matematika 7. razred proporcije

Click here to load reader

Post on 24-Nov-2014

103 views

Category:

Documents

9 download

Embed Size (px)

TRANSCRIPT

Hac1an peae1:Tea:Ypac1:Ma1ea1a Ma1ea1aHpp HppeeCea papea Cea papeaKnukuu1e oape sa yuoc npukasa vaca y Word pokyHeu1y!Bpyr ac Tpe ac He1np1 acKnukuu1e oape pa nornepa1e npeseu1auujy vacaNicrosoft Word DocumentHpn ac

BHAHHHAPYATAT:HPABHAHHK A1YIOBOP A2AKOH A3BHBAHOTKAA4HAAH AOBHOC 2 BPOAB1IOIPAmCKA KAPTAB2AHHHCKA B3BPOBHA B4PAMPA BBHHKH1BAHAAHH2H3H4KOAHHHHK HTAHHAB1HTAHHAB2B3B4BHAKOCT BHPOHOPHHAHPOHOPHHOBPABA

Slide 302 3/1/Yae ea cnc1na ape1e py1e ppac1:PRIMER:Obim (y) kvadrata stranice (h) je: u=4hza h = h1 = 3bi}e:u = y1 = 43=12za h = h2 = 5bi}e:u = y2 = 45=20Uporedi koIi~nike odgovaraju}ih stranica i obima:h1 : h2=u1 : u2KoIi~nici su jednaki !

1: 2 3 : 50.6y1: y2 12 : 203 : 50.6Ba ce ace1 !Hppac1 e eaa a apc1 a myae ancc1. Y y pepa anay ce nee e ce eay. a e cna y1 a c1 a. Hneanay ce cayy c1npee . aeaa pac1e. apyra aaa py1.aea e aa ce e ancenee eay c1 p y1a.Ba ce ace1 !Hppac1 e eaa a apc1 a myae ancc1. Y y pepa anay ce nee e ce eay. a e cna y1 a c1 a. Hneanay ce cayy c1npee . aeaa pac1e. apyra aaa py1.aea e aa ce e ancenee eay c1 p y1a.YOHmT:a ey npeac1 pene 1.y1 k1a ey npeac1 pene 2.y2 k2Oaa e: y1 : y2 k1: k2y1 : y2 1: 2:y1: 1 k y2: 2 kBHAKOCT BBA KOAHHHHKA (BB PAMP)a e: y1 : 1 y2 : 2A e mya ape1a ppac1: y k (k0)HPHMP:Bpee (y) e e 1pe aa e 1epe 120m. a ce pee panep. anca pe pe1aa ():a 15m/s eyy1 24 sa 2 10 m/s eyy2 12 su=120h1aaa e:

1

2

510y1y2

2412

1 : 2 1 : 2.y1 : y2 2 : 1BHAKOCT BBA KOAHHHHKA (BB PAMP)

1 : 2 y2 : y1YOHmT:A e mya py1a ppac1:y k

(k0 . 0)

1 . 2 pne npeac1 pene y1 . y2 arnapaye npeac1 mye yy1 -k

1y2 -k

21aaa e:y1 : y2 - : -k k

1

2-O - -kk

1

2

2

1Bae. na eaac1:y1 : y2 2 : 1AKYHAK :Hea cy a , b , c , d pea pen pa1 a ye.eaac1a bc d: : ana ceHPOHOPHHABpen a d cy ca an ppeBpen b c cy yy1pa an ppeOcn cnc1n ppe:HPOHBOB CHOAmHHX HAAHOBA HPOHOPHHBHAK HPOHBOBY YHYTPAmHHX HAAHOBAa b cd

AHAMTHTH!Yae ea cnc1na ppa:Kpc1e a y peanay aaa1aa!

