Matematika_Matura_Rjesenja

8/19/2019 Matematika_Matura_Rjesenja

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SHEMA ZA BODOVANJ EMATURSKI ISPIT, MATEMATIKA

02. J UN, ŠKOLSKA 2010/2011. GODINA

1

Rješenja zadataka višestrukog izbora

Broj zadatka Tačan odgovor 1. A2. D3. D4. D5. C6. D7. B8. B

9. Ukupno 3 boda

ii 2011 ......................................................................................................................... 1 bod

i

i

i

i z

1

1

1

2 .................................................................................................................. 1 bod

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

10. Ukupno 3 boda 3 21 1

: x x x

x x

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

x

x x

x

x x x 1:

)1)(1( 22

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

1 x ................................................................................................................................. 1 bod

11. Ukupno 2 boda32762557020 x x x x ................................................................................... 1 bod

2 x ................................................................................................................................ 1 bod

12. Ukupno 5 bodova1 0a 0 D ...................................................................................................... 1 bod

2[ ( 3)] 4 1 0k k .................................................................................................... 1 bod

09102 k k ............................................................................................................... 1 bod9,1 21 k k ...................................................................................................................1 bod

91 k ......................................................................................................................... 1 bod

1 . z i


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2

13. Ukupno 4 boda

)3

1

3

1(3)

2

1

2

1(2

323 x x ................................................................................................. 1 bod

27

23

8

32 x x ................................................................................................................ 1 bod

81

16

3

2

x

ili4

3

2

3

2

x

ili16

81

2

3

x

ili4

2

3

2

3

x

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

4 x ................................................................................................................................ 1 bod

14. Ukupno 3 boda

I način

21sin

21sin x x …………………………………………………………………….. 1 bod

2

1sin x Z k k x ,2

6

Z k k x ,26

5

….………...…………………… 1 bod

2

1sin x Z k k x ,2

6

Z k k x ,26

7

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

II način

2

1sin

2

1sin x x …………………………………………………………………….. 1 bod

Z k k x ,6

………………………………………………..................................... 2 boda

15. Ukupno 4 boda

=5a

3

A x 15-xE B

D

C

Iz trougla ΔEBD: o x x x 60cos)15(52)15(5 222 ........................................... 1 bod

cm x 7 .......................................................................................................................... 1 bod

Primjena kosinusne teoreme na jedan od trouglova AEC ili CED:

npr. za ΔAEC,o

AE AC AE AC CE 60cos2222

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

cmCE 13 ..................................................................................................................... 1 bod


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3

16. Ukupno 3 boda

Uočeno da je baza piramide jedan od tri pravougla trougla, npr. EML .......... 1 bodcm EK H 2 .............................................................................................................. 1 bod

3

1 32

2 13 3

B H V cm

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

17. Ukupno 3 boda

)0,(),( Rba ili 2 2 2 x R y R ............................................................................... 1 bod

2 2 2

2 2 R R ........................................................................................................... 1 bod

2 2

2 4 x y ............................................................................................................ 1 bod

18. Ukupno 3 boda

28734)6(8 1111 d ad ad ad a ............................................................... 1 bod

2d ............................................................................................................................... 1 bod

41 a ............................................................................................................................... 1 bod

19. Ukupno 3 boda x x e xe x y )1(2' 2 ...................................................................................................... 1 bod

0)1(' 2 xe y x ............................................................................................................ 1 bod

y R x )( .................................................................................................................... 1 bod

20. Ukupno 3 boda

07

x

x

7 0 x ................................................................................................. 1 bod

)070()070( x x x x .......................................................................... 1 bod

0,7 x .......................................................................................................................... 1 bod

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