zbirka resenih zadataka zavrsnog testa za 6 razred

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Списак задатака за завршни тест за ученике шестог разреда Основни ниво од 1 до 36 од 51 до 56 од 58 до 59 од 62 до 63 од 65 до 66 69 од 76 до 100 од 108 до 110 од 116 до 119 Средњи ниво од 121 до 138 140 од 166 до 171 од 173 до 174 191 од 194 до 200 202 од 206 до 210 од 226 до 230 Напредни ниво од 231 до 240 250 од 271 до 275 од 296 до 301 од 303 до 308 321 од 326 до 327 од 329 до 330

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1 36 51 56 58 59 62 63 65 66 69 76 100 108 110 116 119 121 138 140 166 171 173 174 191 194 200 202 206 210 226 230 231 240 250 271 275 296 301 303 308 321 326 327 329 330 www.matematiranje.com 1 , ) www.matematiranje.com 2 www.matematiranje.com 3 12 , 4 6 9 : 2,5 : 2 5 2,05 : 2 5 2,17 : 2 17 2,175 : 2 175 2,075 : 2 75 ) 2,017 2 010m, ) www.matematiranje.com 4 www.matematiranje.com 5 125 10, 510 2= = 152 10, 210 5= = 152 12, 2 2 210 5= = 125 12, 5 2 210 2= = www.matematiranje.com 6 . 1) ab brojilacimenilac , ( 10 100 1000 ) :3 3 25 750, 754 4 25 100= = = , . :33: 4 0, 754 = = 03028202000 ) / 5/ 51 50, 52 10 = = ) / 25/ 253 750, 754 100 = = ) / 2/ 21 20, 25 10 = = ) / 125/ 1251 1250,1258 1000 = = ) 40, 410 = www.matematiranje.com 7 ) 111,110 = ) 3 3 5 151, 52 2 5 10= = = ) 10, 01100 = . 2 ( 10 100 1000 ) ( ) : 100 75 75: 25 30, 75 0, 75100 100 100: 25 4= = = = :25:2575 30, 75100 4= = ) www.matematiranje.com 8 30, 310= ) ) www.matematiranje.com 9 152, 28 152,18 125, 32 125, 03 > > > ) . 3) ab , . a a kb b k= . 1. , . 3 25 5> . 2. , 2 25 7> : I . . II . . : 34 58 I 3 3 2 64 4 2 8= = 6 58 8> 3 54 8> . 1 II 3 3 5 154 4 5 20= = 15 1520 24> 3 54 8> . 2 5 5 3 158 8 3 24= = www.matematiranje.com 10 , . / 20/ 202 40;3 60 = / 12/ 122 24;5 60 = 0 ; / 30/ 301 30;2 60 = / 15/ 153 45;4 60 = 45 40 30 24060 60 60 60 < < < < /:15 /:20 /:12 /:30/:15 /:20 /:30 /:1245 40 30 24060 60 60 60 < < < < 3 2 1 204 3 2 5 < < < < ) 1 12 22 4> 1 12 4> www.matematiranje.com 11 . 087 1419 1450 1694 1932 7237 7431 9868 10635 15675 < < < < < < < < < , . 132, 5 89, 32 132, 50 89, 32 43,18 = = 132, 589, 32 132, 5089, 3243,18 www.matematiranje.com 12 ) 1 3 4 18 8 8 2+ = = ) 1 3 2 18 8 8 4 = = ) 1 3 38 8 64 = 316 1 3 38 8 16 = ) 1 3 1 8 1:8 8 8 3 3= = ) ) 0,1 0, 011 0,111 + = ) 0,11 0, 001 0111 + = ) 0,1 0, 011 0, 0011 = ) 0,11 0,1 0, 011 = 0,011 ) www.matematiranje.com 13 15 150 : 1 1 150 150150 305 5 1 5 = = = 150: 5 30 = 150 30. ) 3 6 95 5 10+ = 3 6 95 5 5+ = 7 5 211 11 11 13 8 57 7 7 = 1 1 13 3 6+ = 1 1 23 3 3+ = www.matematiranje.com 14 { } 2, 3, 4, 5, 6,8,10,12,15, 20, 30 A = 60 { } 2, 3, 4, 5, 6,10,12,15, 20, 30 A = 8 60 4) 5: 5 0 5. 9: 9 9 519: 9 57 = 4569636 6. ) 5 0 5. 7870 5. ) www.matematiranje.com 15 2355: 7 336 = 21252145423 ) 123: 2 61 = 237 : 3 79 = 128: 5 25 = 120321 2127270 1028253 www.matematiranje.com 16 103 11 (13 ( 4)) 11 9 2 1 1 1 ( 1)5 (18: ( 2)) 5 ( 9) 4 4 85 7 ( 9) 12 9 3 ( 1) 33 (2 5) 3 ( 3) 9 6 3(17 13) ( 3 2) 4 ( 1) 4 1 5 ( 15) : ( 3) + + = + = = = + + = + = = = + = = = = + = + + = = + = = www.matematiranje.com 17 4 ( 5) 10 20 10 10 + = + = ) 1 2 3 4 5 6 7 8 1 3 5 7 2 4 6 8 16 20 4 + + + + = + + + + = + = ) www.matematiranje.com 18 37011100 - 3 1818 315+ == = ) www.matematiranje.com 1 . 5) x a x b = a b . - 0 a , bxa= ; - 0 a = 0 b , ; - 0 a = 0 b = . : 1) 2) 3 9933xxx=== 1 14 22xx == 3) 4) / 3 / 2/ 3 / 21 122 31 122 31 122 33 22612612x xx xxxxx = = = === 0, 5 0, 2 10, 2 1 0, 50, 2 0, 50, 5: 0, 22, 5xxxxx = = === www.matematiranje.com 2 18218:28 21 116xxxx=== = 3 74 47 34 4441x xxxx+ == == 3 92 29 32 21246x xxxx+ == +== 1: 142114214 1 141 2 27xxxx== = == www.matematiranje.com 3 ) 2 ( 3) 0 x + = . 2 0 3 0 x + = 3 03xx+ == ) 24 6 x = 124 6 /24x = /:6/:6624x = 141 124 624 24x = 14x = 14x = ) ) ) ) 1: 22 3112 312 32 1 22 1 3 123xxxxx== = = = 112 3112 33 12 3 322 322 22 343xxxxxx+ == = = = = 113 2112 31 32 3 322 322 22 343xxxxxx == = = = = 112 311:2 3312 1322 2 326xxxxxx === = = = www.matematiranje.com 4 2, 5 1, 51, 5 2, 54 / ( 1)4xxxx = = + = = 2 828 226 / 222 2 6212xxxxx+ == = = = ) 12 www.matematiranje.com 5 . 6) .....n a a a

