9 - razred - matematika - mala matura

UU

FORMULE

Kvadrat zbira: 222 2)( bbaaba

Kvadrat razlike: 222 2)( bbaaba

Razlika kvadrata: )()(22 bababa

Dv}vivivl]Z}v}W nmnm aaa

]ioivivivl]Z}v}Wnmnm aaa :

W}]vl}lW26aP (a t]v]]

u]vl}lW 3aV (a t]v]]

Povrina kvadra: )(2 cbcabaP (a, b i ct]v]]

u]vlW cbaV (a, b i ct]v]]

Oznake: Bt}]vU Mt}]v}u}]H t]v]]v

W}]v]uW MBP 2

u]v]uWHBV

W}]v]u]WMBP

u]v]u]fiW HBV 31

W}]voilW3 %0 U(r+H )(rt]v}ov]l}v}

u]voilWV = B H = r2+(rt]v}ov]l}v}

W}]vlW3 %0 U(r+s)(rt]v}ov]l}v}]st]v]}v]

u]vlWV = 31

B H = 31

r2+

(rt]v}ov]l}v}

UU

MATEMATIKA

U P U T S T V OVRIJEME RJEAVANJA TESTA: 70 MINUTAPribor: JUDWQDRORYNDLJXPLFDKHPLMVNDRORYNDJHRPHWULMVNLSULERU8SRWUHEDGLJLWURQDLNRUHNWRUDnije GR]YROMHQD

3DOMLYRSURLWDMWHXSXWVWYR1HRNUHLWHVWUDQLFHLQHUMHDYDMWH]DGDWNHGRNWRQHGR]YROLGHXUQLQDVWDYQLN7HVWVDGUL]DGDWDND7RNRPUDGDPRHWHNRULVWLWLIRUPXOHNRMHVXGDWHQDVWUDQDPDL

3DOMLYRSURLWDMWH]DGDWNHLUD]PLVOLWHSULMHUMHDYDQMD$NRYDPVHLQLGDMH]DGDWDNSUHWHDNQH]DGUDYDMWHVHSUHGXJRQDQMHPXYHSRNXDMWHGDULMHLWHVOMHGHL1DQHULMHHQH]DGDWNHVHYUDWLWHNDVQLMH

7HVWPRUDELWLSRSXQMHQKHPLMVNRPRORYNRPDJUDWQXRORYNXPRHWHNRULVWLWL]DFUWDQMHLWRNRPUDGD

8NROLNRSRJULMHLWHSUHNULLWHLUMHDYDMWHSRQRYR$NRVWH]DGDWDNULMHLOLQDYLHQDLQDQHGYRVPLVOHQRR]QDLWHNRMHVHUMHHQMHERGXMH.DG]DYULWHVDUMHDYDQMHPSURYMHULWHVYRMHRGJRYRUH

=DGDWDNHVHYUHGQRYDWLVDERGRYDDNRMH QHWDDQ ]DRNUXHQRYLHSRQXHQLKRGJRYRUD QHLWNRLQHMDVQRQDSLVDQ UMHHQMHQDSLVDQRJUDWQRPRORYNRP

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4

2

2

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3

4

2

x

y

0

1

1

1

1

3

3

4

4

2

2

2 3 4

3

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y

0

1

1

1

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3

4

4

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2

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3

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ZiviW

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Karate 22

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X l}}o}]v]v}v}P}i}}]i]}l}l34

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MATEMATIKA EKSTERNA PROVJERA EE:E

MATEMATIKA







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X 30

X 50

X 60

X 80

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X d}l]]lo]uvvi]}ov]luXuioi]vuX

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a) 123 2014

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a]ui}vl~i]]}]ovivl}M

1 + 1*1 2 = 100

1 bod

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1 1

: 0,25 : 23 12

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4

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A

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60m

10m

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MATEMATIKA







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X 1,0

X 1,0

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X i}P}l}vX~] AB) je

A BD

C

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X ]v

X ]uov]

1 bod

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a) ( 3) ( 7) ( 26) 4

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vrijeme

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10

15

20

25

30

35

8h 9h 10h 11h 12h 13h 14h 15h 16h 17h 18h 19h 20h

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MATEMATIKA







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X /vWa) 15 20 6

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1 bod

25 5 1 bod

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X sov}ZiuivPZ}l}u]vX Zo]lv]]iPu}u]uX

Grad 1

Grad 2

1. dan 2. dan 3. dan 4. dan

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

X Z]i]viv]v12 (3 2 ) 7x d

ZiviW

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2 2 1

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x y

x y

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X }lv}uov]uoPo}]iivl]vl]u}PPoX Napomena: El]l}i}P}ll

ZiviW

3 boda

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X D]v]vu]o}vivll}vo]]X El}i}i]]v]ZUZu]v}]ilM

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U P U T S T V O

Vrijeme rjeavanja je 60 minuta.

