2, 3, 5, 6, 10, 15} 14.906 49.59,4 25 15.105 50.421,8 16.112 5. 51.1380 u = 17.390 18.12500 52.0,00045 19.72 53.8,324 6. = 4 1 u = 4 20.234 54.19 21.8164 3 8. =4 22.625240 55.i 11. {6, 12} 23.3 5 = {2, 4, 8, 10} 56.22 24.8 1 u={3, 9} 25.3 57.3 2 12. {1 , 2,3,4, 5,6} 26.2558.6 u ={2, 5, 6, 9} 27.43 2 28.42 59.65 3 29.= 22, U =1 1 38 60.33 30.= 310, U=84 5 6.215 31.275 61.14 7.104 32.1051 8.4062.1'9 33.1.071 354 9.95 10.6.750 11.2365 45 16.523 17.123 18.94 20. 656 1.168 53 5.63 6.412 12.296 13. 143.500 62 4. 36 60 135 24 63 29 5.39 8.39 9. (100+ 4)35 = =100 . 35 + 4 . 35 = =3500 + 140 =3640 11. 240 12.25.080 13.168 71 6.14 7.7 8.6 9.12 10.20 11. 12.35 13.12 14.100 75 1. 5 8 34 26 2. 58 1 18 3. 7 144 16 32 18 23 18 14 150 31 7 82 8.=4 9.=8 10.=5 11.12.=3 13.=4 14.=5 15.=2 16.=1 17. 85 11.60 12. 14.125,250 15.14,18 16.4, 24 87 2. = 3 = 3 7.196 8.4 9.1 13.(Q=7 =11 =8 14.85 15.55,300 16. 34 m, 80,60 18.21 20. 18 17 26 21. 22 11 78 133 7.800 8.1440 9. 400 12.