, R , n N na n ti a : 1. m n m na a a + = 2. :m n m na a a = , ( , 0) m n a > 3.( )nm m na a a = 4. ( )n n na b a b = 5. : ( : ) , ( 0)n n na b a b b = ! - 01 a = ( ) ,n na a = n - - 1nnaa= ( ) ,n na a = n : 0085 1; 1;3 = = ( )222 2 4 = = 3312 ;2= ( )232 2 8 = = ( ) ( )( )2 332 2 2 22 4 8 88 8 8 8 + = + = + + = www.matematiranje.com 6 www.matematiranje.com 7 4 23 22 22 32 4 16 16 322 3 8 9 16 2 36 4 1448 : 2 64: 8 8+ = + = = = = == = :.. ... www.matematiranje.com 8 ( )21006 1006 2 20122 2 2= = ( )nm m na a = . 7) , - : - 3 23 23 2 3 2 3 23 4 5 82 7 2 33 4 5 8 2 7 2 3 (3 2) (4 7) (5 2) 8 3P x x xQ x x xP Q x x x x x x x x x= + + = ++ = + + + + = + + + + 3 25 3 3 5 x x x = + - : ( )3 2 3 23 4 5 8 2 7 2 3 P Q x x x x x x = + + + = 3 2 3 23 4 5 8 2 7 2 3 x x x x x x = + + + + 3 2(3 2) (4 7) (5 2) 8 3 x x x = + + + + + 3 211 7 11 x x x = + + - : 211P xQ x x= = + + 2 2 2 3 2 2 3( 1)( 1) 1 1 1 1 1 1 1 P Q x x x x x x x x x x x x x x x x = + + = + + = + + = 2225A aB a= = ( ) ( )2 2 22 2 22 2 42 5 32 5 72 5 10A B a a aA B a a aA B a a a+ = + = = = = = www.matematiranje.com 9 ) 17 2 13 517 13 5 230 (5 2)30 3x xx x xx + + =+ + =+ =+ ) 22 1 1 1 1 22 22 22 2 52 2 52 10(2 10) 8x x xx x x x x x xx x x x+ = = = = = = 5 ( 7 ) 12 a a a = , 5 ( 7 ) 5 7 2 a a a a a = + = 7 ( 5 ) 35 a a a = , 27 ( 5 ) (7) ( 5) 35 a a a a a = = ( )25 7 35 a a a = , ( ) ( )25 7 5 7 35 a a a a a = = ( ) 5 7 12 a a a + = , ( ) ( ) 5 7 5 ( 7) 12 a a a a + = + = www.matematiranje.com 10 ) ( ) ( )2 2 2 23 7 3 ( 7) 4 x x x x + = + = ) ( ) ( )2 2 2 2 2 23 3 3 3 3 3 6 x x x x x x = + = + = ) ( ) ( )2 2 2 2 43 2 3 2 6 x x x x x = = 2 2 2 2 4x x x x x+ = = ) ( )3 3 3 35 7 5 7 12 a a a a + = + = ) 2 2 2 29 4 (9 4) 5 x x x x = = ) 2 2 32 3 (2 3) 6 b b b b b = = 2 1 2 3n m n nb b bb b b b++ = = = www.matematiranje.com 11 . 8) : y kx n = + - , n . y 1 x = 0, 5 x = ( ) 0, 5 1 1, 20, 5 1, 2 1, 7y = + == + = ( ) 0, 5 0, 5 1, 20, 25 1, 2 1, 45y = + == + = __________0, 5 0, 5 25000, 25 1, 2 y = 0, 5 x = 1, 2 0, 5 1, 20, 5 1, 2 1, 20, 5 00xxxx= + = == 0, 5 0, 5 1, 20, 25 1, 20, 25 1, 20 0, 95y = + == + == + = 1, 200, 250, 95 1,71,4500,95 www.matematiranje.com 12 123y x = + 3 x = , 3 x = 1( 3) 233231 2 1y = += + == + = 3 x = 1. 4 y x = + , 0 y = 0 44xx = += 4 x = . ) www.matematiranje.com 13 122y x = + y x - ) ) 10 2 221 1 11 2 2 22 2 212 2 1 2 32yyy= + == + = + == + = + = 1 1 1( 1) 2 2 1 1, 52 2 210 2 0 2 221 1 11 2 2 22 2 2yyy= + = + = == + = + == + = + = ) ) 10 2 221 11 2 2 0, 5 2 2, 52 212 2 1 2 32yyy= + == + = + = + == + = + = ( )1 1 1 4 31 2 2 1, 52 2 2 2 2y = + = + = + = = ) www.matematiranje.com 14 1 13 2y x = + 2 x = / 2 / 3/ 2 / 31 123 22 13 24 36 616yyyy = += += += ) www.matematiranje.com 1 ) 3 ) 2 ) 1 ) 5 . : ) . www.matematiranje.com 2 . 9) - ; - . 3, 1. HD , BF, CG FG: BF, CG, EF, HG HD FG. www.matematiranje.com 3 www.matematiranje.com 4 . 10) : 1) BC 2) : . www.matematiranje.com 5 . 11) : a b , : 2 2 2a b c + = : 2 2 cc h a bP = = www.matematiranje.com 6 724?AC cmBC cmAB=== 2 2 2AB AC BC = + 2 2 22 2 22 227 2449 57662562525AB cm cmAB cm cmAB cmAB cmAB cm= += +=== ) 22210 8, 4284242AB hPcm cmPcmPP cm==== ) www.matematiranje.com 7 : P a b = 23, 523, 5 27a mb mP a bP m mP m=== = = ) 68a cmb cm== 2 2 2c a b = + 2 2 22 2 22 226 836 6410010010c cm cmc cm cmc cmc cmc cm= += +=== 10cm www.matematiranje.com 8 . 12) : - ; - ; - . - , - () - r - - :2P r = - : 2 O r = 2229?981r cmpp rP cmP cm===== www.matematiranje.com 9 ) C ) 4, 5?22 4, 5 39 327r cmOO rO cmO cmO cm=== ) www.matematiranje.com 10 ) . 13) : - . 2 P B M = + , B - () M - - . V B H = - ( )2242B aM a HD a== = + - 2363P aV aD a=== - ( )2 2 22 P ab bc acV a b cD a b c= + += = + + www.matematiranje.com 11 0, 50, 92, 2?a mb mH mV==== 30, 5 0, 9 2, 20, 45 2, 20, 99V a b HV m m mV m mV m= = = = 30, 99m 6 a cm = 222266 66 36216kockeP aP cmP cmP cm== = = 3336216kockeV aV cmV cm=== www.matematiranje.com 12 ( )( )( )222 9 6 9 4 6 42 54 36 242 114228kvadrataP a b a c b cPPPP cm= + + = + + = + += = 339 6 4216kvadraV a b cV cmV cm= = = 8 a cm = 26 P a = 2 2226 86 64384P cmP cmP cm= = = ) www.matematiranje.com 13 6102a cmH cmP B M=== + 22 4 P a a H = + 22 222 6 4 6 102 36 240312P cm cm cmP cm cmP cm= + = += 2312cm www.matematiranje.com 14 ) 2 5 ) www.matematiranje.com 15 www.matematiranje.com 16 2 2 3 1 1 . 14) . : ) www.matematiranje.com 17 www.matematiranje.com 18 ) www.matematiranje.com 19 www.matematiranje.com 1 . 