A e a:b c:d . aa e b:a d:cDokaz:a:b c:dadbcA e a:b c:d aa e a:c b:dA e a:b c:d aa e (a+b):b (c+d):dA e a:b c:d oaa e (a - b):b (c - d):dT e 1peaaaa1bc adb:a d:cHana ea cnc1na ppa:Ocn cnc1n ppeOcn cnc1n eaac1Ocn cnc1n ppeHc1a1 aa cy cpan acae ppe. ac aa cy 1ae eaac1:

12 : 3 2 : 3 )5 , 15 : 5 45 , 2 : 8 , 0 )1516:5632:43)21 : 9 35 : 15 )

-,

Hac1 ppy cy an ceae pen:8 , 6 , 4 , 2 )6 , 4 , 3 , 2 )12 , 8 , 6 , 4 )4 , 7 , 24 , 42 )5 , 10 , 2 , 25 )

2 2 2 2

315 315 9 35 21 15 ) cc 54545632151643) cc 25 , 12 4 , 12 5 45 , 2 5 , 15 8 , 0 ) cc 3 2 12 3 ) cc Peee:Peee:

2 : 5 10 : 25 ),24 : 42 4 : 7 )4 : 8 6 : 12 )2 2 2 24 : 3 6 : 2 ) aa1 pen e ry 1 ppaenee!Ha ceaa pa1 aa!

Oapea ea1 a () ppe:

24 482): 35 3 : 25e) 0.8 : 0.4 :3.2e) ) ( - 3) : 27 : 498:65:43 Peee:) 25 105 4.2e) 0.4 2.56 6.4543265

e)) 4 (-3) 14 6.5Ocn cnc1nppe !24 : 163 : HAADomaci zadatakBPYIHHACHPOHOPHHHPHMHKa peanaa aaa1aa pn 1pea y1npa1 aa cy nee e cy aa1e y aaa1y BHPKTHO OBPHYTOHPOHOPHHOHAAH!HPHMP:a 80ea aa ce 788 aapa. K ce ea e y1 a 2167 aapa?Peee:80 . . . 788 a . . . 2167 aKa ea (y 1pa ) a na (y aapa) !A ce neana a ea. neana ce a na : 802167 : 78822Ba cy ape1 py1ppae nee?HPOHOPHHA:PAHYH HOBAA cy pen y 1an aa e - k- k . 1 ec1: 3k y4k .aa ae aa cy pen y ppa pena 3 4. : y3k : 4k : y 3:4HPHMP:

3y4Y ea a 560 yea. Bp aeaa p aena ac ce a 3 : 4. K a aeaa. a aena y 1 ?Peee:Bp aeaa:Bp aena:y : y3: 43k . y4k + y5603k + 4k5607k 560k80Beaa a: 380 240Bena a:y480 320k k k k k k k80 80 80 80 80 80 80H ycny aaa1aHPHMP:a pnae aa eae pc1pe 1pe e 35 a npe9.6 dm2. Ko e 1pe a npe 21 dm2 aa ce pep c1 a? Peee:Bp 1pe a npa a !A ce nea npa e. cae ce p 1pe a35 . . .9.6 dm2. . . 21 dm2 : 359.6 : 21 16 Ba cy ape1 py1ppae nee?HPOHOPHHA:HOBHAHA HAIPABACTPAHHH TPOYIAAKOHAH KAHAAAHPOMHA BPHHMOPCKA BOBATPOmKOBH HPBOAAHPHA Y CPBHH1.7.6.5.4.3.2.TPHHACHAAKnukuuuaopa6pauusapa1ak!HOBHAHA HAIPABA: Ha 1aey a1ea1e Caa e cna 70. Maa 83. a Hna 57 ea. Harpaay a 10500 aapa 1pea aa aee cpaep py cne ea. K e a1 cna a ?Peee:Caa:Maa: yHna: zH ycny aaa1a: y : z70 : 83 : 57 k70k . y83k . z57k + y + z1050070k + 83k + 57k10500210k10500k50Caa : 70 503500 Maa: y83 504150Hna: z 57 502850 y z70 83 57 k HOBPATAKCTPAHHH TPOYIAA: O 1pyra e 52 cm. a ayec1paa ace ce ace a 2 : 5 : 6 Oapea aye c1paa 1pyra.Peee:C1pae 1pyra: a , b , cH ycny aaa1a: a : b : c2 : 5 : 6 ka 2k . b 5k . c 6k2k + 5k + 6k52k4a 8cm , b 10cm , c 12cma b cbc2a