=25 =60 =1500,=30 0 =700 13. =650 =50 0 =20 =40 147 6. 150, 750 70 0,1 100 420 7. =1280,=520 , =520 =880,=880, =64 =280 =1200, =60 0 =600, =600 8. =1280, =1420 9. =580 =1160 10.750 11.1350 12.=500,=1300 13.=520 ---- -355 158 4. =600, =1200, =60 =120 =750, + 300 =1050 =75 =105 =630,=610 =530,=410 =1020 6.=790 , =790 7. 1150 8. =680,=600 =1300 172 1. 600 540 350 500 900 680 2.=1270 3.=50 0,f=750 =550 4. =300 =460 5.300 , 600 6. =1400 7. =1220 356 8.=660 9.=320 , f=64 11. =550 12.f=400 15.=880 183 2. =6cm 7. 8.=55 =55 10. =450 185 6.=900 7.=900 8.==300 10. 11.=59 ,f=65 12. =260 18.11 11 ,70 70 19.=1130,=230 ==670 6 196 1. 34, 56 13. 74 79 74 33 106 126 6 925 (8)8 14. 35 17 29 25 48 56 204 2. 28 549 217 515 30=1 (8) 3. =7 =3 = =12 =4 =1 4. 232 321 5. 3 6.= 7,= 8 7. 17 12 303 3 209 2. 5 6 10 12 80 8 3.6 4.5 5.12 210 2. 1 1 4. 312 38 24 5. 4 6 2 2 6 6. 49 204 7. 116 33 1033 5 7 214 1. 68 cm 64 m 2.20 cm 3.360 227 5.140 m 6.80 dm 7.9m,18m 8.56dm 9.16cm2 10.48 m 11. 25m2,24m 56 m2,44 m 32 m2,64 m (d)54 m2,36 cm 232 6.8cm,32cm 7.24cm,12cm 236 6.32dm,8dm 7. 3 dm2 45 cm2 241 3.4cm,12cm 6.8m 244 5. 12 cm 60 cm2 11.168 m2 12.142 m 13.24 m 14.225.000 15. 225 cm2 249 2. m 10 m 24 m 3.33m 4.6m,12m 5.6,72 m 6.136 cm2 }.39 cm2 250 6.4 7.45 8.100 9.192 10.48 m,96 m2 11. 12 m2 12.24 m2 13. 36 cm2 33 dm2 66 cm2 36 cm2 144 cm2 14.167 cm2 15.96 m2 16.192 cm2 17.24m 18. 58 m 156 m2 19.12 cm 20.40 cm 8 265 2. 140 432,132 1005 432 274 3.36 =22. 32,60=2235 320=265 4. 6 5 6 5. 60 120 6. 6 10 14 12 7. 90 8. 720 9.=225 10.12, 5 11.72 12.6 24 1 3 13.34 14. 30 3 15. 240 80 16. 6 19 1 8 17.360 276 1. 2. 23. 3 3. 24 . 34. 53 4. 120 5. 3 6. 315 7. 8. 24 9. 15 10. 2 11. 6 180 12. 36 13. 4 5 14. 1,2,3,5, 7} 15. 2,4} 282 1 7.4 8.30 9.96 357 286 3. = = 6 5. =12 =6 =1 =3 293 1 5_20 .9- 36 2 72_6 .60- 5 5.0=20 6. =8 =39 = = = = 72 297 8181510 1. 20'20'20'20 96610 22'22'22 3. > < 7. 190 10. 12. 305 1. 611(8)1 5153 200 89 2. 20 3. 12 i 4. 2152 12 i 358 1 6.54 29 7.45 17 8.20 310 3 1. 1 16 131 24 310 7 1 1 13 11 202 (8)1 23 90 99 2. 20 610 1 7 12 3. 7 4i 9i 13 4.28 5 5.(3 3 6. 7 740 17 8.1 20 9. 1 10. 11. * i 315 1. 28 130 2. 535 (8)1 49 8 3. 1 111 1; ;6 4. 600 535. 60 0 1080 120 0 288 0 6. 80 120 7.350 8.768,320 4 927 10.182 2 11.43 12. 160 13. 10,20 1 14. 55- 5 15.195 318 1. 2. 121 321 325 1 7 J 1. J90 4 i 9.14m 1. 10 6 10.180 39 3 14 1 3 20 10 11.102 9 25 2. 1 20 18 12.102 000 7 11 713. 115 2. 39 2100m2 7; 1 9 + 2 t 2400 m2 2 fJ 1400 m2 3. 5 8 325 3 4 3)1 10 1. 1 20 18 339 8 51.1 1. 49,82 4,395 12 4. 5 4 1 i 2 0,00322 0,02 - -25 3 2. 13 1,125 1 g 1 3 3,12 300 3 5 4 g 2. 40 cm 3.(0) 31 ,8 36,2 5 7500 cm 3 3,4 256,3 , 10 15000 cm 4. 1,32 39,265.364 1500 cm 1,31 0,23 6.18 _2 3. - 5 7. 14,9 13,99 5 10 7.126 =6 = 22,1 13,13 8,73 7,95 8.45 1 41 8. =4 9.200 4. 1 24 72 1 89.6,803 11 1 20 10. 3-4 10.8 12 3 1 5. 14 11.120 2 3 j3 3 3 100 11. 8 4 5 8 222 1 - -87 341 2 45 1. {1 , 2,3,4,5,6} 7 An B ={3} 6.20 ={2, 4, 6, 7} 7. 1.200 ={7} 8.2625 359 2.=(3,4,5,6} AnB ={3} ={3,4, 5,6, 7} ={1, 2, 3, 4,5,8} ={7,8} 4. 49 59 10 41 5. 6.43m 7. 8. 9. 11.

13.

14.360,540 16.X=S6 17. =650, =500 =50 =80 21.1=18 1=94 =860,=360 =760 22.= = 700 =700 , =1100 25.=660 , =24 =660,=420 =660 29.1=70 1=35 =1250 , =350 =200 360 30. 133 83 110 21 32.316 33.=87,=15, =136 34.60 m,150 m2 35.36m 36.108 cm2 37.120 cm2 38.16 cm 39.8m 41. 2520,60 1200,10 10800,6 42. 100 4 3 2 43. 60 3,2,5 44.363 5 4 1 _19 36 1 7 4 6 1 14 5 216 1 1 12 1156 11 157 7 48.270 49.212 50.2 796 60 90 52.900 53.30,105 54.=355.5 19,16 42,24 11,448 6,07 57. 3,1 290 23,1 11 89,85 19152 59.972,25 60.46 61.58 62.48 m 63.24m,4m ---- -