15) I mm 1 1000 km m = cm 1 10 m dm = dm 1 100 m cm = m 1 1000 m mm = km 1 10 dm cm = II 2mm 2cm 2dm 2m - h - 2 21 100 cm mm = 2 21 100 m dm = 2 21 100 dm cm = 2 21 10000 m cm = 2 221 100 10010000dm mmmm= = 2 21 1000000 m mm = h = 100 1h210000m = = 2100m 21 1 1 m m m = = 2222210 10100100100 10 10100 1001000010 00010 000 10 1010 000 1001 000 000dm dmdmdm dmcm cmcmcmcm cmmm mmmmmm= === == == == == == == == www.matematiranje.com 2 2 2 2 21 100 100 100 10000 m dm cm cm = = = 2 21 101 100dm cmdm cm== III 3m 3dm 3cm 3mm l 31 1 l dm = 3 31 1000 m dm = 3 31 1000000 m cm = IV g kg t 1 10001 1000kg gt kg== V s min h d 1 241 60min 1 36001min 60dan hh h ss== == www.matematiranje.com 3 ), ), ), ) ) 119 mm ) 31cm, , ) 2 km , . . 15 m. ) www.matematiranje.com 4 22400 P m = - 2m : 224002400100P m = = =24 211100m = 224002400100m = ) ) ! - 2m h 224002400100m = =24 24 24100= h=0,24 h 11100= h2424100 h ) )2cm www.matematiranje.com 5 , 2cm . ) 1, 5 1, 5 100 150 m cm cm = = , 1 100 m cm = 1, 5 1, 5 60min 90min h = = , 1 60min h = 1, 5 1, 5 1000 1500 t kg g = = , 1 1000 t kg = 1, 5 1, 5 10 15 dl cl cl = = , 1 10 dl cl = www.matematiranje.com 6 2 = 200 , 1 = 100 2 = 730 , 1 = 365 3 = 91 , 2 = 60 , 1 = 31 4 = 96 , 1 = 24 www.matematiranje.com 7 ) 3 3 1000 3000 km m m = = , 1 1000 km m = ) 20 20 100 2000 , m cm cm = = 1 100 m cm = ) 4, 5 4, 5 1000 4500 , t kg kg = = 1 1000 t kg = ) 4 4 7 28 , = = 1 7 = 2kg 20g 2 2 1000 2000 kg g g = = , 1 1000 kg g = 2000 20 2020 g g g + = ) 2020 = 3 90 , 1124 = 3 10 = 107 70 10 < = < 100 70 < = < 100 100 . ) 100 www.matematiranje.com 8 : 1000-300=700 700=500+200 500 200 ( ), 2 . ) 4850 ) 48 100 4800 = ) 24 200 4800 = ) 9 500 4800 = ) 97 50 4850 = ) www.matematiranje.com 9 : 6 50 7 20300 140 440 + =+ = : 500 500 440 60 = 60 ( ): 100 20 10 5 1100 20 10 5 135+ + + =+ + + = : 22 17 90 129 + + = : 135 129 6 = ) 200 4 50 = 3 200 3 4 50 = 3 200 12 50 = 12 50 . www.matematiranje.com 10 100 =1857g 1857 :100 18, 57 = 19 ) . 16) ; , . 3 . : 1. 5 ( 0, 1, 2, 3 4 ) 2. 5 ( 6, 7, 8 9 ) 3. 5 1. 5 ( 0, 1, 2, 3 4 ) . .1. : 128,4637 - , 5 128,4637 128,4635 www.matematiranje.com 11 -. 2. : 12,37 - , 5 12,37 12,47>5 3+1 3. 5 : 3.1 5 ( ) : ) 5 1, . ) 5 5 . .1. : 123,75 , 5 123,75 123,87neparan broj 7+1 ) ) 3.2 5 5 1. .1. 123,46587 , 5 0 www.matematiranje.com 12 ) : 0,152 0,152 - , 5 0,152 0,21+1=2 3.2 . 16) ) : 0,205 0,205 0 0,205 0,205 2 . 16) ) 1 1 0 . A = , < 0 A A = 1. 1A . www.matematiranje.com 2 www.matematiranje.com 3 : 1 1 10 102 2 10 202 2 2 40, 210 10 2 205 5 5 254 4 5 2011 11 2 2210 10 2 2025 22 4 1020 20 20 205 11 10, 24 10 2 = == = = = = = = < < < < < < ) . 29 29 2 580, 5850 50 2 100= = = 1 1 5 50, 52 2 5 10= = = 11 11 5 550, 5520 20 5 100= = = 490, 49100 = www.matematiranje.com 4 0,54 > b c a > > ) www.matematiranje.com 6 , . b a c b a < < + : 50 , 60 , 90 cm cm cm 60 50 10 90 50 60 100 = < < + = . : 40 , 50 , 100 cm cm cm 50 40 10 100 40 50 90 = < < + = : 40 , 20 , 20 cm cm cm 40 20 20 20 40 20 60 = < < + = : 20 , 10 , 10 cm cm cm 20 10 10 40 20 10 30 = < < + = . : 13 c m = : 5 a m = 2 2 2a b c + = 2 2 22 2 2225 1313 5169 2514414412bbbbbb m+ == = === www.matematiranje.com 7 2a bP = 5 12P =6225 630PP m= = 230m 22 22 2212251225122535P rm rr mr mr m ===== 110 r r m = 1135 1025m r mr m == : 212225625P rPP m= = = 2625 m www.matematiranje.com 8 2 O r = 2 162 168r cmrr cm === 2P r = 22864PP cm== ) 100 R cm = 50 r cm = . 7 000 ( ) 7 000. 2KO r = S 2 50KO = 7000KS O = 100KO cm = 100 7000 S cm = 70000022 1700000 2 200 000 22000 22000 227 1000S cmS cm cm m km km = = = = = 22 km www.matematiranje.com 9 . 21 1 121 121 1162 16 88 64O cm P r cmr cm Pr cm P cm = == == = 22 2 222 222 2102 10 55 25O cm P r cmr cm Pr cm P cm = == == = ( ) ( )( )1 22 2 2 2 2 21 2 1 228 564 25 39P P Pr r r rcm = = = = == = 239 cm ( )2 2 2 21 2 1 2 1 212 21 12 21 1 1116 925 25255P P P r r r rPP cm rP r cm rr cm = = = = = == == 5cm www.matematiranje.com 10 . 23) - . B=432a M= aH 3 P = 2B + M P=2 aHa3432+ V = B H V=432aH - . B = 6 432a M = 6 a H P = 2B + M P = 2 6 432a + 6 a H V = B H V = 6 432a H , . H = a . 2228232 344 32 3 4 2416P B MaP a HPP= += + = + =( )2232428 3 248 3 3P cmP cm+= += + ( )28 3 3 cm + www.matematiranje.com 11 . 232222131 363 41 333 213213 3 3 3219 3 3 32127 3 32V B HaVV a HV a HVVV= = = = = = = 33127 3281240, 5VV cmV cm= == 340, 5cm www.matematiranje.com 12 P B M = + ( )22222 22 2234434436 6 336 36 336 1 3B aaMaP aP a aPPP cm== = + = += += += + ( )236 1 3 cm + .! 