ETF MATF FON GRF TMF FORUM

Prijemni ispit na Tehnološko-metalurškom fakultetu u Beogradu

jun 2019.


Test ima [inline]20[/inline] zadataka na [inline]2[/inline] stranice. Zadaci [inline]1–3[/inline] vrede po [inline]3[/inline] poena, zadaci [inline]4–7[/inline] vrede po [inline]4[/inline] poena, zadaci [inline]8–13[/inline] vrede po [inline]5[/inline] poena, zadaci [inline]14–17[/inline] vrede po [inline]6[/inline] poena i zadaci [inline]18–20[/inline] vrede po [inline]7[/inline] poena. Pogrešan odgovor donosi [inline]−10\%[/inline] od broja poena za tačan odgovor. Zaokruživanje [inline]N[/inline] ne donosi ni pozitivne ni negativne poene. U slučaju zaokruživanja više od jednog, kao i u slučaju nezaokruživanja nijednog odgovora, dobija se [inline]-1[/inline] poen.

1.Link zadatka Rešenje jednačine [inline]\displaystyle\frac{\displaystyle0,24x}{\displaystyle\left(\frac{17}{40}-\frac{5}{24}\right)\cdot2\frac{4}{13}}=\frac{\displaystyle4\frac{3}{8}:7-3\frac{3}{10}:11}{\displaystyle2-\frac{3}{20}\cdot9}[/inline] je:
[inline]\text{A)}[/inline] [inline]2[/inline];      [inline]\text{B)}[/inline] [inline]\displaystyle1\frac{2}{3}[/inline];      [inline]\text{C)}[/inline] [inline]0,1[/inline];      [inline]\text{D)}[/inline] [inline]0,2[/inline];      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{25}{24}[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]2[/inline];      [inline]\text{B)}[/inline] [inline]\displaystyle1\frac{2}{3}[/inline];      [inline]\text{C)}[/inline] [inline]0,1[/inline];      [inline]\text{D)}[/inline] [inline]0,2[/inline];      [inline]\enclose{circle}{\text{E)}}[/inline] [inline]\displaystyle\frac{25}{24}[/inline];              [inline]\text{N)}[/inline] ne znam.

2.Link zadatka Izraz [inline]\left(\left(16^{-2}\right)^{-2}:16^{(-2)^{-2}}\right):16^{-2^{-2}}[/inline], jednak je:
[inline]\text{A)}[/inline] [inline]16^{-4}[/inline];      [inline]\text{B)}[/inline] [inline]16^8[/inline];      [inline]\text{C)}[/inline] [inline]16^4[/inline];      [inline]\text{D)}[/inline] [inline]1[/inline];      [inline]\text{E)}[/inline] [inline]16[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]16^{-4}[/inline];      [inline]\text{B)}[/inline] [inline]16^8[/inline];      [inline]\enclose{circle}{\text{C)}}[/inline] [inline]16^4[/inline];      [inline]\text{D)}[/inline] [inline]1[/inline];      [inline]\text{E)}[/inline] [inline]16[/inline];              [inline]\text{N)}[/inline] ne znam.

3.Link zadatka Zbir svih vrednosti parametra [inline]m[/inline] za koju grafik funkcije
[inline]y=(3-2m)x+1-3m^2[/inline] prolazi kroz tačku [inline]A(0,-2)[/inline] je:
[inline]\text{A)}[/inline] [inline]1[/inline];      [inline]\text{B)}[/inline] [inline]0[/inline];      [inline]\text{C)}[/inline] [inline]-1[/inline];      [inline]\text{D)}[/inline] [inline]-2[/inline];      [inline]\text{E)}[/inline] [inline]2[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]1[/inline];      [inline]\enclose{circle}{\text{B)}}[/inline] [inline]0[/inline];      [inline]\text{C)}[/inline] [inline]-1[/inline];      [inline]\text{D)}[/inline] [inline]-2[/inline];      [inline]\text{E)}[/inline] [inline]2[/inline];              [inline]\text{N)}[/inline] ne znam.