Pribor:JUDWQDRORYNDLJXPLFDKHPLMVNDRORYNDJHRPHWULMVNLSULERU 8SRWUHEDGLJLWURQDLNRUHNWRUDQLMHGR]YROMHQD


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X El}i}i}iv}i}ivi]o]v]ioivl )01(P i )02(T M

X -1 0 1 2 3 4 5 6

P. T. X

-1 0 1 2 3 4 5 6

P. T.

X -1 0 1 2 3 4 5 6

P. T.

X -1 0 1 2 3 4 5 6

P. T.1 bod

X

X h}]i}oivlo]l}iv}vi}]v}]o]v}2314m l}vo]]X

ll}i]o]iii}v}X

X /vW

a) 32 3256 1 bod

b) 5,03852,0 1 bod

UU

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X W]uiv}u(}uoo]ll]v10199 X1 bod

ZiviW

X KPv]}vi}iuiv]l]vv]lX Klv}P}iv]lU

32

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X Z]i]iv]v .4

36

521

xx

2 boda

ZiviW

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X Z]i]viv]v )1(63)2(7 d xxx ]]liviv}i }iv}i}iX

2 bodaZiviW

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

XEPv]v}uoi}l}uu]}v]v]i}}i]}]o l}i]}o]X}]iv]}]]lv]o}uX

motor v]l}auto } kamion

PONEDJELJAK 3 15 14 9UTORAK 5 42 15 13SRIJEDA 0 23 18 12

dsZd< 4 38 16 15PETAK 2 29 27 11

SUBOTA 2 57 30 8NEDJELJA 1 60 29 16

X l}iMP=NP i LP=KPU}liLM=KNX2 boda

L K

M N

P

ZiviW

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X /v}]v}ivv}P]io}P}v]lX3 boda

u

u

u

u

ZiviW

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X /v}]v}u]iiv]]vuU]vivviP} ]iP}voiuX

3 bodaZiviW

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E}li]i]vvlXEvu}l}]o]iP]/yX

X dl )4,2(A i )2,0(B ]iP.l(vl]i

X 2 xy

X 2 xy X 22 xy X 22 xy

1 bod

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3 bodaZiviW

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2

UPUTSTVO ZA BODOVANJE

Napom ena :

3

E}uvWl}}l]}livilv]U]o]l}uvnja je pogr ijeeno jednom, zadatak se boduje sa 2 boda.

10. Ukupno 2 boda

......................................................................................................... 1 bod

............................................................................................................................................ 1 bod

11. Ukupno 2 boda

............................................................................................................................................. 1 bod Kvvv}iv}i}ilivi ....................................................................................... 1 bod

12. Ukupno 3 boda

a) 27 ............................................................................................................................................... 1 bod b) 37 ............................................................................................................................................... 1 bod c) 20% ........................................................................................................................................... 1 bod

13. Ukupno 2 boda

h}v}i ....................................................................................................... 1 bod Pozivanje na drugo pravi lo podudarnost i trouglova (stranica ugao st ranica) ....................... ... 1 bod

( , , NPKMPL kao unakrsni ugovi) 14. Ukupno 3 boda

Povrina kvadrata 2422 cmcmcm ......................................................................................... 1 bod

Povrina trougla 28244

cmcmcm

............................................................................................. 1 bod

ili .............................. 1 bod

15. Ukupno 3 boda

....................................................................................................................... 1 bod

................................................................................................................................... 1 bod

................................................................................................................................. 1 bod

Zadaci navedeni kao ilustracija gradiva IX razreda

4

1.dan odgovor: A

2. Ukupno 3 boda

............................................................................................................................... 1 bod

h}vo u pravouglom trouglu, npr. ...................................................................... 1 bod

............................................................................................................................. 1 bod

[11]

6. PRIMJER TESTA SA SHEMOM ZA BODOVANJE

6.1 PRIMJER TESTA hoi]u]u}l]te o}}]v}P}P}}X

1. a}]ivl}v]vi] )2()5()5( aaa ?