2 a cm = 2 2 422a cmb cmc cm= + === ( ) 2 P a b b c a c = + + ( )( )22 4 2 2 2 4 22 8 4 82 2040PPPP cm= + + = + += = 240cm www.matematiranje.com 13 P B M = + 2 23 334 4a aB M = = , . 2 23 334 4a aP = + 2344aP = 4 . 22238 364 3P aPP cm=== 264 3cm . 24) P = 4 2r V = 34 3r 24 P r = 224 34 936PPP cm= = = 343V r = www.matematiranje.com 14 34334273VV = = 934 936VV cm= = . 25) P = 2r + r s V = 31 2r H 21 1 1 121 131 13115319 5 93125 9375r cm V r HH cm VVV cm= = = = = = 22 2 2 222 232110313 10 33100r cm V r HH cm VV cm= = = = = 375 cm < 3100 cm 1V < 2V ) www.matematiranje.com 15 ( )2233131,31316 2312163V r HV H H r HV HVV= = == = = 32 272 2 2 144 2 V cm = = 3144 2 cm . 26) P = 2 2r + 2 r H V = 2r H ) ) ( )( ) ( )22 22 2 22 2 3 3 82 12 14 6 11336 66A BA BA BA BP r r H P r r HP r r H PP PP cm P cm = + = += + = += = = = www.matematiranje.com 16 ) ( )( )222 6 6 412 10120BBBBP r r HPPP cm= += += = ) 2 21 1 1 2 2 22 21 21 22 31 22 4 4 14 4 16 116 16V r H V r HV VV VV cm V cm = = = = = = = = 1 2V V = j ) . ) www.matematiranje.com 17 . 4 ) . ) S ) S- ) www.matematiranje.com 18 www.matematiranje.com 1 . ) 0,305kg = 0,305 1000g = 305g ) 0,35kg = 0,35 1000g = 350g ) 325g ) 302g 302g < 305g < 325g < 350g 302g ) 302g ) . 2m 5dm = 2 10 dm + 5 dm = 20 dm + 5 dm = 25 dm 2,5 dm < 25 dm 2,5 dm > 2 m 5 dm 2 m = 2 10 dm = 20 dm 20 dm < 22 dm 2 m > 22 dm 3 kg = 3 1000 g = 3000 g 3000 g > 300 g 3 kg < 300 g 2 t = 2 1000 kg = 2000 kg 2000 kg > 200 kg 2 t > 200 kg www.matematiranje.com 2 ( km ) 308 000 m = 308 000 10001 km = 308 km 2 720 000 dm = 2 720 000 101 m = 272 000 m = 272 000 10001 km = 272 km 295 km 308 km 202 km 185 km 272 km , . . ) 1 kg 20 g = 1000 g + 20 g = 1 020 g ) 1,2 kg = 1,2 1000 g = 1 200 g ) 1 022 g ) 1,002 kg = 1,002 1000 g = 1 002 g : 1 002 g < 1 020 g < 1 022 g < 1200g ). ). www.matematiranje.com 3 1, 35 kg = 1, 35 1000 g = 1 350 g 1 kg 290 g = 1 1000 g + 290 g = 1 290 g 1 350 g > 1 340 g > 1 290 g 1, 35 kg > 1 340 g > 1 kg 290 g 1 dolar 0,75 evra 52,99 dolara X evra 1 : 52,99 = 0,75 : X ). 1 118 47 X 1 : 47 = 118 : X X = 118 47 X = 5 546 3 5 546 , 5 800 . 5 800 5 546 = 254 . www.matematiranje.com 4 100 72 75 X 100 : 75 = 72 : X 100 X = 72 75 X = 72 75100 X = 54 75 54 . 1 1,25 200 X 1 : 200 = 1,25 : X X = 1,25 200 X = 250 200 250 . 400 150 . 150 ., 82 . 1 82 150 X 1 : 150 = 82 : X X = 82 150 X = 12 300 12 300 . www.matematiranje.com 5 1 105 10 X 1 : 10 = 105 : X X = 10 105 X = 1 050 10 1050 . 1 12,50 X 1 050 1 : X = 12,50 : 1 050 12,50 X = 1 050 X = 50 , 121050 X = 1250105000 X = 84 10 84 . 1 = 1000 m : 311000 m = 31000 m = 333,3333333 333,3333333 330. ). www.matematiranje.com 6 , : 110 109 109,2 110 109,2 = 0,8 109,2 - 109 = 0,2 109,2 109, 110. . , : 3,5 3,4 3,4556 3,5 3,4556 = 0,0444 3,4556 3,4 = 0,0556 3,4556 3,5. . , : 500 499 499,4 500 499,4 = 0,6 499,4 499 = 0,4 499,4 499. . www.matematiranje.com 7 2103: 7 300, 42100003030282= 2103:7=300,4 ) ) , ) ) : ) 301 300,4 = 0,6 )300,4 300 = 0,4 . 300,4 ) ) ! . 16). . ) 3.2 . 16) ) www.matematiranje.com 8 1 . 16) ) 1 . 16) ) 3.2 . 16) B C 8 9 6 www.matematiranje.com 1 . 27) - - Z (4, 2) A - Ay , 2,Ay = , 2By = . - YO BX - , 4BX = , YO - , CX - YO - . : 4; 2: 4; 2B BC CB X YC X Y= = = = ( )4, 2 B www.matematiranje.com 2 (1,2) www.matematiranje.com 3 www.matematiranje.com 4 (3, 3) F ( 3, 3) B - . (2,1) E ( 2,1) C - . (4, 2) G ( 4, 2) A - . www.matematiranje.com 5 www.matematiranje.com 6 . 28) n . 1 2... na a aASn+ + += Y - 30 - 20 - 25 - 35 - 25 - 45 30 20 25 35 25 45 180306 6x + + + + += = = 30 . www.matematiranje.com 7 : . 81 84 76 78 82 86 72 7386328ASAS+ + + + + + +== 79 AS = 78 4. 4 . www.matematiranje.com 8 . - 88 86 83 107 92 102 558936 6+ + + + += = = 93 . www.matematiranje.com 9 : - 5 1, 5 2 3, 5 5 1535 5+ + += = = . 5 3 www.matematiranje.com 10 a) 395 . ` ) . www.matematiranje.com 11 . 29) - - . . 1 2, 5, 11, 6, 8, 10, 23 -23, 2, 5, 6, 8, 10, 11, - 6 . 2 -32, 4, 64, -3, 567, 4561 -32, -3. 4, 64, 567, 4561 4 64 2562 = 1282 = : 12 9 13 4 11 17 . 4 9 11 12 13 17 , 6, 2. 11 12 232 2M += = 11, 5 M = 11,5 www.matematiranje.com 12 165cm 164 165 168 cm cm 165167168 169 172 cm cm 169170172170 173 175 cm cm 173174 176 178 cm cm 176 178cm 180 www.matematiranje.com 13 1 2 2 2,5 3 3 4 1 5 1,5 6 2 7 1 8 2,5 9 4 10 3 11 1 12 0,5 1 h 4 . 1 3 1 . . 