4.Link zadatka Proizvod rešenja jednačine [inline]\displaystyle\left(\frac{1}{4}\right)^\frac{4-x^2}{2}=8^x[/inline] je:
[inline]\text{A)}[/inline] [inline]7[/inline];      [inline]\text{B)}[/inline] [inline]4[/inline];      [inline]\text{C)}[/inline] [inline]9[/inline];      [inline]\text{D)}[/inline] [inline]0[/inline];      [inline]\text{E)}[/inline] [inline]-4[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]7[/inline];      [inline]\text{B)}[/inline] [inline]4[/inline];      [inline]\text{C)}[/inline] [inline]9[/inline];      [inline]\text{D)}[/inline] [inline]0[/inline];      [inline]\enclose{circle}{\text{E)}}[/inline] [inline]-4[/inline];              [inline]\text{N)}[/inline] ne znam.

5.Link zadatka Zbir rešenja jednačine [inline]\sqrt{2x+1}-\sqrt{x+5}=0[/inline] je:
[inline]\text{A)}[/inline] [inline]1[/inline];      [inline]\text{B)}[/inline] [inline]-4[/inline];      [inline]\text{C)}[/inline] [inline]4[/inline];      [inline]\text{D)}[/inline] [inline]0[/inline];      [inline]\text{E)}[/inline] [inline]5[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]1[/inline];      [inline]\text{B)}[/inline] [inline]-4[/inline];      [inline]\enclose{circle}{\text{C)}}[/inline] [inline]4[/inline];      [inline]\text{D)}[/inline] [inline]0[/inline];      [inline]\text{E)}[/inline] [inline]5[/inline];              [inline]\text{N)}[/inline] ne znam.

6.Link zadatka Zbir rešenja jednačine [inline]2|x+1|-|x-2|-3=0[/inline] je:
[inline]\text{A)}[/inline] [inline]-6[/inline];      [inline]\text{B)}[/inline] [inline]6[/inline];      [inline]\text{C)}[/inline] [inline]-5[/inline];      [inline]\text{D)}[/inline] [inline]-7[/inline];      [inline]\text{E)}[/inline] [inline]7[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]-6[/inline];      [inline]\text{B)}[/inline] [inline]6[/inline];      [inline]\text{C)}[/inline] [inline]-5[/inline];      [inline]\text{D)}[/inline] [inline]-7[/inline];      [inline]\text{E)}[/inline] [inline]7[/inline];              [inline]\text{N)}[/inline] ne znam.

7.Link zadatka Zbir prvih pet članova aritmetičke progresije je [inline]90[/inline], a zbir prvih devet članova je [inline]234[/inline]. Broj prvih članova koje treba sabrati da bi se dobio broj [inline]640[/inline], jednak je:
[inline]\text{A)}[/inline] [inline]9[/inline];      [inline]\text{B)}[/inline] [inline]16[/inline];      [inline]\text{C)}[/inline] [inline]17[/inline];      [inline]\text{D)}[/inline] [inline]20[/inline];      [inline]\text{E)}[/inline] [inline]12[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]9[/inline];      [inline]\enclose{circle}{\text{B)}}[/inline] [inline]16[/inline];      [inline]\text{C)}[/inline] [inline]17[/inline];      [inline]\text{D)}[/inline] [inline]20[/inline];      [inline]\text{E)}[/inline] [inline]12[/inline];              [inline]\text{N)}[/inline] ne znam.

8.Link zadatka Posle dva uzastopna jednaka procentualna povećanja cene proizvoda od [inline]100[/inline] dinara, ona sada iznosi [inline]125,44[/inline] dinara. Procenat povećanja je:
[inline]\text{A)}[/inline] [inline]12\%[/inline];      [inline]\text{B)}[/inline] [inline]9\%[/inline];      [inline]\text{C)}[/inline] [inline]15\%[/inline];      [inline]\text{D)}[/inline] [inline]14\%[/inline];      [inline]\text{E)}[/inline] [inline]25\%[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]12\%[/inline];      [inline]\text{B)}[/inline] [inline]9\%[/inline];      [inline]\text{C)}[/inline] [inline]15\%[/inline];      [inline]\text{D)}[/inline] [inline]14\%[/inline];      [inline]\text{E)}[/inline] [inline]25\%[/inline];              [inline]\text{N)}[/inline] ne znam.