b ck5 6HOBPATAKAHPHA Y CPBHH: Y apy 2008. rae ac paa epaa aaa e 7: 8. K e paa. a epaa aaa?Peee:Bp paa aaa: Bp epaa aaa:yH ycny aaa1a: y7 : 8k 7k . y8k + y307k + 8k3015k30k2B e 14 paa 16 epaa aaa

y7 8kHOBPATAKARPHR 2008R Y1CpHe Re Cy He1 2 3 4 567 8 9 1011121314 15 16 1718192021 22 2324 252627TPOmKOBH HPBOA:a pen 800kg aya. 1200kg na 750kg naa ae e 1100 aapa. A ce pen aa cpaep ac na. apea 1pne pena a cnay npc1y na.Peee:a aye:a ne:ya ne:zH ycny aaa1a: y : z800 : 1200 : 750 k : y : z16 : 24 : 1516k . y24k . z15k + y + z110016k + 24k + 15k110055k1100k20a aye 320 a. . a ne 480 a. . a ne 300 a. HOBPATAKMOPCKA BOBA:eaa 1a pce nae caap 25 kg c.K c a y e1 rpaa pce nae?Peee:Y ane nee: aca pce nae aca c!A ce caye1000 kg25 kg5 kg kg1000 : 525 : 0.125 kg 125 g(neana) a pce nae. aa ce caye(neana) a cBa cy ape1 py1ppae nee?HOBPATAKHPOMHA BPHH: A n pce p 60 km/h. ay1 pehe y1 a 4 aca 15 y1a. a e npee e pe c1 y1 a py nea a 15 km/h?Peee:Y ane nee: cpeay py pe1aa ay1a npee pe1aa!A ce nea60 km/h 255 min75 km/h min75 : 60255 : 3h 24 minpa pe1aa. caye ce npee a e ce pehe y1Ba cy ape1 py1ppae nee?HOBPATAKKOHAH KAHAAA: a 6 ca1paaa paa e ca 54 aaa. A paa c1 p. ae aaa e aa ca a 10 ca1 paaa?Peee:Y: Bpee pneae y paay ae ca e ypahe (y pe1a)!A ce neana6h5410h10 : 6 : 5490npee pneae y paay (y1. ca1. aa).neanace ae ca ce ypaaBa cy ape1 py1ppae nee?HOBPATAKDomaci zadatakTPHHACHPOHOPHHHPHMHHPOHHTHH PAHYHHPOHHTHH PAHYHeaa pea1 e eaa c11 ae ee nee1110099100K pea1a naapa1a e e ee ?12K pea1a naapa1a e e y1 ?K pea1a naapa1a aya mrypa a c ?84Y c y V VI papeayBA HOHOBHMO !HPHMP:Y papeay a 24 yea a e aene1 aeaa. Oapea pea1 aeaa y papeay.Peee:Papea (24 yea)