54 64 72 78 147 194 251 , , : 78 78 ( ) h h 1 1 < h 2 2 < h 3 h > 3 4 3 4 1 www.matematiranje.com 14 ) 5 5 4 7 3 10 2 5 1 3 www.matematiranje.com 15 ) : . 5 5 7 4 10 3 5 2 3 15 7 10 5 325 28 30 10 3 9630 303, 2 = + + + + = =+ + + ++ + + += == 3,2 15% p = : 100: G P p = 4260 G = 4260: 100 :15 P = 100 4260 154260 15100426 15PPP = ==3102426P =32213 3 P= 639 P = 639 . www.matematiranje.com 16 25 20 , 12% I 12% p = 1 = 200 . 25 = 25200=5000 G= 5000 . : 100:5000: 100:12100 5000 1250 00G P pPPP== = =1210050 12 P = 600 P = - 25 5000-600=4400 25 . 4400 . II 200 G = 200: 100 :12 P = 12% p = 100 200 12 P = 2200P =12100 24 P = , . 200-24=176 1 , 25 : 25176=4400 4400 . www.matematiranje.com 17 20048: 100:200: 48 100 :200 48 10048 100GPG P pppp==== = =220048224%pp== 24% . 630 G = 20% 100 20 80% p = = : 100:630: 100: 80100 630 80630 80G P pPPP== = =41005126630P =145126 4504PP = = 504 www.matematiranje.com 18 60660: 6 100:60 6 1006 10060600GPpppp=== = ==6010% p = ) www.matematiranje.com 1 21211 341: ?1 1 1 11 : 1 1 : 14 8 3 61 4 1 8 3 7 3 8 6: :4 4 8 8 4 8 4 7 71 1 1 3 1 6 4 7 4 6 81 : 1 : :3 6 3 3 6 6 3 6 3 7 76 8 6 7 6 3: :7 7 7 8 8 4A BA BABA B=| | | | | | | |= = + + | | | |\ \ \ \ | | | | | |= = = = | | |\ \ \ | | | | | | | |= + + = + + = = = | | | |\ \ \ \ = = = = ( ) ( )( ) ( )( ) ( ) ( ) ( )0, 7 0, 3 4 1: 0, 5 : 0,1 1,10, 7 1, 2 2 : 0,1 1,12, 7 1, 2 : 0,1 1,1 1, 5 : 0,1 1,115:1 1,1 15 1,1 16,1 + + == + + == + + = + == + = + = 1 2 3 1 44 : 12 5 5 5 51 2 3 1 1 1 2 34 : 4 12 5 5 5 5 2 5 51 2 8 9 6 45 12 3342 5 5 2 5 10 10 ( | | | | = ( | |\ \ ( | | (= = + = ` ` | ( (\ ) ) + = = + = = ` ) www.matematiranje.com 2 ( ) ( )( ) { } ( ) ( ) { }{ } { }111 1 14 : 0, 85 : 5, 56 4, 064 2 34, 25: 0, 85 0, 5 : 1, 5 0, 335 0, 5 : 0, 54 4, 5: 0, 5 991 1 3 2 56 6 6 6 6 6 6 5 12 3 6 619 1 1052 2 2AABBA B | |= + = ` ` | ) \ )= == = ==+ | |= + = = = = |\ =+ += = = 1 1121221?6 2 5 8 7 61 3:5 5 4 3 3 75 1 5 1 2 5 1 61 3 1 36 2 2 2 2 28 7 6 8 8 6 223 3 7 3 3 323 2323, , 23A BA BABA BA B A B = += + = + = + = + = = == = = = = == = = 6 2 3. . a 1. 0 2 3 10 23 , . www.matematiranje.com 3 2, (4, 6 8) 3 3. 4, 6 8. 4 10 234 : 1 0 2 3 4 10 + + + + = 3, 4. 6 : 10 236 1 0 2 3 6 12 + + + + = 3 12: 3 4 = 6. : 10236 18 2 9 9999 18. 2 9 9. 999, 27. , 0, 2, 4 ,6 8, 27 9. 27+0=27 9. 0. 9 9990 9990. 180 < < 200 4 6 12 (4,6) 181 199 12. 192 192:12=16 192 . www.matematiranje.com 4 12 3 4 3 4. 999, 4 3 4 99 9+9=18 3 0, 3, 6, 9 4 4 6 996 9+9+6=24 3 96 4 996 3 4 996 4, 2, 4 _ 2 9 9. : 4+2=6 3 12, 6+3=9 6+12=18 , 9. - 3: 3 x y + = X Y : 0 3 X Y = = 1 2 X Y = = - 12: 12 X Y + = X Y : 3 9 X Y = = 4 85 76 6X YX YX Y= == == = : 4023, 4320, 4122, 42214329, 4923, 4428, 48244527, 4725, 4626, . 4122, 4923, 4725 www.matematiranje.com 5 60 600 . 1 10 . 12060 3 = , 3 . , 3 9 . 12 . 1 10 . 12 120 . 120 . - - 32033 2034 2032043553 5 15T HT HT HH HT HHT HHT HHHT= + == + == == == === = 15 . www.matematiranje.com 6 22 2 22 22 22 22 211, 411, 4 2,1 9, 3: 2 9, 3 : 2 4, 65: 3 11, 4 : 3 3, 85 5 3, 8 19: 2 11, 4 : 2 5, 7 P mP m m mP P m mP P m mP P m mP P m m== == = == = == = == = = 2 ! 9, 3 4, 65 3, 8 19 5, 7 2 11, 4 65, 25P = + + + + + = 65,25m P- 1120008 P = - . 12000 8 P = 96000 P = . 23P 2963 000 2 32000 64000 = = : ( ) 96000 64000 12 000 96000 76 000 20000 + = = 20 000 www.matematiranje.com 7 1 : 4 35 435=140 3 25 325=75 60 1 : 140+75+60=275 1500:2755,46 6 1500 6 . www.matematiranje.com 1 ( ) ( )( )22 1 2 1 2 1 0 x x x + ( )22 224 4 1 2 1 04x x xx ( + 24 1 4 x x + 1 02 4 04 22412xxxx+ 12x . 28 a b + = 1 1 33 4 43284728428a b a bb bbb= =+ ===41416728 16 a == 12, 16. www.matematiranje.com 2 3 = ( ) ( ) 10 5 10 = - 10 ( ) 3 10 5 103 10 5 505 3 50 102 4020 = = = == 20 = =320=60 60 . 3 2 1 234 23 2 2 4347 4347 4 127 16x xx xxxx < + < < > + >+ >>> ) www.matematiranje.com 4 5 2 32 50 5 2 4 2 4 5 27 2 7 25 2 4 2 20 2 21 27 2 + + = = += =7 22137= = ) 3 : ( ) ( )4 10 14 10 14 10 2 7 1027 1024 11 1024111023 15 4 210235 4 2: : : : : : : x x x x x x x x x x xxxxxxxx x x x x= = = = = =|||