9.Link zadatka Ako je [inline]\log_a27=b[/inline] onda je [inline]\log_{\sqrt3}\sqrt[3]a[/inline] jednak:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{3(1-a)}{b+1}[/inline];      [inline]\text{B)}[/inline] [inline]1[/inline];      [inline]\text{C)}[/inline] [inline]3[/inline];      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1}{b+1}[/inline];      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{2}{b}[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{3(1-a)}{b+1}[/inline];      [inline]\text{B)}[/inline] [inline]1[/inline];      [inline]\text{C)}[/inline] [inline]3[/inline];      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1}{b+1}[/inline];      [inline]\enclose{circle}{\text{E)}}[/inline] [inline]\displaystyle\frac{2}{b}[/inline];              [inline]\text{N)}[/inline] ne znam.

10.Link zadatka Vrednost izraza [inline]\left(1+i\sqrt3\right)^6[/inline] je:
[inline]\text{A)}[/inline] [inline]48[/inline];      [inline]\text{B)}[/inline] [inline]56[/inline];      [inline]\text{C)}[/inline] [inline]128[/inline];      [inline]\text{D)}[/inline] [inline]64[/inline];      [inline]\text{E)}[/inline] [inline]0[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]48[/inline];      [inline]\text{B)}[/inline] [inline]56[/inline];      [inline]\text{C)}[/inline] [inline]128[/inline];      [inline]\enclose{circle}{\text{D)}}[/inline] [inline]64[/inline];      [inline]\text{E)}[/inline] [inline]0[/inline];              [inline]\text{N)}[/inline] ne znam.

11.Link zadatka Broj celih brojeva koji su rešenje nejednačine [inline](x-3)(7-x)(x-5)^2>0[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]0[/inline];      [inline]\text{B)}[/inline] [inline]1[/inline];      [inline]\text{C)}[/inline] [inline]3[/inline];      [inline]\text{D)}[/inline] [inline]2[/inline];      [inline]\text{E)}[/inline] beskonačno mnogo;              [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]0[/inline];      [inline]\text{B)}[/inline] [inline]1[/inline];      [inline]\text{C)}[/inline] [inline]3[/inline];      [inline]\enclose{circle}{\text{D)}}[/inline] [inline]2[/inline];      [inline]\text{E)}[/inline] beskonačno mnogo;              [inline]\text{N)}[/inline] ne znam.

12.Link zadatka Osnovna ivica pravilne šestostrane prizme je [inline]a=3\text{ m}[/inline] a dijagonala bočne strane je [inline]d=6\text{ m}[/inline]. Zapremina prizme je:
[inline]\text{A)}[/inline] [inline]41\text{ m}^3[/inline];      [inline]\text{B)}[/inline] [inline]243\text{ m}^3[/inline];      [inline]\text{C)}[/inline] [inline]121,5\text{ m}^3[/inline];      [inline]\text{D)}[/inline] [inline]41,5\text{ m}^3[/inline];      [inline]\text{E)}[/inline] [inline]241\text{ m}^3[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]41\text{ m}^3[/inline];      [inline]\text{B)}[/inline] [inline]243\text{ m}^3[/inline];      [inline]\enclose{circle}{\text{C)}}[/inline] [inline]121,5\text{ m}^3[/inline];      [inline]\text{D)}[/inline] [inline]41,5\text{ m}^3[/inline];      [inline]\text{E)}[/inline] [inline]241\text{ m}^3[/inline];              [inline]\text{N)}[/inline] ne znam.