HeaOcna npeac1100Bea ( 9 yea)Be eeHpe1 cHPOHOPHHA :24100924 9 10037.5Y papeay e 37.5 aeaa24 : 9100 : CHHH HHPAH HAOHHA KPOCYmPHA BOBHHAHA KCKYPHH+ PDV1.2.3.4.5.6.HTBPTHHACHAAKnukuuuaopa6pauusapa1ak!CHHH HH: Hea re e 650 aapa. Oapea ey ce cea a 28.Peee:IAABHA ( OCHOBHA) BPBHOCT: 100 650 aapaHPOHHTHH HHOC (ce cea): 100 - 2872 aapaHPOHOPHHA: 100 : 65072 :100 650 72468Hce cea a 28 ea e 468 aapaHOBPATAK+PDV: Hpaaa ea r 1eema e 8450 aapa ycPDV(18). Hpaya ey 1eema.Peee:IAABHA ( OCHOBHA) BPBHOCT: 100 8450 aapaHPOHHTHH HHOC (ce neaa): 100 + 18118 aapaHPOHOPHHA: 100 : 8450118 :100 8450 1189971Hce neaa a 18 ea e 9971 aapaHOBPATAKHA KCKYPHH: Bea e e 1600 aapa a ecypy. Hpnr aaa e 1p 65 na. a apyrr 35 cye a y e c1aa. K e aapa 1p a ecyp?Peee:IAABHABPBHOCT: 100 1600 aHPOHHTHH HHOC:65 aHPOHOPHHA:1600 : 100 : 65 100 560 35 1040Beay e c1a 1600 - 1040560 a.Hpn aa: Bpyr aa:IAABHABPBHOCT:HPOHHTHH HHOC:HPOHOPHHA:560 a 100 a35 560 : 100 : 35 100 1600 65196Bea e 1p:1040 + 1961236 aapaHOBPATAKmPHA BOBHHA: Y 24 kgnae pac1npe e 6 kgeepa.Oapea pea1 eepa y ae pac1npy?Peee:IAABHA BPBHOCT: 100HPOHHTHH HHOC:PACTBOP30kg24kg+6kg 6 kgHPOHOPHHA: 100 : 30 : 620 Y pac1npy e 20 eepaHOBPATAKHA KPOCY: Y 1y 1pe ayc1a e 15 1aapa p e p 136 1paa. K e a c1ap1y 1pe?Peee:IAABHA ( OCHOBHA) BPBHOCT : 100 HHOHATA!HPOHHTHH HHOC :(ce ayc1aaa)100 -1585 136 1paaHPOHOPHHA: 100 : 85 : 13685 136 100160Ha c1ap1y 1pe e 160 1aapaHOBPATAKPAH HAOH: Oa e a naapa1a c1pae 20cm1pea pea1 ane ry pyr. K pea1a a1epaa 1aaa?Peee:

20cmKBABPAT: a20cm Pnaapa1a a2 P1 400cm2KPYI: r-a2Ppyra r26 P2 1006cm2 10cmHnpa 1a1a:P1a1aP1 - P2 86cm2HPOHOPHHA:Pnaapa1a : P1a1a 100 : 400 : 86100 : 400 860021.5Hp peaa 1aaa 21.5 a1epaa10cmHOBPATAKDomaci zadatakHTBPTHHACHPOHOPHHHPHMHmHHKACPHCKH HKenc1IOIPAmHAAHKOBHAKYATYPAXMHAHAAKnukuuuaopa6pauy uac1aauy o6nac1MYHHKAKYATYPA

1 45N

2 70N

1 3.6 cm

2 ?HPOHOPHHA:

1: 2

:

45N : 70N 3.6cm :

5.6cmOpyra ce crere 5,6 cm.