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= x ( )6 , 32 6 , 0 6 22 6 , 0 363232 36 , 0 69432 = = = -3,6 www.matematiranje.com 5 ( )7 777 771 11 1 : 2 80 2 4 52 33 4: 2 16 5 2 4 52 3| | | | = | |\ \ | | | | | |\ \ ( )7 773 4: 2 4 52 3=| | | | | |\ \ 2 4 5 ( )72717 73 4: 2 22 32 : 2 2 1 2 3=| | + = |\ = + = + = 3 232 1024) 10, 24 3, 2) 102400 320) 0,1021 0, 32a==== www.matematiranje.com 6 2 2 + ( )22 2 22 + + + + : ( )22 22 + = + 2 2 + + 15,4 a b + = = ( )( )22 2122 222 22 2215 2412521242a b a b aba ba ba b+ = + + = + = + = ) www.matematiranje.com 7 : ( )22 22 a b a ab b + = + + ( ) ( )( ) ( )( )22 2 22 2 223 2 1 2 2 1 46 9 2 4 2 2 86 9 2 4 2 2 85 11 7a a a a aa a a a a a aa a a a a a aa a+ + + + == + + + + + == + + + + + == + + : ( )22 22 a b a ab b + = + + 2x 5y ( )22 5 x y + 3x 4y ( ) ( )2 23 4 x y + ( ) ( ) ( ){ }{ }2 2 22 2 2 22 2 2 22 22 5 3 44 20 25 9 164 20 25 9 165 20 9x y x yx xy y x yx xy y x yx xy y+ + == + + += + + == + + : ( )( )2 2a b a b a b = + ( ) ( ) ( ) ( )( )2 22 221 2 1 6 62 2 1 362 1 3635a a a aa a a aa a aa a + + == + == + == + ) www.matematiranje.com 8 ) ( ) ( )2 27 3 7 3 7 3 4 10 40 = + = = ) ( )22 27 3 7 2 7 3 3 49 42 9 16 = + = + = ) 2 27 3 49 9 58 + = + = ) ( )22 27 3 7 2 7 3 3 49 42 9 100 + = + + = + + = y kx n = + k n 3992y x = + 1 2k k = 32k = ( ) 4, 8 A , . ( )38 428 3 28 62nnnn= += += = k n , : 322y x = + www.matematiranje.com 9 5 88 / 2 3 , 8 . 5: 8 : 88 5 85 88xxx= = = 5 x = 5 5 2+5=7 : 7 . 1, 75 60 /1, 5 /h km hh x km h . 1, 75:1, 5 : 601, 5 1, 75 601, 75 601, 570 /xxxx km h== == 70 / km h . www.matematiranje.com 10 9 43 . 319: 3: 43 9 49 433 4xxxx== == 12 x = 12-9=3 , 3 . 3 y x = + 1 k = ) ) 3 n = - (0,3) ) ) www.matematiranje.com 11 x y . 3 2 6200 x y + = 2 6200 . 6 x y = 6 3 6 2 6200 y y + = 6 x y = 18 2 6200620 6200662002063106 310 1860y yx yyx yyx yyx+ ======== = 1860 , 310 . 1 80 60 4800 cm cm = - 1 . 9 4800 9 43200cm = - 9 . 1 100 75 7500KORAKA cm cm = 4800cm 43200cm 7500cm 16 . 43200 4800 75007500 4800 432002700 4320043200270016 x xx xxxx+ = = ===www.matematiranje.com 12 " " 52 " " ( ) 52 4 56 x + = 4 " " ( ) ( )156 56 3 25 25 3 x + =

13 ( ) ( )( )156 56 3 253256 25 332 56 2223 3112 222 / 33 3112 66 22 46x xxxxxx + = = = = == 23 x = " " 23 . www.matematiranje.com 13 ( )2 41 / 22x yyx =+ = + . 322 42 22 42 24 62 26 34 232 22322 3 1x yx yy xx yxx yxyxy =+ == + ==+ == = + === = ( )222 23213 94 4 1 4 1 9 1 102 4xyx y== | |+ = + = + = + = |\ ) www.matematiranje.com 14 - - ( )910 15 110910 15 110910 9 15 110990 10 15 11095 20949 4 54x yx yx yx yx yy yx yy yx yyx yyxy+ =+ == + == + == + == == == == 54xy== 4 5 www.matematiranje.com 1 0 0 00 00 0002 30 90 3 1805 60 1805 180 605 12024 + + =+ == == 0 0 00 0 00001290 65 180180 90 6525125250SAC ASACSACSACAA=+ + == === www.matematiranje.com 2 00 0 00 0 0018050 90 180180 50 9040B A CBBB+ + =+ + == = 050 040 044 = . 0144 = = . 0130 : 0 0 0180 130 50 = ( ). : 0 044 , , 50 = : 0 0 044 50 180 + + = 0 00 0094 180180 9486+ == = 044 = 086 = 044 =044www.matematiranje.com 3 '' 0 0 ' 0 '100 ' 0 ' 00 0 ' 0 '0 0025 1560 15 180 60 15 119 45180119 45 25 15 180180 25 15 119 45180 14535oo == = =+ + =+ + == = = 20 ' 00 ' 00 0 '0 '0 '0 '35 30 2 18035 30 3 1803 180 35 303 144 30144 30348 10 + + =+ == ===www.matematiranje.com 4 ABD . 6 AD AB cm = = 2 2 2BD AB AD = + 2 2 2226 636 36727236 2 6 2BDBDBDBDBD= += +=== = BCD. BD 030 , : 1222 6 212 2BD BCBD BCBCBC= = == D , D . ( )2 3236 2 36 66 12 2 6 6 612 12 2 6 66 2 2 2 6BDCDCD BDCDCDO AB BC CD ADOOO cm===== + + += + + += + += + + AMN : ( )22 22 2 22 222239 1010 10101010a a MNa aaaa+ =+ ==== AMNwww.matematiranje.com 5 : 2 210 P a a a cm = = = 5 . 2 22210555 10 50 P a a a cmP P P cm= = == = = = , . , : 6 2 8 h cm = + = 2a bP h+= 41212 48216 464PPP cm+= = = 045.045.045.b=4cm 2cm1 2 6cmwww.matematiranje.com 6 : AHC 5 AH CH cm = = AC 2 2 22 2 225 525 255050 25 25 2AC AH CHACACACACAC cm= += += +== = = BHC 060 030 : 1222 510CH BCCH BCcm BCBC cm = = == BH . 2 2 22 2 22 2 22210 5100 257575 3 755 3BH CH BCBH BC CHBHBHBHBHBH+ == = = == = = : ( )5 5 3 5 1 3 . AB AH BH cm cm cm = + = + = + 030 ( )5 5 3 10 5 215 5 2 5 35 3 2 3O AB BC ACOOO cm= + += + + += + += + +030.04504510cm5cm5cmA BCH5 25 2www.matematiranje.com 7 b=612a=15c a-b15-6=9h=12 ! . : ( )( )22 222 22 2 22215 6 129 1281 14422522515c a b hcccccc m= += += += +=== 15 6 15 1248O a b c hOO m= + + += + + += 48m . www.matematiranje.com 8 : 0180rl = 0020 721808ll cm == 8 O l cm = = 28 28 22 8KRUGAO rrrr ==== 4 r cm = 4cm www.matematiranje.com 9 01350135 : 0 001 1 1360 360458 n = = = 0 0 0 010180 180 45 135135 + = = == . 0135 , , : 0 00 000 '2 135 1802 180 1352 4522 30+ == == .1 0135 , , : 0 0 01 10 010101135 135 3602 360 2702 9045 + + + == == : 01135 + + = . 