13.Link zadatka Ako je [inline]\displaystyle f\left(\frac{2x}{x+2}\right)=x^2+2x-4[/inline] onda je [inline]f(5)[/inline] jednako:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{3}{4}[/inline];      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{4}{9}[/inline];      [inline]\text{C)}[/inline] [inline]5[/inline];      [inline]\text{D)}[/inline] [inline]6[/inline];      [inline]\text{E)}[/inline] [inline]0[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{3}{4}[/inline];      [inline]\enclose{circle}{\text{B)}}[/inline] [inline]\displaystyle\frac{4}{9}[/inline];      [inline]\text{C)}[/inline] [inline]5[/inline];      [inline]\text{D)}[/inline] [inline]6[/inline];      [inline]\text{E)}[/inline] [inline]0[/inline];              [inline]\text{N)}[/inline] ne znam.

14.Link zadatka Ako se u razvoju [inline]\displaystyle\left(\sqrt[3]2+\frac{1}{\sqrt[3]3}\right)^n[/inline] sedmi član od početka i sedmi član od kraja odnose kao [inline]1:6[/inline] onda je [inline]n[/inline] jednako:
[inline]\text{A)}[/inline] [inline]6[/inline];      [inline]\text{B)}[/inline] [inline]7[/inline];      [inline]\text{C)}[/inline] [inline]8[/inline];      [inline]\text{D)}[/inline] [inline]9[/inline];      [inline]\text{E)}[/inline] [inline]10[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]6[/inline];      [inline]\text{B)}[/inline] [inline]7[/inline];      [inline]\text{C)}[/inline] [inline]8[/inline];      [inline]\enclose{circle}{\text{D)}}[/inline] [inline]9[/inline];      [inline]\text{E)}[/inline] [inline]10[/inline];              [inline]\text{N)}[/inline] ne znam.

Obrađeno u temama: LINK1 LINK2

15.Link zadatka Rešenje jednačine [inline]5^{\log_2x}+2\cdot x^{\log_25}=15[/inline] je:
[inline]\text{A)}[/inline] [inline]3[/inline];      [inline]\text{B)}[/inline] [inline]4[/inline];      [inline]\text{C)}[/inline] [inline]1[/inline];      [inline]\text{D)}[/inline] [inline]5[/inline];      [inline]\text{E)}[/inline] [inline]2[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]3[/inline];      [inline]\text{B)}[/inline] [inline]4[/inline];      [inline]\text{C)}[/inline] [inline]1[/inline];      [inline]\text{D)}[/inline] [inline]5[/inline];      [inline]\enclose{circle}{\text{E)}}[/inline] [inline]2[/inline];              [inline]\text{N)}[/inline] ne znam.

16.Link zadatka Centralni ugao kružnog odsečka je [inline]120^\circ[/inline], a dužina njegovog luka je [inline]l=48\pi\text{ cm}[/inline]. Dužina obima kruga upisanog u taj odsečak je:
[inline]\text{A)}[/inline] [inline]l=44\pi\text{ cm}[/inline];      [inline]\text{B)}[/inline] [inline]l=96\pi\text{ cm}[/inline];      [inline]\text{C)}[/inline] [inline]l=24\pi\text{ cm}[/inline];      [inline]\text{D)}[/inline] [inline]l=36\pi\text{ cm}[/inline];      [inline]\text{E)}[/inline] [inline]l=30\pi\text{ cm}[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]l=44\pi\text{ cm}[/inline];      [inline]\text{B)}[/inline] [inline]l=96\pi\text{ cm}[/inline];      [inline]\text{C)}[/inline] [inline]l=24\pi\text{ cm}[/inline];      [inline]\enclose{circle}{\text{D)}}[/inline] [inline]l=36\pi\text{ cm}[/inline];      [inline]\text{E)}[/inline] [inline]l=30\pi\text{ cm}[/inline];              [inline]\text{N)}[/inline] ne znam.