BYHHA HCTAHA OHPYI(y cm)BHPKTHO CPAMPHAAHHHH CHA KOA BAYHA OHPYIY AACTHHHA OHPYIA: A ce eac1y pyry a 1er 1ee 45N. pyra ce c1ere 3.6cm. K ce c1ere pyra a ce a 1er 1ee 70N ?1.HOBPATAKm H H K AAACTHHHA OHPYIABHOCTPAHA HOAYIABBOCTPAHA HOAYIAXHBPAYAHHHA MAmHHA(BHAAHHA)1.2.3.4.HOBPATAKKnukuuuaopa6pauusapa1ak!XHBPAYAHHHA MAmHHA ( BHAAHHA):Ha nee y apaye ae aa ce ay1 ca nae yye 1ee 5500N. a a ae e 1ee 18N. Hnpa neer a e 4.5m2. Oapea npy aer a.Tea na: Q1 5500NHnpa a: S1 4.5m2Tea ea : Q2 18NHnpa a:S2?Kn pyy - Hp1c a a a cyeaaHPOHOPHHAQ1 : S1 Q2 : S25500N : 4.5m2 18N : S2S2 0.015m2A. a a ec1 ar ea c 1e e! m1a ce araha?2.HOBPATAKBBOCTPAHA HOAYIA:Hne 1ee 750N cea a aa yaae e a 1ae ca 0.5m. Ha y yaaec1 a 1ae ca 1pea aa ceae aea 1ee 250Naa aaa a y pan1e?Tea nea: Q1 750NTea ae1e1a : Q2 250NKpa ce nea: a 0.5 mHPOHOPHHA:Q1: Q2 b : a750N : 250Nb : 0.5mb 1.5 mab3.TPTOCAOHAHHOAYIAKpa ce aeaa: b?HOBPATAKBHOCTPAHA HOAYIA:Beaae a (a c) ca 1epe1 yye ace 50kg.K c 1pea aa aeye a a aa ara 1epe1?140cm40cmTea 1epe1a: Q500NKpa 1epe1a: b40cm0.4mKpa ce: a 140cm1.4mCa aea aeye: ?HPOHOPHHA : Qb : a : 500N1.4m : 0.4m175NHHTHHTT CHA MAHH OB THH TPTAOHOAHKO HYTA KOAHKO HYTA HH KPAK BYH OB KPAKA TPTA!4.HOBPATAKXM H A1. 2. KOHHHTPAHHA PACTBOPAOBHOC MACA AMHATA YBHHHHMA (Hpyc1n a)Y ay e 20 e1pe1r pac1npa c.a) Ca c 5 nae y a) Baa c 5kgc y pac1npOapea pea1 c y ae pac1npa.a)Y pac1npy a 5 c:5 a 200.05 201Pac1np caap 19kg nae 1 c.A ca 5 nae, n pac1np aacy 25kg caap 24 nae 1 kg c.HPOHOPHHA25 : 1100 : 4) Hn pac1np a 19 6 kg c25 : 6100 : 24 Oapea ac aca a1a. naa cea y NH4NO3.a) Pea1ne a1ce ace eeea1a cy: Ar(N)21428 . Ar(H)414 . Ar(O)316483. AKOH O OBPAHY MACOapea rpaa rnha pearye ca 30gcypa y eaey eS ?Mace: m(e)?.m(S)30gHpn: apea1 ac aca e SyeSBpyr: c1an1 HPOHOPHHY:7:4 : 30 52.552.5 g rnha pearye ca 30g cypa7g epearye ca4g S g e pearnae ca 30g Se : S56 : 327 : 4Oac: N : H : O28 : 4 :487 : 1 :12HOBPATAKIO I P A m H AHa ap1 paepe 1:50000 pac1ae ehy ana ec1a e 4.5cm. K e pac1ae ehy 1a ana ec1a y ppa?Pac1ae ehy Berpaaa Apahena e 84km. K c pac1ae ehy n rpaana a ap1 paepe 1:400000?1 : 500001 cm a ap150000 cm y ppa4.5 cm a ap1 cm y ppa1 : 500004.5 : 4.5 50000 225000cm2250 mHPOHOPHHA1 : 400000 : 84000m84000 : 400000 0.21m 21 cmHOBPATAKAHKOBHA KYATYPABe n afx epeea cap eaap cy xfe na ace fay "ee ecfefe y afeafe. Bfpyee e f ene y pp neea y apfefe reefpe.Peapn e ypae Bfpyeeex nea pyaea ppe yncr fea. Oea ca pya caepe pep Peapner fepeceaa a peafy ppa. Rpen fra ea ca peefye feee Peapnex yaa y eeeay eea ppne. T e a aya aaa a e aa yefa c aa (pecnea ehy eea ceepa) yef-paea pa yncr fea cfeapae apxfefype a ppaa yncr fea. He cfpaea eepyy na Peapn e pfe cye afepay ercfey eanpaf,a nyxey pyr.Bfpyeee ee e af Peapne pfe yfye eeaa. Hacfa e 