2 110 ' 0 00 0 0 '0 0 '0 '22 30 45 135135 45 22 3090 22 3067 30+ + == = =www.matematiranje.com 10 , . - 1 12 6 3 r m r cm = = : 1 1 12 2 3 6 O r O cm = = = - 2 292 92r cm r cm = = : 2 2 292 2 92O r O cm = = = - 3 3122 12 62r cm r cm cm = = = : 3 3 32 2 6 12 O r O cm = = = : 3 1 22 2 26 9 122 2 227213, 5O O OOOOO cm = + += + +== 13, 5 cm www.matematiranje.com 11 AB AB OA OB = = AOB 060 , . , AOB ACB 00260 230AOB ACBACBACB=== 030 A BCO060060060www.matematiranje.com 12 20360rl = 2P r = 2 030 rl =10360122112112l rl P = = 12 . : 0360 030 . : 0 0360 : 30 12 = 12 . www.matematiranje.com 13 : 2 125, 6125, 62125, 62 3,14125, 66, 28O r cmrrr= ==== 20 r cm = . . : 22 20r aa cm== 40 a cm = . ) www.matematiranje.com 14 AOS . 2dH = 2 d a = ( a ) 22aH = 223131 23 212636 2V a HaV aV a= = =2126a =33 333 3 3 336 621621636 6 6 6 6 6 66aa cmaaa cm= === = = == 6cm 22232 348 356 3 2 3 8464 356 3 24P B MaP a HH= += + = + = 246456 3H + =324256 3 32 3 2424 56 3 32 324 24 324HHHHH+ = + = ==3243 H cm = 3cm A BCD H.045 Od/2Swww.matematiranje.com 15 ( )37: 3: 5 3 5420?2a cmb c b k c kV cmPP ab ac bc== = ==== + + b c . 2222420 7 3 5420 7 15420 105420105423 3 2 65 5 2 10V a b ck kkkkkkb kc k= = = ===== = == = = ( )( )( )222 7 6 6 10 7 102 72 60 702 172344P ab bc acPPPP cm= + += + + = + += = 344cm www.matematiranje.com 16 SOA : 22 222 22 2222210132169 5169 25169 2514414412ah HHHHHHHH = + = + = += += === 221313110 12313V B HV a HVV= = = =1100 12 43100 4400VV cm= = 400cm www.matematiranje.com 17 : 22210810810836 36 3OP rrrrrr cm ===== = ! , 2 r 32ah = 26 3h ra H==2 3 H = 62 H cm = 213 131108 63216V B HVV cm= = = 030030060060HHwww.matematiranje.com 18 33 4V r34V 334V3= = =127 92V 4 9V 36 cm= = : : 216 : 3636 216216366 V VV VV VV V = = = = 6 . : 2 22218 3241622 2 2PPrP cm == = = = , 2162P M cm = = 2162 M cm = 18 S cm = - ( ) 162 1816218M r Srr == = 9 r cm = S Hrwww.matematiranje.com 19 : 2 2 22 22 2 22218 918 9324 81243243 81 3 9 3S r HHHHHH cm= += += = == = = : 221319 9 3313V r HVV== =181 2739 327 9 3243 3VV cm = = ( ) 3 3 6cm + = . 1V . ( ), 3cm 2V . 31 131114346342163V rVV== = 721314 72288VV cm= = 32 23222232434334 34 936V rVVVV cm== = = = 1 23 33288 36252V V VV cm cmV cm = = = 3252 cm 1 2V V V = www.matematiranje.com 20 b=12cma=9cmH=ba . 2 2 22 2 229 1281 14422522515S r HSSSSS cm= += += +=== : 2223: :: :: :: 9:15: 3: 5B rM rB M r r SB M r r SB M r r r SB MB M ==== = == ) 3:5 www.matematiranje.com 21 2 20 r cm = 10 r cm = 24 P r = 224 104 100400PPP cm= = = 2400 cm . AB . 2 2 22 2 2225 1225 14416916913AB BC ACABABABABAB= += += +=== . 1 1 1 11 11 11 1: :: 5 3, 25:1313 3, 25 53, 25 513BC BC A B ABBCBCBC== = = 1 1 1 11 11 11 1: ::12 3, 25:1313 12 3, 2512 3, 2513AC AC AB ABACACAC== = = 1 11, 25 BC cm = 1 13 AC cm = www.matematiranje.com 22 212ABCABCAC BCPP==61256 5230ABCP cm = = 1 1 11 1 11 1 11 1 11 1 1 12223 1, 2521, 87530 1,875 28,125A B CA B CA B CABC A B CAC BCPPP cmP P cm=== = = 28,125 2cm BDE . . ( )( ): :5 : 12: 99 5 129 45 1212 9 453 4515AB BE AC DEx xx xx xx xxx cm=+ =+ =+ = === 15 EB cm = www.matematiranje.com 23 2 O a b = + 140 182O cm a cmb a= == + ( )40 240 2 240 2 440 4 336 33631212 2 14a ba aa aaaaa cmb cm= += + += + + ===== + = : 1 11111: :12:18 40:12 40 1840 181260a a O OOOOO cm== = == . 30) I ABC 1 1 1ABC , x . II ABC 1 1 1ABC III ABC 1 1 1ABC . IV ABA ABC 1 1 1ABC , , , . www.matematiranje.com 24 : 2: 3: ?MN ABCM MA== CMN ABC II. ( ) MCN ACB CMN CAB = = . : : MN AB CM AC = III . : : 2: 3: 2: 3MN AB CM ACCM AC= = = : : 2:1 CM MA = ) A BC3M N2www.matematiranje.com 25 1. ( 060 ) 2. 3. 030 , ( 072 ) 4. www.matematiranje.com 1 : 25,24 = 25,24 * 100 m2 = 2 524 m2 1 = 100 m2 126 200 000 : 2 524 m2 = 50 000 . 50 000 . S = S91 + S187 + 56 dm S = 187 2 S S + + 56 dm S = S189 + 56 dm S = S21 +56 dm S - S21 = 56 dm www.matematiranje.com 2 S21 = 56 dm S = 2 * 56 dm S = 112 dm 112 dm = 112 * 101 m = 11,2 m 11,2 m. 7 , . 120 7 120 17 1 . 17 , 120 , . 120 . 3,52 ha 2 a = 3,52 * 100 a 2 a = 352 a 2 a = 350 a 1 ha = 100 a 350 a = 350 * 100 m2 = 3 500 m2 1 a = 100 m2 3 500 m2 ) www.matematiranje.com 3 22 15 = 22 * 60 + 15 = 1 320 + 15 = 1 335 1 335 115 = 1 220 1 220 = 1 220 * 601 = 20, 3 = 20 + 0,3 = 20 + 0,3 * 60 = 20 + 18 59 46 64 41 22 41 59 + 64 + 22 + 46 + 41 + 41 = 273 . 58,52 + 63,89 + 22,02 + 45,90 + 40,55 + 40,51 = 271,39 271 . 