A. 23 a

B. 23 a

C. 2a

D. 2a

1 bod

2. Vrijednost izraza 23 32 je:

A. 36

B. 72

C. 36

D. 56

1 bod

3. Ako se brojiocu i imeniocu razlomka 43

doda broj 1 onda se vrijednost razlomka:

A. ne mijenja

B. }1

C. smanji za 201

D. }201

1 bod

[12]

4.

[13]

ll}i]o]iii}v}XBodovi se dodjeljuju na }v}v postavke, postupka ivi]rezultata koji slijedi iz korektnog rada.

7. Za koje je vrijednosti parametra p funkcija 3)42( xpy M ZiviW 1 bod 8.

a) E}iv}i}i}v]}iFs, 57

i rw.

1 bod

/v]]iv}]5 5 5 7

:4 6 3 8

.

2 boda

9. W}l}ll]u]o]uU]P }uvl}u}}]]}v~o}}vviU}v (iz igre) ili 3 poena (iz igre sa uoiv}]}U75m). hlu]ivo}uWXd}l}ulu]iv}o]}vlv} slobodna bacanja i 9 trojki.

[14]

11. Anastasija je tokom sedmice sakupljala novac da bi drugarici kupila poklon. U tabeli je zapisivala, koliko je novca sakupila po danima.

dan u sedmici ponedjeljak utorak srijeda l petak subota nedjelja ]v}~ 3,10 1,40 2,50 0,80 3,00 4,80 2,70

a) }l]l]]u]iPu}m.

1bod b) Anastasija je u petak sakupila 12% od sume koju je planirala. Koliko iznosi planirana suma? ZiviW 2 boda

[15]

12. av]l]}]o]iv}}vXW}v]]abelu zavisnosti promjene broja radnika ]uvl}i}}]]}oivX

broj radnika 6 3 vrijeme (dani) 30 2

2 boda 13. ]vv] paralelograma su 8cm i cm6 Xs}iv]] }P}]]v]vcm3 . /vi]v]]vl}i}P}uvi}iv]]X ZiviW 2 boda 14. /vi}]v}v}]ul}}]v]u262cm i povr]vviv}P}u}230cm .

ZiviW 1 bod 15. }u]o]il]u}o]llU]i]i}]u}v}mS12 , a visina m4 . Koliko kubnih metara ima u toj gomili pijeska? ZiviW 2 boda

[16]

6.2. SHEMA ZA BODOVANJE

Rivil]l}P]}

Broj zadatka dv}P}} 1. A 2. B 3. D 4. C 5. A 6. C

7. Ukupno 1 bod

242042 !!! ppp 1 bod

8. a) Ukupno 1 bod dv}v]iete sve tri vrijednosti

b) Ukupno 2 boda 5 5 5 7 5 1 7

:4 6 3 8 4 2 8

1 bod

18

1 bod

9. Ukupno 2 boda

796923923 x 1 bod 49 x 1 bod 10. Ukupno 3 boda x t }i]]P}v y t }i]]P]}v

flfi

8

1932

yx

yx 1 bod

Tvo primijenjena npr. metoda zamjene ili metoda suprotnih koeficjenata 1 bod 3 y 1 bod

[17]

11. a) Ukupno 1 bod

1 bod 11. b) Ukupno 2 boda

310012

x 1 bod

tw 1 bod 12. Ukupno 2 boda dv}}oiv]]iv}}]iUvX 6 30 3 x

x:306:3 60 x 1 bod

dv}}oiv]]iv}}]iUvX 6 30 x 2

2:306: x 90 x 1 bod

broj radnika 6 3 90

vrijeme (dani) 30 60 2

[18]

13. Ukupno 2 boda

a ba h b h , cmhb )38(6 1 bod

cmhb 4 1 bod 14. Ukupno 1 bod

MBP 2 22 30262 cmBcm

216cmB 1 bod 15. Ukupno 2 boda

,2 SrH ,212 SS rm cmr 6 1bod

3

2 HrV

S ,

34)6( 2 mm

V

S

, 33 483

144mmV S

S ili 372,150 mV | 1 bod

Documents

9 - razred - matematika - mala matura