1492 rne. Y ey e paa yapa y nea aa a cy cfepee ycaa y pyr eanpaf. Upfe fecf ce ean ey 3a ppa , pehe, ppe.W nya ae e 1/10 eceW na e pe 4 pcfa cfa e pe 4 naa aaf e pe 6 naea eca yapa e 4 afa pa e 4 afa nya yea e 1/3 nye aW nya papex pyy enaa e ec ynaecf n e ce n pane e 1/10 ece ynaecf n epxa raee n pane e1/8 ece acaa pa paea e 1/4 ece ynaecf n afa n epxa pye e 1/5 ece ynaecf n afa n ayxa e1/8 ece ynaencf n pane n ca e 1/3 nye raee Onc fea raee n "Ke e1 : 7Hapae, e cf yeepa cy ppa yncr fea. Haya eey e cfepea c e ceaa fx nenyax eapaa.Ofpa pane Peapna na Ba cy cea paeaa peca cfaa aa eefa yefa.Hca1pa aea capa. naapa. rpamapa!O1pe r 1raer yyanr! Ye1c1. a a1ea1a. yac y ana y apy.HOBPATAKMYHHKA KYATYPAHOBPATAKH1arpa e. pea p. pae pea nae y nyne yaapaa ea ana y 1anaa. Ya e nae aa cy e apane y paep 1:2 (eaa e anc1py ne a apyrr). Te ce c1np ppaa ac: a e peaneee a 1a C pea 1 C1.T 1pe ry y e c1panae cpne aca ehy c1napa e e e cnyrae paa1.ya c1a pane ee ne aye a cy 1a c1np a1ea1y 1epy ye.Ta aya. a ca e ae. pyana yy en a nya 1a a a acanpe a. Ocn pe a1ea1e 1epe ye e ppa nenae 1a(cnr meea ye) pa (cnr a a1ea1e). Hae caaa y pc1!Ona pe apan peac1ana pe paaea y caa e apa1e nye e ce a pece a c1pye1e. a y npy . 1a apehnay aa cnar 1a. pn e peana a1 mm. a1ea1ap y 1epe1ap H1arpa. O ern ye cy ea ayy e a e a a c1a a ye1ae pe1e e. Haa cy aa ce nee e aa 1ana a n1 arnapa p ac 3:2 a nap1 4:3.a1 cy apea arnapaye pene a cne c1ae 1epnae aa aa aanenay ana 1ca 1epnaa arnapa ee n paca.OKTABAKBHHTAKBAPTAMap Mapce. mpayc a1ea1ap. mm 1epe1ap ye. mpyca e ceaea pana a y er yr c1pye1a a 1peep:1. Bp 1pe1aa e p c1a1 ay py1 e ppaa ay2. Bp 1pe1aa e p c1a ay ppaa e naapa1 pey aa3. Bp caa ane e pa1r a1epaa. a c1e aye aa. py1 e ppaa naapa1 pey 1ee eCna 1 ea neae (aena.acnpa...) c y ce 1n apyr 1na ce cae yy. A a1peep a. ee 1peep1 ca ea aya ne na. 1pea... e apyr p. a1peep naay. a1epa c1pye1a c1a. T aana ny c1pye1a aae y 1 ne a nya. Te pa1ee 1ne ne AAHKBOTHH 1n ce ace pea cn 1y er ye a 1:2:3:4: ...Hca1pa pepe npeac1 n pena: [email protected] Tn arnapay n pena ny ce ap. a pen aanay ae e 1peep p nhea 1a.Bpen 1pe1aa: 64 128 192 256320384 448 512570640Pea p an. 1na: 1234 5 678 910Bya e (C1): 1 = ? @ B D E6cn 1Y cna pan pe1ay a ye.Mya e aea pe1ae.$RP$KI JEZIKK apa, f ye !Cf yn-cf yn ! Rpe pee-a e !Cear rcfa fp naa ncfa !Jeny pe, a nee y !Eap rac ce nae ye, a nae !Fne ce nea ceahay fpe ce pcf !Maa nea-aa pra, eea nea-eea pra.R fyh eha cf faa e ; ce ena e r.He n ay pay a ee eefap !Rf y f pna !K ec ef - c ana !Eecef epa pe e c a ey ee cy e acee neeef, a eey e pecfaa ca ena.Eeer ax yaa,Ry pe a a!M ce npar aa xea,Eecef pee, a ena y a !Hpee. cne y1npea ce a yaap ayn1 acayy yaa. ppa acana. arahaa n1a e yac ca. npa aa.nketni listHOBPATAK