273 271 = 2 ) www.matematiranje.com 4 : 10 1 , 10 = a m 8 9 , 7 = b m 3 8 , 2 = c m 31 03 , 31 V = abc V = 10 * 8 * 3 = 240 m3 43 V = 43 * 240 = 3 * 60 = 180 m3 180 m * 31 = 5 580 . ) 5 400 ) www.matematiranje.com 5 : 1,315 1,3 = 0,015 m = 0,015 100 cm =1,5 cm : 1,3 m = 1,3 100 cm = 130 cm 128 cm = 2 cm : 13,3 dm = 13,310 cm = 133 cm ; 1,3 m = 130 cm; 133 cm 130 cm = 3 cm : 1309 mm = 1309101 cm =130,9 cm 130 cm = 0,9 cm . 2,85 2,85 3 7,12 - 7,12 7 192 192 190 48 - 48 50 1903 = 570 507 = 350 : 570 + 350 = 920 920 . www.matematiranje.com 6 : 4,6 5 6,2 6 5,6 6 5 + 6 + 6 = 17 : , 4,6 + 6,2 + 5,6 = 16,4 16 ) www.matematiranje.com 1 , . ( )( )3 32 2 03 32 2 3 3 03 32 2 3 3 03 35 5 03 35 53 3553 3113 1 310y xx yy xx xy xx xy xxy xxy xxy xxxyxy= + == + + == + == + == + == += = += = = += = ( ) 1, 0 A . (-1,0) . : ( )1 1, A x y ( )2 2, B x y , , , ( ) ,S SS x y : 1 22S x xx += 1 22S y yy += ( )1 1, A x y ( )2 2, B x y ( ) ( ) ( )2 22 1 2 1, d A B x x y y = + www.matematiranje.com 2 ( ) ,S SS x y ; ( ) ( )1 1 2 2; A x y B x y + + 1 21 26 2 842 2 22 6 842 2 2SSx xxy yy+ += = = =+ += = = = S ( ) 4, 4 S BS , ( ) ,M MM x y 222 4 632 2 26 4 1052 2 2SMSMx xxy yy+ += = = =+ += = = = : (3,5) (3,5) (0,0) ( ) ( ) ( )2 22 2, 3 0 5 03 59 2534d O M = + == += += BS 34 www.matematiranje.com 3 (-2, 2), : ( ) 2 2 4 2 2 4 = = , : 4 44 4x xy y= == = : ( )( )( )( )4, 44, 44, 44, 4 (-4,4)(4,4)(4,-4) (-4,-4)Aiwww.matematiranje.com 4 (2,-3) (2, 5) , ( ) ,S SS x y ( )2 2 4 3 5 22; 1 2,12 2 2 2S Sx y S+ += = = = = = , D =1 D 1, = 5 D 1 y =www.matematiranje.com 5 ( ) ( ) ( )( ) ( ) ( )( )( )( )( )2 22 22222222,5 2 1 35 2 45 2 16 /5 2 162 25 16B A B ABBBBBd A B x x y yxxx xx= + = + = += += + = ( )22 9Bx = / ( )22 9Bx = + ( ) 2 92 35BBBxxx = + == 2 92 31DDDxxx = = = (5,1) D(-1,1) (2,-3) - - 3 - 3 : ( ) , 3 x ( ) , 3 x .... 1 - - 2 - . 22=4 : ( ) 4, y ( ) 4, y ..... 2 www.matematiranje.com 6 1 2 : ( ) ( ) ( ) ( )1 2 3 44, 3 ; 4, 3 ; 4, 3 ; 4, 3 A A A A 1K 10h 3K 11h 2K 10h ) 2K 10h 4-4A3A1A2 A4www.matematiranje.com 7 ) : S Vt = 1K : 1150 S km = ( ) 12 t h = ( 10h 12h ) 111150752S km kmVt h h= = = 2K : 2120 S km = ( 60km 180km 180-60=120km ) 22 t h = ( 10h 12h ) 222120602S km kmVt h h= = = 3K : 360 S km = 31 t h = ( 11h 12h ) 33360601S km kmVt h h= = = 1 2 3, , V V V 1V 1K ) 1K www.matematiranje.com 8 : 8h 9h 40 . ( - ) ) 9h 40 . . ) 12h 20 . ( - ) 32km 12km (32km - 20km ) 32 km +12 km=44 km ) 44 km . www.matematiranje.com 9 - - . 15l . 1. 40- 5l 40, 35l . 2. 85- 15l 45l , 30l . 1. 2. 35l +30l =65l 65l . www.matematiranje.com 10 : 1: VIII 32 2 4 2 8 + + = 32-8=24 . : 2: VIII 36 3+3=6 36-6=30 . : 3: VIII 35 3+1+3=7 35-7=28 . 4: VIII 27 5+2+2+2=11 27-11=16 2: VIII 30 . 2VIII www.matematiranje.com 11 ) ) ) 42km ) , : , . : 239, 271, 236 www.matematiranje.com 12 .. 1 500 000 + 225 000 + 255 000 + 195 000 + 150 000= 2 325 000 . : 20% + 3% + 3,4% + 2,6% + 2%= 31% 31% . : 100:: 2 325 000 100: 3131 2 325 000 1002 325 000 100 323 500 00031 317 500 00G P pGGGG=== = == : 5 2 325 000 ( ) 31% . : 100: G P p = = 2 325 000 31% p = . 2002 7 500 000 . www.matematiranje.com 13 9 , 6 / km h : 9 3 11 1 30min6 / 2 2SVtS kmt h h h V km h== = = = = 11h 30min , 1h 30min 11h 30min +1h 30min 13h = 13h www.matematiranje.com 14 1234I II III IV V VI VIIVIII IX X ()t ) "" 3,5 ) 2,5 . www.matematiranje.com 15 7+18+50+25=100 www.matematiranje.com 16 10 35 . 1 1 / km h , 2 2 / km h , . www.matematiranje.com 17 P a b = . 1P 1a 1b a 20% 112020% 100% 20% 120% 1, 2100a a a a a a a a = + = + = = = b 20% 18020% 100% 20% 80% 0, 80100b b b b b b b b = = = = = 1 1 11961, 2 0, 8 0, 96 0, 96 96%10096% PP a b a b a b P P PP P= = = = = == ) I - 880 II 15% . ( )880100 15 85%: 100:880: 100: 85100 85 88085 880100GpG P pPPP== ==== = 748 P = II I II : 880+748=1628 1628 www.matematiranje.com 18 10% 4 212 : 100:: 4212 100:1010 4212 1004212 100G P pGGG== = =1010 42120 G = - 4% : 4% 42 120 4% : 42 120 100:104104 42 120 10042 120 10010440 500GGGG = = == 40 500 . 10%, 30 000 , 10% 30 000: 100:110100 30 000 11033 000 11010033 000PPPP= = == 33 000 , 10% . 30 000: 100:110100 30 000 11033 000 11010036 300PPPP= = == 36 300 36300 . www.matematiranje.com 19 10% 198 P = 10% 100 10 90% p = = : 100::198 100 : 9090 198 100198 10090220G P pGGGG == = == 10% 10% : 10% 220 : : 220 100 :110110 220 100220 100110200GGGG = = == . )