17.Link zadatka Proizvod svih rešenja jednačine [inline]2x^3-5x^2-x+6=0[/inline] je:
[inline]\text{A)}[/inline] [inline]2[/inline];      [inline]\text{B)}[/inline] [inline]-3[/inline];      [inline]\text{C)}[/inline] [inline]3[/inline];      [inline]\text{D)}[/inline] [inline]4[/inline];      [inline]\text{E)}[/inline] [inline]-2[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]2[/inline];      [inline]\enclose{circle}{\text{B)}}[/inline] [inline]-3[/inline];      [inline]\text{C)}[/inline] [inline]3[/inline];      [inline]\text{D)}[/inline] [inline]4[/inline];      [inline]\text{E)}[/inline] [inline]-2[/inline];              [inline]\text{N)}[/inline] ne znam.

18.Link zadatka Jednakostranični trougao [inline]ABC[/inline] stranice [inline]a=2\text{ cm}[/inline] rotira oko prave [inline]p[/inline] koja je normalna na osnovicu [inline]AB[/inline] trougla i sadrži teme [inline]A[/inline] tog trougla. Zapremina nastalog obrtnog tela jednaka je:
[inline]\text{A)}[/inline] [inline]\pi[/inline];      [inline]\text{B)}[/inline] [inline]7\pi\sqrt3[/inline];      [inline]\text{C)}[/inline] [inline]3\sqrt2\pi[/inline];      [inline]\text{D)}[/inline] [inline]2\sqrt3\pi[/inline];      [inline]\text{E)}[/inline] [inline]2\pi\sqrt5[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]\pi[/inline];      [inline]\text{B)}[/inline] [inline]7\pi\sqrt3[/inline];      [inline]\text{C)}[/inline] [inline]3\sqrt2\pi[/inline];      [inline]\enclose{circle}{\text{D)}}[/inline] [inline]2\sqrt3\pi[/inline];      [inline]\text{E)}[/inline] [inline]2\pi\sqrt5[/inline];              [inline]\text{N)}[/inline] ne znam.

Obrađeno u temi: LINK

19.Link zadatka Broj rešenja jednačine [inline]2\sin^4x-2\cos^4x-1=0[/inline] koja pripadaju intervalu [inline][-\pi,\pi][/inline] je:
[inline]\text{A)}[/inline] [inline]6[/inline];      [inline]\text{B)}[/inline] [inline]3[/inline];      [inline]\text{C)}[/inline] [inline]4[/inline];      [inline]\text{D)}[/inline] [inline]5[/inline];      [inline]\text{E)}[/inline] [inline]2[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]6[/inline];      [inline]\text{B)}[/inline] [inline]3[/inline];      [inline]\enclose{circle}{\text{C)}}[/inline] [inline]4[/inline];      [inline]\text{D)}[/inline] [inline]5[/inline];      [inline]\text{E)}[/inline] [inline]2[/inline];              [inline]\text{N)}[/inline] ne znam.

Obrađeno u temi: LINK

20.Link zadatka Jednačina prave koja je tangenta elipse [inline]\displaystyle\frac{x^2}{40}+\frac{y^2}{24}=1[/inline] i koja odseca jednake odsečke na koordinatnim osama je:
[inline]\text{A)}[/inline] [inline]x+y+4=0[/inline];      [inline]\text{B)}[/inline] [inline]x+y-4=0[/inline];      [inline]\text{C)}[/inline] [inline]x+y+6=0[/inline];      [inline]\text{D)}[/inline] [inline]x+y-6=0[/inline];      [inline]\text{E)}[/inline] [inline]x+y-8=0[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]x+y+4=0[/inline];      [inline]\text{B)}[/inline] [inline]x+y-4=0[/inline];      [inline]\text{C)}[/inline] [inline]x+y+6=0[/inline];      [inline]\text{D)}[/inline] [inline]x+y-6=0[/inline];      [inline]\enclose{circle}{\text{E)}}[/inline] [inline]x+y-8=0[/inline];              [inline]\text{N)}[/inline] ne znam.


Izvor: LINK


Napomena: Ukoliko vam treba pomoć oko rešavanja nekog od zadataka koji dosad nije obrađivan ni na jednoj temi, slobodno zatražite pomoć na forumu „Matemanija“, naravno uz poštovanje forumskih pravila.